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mxnet
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Classes | |
| class | Accuracy |
| class | AdaDeltaOptimizer |
| class | AdaGradOptimizer |
| class | AdamOptimizer |
| class | Bilinear |
| class | Constant |
| class | Context |
| Context interface. More... | |
| class | DataBatch |
| Default object for holding a mini-batch of data and related information. More... | |
| class | DataIter |
| class | EvalMetric |
| class | Executor |
| Executor interface. More... | |
| class | FactorScheduler |
| class | FeedForward |
| struct | FeedForwardConfig |
| class | Initializer |
| class | KVStore |
| class | LogLoss |
| class | LRScheduler |
| lr scheduler interface More... | |
| class | MAE |
| class | Monitor |
| Monitor interface. More... | |
| class | MSE |
| class | MSRAPrelu |
| class | MXDataIter |
| struct | MXDataIterBlob |
| class | MXDataIterMap |
| class | NDArray |
| NDArray interface. More... | |
| struct | NDBlob |
| struct to store NDArrayHandle More... | |
| class | Normal |
| class | One |
| class | Operator |
| Operator interface. More... | |
| class | OpMap |
| OpMap instance holds a map of all the symbol creators so we can get symbol creators by name. This is used internally by Symbol and Operator. More... | |
| class | Optimizer |
| Optimizer interface. More... | |
| class | OptimizerRegistry |
| class | PSNR |
| class | RMSE |
| class | RMSPropOptimizer |
| class | SGDOptimizer |
| struct | Shape |
| dynamic shape class that can hold shape of arbirary dimension More... | |
| class | SignumOptimizer |
| struct | SymBlob |
| struct to store SymbolHandle More... | |
| class | Symbol |
| Symbol interface. More... | |
| class | Uniform |
| class | Xavier |
| class | Zero |
Typedefs | |
| typedef unsigned | index_t |
| typedef std::function< Optimizer *()> | OptimizerCreator |
Functions | |
| NDArray | _default_monitor_func (const NDArray &x) |
| Default function for monitor that computes statistics of the input tensor, which is the mean absolute |x|/size(x) More... | |
| std::ostream & | operator<< (std::ostream &out, const NDArray &ndarray) |
| Symbol | khatri_rao (const std::string &symbol_name, const std::vector< Symbol > &args) |
| Symbol | Custom (const std::string &symbol_name, const std::vector< Symbol > &data, const std::string &op_type) |
| Symbol | broadcast_power (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_maximum (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_minimum (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_hypot (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | Reshape (const std::string &symbol_name, Symbol data, Shape shape=Shape(), bool reverse=false, Shape target_shape=Shape(), bool keep_highest=false) |
| Symbol | Flatten (const std::string &symbol_name, Symbol data) |
| Symbol | transpose (const std::string &symbol_name, Symbol data, Shape axes=Shape()) |
| Symbol | expand_dims (const std::string &symbol_name, Symbol data, int axis) |
| Symbol | slice (const std::string &symbol_name, Symbol data, Shape begin, Shape end, Shape step=Shape()) |
| Symbol | slice_axis (const std::string &symbol_name, Symbol data, int axis, int begin, dmlc::optional< int > end) |
| Symbol | slice_like (const std::string &symbol_name, Symbol data, Symbol shape_like, Shape axes=Shape()) |
| Symbol | clip (const std::string &symbol_name, Symbol data, mx_float a_min, mx_float a_max) |
| Symbol | repeat (const std::string &symbol_name, Symbol data, int repeats, dmlc::optional< int > axis=dmlc::optional< int >()) |
| Symbol | tile (const std::string &symbol_name, Symbol data, Shape reps) |
| Symbol | reverse (const std::string &symbol_name, Symbol data, Shape axis) |
| Symbol | stack (const std::string &symbol_name, const std::vector< Symbol > &data, int num_args, int axis=0) |
| Symbol | squeeze (const std::string &symbol_name, const std::vector< Symbol > &data, dmlc::optional< Shape > axis=dmlc::optional< Shape >()) |
| Symbol | depth_to_space (const std::string &symbol_name, Symbol data, int block_size) |
| Symbol | space_to_depth (const std::string &symbol_name, Symbol data, int block_size) |
| Symbol | zeros_like (const std::string &symbol_name, Symbol data) |
| Symbol | ones_like (const std::string &symbol_name, Symbol data) |
| Symbol | broadcast_add (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_sub (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_mul (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_div (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_mod (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | add_n (const std::string &symbol_name, const std::vector< Symbol > &args) |
| Symbol | argmax (const std::string &symbol_name, Symbol data, dmlc::optional< int > axis=dmlc::optional< int >(), bool keepdims=false) |
| Symbol | argmin (const std::string &symbol_name, Symbol data, dmlc::optional< int > axis=dmlc::optional< int >(), bool keepdims=false) |
| Symbol | argmax_channel (const std::string &symbol_name, Symbol data) |
| Symbol | pick (const std::string &symbol_name, Symbol data, Symbol index, dmlc::optional< int > axis=dmlc::optional< int >(-1), bool keepdims=false, PickMode mode=PickMode::kClip) |
| Symbol | dot (const std::string &symbol_name, Symbol lhs, Symbol rhs, bool transpose_a=false, bool transpose_b=false, DotForwardStype forward_stype=DotForwardStype::kNone) |
| Symbol | batch_dot (const std::string &symbol_name, Symbol lhs, Symbol rhs, bool transpose_a=false, bool transpose_b=false, Batch_dotForwardStype forward_stype=Batch_dotForwardStype::kNone) |
| Symbol | relu (const std::string &symbol_name, Symbol data) |
| Symbol | sigmoid (const std::string &symbol_name, Symbol data) |
| Symbol | hard_sigmoid (const std::string &symbol_name, Symbol data, mx_float alpha=0.2, mx_float beta=0.5) |
| Symbol | softsign (const std::string &symbol_name, Symbol data) |
| Symbol | BlockGrad (const std::string &symbol_name, Symbol data) |
| Symbol | make_loss (const std::string &symbol_name, Symbol data) |
| Symbol | reshape_like (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | shape_array (const std::string &symbol_name, Symbol data, dmlc::optional< int > lhs_begin=dmlc::optional< int >(), dmlc::optional< int > lhs_end=dmlc::optional< int >(), dmlc::optional< int > rhs_begin=dmlc::optional< int >(), dmlc::optional< int > rhs_end=dmlc::optional< int >()) |
| Symbol | size_array (const std::string &symbol_name, Symbol data) |
| Symbol | Cast (const std::string &symbol_name, Symbol data, CastDtype dtype) |
| Symbol | negative (const std::string &symbol_name, Symbol data) |
| Symbol | reciprocal (const std::string &symbol_name, Symbol data) |
| Symbol | abs (const std::string &symbol_name, Symbol data) |
| Symbol | sign (const std::string &symbol_name, Symbol data) |
| Symbol | round (const std::string &symbol_name, Symbol data) |
| Symbol | rint (const std::string &symbol_name, Symbol data) |
| Symbol | ceil (const std::string &symbol_name, Symbol data) |
| Symbol | floor (const std::string &symbol_name, Symbol data) |
| Symbol | trunc (const std::string &symbol_name, Symbol data) |
| Symbol | fix (const std::string &symbol_name, Symbol data) |
| Symbol | square (const std::string &symbol_name, Symbol data) |
| Symbol | sqrt (const std::string &symbol_name, Symbol data) |
| Symbol | rsqrt (const std::string &symbol_name, Symbol data) |
| Symbol | cbrt (const std::string &symbol_name, Symbol data) |
| Symbol | rcbrt (const std::string &symbol_name, Symbol data) |
| Symbol | exp (const std::string &symbol_name, Symbol data) |
| Symbol | log (const std::string &symbol_name, Symbol data) |
| Symbol | log10 (const std::string &symbol_name, Symbol data) |
| Symbol | log2 (const std::string &symbol_name, Symbol data) |
| Symbol | log1p (const std::string &symbol_name, Symbol data) |
| Symbol | expm1 (const std::string &symbol_name, Symbol data) |
| Symbol | gamma (const std::string &symbol_name, Symbol data) |
| Symbol | gammaln (const std::string &symbol_name, Symbol data) |
| Symbol | logical_not (const std::string &symbol_name, Symbol data) |
| Symbol | sum (const std::string &symbol_name, Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | mean (const std::string &symbol_name, Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | prod (const std::string &symbol_name, Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | nansum (const std::string &symbol_name, Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | nanprod (const std::string &symbol_name, Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | max (const std::string &symbol_name, Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | min (const std::string &symbol_name, Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | broadcast_axis (const std::string &symbol_name, Symbol data, Shape axis=Shape(), Shape size=Shape()) |
| Symbol | broadcast_to (const std::string &symbol_name, Symbol data, Shape shape=Shape()) |
| Symbol | broadcast_like (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | norm (const std::string &symbol_name, Symbol data, int ord=2, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false) |
| Symbol | topk (const std::string &symbol_name, Symbol data, dmlc::optional< int > axis=dmlc::optional< int >(-1), int k=1, TopkRetTyp ret_typ=TopkRetTyp::kIndices, bool is_ascend=false, TopkDtype dtype=TopkDtype::kFloat32) |
| Symbol | sort (const std::string &symbol_name, Symbol data, dmlc::optional< int > axis=dmlc::optional< int >(-1), bool is_ascend=true) |
| Symbol | argsort (const std::string &symbol_name, Symbol data, dmlc::optional< int > axis=dmlc::optional< int >(-1), bool is_ascend=true, ArgsortDtype dtype=ArgsortDtype::kFloat32) |
| Symbol | elemwise_add (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | elemwise_sub (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | elemwise_mul (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | elemwise_div (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | Embedding (const std::string &symbol_name, Symbol data, Symbol weight, int input_dim, int output_dim, EmbeddingDtype dtype=EmbeddingDtype::kFloat32, bool sparse_grad=false) |
| Symbol | take (const std::string &symbol_name, Symbol a, Symbol indices, int axis=0, TakeMode mode=TakeMode::kClip) |
| Symbol | batch_take (const std::string &symbol_name, Symbol a, Symbol indices) |
| Symbol | one_hot (const std::string &symbol_name, Symbol indices, int depth, double on_value=1, double off_value=0, One_hotDtype dtype=One_hotDtype::kFloat32) |
| Symbol | gather_nd (const std::string &symbol_name, Symbol data, Symbol indices) |
| Symbol | scatter_nd (const std::string &symbol_name, Symbol data, Symbol indices, Shape shape) |
| Symbol | broadcast_equal (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_not_equal (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_greater (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_greater_equal (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_lesser (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_lesser_equal (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_logical_and (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_logical_or (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | broadcast_logical_xor (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | diag (const std::string &symbol_name, Symbol data, dmlc::optional< int > k=dmlc::optional< int >(0)) |
| Symbol | where (const std::string &symbol_name, Symbol condition, Symbol x, Symbol y) |
| Symbol | smooth_l1 (const std::string &symbol_name, Symbol data, mx_float scalar) |
| Symbol | cast_storage (const std::string &symbol_name, Symbol data, Cast_storageStype stype) |
| Symbol | sin (const std::string &symbol_name, Symbol data) |
| Symbol | cos (const std::string &symbol_name, Symbol data) |
| Symbol | tan (const std::string &symbol_name, Symbol data) |
| Symbol | arcsin (const std::string &symbol_name, Symbol data) |
| Symbol | arccos (const std::string &symbol_name, Symbol data) |
| Symbol | arctan (const std::string &symbol_name, Symbol data) |
| Symbol | degrees (const std::string &symbol_name, Symbol data) |
| Symbol | radians (const std::string &symbol_name, Symbol data) |
| Symbol | sinh (const std::string &symbol_name, Symbol data) |
| Symbol | cosh (const std::string &symbol_name, Symbol data) |
| Symbol | tanh (const std::string &symbol_name, Symbol data) |
| Symbol | arcsinh (const std::string &symbol_name, Symbol data) |
| Symbol | arccosh (const std::string &symbol_name, Symbol data) |
| Symbol | arctanh (const std::string &symbol_name, Symbol data) |
| Symbol | Pooling (const std::string &symbol_name, Symbol data, Shape kernel=Shape(), PoolingPoolType pool_type=PoolingPoolType::kMax, bool global_pool=false, bool cudnn_off=false, PoolingPoolingConvention pooling_convention=PoolingPoolingConvention::kValid, Shape stride=Shape(), Shape pad=Shape(), dmlc::optional< int > p_value=dmlc::optional< int >(), dmlc::optional< bool > count_include_pad=dmlc::optional< bool >()) |
| Symbol | softmax (const std::string &symbol_name, Symbol data, int axis=-1, dmlc::optional< double > temperature=dmlc::optional< double >()) |
| Symbol | log_softmax (const std::string &symbol_name, Symbol data, int axis=-1, dmlc::optional< double > temperature=dmlc::optional< double >()) |
| Symbol | Deconvolution (const std::string &symbol_name, Symbol data, Symbol weight, Symbol bias, Shape kernel, uint32_t num_filter, Shape stride=Shape(), Shape dilate=Shape(), Shape pad=Shape(), Shape adj=Shape(), Shape target_shape=Shape(), uint32_t num_group=1, uint64_t workspace=512, bool no_bias=true, DeconvolutionCudnnTune cudnn_tune=DeconvolutionCudnnTune::kNone, bool cudnn_off=false, DeconvolutionLayout layout=DeconvolutionLayout::kNone) |
| Symbol | Activation (const std::string &symbol_name, Symbol data, ActivationActType act_type) |
| Symbol | BatchNorm (const std::string &symbol_name, Symbol data, Symbol gamma, Symbol beta, Symbol moving_mean, Symbol moving_var, double eps=0.001, mx_float momentum=0.9, bool fix_gamma=true, bool use_global_stats=false, bool output_mean_var=false, int axis=1, bool cudnn_off=false) |
| Symbol | Convolution (const std::string &symbol_name, Symbol data, Symbol weight, Symbol bias, Shape kernel, uint32_t num_filter, Shape stride=Shape(), Shape dilate=Shape(), Shape pad=Shape(), uint32_t num_group=1, uint64_t workspace=1024, bool no_bias=false, ConvolutionCudnnTune cudnn_tune=ConvolutionCudnnTune::kNone, bool cudnn_off=false, ConvolutionLayout layout=ConvolutionLayout::kNone) |
| Symbol | UpSampling (const std::string &symbol_name, const std::vector< Symbol > &data, uint32_t scale, UpSamplingSampleType sample_type, int num_args, uint32_t num_filter=0, UpSamplingMultiInputMode multi_input_mode=UpSamplingMultiInputMode::kConcat, uint64_t workspace=512) |
| Symbol | Concat (const std::string &symbol_name, const std::vector< Symbol > &data, int num_args, int dim=1) |
| Symbol | LayerNorm (const std::string &symbol_name, Symbol data, Symbol gamma, Symbol beta, int axis=-1, mx_float eps=1e-05, bool output_mean_var=false) |
| Symbol | LRN (const std::string &symbol_name, Symbol data, uint32_t nsize, mx_float alpha=0.0001, mx_float beta=0.75, mx_float knorm=2) |
| Symbol | Dropout (const std::string &symbol_name, Symbol data, mx_float p=0.5, DropoutMode mode=DropoutMode::kTraining, Shape axes=Shape()) |
| Symbol | SoftmaxActivation (const std::string &symbol_name, Symbol data, SoftmaxActivationMode mode=SoftmaxActivationMode::kInstance) |
| Symbol | FullyConnected (const std::string &symbol_name, Symbol data, Symbol weight, Symbol bias, int num_hidden, bool no_bias=false, bool flatten=true) |
| Symbol | Pad (const std::string &symbol_name, Symbol data, PadMode mode, Shape pad_width, double constant_value=0) |
| Symbol | LeakyReLU (const std::string &symbol_name, Symbol data, Symbol gamma, LeakyReLUActType act_type=LeakyReLUActType::kLeaky, mx_float slope=0.25, mx_float lower_bound=0.125, mx_float upper_bound=0.334) |
| Symbol | SwapAxis (const std::string &symbol_name, Symbol data, uint32_t dim1=0, uint32_t dim2=0) |
| Symbol | BatchNorm_v1 (const std::string &symbol_name, Symbol data, Symbol gamma, Symbol beta, mx_float eps=0.001, mx_float momentum=0.9, bool fix_gamma=true, bool use_global_stats=false, bool output_mean_var=false) |
| Symbol | softmax_cross_entropy (const std::string &symbol_name, Symbol data, Symbol label) |
| Symbol | LinearRegressionOutput (const std::string &symbol_name, Symbol data, Symbol label, mx_float grad_scale=1) |
| Symbol | MAERegressionOutput (const std::string &symbol_name, Symbol data, Symbol label, mx_float grad_scale=1) |
| Symbol | LogisticRegressionOutput (const std::string &symbol_name, Symbol data, Symbol label, mx_float grad_scale=1) |
| Symbol | IdentityAttachKLSparseReg (const std::string &symbol_name, Symbol data, mx_float sparseness_target=0.1, mx_float penalty=0.001, mx_float momentum=0.9) |
| Symbol | signsgd_update (const std::string &symbol_name, Symbol weight, Symbol grad, mx_float lr, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1) |
| Symbol | signum_update (const std::string &symbol_name, Symbol weight, Symbol grad, Symbol mom, mx_float lr, mx_float momentum=0, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, mx_float wd_lh=0) |
| Symbol | sgd_update (const std::string &symbol_name, Symbol weight, Symbol grad, mx_float lr, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, bool lazy_update=true) |
| Symbol | sgd_mom_update (const std::string &symbol_name, Symbol weight, Symbol grad, Symbol mom, mx_float lr, mx_float momentum=0, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, bool lazy_update=true) |
| Symbol | mp_sgd_update (const std::string &symbol_name, Symbol weight, Symbol grad, Symbol weight32, mx_float lr, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, bool lazy_update=true) |
| Symbol | mp_sgd_mom_update (const std::string &symbol_name, Symbol weight, Symbol grad, Symbol mom, Symbol weight32, mx_float lr, mx_float momentum=0, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, bool lazy_update=true) |
| Symbol | ftml_update (const std::string &symbol_name, Symbol weight, Symbol grad, Symbol d, Symbol v, Symbol z, mx_float lr, int t, mx_float beta1=0.6, mx_float beta2=0.999, double epsilon=1e-08, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_grad=-1) |
| Symbol | adam_update (const std::string &symbol_name, Symbol weight, Symbol grad, Symbol mean, Symbol var, mx_float lr, mx_float beta1=0.9, mx_float beta2=0.999, mx_float epsilon=1e-08, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, bool lazy_update=true) |
| Symbol | rmsprop_update (const std::string &symbol_name, Symbol weight, Symbol grad, Symbol n, mx_float lr, mx_float gamma1=0.95, mx_float epsilon=1e-08, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, mx_float clip_weights=-1) |
| Symbol | rmspropalex_update (const std::string &symbol_name, Symbol weight, Symbol grad, Symbol n, Symbol g, Symbol delta, mx_float lr, mx_float gamma1=0.95, mx_float gamma2=0.9, mx_float epsilon=1e-08, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, mx_float clip_weights=-1) |
| Symbol | ftrl_update (const std::string &symbol_name, Symbol weight, Symbol grad, Symbol z, Symbol n, mx_float lr, mx_float lamda1=0.01, mx_float beta=1, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1) |
| Symbol | SliceChannel (const std::string &symbol_name, Symbol data, int num_outputs, int axis=1, bool squeeze_axis=false) |
| Symbol | InstanceNorm (const std::string &symbol_name, Symbol data, Symbol gamma, Symbol beta, mx_float eps=0.001) |
| Symbol | GridGenerator (const std::string &symbol_name, Symbol data, GridGeneratorTransformType transform_type, Shape target_shape=Shape(0, 0)) |
| Symbol | Pooling_v1 (const std::string &symbol_name, Symbol data, Shape kernel=Shape(), Pooling_v1PoolType pool_type=Pooling_v1PoolType::kMax, bool global_pool=false, Pooling_v1PoolingConvention pooling_convention=Pooling_v1PoolingConvention::kValid, Shape stride=Shape(), Shape pad=Shape()) |
| Symbol | RNN (const std::string &symbol_name, Symbol data, Symbol parameters, Symbol state, Symbol state_cell, uint32_t state_size, uint32_t num_layers, RNNMode mode, bool bidirectional=false, mx_float p=0, bool state_outputs=false, dmlc::optional< int > projection_size=dmlc::optional< int >(), dmlc::optional< double > lstm_state_clip_min=dmlc::optional< double >(), dmlc::optional< double > lstm_state_clip_max=dmlc::optional< double >(), bool lstm_state_clip_nan=false) |
| Symbol | Convolution_v1 (const std::string &symbol_name, Symbol data, Symbol weight, Symbol bias, Shape kernel, uint32_t num_filter, Shape stride=Shape(), Shape dilate=Shape(), Shape pad=Shape(), uint32_t num_group=1, uint64_t workspace=1024, bool no_bias=false, Convolution_v1CudnnTune cudnn_tune=Convolution_v1CudnnTune::kNone, bool cudnn_off=false, Convolution_v1Layout layout=Convolution_v1Layout::kNone) |
| Symbol | Crop (const std::string &symbol_name, const std::vector< Symbol > &data, int num_args, Shape offset=Shape(0, 0), Shape h_w=Shape(0, 0), bool center_crop=false) |
| Symbol | SequenceReverse (const std::string &symbol_name, Symbol data, Symbol sequence_length, bool use_sequence_length=false, int axis=0) |
| Symbol | SpatialTransformer (const std::string &symbol_name, Symbol data, Symbol loc, SpatialTransformerTransformType transform_type, SpatialTransformerSamplerType sampler_type, Shape target_shape=Shape(0, 0)) |
| Symbol | SoftmaxOutput (const std::string &symbol_name, Symbol data, Symbol label, mx_float grad_scale=1, mx_float ignore_label=-1, bool multi_output=false, bool use_ignore=false, bool preserve_shape=false, SoftmaxOutputNormalization normalization=SoftmaxOutputNormalization::kNull, bool out_grad=false, mx_float smooth_alpha=0) |
| Symbol | Softmax (const std::string &symbol_name, Symbol data, mx_float grad_scale=1, mx_float ignore_label=-1, bool multi_output=false, bool use_ignore=false, bool preserve_shape=false, SoftmaxNormalization normalization=SoftmaxNormalization::kNull, bool out_grad=false, mx_float smooth_alpha=0) |
| Symbol | BilinearSampler (const std::string &symbol_name, Symbol data, Symbol grid) |
| Symbol | ROIPooling (const std::string &symbol_name, Symbol data, Symbol rois, Shape pooled_size, mx_float spatial_scale) |
| Symbol | SequenceLast (const std::string &symbol_name, Symbol data, Symbol sequence_length, bool use_sequence_length=false, int axis=0) |
| Symbol | L2Normalization (const std::string &symbol_name, Symbol data, mx_float eps=1e-10, L2NormalizationMode mode=L2NormalizationMode::kInstance) |
| Symbol | MakeLoss (const std::string &symbol_name, Symbol data, mx_float grad_scale=1, mx_float valid_thresh=0, MakeLossNormalization normalization=MakeLossNormalization::kNull) |
| Symbol | SVMOutput (const std::string &symbol_name, Symbol data, Symbol label, mx_float margin=1, mx_float regularization_coefficient=1, bool use_linear=false) |
| Symbol | Correlation (const std::string &symbol_name, Symbol data1, Symbol data2, uint32_t kernel_size=1, uint32_t max_displacement=1, uint32_t stride1=1, uint32_t stride2=1, uint32_t pad_size=0, bool is_multiply=true) |
| Symbol | SequenceMask (const std::string &symbol_name, Symbol data, Symbol sequence_length, bool use_sequence_length=false, mx_float value=0, int axis=0) |
| Symbol | choose_element_0index (const std::string &symbol_name, Symbol lhs, Symbol rhs) |
| Symbol | fill_element_0index (const std::string &symbol_name, Symbol lhs, Symbol mhs, Symbol rhs) |
| Symbol | khatri_rao (const std::vector< Symbol > &args) |
| Symbol | Custom (const std::vector< Symbol > &data, const std::string &op_type) |
| Symbol | broadcast_power (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_maximum (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_minimum (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_hypot (Symbol lhs, Symbol rhs) |
| Symbol | Reshape (Symbol data, Shape shape=Shape(), bool reverse=false, Shape target_shape=Shape(), bool keep_highest=false) |
| Symbol | Flatten (Symbol data) |
| Symbol | transpose (Symbol data, Shape axes=Shape()) |
| Symbol | expand_dims (Symbol data, int axis) |
| Symbol | slice (Symbol data, Shape begin, Shape end, Shape step=Shape()) |
| Symbol | slice_axis (Symbol data, int axis, int begin, dmlc::optional< int > end) |
| Symbol | slice_like (Symbol data, Symbol shape_like, Shape axes=Shape()) |
| Symbol | clip (Symbol data, mx_float a_min, mx_float a_max) |
| Symbol | repeat (Symbol data, int repeats, dmlc::optional< int > axis=dmlc::optional< int >()) |
| Symbol | tile (Symbol data, Shape reps) |
| Symbol | reverse (Symbol data, Shape axis) |
| Symbol | stack (const std::vector< Symbol > &data, int num_args, int axis=0) |
| Symbol | squeeze (const std::vector< Symbol > &data, dmlc::optional< Shape > axis=dmlc::optional< Shape >()) |
| Symbol | depth_to_space (Symbol data, int block_size) |
| Symbol | space_to_depth (Symbol data, int block_size) |
| Symbol | zeros_like (Symbol data) |
| Symbol | ones_like (Symbol data) |
| Symbol | broadcast_add (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_sub (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_mul (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_div (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_mod (Symbol lhs, Symbol rhs) |
| Symbol | add_n (const std::vector< Symbol > &args) |
| Symbol | argmax (Symbol data, dmlc::optional< int > axis=dmlc::optional< int >(), bool keepdims=false) |
| Symbol | argmin (Symbol data, dmlc::optional< int > axis=dmlc::optional< int >(), bool keepdims=false) |
| Symbol | argmax_channel (Symbol data) |
| Symbol | pick (Symbol data, Symbol index, dmlc::optional< int > axis=dmlc::optional< int >(-1), bool keepdims=false, PickMode mode=PickMode::kClip) |
| Symbol | dot (Symbol lhs, Symbol rhs, bool transpose_a=false, bool transpose_b=false, DotForwardStype forward_stype=DotForwardStype::kNone) |
| Symbol | batch_dot (Symbol lhs, Symbol rhs, bool transpose_a=false, bool transpose_b=false, Batch_dotForwardStype forward_stype=Batch_dotForwardStype::kNone) |
| Symbol | relu (Symbol data) |
| Symbol | sigmoid (Symbol data) |
| Symbol | hard_sigmoid (Symbol data, mx_float alpha=0.2, mx_float beta=0.5) |
| Symbol | softsign (Symbol data) |
| Symbol | BlockGrad (Symbol data) |
| Symbol | make_loss (Symbol data) |
| Symbol | reshape_like (Symbol lhs, Symbol rhs) |
| Symbol | shape_array (Symbol data, dmlc::optional< int > lhs_begin=dmlc::optional< int >(), dmlc::optional< int > lhs_end=dmlc::optional< int >(), dmlc::optional< int > rhs_begin=dmlc::optional< int >(), dmlc::optional< int > rhs_end=dmlc::optional< int >()) |
| Symbol | size_array (Symbol data) |
| Symbol | Cast (Symbol data, CastDtype dtype) |
| Symbol | negative (Symbol data) |
| Symbol | reciprocal (Symbol data) |
| Symbol | abs (Symbol data) |
| Symbol | sign (Symbol data) |
| Symbol | round (Symbol data) |
| Symbol | rint (Symbol data) |
| Symbol | ceil (Symbol data) |
| Symbol | floor (Symbol data) |
| Symbol | trunc (Symbol data) |
| Symbol | fix (Symbol data) |
| Symbol | square (Symbol data) |
| Symbol | sqrt (Symbol data) |
| Symbol | rsqrt (Symbol data) |
| Symbol | cbrt (Symbol data) |
| Symbol | rcbrt (Symbol data) |
| Symbol | exp (Symbol data) |
| Symbol | log (Symbol data) |
| Symbol | log10 (Symbol data) |
| Symbol | log2 (Symbol data) |
| Symbol | log1p (Symbol data) |
| Symbol | expm1 (Symbol data) |
| Symbol | gamma (Symbol data) |
| Symbol | gammaln (Symbol data) |
| Symbol | logical_not (Symbol data) |
| Symbol | sum (Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | mean (Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | prod (Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | nansum (Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | nanprod (Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | max (Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | min (Symbol data, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false, bool exclude=false) |
| Symbol | broadcast_axis (Symbol data, Shape axis=Shape(), Shape size=Shape()) |
| Symbol | broadcast_to (Symbol data, Shape shape=Shape()) |
| Symbol | broadcast_like (Symbol lhs, Symbol rhs) |
| Symbol | norm (Symbol data, int ord=2, dmlc::optional< Shape > axis=dmlc::optional< Shape >(), bool keepdims=false) |
| Symbol | topk (Symbol data, dmlc::optional< int > axis=dmlc::optional< int >(-1), int k=1, TopkRetTyp ret_typ=TopkRetTyp::kIndices, bool is_ascend=false, TopkDtype dtype=TopkDtype::kFloat32) |
| Symbol | sort (Symbol data, dmlc::optional< int > axis=dmlc::optional< int >(-1), bool is_ascend=true) |
| Symbol | argsort (Symbol data, dmlc::optional< int > axis=dmlc::optional< int >(-1), bool is_ascend=true, ArgsortDtype dtype=ArgsortDtype::kFloat32) |
| Symbol | elemwise_add (Symbol lhs, Symbol rhs) |
| Symbol | elemwise_sub (Symbol lhs, Symbol rhs) |
| Symbol | elemwise_mul (Symbol lhs, Symbol rhs) |
| Symbol | elemwise_div (Symbol lhs, Symbol rhs) |
| Symbol | Embedding (Symbol data, Symbol weight, int input_dim, int output_dim, EmbeddingDtype dtype=EmbeddingDtype::kFloat32, bool sparse_grad=false) |
| Symbol | take (Symbol a, Symbol indices, int axis=0, TakeMode mode=TakeMode::kClip) |
| Symbol | batch_take (Symbol a, Symbol indices) |
| Symbol | one_hot (Symbol indices, int depth, double on_value=1, double off_value=0, One_hotDtype dtype=One_hotDtype::kFloat32) |
| Symbol | gather_nd (Symbol data, Symbol indices) |
| Symbol | scatter_nd (Symbol data, Symbol indices, Shape shape) |
| Symbol | broadcast_equal (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_not_equal (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_greater (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_greater_equal (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_lesser (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_lesser_equal (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_logical_and (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_logical_or (Symbol lhs, Symbol rhs) |
| Symbol | broadcast_logical_xor (Symbol lhs, Symbol rhs) |
| Symbol | diag (Symbol data, dmlc::optional< int > k=dmlc::optional< int >(0)) |
| Symbol | where (Symbol condition, Symbol x, Symbol y) |
| Symbol | smooth_l1 (Symbol data, mx_float scalar) |
| Symbol | cast_storage (Symbol data, Cast_storageStype stype) |
| Symbol | sin (Symbol data) |
| Symbol | cos (Symbol data) |
| Symbol | tan (Symbol data) |
| Symbol | arcsin (Symbol data) |
| Symbol | arccos (Symbol data) |
| Symbol | arctan (Symbol data) |
| Symbol | degrees (Symbol data) |
| Symbol | radians (Symbol data) |
| Symbol | sinh (Symbol data) |
| Symbol | cosh (Symbol data) |
| Symbol | tanh (Symbol data) |
| Symbol | arcsinh (Symbol data) |
| Symbol | arccosh (Symbol data) |
| Symbol | arctanh (Symbol data) |
| Symbol | Pooling (Symbol data, Shape kernel=Shape(), PoolingPoolType pool_type=PoolingPoolType::kMax, bool global_pool=false, bool cudnn_off=false, PoolingPoolingConvention pooling_convention=PoolingPoolingConvention::kValid, Shape stride=Shape(), Shape pad=Shape(), dmlc::optional< int > p_value=dmlc::optional< int >(), dmlc::optional< bool > count_include_pad=dmlc::optional< bool >()) |
| Symbol | softmax (Symbol data, int axis=-1, dmlc::optional< double > temperature=dmlc::optional< double >()) |
| Symbol | log_softmax (Symbol data, int axis=-1, dmlc::optional< double > temperature=dmlc::optional< double >()) |
| Symbol | Deconvolution (Symbol data, Symbol weight, Symbol bias, Shape kernel, uint32_t num_filter, Shape stride=Shape(), Shape dilate=Shape(), Shape pad=Shape(), Shape adj=Shape(), Shape target_shape=Shape(), uint32_t num_group=1, uint64_t workspace=512, bool no_bias=true, DeconvolutionCudnnTune cudnn_tune=DeconvolutionCudnnTune::kNone, bool cudnn_off=false, DeconvolutionLayout layout=DeconvolutionLayout::kNone) |
| Symbol | Activation (Symbol data, ActivationActType act_type) |
| Symbol | BatchNorm (Symbol data, Symbol gamma, Symbol beta, Symbol moving_mean, Symbol moving_var, double eps=0.001, mx_float momentum=0.9, bool fix_gamma=true, bool use_global_stats=false, bool output_mean_var=false, int axis=1, bool cudnn_off=false) |
| Symbol | Convolution (Symbol data, Symbol weight, Symbol bias, Shape kernel, uint32_t num_filter, Shape stride=Shape(), Shape dilate=Shape(), Shape pad=Shape(), uint32_t num_group=1, uint64_t workspace=1024, bool no_bias=false, ConvolutionCudnnTune cudnn_tune=ConvolutionCudnnTune::kNone, bool cudnn_off=false, ConvolutionLayout layout=ConvolutionLayout::kNone) |
| Symbol | UpSampling (const std::vector< Symbol > &data, uint32_t scale, UpSamplingSampleType sample_type, int num_args, uint32_t num_filter=0, UpSamplingMultiInputMode multi_input_mode=UpSamplingMultiInputMode::kConcat, uint64_t workspace=512) |
| Symbol | Concat (const std::vector< Symbol > &data, int num_args, int dim=1) |
| Symbol | LayerNorm (Symbol data, Symbol gamma, Symbol beta, int axis=-1, mx_float eps=1e-05, bool output_mean_var=false) |
| Symbol | LRN (Symbol data, uint32_t nsize, mx_float alpha=0.0001, mx_float beta=0.75, mx_float knorm=2) |
| Symbol | Dropout (Symbol data, mx_float p=0.5, DropoutMode mode=DropoutMode::kTraining, Shape axes=Shape()) |
| Symbol | SoftmaxActivation (Symbol data, SoftmaxActivationMode mode=SoftmaxActivationMode::kInstance) |
| Symbol | FullyConnected (Symbol data, Symbol weight, Symbol bias, int num_hidden, bool no_bias=false, bool flatten=true) |
| Symbol | Pad (Symbol data, PadMode mode, Shape pad_width, double constant_value=0) |
| Symbol | LeakyReLU (Symbol data, Symbol gamma, LeakyReLUActType act_type=LeakyReLUActType::kLeaky, mx_float slope=0.25, mx_float lower_bound=0.125, mx_float upper_bound=0.334) |
| Symbol | SwapAxis (Symbol data, uint32_t dim1=0, uint32_t dim2=0) |
| Symbol | BatchNorm_v1 (Symbol data, Symbol gamma, Symbol beta, mx_float eps=0.001, mx_float momentum=0.9, bool fix_gamma=true, bool use_global_stats=false, bool output_mean_var=false) |
| Symbol | softmax_cross_entropy (Symbol data, Symbol label) |
| Symbol | LinearRegressionOutput (Symbol data, Symbol label, mx_float grad_scale=1) |
| Symbol | MAERegressionOutput (Symbol data, Symbol label, mx_float grad_scale=1) |
| Symbol | LogisticRegressionOutput (Symbol data, Symbol label, mx_float grad_scale=1) |
| Symbol | IdentityAttachKLSparseReg (Symbol data, mx_float sparseness_target=0.1, mx_float penalty=0.001, mx_float momentum=0.9) |
| Symbol | signsgd_update (Symbol weight, Symbol grad, mx_float lr, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1) |
| Symbol | signum_update (Symbol weight, Symbol grad, Symbol mom, mx_float lr, mx_float momentum=0, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, mx_float wd_lh=0) |
| Symbol | sgd_update (Symbol weight, Symbol grad, mx_float lr, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, bool lazy_update=true) |
| Symbol | sgd_mom_update (Symbol weight, Symbol grad, Symbol mom, mx_float lr, mx_float momentum=0, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, bool lazy_update=true) |
| Symbol | mp_sgd_update (Symbol weight, Symbol grad, Symbol weight32, mx_float lr, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, bool lazy_update=true) |
| Symbol | mp_sgd_mom_update (Symbol weight, Symbol grad, Symbol mom, Symbol weight32, mx_float lr, mx_float momentum=0, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, bool lazy_update=true) |
| Symbol | ftml_update (Symbol weight, Symbol grad, Symbol d, Symbol v, Symbol z, mx_float lr, int t, mx_float beta1=0.6, mx_float beta2=0.999, double epsilon=1e-08, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_grad=-1) |
| Symbol | adam_update (Symbol weight, Symbol grad, Symbol mean, Symbol var, mx_float lr, mx_float beta1=0.9, mx_float beta2=0.999, mx_float epsilon=1e-08, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, bool lazy_update=true) |
| Symbol | rmsprop_update (Symbol weight, Symbol grad, Symbol n, mx_float lr, mx_float gamma1=0.95, mx_float epsilon=1e-08, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, mx_float clip_weights=-1) |
| Symbol | rmspropalex_update (Symbol weight, Symbol grad, Symbol n, Symbol g, Symbol delta, mx_float lr, mx_float gamma1=0.95, mx_float gamma2=0.9, mx_float epsilon=1e-08, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1, mx_float clip_weights=-1) |
| Symbol | ftrl_update (Symbol weight, Symbol grad, Symbol z, Symbol n, mx_float lr, mx_float lamda1=0.01, mx_float beta=1, mx_float wd=0, mx_float rescale_grad=1, mx_float clip_gradient=-1) |
| Symbol | SliceChannel (Symbol data, int num_outputs, int axis=1, bool squeeze_axis=false) |
| Symbol | InstanceNorm (Symbol data, Symbol gamma, Symbol beta, mx_float eps=0.001) |
| Symbol | GridGenerator (Symbol data, GridGeneratorTransformType transform_type, Shape target_shape=Shape(0, 0)) |
| Symbol | Pooling_v1 (Symbol data, Shape kernel=Shape(), Pooling_v1PoolType pool_type=Pooling_v1PoolType::kMax, bool global_pool=false, Pooling_v1PoolingConvention pooling_convention=Pooling_v1PoolingConvention::kValid, Shape stride=Shape(), Shape pad=Shape()) |
| Symbol | RNN (Symbol data, Symbol parameters, Symbol state, Symbol state_cell, uint32_t state_size, uint32_t num_layers, RNNMode mode, bool bidirectional=false, mx_float p=0, bool state_outputs=false, dmlc::optional< int > projection_size=dmlc::optional< int >(), dmlc::optional< double > lstm_state_clip_min=dmlc::optional< double >(), dmlc::optional< double > lstm_state_clip_max=dmlc::optional< double >(), bool lstm_state_clip_nan=false) |
| Symbol | Convolution_v1 (Symbol data, Symbol weight, Symbol bias, Shape kernel, uint32_t num_filter, Shape stride=Shape(), Shape dilate=Shape(), Shape pad=Shape(), uint32_t num_group=1, uint64_t workspace=1024, bool no_bias=false, Convolution_v1CudnnTune cudnn_tune=Convolution_v1CudnnTune::kNone, bool cudnn_off=false, Convolution_v1Layout layout=Convolution_v1Layout::kNone) |
| Symbol | Crop (const std::vector< Symbol > &data, int num_args, Shape offset=Shape(0, 0), Shape h_w=Shape(0, 0), bool center_crop=false) |
| Symbol | SequenceReverse (Symbol data, Symbol sequence_length, bool use_sequence_length=false, int axis=0) |
| Symbol | SpatialTransformer (Symbol data, Symbol loc, SpatialTransformerTransformType transform_type, SpatialTransformerSamplerType sampler_type, Shape target_shape=Shape(0, 0)) |
| Symbol | SoftmaxOutput (Symbol data, Symbol label, mx_float grad_scale=1, mx_float ignore_label=-1, bool multi_output=false, bool use_ignore=false, bool preserve_shape=false, SoftmaxOutputNormalization normalization=SoftmaxOutputNormalization::kNull, bool out_grad=false, mx_float smooth_alpha=0) |
| Symbol | Softmax (Symbol data, mx_float grad_scale=1, mx_float ignore_label=-1, bool multi_output=false, bool use_ignore=false, bool preserve_shape=false, SoftmaxNormalization normalization=SoftmaxNormalization::kNull, bool out_grad=false, mx_float smooth_alpha=0) |
| Symbol | BilinearSampler (Symbol data, Symbol grid) |
| Symbol | ROIPooling (Symbol data, Symbol rois, Shape pooled_size, mx_float spatial_scale) |
| Symbol | SequenceLast (Symbol data, Symbol sequence_length, bool use_sequence_length=false, int axis=0) |
| Symbol | L2Normalization (Symbol data, mx_float eps=1e-10, L2NormalizationMode mode=L2NormalizationMode::kInstance) |
| Symbol | MakeLoss (Symbol data, mx_float grad_scale=1, mx_float valid_thresh=0, MakeLossNormalization normalization=MakeLossNormalization::kNull) |
| Symbol | SVMOutput (Symbol data, Symbol label, mx_float margin=1, mx_float regularization_coefficient=1, bool use_linear=false) |
| Symbol | Correlation (Symbol data1, Symbol data2, uint32_t kernel_size=1, uint32_t max_displacement=1, uint32_t stride1=1, uint32_t stride2=1, uint32_t pad_size=0, bool is_multiply=true) |
| Symbol | SequenceMask (Symbol data, Symbol sequence_length, bool use_sequence_length=false, mx_float value=0, int axis=0) |
| Symbol | choose_element_0index (Symbol lhs, Symbol rhs) |
| Symbol | fill_element_0index (Symbol lhs, Symbol mhs, Symbol rhs) |
| Symbol | _Plus (Symbol lhs, Symbol rhs) |
| Symbol | _Mul (Symbol lhs, Symbol rhs) |
| Symbol | _Minus (Symbol lhs, Symbol rhs) |
| Symbol | _Div (Symbol lhs, Symbol rhs) |
| Symbol | _Mod (Symbol lhs, Symbol rhs) |
| Symbol | _Power (Symbol lhs, Symbol rhs) |
| Symbol | _Maximum (Symbol lhs, Symbol rhs) |
| Symbol | _Minimum (Symbol lhs, Symbol rhs) |
| Symbol | _PlusScalar (Symbol lhs, mx_float scalar) |
| Symbol | _MinusScalar (Symbol lhs, mx_float scalar) |
| Symbol | _RMinusScalar (mx_float scalar, Symbol rhs) |
| Symbol | _MulScalar (Symbol lhs, mx_float scalar) |
| Symbol | _DivScalar (Symbol lhs, mx_float scalar) |
| Symbol | _RDivScalar (mx_float scalar, Symbol rhs) |
| Symbol | _ModScalar (Symbol lhs, mx_float scalar) |
| Symbol | _RModScalar (mx_float scalar, Symbol rhs) |
| Symbol | _PowerScalar (Symbol lhs, mx_float scalar) |
| Symbol | _RPowerScalar (mx_float scalar, Symbol rhs) |
| Symbol | _MaximumScalar (Symbol lhs, mx_float scalar) |
| Symbol | _MinimumScalar (Symbol lhs, mx_float scalar) |
| Symbol | Crop (const std::string &symbol_name, int num_args, Symbol data, Symbol crop_like, Shape offset=Shape(0, 0), Shape h_w=Shape(0, 0), bool center_crop=false) |
| Symbol | Activation (const std::string &symbol_name, Symbol data, const std::string &act_type) |
| Apply activation function to input. Softmax Activation is only available with CUDNN on GPUand will be computed at each location across channel if input is 4D. More... | |
| std::ostream & | operator<< (std::ostream &os, const Shape &shape) |
| allow string printing of the shape More... | |
| std::istream & | operator>> (std::istream &is, Shape &shape) |
| read shape from the istream More... | |
| Symbol | operator+ (mx_float lhs, const Symbol &rhs) |
| Symbol | operator- (mx_float lhs, const Symbol &rhs) |
| Symbol | operator* (mx_float lhs, const Symbol &rhs) |
| Symbol | operator/ (mx_float lhs, const Symbol &rhs) |
| Symbol | operator% (mx_float lhs, const Symbol &rhs) |
| typedef unsigned mxnet::cpp::index_t |
| typedef std::function<Optimizer*()> mxnet::cpp::OptimizerCreator |
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Whether to pick convolution algo by running performance test. Leads to higher startup time but may give faster speed. Options are: 'off': no tuning 'limited_workspace': run test and pick the fastest algorithm that doesn't 'fastest': pick the fastest algorithm and ignore workspace limit. If set to None (default), behavior is determined by environment variable MXNET_CUDNN_AUTOTUNE_DEFAULT: 0 for off, 1 for limited workspace (default), 2 for fastest.
| Enumerator | |
|---|---|
| kNone | |
| kFastest | |
| kLimited_workspace | |
| kOff | |
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Default function for monitor that computes statistics of the input tensor, which is the mean absolute |x|/size(x)
| x | The input tensor |
Returns element-wise absolute value of the input.
Example:: abs([-2, 0, 3]) = [2, 0, 3] The storage type of ``abs`` output depends upon the input storage type: - abs(default) = default - abs(row_sparse) = row_sparse - abs(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L668
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise absolute value of the input.
Example:: abs([-2, 0, 3]) = [2, 0, 3] The storage type of ``abs`` output depends upon the input storage type: - abs(default) = default - abs(row_sparse) = row_sparse - abs(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L668
| data | The input array. |
|
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Apply activation function to input. Softmax Activation is only available with CUDNN on GPUand will be computed at each location across channel if input is 4D.
| symbol_name | name of the resulting symbol. |
| data | Input data to activation function. |
| act_type | Activation function to be applied. |
|
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Applies an activation function element-wise to the input.
The following activation functions are supported:
- `relu`: Rectified Linear Unit, :math:`y = max(x, 0)`
- `sigmoid`: :math:`y = \frac{1}{1 + exp(-x)}`
- `tanh`: Hyperbolic tangent, :math:`y = \frac{exp(x) - exp(-x)}{exp(x) +
- `softrelu`: Soft ReLU, or SoftPlus, :math:`y = log(1 + exp(x))`
- `softsign`: :math:`y = \frac{x}{1 + abs(x)}`
Defined in src/operator/nn/activation.cc:L184
| symbol_name | name of the resulting symbol |
| data | The input array. |
| act_type | Activation function to be applied. |
|
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Applies an activation function element-wise to the input.
The following activation functions are supported:
- `relu`: Rectified Linear Unit, :math:`y = max(x, 0)`
- `sigmoid`: :math:`y = \frac{1}{1 + exp(-x)}`
- `tanh`: Hyperbolic tangent, :math:`y = \frac{exp(x) - exp(-x)}{exp(x) +
- `softrelu`: Soft ReLU, or SoftPlus, :math:`y = log(1 + exp(x))`
- `softsign`: :math:`y = \frac{x}{1 + abs(x)}`
Defined in src/operator/nn/activation.cc:L184
| data | The input array. |
| act_type | Activation function to be applied. |
|
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Update function for Adam optimizer. Adam is seen as a generalization of AdaGrad.
Adam update consists of the following steps, where g represents gradient and m, are 1st and 2nd order moment estimates (mean and variance).
.. math::
g_t = J(W_{t-1})\ m_t = m_{t-1} + (1 - ) g_t\ v_t = v_{t-1} + (1 - ) g_t^2\ W_t = W_{t-1} - { m_t }{ { v_t } + }
It updates the weights using::
m = beta1*m + (1-beta1)*grad v = beta2*v + (1-beta2)*(grad**2) w += - learning_rate * m / (sqrt(v) + epsilon)
However, if grad's storage type is row_sparse, lazy_update is True and type of weight is the same as those of m and v, only the row slices whose indices appear in grad.indices are updated (for w, m
for row in grad.indices: m[row] = beta1*m[row] + (1-beta1)*grad[row] v[row] = beta2*v[row] + (1-beta2)*(grad[row]**2) w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)
Defined in src/operator/optimizer_op.cc:L495
| symbol_name | name of the resulting symbol |
| weight | Weight |
| grad | Gradient |
| mean | Moving mean |
| var | Moving variance |
| lr | Learning rate |
| beta1 | The decay rate for the 1st moment estimates. |
| beta2 | The decay rate for the 2nd moment estimates. |
| epsilon | A small constant for numerical stability. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| lazy_update | If true, lazy updates are applied if gradient's stype is row_sparse |
|
inline |
Update function for Adam optimizer. Adam is seen as a generalization of AdaGrad.
Adam update consists of the following steps, where g represents gradient and m, are 1st and 2nd order moment estimates (mean and variance).
.. math::
g_t = J(W_{t-1})\ m_t = m_{t-1} + (1 - ) g_t\ v_t = v_{t-1} + (1 - ) g_t^2\ W_t = W_{t-1} - { m_t }{ { v_t } + }
It updates the weights using::
m = beta1*m + (1-beta1)*grad v = beta2*v + (1-beta2)*(grad**2) w += - learning_rate * m / (sqrt(v) + epsilon)
However, if grad's storage type is row_sparse, lazy_update is True and type of weight is the same as those of m and v, only the row slices whose indices appear in grad.indices are updated (for w, m
for row in grad.indices: m[row] = beta1*m[row] + (1-beta1)*grad[row] v[row] = beta2*v[row] + (1-beta2)*(grad[row]**2) w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)
Defined in src/operator/optimizer_op.cc:L495
| weight | Weight |
| grad | Gradient |
| mean | Moving mean |
| var | Moving variance |
| lr | Learning rate |
| beta1 | The decay rate for the 1st moment estimates. |
| beta2 | The decay rate for the 2nd moment estimates. |
| epsilon | A small constant for numerical stability. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| lazy_update | If true, lazy updates are applied if gradient's stype is row_sparse |
|
inline |
Adds all input arguments element-wise.
.. math:: add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n ``add_n`` is potentially more efficient than calling ``add`` by `n` times. The storage type of ``add_n`` output depends on storage types of inputs - add_n(row_sparse, row_sparse, ..) = row_sparse - add_n(default, csr, default) = default - add_n(any input combinations longer than 4 (>4) with at least one default - otherwise, ``add_n`` falls all inputs back to default storage and generates Defined in src/operator/tensor/elemwise_sum.cc:L156
| symbol_name | name of the resulting symbol |
| args | Positional input arguments |
Adds all input arguments element-wise.
.. math:: add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n ``add_n`` is potentially more efficient than calling ``add`` by `n` times. The storage type of ``add_n`` output depends on storage types of inputs - add_n(row_sparse, row_sparse, ..) = row_sparse - add_n(default, csr, default) = default - add_n(any input combinations longer than 4 (>4) with at least one default - otherwise, ``add_n`` falls all inputs back to default storage and generates Defined in src/operator/tensor/elemwise_sum.cc:L156
| args | Positional input arguments |
Returns element-wise inverse cosine of the input array.
The input should be in range `[-1, 1]`. The output is in the closed interval :math:`[0, \pi]` .. math:: arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0] The storage type of ``arccos`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L123
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise inverse cosine of the input array.
The input should be in range `[-1, 1]`. The output is in the closed interval :math:`[0, \pi]` .. math:: arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0] The storage type of ``arccos`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L123
| data | The input array. |
Returns the element-wise inverse hyperbolic cosine of the input array, \ computed element-wise.
The storage type of arccosh output is always dense
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L264
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns the element-wise inverse hyperbolic cosine of the input array, \ computed element-wise.
The storage type of arccosh output is always dense
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L264
| data | The input array. |
Returns element-wise inverse sine of the input array.
The input should be in the range `[-1, 1]`. The output is in the closed interval of [:math:`-\pi/2`, :math:`\pi/2`]. .. math:: arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2] The storage type of ``arcsin`` output depends upon the input storage type: - arcsin(default) = default - arcsin(row_sparse) = row_sparse - arcsin(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L104
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise inverse sine of the input array.
The input should be in the range `[-1, 1]`. The output is in the closed interval of [:math:`-\pi/2`, :math:`\pi/2`]. .. math:: arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2] The storage type of ``arcsin`` output depends upon the input storage type: - arcsin(default) = default - arcsin(row_sparse) = row_sparse - arcsin(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L104
| data | The input array. |
Returns the element-wise inverse hyperbolic sine of the input array, \ computed element-wise.
The storage type of arcsinh output depends upon the input storage type:
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L250
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns the element-wise inverse hyperbolic sine of the input array, \ computed element-wise.
The storage type of arcsinh output depends upon the input storage type:
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L250
| data | The input array. |
Returns element-wise inverse tangent of the input array.
The output is in the closed interval :math:`[-\pi/2, \pi/2]` .. math:: arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4] The storage type of ``arctan`` output depends upon the input storage type: - arctan(default) = default - arctan(row_sparse) = row_sparse - arctan(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L144
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise inverse tangent of the input array.
The output is in the closed interval :math:`[-\pi/2, \pi/2]` .. math:: arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4] The storage type of ``arctan`` output depends upon the input storage type: - arctan(default) = default - arctan(row_sparse) = row_sparse - arctan(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L144
| data | The input array. |
Returns the element-wise inverse hyperbolic tangent of the input array, \ computed element-wise.
The storage type of arctanh output depends upon the input storage type:
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L281
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns the element-wise inverse hyperbolic tangent of the input array, \ computed element-wise.
The storage type of arctanh output depends upon the input storage type:
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L281
| data | The input array. |
|
inline |
Returns indices of the maximum values along an axis.
In the case of multiple occurrences of maximum values, the indices are returned. Examples:: x = [[ 0., 1., 2.], [ 3., 4., 5.]] // argmax along axis 0 argmax(x, axis=0) = [ 1., 1., 1.] // argmax along axis 1 argmax(x, axis=1) = [ 2., 2.] // argmax along axis 1 keeping same dims as an input array argmax(x, axis=1, keepdims=True) = [[ 2.], [ 2.]] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L52
| symbol_name | name of the resulting symbol |
| data | The input |
| axis | The axis along which to perform the reduction. Negative values means indexing from right to left. `Requires axis to be set as int, because global \param keepdims If this is set toTrue`, the reduced axis is left in the result as |
|
inline |
Returns indices of the maximum values along an axis.
In the case of multiple occurrences of maximum values, the indices are returned. Examples:: x = [[ 0., 1., 2.], [ 3., 4., 5.]] // argmax along axis 0 argmax(x, axis=0) = [ 1., 1., 1.] // argmax along axis 1 argmax(x, axis=1) = [ 2., 2.] // argmax along axis 1 keeping same dims as an input array argmax(x, axis=1, keepdims=True) = [[ 2.], [ 2.]] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L52
| data | The input |
| axis | The axis along which to perform the reduction. Negative values means indexing from right to left. `Requires axis to be set as int, because global \param keepdims If this is set toTrue`, the reduced axis is left in the result as |
Returns argmax indices of each channel from the input array.
The result will be an NDArray of shape (num_channel,). In case of multiple occurrences of the maximum values, the indices are returned. Examples:: x = [[ 0., 1., 2.], [ 3., 4., 5.]] argmax_channel(x) = [ 2., 2.] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L97
| symbol_name | name of the resulting symbol |
| data | The input array |
Returns argmax indices of each channel from the input array.
The result will be an NDArray of shape (num_channel,). In case of multiple occurrences of the maximum values, the indices are returned. Examples:: x = [[ 0., 1., 2.], [ 3., 4., 5.]] argmax_channel(x) = [ 2., 2.] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L97
| data | The input array |
|
inline |
Returns indices of the minimum values along an axis.
In the case of multiple occurrences of minimum values, the indices are returned. Examples:: x = [[ 0., 1., 2.], [ 3., 4., 5.]] // argmin along axis 0 argmin(x, axis=0) = [ 0., 0., 0.] // argmin along axis 1 argmin(x, axis=1) = [ 0., 0.] // argmin along axis 1 keeping same dims as an input array argmin(x, axis=1, keepdims=True) = [[ 0.], [ 0.]] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L77
| symbol_name | name of the resulting symbol |
| data | The input |
| axis | The axis along which to perform the reduction. Negative values means indexing from right to left. `Requires axis to be set as int, because global \param keepdims If this is set toTrue`, the reduced axis is left in the result as |
|
inline |
Returns indices of the minimum values along an axis.
In the case of multiple occurrences of minimum values, the indices are returned. Examples:: x = [[ 0., 1., 2.], [ 3., 4., 5.]] // argmin along axis 0 argmin(x, axis=0) = [ 0., 0., 0.] // argmin along axis 1 argmin(x, axis=1) = [ 0., 0.] // argmin along axis 1 keeping same dims as an input array argmin(x, axis=1, keepdims=True) = [[ 0.], [ 0.]] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L77
| data | The input |
| axis | The axis along which to perform the reduction. Negative values means indexing from right to left. `Requires axis to be set as int, because global \param keepdims If this is set toTrue`, the reduced axis is left in the result as |
|
inline |
Returns the indices that would sort an input array along the given axis.
This function performs sorting along the given axis and returns an array of as an input array that index data in sorted order. Examples:: x = [[ 0.3, 0.2, 0.4], [ 0.1, 0.3, 0.2]] // sort along axis -1 argsort(x) = [[ 1., 0., 2.], [ 0., 2., 1.]] // sort along axis 0 argsort(x, axis=0) = [[ 1., 0., 1.] [ 0., 1., 0.]] // flatten and then sort argsort(x) = [ 3., 1., 5., 0., 4., 2.] Defined in src/operator/tensor/ordering_op.cc:L177
| symbol_name | name of the resulting symbol |
| data | The input array |
| axis | Axis along which to sort the input tensor. If not given, the flattened |
| is_ascend | Whether to sort in ascending or descending order. |
| dtype | DType of the output indices. It is only valid when ret_typ is "indices" or "both". An error will be raised if the selected data type cannot precisely |
|
inline |
Returns the indices that would sort an input array along the given axis.
This function performs sorting along the given axis and returns an array of as an input array that index data in sorted order. Examples:: x = [[ 0.3, 0.2, 0.4], [ 0.1, 0.3, 0.2]] // sort along axis -1 argsort(x) = [[ 1., 0., 2.], [ 0., 2., 1.]] // sort along axis 0 argsort(x, axis=0) = [[ 1., 0., 1.] [ 0., 1., 0.]] // flatten and then sort argsort(x) = [ 3., 1., 5., 0., 4., 2.] Defined in src/operator/tensor/ordering_op.cc:L177
| data | The input array |
| axis | Axis along which to sort the input tensor. If not given, the flattened |
| is_ascend | Whether to sort in ascending or descending order. |
| dtype | DType of the output indices. It is only valid when ret_typ is "indices" or "both". An error will be raised if the selected data type cannot precisely |
|
inline |
Batchwise dot product.
``batch_dot`` is used to compute dot product of ``x`` and ``y`` when ``x`` and ``y`` are data in batch, namely 3D arrays in shape of `(batch_size, :, :)`. For example, given ``x`` with shape `(batch_size, n, m)` and ``y`` with shape `(batch_size, m, k)`, the result array will have shape `(batch_size, n, k)`, which is computed by:: batch_dot(x,y)[i,:,:] = dot(x[i,:,:], y[i,:,:]) Defined in src/operator/tensor/dot.cc:L125
| symbol_name | name of the resulting symbol |
| lhs | The first input |
| rhs | The second input |
| transpose_a | If true then transpose the first input before dot. |
| transpose_b | If true then transpose the second input before dot. |
| forward_stype | The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still |
|
inline |
Batchwise dot product.
``batch_dot`` is used to compute dot product of ``x`` and ``y`` when ``x`` and ``y`` are data in batch, namely 3D arrays in shape of `(batch_size, :, :)`. For example, given ``x`` with shape `(batch_size, n, m)` and ``y`` with shape `(batch_size, m, k)`, the result array will have shape `(batch_size, n, k)`, which is computed by:: batch_dot(x,y)[i,:,:] = dot(x[i,:,:], y[i,:,:]) Defined in src/operator/tensor/dot.cc:L125
| lhs | The first input |
| rhs | The second input |
| transpose_a | If true then transpose the first input before dot. |
| transpose_b | If true then transpose the second input before dot. |
| forward_stype | The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still |
Takes elements from a data batch.
.. note:: `batch_take` is deprecated. Use `pick` instead. Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the an output array of shape ``(i0,)`` with:: output[i] = input[i, indices[i]] Examples:: x = [[ 1., 2.], [ 3., 4.], [ 5., 6.]] // takes elements with specified indices batch_take(x, [0,1,0]) = [ 1. 4. 5.] Defined in src/operator/tensor/indexing_op.cc:L490
| symbol_name | name of the resulting symbol |
| a | The input array |
| indices | The index array |
Takes elements from a data batch.
.. note:: `batch_take` is deprecated. Use `pick` instead. Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the an output array of shape ``(i0,)`` with:: output[i] = input[i, indices[i]] Examples:: x = [[ 1., 2.], [ 3., 4.], [ 5., 6.]] // takes elements with specified indices batch_take(x, [0,1,0]) = [ 1. 4. 5.] Defined in src/operator/tensor/indexing_op.cc:L490
| a | The input array |
| indices | The index array |
|
inline |
Batch normalization.
Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
well as offset ``beta``.
Assume the input has more than one dimension and we normalize along axis 1.
We first compute the mean and variance along this axis:
.. math::
data\_mean[i] = mean(data[:,i,:,...]) \\
data\_var[i] = var(data[:,i,:,...])
Then compute the normalized output, which has the same shape as input, as
.. math::
out[:,i,:,...] = \frac{data[:,i,:,...] -
Both *mean* and *var* returns a scalar by treating the input as a vector.
Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both
the inverse of ``data_var``, which are needed for the backward pass. Note that
two outputs are blocked.
Besides the inputs and the outputs, this operator accepts two auxiliary
states, ``moving_mean`` and ``moving_var``, which are *k*-length
vectors. They are global statistics for the whole dataset, which are updated
by::
moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
moving_var = moving_var * momentum + data_var * (1 - momentum)
If ``use_global_stats`` is set to be true, then ``moving_mean`` and
``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
the output. It is often used during inference.
The parameter ``axis`` specifies which axis of the input shape denotes
the 'channel' (separately normalized groups). The default is 1. Specifying -1
axis to be the last item in the input shape.
Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is
then set ``gamma`` to 1 and its gradient to 0.
Note::
When fix_gamma is set to True, no sparse support is provided. If fix_gamma is
the sparse tensors will fallback.
Defined in src/operator/nn/batch_norm.cc:L574
| symbol_name | name of the resulting symbol |
| data | Input data to batch normalization |
| gamma | gamma array |
| beta | beta array |
| moving_mean | running mean of input |
| moving_var | running variance of input |
| eps | Epsilon to prevent div 0. Must be no less than CUDNN_BN_MIN_EPSILON defined |
| momentum | Momentum for moving average |
| fix_gamma | Fix gamma while training |
| use_global_stats | Whether use global moving statistics instead of local |
| output_mean_var | Output the mean and inverse std |
| axis | Specify which shape axis the channel is specified |
| cudnn_off | Do not select CUDNN operator, if available |
|
inline |
Batch normalization.
Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
well as offset ``beta``.
Assume the input has more than one dimension and we normalize along axis 1.
We first compute the mean and variance along this axis:
.. math::
data\_mean[i] = mean(data[:,i,:,...]) \\
data\_var[i] = var(data[:,i,:,...])
Then compute the normalized output, which has the same shape as input, as
.. math::
out[:,i,:,...] = \frac{data[:,i,:,...] -
Both *mean* and *var* returns a scalar by treating the input as a vector.
Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both
the inverse of ``data_var``, which are needed for the backward pass. Note that
two outputs are blocked.
Besides the inputs and the outputs, this operator accepts two auxiliary
states, ``moving_mean`` and ``moving_var``, which are *k*-length
vectors. They are global statistics for the whole dataset, which are updated
by::
moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
moving_var = moving_var * momentum + data_var * (1 - momentum)
If ``use_global_stats`` is set to be true, then ``moving_mean`` and
``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
the output. It is often used during inference.
The parameter ``axis`` specifies which axis of the input shape denotes
the 'channel' (separately normalized groups). The default is 1. Specifying -1
axis to be the last item in the input shape.
Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is
then set ``gamma`` to 1 and its gradient to 0.
Note::
When fix_gamma is set to True, no sparse support is provided. If fix_gamma is
the sparse tensors will fallback.
Defined in src/operator/nn/batch_norm.cc:L574
| data | Input data to batch normalization |
| gamma | gamma array |
| beta | beta array |
| moving_mean | running mean of input |
| moving_var | running variance of input |
| eps | Epsilon to prevent div 0. Must be no less than CUDNN_BN_MIN_EPSILON defined |
| momentum | Momentum for moving average |
| fix_gamma | Fix gamma while training |
| use_global_stats | Whether use global moving statistics instead of local |
| output_mean_var | Output the mean and inverse std |
| axis | Specify which shape axis the channel is specified |
| cudnn_off | Do not select CUDNN operator, if available |
|
inline |
Batch normalization.
This operator is DEPRECATED. Perform BatchNorm on the input.
Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
well as offset ``beta``.
Assume the input has more than one dimension and we normalize along axis 1.
We first compute the mean and variance along this axis:
.. math::
data\_mean[i] = mean(data[:,i,:,...]) \\
data\_var[i] = var(data[:,i,:,...])
Then compute the normalized output, which has the same shape as input, as
.. math::
out[:,i,:,...] = \frac{data[:,i,:,...] -
Both *mean* and *var* returns a scalar by treating the input as a vector.
Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both
``data_var`` as well, which are needed for the backward pass.
Besides the inputs and the outputs, this operator accepts two auxiliary
states, ``moving_mean`` and ``moving_var``, which are *k*-length
vectors. They are global statistics for the whole dataset, which are updated
by::
moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
moving_var = moving_var * momentum + data_var * (1 - momentum)
If ``use_global_stats`` is set to be true, then ``moving_mean`` and
``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
the output. It is often used during inference.
Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is
then set ``gamma`` to 1 and its gradient to 0.
There's no sparse support for this operator, and it will exhibit problematic
sparse tensors.
Defined in src/operator/batch_norm_v1.cc:L95
| symbol_name | name of the resulting symbol |
| data | Input data to batch normalization |
| gamma | gamma array |
| beta | beta array |
| eps | Epsilon to prevent div 0 |
| momentum | Momentum for moving average |
| fix_gamma | Fix gamma while training |
| use_global_stats | Whether use global moving statistics instead of local |
| output_mean_var | Output All,normal mean and var |
|
inline |
Batch normalization.
This operator is DEPRECATED. Perform BatchNorm on the input.
Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
well as offset ``beta``.
Assume the input has more than one dimension and we normalize along axis 1.
We first compute the mean and variance along this axis:
.. math::
data\_mean[i] = mean(data[:,i,:,...]) \\
data\_var[i] = var(data[:,i,:,...])
Then compute the normalized output, which has the same shape as input, as
.. math::
out[:,i,:,...] = \frac{data[:,i,:,...] -
Both *mean* and *var* returns a scalar by treating the input as a vector.
Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both
``data_var`` as well, which are needed for the backward pass.
Besides the inputs and the outputs, this operator accepts two auxiliary
states, ``moving_mean`` and ``moving_var``, which are *k*-length
vectors. They are global statistics for the whole dataset, which are updated
by::
moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
moving_var = moving_var * momentum + data_var * (1 - momentum)
If ``use_global_stats`` is set to be true, then ``moving_mean`` and
``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
the output. It is often used during inference.
Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is
then set ``gamma`` to 1 and its gradient to 0.
There's no sparse support for this operator, and it will exhibit problematic
sparse tensors.
Defined in src/operator/batch_norm_v1.cc:L95
| data | Input data to batch normalization |
| gamma | gamma array |
| beta | beta array |
| eps | Epsilon to prevent div 0 |
| momentum | Momentum for moving average |
| fix_gamma | Fix gamma while training |
| use_global_stats | Whether use global moving statistics instead of local |
| output_mean_var | Output All,normal mean and var |
|
inline |
Applies bilinear sampling to input feature map.
Bilinear Sampling is the key of [NIPS2015] \"Spatial Transformer Networks\".
except that the operator has the backward pass.
Given :math:`data` and :math:`grid`, then the output is computed by
.. math::
x_{src} = grid[batch, 0, y_{dst}, x_{dst}] \\
y_{src} = grid[batch, 1, y_{dst}, x_{dst}] \\
output[batch, channel, y_{dst}, x_{dst}] = G(data[batch, channel, y_{src},
:math:`x_{dst}`, :math:`y_{dst}` enumerate all spatial locations in
The out-boundary points will be padded with zeros.The shape of the output will
The operator assumes that :math:`data` has 'NCHW' layout and :math:`grid` has
BilinearSampler often cooperates with GridGenerator which generates sampling
GridGenerator supports two kinds of transformation: ``affine`` and ``warp``.
If users want to design a CustomOp to manipulate :math:`grid`, please firstly
Example 1::
## Zoom out data two times
data = array([[[[1, 4, 3, 6],
[1, 8, 8, 9],
[0, 4, 1, 5],
[1, 0, 1, 3]]]])
affine_matrix = array([[2, 0, 0],
[0, 2, 0]])
affine_matrix = reshape(affine_matrix, shape=(1, 6))
grid = GridGenerator(data=affine_matrix, transform_type='affine',
out = BilinearSampler(data, grid)
out
[[[[ 0, 0, 0, 0],
[ 0, 3.5, 6.5, 0],
[ 0, 1.25, 2.5, 0],
[ 0, 0, 0, 0]]]
Example 2::
## shift data horizontally by -1 pixel
data = array([[[[1, 4, 3, 6],
[1, 8, 8, 9],
[0, 4, 1, 5],
[1, 0, 1, 3]]]])
warp_maxtrix = array([[[[1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 1]],
[[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]]])
grid = GridGenerator(data=warp_matrix, transform_type='warp')
out = BilinearSampler(data, grid)
out
[[[[ 4, 3, 6, 0],
[ 8, 8, 9, 0],
[ 4, 1, 5, 0],
[ 0, 1, 3, 0]]]
Defined in src/operator/bilinear_sampler.cc:L245
| symbol_name | name of the resulting symbol |
| data | Input data to the BilinearsamplerOp. |
| grid | Input grid to the BilinearsamplerOp.grid has two channels: x_src, y_src |
Applies bilinear sampling to input feature map.
Bilinear Sampling is the key of [NIPS2015] \"Spatial Transformer Networks\".
except that the operator has the backward pass.
Given :math:`data` and :math:`grid`, then the output is computed by
.. math::
x_{src} = grid[batch, 0, y_{dst}, x_{dst}] \\
y_{src} = grid[batch, 1, y_{dst}, x_{dst}] \\
output[batch, channel, y_{dst}, x_{dst}] = G(data[batch, channel, y_{src},
:math:`x_{dst}`, :math:`y_{dst}` enumerate all spatial locations in
The out-boundary points will be padded with zeros.The shape of the output will
The operator assumes that :math:`data` has 'NCHW' layout and :math:`grid` has
BilinearSampler often cooperates with GridGenerator which generates sampling
GridGenerator supports two kinds of transformation: ``affine`` and ``warp``.
If users want to design a CustomOp to manipulate :math:`grid`, please firstly
Example 1::
## Zoom out data two times
data = array([[[[1, 4, 3, 6],
[1, 8, 8, 9],
[0, 4, 1, 5],
[1, 0, 1, 3]]]])
affine_matrix = array([[2, 0, 0],
[0, 2, 0]])
affine_matrix = reshape(affine_matrix, shape=(1, 6))
grid = GridGenerator(data=affine_matrix, transform_type='affine',
out = BilinearSampler(data, grid)
out
[[[[ 0, 0, 0, 0],
[ 0, 3.5, 6.5, 0],
[ 0, 1.25, 2.5, 0],
[ 0, 0, 0, 0]]]
Example 2::
## shift data horizontally by -1 pixel
data = array([[[[1, 4, 3, 6],
[1, 8, 8, 9],
[0, 4, 1, 5],
[1, 0, 1, 3]]]])
warp_maxtrix = array([[[[1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 1]],
[[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]]])
grid = GridGenerator(data=warp_matrix, transform_type='warp')
out = BilinearSampler(data, grid)
out
[[[[ 4, 3, 6, 0],
[ 8, 8, 9, 0],
[ 4, 1, 5, 0],
[ 0, 1, 3, 0]]]
Defined in src/operator/bilinear_sampler.cc:L245
| data | Input data to the BilinearsamplerOp. |
| grid | Input grid to the BilinearsamplerOp.grid has two channels: x_src, y_src |
Stops gradient computation.
Stops the accumulated gradient of the inputs from flowing through this operator
in the backward direction. In other words, this operator prevents the
of its inputs to be taken into account for computing gradients.
Example::
v1 = [1, 2]
v2 = [0, 1]
a = Variable('a')
b = Variable('b')
b_stop_grad = stop_gradient(3 * b)
loss = MakeLoss(b_stop_grad + a)
executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2))
executor.forward(is_train=True, a=v1, b=v2)
executor.outputs
[ 1. 5.]
executor.backward()
executor.grad_arrays
[ 0. 0.]
[ 1. 1.]
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L265
| symbol_name | name of the resulting symbol |
| data | The input array. |
Stops gradient computation.
Stops the accumulated gradient of the inputs from flowing through this operator
in the backward direction. In other words, this operator prevents the
of its inputs to be taken into account for computing gradients.
Example::
v1 = [1, 2]
v2 = [0, 1]
a = Variable('a')
b = Variable('b')
b_stop_grad = stop_gradient(3 * b)
loss = MakeLoss(b_stop_grad + a)
executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2))
executor.forward(is_train=True, a=v1, b=v2)
executor.outputs
[ 1. 5.]
executor.backward()
executor.grad_arrays
[ 0. 0.]
[ 1. 1.]
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L265
| data | The input array. |
Returns element-wise sum of the input arrays with broadcasting.
`broadcast_plus` is an alias to the function `broadcast_add`. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_add(x, y) = [[ 1., 1., 1.], [ 2., 2., 2.]] broadcast_plus(x, y) = [[ 1., 1., 1.], [ 2., 2., 2.]] Supported sparse operations: broadcast_add(csr, dense(1D)) = dense broadcast_add(dense(1D), csr) = dense Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns element-wise sum of the input arrays with broadcasting.
`broadcast_plus` is an alias to the function `broadcast_add`. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_add(x, y) = [[ 1., 1., 1.], [ 2., 2., 2.]] broadcast_plus(x, y) = [[ 1., 1., 1.], [ 2., 2., 2.]] Supported sparse operations: broadcast_add(csr, dense(1D)) = dense broadcast_add(dense(1D), csr) = dense Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Broadcasts the input array over particular axes.
Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. Example:: // given x of shape (1,2,1) x = [[[ 1.], [ 2.]]] // broadcast x on on axis 2 broadcast_axis(x, axis=2, size=3) = [[[ 1., 1., 1.], [ 2., 2., 2.]]] // broadcast x on on axes 0 and 2 broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1., 1., 1.], [ 2., 2., 2.]], [[ 1., 1., 1.], [ 2., 2., 2.]]] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L237
| symbol_name | name of the resulting symbol |
| data | The input |
| axis | The axes to perform the broadcasting. |
| size | Target sizes of the broadcasting axes. |
|
inline |
Broadcasts the input array over particular axes.
Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. Example:: // given x of shape (1,2,1) x = [[[ 1.], [ 2.]]] // broadcast x on on axis 2 broadcast_axis(x, axis=2, size=3) = [[[ 1., 1., 1.], [ 2., 2., 2.]]] // broadcast x on on axes 0 and 2 broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1., 1., 1.], [ 2., 2., 2.]], [[ 1., 1., 1.], [ 2., 2., 2.]]] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L237
| data | The input |
| axis | The axes to perform the broadcasting. |
| size | Target sizes of the broadcasting axes. |
Returns element-wise division of the input arrays with broadcasting.
Example:: x = [[ 6., 6., 6.], [ 6., 6., 6.]] y = [[ 2.], [ 3.]] broadcast_div(x, y) = [[ 3., 3., 3.], [ 2., 2., 2.]] Supported sparse operations: broadcast_div(csr, dense(1D)) = csr Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L187
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns element-wise division of the input arrays with broadcasting.
Example:: x = [[ 6., 6., 6.], [ 6., 6., 6.]] y = [[ 2.], [ 3.]] broadcast_div(x, y) = [[ 3., 3., 3.], [ 2., 2., 2.]] Supported sparse operations: broadcast_div(csr, dense(1D)) = csr Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L187
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Returns the result of element-wise equal to (==) comparison operation with
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_equal(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L46
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns the result of element-wise equal to (==) comparison operation with
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_equal(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L46
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Returns the result of element-wise greater than (>) comparison operation
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_greater(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L82
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns the result of element-wise greater than (>) comparison operation
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_greater(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L82
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Returns the result of element-wise greater than or equal to (>=) comparison
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_greater_equal(x, y) = [[ 1., 1., 1.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L100
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns the result of element-wise greater than or equal to (>=) comparison
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_greater_equal(x, y) = [[ 1., 1., 1.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L100
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Returns the hypotenuse of a right angled triangle, given its "legs" with broadcasting.
It is equivalent to doing :math:sqrt(x_1^2 + x_2^2).
Example::
x = [[ 3., 3., 3.]]
y = [[ 4.], [ 4.]]
broadcast_hypot(x, y) = [[ 5., 5., 5.], [ 5., 5., 5.]]
z = [[ 0.], [ 4.]]
broadcast_hypot(x, z) = [[ 3., 3., 3.], [ 5., 5., 5.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L156
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns the hypotenuse of a right angled triangle, given its "legs" with broadcasting.
It is equivalent to doing :math:sqrt(x_1^2 + x_2^2).
Example::
x = [[ 3., 3., 3.]]
y = [[ 4.], [ 4.]]
broadcast_hypot(x, y) = [[ 5., 5., 5.], [ 5., 5., 5.]]
z = [[ 0.], [ 4.]]
broadcast_hypot(x, z) = [[ 3., 3., 3.], [ 5., 5., 5.]]
Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L156
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Returns the result of element-wise lesser than (<) comparison operation
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_lesser(x, y) = [[ 0., 0., 0.], [ 0., 0., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L118
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns the result of element-wise lesser than (<) comparison operation
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_lesser(x, y) = [[ 0., 0., 0.], [ 0., 0., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L118
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Returns the result of element-wise lesser than or equal to (<=) comparison
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_lesser_equal(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L136
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns the result of element-wise lesser than or equal to (<=) comparison
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_lesser_equal(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L136
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Broadcasts lhs to have the same shape as rhs.
Broadcasting is a mechanism that allows NDArrays to perform arithmetic with arrays of different shapes efficiently without creating multiple copies of Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_ for more Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. For example:: broadcast_like([[1,2,3]], [[5,6,7],[7,8,9]]) = [[ 1., 2., 3.], [ 1., 2., 3.]]) Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L312
| symbol_name | name of the resulting symbol |
| lhs | First input. |
| rhs | Second input. |
Broadcasts lhs to have the same shape as rhs.
Broadcasting is a mechanism that allows NDArrays to perform arithmetic with arrays of different shapes efficiently without creating multiple copies of Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_ for more Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. For example:: broadcast_like([[1,2,3]], [[5,6,7],[7,8,9]]) = [[ 1., 2., 3.], [ 1., 2., 3.]]) Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L312
| lhs | First input. |
| rhs | Second input. |
|
inline |
Returns the result of element-wise logical and with broadcasting.
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_logical_and(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L154
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns the result of element-wise logical and with broadcasting.
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_logical_and(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L154
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Returns the result of element-wise logical or with broadcasting.
Example:: x = [[ 1., 1., 0.], [ 1., 1., 0.]] y = [[ 1.], [ 0.]] broadcast_logical_or(x, y) = [[ 1., 1., 1.], [ 1., 1., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L172
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns the result of element-wise logical or with broadcasting.
Example:: x = [[ 1., 1., 0.], [ 1., 1., 0.]] y = [[ 1.], [ 0.]] broadcast_logical_or(x, y) = [[ 1., 1., 1.], [ 1., 1., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L172
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Returns the result of element-wise logical xor with broadcasting.
Example:: x = [[ 1., 1., 0.], [ 1., 1., 0.]] y = [[ 1.], [ 0.]] broadcast_logical_xor(x, y) = [[ 0., 0., 1.], [ 1., 1., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L190
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns the result of element-wise logical xor with broadcasting.
Example:: x = [[ 1., 1., 0.], [ 1., 1., 0.]] y = [[ 1.], [ 0.]] broadcast_logical_xor(x, y) = [[ 0., 0., 1.], [ 1., 1., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L190
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Returns element-wise maximum of the input arrays with broadcasting.
This function compares two input arrays and returns a new array having the Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_maximum(x, y) = [[ 1., 1., 1.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L80
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns element-wise maximum of the input arrays with broadcasting.
This function compares two input arrays and returns a new array having the Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_maximum(x, y) = [[ 1., 1., 1.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L80
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Returns element-wise minimum of the input arrays with broadcasting.
This function compares two input arrays and returns a new array having the Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_maximum(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L115
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns element-wise minimum of the input arrays with broadcasting.
This function compares two input arrays and returns a new array having the Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_maximum(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L115
| lhs | First input to the function |
| rhs | Second input to the function |
Returns element-wise modulo of the input arrays with broadcasting.
Example:: x = [[ 8., 8., 8.], [ 8., 8., 8.]] y = [[ 2.], [ 3.]] broadcast_mod(x, y) = [[ 0., 0., 0.], [ 2., 2., 2.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L222
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns element-wise modulo of the input arrays with broadcasting.
Example:: x = [[ 8., 8., 8.], [ 8., 8., 8.]] y = [[ 2.], [ 3.]] broadcast_mod(x, y) = [[ 0., 0., 0.], [ 2., 2., 2.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L222
| lhs | First input to the function |
| rhs | Second input to the function |
Returns element-wise product of the input arrays with broadcasting.
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_mul(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Supported sparse operations: broadcast_mul(csr, dense(1D)) = csr Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L146
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns element-wise product of the input arrays with broadcasting.
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_mul(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Supported sparse operations: broadcast_mul(csr, dense(1D)) = csr Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L146
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Returns the result of element-wise not equal to (!=) comparison operation
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_not_equal(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L64
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns the result of element-wise not equal to (!=) comparison operation
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_not_equal(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L64
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Returns result of first array elements raised to powers from second array,
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_power(x, y) = [[ 2., 2., 2.], [ 4., 4., 4.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L45
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns result of first array elements raised to powers from second array,
Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_power(x, y) = [[ 2., 2., 2.], [ 4., 4., 4.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L45
| lhs | First input to the function |
| rhs | Second input to the function |
Returns element-wise difference of the input arrays with broadcasting.
`broadcast_minus` is an alias to the function `broadcast_sub`. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_sub(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] broadcast_minus(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] Supported sparse operations: broadcast_sub/minus(csr, dense(1D)) = dense broadcast_sub/minus(dense(1D), csr) = dense Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
| symbol_name | name of the resulting symbol |
| lhs | First input to the function |
| rhs | Second input to the function |
Returns element-wise difference of the input arrays with broadcasting.
`broadcast_minus` is an alias to the function `broadcast_sub`. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_sub(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] broadcast_minus(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] Supported sparse operations: broadcast_sub/minus(csr, dense(1D)) = dense broadcast_sub/minus(dense(1D), csr) = dense Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
| lhs | First input to the function |
| rhs | Second input to the function |
|
inline |
Broadcasts the input array to a new shape.
Broadcasting is a mechanism that allows NDArrays to perform arithmetic with arrays of different shapes efficiently without creating multiple copies of Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_ for more Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. For example:: broadcast_to([[1,2,3]], shape=(2,3)) = [[ 1., 2., 3.], [ 1., 2., 3.]]) The dimension which you do not want to change can also be kept as `0` which So with `shape=(2,0)`, we will obtain the same result as in the above example. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L261
| symbol_name | name of the resulting symbol |
| data | The input |
| shape | The shape of the desired array. We can set the dim to zero if it's same as the original. E.g A = broadcast_to(B, shape=(10, 0, 0)) has the same |
Broadcasts the input array to a new shape.
Broadcasting is a mechanism that allows NDArrays to perform arithmetic with arrays of different shapes efficiently without creating multiple copies of Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_ for more Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. For example:: broadcast_to([[1,2,3]], shape=(2,3)) = [[ 1., 2., 3.], [ 1., 2., 3.]]) The dimension which you do not want to change can also be kept as `0` which So with `shape=(2,0)`, we will obtain the same result as in the above example. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L261
| data | The input |
| shape | The shape of the desired array. We can set the dim to zero if it's same as the original. E.g A = broadcast_to(B, shape=(10, 0, 0)) has the same |
Casts all elements of the input to a new type.
.. note:: ``Cast`` is deprecated. Use ``cast`` instead. Example:: cast([0.9, 1.3], dtype='int32') = [0, 1] cast([1e20, 11.1], dtype='float16') = [inf, 11.09375] cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594
| symbol_name | name of the resulting symbol |
| data | The input. |
| dtype | Output data type. |
Casts all elements of the input to a new type.
.. note:: ``Cast`` is deprecated. Use ``cast`` instead. Example:: cast([0.9, 1.3], dtype='int32') = [0, 1] cast([1e20, 11.1], dtype='float16') = [inf, 11.09375] cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594
| data | The input. |
| dtype | Output data type. |
|
inline |
Casts tensor storage type to the new type.
When an NDArray with default storage type is cast to csr or row_sparse storage, the result is compact, which means: - for csr, zero values will not be retained - for row_sparse, row slices of all zeros will not be retained The storage type of ``cast_storage`` output depends on stype parameter: - cast_storage(csr, 'default') = default - cast_storage(row_sparse, 'default') = default - cast_storage(default, 'csr') = csr - cast_storage(default, 'row_sparse') = row_sparse - cast_storage(csr, 'csr') = csr - cast_storage(row_sparse, 'row_sparse') = row_sparse Example:: dense = [[ 0., 1., 0.], [ 2., 0., 3.], [ 0., 0., 0.], [ 0., 0., 0.]] # cast to row_sparse storage type rsp = cast_storage(dense, 'row_sparse') rsp.indices = [0, 1] rsp.values = [[ 0., 1., 0.], [ 2., 0., 3.]] # cast to csr storage type csr = cast_storage(dense, 'csr') csr.indices = [1, 0, 2] csr.values = [ 1., 2., 3.] csr.indptr = [0, 1, 3, 3, 3] Defined in src/operator/tensor/cast_storage.cc:L71
| symbol_name | name of the resulting symbol |
| data | The input. |
| stype | Output storage type. |
|
inline |
Casts tensor storage type to the new type.
When an NDArray with default storage type is cast to csr or row_sparse storage, the result is compact, which means: - for csr, zero values will not be retained - for row_sparse, row slices of all zeros will not be retained The storage type of ``cast_storage`` output depends on stype parameter: - cast_storage(csr, 'default') = default - cast_storage(row_sparse, 'default') = default - cast_storage(default, 'csr') = csr - cast_storage(default, 'row_sparse') = row_sparse - cast_storage(csr, 'csr') = csr - cast_storage(row_sparse, 'row_sparse') = row_sparse Example:: dense = [[ 0., 1., 0.], [ 2., 0., 3.], [ 0., 0., 0.], [ 0., 0., 0.]] # cast to row_sparse storage type rsp = cast_storage(dense, 'row_sparse') rsp.indices = [0, 1] rsp.values = [[ 0., 1., 0.], [ 2., 0., 3.]] # cast to csr storage type csr = cast_storage(dense, 'csr') csr.indices = [1, 0, 2] csr.values = [ 1., 2., 3.] csr.indptr = [0, 1, 3, 3, 3] Defined in src/operator/tensor/cast_storage.cc:L71
| data | The input. |
| stype | Output storage type. |
Returns element-wise cube-root value of the input.
.. math::
cbrt(x) = \sqrt[3]{x}
Example::
cbrt([1, 8, -125]) = [1, 2, -5]
The storage type of ``cbrt`` output depends upon the input storage type:
- cbrt(default) = default
- cbrt(row_sparse) = row_sparse
- cbrt(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L889
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise cube-root value of the input.
.. math::
cbrt(x) = \sqrt[3]{x}
Example::
cbrt([1, 8, -125]) = [1, 2, -5]
The storage type of ``cbrt`` output depends upon the input storage type:
- cbrt(default) = default
- cbrt(row_sparse) = row_sparse
- cbrt(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L889
| data | The input array. |
Returns element-wise ceiling of the input.
The ceil of the scalar x is the smallest integer i, such that i >= x. Example:: ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1., 2., 2., 3.] The storage type of ``ceil`` output depends upon the input storage type: - ceil(default) = default - ceil(row_sparse) = row_sparse - ceil(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L746
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise ceiling of the input.
The ceil of the scalar x is the smallest integer i, such that i >= x. Example:: ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1., 2., 2., 3.] The storage type of ``ceil`` output depends upon the input storage type: - ceil(default) = default - ceil(row_sparse) = row_sparse - ceil(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L746
| data | The input array. |
|
inline |
Choose one element from each line(row for python, column for R/Julia) in lhs according to index indicated by rhs. This function assume rhs uses 0-based
| symbol_name | name of the resulting symbol |
| lhs | Left operand to the function. |
| rhs | Right operand to the function. |
Choose one element from each line(row for python, column for R/Julia) in lhs according to index indicated by rhs. This function assume rhs uses 0-based
| lhs | Left operand to the function. |
| rhs | Right operand to the function. |
|
inline |
Clips (limits) the values in an array.
Given an interval, values outside the interval are clipped to the interval Clipping ``x`` between `a_min` and `a_x` would be:: clip(x, a_min, a_max) = max(min(x, a_max), a_min)) Example:: x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] clip(x,1,8) = [ 1., 1., 2., 3., 4., 5., 6., 7., 8., 8.] The storage type of ``clip`` output depends on storage types of inputs and the parameter values: - clip(default) = default - clip(row_sparse, a_min <= 0, a_max >= 0) = row_sparse - clip(csr, a_min <= 0, a_max >= 0) = csr - clip(row_sparse, a_min < 0, a_max < 0) = default - clip(row_sparse, a_min > 0, a_max > 0) = default - clip(csr, a_min < 0, a_max < 0) = csr - clip(csr, a_min > 0, a_max > 0) = csr Defined in src/operator/tensor/matrix_op.cc:L618
| symbol_name | name of the resulting symbol |
| data | Input array. |
| a_min | Minimum value |
| a_max | Maximum value |
Clips (limits) the values in an array.
Given an interval, values outside the interval are clipped to the interval Clipping ``x`` between `a_min` and `a_x` would be:: clip(x, a_min, a_max) = max(min(x, a_max), a_min)) Example:: x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] clip(x,1,8) = [ 1., 1., 2., 3., 4., 5., 6., 7., 8., 8.] The storage type of ``clip`` output depends on storage types of inputs and the parameter values: - clip(default) = default - clip(row_sparse, a_min <= 0, a_max >= 0) = row_sparse - clip(csr, a_min <= 0, a_max >= 0) = csr - clip(row_sparse, a_min < 0, a_max < 0) = default - clip(row_sparse, a_min > 0, a_max > 0) = default - clip(csr, a_min < 0, a_max < 0) = csr - clip(csr, a_min > 0, a_max > 0) = csr Defined in src/operator/tensor/matrix_op.cc:L618
| data | Input array. |
| a_min | Minimum value |
| a_max | Maximum value |
|
inline |
Joins input arrays along a given axis.
.. note:: `Concat` is deprecated. Use `concat` instead. The dimensions of the input arrays should be the same except the axis along which they will be concatenated. The dimension of the output array along the concatenated axis will be equal to the sum of the corresponding dimensions of the input arrays. The storage type of ``concat`` output depends on storage types of inputs - concat(csr, csr, ..., csr, dim=0) = csr - otherwise, ``concat`` generates output with default storage Example:: x = [[1,1],[2,2]] y = [[3,3],[4,4],[5,5]] z = [[6,6], [7,7],[8,8]] concat(x,y,z,dim=0) = [[ 1., 1.], [ 2., 2.], [ 3., 3.], [ 4., 4.], [ 5., 5.], [ 6., 6.], [ 7., 7.], [ 8., 8.]] Note that you cannot concat x,y,z along dimension 1 since dimension 0 is not the same for all the input arrays. concat(y,z,dim=1) = [[ 3., 3., 6., 6.], [ 4., 4., 7., 7.], [ 5., 5., 8., 8.]] Defined in src/operator/nn/concat.cc:L368
| symbol_name | name of the resulting symbol |
| data | List of arrays to concatenate |
| num_args | Number of inputs to be concated. |
| dim | the dimension to be concated. |
Joins input arrays along a given axis.
.. note:: `Concat` is deprecated. Use `concat` instead. The dimensions of the input arrays should be the same except the axis along which they will be concatenated. The dimension of the output array along the concatenated axis will be equal to the sum of the corresponding dimensions of the input arrays. The storage type of ``concat`` output depends on storage types of inputs - concat(csr, csr, ..., csr, dim=0) = csr - otherwise, ``concat`` generates output with default storage Example:: x = [[1,1],[2,2]] y = [[3,3],[4,4],[5,5]] z = [[6,6], [7,7],[8,8]] concat(x,y,z,dim=0) = [[ 1., 1.], [ 2., 2.], [ 3., 3.], [ 4., 4.], [ 5., 5.], [ 6., 6.], [ 7., 7.], [ 8., 8.]] Note that you cannot concat x,y,z along dimension 1 since dimension 0 is not the same for all the input arrays. concat(y,z,dim=1) = [[ 3., 3., 6., 6.], [ 4., 4., 7., 7.], [ 5., 5., 8., 8.]] Defined in src/operator/nn/concat.cc:L368
| data | List of arrays to concatenate |
| num_args | Number of inputs to be concated. |
| dim | the dimension to be concated. |
|
inline |
Compute N-D convolution on *(N+2)*-D input.
In the 2-D convolution, given input data with shape *(batch_size,
channel, height, width)*, the output is computed by
.. math::
out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star
weight[i,j,:,:]
where :math:`\star` is the 2-D cross-correlation operator.
For general 2-D convolution, the shapes are
- **data**: *(batch_size, channel, height, width)*
- **weight**: *(num_filter, channel, kernel[0], kernel[1])*
- **bias**: *(num_filter,)*
- **out**: *(batch_size, num_filter, out_height, out_width)*.
Define::
f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1
then we have::
out_height=f(height, kernel[0], pad[0], stride[0], dilate[0])
out_width=f(width, kernel[1], pad[1], stride[1], dilate[1])
If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
The default data ``layout`` is *NCHW*, namely *(batch_size, channel, height,
width)*. We can choose other layouts such as *NWC*.
If ``num_group`` is larger than 1, denoted by *g*, then split the input ``data``
evenly into *g* parts along the channel axis, and also evenly split ``weight``
along the first dimension. Next compute the convolution on the *i*-th part of
the data with the *i*-th weight part. The output is obtained by concatenating
the *g* results.
1-D convolution does not have *height* dimension but only *width* in space.
- **data**: *(batch_size, channel, width)*
- **weight**: *(num_filter, channel, kernel[0])*
- **bias**: *(num_filter,)*
- **out**: *(batch_size, num_filter, out_width)*.
3-D convolution adds an additional *depth* dimension besides *height* and
*width*. The shapes are
- **data**: *(batch_size, channel, depth, height, width)*
- **weight**: *(num_filter, channel, kernel[0], kernel[1], kernel[2])*
- **bias**: *(num_filter,)*
- **out**: *(batch_size, num_filter, out_depth, out_height, out_width)*.
Both ``weight`` and ``bias`` are learnable parameters.
There are other options to tune the performance.
- **cudnn_tune**: enable this option leads to higher startup time but may give
faster speed. Options are
- **off**: no tuning
- **limited_workspace**:run test and pick the fastest algorithm that doesn't
exceed workspace limit.
- **fastest**: pick the fastest algorithm and ignore workspace limit.
- **None** (default): the behavior is determined by environment variable
``MXNET_CUDNN_AUTOTUNE_DEFAULT``. 0 for off, 1 for limited workspace
(default), 2 for fastest.
- **workspace**: A large number leads to more (GPU) memory usage but may improve
the performance.
Defined in src/operator/nn/convolution.cc:L474
| symbol_name | name of the resulting symbol |
| data | Input data to the ConvolutionOp. |
| weight | Weight matrix. |
| bias | Bias parameter. |
| kernel | Convolution kernel size: (w,), (h, w) or (d, h, w) |
| num_filter | Convolution filter(channel) number |
| stride | Convolution stride: (w,), (h, w) or (d, h, w). Defaults to 1 for each |
| dilate | Convolution dilate: (w,), (h, w) or (d, h, w). Defaults to 1 for each |
| pad | Zero pad for convolution: (w,), (h, w) or (d, h, w). Defaults to no padding. |
| num_group | Number of group partitions. |
| workspace | Maximum temporary workspace allowed (MB) in convolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the convolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when |
| no_bias | Whether to disable bias parameter. |
| cudnn_tune | Whether to pick convolution algo by running performance test. |
| cudnn_off | Turn off cudnn for this layer. |
| layout | Set layout for input, output and weight. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.NHWC and NDHWC are |
|
inline |
Compute N-D convolution on *(N+2)*-D input.
In the 2-D convolution, given input data with shape *(batch_size,
channel, height, width)*, the output is computed by
.. math::
out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star
weight[i,j,:,:]
where :math:`\star` is the 2-D cross-correlation operator.
For general 2-D convolution, the shapes are
- **data**: *(batch_size, channel, height, width)*
- **weight**: *(num_filter, channel, kernel[0], kernel[1])*
- **bias**: *(num_filter,)*
- **out**: *(batch_size, num_filter, out_height, out_width)*.
Define::
f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1
then we have::
out_height=f(height, kernel[0], pad[0], stride[0], dilate[0])
out_width=f(width, kernel[1], pad[1], stride[1], dilate[1])
If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
The default data ``layout`` is *NCHW*, namely *(batch_size, channel, height,
width)*. We can choose other layouts such as *NWC*.
If ``num_group`` is larger than 1, denoted by *g*, then split the input ``data``
evenly into *g* parts along the channel axis, and also evenly split ``weight``
along the first dimension. Next compute the convolution on the *i*-th part of
the data with the *i*-th weight part. The output is obtained by concatenating
the *g* results.
1-D convolution does not have *height* dimension but only *width* in space.
- **data**: *(batch_size, channel, width)*
- **weight**: *(num_filter, channel, kernel[0])*
- **bias**: *(num_filter,)*
- **out**: *(batch_size, num_filter, out_width)*.
3-D convolution adds an additional *depth* dimension besides *height* and
*width*. The shapes are
- **data**: *(batch_size, channel, depth, height, width)*
- **weight**: *(num_filter, channel, kernel[0], kernel[1], kernel[2])*
- **bias**: *(num_filter,)*
- **out**: *(batch_size, num_filter, out_depth, out_height, out_width)*.
Both ``weight`` and ``bias`` are learnable parameters.
There are other options to tune the performance.
- **cudnn_tune**: enable this option leads to higher startup time but may give
faster speed. Options are
- **off**: no tuning
- **limited_workspace**:run test and pick the fastest algorithm that doesn't
exceed workspace limit.
- **fastest**: pick the fastest algorithm and ignore workspace limit.
- **None** (default): the behavior is determined by environment variable
``MXNET_CUDNN_AUTOTUNE_DEFAULT``. 0 for off, 1 for limited workspace
(default), 2 for fastest.
- **workspace**: A large number leads to more (GPU) memory usage but may improve
the performance.
Defined in src/operator/nn/convolution.cc:L474
| data | Input data to the ConvolutionOp. |
| weight | Weight matrix. |
| bias | Bias parameter. |
| kernel | Convolution kernel size: (w,), (h, w) or (d, h, w) |
| num_filter | Convolution filter(channel) number |
| stride | Convolution stride: (w,), (h, w) or (d, h, w). Defaults to 1 for each |
| dilate | Convolution dilate: (w,), (h, w) or (d, h, w). Defaults to 1 for each |
| pad | Zero pad for convolution: (w,), (h, w) or (d, h, w). Defaults to no padding. |
| num_group | Number of group partitions. |
| workspace | Maximum temporary workspace allowed (MB) in convolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the convolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when |
| no_bias | Whether to disable bias parameter. |
| cudnn_tune | Whether to pick convolution algo by running performance test. |
| cudnn_off | Turn off cudnn for this layer. |
| layout | Set layout for input, output and weight. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.NHWC and NDHWC are |
|
inline |
This operator is DEPRECATED. Apply convolution to input then add a bias.
| symbol_name | name of the resulting symbol |
| data | Input data to the ConvolutionV1Op. |
| weight | Weight matrix. |
| bias | Bias parameter. |
| kernel | convolution kernel size: (h, w) or (d, h, w) |
| num_filter | convolution filter(channel) number |
| stride | convolution stride: (h, w) or (d, h, w) |
| dilate | convolution dilate: (h, w) or (d, h, w) |
| pad | pad for convolution: (h, w) or (d, h, w) |
| num_group | Number of group partitions. Equivalent to slicing input into num_group partitions, apply convolution on each, then concatenate the results |
| workspace | Maximum temporary workspace allowed for convolution (MB).This parameter determines the effective batch size of the convolution kernel, which may be smaller than the given batch size. Also, the workspace will be |
| no_bias | Whether to disable bias parameter. |
| cudnn_tune | Whether to pick convolution algo by running performance test. Leads to higher startup time but may give faster speed. Options are: 'off': no tuning 'limited_workspace': run test and pick the fastest algorithm that doesn't 'fastest': pick the fastest algorithm and ignore workspace limit. If set to None (default), behavior is determined by environment variable MXNET_CUDNN_AUTOTUNE_DEFAULT: 0 for off, 1 for limited workspace (default), 2 for fastest. |
| cudnn_off | Turn off cudnn for this layer. |
| layout | Set layout for input, output and weight. Empty for default layout: NCHW for 2d and NCDHW for 3d. |
|
inline |
This operator is DEPRECATED. Apply convolution to input then add a bias.
| data | Input data to the ConvolutionV1Op. |
| weight | Weight matrix. |
| bias | Bias parameter. |
| kernel | convolution kernel size: (h, w) or (d, h, w) |
| num_filter | convolution filter(channel) number |
| stride | convolution stride: (h, w) or (d, h, w) |
| dilate | convolution dilate: (h, w) or (d, h, w) |
| pad | pad for convolution: (h, w) or (d, h, w) |
| num_group | Number of group partitions. Equivalent to slicing input into num_group partitions, apply convolution on each, then concatenate the results |
| workspace | Maximum temporary workspace allowed for convolution (MB).This parameter determines the effective batch size of the convolution kernel, which may be smaller than the given batch size. Also, the workspace will be |
| no_bias | Whether to disable bias parameter. |
| cudnn_tune | Whether to pick convolution algo by running performance test. Leads to higher startup time but may give faster speed. Options are: 'off': no tuning 'limited_workspace': run test and pick the fastest algorithm that doesn't 'fastest': pick the fastest algorithm and ignore workspace limit. If set to None (default), behavior is determined by environment variable MXNET_CUDNN_AUTOTUNE_DEFAULT: 0 for off, 1 for limited workspace (default), 2 for fastest. |
| cudnn_off | Turn off cudnn for this layer. |
| layout | Set layout for input, output and weight. Empty for default layout: NCHW for 2d and NCDHW for 3d. |
|
inline |
Applies correlation to inputs.
The correlation layer performs multiplicative patch comparisons between two
Given two multi-channel feature maps :math:`f_{1}, f_{2}`, with :math:`w`,
the correlation layer lets the network compare each patch from :math:`f_{1}`
For now we consider only a single comparison of two patches. The 'correlation'
:math:`x_{2}` in the second map is then defined as:
.. math::
c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]} <f_{1}(x_{1} + o),
for a square patch of size :math:`K:=2k+1`.
Note that the equation above is identical to one step of a convolution in
neural networks, but instead of convolving data with a filter, it convolves
data. For this reason, it has no training weights.
Computing :math:`c(x_{1}, x_{2})` involves :math:`c * K^{2}` multiplications.
Given a maximum displacement :math:`d`, for each location :math:`x_{1}` it
computes correlations :math:`c(x_{1}, x_{2})` only in a neighborhood of size
by limiting the range of :math:`x_{2}`. We use strides :math:`s_{1}, s_{2}`, to
quantize :math:`x_{1}` globally and to quantize :math:`x_{2}` within the
centered around :math:`x_{1}`.
The final output is defined by the following expression:
.. math::
out[n, q, i, j] = c(x_{i, j}, x_{q})
where :math:`i` and :math:`j` enumerate spatial locations in :math:`f_{1}`, and
Defined in src/operator/correlation.cc:L198
| symbol_name | name of the resulting symbol |
| data1 | Input data1 to the correlation. |
| data2 | Input data2 to the correlation. |
| kernel_size | kernel size for Correlation must be an odd number |
| max_displacement | Max displacement of Correlation |
| stride1 | stride1 quantize data1 globally |
| stride2 | stride2 quantize data2 within the neighborhood centered around data1 |
| pad_size | pad for Correlation |
| is_multiply | operation type is either multiplication or subduction |
|
inline |
Applies correlation to inputs.
The correlation layer performs multiplicative patch comparisons between two
Given two multi-channel feature maps :math:`f_{1}, f_{2}`, with :math:`w`,
the correlation layer lets the network compare each patch from :math:`f_{1}`
For now we consider only a single comparison of two patches. The 'correlation'
:math:`x_{2}` in the second map is then defined as:
.. math::
c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]} <f_{1}(x_{1} + o),
for a square patch of size :math:`K:=2k+1`.
Note that the equation above is identical to one step of a convolution in
neural networks, but instead of convolving data with a filter, it convolves
data. For this reason, it has no training weights.
Computing :math:`c(x_{1}, x_{2})` involves :math:`c * K^{2}` multiplications.
Given a maximum displacement :math:`d`, for each location :math:`x_{1}` it
computes correlations :math:`c(x_{1}, x_{2})` only in a neighborhood of size
by limiting the range of :math:`x_{2}`. We use strides :math:`s_{1}, s_{2}`, to
quantize :math:`x_{1}` globally and to quantize :math:`x_{2}` within the
centered around :math:`x_{1}`.
The final output is defined by the following expression:
.. math::
out[n, q, i, j] = c(x_{i, j}, x_{q})
where :math:`i` and :math:`j` enumerate spatial locations in :math:`f_{1}`, and
Defined in src/operator/correlation.cc:L198
| data1 | Input data1 to the correlation. |
| data2 | Input data2 to the correlation. |
| kernel_size | kernel size for Correlation must be an odd number |
| max_displacement | Max displacement of Correlation |
| stride1 | stride1 quantize data1 globally |
| stride2 | stride2 quantize data2 within the neighborhood centered around data1 |
| pad_size | pad for Correlation |
| is_multiply | operation type is either multiplication or subduction |
Computes the element-wise cosine of the input array.
The input should be in radians (:math:`2\pi` rad equals 360 degrees). .. math:: cos([0, \pi/4, \pi/2]) = [1, 0.707, 0] The storage type of ``cos`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L63
| symbol_name | name of the resulting symbol |
| data | The input array. |
Computes the element-wise cosine of the input array.
The input should be in radians (:math:`2\pi` rad equals 360 degrees). .. math:: cos([0, \pi/4, \pi/2]) = [1, 0.707, 0] The storage type of ``cos`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L63
| data | The input array. |
Returns the hyperbolic cosine of the input array, computed element-wise.
.. math:: cosh(x) = 0.5\times(exp(x) + exp(-x)) The storage type of ``cosh`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L216
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns the hyperbolic cosine of the input array, computed element-wise.
.. math:: cosh(x) = 0.5\times(exp(x) + exp(-x)) The storage type of ``cosh`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L216
| data | The input array. |
|
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|
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.. note:: `Crop` is deprecated. Use `slice` instead. Crop the 2nd and 3rd dim of input data, with the corresponding size of h_w or with width and height of the second input symbol, i.e., with one input, we need specify the crop height and width, otherwise the second input symbol's size Defined in src/operator/crop.cc:L50
| symbol_name | name of the resulting symbol |
| data | Tensor or List of Tensors, the second input will be used as crop_like |
| num_args | Number of inputs for crop, if equals one, then we will use the h_wfor crop height and width, else if equals two, then we will use the heightand width |
| offset | crop offset coordinate: (y, x) |
| h_w | crop height and width: (h, w) |
| center_crop | If set to true, then it will use be the center_crop,or it will crop |
|
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.. note:: `Crop` is deprecated. Use `slice` instead. Crop the 2nd and 3rd dim of input data, with the corresponding size of h_w or with width and height of the second input symbol, i.e., with one input, we need specify the crop height and width, otherwise the second input symbol's size Defined in src/operator/crop.cc:L50
| data | Tensor or List of Tensors, the second input will be used as crop_like |
| num_args | Number of inputs for crop, if equals one, then we will use the h_wfor crop height and width, else if equals two, then we will use the heightand width |
| offset | crop offset coordinate: (y, x) |
| h_w | crop height and width: (h, w) |
| center_crop | If set to true, then it will use be the center_crop,or it will crop |
|
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Apply a custom operator implemented in a frontend language (like Python).
Custom operators should override required methods like `forward` and `backward`. The custom operator must be registered before it can be used. Please check the tutorial here: /versions/1.3.1/faq/new_op.html. Defined in src/operator/custom/custom.cc:L547
| symbol_name | name of the resulting symbol |
| data | Input data for the custom operator. |
| op_type | Name of the custom operator. This is the name that is passed to |
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Apply a custom operator implemented in a frontend language (like Python).
Custom operators should override required methods like `forward` and `backward`. The custom operator must be registered before it can be used. Please check the tutorial here: /versions/1.3.1/faq/new_op.html. Defined in src/operator/custom/custom.cc:L547
| data | Input data for the custom operator. |
| op_type | Name of the custom operator. This is the name that is passed to |
|
inline |
Computes 1D or 2D transposed convolution (aka fractionally strided convolution) of the input tensor. This operation can be seen as the gradient of Convolution operation with respect to its input. Convolution usually reduces the size of the input. Transposed convolution works the other way, going from a smaller
| symbol_name | name of the resulting symbol |
| data | Input tensor to the deconvolution operation. |
| weight | Weights representing the kernel. |
| bias | Bias added to the result after the deconvolution operation. |
| kernel | Deconvolution kernel size: (w,), (h, w) or (d, h, w). This is same as |
| num_filter | Number of output filters. |
| stride | The stride used for the corresponding convolution: (w,), (h, w) or (d, |
| dilate | Dilation factor for each dimension of the input: (w,), (h, w) or (d, h, |
| pad | The amount of implicit zero padding added during convolution for each dimension of the input: (w,), (h, w) or (d, h, w). (kernel-1)/2 is usually a good choice. If target_shape is set, pad will be ignored and a padding |
| adj | Adjustment for output shape: (w,), (h, w) or (d, h, w). If target_shape |
| target_shape | Shape of the output tensor: (w,), (h, w) or (d, h, w). |
| num_group | Number of groups partition. |
| workspace | Maximum temporary workspace allowed (MB) in deconvolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the deconvolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when |
| no_bias | Whether to disable bias parameter. |
| cudnn_tune | Whether to pick convolution algorithm by running performance test. |
| cudnn_off | Turn off cudnn for this layer. |
| layout | Set layout for input, output and weight. Empty for default layout, NCW |
|
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Computes 1D or 2D transposed convolution (aka fractionally strided convolution) of the input tensor. This operation can be seen as the gradient of Convolution operation with respect to its input. Convolution usually reduces the size of the input. Transposed convolution works the other way, going from a smaller
| data | Input tensor to the deconvolution operation. |
| weight | Weights representing the kernel. |
| bias | Bias added to the result after the deconvolution operation. |
| kernel | Deconvolution kernel size: (w,), (h, w) or (d, h, w). This is same as |
| num_filter | Number of output filters. |
| stride | The stride used for the corresponding convolution: (w,), (h, w) or (d, |
| dilate | Dilation factor for each dimension of the input: (w,), (h, w) or (d, h, |
| pad | The amount of implicit zero padding added during convolution for each dimension of the input: (w,), (h, w) or (d, h, w). (kernel-1)/2 is usually a good choice. If target_shape is set, pad will be ignored and a padding |
| adj | Adjustment for output shape: (w,), (h, w) or (d, h, w). If target_shape |
| target_shape | Shape of the output tensor: (w,), (h, w) or (d, h, w). |
| num_group | Number of groups partition. |
| workspace | Maximum temporary workspace allowed (MB) in deconvolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the deconvolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when |
| no_bias | Whether to disable bias parameter. |
| cudnn_tune | Whether to pick convolution algorithm by running performance test. |
| cudnn_off | Turn off cudnn for this layer. |
| layout | Set layout for input, output and weight. Empty for default layout, NCW |
Converts each element of the input array from radians to degrees.
.. math:: degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360] The storage type of ``degrees`` output depends upon the input storage type: - degrees(default) = default - degrees(row_sparse) = row_sparse - degrees(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L163
| symbol_name | name of the resulting symbol |
| data | The input array. |
Converts each element of the input array from radians to degrees.
.. math:: degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360] The storage type of ``degrees`` output depends upon the input storage type: - degrees(default) = default - degrees(row_sparse) = row_sparse - degrees(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L163
| data | The input array. |
|
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Rearranges(permutes) data from depth into blocks of spatial data. Similar to ONNX DepthToSpace operator: https://github.com/onnx/onnx/blob/master/docs/Operators.md#DepthToSpace. The output is a new tensor where the values from depth dimension are moved in to height and width dimension. The reverse of this operation is
.. math::
{gather*} x = reshape(x, [N, block_size, block_size, C / (block_size ^ 2), H * x = transpose(x , [0, 3, 4, 1, 5, 2]) \ y = reshape(x , [N, C / (block_size ^ 2), H * block_size, W * {gather*}
where :math:x is an input tensor with default layout as :math:[N, C, H, W]: and :math:y is the output tensor of layout :math:`[N, C / (block_size ^ 2),
Example::
x = [[[[0, 1, 2], [3, 4, 5]], [[6, 7, 8], [9, 10, 11]], [[12, 13, 14], [15, 16, 17]], [[18, 19, 20], [21, 22, 23]]]]
depth_to_space(x, 2) = [[[[0, 6, 1, 7, 2, 8], [12, 18, 13, 19, 14, 20], [3, 9, 4, 10, 5, 11], [15, 21, 16, 22, 17, 23]]]]
Defined in src/operator/tensor/matrix_op.cc:L945
| symbol_name | name of the resulting symbol |
| data | Input ndarray |
| block_size | Blocks of [block_size. block_size] are moved |
Rearranges(permutes) data from depth into blocks of spatial data. Similar to ONNX DepthToSpace operator: https://github.com/onnx/onnx/blob/master/docs/Operators.md#DepthToSpace. The output is a new tensor where the values from depth dimension are moved in to height and width dimension. The reverse of this operation is
.. math::
{gather*} x = reshape(x, [N, block_size, block_size, C / (block_size ^ 2), H * x = transpose(x , [0, 3, 4, 1, 5, 2]) \ y = reshape(x , [N, C / (block_size ^ 2), H * block_size, W * {gather*}
where :math:x is an input tensor with default layout as :math:[N, C, H, W]: and :math:y is the output tensor of layout :math:`[N, C / (block_size ^ 2),
Example::
x = [[[[0, 1, 2], [3, 4, 5]], [[6, 7, 8], [9, 10, 11]], [[12, 13, 14], [15, 16, 17]], [[18, 19, 20], [21, 22, 23]]]]
depth_to_space(x, 2) = [[[[0, 6, 1, 7, 2, 8], [12, 18, 13, 19, 14, 20], [3, 9, 4, 10, 5, 11], [15, 21, 16, 22, 17, 23]]]]
Defined in src/operator/tensor/matrix_op.cc:L945
| data | Input ndarray |
| block_size | Blocks of [block_size. block_size] are moved |
|
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Extracts a diagonal or constructs a diagonal array.
``diag``'s behavior depends on the input array dimensions: - 1-D arrays: constructs a 2-D array with the input as its diagonal, all other - 2-D arrays: returns elements in the diagonal as a new 1-D array - N-D arrays: not supported yet Examples:: x = [[1, 2, 3], [4, 5, 6]] diag(x) = [1, 5] diag(x, k=1) = [2, 6] diag(x, k=-1) = [4] x = [1, 2, 3] diag(x) = [[1, 0, 0], [0, 2, 0], [0, 0, 3]] diag(x, k=1) = [[0, 1, 0], [0, 0, 2], [0, 0, 0]] diag(x, k=-1) = [[0, 0, 0], [1, 0, 0], [0, 2, 0]] Defined in src/operator/tensor/diag_op.cc:L68
| symbol_name | name of the resulting symbol |
| data | Input ndarray |
| k | Diagonal in question. The default is 0. Use k>0 for diagonals above the main diagonal, and k<0 for diagonals below the main diagonal. If input has shape (S0 |
Extracts a diagonal or constructs a diagonal array.
``diag``'s behavior depends on the input array dimensions: - 1-D arrays: constructs a 2-D array with the input as its diagonal, all other - 2-D arrays: returns elements in the diagonal as a new 1-D array - N-D arrays: not supported yet Examples:: x = [[1, 2, 3], [4, 5, 6]] diag(x) = [1, 5] diag(x, k=1) = [2, 6] diag(x, k=-1) = [4] x = [1, 2, 3] diag(x) = [[1, 0, 0], [0, 2, 0], [0, 0, 3]] diag(x, k=1) = [[0, 1, 0], [0, 0, 2], [0, 0, 0]] diag(x, k=-1) = [[0, 0, 0], [1, 0, 0], [0, 2, 0]] Defined in src/operator/tensor/diag_op.cc:L68
| data | Input ndarray |
| k | Diagonal in question. The default is 0. Use k>0 for diagonals above the main diagonal, and k<0 for diagonals below the main diagonal. If input has shape (S0 |
|
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Dot product of two arrays.
``dot``'s behavior depends on the input array dimensions: - 1-D arrays: inner product of vectors - 2-D arrays: matrix multiplication - N-D arrays: a sum product over the last axis of the first input and the first axis of the second input For example, given 3-D ``x`` with shape `(n,m,k)` and ``y`` with shape result array will have shape `(n,m,r,s)`. It is computed by:: dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b]) Example:: x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2)) y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2)) dot(x,y)[0,0,1,1] = 0 sum(x[0,0,:]*y[:,1,1]) = 0 The storage type of ``dot`` output depends on storage types of inputs, forward_stype option for output storage type. Implemented sparse operations - dot(default, default, transpose_a=True/False, transpose_b=True/False) = - dot(csr, default, transpose_a=True) = default - dot(csr, default, transpose_a=True) = row_sparse - dot(csr, default) = default - dot(csr, row_sparse) = default - dot(default, csr) = csr (CPU only) - dot(default, csr, forward_stype='default') = default - dot(default, csr, transpose_b=True, forward_stype='default') = default If the combination of input storage types and forward_stype does not match any above patterns, ``dot`` will fallback and generate output with default storage. .. Note:: If the storage type of the lhs is "csr", the storage type of gradient w.r.t rhs "row_sparse". Only a subset of optimizers support sparse gradients, including and Adam. Note that by default lazy updates is turned on, which may perform from standard updates. For more details, please check the Optimization API at: /api/python/optimization/optimization.html Defined in src/operator/tensor/dot.cc:L77
| symbol_name | name of the resulting symbol |
| lhs | The first input |
| rhs | The second input |
| transpose_a | If true then transpose the first input before dot. |
| transpose_b | If true then transpose the second input before dot. |
| forward_stype | The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still |
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Dot product of two arrays.
``dot``'s behavior depends on the input array dimensions: - 1-D arrays: inner product of vectors - 2-D arrays: matrix multiplication - N-D arrays: a sum product over the last axis of the first input and the first axis of the second input For example, given 3-D ``x`` with shape `(n,m,k)` and ``y`` with shape result array will have shape `(n,m,r,s)`. It is computed by:: dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b]) Example:: x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2)) y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2)) dot(x,y)[0,0,1,1] = 0 sum(x[0,0,:]*y[:,1,1]) = 0 The storage type of ``dot`` output depends on storage types of inputs, forward_stype option for output storage type. Implemented sparse operations - dot(default, default, transpose_a=True/False, transpose_b=True/False) = - dot(csr, default, transpose_a=True) = default - dot(csr, default, transpose_a=True) = row_sparse - dot(csr, default) = default - dot(csr, row_sparse) = default - dot(default, csr) = csr (CPU only) - dot(default, csr, forward_stype='default') = default - dot(default, csr, transpose_b=True, forward_stype='default') = default If the combination of input storage types and forward_stype does not match any above patterns, ``dot`` will fallback and generate output with default storage. .. Note:: If the storage type of the lhs is "csr", the storage type of gradient w.r.t rhs "row_sparse". Only a subset of optimizers support sparse gradients, including and Adam. Note that by default lazy updates is turned on, which may perform from standard updates. For more details, please check the Optimization API at: /api/python/optimization/optimization.html Defined in src/operator/tensor/dot.cc:L77
| lhs | The first input |
| rhs | The second input |
| transpose_a | If true then transpose the first input before dot. |
| transpose_b | If true then transpose the second input before dot. |
| forward_stype | The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still |
|
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Applies dropout operation to input array.
- During training, each element of the input is set to zero with probability p.
The whole array is rescaled by :math:`1/(1-p)` to keep the expected
sum of the input unchanged.
- During testing, this operator does not change the input if mode is 'training'.
If mode is 'always', the same computaion as during training will be applied.
Example::
random.seed(998)
input_array = array([[3., 0.5, -0.5, 2., 7.],
[2., -0.4, 7., 3., 0.2]])
a = symbol.Variable('a')
dropout = symbol.Dropout(a, p = 0.2)
executor = dropout.simple_bind(a = input_array.shape)
## If training
executor.forward(is_train = True, a = input_array)
executor.outputs
[[ 3.75 0.625 -0. 2.5 8.75 ]
[ 2.5 -0.5 8.75 3.75 0. ]]
## If testing
executor.forward(is_train = False, a = input_array)
executor.outputs
[[ 3. 0.5 -0.5 2. 7. ]
[ 2. -0.4 7. 3. 0.2 ]]
Defined in src/operator/nn/dropout.cc:L76
| symbol_name | name of the resulting symbol |
| data | Input array to which dropout will be applied. |
| p | Fraction of the input that gets dropped out during training time. |
| mode | Whether to only turn on dropout during training or to also turn on for |
| axes | Axes for variational dropout kernel. |
|
inline |
Applies dropout operation to input array.
- During training, each element of the input is set to zero with probability p.
The whole array is rescaled by :math:`1/(1-p)` to keep the expected
sum of the input unchanged.
- During testing, this operator does not change the input if mode is 'training'.
If mode is 'always', the same computaion as during training will be applied.
Example::
random.seed(998)
input_array = array([[3., 0.5, -0.5, 2., 7.],
[2., -0.4, 7., 3., 0.2]])
a = symbol.Variable('a')
dropout = symbol.Dropout(a, p = 0.2)
executor = dropout.simple_bind(a = input_array.shape)
## If training
executor.forward(is_train = True, a = input_array)
executor.outputs
[[ 3.75 0.625 -0. 2.5 8.75 ]
[ 2.5 -0.5 8.75 3.75 0. ]]
## If testing
executor.forward(is_train = False, a = input_array)
executor.outputs
[[ 3. 0.5 -0.5 2. 7. ]
[ 2. -0.4 7. 3. 0.2 ]]
Defined in src/operator/nn/dropout.cc:L76
| data | Input array to which dropout will be applied. |
| p | Fraction of the input that gets dropped out during training time. |
| mode | Whether to only turn on dropout during training or to also turn on for |
| axes | Axes for variational dropout kernel. |
Adds arguments element-wise.
The storage type of ``elemwise_add`` output depends on storage types of inputs - elemwise_add(row_sparse, row_sparse) = row_sparse - elemwise_add(csr, csr) = csr - elemwise_add(default, csr) = default - elemwise_add(csr, default) = default - elemwise_add(default, rsp) = default - elemwise_add(rsp, default) = default - otherwise, ``elemwise_add`` generates output with default storage
| symbol_name | name of the resulting symbol |
| lhs | first input |
| rhs | second input |
Adds arguments element-wise.
The storage type of ``elemwise_add`` output depends on storage types of inputs - elemwise_add(row_sparse, row_sparse) = row_sparse - elemwise_add(csr, csr) = csr - elemwise_add(default, csr) = default - elemwise_add(csr, default) = default - elemwise_add(default, rsp) = default - elemwise_add(rsp, default) = default - otherwise, ``elemwise_add`` generates output with default storage
| lhs | first input |
| rhs | second input |
Divides arguments element-wise.
The storage type of ``elemwise_div`` output is always dense
| symbol_name | name of the resulting symbol |
| lhs | first input |
| rhs | second input |
Divides arguments element-wise.
The storage type of ``elemwise_div`` output is always dense
| lhs | first input |
| rhs | second input |
Multiplies arguments element-wise.
The storage type of ``elemwise_mul`` output depends on storage types of inputs - elemwise_mul(default, default) = default - elemwise_mul(row_sparse, row_sparse) = row_sparse - elemwise_mul(default, row_sparse) = row_sparse - elemwise_mul(row_sparse, default) = row_sparse - elemwise_mul(csr, csr) = csr - otherwise, ``elemwise_mul`` generates output with default storage
| symbol_name | name of the resulting symbol |
| lhs | first input |
| rhs | second input |
Multiplies arguments element-wise.
The storage type of ``elemwise_mul`` output depends on storage types of inputs - elemwise_mul(default, default) = default - elemwise_mul(row_sparse, row_sparse) = row_sparse - elemwise_mul(default, row_sparse) = row_sparse - elemwise_mul(row_sparse, default) = row_sparse - elemwise_mul(csr, csr) = csr - otherwise, ``elemwise_mul`` generates output with default storage
| lhs | first input |
| rhs | second input |
Subtracts arguments element-wise.
The storage type of ``elemwise_sub`` output depends on storage types of inputs - elemwise_sub(row_sparse, row_sparse) = row_sparse - elemwise_sub(csr, csr) = csr - elemwise_sub(default, csr) = default - elemwise_sub(csr, default) = default - elemwise_sub(default, rsp) = default - elemwise_sub(rsp, default) = default - otherwise, ``elemwise_sub`` generates output with default storage
| symbol_name | name of the resulting symbol |
| lhs | first input |
| rhs | second input |
Subtracts arguments element-wise.
The storage type of ``elemwise_sub`` output depends on storage types of inputs - elemwise_sub(row_sparse, row_sparse) = row_sparse - elemwise_sub(csr, csr) = csr - elemwise_sub(default, csr) = default - elemwise_sub(csr, default) = default - elemwise_sub(default, rsp) = default - elemwise_sub(rsp, default) = default - otherwise, ``elemwise_sub`` generates output with default storage
| lhs | first input |
| rhs | second input |
|
inline |
Maps integer indices to vector representations (embeddings).
This operator maps words to real-valued vectors in a high-dimensional space, called word embeddings. These embeddings can capture semantic and syntactic For example, it has been noted that in the learned embedding spaces, similar to be close to each other and dissimilar words far apart. For an input array of shape (d1, ..., dK), the shape of an output array is (d1, ..., dK, output_dim). All the input values should be integers in the range [0, input_dim). If the input_dim is ip0 and output_dim is op0, then shape of the embedding (ip0, op0). By default, if any index mentioned is too large, it is replaced by the index the last vector in an embedding matrix. Examples:: input_dim = 4 output_dim = 5 // Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3) y = [[ 0., 1., 2., 3., 4.], [ 5., 6., 7., 8., 9.], [ 10., 11., 12., 13., 14.], [ 15., 16., 17., 18., 19.]] // Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)] x = [[ 1., 3.], [ 0., 2.]] // Mapped input x to its vector representation y. Embedding(x, y, 4, 5) = [[[ 5., 6., 7., 8., 9.], [ 15., 16., 17., 18., 19.]], [[ 0., 1., 2., 3., 4.], [ 10., 11., 12., 13., 14.]]] The storage type of weight can be either row_sparse or default. .. Note:: If "sparse_grad" is set to True, the storage type of gradient w.r.t weights "row_sparse". Only a subset of optimizers support sparse gradients, including and Adam. Note that by default lazy updates is turned on, which may perform from standard updates. For more details, please check the Optimization API at: /api/python/optimization/optimization.html Defined in src/operator/tensor/indexing_op.cc:L267
| symbol_name | name of the resulting symbol |
| data | The input array to the embedding operator. |
| weight | The embedding weight matrix. |
| input_dim | Vocabulary size of the input indices. |
| output_dim | Dimension of the embedding vectors. |
| dtype | Data type of weight. |
| sparse_grad | Compute row sparse gradient in the backward calculation. If set to |
|
inline |
Maps integer indices to vector representations (embeddings).
This operator maps words to real-valued vectors in a high-dimensional space, called word embeddings. These embeddings can capture semantic and syntactic For example, it has been noted that in the learned embedding spaces, similar to be close to each other and dissimilar words far apart. For an input array of shape (d1, ..., dK), the shape of an output array is (d1, ..., dK, output_dim). All the input values should be integers in the range [0, input_dim). If the input_dim is ip0 and output_dim is op0, then shape of the embedding (ip0, op0). By default, if any index mentioned is too large, it is replaced by the index the last vector in an embedding matrix. Examples:: input_dim = 4 output_dim = 5 // Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3) y = [[ 0., 1., 2., 3., 4.], [ 5., 6., 7., 8., 9.], [ 10., 11., 12., 13., 14.], [ 15., 16., 17., 18., 19.]] // Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)] x = [[ 1., 3.], [ 0., 2.]] // Mapped input x to its vector representation y. Embedding(x, y, 4, 5) = [[[ 5., 6., 7., 8., 9.], [ 15., 16., 17., 18., 19.]], [[ 0., 1., 2., 3., 4.], [ 10., 11., 12., 13., 14.]]] The storage type of weight can be either row_sparse or default. .. Note:: If "sparse_grad" is set to True, the storage type of gradient w.r.t weights "row_sparse". Only a subset of optimizers support sparse gradients, including and Adam. Note that by default lazy updates is turned on, which may perform from standard updates. For more details, please check the Optimization API at: /api/python/optimization/optimization.html Defined in src/operator/tensor/indexing_op.cc:L267
| data | The input array to the embedding operator. |
| weight | The embedding weight matrix. |
| input_dim | Vocabulary size of the input indices. |
| output_dim | Dimension of the embedding vectors. |
| dtype | Data type of weight. |
| sparse_grad | Compute row sparse gradient in the backward calculation. If set to |
Returns element-wise exponential value of the input.
.. math:: exp(x) = e^x \approx 2.718^x Example:: exp([0, 1, 2]) = [1., 2.71828175, 7.38905621] The storage type of ``exp`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L929
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise exponential value of the input.
.. math:: exp(x) = e^x \approx 2.718^x Example:: exp([0, 1, 2]) = [1., 2.71828175, 7.38905621] The storage type of ``exp`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L929
| data | The input array. |
Inserts a new axis of size 1 into the array shape
For example, given ``x`` with shape ``(2,3,4)``, then ``expand_dims(x, axis=1)`` will return a new array with shape ``(2,1,3,4)``. Defined in src/operator/tensor/matrix_op.cc:L347
| symbol_name | name of the resulting symbol |
| data | Source input |
| axis | Position where new axis is to be inserted. Suppose that the input NDArray's dimension is ndim, the range of the inserted axis is `[-ndim, |
Inserts a new axis of size 1 into the array shape
For example, given ``x`` with shape ``(2,3,4)``, then ``expand_dims(x, axis=1)`` will return a new array with shape ``(2,1,3,4)``. Defined in src/operator/tensor/matrix_op.cc:L347
| data | Source input |
| axis | Position where new axis is to be inserted. Suppose that the input NDArray's dimension is ndim, the range of the inserted axis is `[-ndim, |
Returns exp(x) - 1 computed element-wise on the input.
This function provides greater precision than ``exp(x) - 1`` for small values The storage type of ``expm1`` output depends upon the input storage type: - expm1(default) = default - expm1(row_sparse) = row_sparse - expm1(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1008
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns exp(x) - 1 computed element-wise on the input.
This function provides greater precision than ``exp(x) - 1`` for small values The storage type of ``expm1`` output depends upon the input storage type: - expm1(default) = default - expm1(row_sparse) = row_sparse - expm1(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1008
| data | The input array. |
|
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Fill one element of each line(row for python, column for R/Julia) in lhs according to index indicated by rhs and values indicated by mhs. This function
| symbol_name | name of the resulting symbol |
| lhs | Left operand to the function. |
| mhs | Middle operand to the function. |
| rhs | Right operand to the function. |
Fill one element of each line(row for python, column for R/Julia) in lhs according to index indicated by rhs and values indicated by mhs. This function
| lhs | Left operand to the function. |
| mhs | Middle operand to the function. |
| rhs | Right operand to the function. |
Returns element-wise rounded value to the nearest \ integer towards zero of the input.
Example::
fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1., 1., 2.]
The storage type of fix output depends upon the input storage type:
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L803
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise rounded value to the nearest \ integer towards zero of the input.
Example::
fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1., 1., 2.]
The storage type of fix output depends upon the input storage type:
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L803
| data | The input array. |
Flattens the input array into a 2-D array by collapsing the higher dimensions.
.. note:: `Flatten` is deprecated. Use `flatten` instead. For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation the input array into an output array of shape ``(d1, d2*...*dk)``. Note that the bahavior of this function is different from numpy.ndarray.flatten, which behaves similar to mxnet.ndarray.reshape((-1,)). Example:: x = [[ [1,2,3], [4,5,6], [7,8,9] ], [ [1,2,3], [4,5,6], [7,8,9] ]], flatten(x) = [[ 1., 2., 3., 4., 5., 6., 7., 8., 9.], [ 1., 2., 3., 4., 5., 6., 7., 8., 9.]] Defined in src/operator/tensor/matrix_op.cc:L259
| symbol_name | name of the resulting symbol |
| data | Input array. |
Flattens the input array into a 2-D array by collapsing the higher dimensions.
.. note:: `Flatten` is deprecated. Use `flatten` instead. For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation the input array into an output array of shape ``(d1, d2*...*dk)``. Note that the bahavior of this function is different from numpy.ndarray.flatten, which behaves similar to mxnet.ndarray.reshape((-1,)). Example:: x = [[ [1,2,3], [4,5,6], [7,8,9] ], [ [1,2,3], [4,5,6], [7,8,9] ]], flatten(x) = [[ 1., 2., 3., 4., 5., 6., 7., 8., 9.], [ 1., 2., 3., 4., 5., 6., 7., 8., 9.]] Defined in src/operator/tensor/matrix_op.cc:L259
| data | Input array. |
Returns element-wise floor of the input.
The floor of the scalar x is the largest integer i, such that i <= x. Example:: floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2., 1., 1., 2.] The storage type of ``floor`` output depends upon the input storage type: - floor(default) = default - floor(row_sparse) = row_sparse - floor(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L765
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise floor of the input.
The floor of the scalar x is the largest integer i, such that i <= x. Example:: floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2., 1., 1., 2.] The storage type of ``floor`` output depends upon the input storage type: - floor(default) = default - floor(row_sparse) = row_sparse - floor(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L765
| data | The input array. |
|
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The FTML optimizer described in FTML - Follow the Moving Leader in Deep Learning, available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.
.. math::
g_t = J(W_{t-1})\ v_t = v_{t-1} + (1 - ) g_t^2\ d_t = { 1 - ^t }{ } ({ { v_t }{ 1 - ^t } } = d_t - d_{t-1} z_t = z_{ t-1 } + (1 - ^t) g_t - W_{t-1} W_t = - { z_t }{ d_t }
Defined in src/operator/optimizer_op.cc:L447
| symbol_name | name of the resulting symbol |
| weight | Weight |
| grad | Gradient |
| d | Internal state d_t |
| v | Internal state v_t |
| z | Internal state z_t |
| lr | Learning rate. |
| t | Number of update. |
| beta1 | Generally close to 0.5. |
| beta2 | Generally close to 1. |
| epsilon | Epsilon to prevent div 0. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_grad | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
|
inline |
The FTML optimizer described in FTML - Follow the Moving Leader in Deep Learning, available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.
.. math::
g_t = J(W_{t-1})\ v_t = v_{t-1} + (1 - ) g_t^2\ d_t = { 1 - ^t }{ } ({ { v_t }{ 1 - ^t } } = d_t - d_{t-1} z_t = z_{ t-1 } + (1 - ^t) g_t - W_{t-1} W_t = - { z_t }{ d_t }
Defined in src/operator/optimizer_op.cc:L447
| weight | Weight |
| grad | Gradient |
| d | Internal state d_t |
| v | Internal state v_t |
| z | Internal state z_t |
| lr | Learning rate. |
| t | Number of update. |
| beta1 | Generally close to 0.5. |
| beta2 | Generally close to 1. |
| epsilon | Epsilon to prevent div 0. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_grad | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
|
inline |
Update function for Ftrl optimizer. Referenced from Ad Click Prediction: a View from the Trenches, available at http://dl.acm.org/citation.cfm?id=2488200.
It updates the weights using::
rescaled_grad = clip(grad * rescale_grad, clip_gradient) z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / n += rescaled_grad**2 w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z)
If w, z and n are all of row_sparse storage type, only the row slices whose indices appear in grad.indices are updated (for w, z
for row in grad.indices: rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient) z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - n[row] += rescaled_grad[row]**2 w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) /
Defined in src/operator/optimizer_op.cc:L632
| symbol_name | name of the resulting symbol |
| weight | Weight |
| grad | Gradient |
| z | z |
| n | Square of grad |
| lr | Learning rate |
| lamda1 | The L1 regularization coefficient. |
| beta | Per-Coordinate Learning Rate beta. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
|
inline |
Update function for Ftrl optimizer. Referenced from Ad Click Prediction: a View from the Trenches, available at http://dl.acm.org/citation.cfm?id=2488200.
It updates the weights using::
rescaled_grad = clip(grad * rescale_grad, clip_gradient) z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / n += rescaled_grad**2 w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z)
If w, z and n are all of row_sparse storage type, only the row slices whose indices appear in grad.indices are updated (for w, z
for row in grad.indices: rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient) z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - n[row] += rescaled_grad[row]**2 w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) /
Defined in src/operator/optimizer_op.cc:L632
| weight | Weight |
| grad | Gradient |
| z | z |
| n | Square of grad |
| lr | Learning rate |
| lamda1 | The L1 regularization coefficient. |
| beta | Per-Coordinate Learning Rate beta. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
|
inline |
Applies a linear transformation: :math:Y = XW^T + b.
If ``flatten`` is set to be true, then the shapes are: - **data**: `(batch_size, x1, x2, ..., xn)` - **weight**: `(num_hidden, x1 * x2 * ... * xn)` - **bias**: `(num_hidden,)` - **out**: `(batch_size, num_hidden)` If ``flatten`` is set to be false, then the shapes are: - **data**: `(x1, x2, ..., xn, input_dim)` - **weight**: `(num_hidden, input_dim)` - **bias**: `(num_hidden,)` - **out**: `(x1, x2, ..., xn, num_hidden)` The learnable parameters include both ``weight`` and ``bias``. If ``no_bias`` is set to be true, then the ``bias`` term is ignored. .. Note:: The sparse support for FullyConnected is limited to forward evaluation with weight and bias, where the length of `weight.indices` and `bias.indices` must to `num_hidden`. This could be useful for model inference with `row_sparse` trained with importance sampling or noise contrastive estimation. To compute linear transformation with 'csr' sparse data, sparse.dot is of sparse.FullyConnected. Defined in src/operator/nn/fully_connected.cc:L272
| symbol_name | name of the resulting symbol |
| data | Input data. |
| weight | Weight matrix. |
| bias | Bias parameter. |
| num_hidden | Number of hidden nodes of the output. |
| no_bias | Whether to disable bias parameter. |
| flatten | Whether to collapse all but the first axis of the input data tensor. |
|
inline |
Applies a linear transformation: :math:Y = XW^T + b.
If ``flatten`` is set to be true, then the shapes are: - **data**: `(batch_size, x1, x2, ..., xn)` - **weight**: `(num_hidden, x1 * x2 * ... * xn)` - **bias**: `(num_hidden,)` - **out**: `(batch_size, num_hidden)` If ``flatten`` is set to be false, then the shapes are: - **data**: `(x1, x2, ..., xn, input_dim)` - **weight**: `(num_hidden, input_dim)` - **bias**: `(num_hidden,)` - **out**: `(x1, x2, ..., xn, num_hidden)` The learnable parameters include both ``weight`` and ``bias``. If ``no_bias`` is set to be true, then the ``bias`` term is ignored. .. Note:: The sparse support for FullyConnected is limited to forward evaluation with weight and bias, where the length of `weight.indices` and `bias.indices` must to `num_hidden`. This could be useful for model inference with `row_sparse` trained with importance sampling or noise contrastive estimation. To compute linear transformation with 'csr' sparse data, sparse.dot is of sparse.FullyConnected. Defined in src/operator/nn/fully_connected.cc:L272
| data | Input data. |
| weight | Weight matrix. |
| bias | Bias parameter. |
| num_hidden | Number of hidden nodes of the output. |
| no_bias | Whether to disable bias parameter. |
| flatten | Whether to collapse all but the first axis of the input data tensor. |
Returns the gamma function (extension of the factorial function \ to the reals), computed element-wise on the input array.
The storage type of gamma output is always dense
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns the gamma function (extension of the factorial function \ to the reals), computed element-wise on the input array.
The storage type of gamma output is always dense
| data | The input array. |
Returns element-wise log of the absolute value of the gamma function \ of the input.
The storage type of gammaln output is always dense
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise log of the absolute value of the gamma function \ of the input.
The storage type of gammaln output is always dense
| data | The input array. |
|
inline |
Gather elements or slices from data and store to a tensor whose shape is defined by indices.
Given data with shape (X_0, X_1, ..., X_{N-1}) and indices with shape (M, Y_0, ..., Y_{K-1}), the output will have shape (Y_0, ..., Y_{K-1}, X_M, whereM <= N. IfM == N, output shape will simply be(Y_0, ..., Y_{K-1})`.
The elements in output is defined as follows::
output[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] = data[indices[0, y_0, ..., ..., indices[M-1, y_0, ..., y_{K-1}], x_M, ..., x_{N-1}]
Examples::
data = [[0, 1], [2, 3]] indices = [[1, 1, 0], [0, 1, 0]] gather_nd(data, indices) = [2, 3, 0]
data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]] indices = [[0, 1], [1, 0]] gather_nd(data, indices) = [[3, 4], [5, 6]]
| symbol_name | name of the resulting symbol |
| data | data |
| indices | indices |
Gather elements or slices from data and store to a tensor whose shape is defined by indices.
Given data with shape (X_0, X_1, ..., X_{N-1}) and indices with shape (M, Y_0, ..., Y_{K-1}), the output will have shape (Y_0, ..., Y_{K-1}, X_M, whereM <= N. IfM == N, output shape will simply be(Y_0, ..., Y_{K-1})`.
The elements in output is defined as follows::
output[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] = data[indices[0, y_0, ..., ..., indices[M-1, y_0, ..., y_{K-1}], x_M, ..., x_{N-1}]
Examples::
data = [[0, 1], [2, 3]] indices = [[1, 1, 0], [0, 1, 0]] gather_nd(data, indices) = [2, 3, 0]
data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]] indices = [[0, 1], [1, 0]] gather_nd(data, indices) = [[3, 4], [5, 6]]
| data | data |
| indices | indices |
|
inline |
Generates 2D sampling grid for bilinear sampling.
| symbol_name | name of the resulting symbol |
| data | Input data to the function. |
| transform_type | The type of transformation. For affine, input data should be an affine matrix of size (batch, 6). For warp, input data should be an |
| target_shape | Specifies the output shape (H, W). This is required if transformation type is affine. If transformation type is warp, this |
|
inline |
Generates 2D sampling grid for bilinear sampling.
| data | Input data to the function. |
| transform_type | The type of transformation. For affine, input data should be an affine matrix of size (batch, 6). For warp, input data should be an |
| target_shape | Specifies the output shape (H, W). This is required if transformation type is affine. If transformation type is warp, this |
|
inline |
Computes hard sigmoid of x element-wise.
.. math:: y = max(0, min(1, alpha * x + beta)) Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L115
| symbol_name | name of the resulting symbol |
| data | The input array. |
| alpha | Slope of hard sigmoid |
| beta | Bias of hard sigmoid. |
Computes hard sigmoid of x element-wise.
.. math:: y = max(0, min(1, alpha * x + beta)) Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L115
| data | The input array. |
| alpha | Slope of hard sigmoid |
| beta | Bias of hard sigmoid. |
|
inline |
Apply a sparse regularization to the output a sigmoid activation function.
| symbol_name | name of the resulting symbol |
| data | Input data. |
| sparseness_target | The sparseness target |
| penalty | The tradeoff parameter for the sparseness penalty |
| momentum | The momentum for running average |
|
inline |
Apply a sparse regularization to the output a sigmoid activation function.
| data | Input data. |
| sparseness_target | The sparseness target |
| penalty | The tradeoff parameter for the sparseness penalty |
| momentum | The momentum for running average |
|
inline |
Applies instance normalization to the n-dimensional input array.
This operator takes an n-dimensional input array where (n>2) and normalizes
the input using the following formula:
.. math::
out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta
This layer is similar to batch normalization layer (`BatchNorm`)
with two differences: first, the normalization is
carried out per example (instance), not over a batch. Second, the
same normalization is applied both at test and train time. This
operation is also known as `contrast normalization`.
If the input data is of shape [batch, channel, spacial_dim1, spacial_dim2, ...],
`gamma` and `beta` parameters must be vectors of shape [channel].
This implementation is based on paper:
.. [1] Instance Normalization: The Missing Ingredient for Fast Stylization,
D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2).
Examples::
// Input of shape (2,1,2)
x = [[[ 1.1, 2.2]],
[[ 3.3, 4.4]]]
// gamma parameter of length 1
gamma = [1.5]
// beta parameter of length 1
beta = [0.5]
// Instance normalization is calculated with the above formula
InstanceNorm(x,gamma,beta) = [[[-0.997527 , 1.99752665]],
[[-0.99752653, 1.99752724]]]
Defined in src/operator/instance_norm.cc:L95
| symbol_name | name of the resulting symbol |
| data | An n-dimensional input array (n > 2) of the form [batch, channel, |
| gamma | A vector of length 'channel', which multiplies the normalized input. |
| beta | A vector of length 'channel', which is added to the product of the |
| eps | An epsilon parameter to prevent division by 0. |
|
inline |
Applies instance normalization to the n-dimensional input array.
This operator takes an n-dimensional input array where (n>2) and normalizes
the input using the following formula:
.. math::
out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta
This layer is similar to batch normalization layer (`BatchNorm`)
with two differences: first, the normalization is
carried out per example (instance), not over a batch. Second, the
same normalization is applied both at test and train time. This
operation is also known as `contrast normalization`.
If the input data is of shape [batch, channel, spacial_dim1, spacial_dim2, ...],
`gamma` and `beta` parameters must be vectors of shape [channel].
This implementation is based on paper:
.. [1] Instance Normalization: The Missing Ingredient for Fast Stylization,
D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2).
Examples::
// Input of shape (2,1,2)
x = [[[ 1.1, 2.2]],
[[ 3.3, 4.4]]]
// gamma parameter of length 1
gamma = [1.5]
// beta parameter of length 1
beta = [0.5]
// Instance normalization is calculated with the above formula
InstanceNorm(x,gamma,beta) = [[[-0.997527 , 1.99752665]],
[[-0.99752653, 1.99752724]]]
Defined in src/operator/instance_norm.cc:L95
| data | An n-dimensional input array (n > 2) of the form [batch, channel, |
| gamma | A vector of length 'channel', which multiplies the normalized input. |
| beta | A vector of length 'channel', which is added to the product of the |
| eps | An epsilon parameter to prevent division by 0. |
|
inline |
Computes the Khatri-Rao product of the input matrices.
Given a collection of :math:`n` input matrices,
.. math::
A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N},
the (column-wise) Khatri-Rao product is defined as the matrix,
.. math::
X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N},
where the :math:`k` th column is equal to the column-wise outer product
:math:`{A_1}_k \otimes \cdots \otimes {A_n}_k` where :math:`{A_i}_k` is the kth
column of the ith matrix.
Example::
>>> A = mx.nd.array([[1, -1],
>>> [2, -3]])
>>> B = mx.nd.array([[1, 4],
>>> [2, 5],
>>> [3, 6]])
>>> C = mx.nd.khatri_rao(A, B)
>>> print(C.asnumpy())
[[ 1. -4.]
[ 2. -5.]
[ 3. -6.]
[ 2. -12.]
[ 4. -15.]
[ 6. -18.]]
Defined in src/operator/contrib/krprod.cc:L108
| symbol_name | name of the resulting symbol |
| args | Positional input matrices |
Computes the Khatri-Rao product of the input matrices.
Given a collection of :math:`n` input matrices,
.. math::
A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N},
the (column-wise) Khatri-Rao product is defined as the matrix,
.. math::
X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N},
where the :math:`k` th column is equal to the column-wise outer product
:math:`{A_1}_k \otimes \cdots \otimes {A_n}_k` where :math:`{A_i}_k` is the kth
column of the ith matrix.
Example::
>>> A = mx.nd.array([[1, -1],
>>> [2, -3]])
>>> B = mx.nd.array([[1, 4],
>>> [2, 5],
>>> [3, 6]])
>>> C = mx.nd.khatri_rao(A, B)
>>> print(C.asnumpy())
[[ 1. -4.]
[ 2. -5.]
[ 3. -6.]
[ 2. -12.]
[ 4. -15.]
[ 6. -18.]]
Defined in src/operator/contrib/krprod.cc:L108
| args | Positional input matrices |
|
inline |
Normalize the input array using the L2 norm.
For 1-D NDArray, it computes:: out = data / sqrt(sum(data ** 2) + eps) For N-D NDArray, if the input array has shape (N, N, ..., N), with ``mode`` = ``instance``, it normalizes each instance in the array by its L2 norm.:: for i in 0...N out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps) with ``mode`` = ``channel``, it normalizes each channel in the array by its L2 for i in 0...N out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps) with ``mode`` = ``spatial``, it normalizes the cross channel norm for each in the array by its L2 norm.:: for dim in 2...N for i in 0...N out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, -dim- Example:: x = [[[1,2], [3,4]], [[2,2], [5,6]]] L2Normalization(x, mode='instance') =[[[ 0.18257418 0.36514837] [ 0.54772252 0.73029673]] [[ 0.24077171 0.24077171] [ 0.60192931 0.72231513]]] L2Normalization(x, mode='channel') =[[[ 0.31622776 0.44721359] [ 0.94868326 0.89442718]] [[ 0.37139067 0.31622776] [ 0.92847669 0.94868326]]] L2Normalization(x, mode='spatial') =[[[ 0.44721359 0.89442718] [ 0.60000002 0.80000001]] [[ 0.70710677 0.70710677] [ 0.6401844 0.76822126]]] Defined in src/operator/l2_normalization.cc:L98
| symbol_name | name of the resulting symbol |
| data | Input array to normalize. |
| eps | A small constant for numerical stability. |
| mode | Specify the dimension along which to compute L2 norm. |
|
inline |
Normalize the input array using the L2 norm.
For 1-D NDArray, it computes:: out = data / sqrt(sum(data ** 2) + eps) For N-D NDArray, if the input array has shape (N, N, ..., N), with ``mode`` = ``instance``, it normalizes each instance in the array by its L2 norm.:: for i in 0...N out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps) with ``mode`` = ``channel``, it normalizes each channel in the array by its L2 for i in 0...N out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps) with ``mode`` = ``spatial``, it normalizes the cross channel norm for each in the array by its L2 norm.:: for dim in 2...N for i in 0...N out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, -dim- Example:: x = [[[1,2], [3,4]], [[2,2], [5,6]]] L2Normalization(x, mode='instance') =[[[ 0.18257418 0.36514837] [ 0.54772252 0.73029673]] [[ 0.24077171 0.24077171] [ 0.60192931 0.72231513]]] L2Normalization(x, mode='channel') =[[[ 0.31622776 0.44721359] [ 0.94868326 0.89442718]] [[ 0.37139067 0.31622776] [ 0.92847669 0.94868326]]] L2Normalization(x, mode='spatial') =[[[ 0.44721359 0.89442718] [ 0.60000002 0.80000001]] [[ 0.70710677 0.70710677] [ 0.6401844 0.76822126]]] Defined in src/operator/l2_normalization.cc:L98
| data | Input array to normalize. |
| eps | A small constant for numerical stability. |
| mode | Specify the dimension along which to compute L2 norm. |
|
inline |
Layer normalization.
Normalizes the channels of the input tensor by mean and variance, and applies a
well as offset ``beta``.
Assume the input has more than one dimension and we normalize along axis 1.
We first compute the mean and variance along this axis and then
compute the normalized output, which has the same shape as input, as following:
.. math::
out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma
Both ``gamma`` and ``beta`` are learnable parameters.
Unlike BatchNorm and InstanceNorm, the *mean* and *var* are computed along the
Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both
``data_std``. Note that no gradient will be passed through these two outputs.
The parameter ``axis`` specifies which axis of the input shape denotes
the 'channel' (separately normalized groups). The default is -1, which sets
axis to be the last item in the input shape.
Defined in src/operator/nn/layer_norm.cc:L94
| symbol_name | name of the resulting symbol |
| data | Input data to layer normalization |
| gamma | gamma array |
| beta | beta array |
| axis | The axis to perform layer normalization. Usually, this should be be axis |
| eps | An epsilon parameter to prevent division by 0. |
| output_mean_var | Output the mean and std calculated along the given axis. |
|
inline |
Layer normalization.
Normalizes the channels of the input tensor by mean and variance, and applies a
well as offset ``beta``.
Assume the input has more than one dimension and we normalize along axis 1.
We first compute the mean and variance along this axis and then
compute the normalized output, which has the same shape as input, as following:
.. math::
out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma
Both ``gamma`` and ``beta`` are learnable parameters.
Unlike BatchNorm and InstanceNorm, the *mean* and *var* are computed along the
Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both
``data_std``. Note that no gradient will be passed through these two outputs.
The parameter ``axis`` specifies which axis of the input shape denotes
the 'channel' (separately normalized groups). The default is -1, which sets
axis to be the last item in the input shape.
Defined in src/operator/nn/layer_norm.cc:L94
| data | Input data to layer normalization |
| gamma | gamma array |
| beta | beta array |
| axis | The axis to perform layer normalization. Usually, this should be be axis |
| eps | An epsilon parameter to prevent division by 0. |
| output_mean_var | Output the mean and std calculated along the given axis. |
|
inline |
Applies Leaky rectified linear unit activation element-wise to the input.
Leaky ReLUs attempt to fix the "dying ReLU" problem by allowing a small `slope` when the input is negative and has a slope of one when input is positive. The following modified ReLU Activation functions are supported: - *elu*: Exponential Linear Unit. `y = x > 0 ? x : slope * (exp(x)-1)` - *selu*: Scaled Exponential Linear Unit. `y = lambda * (x > 0 ? x : alpha * *lambda = 1.0507009873554804934193349852946* and *alpha = - *leaky*: Leaky ReLU. `y = x > 0 ? x : slope * x` - *prelu*: Parametric ReLU. This is same as *leaky* except that `slope` is - *rrelu*: Randomized ReLU. same as *leaky* but the `slope` is uniformly and *[lower_bound, upper_bound)* for training, while fixed to be *(lower_bound+upper_bound)/2* for inference. Defined in src/operator/leaky_relu.cc:L65
| symbol_name | name of the resulting symbol |
| data | Input data to activation function. |
| gamma | Slope parameter for PReLU. Only required when act_type is 'prelu'. It should be either a vector of size 1, or the same size as the second dimension |
| act_type | Activation function to be applied. |
| slope | Init slope for the activation. (For leaky and elu only) |
| lower_bound | Lower bound of random slope. (For rrelu only) |
| upper_bound | Upper bound of random slope. (For rrelu only) |
|
inline |
Applies Leaky rectified linear unit activation element-wise to the input.
Leaky ReLUs attempt to fix the "dying ReLU" problem by allowing a small `slope` when the input is negative and has a slope of one when input is positive. The following modified ReLU Activation functions are supported: - *elu*: Exponential Linear Unit. `y = x > 0 ? x : slope * (exp(x)-1)` - *selu*: Scaled Exponential Linear Unit. `y = lambda * (x > 0 ? x : alpha * *lambda = 1.0507009873554804934193349852946* and *alpha = - *leaky*: Leaky ReLU. `y = x > 0 ? x : slope * x` - *prelu*: Parametric ReLU. This is same as *leaky* except that `slope` is - *rrelu*: Randomized ReLU. same as *leaky* but the `slope` is uniformly and *[lower_bound, upper_bound)* for training, while fixed to be *(lower_bound+upper_bound)/2* for inference. Defined in src/operator/leaky_relu.cc:L65
| data | Input data to activation function. |
| gamma | Slope parameter for PReLU. Only required when act_type is 'prelu'. It should be either a vector of size 1, or the same size as the second dimension |
| act_type | Activation function to be applied. |
| slope | Init slope for the activation. (For leaky and elu only) |
| lower_bound | Lower bound of random slope. (For rrelu only) |
| upper_bound | Upper bound of random slope. (For rrelu only) |
|
inline |
Computes and optimizes for squared loss during backward propagation. Just outputs data during forward propagation.
If :math:\hat{y}_i is the predicted value of the i-th sample, and :math:y_i then the squared loss estimated over :math:n samples is defined as
:math:`{SquaredLoss}({Y}, {{Y}} ) = {1}{n}
.. note:: Use the LinearRegressionOutput as the final output layer of a net.
The storage type of label can be default or csr
By default, gradients of this loss function are scaled by factor 1/m, where m The parameter grad_scale can be used to change this scale to grad_scale/m.
Defined in src/operator/regression_output.cc:L92
| symbol_name | name of the resulting symbol |
| data | Input data to the function. |
| label | Input label to the function. |
| grad_scale | Scale the gradient by a float factor |
|
inline |
Computes and optimizes for squared loss during backward propagation. Just outputs data during forward propagation.
If :math:\hat{y}_i is the predicted value of the i-th sample, and :math:y_i then the squared loss estimated over :math:n samples is defined as
:math:`{SquaredLoss}({Y}, {{Y}} ) = {1}{n}
.. note:: Use the LinearRegressionOutput as the final output layer of a net.
The storage type of label can be default or csr
By default, gradients of this loss function are scaled by factor 1/m, where m The parameter grad_scale can be used to change this scale to grad_scale/m.
Defined in src/operator/regression_output.cc:L92
| data | Input data to the function. |
| label | Input label to the function. |
| grad_scale | Scale the gradient by a float factor |
Returns element-wise Natural logarithmic value of the input.
The natural logarithm is logarithm in base *e*, so that ``log(exp(x)) = x`` The storage type of ``log`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L941
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise Natural logarithmic value of the input.
The natural logarithm is logarithm in base *e*, so that ``log(exp(x)) = x`` The storage type of ``log`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L941
| data | The input array. |
Returns element-wise Base-10 logarithmic value of the input.
``10**log10(x) = x`` The storage type of ``log10`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L953
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise Base-10 logarithmic value of the input.
``10**log10(x) = x`` The storage type of ``log10`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L953
| data | The input array. |
Returns element-wise log(1 + x) value of the input.
This function is more accurate than ``log(1 + x)`` for small ``x`` so that :math:`1+x\approx 1` The storage type of ``log1p`` output depends upon the input storage type: - log1p(default) = default - log1p(row_sparse) = row_sparse - log1p(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L990
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise log(1 + x) value of the input.
This function is more accurate than ``log(1 + x)`` for small ``x`` so that :math:`1+x\approx 1` The storage type of ``log1p`` output depends upon the input storage type: - log1p(default) = default - log1p(row_sparse) = row_sparse - log1p(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L990
| data | The input array. |
Returns element-wise Base-2 logarithmic value of the input.
``2**log2(x) = x`` The storage type of ``log2`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L965
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise Base-2 logarithmic value of the input.
``2**log2(x) = x`` The storage type of ``log2`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L965
| data | The input array. |
|
inline |
Computes the log softmax of the input. This is equivalent to computing softmax followed by log.
Examples::
>>> x = mx.nd.array([1, 2, .1]) >>> mx.nd.log_softmax(x).asnumpy() array([-1.41702998, -0.41702995, -2.31702995], dtype=float32)
>>> x = mx.nd.array( [[1, 2, .1],[.1, 2, 1]] ) >>> mx.nd.log_softmax(x, axis=0).asnumpy() array([[-0.34115392, -0.69314718, -1.24115396], [-1.24115396, -0.69314718, -0.34115392]], dtype=float32)
| symbol_name | name of the resulting symbol |
| data | The input array. |
| axis | The axis along which to compute softmax. |
| temperature | Temperature parameter in softmax |
|
inline |
Computes the log softmax of the input. This is equivalent to computing softmax followed by log.
Examples::
>>> x = mx.nd.array([1, 2, .1]) >>> mx.nd.log_softmax(x).asnumpy() array([-1.41702998, -0.41702995, -2.31702995], dtype=float32)
>>> x = mx.nd.array( [[1, 2, .1],[.1, 2, 1]] ) >>> mx.nd.log_softmax(x, axis=0).asnumpy() array([[-0.34115392, -0.69314718, -1.24115396], [-1.24115396, -0.69314718, -0.34115392]], dtype=float32)
| data | The input array. |
| axis | The axis along which to compute softmax. |
| temperature | Temperature parameter in softmax |
Returns the result of logical NOT (!) function
Example: logical_not([-2., 0., 1.]) = [0., 1., 0.]
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns the result of logical NOT (!) function
Example: logical_not([-2., 0., 1.]) = [0., 1., 0.]
| data | The input array. |
|
inline |
Applies a logistic function to the input.
The logistic function, also known as the sigmoid function, is computed as
:math:`\frac{1}{1+exp(-\textbf{x})}`.
Commonly, the sigmoid is used to squash the real-valued output of a linear model
:math:`wTx+b` into the [0,1] range so that it can be interpreted as a
It is suitable for binary classification or probability prediction tasks.
.. note::
Use the LogisticRegressionOutput as the final output layer of a net.
The storage type of ``label`` can be ``default`` or ``csr``
- LogisticRegressionOutput(default, default) = default
- LogisticRegressionOutput(default, csr) = default
The loss function used is the Binary Cross Entropy Loss:
:math:`-{(y\log(p) + (1 - y)\log(1 - p))}`
Where `y` is the ground truth probability of positive outcome for a given
example, and `p` the probability predicted by the model. By default, gradients
of this loss function are scaled by factor `1/m`, where m is the number of
The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
Defined in src/operator/regression_output.cc:L152
| symbol_name | name of the resulting symbol |
| data | Input data to the function. |
| label | Input label to the function. |
| grad_scale | Scale the gradient by a float factor |
|
inline |
Applies a logistic function to the input.
The logistic function, also known as the sigmoid function, is computed as
:math:`\frac{1}{1+exp(-\textbf{x})}`.
Commonly, the sigmoid is used to squash the real-valued output of a linear model
:math:`wTx+b` into the [0,1] range so that it can be interpreted as a
It is suitable for binary classification or probability prediction tasks.
.. note::
Use the LogisticRegressionOutput as the final output layer of a net.
The storage type of ``label`` can be ``default`` or ``csr``
- LogisticRegressionOutput(default, default) = default
- LogisticRegressionOutput(default, csr) = default
The loss function used is the Binary Cross Entropy Loss:
:math:`-{(y\log(p) + (1 - y)\log(1 - p))}`
Where `y` is the ground truth probability of positive outcome for a given
example, and `p` the probability predicted by the model. By default, gradients
of this loss function are scaled by factor `1/m`, where m is the number of
The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
Defined in src/operator/regression_output.cc:L152
| data | Input data to the function. |
| label | Input label to the function. |
| grad_scale | Scale the gradient by a float factor |
|
inline |
Applies local response normalization to the input.
The local response normalization layer performs "lateral inhibition" by
over local input regions.
If :math:`a_{x,y}^{i}` is the activity of a neuron computed by applying kernel
:math:`(x, y)` and then applying the ReLU nonlinearity, the response-normalized
activity :math:`b_{x,y}^{i}` is given by the expression:
.. math::
b_{x,y}^{i} = \frac{a_{x,y}^{i}}{\Bigg({k + \frac{\alpha}{n} \sum_{j=max(0,
where the sum runs over :math:`n` "adjacent" kernel maps at the same spatial
number of kernels in the layer.
Defined in src/operator/nn/lrn.cc:L178
| symbol_name | name of the resulting symbol |
| data | Input data to LRN |
| nsize | normalization window width in elements. |
| alpha | The variance scaling parameter :math:lpha in the LRN expression. |
| beta | The power parameter :math:eta in the LRN expression. |
| knorm | The parameter :math:k in the LRN expression. |
|
inline |
Applies local response normalization to the input.
The local response normalization layer performs "lateral inhibition" by
over local input regions.
If :math:`a_{x,y}^{i}` is the activity of a neuron computed by applying kernel
:math:`(x, y)` and then applying the ReLU nonlinearity, the response-normalized
activity :math:`b_{x,y}^{i}` is given by the expression:
.. math::
b_{x,y}^{i} = \frac{a_{x,y}^{i}}{\Bigg({k + \frac{\alpha}{n} \sum_{j=max(0,
where the sum runs over :math:`n` "adjacent" kernel maps at the same spatial
number of kernels in the layer.
Defined in src/operator/nn/lrn.cc:L178
| data | Input data to LRN |
| nsize | normalization window width in elements. |
| alpha | The variance scaling parameter :math:lpha in the LRN expression. |
| beta | The power parameter :math:eta in the LRN expression. |
| knorm | The parameter :math:k in the LRN expression. |
|
inline |
Computes mean absolute error of the input.
MAE is a risk metric corresponding to the expected value of the absolute error.
If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i`
then the mean absolute error (MAE) estimated over :math:`n` samples is defined
:math:`\text{MAE}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1}
.. note::
Use the MAERegressionOutput as the final output layer of a net.
The storage type of ``label`` can be ``default`` or ``csr``
- MAERegressionOutput(default, default) = default
- MAERegressionOutput(default, csr) = default
By default, gradients of this loss function are scaled by factor `1/m`, where m
The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
Defined in src/operator/regression_output.cc:L120
| symbol_name | name of the resulting symbol |
| data | Input data to the function. |
| label | Input label to the function. |
| grad_scale | Scale the gradient by a float factor |
|
inline |
Computes mean absolute error of the input.
MAE is a risk metric corresponding to the expected value of the absolute error.
If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i`
then the mean absolute error (MAE) estimated over :math:`n` samples is defined
:math:`\text{MAE}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1}
.. note::
Use the MAERegressionOutput as the final output layer of a net.
The storage type of ``label`` can be ``default`` or ``csr``
- MAERegressionOutput(default, default) = default
- MAERegressionOutput(default, csr) = default
By default, gradients of this loss function are scaled by factor `1/m`, where m
The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
Defined in src/operator/regression_output.cc:L120
| data | Input data to the function. |
| label | Input label to the function. |
| grad_scale | Scale the gradient by a float factor |
Make your own loss function in network construction.
This operator accepts a customized loss function symbol as a terminal loss and the symbol should be an operator with no backward dependency. The output of this function is the gradient of loss with respect to the input For example, if you are a making a cross entropy loss function. Assume ``out`` predicted output and ``label`` is the true label, then the cross entropy can be cross_entropy = label * log(out) + (1 - label) * log(1 - out) loss = make_loss(cross_entropy) We will need to use ``make_loss`` when we are creating our own loss function or combine multiple loss functions. Also we may want to stop some variables' from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``. The storage type of ``make_loss`` output depends upon the input storage type: - make_loss(default) = default - make_loss(row_sparse) = row_sparse Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L298
| symbol_name | name of the resulting symbol |
| data | The input array. |
Make your own loss function in network construction.
This operator accepts a customized loss function symbol as a terminal loss and the symbol should be an operator with no backward dependency. The output of this function is the gradient of loss with respect to the input For example, if you are a making a cross entropy loss function. Assume ``out`` predicted output and ``label`` is the true label, then the cross entropy can be cross_entropy = label * log(out) + (1 - label) * log(1 - out) loss = make_loss(cross_entropy) We will need to use ``make_loss`` when we are creating our own loss function or combine multiple loss functions. Also we may want to stop some variables' from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``. The storage type of ``make_loss`` output depends upon the input storage type: - make_loss(default) = default - make_loss(row_sparse) = row_sparse Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L298
| data | The input array. |
|
inline |
Make your own loss function in network construction.
This operator accepts a customized loss function symbol as a terminal loss and the symbol should be an operator with no backward dependency. The output of this function is the gradient of loss with respect to the input For example, if you are a making a cross entropy loss function. Assume ``out`` predicted output and ``label`` is the true label, then the cross entropy can be cross_entropy = label * log(out) + (1 - label) * log(1 - out) loss = MakeLoss(cross_entropy) We will need to use ``MakeLoss`` when we are creating our own loss function or combine multiple loss functions. Also we may want to stop some variables' from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``. In addition, we can give a scale to the loss by setting ``grad_scale``, so that the gradient of the loss will be rescaled in the backpropagation. .. note:: This operator should be used as a Symbol instead of NDArray. Defined in src/operator/make_loss.cc:L71
| symbol_name | name of the resulting symbol |
| data | Input array. |
| grad_scale | Gradient scale as a supplement to unary and binary operators |
| valid_thresh | clip each element in the array to 0 when it is less than |
| normalization | If this is set to null, the output gradient will not be normalized. If this is set to batch, the output gradient will be divided by the batch size. If this is set to valid, the output gradient will be divided by the |
|
inline |
Make your own loss function in network construction.
This operator accepts a customized loss function symbol as a terminal loss and the symbol should be an operator with no backward dependency. The output of this function is the gradient of loss with respect to the input For example, if you are a making a cross entropy loss function. Assume ``out`` predicted output and ``label`` is the true label, then the cross entropy can be cross_entropy = label * log(out) + (1 - label) * log(1 - out) loss = MakeLoss(cross_entropy) We will need to use ``MakeLoss`` when we are creating our own loss function or combine multiple loss functions. Also we may want to stop some variables' from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``. In addition, we can give a scale to the loss by setting ``grad_scale``, so that the gradient of the loss will be rescaled in the backpropagation. .. note:: This operator should be used as a Symbol instead of NDArray. Defined in src/operator/make_loss.cc:L71
| data | Input array. |
| grad_scale | Gradient scale as a supplement to unary and binary operators |
| valid_thresh | clip each element in the array to 0 when it is less than |
| normalization | If this is set to null, the output gradient will not be normalized. If this is set to batch, the output gradient will be divided by the batch size. If this is set to valid, the output gradient will be divided by the |
|
inline |
Computes the max of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L190
| symbol_name | name of the resulting symbol |
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
|
inline |
Computes the max of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L190
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
|
inline |
Computes the mean of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L131
| symbol_name | name of the resulting symbol |
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
|
inline |
Computes the mean of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L131
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
|
inline |
Computes the min of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L204
| symbol_name | name of the resulting symbol |
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
|
inline |
Computes the min of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L204
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
|
inline |
Updater function for multi-precision sgd optimizer
| symbol_name | name of the resulting symbol |
| weight | Weight |
| grad | Gradient |
| mom | Momentum |
| weight32 | Weight32 |
| lr | Learning rate |
| momentum | The decay rate of momentum estimates at each epoch. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| lazy_update | If true, lazy updates are applied if gradient's stype is row_sparse |
|
inline |
Updater function for multi-precision sgd optimizer
| weight | Weight |
| grad | Gradient |
| mom | Momentum |
| weight32 | Weight32 |
| lr | Learning rate |
| momentum | The decay rate of momentum estimates at each epoch. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| lazy_update | If true, lazy updates are applied if gradient's stype is row_sparse |
|
inline |
Updater function for multi-precision sgd optimizer
| symbol_name | name of the resulting symbol |
| weight | Weight |
| grad | gradient |
| weight32 | Weight32 |
| lr | Learning rate |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| lazy_update | If true, lazy updates are applied if gradient's stype is row_sparse. |
|
inline |
Updater function for multi-precision sgd optimizer
| weight | Weight |
| grad | gradient |
| weight32 | Weight32 |
| lr | Learning rate |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| lazy_update | If true, lazy updates are applied if gradient's stype is row_sparse. |
|
inline |
Computes the product of array elements over given axes treating Not a Numbers
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L176
| symbol_name | name of the resulting symbol |
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
|
inline |
Computes the product of array elements over given axes treating Not a Numbers
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L176
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
|
inline |
Computes the sum of array elements over given axes treating Not a Numbers
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L161
| symbol_name | name of the resulting symbol |
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
|
inline |
Computes the sum of array elements over given axes treating Not a Numbers
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L161
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
Numerical negative of the argument, element-wise.
The storage type of ``negative`` output depends upon the input storage type: - negative(default) = default - negative(row_sparse) = row_sparse - negative(csr) = csr
| symbol_name | name of the resulting symbol |
| data | The input array. |
Numerical negative of the argument, element-wise.
The storage type of ``negative`` output depends upon the input storage type: - negative(default) = default - negative(row_sparse) = row_sparse - negative(csr) = csr
| data | The input array. |
|
inline |
Computes the norm on an NDArray.
This operator computes the norm on an NDArray with the specified axis, depending
on the value of the ord parameter. By default, it computes the L2 norm on the
array. Currently only ord=2 supports sparse ndarrays.
Examples::
x = [[[1, 2],
[3, 4]],
[[2, 2],
[5, 6]]]
norm(x, ord=2, axis=1) = [[3.1622777 4.472136 ]
[5.3851647 6.3245554]]
norm(x, ord=1, axis=1) = [[4., 6.],
[7., 8.]]
rsp = x.cast_storage('row_sparse')
norm(rsp) = [5.47722578]
csr = x.cast_storage('csr')
norm(csr) = [5.47722578]
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L345
| symbol_name | name of the resulting symbol |
| data | The input |
| ord | Order of the norm. Currently ord=1 and ord=2 is supported. |
| axis | The axis or axes along which to perform the reduction. The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. |
| keepdims | If this is set to True, the reduced axis is left in the result as |
|
inline |
Computes the norm on an NDArray.
This operator computes the norm on an NDArray with the specified axis, depending
on the value of the ord parameter. By default, it computes the L2 norm on the
array. Currently only ord=2 supports sparse ndarrays.
Examples::
x = [[[1, 2],
[3, 4]],
[[2, 2],
[5, 6]]]
norm(x, ord=2, axis=1) = [[3.1622777 4.472136 ]
[5.3851647 6.3245554]]
norm(x, ord=1, axis=1) = [[4., 6.],
[7., 8.]]
rsp = x.cast_storage('row_sparse')
norm(rsp) = [5.47722578]
csr = x.cast_storage('csr')
norm(csr) = [5.47722578]
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L345
| data | The input |
| ord | Order of the norm. Currently ord=1 and ord=2 is supported. |
| axis | The axis or axes along which to perform the reduction. The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. |
| keepdims | If this is set to True, the reduced axis is left in the result as |
|
inline |
Returns a one-hot array.
The locations represented by `indices` take value `on_value`, while all other locations take value `off_value`. `one_hot` operation with `indices` of shape ``(i0, i1)`` and `depth` of ``d`` in an output array of shape ``(i0, i1, d)`` with:: output[i,j,:] = off_value output[i,j,indices[i,j]] = on_value Examples:: one_hot([1,0,2,0], 3) = [[ 0. 1. 0.] [ 1. 0. 0.] [ 0. 0. 1.] [ 1. 0. 0.]] one_hot([1,0,2,0], 3, on_value=8, off_value=1, dtype='int32') = [[1 8 1] [8 1 1] [1 1 8] [8 1 1]] one_hot([[1,0],[1,0],[2,0]], 3) = [[[ 0. 1. 0.] [ 1. 0. 0.]] [[ 0. 1. 0.] [ 1. 0. 0.]] [[ 0. 0. 1.] [ 1. 0. 0.]]] Defined in src/operator/tensor/indexing_op.cc:L536
| symbol_name | name of the resulting symbol |
| indices | array of locations where to set on_value |
| depth | Depth of the one hot dimension. |
| on_value | The value assigned to the locations represented by indices. |
| off_value | The value assigned to the locations not represented by indices. |
| dtype | DType of the output |
|
inline |
Returns a one-hot array.
The locations represented by `indices` take value `on_value`, while all other locations take value `off_value`. `one_hot` operation with `indices` of shape ``(i0, i1)`` and `depth` of ``d`` in an output array of shape ``(i0, i1, d)`` with:: output[i,j,:] = off_value output[i,j,indices[i,j]] = on_value Examples:: one_hot([1,0,2,0], 3) = [[ 0. 1. 0.] [ 1. 0. 0.] [ 0. 0. 1.] [ 1. 0. 0.]] one_hot([1,0,2,0], 3, on_value=8, off_value=1, dtype='int32') = [[1 8 1] [8 1 1] [1 1 8] [8 1 1]] one_hot([[1,0],[1,0],[2,0]], 3) = [[[ 0. 1. 0.] [ 1. 0. 0.]] [[ 0. 1. 0.] [ 1. 0. 0.]] [[ 0. 0. 1.] [ 1. 0. 0.]]] Defined in src/operator/tensor/indexing_op.cc:L536
| indices | array of locations where to set on_value |
| depth | Depth of the one hot dimension. |
| on_value | The value assigned to the locations represented by indices. |
| off_value | The value assigned to the locations not represented by indices. |
| dtype | DType of the output |
Return an array of ones with the same shape and type as the input array.
Examples::
x = [[ 0., 0., 0.], [ 0., 0., 0.]]
ones_like(x) = [[ 1., 1., 1.], [ 1., 1., 1.]]
| symbol_name | name of the resulting symbol |
| data | The input |
Return an array of ones with the same shape and type as the input array.
Examples::
x = [[ 0., 0., 0.], [ 0., 0., 0.]]
ones_like(x) = [[ 1., 1., 1.], [ 1., 1., 1.]]
| data | The input |
|
inline |
allow string printing of the shape
| os | the output stream |
| shape | the shape |
| std::ostream& mxnet::cpp::operator<< | ( | std::ostream & | out, |
| const NDArray & | ndarray | ||
| ) |
|
inline |
read shape from the istream
| is | the input stream |
| shape | the shape |
|
inline |
Pads an input array with a constant or edge values of the array.
.. note:: `Pad` is deprecated. Use `pad` instead. .. note:: Current implementation only supports 4D and 5D input arrays with only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero. This operation pads an input array with either a `constant_value` or edge values along each axis of the input array. The amount of padding is specified by `pad_width` is a tuple of integer padding widths for each axis of the format ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of where ``N`` is the number of dimensions of the array. For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates to add before and after the elements of the array along dimension ``N``. The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``, ``after_2`` must be 0. Example:: x = [[[[ 1. 2. 3.] [ 4. 5. 6.]] [[ 7. 8. 9.] [ 10. 11. 12.]]] [[[ 11. 12. 13.] [ 14. 15. 16.]] [[ 17. 18. 19.] [ 20. 21. 22.]]]] pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) = [[[[ 1. 1. 2. 3. 3.] [ 1. 1. 2. 3. 3.] [ 4. 4. 5. 6. 6.] [ 4. 4. 5. 6. 6.]] [[ 7. 7. 8. 9. 9.] [ 7. 7. 8. 9. 9.] [ 10. 10. 11. 12. 12.] [ 10. 10. 11. 12. 12.]]] [[[ 11. 11. 12. 13. 13.] [ 11. 11. 12. 13. 13.] [ 14. 14. 15. 16. 16.] [ 14. 14. 15. 16. 16.]] [[ 17. 17. 18. 19. 19.] [ 17. 17. 18. 19. 19.] [ 20. 20. 21. 22. 22.] [ 20. 20. 21. 22. 22.]]]] pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) = [[[[ 0. 0. 0. 0. 0.] [ 0. 1. 2. 3. 0.] [ 0. 4. 5. 6. 0.] [ 0. 0. 0. 0. 0.]] [[ 0. 0. 0. 0. 0.] [ 0. 7. 8. 9. 0.] [ 0. 10. 11. 12. 0.] [ 0. 0. 0. 0. 0.]]] [[[ 0. 0. 0. 0. 0.] [ 0. 11. 12. 13. 0.] [ 0. 14. 15. 16. 0.] [ 0. 0. 0. 0. 0.]] [[ 0. 0. 0. 0. 0.] [ 0. 17. 18. 19. 0.] [ 0. 20. 21. 22. 0.] [ 0. 0. 0. 0. 0.]]]] Defined in src/operator/pad.cc:L766
| symbol_name | name of the resulting symbol |
| data | An n-dimensional input array. |
| mode | Padding type to use. "constant" pads with constant_value "edge" pads using the edge values of the input array "reflect" pads by reflecting values |
| pad_width | Widths of the padding regions applied to the edges of each axis. It is a tuple of integer padding widths for each axis of the format (before_1, after_1, ... , before_N, after_N). It should be of length 2*N where N is the number of dimensions of the array.This is equivalent to pad_width in |
| constant_value | The value used for padding when mode is "constant". |
|
inline |
Pads an input array with a constant or edge values of the array.
.. note:: `Pad` is deprecated. Use `pad` instead. .. note:: Current implementation only supports 4D and 5D input arrays with only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero. This operation pads an input array with either a `constant_value` or edge values along each axis of the input array. The amount of padding is specified by `pad_width` is a tuple of integer padding widths for each axis of the format ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of where ``N`` is the number of dimensions of the array. For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates to add before and after the elements of the array along dimension ``N``. The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``, ``after_2`` must be 0. Example:: x = [[[[ 1. 2. 3.] [ 4. 5. 6.]] [[ 7. 8. 9.] [ 10. 11. 12.]]] [[[ 11. 12. 13.] [ 14. 15. 16.]] [[ 17. 18. 19.] [ 20. 21. 22.]]]] pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) = [[[[ 1. 1. 2. 3. 3.] [ 1. 1. 2. 3. 3.] [ 4. 4. 5. 6. 6.] [ 4. 4. 5. 6. 6.]] [[ 7. 7. 8. 9. 9.] [ 7. 7. 8. 9. 9.] [ 10. 10. 11. 12. 12.] [ 10. 10. 11. 12. 12.]]] [[[ 11. 11. 12. 13. 13.] [ 11. 11. 12. 13. 13.] [ 14. 14. 15. 16. 16.] [ 14. 14. 15. 16. 16.]] [[ 17. 17. 18. 19. 19.] [ 17. 17. 18. 19. 19.] [ 20. 20. 21. 22. 22.] [ 20. 20. 21. 22. 22.]]]] pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) = [[[[ 0. 0. 0. 0. 0.] [ 0. 1. 2. 3. 0.] [ 0. 4. 5. 6. 0.] [ 0. 0. 0. 0. 0.]] [[ 0. 0. 0. 0. 0.] [ 0. 7. 8. 9. 0.] [ 0. 10. 11. 12. 0.] [ 0. 0. 0. 0. 0.]]] [[[ 0. 0. 0. 0. 0.] [ 0. 11. 12. 13. 0.] [ 0. 14. 15. 16. 0.] [ 0. 0. 0. 0. 0.]] [[ 0. 0. 0. 0. 0.] [ 0. 17. 18. 19. 0.] [ 0. 20. 21. 22. 0.] [ 0. 0. 0. 0. 0.]]]] Defined in src/operator/pad.cc:L766
| data | An n-dimensional input array. |
| mode | Padding type to use. "constant" pads with constant_value "edge" pads using the edge values of the input array "reflect" pads by reflecting values |
| pad_width | Widths of the padding regions applied to the edges of each axis. It is a tuple of integer padding widths for each axis of the format (before_1, after_1, ... , before_N, after_N). It should be of length 2*N where N is the number of dimensions of the array.This is equivalent to pad_width in |
| constant_value | The value used for padding when mode is "constant". |
|
inline |
Picks elements from an input array according to the input indices along the
Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the an output array of shape ``(i0,)`` with:: output[i] = input[i, indices[i]] By default, if any index mentioned is too large, it is replaced by the index the last element along an axis (the `clip` mode). This function supports n-dimensional input and (n-1)-dimensional indices arrays. Examples:: x = [[ 1., 2.], [ 3., 4.], [ 5., 6.]] // picks elements with specified indices along axis 0 pick(x, y=[0,1], 0) = [ 1., 4.] // picks elements with specified indices along axis 1 pick(x, y=[0,1,0], 1) = [ 1., 4., 5.] y = [[ 1.], [ 0.], [ 2.]] // picks elements with specified indices along axis 1 using 'wrap' mode // to place indicies that would normally be out of bounds pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1., 4., 5.] y = [[ 1.], [ 0.], [ 2.]] // picks elements with specified indices along axis 1 and dims are maintained pick(x,y, 1, keepdims=True) = [[ 2.], [ 3.], [ 6.]] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L153
| symbol_name | name of the resulting symbol |
| data | The input array |
| index | The index array |
| axis | int or None. The axis to picking the elements. Negative values means indexing from right to left. If is None, the elements in the index w.r.t the |
| keepdims | If true, the axis where we pick the elements is left in the result as |
| mode | Specify how out-of-bound indices behave. Default is "clip". "clip" means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis. "wrap" |
|
inline |
Picks elements from an input array according to the input indices along the
Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the an output array of shape ``(i0,)`` with:: output[i] = input[i, indices[i]] By default, if any index mentioned is too large, it is replaced by the index the last element along an axis (the `clip` mode). This function supports n-dimensional input and (n-1)-dimensional indices arrays. Examples:: x = [[ 1., 2.], [ 3., 4.], [ 5., 6.]] // picks elements with specified indices along axis 0 pick(x, y=[0,1], 0) = [ 1., 4.] // picks elements with specified indices along axis 1 pick(x, y=[0,1,0], 1) = [ 1., 4., 5.] y = [[ 1.], [ 0.], [ 2.]] // picks elements with specified indices along axis 1 using 'wrap' mode // to place indicies that would normally be out of bounds pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1., 4., 5.] y = [[ 1.], [ 0.], [ 2.]] // picks elements with specified indices along axis 1 and dims are maintained pick(x,y, 1, keepdims=True) = [[ 2.], [ 3.], [ 6.]] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L153
| data | The input array |
| index | The index array |
| axis | int or None. The axis to picking the elements. Negative values means indexing from right to left. If is None, the elements in the index w.r.t the |
| keepdims | If true, the axis where we pick the elements is left in the result as |
| mode | Specify how out-of-bound indices behave. Default is "clip". "clip" means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis. "wrap" |
|
inline |
Performs pooling on the input.
The shapes for 1-D pooling are
- **data**: *(batch_size, channel, width)*,
- **out**: *(batch_size, num_filter, out_width)*.
The shapes for 2-D pooling are
- **data**: *(batch_size, channel, height, width)*
- **out**: *(batch_size, num_filter, out_height, out_width)*, with::
out_height = f(height, kernel[0], pad[0], stride[0])
out_width = f(width, kernel[1], pad[1], stride[1])
The definition of *f* depends on ``pooling_convention``, which has two options:
- **valid** (default)::
f(x, k, p, s) = floor((x+2*p-k)/s)+1
- **full**, which is compatible with Caffe::
f(x, k, p, s) = ceil((x+2*p-k)/s)+1
But ``global_pool`` is set to be true, then do a global pooling, namely reset
``kernel=(height, width)``.
Three pooling options are supported by ``pool_type``:
- **avg**: average pooling
- **max**: max pooling
- **sum**: sum pooling
- **lp**: Lp pooling
For 3-D pooling, an additional *depth* dimension is added before
*height*. Namely the input data will have shape *(batch_size, channel, depth,
height, width)*.
Notes on Lp pooling:
Lp pooling was first introduced by this paper:
L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling.
We can see that Lp pooling stands between those two, in practice the most
For each window ``X``, the mathematical expression for Lp pooling is:
:math:`f(X) = \sqrt[p]{\sum_{x}^{X} x^p}`
Defined in src/operator/nn/pooling.cc:L388
| symbol_name | name of the resulting symbol |
| data | Input data to the pooling operator. |
| kernel | Pooling kernel size: (y, x) or (d, y, x) |
| pool_type | Pooling type to be applied. |
| global_pool | Ignore kernel size, do global pooling based on current input |
| cudnn_off | Turn off cudnn pooling and use MXNet pooling operator. |
| pooling_convention | Pooling convention to be applied. |
| stride | Stride: for pooling (y, x) or (d, y, x). Defaults to 1 for each |
| pad | Pad for pooling: (y, x) or (d, y, x). Defaults to no padding. |
| p_value | Value of p for Lp pooling, can be 1 or 2, required for Lp Pooling. |
| count_include_pad | Only used for AvgPool, specify whether to count padding elements for averagecalculation. For example, with a 5*5 kernel on a 3*3 corner of a image,the sum of the 9 valid elements will be divided by 25 if this is set |
|
inline |
Performs pooling on the input.
The shapes for 1-D pooling are
- **data**: *(batch_size, channel, width)*,
- **out**: *(batch_size, num_filter, out_width)*.
The shapes for 2-D pooling are
- **data**: *(batch_size, channel, height, width)*
- **out**: *(batch_size, num_filter, out_height, out_width)*, with::
out_height = f(height, kernel[0], pad[0], stride[0])
out_width = f(width, kernel[1], pad[1], stride[1])
The definition of *f* depends on ``pooling_convention``, which has two options:
- **valid** (default)::
f(x, k, p, s) = floor((x+2*p-k)/s)+1
- **full**, which is compatible with Caffe::
f(x, k, p, s) = ceil((x+2*p-k)/s)+1
But ``global_pool`` is set to be true, then do a global pooling, namely reset
``kernel=(height, width)``.
Three pooling options are supported by ``pool_type``:
- **avg**: average pooling
- **max**: max pooling
- **sum**: sum pooling
- **lp**: Lp pooling
For 3-D pooling, an additional *depth* dimension is added before
*height*. Namely the input data will have shape *(batch_size, channel, depth,
height, width)*.
Notes on Lp pooling:
Lp pooling was first introduced by this paper:
L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling.
We can see that Lp pooling stands between those two, in practice the most
For each window ``X``, the mathematical expression for Lp pooling is:
:math:`f(X) = \sqrt[p]{\sum_{x}^{X} x^p}`
Defined in src/operator/nn/pooling.cc:L388
| data | Input data to the pooling operator. |
| kernel | Pooling kernel size: (y, x) or (d, y, x) |
| pool_type | Pooling type to be applied. |
| global_pool | Ignore kernel size, do global pooling based on current input |
| cudnn_off | Turn off cudnn pooling and use MXNet pooling operator. |
| pooling_convention | Pooling convention to be applied. |
| stride | Stride: for pooling (y, x) or (d, y, x). Defaults to 1 for each |
| pad | Pad for pooling: (y, x) or (d, y, x). Defaults to no padding. |
| p_value | Value of p for Lp pooling, can be 1 or 2, required for Lp Pooling. |
| count_include_pad | Only used for AvgPool, specify whether to count padding elements for averagecalculation. For example, with a 5*5 kernel on a 3*3 corner of a image,the sum of the 9 valid elements will be divided by 25 if this is set |
|
inline |
This operator is DEPRECATED. Perform pooling on the input.
The shapes for 2-D pooling is
out_height = f(height, kernel[0], pad[0], stride[0]) out_width = f(width, kernel[1], pad[1], stride[1])
The definition of f depends on pooling_convention, which has two options:
f(x, k, p, s) = floor((x+2*p-k)/s)+1
f(x, k, p, s) = ceil((x+2*p-k)/s)+1
But global_pool is set to be true, then do a global pooling, namely reset kernel=(height, width).
Three pooling options are supported by pool_type:
1-D pooling is special case of 2-D pooling with weight=1 and kernel[1]=1.
For 3-D pooling, an additional depth dimension is added before height. Namely the input data will have shape *(batch_size, channel, depth, height, width)*.
Defined in src/operator/pooling_v1.cc:L104
| symbol_name | name of the resulting symbol |
| data | Input data to the pooling operator. |
| kernel | pooling kernel size: (y, x) or (d, y, x) |
| pool_type | Pooling type to be applied. |
| global_pool | Ignore kernel size, do global pooling based on current input |
| pooling_convention | Pooling convention to be applied. |
| stride | stride: for pooling (y, x) or (d, y, x) |
| pad | pad for pooling: (y, x) or (d, y, x) |
|
inline |
This operator is DEPRECATED. Perform pooling on the input.
The shapes for 2-D pooling is
out_height = f(height, kernel[0], pad[0], stride[0]) out_width = f(width, kernel[1], pad[1], stride[1])
The definition of f depends on pooling_convention, which has two options:
f(x, k, p, s) = floor((x+2*p-k)/s)+1
f(x, k, p, s) = ceil((x+2*p-k)/s)+1
But global_pool is set to be true, then do a global pooling, namely reset kernel=(height, width).
Three pooling options are supported by pool_type:
1-D pooling is special case of 2-D pooling with weight=1 and kernel[1]=1.
For 3-D pooling, an additional depth dimension is added before height. Namely the input data will have shape *(batch_size, channel, depth, height, width)*.
Defined in src/operator/pooling_v1.cc:L104
| data | Input data to the pooling operator. |
| kernel | pooling kernel size: (y, x) or (d, y, x) |
| pool_type | Pooling type to be applied. |
| global_pool | Ignore kernel size, do global pooling based on current input |
| pooling_convention | Pooling convention to be applied. |
| stride | stride: for pooling (y, x) or (d, y, x) |
| pad | pad for pooling: (y, x) or (d, y, x) |
|
inline |
Computes the product of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L146
| symbol_name | name of the resulting symbol |
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
|
inline |
Computes the product of array elements over given axes.
Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L146
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
Converts each element of the input array from degrees to radians.
.. math:: radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi] The storage type of ``radians`` output depends upon the input storage type: - radians(default) = default - radians(row_sparse) = row_sparse - radians(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L182
| symbol_name | name of the resulting symbol |
| data | The input array. |
Converts each element of the input array from degrees to radians.
.. math:: radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi] The storage type of ``radians`` output depends upon the input storage type: - radians(default) = default - radians(row_sparse) = row_sparse - radians(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L182
| data | The input array. |
Returns element-wise inverse cube-root value of the input.
.. math::
rcbrt(x) = 1/\sqrt[3]{x}
Example::
rcbrt([1,8,-125]) = [1.0, 0.5, -0.2]
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L906
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise inverse cube-root value of the input.
.. math::
rcbrt(x) = 1/\sqrt[3]{x}
Example::
rcbrt([1,8,-125]) = [1.0, 0.5, -0.2]
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L906
| data | The input array. |
Returns the reciprocal of the argument, element-wise.
Calculates 1/x. Example:: reciprocal([-2, 1, 3, 1.6, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L646
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns the reciprocal of the argument, element-wise.
Calculates 1/x. Example:: reciprocal([-2, 1, 3, 1.6, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L646
| data | The input array. |
Computes rectified linear.
.. math:: max(features, 0) The storage type of ``relu`` output depends upon the input storage type: - relu(default) = default - relu(row_sparse) = row_sparse - relu(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L85
| symbol_name | name of the resulting symbol |
| data | The input array. |
Computes rectified linear.
.. math:: max(features, 0) The storage type of ``relu`` output depends upon the input storage type: - relu(default) = default - relu(row_sparse) = row_sparse - relu(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L85
| data | The input array. |
|
inline |
Repeats elements of an array.
By default, ``repeat`` flattens the input array into 1-D and then repeats the elements:: x = [[ 1, 2], [ 3, 4]] repeat(x, repeats=2) = [ 1., 1., 2., 2., 3., 3., 4., 4.] The parameter ``axis`` specifies the axis along which to perform repeat:: repeat(x, repeats=2, axis=1) = [[ 1., 1., 2., 2.], [ 3., 3., 4., 4.]] repeat(x, repeats=2, axis=0) = [[ 1., 2.], [ 1., 2.], [ 3., 4.], [ 3., 4.]] repeat(x, repeats=2, axis=-1) = [[ 1., 1., 2., 2.], [ 3., 3., 4., 4.]] Defined in src/operator/tensor/matrix_op.cc:L691
| symbol_name | name of the resulting symbol |
| data | Input data array |
| repeats | The number of repetitions for each element. |
| axis | The axis along which to repeat values. The negative numbers are interpreted counting from the backward. By default, use the flattened input |
|
inline |
Repeats elements of an array.
By default, ``repeat`` flattens the input array into 1-D and then repeats the elements:: x = [[ 1, 2], [ 3, 4]] repeat(x, repeats=2) = [ 1., 1., 2., 2., 3., 3., 4., 4.] The parameter ``axis`` specifies the axis along which to perform repeat:: repeat(x, repeats=2, axis=1) = [[ 1., 1., 2., 2.], [ 3., 3., 4., 4.]] repeat(x, repeats=2, axis=0) = [[ 1., 2.], [ 1., 2.], [ 3., 4.], [ 3., 4.]] repeat(x, repeats=2, axis=-1) = [[ 1., 1., 2., 2.], [ 3., 3., 4., 4.]] Defined in src/operator/tensor/matrix_op.cc:L691
| data | Input data array |
| repeats | The number of repetitions for each element. |
| axis | The axis along which to repeat values. The negative numbers are interpreted counting from the backward. By default, use the flattened input |
|
inline |
Reshapes the input array.
.. note:: ``Reshape`` is deprecated, use ``reshape``
Given an array and a shape, this function returns a copy of the array in the
The shape is a tuple of integers such as (2,3,4). The size of the new shape
Example::
reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]
Some dimensions of the shape can take special values from the set {0, -1, -2,
- ``0`` copy this dimension from the input to the output shape.
Example::
- input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
- input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
- ``-1`` infers the dimension of the output shape by using the remainder of the
keeping the size of the new array same as that of the input array.
At most one dimension of shape can be -1.
Example::
- input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
- input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
- input shape = (2,3,4), shape=(-1,), output shape = (24,)
- ``-2`` copy all/remainder of the input dimensions to the output shape.
Example::
- input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
- input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
- input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
- ``-3`` use the product of two consecutive dimensions of the input shape as
Example::
- input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
- input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
- input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
- input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
- ``-4`` split one dimension of the input into two dimensions passed subsequent
Example::
- input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
- input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
If the argument `reverse` is set to 1, then the special values are inferred
Example::
- without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape
- with reverse=1, output shape will be (50,4).
Defined in src/operator/tensor/matrix_op.cc:L169
| symbol_name | name of the resulting symbol |
| data | Input data to reshape. |
| shape | The target shape |
| reverse | If true then the special values are inferred from right to left |
| target_shape | (Deprecated! Use shape instead.) Target new shape. One and |
| keep_highest | (Deprecated! Use shape instead.) Whether keep the highest dim unchanged.If set to true, then the first dim in target_shape is ignored,and |
|
inline |
Reshapes the input array.
.. note:: ``Reshape`` is deprecated, use ``reshape``
Given an array and a shape, this function returns a copy of the array in the
The shape is a tuple of integers such as (2,3,4). The size of the new shape
Example::
reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]
Some dimensions of the shape can take special values from the set {0, -1, -2,
- ``0`` copy this dimension from the input to the output shape.
Example::
- input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
- input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
- ``-1`` infers the dimension of the output shape by using the remainder of the
keeping the size of the new array same as that of the input array.
At most one dimension of shape can be -1.
Example::
- input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
- input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
- input shape = (2,3,4), shape=(-1,), output shape = (24,)
- ``-2`` copy all/remainder of the input dimensions to the output shape.
Example::
- input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
- input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
- input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
- ``-3`` use the product of two consecutive dimensions of the input shape as
Example::
- input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
- input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
- input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
- input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
- ``-4`` split one dimension of the input into two dimensions passed subsequent
Example::
- input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
- input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
If the argument `reverse` is set to 1, then the special values are inferred
Example::
- without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape
- with reverse=1, output shape will be (50,4).
Defined in src/operator/tensor/matrix_op.cc:L169
| data | Input data to reshape. |
| shape | The target shape |
| reverse | If true then the special values are inferred from right to left |
| target_shape | (Deprecated! Use shape instead.) Target new shape. One and |
| keep_highest | (Deprecated! Use shape instead.) Whether keep the highest dim unchanged.If set to true, then the first dim in target_shape is ignored,and |
Reshape some or all dimensions of lhs to have the same shape as some or all
Returns a **view** of the `lhs` array with a new shape without altering any Example:: x = [1, 2, 3, 4, 5, 6] y = [[0, -4], [3, 2], [2, 2]] reshape_like(x, y) = [[1, 2], [3, 4], [5, 6]] More precise control over how dimensions are inherited is achieved by slices over the `lhs` and `rhs` array dimensions. Only the sliced `lhs` are reshaped to the `rhs` sliced dimensions, with the non-sliced `lhs` Examples:: - lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, - lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, Negative indices are supported, and `None` can be used for either `lhs_end` or Example:: - lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L453
| symbol_name | name of the resulting symbol |
| lhs | First input. |
| rhs | Second input. |
Reshape some or all dimensions of lhs to have the same shape as some or all
Returns a **view** of the `lhs` array with a new shape without altering any Example:: x = [1, 2, 3, 4, 5, 6] y = [[0, -4], [3, 2], [2, 2]] reshape_like(x, y) = [[1, 2], [3, 4], [5, 6]] More precise control over how dimensions are inherited is achieved by slices over the `lhs` and `rhs` array dimensions. Only the sliced `lhs` are reshaped to the `rhs` sliced dimensions, with the non-sliced `lhs` Examples:: - lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, - lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, Negative indices are supported, and `None` can be used for either `lhs_end` or Example:: - lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L453
| lhs | First input. |
| rhs | Second input. |
Reverses the order of elements along given axis while preserving array shape.
Note: reverse and flip are equivalent. We use reverse in the following examples. Examples:: x = [[ 0., 1., 2., 3., 4.], [ 5., 6., 7., 8., 9.]] reverse(x, axis=0) = [[ 5., 6., 7., 8., 9.], [ 0., 1., 2., 3., 4.]] reverse(x, axis=1) = [[ 4., 3., 2., 1., 0.], [ 9., 8., 7., 6., 5.]] Defined in src/operator/tensor/matrix_op.cc:L793
| symbol_name | name of the resulting symbol |
| data | Input data array |
| axis | The axis which to reverse elements. |
Reverses the order of elements along given axis while preserving array shape.
Note: reverse and flip are equivalent. We use reverse in the following examples. Examples:: x = [[ 0., 1., 2., 3., 4.], [ 5., 6., 7., 8., 9.]] reverse(x, axis=0) = [[ 5., 6., 7., 8., 9.], [ 0., 1., 2., 3., 4.]] reverse(x, axis=1) = [[ 4., 3., 2., 1., 0.], [ 9., 8., 7., 6., 5.]] Defined in src/operator/tensor/matrix_op.cc:L793
| data | Input data array |
| axis | The axis which to reverse elements. |
Returns element-wise rounded value to the nearest integer of the input.
.. note:: - For input ``n.5`` ``rint`` returns ``n`` while ``round`` returns ``n+1``. - For input ``-n.5`` both ``rint`` and ``round`` returns ``-n-1``. Example:: rint([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2., 1., -2., 2., 2.] The storage type of ``rint`` output depends upon the input storage type: - rint(default) = default - rint(row_sparse) = row_sparse - rint(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L727
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise rounded value to the nearest integer of the input.
.. note:: - For input ``n.5`` ``rint`` returns ``n`` while ``round`` returns ``n+1``. - For input ``-n.5`` both ``rint`` and ``round`` returns ``-n-1``. Example:: rint([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2., 1., -2., 2., 2.] The storage type of ``rint`` output depends upon the input storage type: - rint(default) = default - rint(row_sparse) = row_sparse - rint(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L727
| data | The input array. |
|
inline |
Update function for RMSProp optimizer.
`RMSprop` is a variant of stochastic gradient descent where the gradients are
divided by a cache which grows with the sum of squares of recent gradients?
`RMSProp` is similar to `AdaGrad`, a popular variant of `SGD` which adaptively
tunes the learning rate of each parameter. `AdaGrad` lowers the learning rate
each parameter monotonically over the course of training.
While this is analytically motivated for convex optimizations, it may not be
for non-convex problems. `RMSProp` deals with this heuristically by allowing the
learning rates to rebound as the denominator decays over time.
Define the Root Mean Square (RMS) error criterion of the gradient as
:math:`RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}`, where :math:`g` represents
gradient and :math:`E[g^2]_t` is the decaying average over past squared
The :math:`E[g^2]_t` is given by:
.. math::
E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2
The update step is
.. math::
\theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t
The RMSProp code follows the version in
http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf
Tieleman & Hinton, 2012.
Hinton suggests the momentum term :math:`\gamma` to be 0.9 and the learning rate
:math:`\eta` to be 0.001.
Defined in src/operator/optimizer_op.cc:L553
| symbol_name | name of the resulting symbol |
| weight | Weight |
| grad | Gradient |
| n | n |
| lr | Learning rate |
| gamma1 | The decay rate of momentum estimates. |
| epsilon | A small constant for numerical stability. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| clip_weights | Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, |
|
inline |
Update function for RMSProp optimizer.
`RMSprop` is a variant of stochastic gradient descent where the gradients are
divided by a cache which grows with the sum of squares of recent gradients?
`RMSProp` is similar to `AdaGrad`, a popular variant of `SGD` which adaptively
tunes the learning rate of each parameter. `AdaGrad` lowers the learning rate
each parameter monotonically over the course of training.
While this is analytically motivated for convex optimizations, it may not be
for non-convex problems. `RMSProp` deals with this heuristically by allowing the
learning rates to rebound as the denominator decays over time.
Define the Root Mean Square (RMS) error criterion of the gradient as
:math:`RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}`, where :math:`g` represents
gradient and :math:`E[g^2]_t` is the decaying average over past squared
The :math:`E[g^2]_t` is given by:
.. math::
E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2
The update step is
.. math::
\theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t
The RMSProp code follows the version in
http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf
Tieleman & Hinton, 2012.
Hinton suggests the momentum term :math:`\gamma` to be 0.9 and the learning rate
:math:`\eta` to be 0.001.
Defined in src/operator/optimizer_op.cc:L553
| weight | Weight |
| grad | Gradient |
| n | n |
| lr | Learning rate |
| gamma1 | The decay rate of momentum estimates. |
| epsilon | A small constant for numerical stability. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| clip_weights | Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, |
|
inline |
Update function for RMSPropAlex optimizer.
`RMSPropAlex` is non-centered version of `RMSProp`.
Define :math:`E[g^2]_t` is the decaying average over past squared gradient and
:math:`E[g]_t` is the decaying average over past gradient.
.. math::
E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\
E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\
\Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 +
The update step is
.. math::
\theta_{t+1} = \theta_t + \Delta_t
The RMSPropAlex code follows the version in
http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.
Graves suggests the momentum term :math:`\gamma_1` to be 0.95, :math:`\gamma_2`
to be 0.9 and the learning rate :math:`\eta` to be 0.0001.
Defined in src/operator/optimizer_op.cc:L592
| symbol_name | name of the resulting symbol |
| weight | Weight |
| grad | Gradient |
| n | n |
| g | g |
| delta | delta |
| lr | Learning rate |
| gamma1 | Decay rate. |
| gamma2 | Decay rate. |
| epsilon | A small constant for numerical stability. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| clip_weights | Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, |
|
inline |
Update function for RMSPropAlex optimizer.
`RMSPropAlex` is non-centered version of `RMSProp`.
Define :math:`E[g^2]_t` is the decaying average over past squared gradient and
:math:`E[g]_t` is the decaying average over past gradient.
.. math::
E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\
E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\
\Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 +
The update step is
.. math::
\theta_{t+1} = \theta_t + \Delta_t
The RMSPropAlex code follows the version in
http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.
Graves suggests the momentum term :math:`\gamma_1` to be 0.95, :math:`\gamma_2`
to be 0.9 and the learning rate :math:`\eta` to be 0.0001.
Defined in src/operator/optimizer_op.cc:L592
| weight | Weight |
| grad | Gradient |
| n | n |
| g | g |
| delta | delta |
| lr | Learning rate |
| gamma1 | Decay rate. |
| gamma2 | Decay rate. |
| epsilon | A small constant for numerical stability. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| clip_weights | Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, |
|
inline |
Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are implemented, with both multi-layer and bidirectional support.
Vanilla RNN
Applies a single-gate recurrent layer to input X. Two kinds of activation ReLU and Tanh.
With ReLU activation function:
.. math:: h_t = relu(W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh})
With Tanh activtion function:
.. math:: h_t = (W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh})
Reference paper: Finding structure in time - Elman, 1988. https://crl.ucsd.edu/~elman/Papers/fsit.pdf
LSTM
Long Short-Term Memory - Hochreiter, 1997.
.. math:: {array}{ll} i_t = {sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \ f_t = {sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \ g_t = (W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \ o_t = {sigmoid}(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \ c_t = f_t * c_{(t-1)} + i_t * g_t \ h_t = o_t * (c_t) {array}
GRU
Gated Recurrent Unit - Cho et al. 2014. http://arxiv.org/abs/1406.1078
The definition of GRU here is slightly different from paper but compatible with
.. math:: {array}{ll} r_t = {sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \ z_t = {sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \ n_t = (W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \ h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \ {array}
| symbol_name | name of the resulting symbol |
| data | Input data to RNN |
| parameters | Vector of all RNN trainable parameters concatenated |
| state | initial hidden state of the RNN |
| state_cell | initial cell state for LSTM networks (only for LSTM) |
| state_size | size of the state for each layer |
| num_layers | number of stacked layers |
| mode | the type of RNN to compute |
| bidirectional | whether to use bidirectional recurrent layers |
| p | drop rate of the dropout on the outputs of each RNN layer, except the last |
| state_outputs | Whether to have the states as symbol outputs. |
| projection_size | size of project size |
| lstm_state_clip_min | Minimum clip value of LSTM states. This option must be used |
| lstm_state_clip_max | Maximum clip value of LSTM states. This option must be used |
| lstm_state_clip_nan | Whether to stop NaN from propagating in state by clipping |
|
inline |
Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are implemented, with both multi-layer and bidirectional support.
Vanilla RNN
Applies a single-gate recurrent layer to input X. Two kinds of activation ReLU and Tanh.
With ReLU activation function:
.. math:: h_t = relu(W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh})
With Tanh activtion function:
.. math:: h_t = (W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh})
Reference paper: Finding structure in time - Elman, 1988. https://crl.ucsd.edu/~elman/Papers/fsit.pdf
LSTM
Long Short-Term Memory - Hochreiter, 1997.
.. math:: {array}{ll} i_t = {sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \ f_t = {sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \ g_t = (W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \ o_t = {sigmoid}(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \ c_t = f_t * c_{(t-1)} + i_t * g_t \ h_t = o_t * (c_t) {array}
GRU
Gated Recurrent Unit - Cho et al. 2014. http://arxiv.org/abs/1406.1078
The definition of GRU here is slightly different from paper but compatible with
.. math:: {array}{ll} r_t = {sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \ z_t = {sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \ n_t = (W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \ h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \ {array}
| data | Input data to RNN |
| parameters | Vector of all RNN trainable parameters concatenated |
| state | initial hidden state of the RNN |
| state_cell | initial cell state for LSTM networks (only for LSTM) |
| state_size | size of the state for each layer |
| num_layers | number of stacked layers |
| mode | the type of RNN to compute |
| bidirectional | whether to use bidirectional recurrent layers |
| p | drop rate of the dropout on the outputs of each RNN layer, except the last |
| state_outputs | Whether to have the states as symbol outputs. |
| projection_size | size of project size |
| lstm_state_clip_min | Minimum clip value of LSTM states. This option must be used |
| lstm_state_clip_max | Maximum clip value of LSTM states. This option must be used |
| lstm_state_clip_nan | Whether to stop NaN from propagating in state by clipping |
|
inline |
Performs region of interest(ROI) pooling on the input array.
ROI pooling is a variant of a max pooling layer, in which the output size is region of interest is a parameter. Its purpose is to perform max pooling on the of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a layer mostly used in training a `Fast R-CNN` network for object detection. This operator takes a 4D feature map as an input array and region proposals as then it pools over sub-regions of input and produces a fixed-sized output array regardless of the ROI size. To crop the feature map accordingly, you can resize the bounding box coordinates by changing the parameters `rois` and `spatial_scale`. The cropped feature maps are pooled by standard max pooling operation to a indicated by a `pooled_size` parameter. batch_size will change to the number of bounding boxes after `ROIPooling`. The size of each region of interest doesn't have to be perfectly divisible by the number of pooling sections(`pooled_size`). Example:: x = [[[[ 0., 1., 2., 3., 4., 5.], [ 6., 7., 8., 9., 10., 11.], [ 12., 13., 14., 15., 16., 17.], [ 18., 19., 20., 21., 22., 23.], [ 24., 25., 26., 27., 28., 29.], [ 30., 31., 32., 33., 34., 35.], [ 36., 37., 38., 39., 40., 41.], [ 42., 43., 44., 45., 46., 47.]]]] // region of interest i.e. bounding box coordinates. y = [[0,0,0,4,4]] // returns array of shape (2,2) according to the given roi with max pooling. ROIPooling(x, y, (2,2), 1.0) = [[[[ 14., 16.], [ 26., 28.]]]] // region of interest is changed due to the change in `spacial_scale` parameter. ROIPooling(x, y, (2,2), 0.7) = [[[[ 7., 9.], [ 19., 21.]]]] Defined in src/operator/roi_pooling.cc:L295
| symbol_name | name of the resulting symbol |
| data | The input array to the pooling operator, a 4D Feature maps |
| rois | Bounding box coordinates, a 2D array of [[batch_index, x1, y1, x2, y2]], where (x1, y1) and (x2, y2) are top left and bottom right corners of designated region of interest. batch_index indicates the index of corresponding image in |
| pooled_size | ROI pooling output shape (h,w) |
| spatial_scale | Ratio of input feature map height (or w) to raw image height (or |
|
inline |
Performs region of interest(ROI) pooling on the input array.
ROI pooling is a variant of a max pooling layer, in which the output size is region of interest is a parameter. Its purpose is to perform max pooling on the of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a layer mostly used in training a `Fast R-CNN` network for object detection. This operator takes a 4D feature map as an input array and region proposals as then it pools over sub-regions of input and produces a fixed-sized output array regardless of the ROI size. To crop the feature map accordingly, you can resize the bounding box coordinates by changing the parameters `rois` and `spatial_scale`. The cropped feature maps are pooled by standard max pooling operation to a indicated by a `pooled_size` parameter. batch_size will change to the number of bounding boxes after `ROIPooling`. The size of each region of interest doesn't have to be perfectly divisible by the number of pooling sections(`pooled_size`). Example:: x = [[[[ 0., 1., 2., 3., 4., 5.], [ 6., 7., 8., 9., 10., 11.], [ 12., 13., 14., 15., 16., 17.], [ 18., 19., 20., 21., 22., 23.], [ 24., 25., 26., 27., 28., 29.], [ 30., 31., 32., 33., 34., 35.], [ 36., 37., 38., 39., 40., 41.], [ 42., 43., 44., 45., 46., 47.]]]] // region of interest i.e. bounding box coordinates. y = [[0,0,0,4,4]] // returns array of shape (2,2) according to the given roi with max pooling. ROIPooling(x, y, (2,2), 1.0) = [[[[ 14., 16.], [ 26., 28.]]]] // region of interest is changed due to the change in `spacial_scale` parameter. ROIPooling(x, y, (2,2), 0.7) = [[[[ 7., 9.], [ 19., 21.]]]] Defined in src/operator/roi_pooling.cc:L295
| data | The input array to the pooling operator, a 4D Feature maps |
| rois | Bounding box coordinates, a 2D array of [[batch_index, x1, y1, x2, y2]], where (x1, y1) and (x2, y2) are top left and bottom right corners of designated region of interest. batch_index indicates the index of corresponding image in |
| pooled_size | ROI pooling output shape (h,w) |
| spatial_scale | Ratio of input feature map height (or w) to raw image height (or |
Returns element-wise rounded value to the nearest integer of the input.
Example:: round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2., 2., -2., 2., 2.] The storage type of ``round`` output depends upon the input storage type: - round(default) = default - round(row_sparse) = row_sparse - round(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L706
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise rounded value to the nearest integer of the input.
Example:: round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2., 2., -2., 2., 2.] The storage type of ``round`` output depends upon the input storage type: - round(default) = default - round(row_sparse) = row_sparse - round(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L706
| data | The input array. |
Returns element-wise inverse square-root value of the input.
.. math::
rsqrt(x) = 1/\sqrt{x}
Example::
rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25]
The storage type of ``rsqrt`` output is always dense
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L866
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise inverse square-root value of the input.
.. math::
rsqrt(x) = 1/\sqrt{x}
Example::
rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25]
The storage type of ``rsqrt`` output is always dense
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L866
| data | The input array. |
|
inline |
Scatters data into a new tensor according to indices.
Given `data` with shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})` and indices
`(M, Y_0, ..., Y_{K-1})`, the output will have shape `(X_0, X_1, ..., X_{N-1})`,
where `M <= N`. If `M == N`, data shape should simply be `(Y_0, ..., Y_{K-1})`.
The elements in output is defined as follows::
output[indices[0, y_0, ..., y_{K-1}],
...,
indices[M-1, y_0, ..., y_{K-1}],
x_M, ..., x_{N-1}] = data[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}]
all other entries in output are 0.
.. warning::
If the indices have duplicates, the result will be non-deterministic and
the gradient of `scatter_nd` will not be correct!!
Examples::
data = [2, 3, 0]
indices = [[1, 1, 0], [0, 1, 0]]
shape = (2, 2)
scatter_nd(data, indices, shape) = [[0, 0], [2, 3]]
data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]
indices = [[0, 1], [1, 1]]
shape = (2, 2, 2, 2)
scatter_nd(data, indices, shape) = [[[[0, 0],
[0, 0]],
[[1, 2],
[3, 4]]],
[[[0, 0],
[0, 0]],
[[5, 6],
[7, 8]]]]
| symbol_name | name of the resulting symbol |
| data | data |
| indices | indices |
| shape | Shape of output. |
Scatters data into a new tensor according to indices.
Given `data` with shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})` and indices
`(M, Y_0, ..., Y_{K-1})`, the output will have shape `(X_0, X_1, ..., X_{N-1})`,
where `M <= N`. If `M == N`, data shape should simply be `(Y_0, ..., Y_{K-1})`.
The elements in output is defined as follows::
output[indices[0, y_0, ..., y_{K-1}],
...,
indices[M-1, y_0, ..., y_{K-1}],
x_M, ..., x_{N-1}] = data[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}]
all other entries in output are 0.
.. warning::
If the indices have duplicates, the result will be non-deterministic and
the gradient of `scatter_nd` will not be correct!!
Examples::
data = [2, 3, 0]
indices = [[1, 1, 0], [0, 1, 0]]
shape = (2, 2)
scatter_nd(data, indices, shape) = [[0, 0], [2, 3]]
data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]
indices = [[0, 1], [1, 1]]
shape = (2, 2, 2, 2)
scatter_nd(data, indices, shape) = [[[[0, 0],
[0, 0]],
[[1, 2],
[3, 4]]],
[[[0, 0],
[0, 0]],
[[5, 6],
[7, 8]]]]
| data | data |
| indices | indices |
| shape | Shape of output. |
|
inline |
Takes the last element of a sequence.
This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns a of the form [batch_size, other_feature_dims]. Parameter `sequence_length` is used to handle variable-length sequences. an input array of positive ints of dimension [batch_size]. To use this set `use_sequence_length` to `True`, otherwise each example in the batch is to have the max sequence length. .. note:: Alternatively, you can also use `take` operator. Example:: x = [[[ 1., 2., 3.], [ 4., 5., 6.], [ 7., 8., 9.]], [[ 10., 11., 12.], [ 13., 14., 15.], [ 16., 17., 18.]], [[ 19., 20., 21.], [ 22., 23., 24.], [ 25., 26., 27.]]] // returns last sequence when sequence_length parameter is not used SequenceLast(x) = [[ 19., 20., 21.], [ 22., 23., 24.], [ 25., 26., 27.]] // sequence_length is used SequenceLast(x, sequence_length=[1,1,1], use_sequence_length=True) = [[ 1., 2., 3.], [ 4., 5., 6.], [ 7., 8., 9.]] // sequence_length is used SequenceLast(x, sequence_length=[1,2,3], use_sequence_length=True) = [[ 1., 2., 3.], [ 13., 14., 15.], [ 25., 26., 27.]] Defined in src/operator/sequence_last.cc:L92
| symbol_name | name of the resulting symbol |
| data | n-dimensional input array of the form [max_sequence_length, batch_size, |
| sequence_length | vector of sequence lengths of the form [batch_size] |
| use_sequence_length | If set to true, this layer takes in an extra input |
| axis | The sequence axis. Only values of 0 and 1 are currently supported. |
|
inline |
Takes the last element of a sequence.
This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns a of the form [batch_size, other_feature_dims]. Parameter `sequence_length` is used to handle variable-length sequences. an input array of positive ints of dimension [batch_size]. To use this set `use_sequence_length` to `True`, otherwise each example in the batch is to have the max sequence length. .. note:: Alternatively, you can also use `take` operator. Example:: x = [[[ 1., 2., 3.], [ 4., 5., 6.], [ 7., 8., 9.]], [[ 10., 11., 12.], [ 13., 14., 15.], [ 16., 17., 18.]], [[ 19., 20., 21.], [ 22., 23., 24.], [ 25., 26., 27.]]] // returns last sequence when sequence_length parameter is not used SequenceLast(x) = [[ 19., 20., 21.], [ 22., 23., 24.], [ 25., 26., 27.]] // sequence_length is used SequenceLast(x, sequence_length=[1,1,1], use_sequence_length=True) = [[ 1., 2., 3.], [ 4., 5., 6.], [ 7., 8., 9.]] // sequence_length is used SequenceLast(x, sequence_length=[1,2,3], use_sequence_length=True) = [[ 1., 2., 3.], [ 13., 14., 15.], [ 25., 26., 27.]] Defined in src/operator/sequence_last.cc:L92
| data | n-dimensional input array of the form [max_sequence_length, batch_size, |
| sequence_length | vector of sequence lengths of the form [batch_size] |
| use_sequence_length | If set to true, this layer takes in an extra input |
| axis | The sequence axis. Only values of 0 and 1 are currently supported. |
|
inline |
Sets all elements outside the sequence to a constant value.
This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns an array of Parameter `sequence_length` is used to handle variable-length sequences. should be an input array of positive ints of dimension [batch_size]. To use this parameter, set `use_sequence_length` to `True`, otherwise each example in the batch is assumed to have the max sequence length this operator works as the `identity` operator. Example:: x = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // Batch 1 B1 = [[ 1., 2., 3.], [ 7., 8., 9.], [ 13., 14., 15.]] // Batch 2 B2 = [[ 4., 5., 6.], [ 10., 11., 12.], [ 16., 17., 18.]] // works as identity operator when sequence_length parameter is not used SequenceMask(x) = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // sequence_length [1,1] means 1 of each batch will be kept // and other rows are masked with default mask value = 0 SequenceMask(x, sequence_length=[1,1], use_sequence_length=True) = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 0., 0., 0.], [ 0., 0., 0.]], [[ 0., 0., 0.], [ 0., 0., 0.]]] // sequence_length [2,3] means 2 of batch B1 and 3 of batch B2 will be kept // and other rows are masked with value = 1 SequenceMask(x, sequence_length=[2,3], use_sequence_length=True, value=1) = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 1., 1., 1.], [ 16., 17., 18.]]] Defined in src/operator/sequence_mask.cc:L114
| symbol_name | name of the resulting symbol |
| data | n-dimensional input array of the form [max_sequence_length, batch_size, |
| sequence_length | vector of sequence lengths of the form [batch_size] |
| use_sequence_length | If set to true, this layer takes in an extra input |
| value | The value to be used as a mask. |
| axis | The sequence axis. Only values of 0 and 1 are currently supported. |
|
inline |
Sets all elements outside the sequence to a constant value.
This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns an array of Parameter `sequence_length` is used to handle variable-length sequences. should be an input array of positive ints of dimension [batch_size]. To use this parameter, set `use_sequence_length` to `True`, otherwise each example in the batch is assumed to have the max sequence length this operator works as the `identity` operator. Example:: x = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // Batch 1 B1 = [[ 1., 2., 3.], [ 7., 8., 9.], [ 13., 14., 15.]] // Batch 2 B2 = [[ 4., 5., 6.], [ 10., 11., 12.], [ 16., 17., 18.]] // works as identity operator when sequence_length parameter is not used SequenceMask(x) = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // sequence_length [1,1] means 1 of each batch will be kept // and other rows are masked with default mask value = 0 SequenceMask(x, sequence_length=[1,1], use_sequence_length=True) = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 0., 0., 0.], [ 0., 0., 0.]], [[ 0., 0., 0.], [ 0., 0., 0.]]] // sequence_length [2,3] means 2 of batch B1 and 3 of batch B2 will be kept // and other rows are masked with value = 1 SequenceMask(x, sequence_length=[2,3], use_sequence_length=True, value=1) = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 1., 1., 1.], [ 16., 17., 18.]]] Defined in src/operator/sequence_mask.cc:L114
| data | n-dimensional input array of the form [max_sequence_length, batch_size, |
| sequence_length | vector of sequence lengths of the form [batch_size] |
| use_sequence_length | If set to true, this layer takes in an extra input |
| value | The value to be used as a mask. |
| axis | The sequence axis. Only values of 0 and 1 are currently supported. |
|
inline |
Reverses the elements of each sequence.
This function takes an n-dimensional input array of the form and returns an array of the same shape. Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be an input array of positive ints of dimension To use this parameter, set `use_sequence_length` to `True`, otherwise each example in the batch is assumed to have the max sequence length. Example:: x = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // Batch 1 B1 = [[ 1., 2., 3.], [ 7., 8., 9.], [ 13., 14., 15.]] // Batch 2 B2 = [[ 4., 5., 6.], [ 10., 11., 12.], [ 16., 17., 18.]] // returns reverse sequence when sequence_length parameter is not used SequenceReverse(x) = [[[ 13., 14., 15.], [ 16., 17., 18.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 1., 2., 3.], [ 4., 5., 6.]]] // sequence_length [2,2] means 2 rows of // both batch B1 and B2 will be reversed. SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) = [[[ 7., 8., 9.], [ 10., 11., 12.]], [[ 1., 2., 3.], [ 4., 5., 6.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // sequence_length [2,3] means 2 of batch B2 and 3 of batch B3 // will be reversed. SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) = [[[ 7., 8., 9.], [ 16., 17., 18.]], [[ 1., 2., 3.], [ 10., 11., 12.]], [[ 13., 14, 15.], [ 4., 5., 6.]]] Defined in src/operator/sequence_reverse.cc:L113
| symbol_name | name of the resulting symbol |
| data | n-dimensional input array of the form [max_sequence_length, batch_size, |
| sequence_length | vector of sequence lengths of the form [batch_size] |
| use_sequence_length | If set to true, this layer takes in an extra input |
| axis | The sequence axis. Only 0 is currently supported. |
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Reverses the elements of each sequence.
This function takes an n-dimensional input array of the form and returns an array of the same shape. Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be an input array of positive ints of dimension To use this parameter, set `use_sequence_length` to `True`, otherwise each example in the batch is assumed to have the max sequence length. Example:: x = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // Batch 1 B1 = [[ 1., 2., 3.], [ 7., 8., 9.], [ 13., 14., 15.]] // Batch 2 B2 = [[ 4., 5., 6.], [ 10., 11., 12.], [ 16., 17., 18.]] // returns reverse sequence when sequence_length parameter is not used SequenceReverse(x) = [[[ 13., 14., 15.], [ 16., 17., 18.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 1., 2., 3.], [ 4., 5., 6.]]] // sequence_length [2,2] means 2 rows of // both batch B1 and B2 will be reversed. SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) = [[[ 7., 8., 9.], [ 10., 11., 12.]], [[ 1., 2., 3.], [ 4., 5., 6.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // sequence_length [2,3] means 2 of batch B2 and 3 of batch B3 // will be reversed. SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) = [[[ 7., 8., 9.], [ 16., 17., 18.]], [[ 1., 2., 3.], [ 10., 11., 12.]], [[ 13., 14, 15.], [ 4., 5., 6.]]] Defined in src/operator/sequence_reverse.cc:L113
| data | n-dimensional input array of the form [max_sequence_length, batch_size, |
| sequence_length | vector of sequence lengths of the form [batch_size] |
| use_sequence_length | If set to true, this layer takes in an extra input |
| axis | The sequence axis. Only 0 is currently supported. |
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Momentum update function for Stochastic Gradient Descent (SGD) optimizer.
Momentum update has better convergence rates on neural networks. Mathematically
like below:
.. math::
v_1 = \alpha * \nabla J(W_0)\\
v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
W_t = W_{t-1} + v_t
It updates the weights using::
v = momentum * v - learning_rate * gradient
weight += v
Where the parameter ``momentum`` is the decay rate of momentum estimates at
However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and
type is the same as momentum's storage type,
only the row slices whose indices appear in grad.indices are updated (for both
for row in gradient.indices:
v[row] = momentum[row] * v[row] - learning_rate * gradient[row]
weight[row] += v[row]
Defined in src/operator/optimizer_op.cc:L372
| symbol_name | name of the resulting symbol |
| weight | Weight |
| grad | Gradient |
| mom | Momentum |
| lr | Learning rate |
| momentum | The decay rate of momentum estimates at each epoch. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| lazy_update | If true, lazy updates are applied if gradient's stype is row_sparse |
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Momentum update function for Stochastic Gradient Descent (SGD) optimizer.
Momentum update has better convergence rates on neural networks. Mathematically
like below:
.. math::
v_1 = \alpha * \nabla J(W_0)\\
v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
W_t = W_{t-1} + v_t
It updates the weights using::
v = momentum * v - learning_rate * gradient
weight += v
Where the parameter ``momentum`` is the decay rate of momentum estimates at
However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and
type is the same as momentum's storage type,
only the row slices whose indices appear in grad.indices are updated (for both
for row in gradient.indices:
v[row] = momentum[row] * v[row] - learning_rate * gradient[row]
weight[row] += v[row]
Defined in src/operator/optimizer_op.cc:L372
| weight | Weight |
| grad | Gradient |
| mom | Momentum |
| lr | Learning rate |
| momentum | The decay rate of momentum estimates at each epoch. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| lazy_update | If true, lazy updates are applied if gradient's stype is row_sparse |
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Update function for Stochastic Gradient Descent (SDG) optimizer.
It updates the weights using:: weight = weight - learning_rate * (gradient + wd * weight) However, if gradient is of ``row_sparse`` storage type and ``lazy_update`` is only the row slices whose indices appear in grad.indices are updated:: for row in gradient.indices: weight[row] = weight[row] - learning_rate * (gradient[row] + wd * weight[row]) Defined in src/operator/optimizer_op.cc:L331
| symbol_name | name of the resulting symbol |
| weight | Weight |
| grad | Gradient |
| lr | Learning rate |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| lazy_update | If true, lazy updates are applied if gradient's stype is row_sparse. |
|
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Update function for Stochastic Gradient Descent (SDG) optimizer.
It updates the weights using:: weight = weight - learning_rate * (gradient + wd * weight) However, if gradient is of ``row_sparse`` storage type and ``lazy_update`` is only the row slices whose indices appear in grad.indices are updated:: for row in gradient.indices: weight[row] = weight[row] - learning_rate * (gradient[row] + wd * weight[row]) Defined in src/operator/optimizer_op.cc:L331
| weight | Weight |
| grad | Gradient |
| lr | Learning rate |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| lazy_update | If true, lazy updates are applied if gradient's stype is row_sparse. |
|
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Returns a 1D int64 array containing the shape of data.
Example:: shape_array([[1,2,3,4], [5,6,7,8]]) = [2,4] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L504
| symbol_name | name of the resulting symbol |
| data | Input Array. |
| lhs_begin | Defaults to 0. The beginning index along which the lhs dimensions are |
| lhs_end | Defaults to None. The ending index along which the lhs dimensions are |
| rhs_begin | Defaults to 0. The beginning index along which the rhs dimensions are |
| rhs_end | Defaults to None. The ending index along which the rhs dimensions are |
|
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Returns a 1D int64 array containing the shape of data.
Example:: shape_array([[1,2,3,4], [5,6,7,8]]) = [2,4] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L504
| data | Input Array. |
| lhs_begin | Defaults to 0. The beginning index along which the lhs dimensions are |
| lhs_end | Defaults to None. The ending index along which the lhs dimensions are |
| rhs_begin | Defaults to 0. The beginning index along which the rhs dimensions are |
| rhs_end | Defaults to None. The ending index along which the rhs dimensions are |
Computes sigmoid of x element-wise.
.. math:: y = 1 / (1 + exp(-x)) The storage type of ``sigmoid`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L101
| symbol_name | name of the resulting symbol |
| data | The input array. |
Computes sigmoid of x element-wise.
.. math:: y = 1 / (1 + exp(-x)) The storage type of ``sigmoid`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L101
| data | The input array. |
Returns element-wise sign of the input.
Example:: sign([-2, 0, 3]) = [-1, 0, 1] The storage type of ``sign`` output depends upon the input storage type: - sign(default) = default - sign(row_sparse) = row_sparse - sign(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L687
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise sign of the input.
Example:: sign([-2, 0, 3]) = [-1, 0, 1] The storage type of ``sign`` output depends upon the input storage type: - sign(default) = default - sign(row_sparse) = row_sparse - sign(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L687
| data | The input array. |
|
inline |
Update function for SignSGD optimizer.
.. math::
g_t = \nabla J(W_{t-1})\\
W_t = W_{t-1} - \eta_t \text{sign}(g_t)
It updates the weights using::
weight = weight - learning_rate * sign(gradient)
.. note::
- sparse ndarray not supported for this optimizer yet.
Defined in src/operator/optimizer_op.cc:L57
| symbol_name | name of the resulting symbol |
| weight | Weight |
| grad | Gradient |
| lr | Learning rate |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
|
inline |
Update function for SignSGD optimizer.
.. math::
g_t = \nabla J(W_{t-1})\\
W_t = W_{t-1} - \eta_t \text{sign}(g_t)
It updates the weights using::
weight = weight - learning_rate * sign(gradient)
.. note::
- sparse ndarray not supported for this optimizer yet.
Defined in src/operator/optimizer_op.cc:L57
| weight | Weight |
| grad | Gradient |
| lr | Learning rate |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
|
inline |
SIGN momentUM (Signum) optimizer.
.. math::
g_t = \nabla J(W_{t-1})\\
m_t = \beta m_{t-1} + (1 - \beta) g_t\\
W_t = W_{t-1} - \eta_t \text{sign}(m_t)
It updates the weights using::
state = momentum * state + (1-momentum) * gradient
weight = weight - learning_rate * sign(state)
Where the parameter ``momentum`` is the decay rate of momentum estimates at
.. note::
- sparse ndarray not supported for this optimizer yet.
Defined in src/operator/optimizer_op.cc:L86
| symbol_name | name of the resulting symbol |
| weight | Weight |
| grad | Gradient |
| mom | Momentum |
| lr | Learning rate |
| momentum | The decay rate of momentum estimates at each epoch. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| wd_lh | The amount of weight decay that does not go into gradient/momentum |
|
inline |
SIGN momentUM (Signum) optimizer.
.. math::
g_t = \nabla J(W_{t-1})\\
m_t = \beta m_{t-1} + (1 - \beta) g_t\\
W_t = W_{t-1} - \eta_t \text{sign}(m_t)
It updates the weights using::
state = momentum * state + (1-momentum) * gradient
weight = weight - learning_rate * sign(state)
Where the parameter ``momentum`` is the decay rate of momentum estimates at
.. note::
- sparse ndarray not supported for this optimizer yet.
Defined in src/operator/optimizer_op.cc:L86
| weight | Weight |
| grad | Gradient |
| mom | Momentum |
| lr | Learning rate |
| momentum | The decay rate of momentum estimates at each epoch. |
| wd | Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of |
| rescale_grad | Rescale gradient to grad = rescale_grad*grad. |
| clip_gradient | Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, |
| wd_lh | The amount of weight decay that does not go into gradient/momentum |
Computes the element-wise sine of the input array.
The input should be in radians (:math:`2\pi` rad equals 360 degrees). .. math:: sin([0, \pi/4, \pi/2]) = [0, 0.707, 1] The storage type of ``sin`` output depends upon the input storage type: - sin(default) = default - sin(row_sparse) = row_sparse - sin(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L46
| symbol_name | name of the resulting symbol |
| data | The input array. |
Computes the element-wise sine of the input array.
The input should be in radians (:math:`2\pi` rad equals 360 degrees). .. math:: sin([0, \pi/4, \pi/2]) = [0, 0.707, 1] The storage type of ``sin`` output depends upon the input storage type: - sin(default) = default - sin(row_sparse) = row_sparse - sin(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L46
| data | The input array. |
Returns the hyperbolic sine of the input array, computed element-wise.
.. math:: sinh(x) = 0.5\times(exp(x) - exp(-x)) The storage type of ``sinh`` output depends upon the input storage type: - sinh(default) = default - sinh(row_sparse) = row_sparse - sinh(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L201
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns the hyperbolic sine of the input array, computed element-wise.
.. math:: sinh(x) = 0.5\times(exp(x) - exp(-x)) The storage type of ``sinh`` output depends upon the input storage type: - sinh(default) = default - sinh(row_sparse) = row_sparse - sinh(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L201
| data | The input array. |
Returns a 1D int64 array containing the size of data.
Example:: size_array([[1,2,3,4], [5,6,7,8]]) = [8] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L556
| symbol_name | name of the resulting symbol |
| data | Input Array. |
Returns a 1D int64 array containing the size of data.
Example:: size_array([[1,2,3,4], [5,6,7,8]]) = [8] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L556
| data | Input Array. |
|
inline |
Slices a region of the array.
.. note:: ``crop`` is deprecated. Use ``slice`` instead. This function returns a sliced array between the indices given by `begin` and `end` with the corresponding `step`. For an input array of ``shape=(d_0, d_1, ..., d_n-1)``, slice operation with ``begin=(b_0, b_1...b_m-1)``, ``end=(e_0, e_1, ..., e_m-1)``, and ``step=(s_0, s_1, ..., s_m-1)``, where m <= n, results in an array with the shape ``(|e_0-b_0|/|s_0|, ..., |e_m-1-b_m-1|/|s_m-1|, d_m, ..., d_n-1)``. The resulting array's *k*-th dimension contains elements from the *k*-th dimension of the input array starting from index ``b_k`` (inclusive) with step ``s_k`` until reaching ``e_k`` (exclusive). If the *k*-th elements are `None` in the sequence of `begin`, `end`, and `step`, the following rule will be used to set default values. If `s_k` is `None`, set `s_k=1`. If `s_k > 0`, set `b_k=0`, `e_k=d_k`; else, set `b_k=d_k-1`, `e_k=-1`. The storage type of ``slice`` output depends on storage types of inputs - slice(csr) = csr - otherwise, ``slice`` generates output with default storage .. note:: When input data storage type is csr, it only supports step=(), or step=(None,), or step=(1,) to generate a csr output. For other step parameter values, it falls back to slicing a dense tensor. Example:: x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice(x, begin=(0,1), end=(2,4)) = [[ 2., 3., 4.], [ 6., 7., 8.]] slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = [[9., 11.], [5., 7.], [1., 3.]] Defined in src/operator/tensor/matrix_op.cc:L413
| symbol_name | name of the resulting symbol |
| data | Source input |
| begin | starting indices for the slice operation, supports negative indices. |
| end | ending indices for the slice operation, supports negative indices. |
| step | step for the slice operation, supports negative values. |
Slices a region of the array.
.. note:: ``crop`` is deprecated. Use ``slice`` instead. This function returns a sliced array between the indices given by `begin` and `end` with the corresponding `step`. For an input array of ``shape=(d_0, d_1, ..., d_n-1)``, slice operation with ``begin=(b_0, b_1...b_m-1)``, ``end=(e_0, e_1, ..., e_m-1)``, and ``step=(s_0, s_1, ..., s_m-1)``, where m <= n, results in an array with the shape ``(|e_0-b_0|/|s_0|, ..., |e_m-1-b_m-1|/|s_m-1|, d_m, ..., d_n-1)``. The resulting array's *k*-th dimension contains elements from the *k*-th dimension of the input array starting from index ``b_k`` (inclusive) with step ``s_k`` until reaching ``e_k`` (exclusive). If the *k*-th elements are `None` in the sequence of `begin`, `end`, and `step`, the following rule will be used to set default values. If `s_k` is `None`, set `s_k=1`. If `s_k > 0`, set `b_k=0`, `e_k=d_k`; else, set `b_k=d_k-1`, `e_k=-1`. The storage type of ``slice`` output depends on storage types of inputs - slice(csr) = csr - otherwise, ``slice`` generates output with default storage .. note:: When input data storage type is csr, it only supports step=(), or step=(None,), or step=(1,) to generate a csr output. For other step parameter values, it falls back to slicing a dense tensor. Example:: x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice(x, begin=(0,1), end=(2,4)) = [[ 2., 3., 4.], [ 6., 7., 8.]] slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = [[9., 11.], [5., 7.], [1., 3.]] Defined in src/operator/tensor/matrix_op.cc:L413
| data | Source input |
| begin | starting indices for the slice operation, supports negative indices. |
| end | ending indices for the slice operation, supports negative indices. |
| step | step for the slice operation, supports negative values. |
|
inline |
Slices along a given axis.
Returns an array slice along a given `axis` starting from the `begin` index to the `end` index. Examples:: x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice_axis(x, axis=0, begin=1, end=3) = [[ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice_axis(x, axis=1, begin=0, end=2) = [[ 1., 2.], [ 5., 6.], [ 9., 10.]] slice_axis(x, axis=1, begin=-3, end=-1) = [[ 2., 3.], [ 6., 7.], [ 10., 11.]] Defined in src/operator/tensor/matrix_op.cc:L500
| symbol_name | name of the resulting symbol |
| data | Source input |
| axis | Axis along which to be sliced, supports negative indexes. |
| begin | The beginning index along the axis to be sliced, supports negative |
| end | The ending index along the axis to be sliced, supports negative indexes. |
|
inline |
Slices along a given axis.
Returns an array slice along a given `axis` starting from the `begin` index to the `end` index. Examples:: x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice_axis(x, axis=0, begin=1, end=3) = [[ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice_axis(x, axis=1, begin=0, end=2) = [[ 1., 2.], [ 5., 6.], [ 9., 10.]] slice_axis(x, axis=1, begin=-3, end=-1) = [[ 2., 3.], [ 6., 7.], [ 10., 11.]] Defined in src/operator/tensor/matrix_op.cc:L500
| data | Source input |
| axis | Axis along which to be sliced, supports negative indexes. |
| begin | The beginning index along the axis to be sliced, supports negative |
| end | The ending index along the axis to be sliced, supports negative indexes. |
|
inline |
Slices a region of the array like the shape of another array.
This function is similar to ``slice``, however, the `begin` are always `0`s and `end` of specific axes are inferred from the second input `shape_like`. Given the second `shape_like` input of ``shape=(d_0, d_1, ..., d_n-1)``, a ``slice_like`` operator with default empty `axes`, it performs the following operation: `` out = slice(input, begin=(0, 0, ..., 0), end=(d_0, d_1, ..., d_n-1))``. When `axes` is not empty, it is used to speficy which axes are being sliced. Given a 4-d input data, ``slice_like`` operator with ``axes=(0, 2, -1)`` will perform the following operation: `` out = slice(input, begin=(0, 0, 0, 0), end=(d_0, None, d_2, d_3))``. Note that it is allowed to have first and second input with different however, you have to make sure the `axes` are specified and not exceeding the dimension limits. For example, given `input_1` with ``shape=(2,3,4,5)`` and `input_2` with ``shape=(1,2,3)``, it is not allowed to use: `` out = slice_like(a, b)`` because ndim of `input_1` is 4, and ndim of is 3. The following is allowed in this situation: `` out = slice_like(a, b, axes=(0, 2))`` Example:: x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] y = [[ 0., 0., 0.], [ 0., 0., 0.]] slice_like(x, y) = [[ 1., 2., 3.] [ 5., 6., 7.]] slice_like(x, y, axes=(0, 1)) = [[ 1., 2., 3.] [ 5., 6., 7.]] slice_like(x, y, axes=(0)) = [[ 1., 2., 3., 4.] [ 5., 6., 7., 8.]] slice_like(x, y, axes=(-1)) = [[ 1., 2., 3.] [ 5., 6., 7.] [ 9., 10., 11.]] Defined in src/operator/tensor/matrix_op.cc:L569
| symbol_name | name of the resulting symbol |
| data | Source input |
| shape_like | Shape like input |
| axes | List of axes on which input data will be sliced according to the corresponding size of the second input. By default will slice on all axes. |
Slices a region of the array like the shape of another array.
This function is similar to ``slice``, however, the `begin` are always `0`s and `end` of specific axes are inferred from the second input `shape_like`. Given the second `shape_like` input of ``shape=(d_0, d_1, ..., d_n-1)``, a ``slice_like`` operator with default empty `axes`, it performs the following operation: `` out = slice(input, begin=(0, 0, ..., 0), end=(d_0, d_1, ..., d_n-1))``. When `axes` is not empty, it is used to speficy which axes are being sliced. Given a 4-d input data, ``slice_like`` operator with ``axes=(0, 2, -1)`` will perform the following operation: `` out = slice(input, begin=(0, 0, 0, 0), end=(d_0, None, d_2, d_3))``. Note that it is allowed to have first and second input with different however, you have to make sure the `axes` are specified and not exceeding the dimension limits. For example, given `input_1` with ``shape=(2,3,4,5)`` and `input_2` with ``shape=(1,2,3)``, it is not allowed to use: `` out = slice_like(a, b)`` because ndim of `input_1` is 4, and ndim of is 3. The following is allowed in this situation: `` out = slice_like(a, b, axes=(0, 2))`` Example:: x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] y = [[ 0., 0., 0.], [ 0., 0., 0.]] slice_like(x, y) = [[ 1., 2., 3.] [ 5., 6., 7.]] slice_like(x, y, axes=(0, 1)) = [[ 1., 2., 3.] [ 5., 6., 7.]] slice_like(x, y, axes=(0)) = [[ 1., 2., 3., 4.] [ 5., 6., 7., 8.]] slice_like(x, y, axes=(-1)) = [[ 1., 2., 3.] [ 5., 6., 7.] [ 9., 10., 11.]] Defined in src/operator/tensor/matrix_op.cc:L569
| data | Source input |
| shape_like | Shape like input |
| axes | List of axes on which input data will be sliced according to the corresponding size of the second input. By default will slice on all axes. |
|
inline |
Splits an array along a particular axis into multiple sub-arrays.
.. note:: ``SliceChannel`` is deprecated. Use ``split`` instead. **Note** that `num_outputs` should evenly divide the length of the axis along which to split the array. Example:: x = [[[ 1.] [ 2.]] [[ 3.] [ 4.]] [[ 5.] [ 6.]]] x.shape = (3, 2, 1) y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1) y = [[[ 1.]] [[ 3.]] [[ 5.]]] [[[ 2.]] [[ 4.]] [[ 6.]]] y[0].shape = (3, 1, 1) z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1) z = [[[ 1.] [ 2.]]] [[[ 3.] [ 4.]]] [[[ 5.] [ 6.]]] z[0].shape = (1, 2, 1) `squeeze_axis=1` removes the axis with length 1 from the shapes of the output **Note** that setting `squeeze_axis` to ``1`` removes axis with length 1 only along the `axis` which it is split. Also `squeeze_axis` can be set to true only if ``input.shape[axis] == Example:: z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with z = [[ 1.] [ 2.]] [[ 3.] [ 4.]] [[ 5.] [ 6.]] z[0].shape = (2 ,1 ) Defined in src/operator/slice_channel.cc:L107
| symbol_name | name of the resulting symbol |
| data | The input |
| num_outputs | Number of splits. Note that this should evenly divide the length of |
| axis | Axis along which to split. |
| squeeze_axis | If true, Removes the axis with length 1 from the shapes of the output arrays. Note that setting squeeze_axis to true removes axis with length 1 only along the axis which it is split. Also squeeze_axis can |
|
inline |
Splits an array along a particular axis into multiple sub-arrays.
.. note:: ``SliceChannel`` is deprecated. Use ``split`` instead. **Note** that `num_outputs` should evenly divide the length of the axis along which to split the array. Example:: x = [[[ 1.] [ 2.]] [[ 3.] [ 4.]] [[ 5.] [ 6.]]] x.shape = (3, 2, 1) y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1) y = [[[ 1.]] [[ 3.]] [[ 5.]]] [[[ 2.]] [[ 4.]] [[ 6.]]] y[0].shape = (3, 1, 1) z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1) z = [[[ 1.] [ 2.]]] [[[ 3.] [ 4.]]] [[[ 5.] [ 6.]]] z[0].shape = (1, 2, 1) `squeeze_axis=1` removes the axis with length 1 from the shapes of the output **Note** that setting `squeeze_axis` to ``1`` removes axis with length 1 only along the `axis` which it is split. Also `squeeze_axis` can be set to true only if ``input.shape[axis] == Example:: z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with z = [[ 1.] [ 2.]] [[ 3.] [ 4.]] [[ 5.] [ 6.]] z[0].shape = (2 ,1 ) Defined in src/operator/slice_channel.cc:L107
| data | The input |
| num_outputs | Number of splits. Note that this should evenly divide the length of |
| axis | Axis along which to split. |
| squeeze_axis | If true, Removes the axis with length 1 from the shapes of the output arrays. Note that setting squeeze_axis to true removes axis with length 1 only along the axis which it is split. Also squeeze_axis can |
|
inline |
Calculate Smooth L1 Loss(lhs, scalar) by summing
.. math::
f(x) =
\begin{cases}
(\sigma x)^2/2,& \text{if }x < 1/\sigma^2\\
|x|-0.5/\sigma^2,& \text{otherwise}
\end{cases}
where :math:`x` is an element of the tensor *lhs* and :math:`\sigma` is the
Example::
smooth_l1([1, 2, 3, 4], scalar=1) = [0.5, 1.5, 2.5, 3.5]
Defined in src/operator/tensor/elemwise_binary_scalar_op_extended.cc:L103
| symbol_name | name of the resulting symbol |
| data | source input |
| scalar | scalar input |
Calculate Smooth L1 Loss(lhs, scalar) by summing
.. math::
f(x) =
\begin{cases}
(\sigma x)^2/2,& \text{if }x < 1/\sigma^2\\
|x|-0.5/\sigma^2,& \text{otherwise}
\end{cases}
where :math:`x` is an element of the tensor *lhs* and :math:`\sigma` is the
Example::
smooth_l1([1, 2, 3, 4], scalar=1) = [0.5, 1.5, 2.5, 3.5]
Defined in src/operator/tensor/elemwise_binary_scalar_op_extended.cc:L103
| data | source input |
| scalar | scalar input |
|
inline |
Applies the softmax function.
The resulting array contains elements in the range (0,1) and the elements along
.. math::
softmax(\mathbf{z/t})_j = \frac{e^{z_j/t}}{\sum_{k=1}^K e^{z_k/t}}
for :math:`j = 1, ..., K`
t is the temperature parameter in softmax function. By default, t equals 1.0
Example::
x = [[ 1. 1. 1.]
[ 1. 1. 1.]]
softmax(x,axis=0) = [[ 0.5 0.5 0.5]
[ 0.5 0.5 0.5]]
softmax(x,axis=1) = [[ 0.33333334, 0.33333334, 0.33333334],
[ 0.33333334, 0.33333334, 0.33333334]]
Defined in src/operator/nn/softmax.cc:L100
| symbol_name | name of the resulting symbol |
| data | The input array. |
| axis | The axis along which to compute softmax. |
| temperature | Temperature parameter in softmax |
|
inline |
Please use SoftmaxOutput.
.. note:: This operator has been renamed to `SoftmaxOutput`, which computes the gradient of cross-entropy loss w.r.t softmax output. To just compute softmax output, use the `softmax` operator. Defined in src/operator/softmax_output.cc:L138
| symbol_name | name of the resulting symbol |
| data | Input array. |
| grad_scale | Scales the gradient by a float factor. |
| ignore_label | The instances whose labels == ignore_label will be ignored |
| multi_output | If set to true, the softmax function will be computed along axis 1. This is applied when the shape of input array differs from the |
| use_ignore | If set to true, the ignore_label value will not contribute to |
| preserve_shape | If set to true, the softmax function will be computed along |
| normalization | Normalizes the gradient. |
| out_grad | Multiplies gradient with output gradient element-wise. |
| smooth_alpha | Constant for computing a label smoothed version of cross-entropyfor the backwards pass. This constant gets subtracted from theone-hot encoding of the gold label and distributed uniformly toall other |
|
inline |
Applies the softmax function.
The resulting array contains elements in the range (0,1) and the elements along
.. math::
softmax(\mathbf{z/t})_j = \frac{e^{z_j/t}}{\sum_{k=1}^K e^{z_k/t}}
for :math:`j = 1, ..., K`
t is the temperature parameter in softmax function. By default, t equals 1.0
Example::
x = [[ 1. 1. 1.]
[ 1. 1. 1.]]
softmax(x,axis=0) = [[ 0.5 0.5 0.5]
[ 0.5 0.5 0.5]]
softmax(x,axis=1) = [[ 0.33333334, 0.33333334, 0.33333334],
[ 0.33333334, 0.33333334, 0.33333334]]
Defined in src/operator/nn/softmax.cc:L100
| data | The input array. |
| axis | The axis along which to compute softmax. |
| temperature | Temperature parameter in softmax |
|
inline |
Please use SoftmaxOutput.
.. note:: This operator has been renamed to `SoftmaxOutput`, which computes the gradient of cross-entropy loss w.r.t softmax output. To just compute softmax output, use the `softmax` operator. Defined in src/operator/softmax_output.cc:L138
| data | Input array. |
| grad_scale | Scales the gradient by a float factor. |
| ignore_label | The instances whose labels == ignore_label will be ignored |
| multi_output | If set to true, the softmax function will be computed along axis 1. This is applied when the shape of input array differs from the |
| use_ignore | If set to true, the ignore_label value will not contribute to |
| preserve_shape | If set to true, the softmax function will be computed along |
| normalization | Normalizes the gradient. |
| out_grad | Multiplies gradient with output gradient element-wise. |
| smooth_alpha | Constant for computing a label smoothed version of cross-entropyfor the backwards pass. This constant gets subtracted from theone-hot encoding of the gold label and distributed uniformly toall other |
|
inline |
Calculate cross entropy of softmax output and one-hot label.
- This operator computes the cross entropy in two steps:
- Applies softmax function on the input array.
- Computes and returns the cross entropy loss between the softmax output and
- The softmax function and cross entropy loss is given by:
- Softmax Function:
.. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}
- Cross Entropy Function:
.. math:: \text{CE(label, output)} = - \sum_i \text{label}_i
Example::
x = [[1, 2, 3],
[11, 7, 5]]
label = [2, 0]
softmax(x) = [[0.09003057, 0.24472848, 0.66524094],
[0.97962922, 0.01794253, 0.00242826]]
softmax_cross_entropy(data, label) = - log(0.66524084) - log(0.97962922) =
Defined in src/operator/loss_binary_op.cc:L59
| symbol_name | name of the resulting symbol |
| data | Input data |
| label | Input label |
Calculate cross entropy of softmax output and one-hot label.
- This operator computes the cross entropy in two steps:
- Applies softmax function on the input array.
- Computes and returns the cross entropy loss between the softmax output and
- The softmax function and cross entropy loss is given by:
- Softmax Function:
.. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}
- Cross Entropy Function:
.. math:: \text{CE(label, output)} = - \sum_i \text{label}_i
Example::
x = [[1, 2, 3],
[11, 7, 5]]
label = [2, 0]
softmax(x) = [[0.09003057, 0.24472848, 0.66524094],
[0.97962922, 0.01794253, 0.00242826]]
softmax_cross_entropy(data, label) = - log(0.66524084) - log(0.97962922) =
Defined in src/operator/loss_binary_op.cc:L59
| data | Input data |
| label | Input label |
|
inline |
Applies softmax activation to input. This is intended for internal layers.
.. note:: This operator has been deprecated, please use `softmax`. If `mode` = ``instance``, this operator will compute a softmax for each This is the default mode. If `mode` = ``channel``, this operator will compute a k-class softmax at each of each instance, where `k` = ``num_channel``. This mode can only be used when has at least 3 dimensions. This can be used for `fully convolutional network`, `image segmentation`, etc. Example:: >>> input_array = mx.nd.array([[3., 0.5, -0.5, 2., 7.], >>> [2., -.4, 7., 3., 0.2]]) >>> softmax_act = mx.nd.SoftmaxActivation(input_array) >>> print softmax_act.asnumpy() [[ 1.78322066e-02 1.46375655e-03 5.38485940e-04 6.56010211e-03 [ 6.56221947e-03 5.95310994e-04 9.73919690e-01 1.78379621e-02 Defined in src/operator/nn/softmax_activation.cc:L59
| symbol_name | name of the resulting symbol |
| data | The input array. |
| mode | Specifies how to compute the softmax. If set to instance, it computes softmax for each instance. If set to channel, It computes cross channel |
|
inline |
Applies softmax activation to input. This is intended for internal layers.
.. note:: This operator has been deprecated, please use `softmax`. If `mode` = ``instance``, this operator will compute a softmax for each This is the default mode. If `mode` = ``channel``, this operator will compute a k-class softmax at each of each instance, where `k` = ``num_channel``. This mode can only be used when has at least 3 dimensions. This can be used for `fully convolutional network`, `image segmentation`, etc. Example:: >>> input_array = mx.nd.array([[3., 0.5, -0.5, 2., 7.], >>> [2., -.4, 7., 3., 0.2]]) >>> softmax_act = mx.nd.SoftmaxActivation(input_array) >>> print softmax_act.asnumpy() [[ 1.78322066e-02 1.46375655e-03 5.38485940e-04 6.56010211e-03 [ 6.56221947e-03 5.95310994e-04 9.73919690e-01 1.78379621e-02 Defined in src/operator/nn/softmax_activation.cc:L59
| data | The input array. |
| mode | Specifies how to compute the softmax. If set to instance, it computes softmax for each instance. If set to channel, It computes cross channel |
|
inline |
Computes the gradient of cross entropy loss with respect to softmax output.
- This operator computes the gradient in two steps.
The cross entropy loss does not actually need to be computed.
- Applies softmax function on the input array.
- Computes and returns the gradient of cross entropy loss w.r.t. the softmax
- The softmax function, cross entropy loss and gradient is given by:
- Softmax Function:
.. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}
- Cross Entropy Function:
.. math:: \text{CE(label, output)} = - \sum_i \text{label}_i
- The gradient of cross entropy loss w.r.t softmax output:
.. math:: \text{gradient} = \text{output} - \text{label}
- During forward propagation, the softmax function is computed for each
For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The
:math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters
and `multi_output` to specify the way to compute softmax:
- By default, `preserve_shape` is ``false``. This operator will reshape the
into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the
each row in the reshaped array, and afterwards reshape it back to the original
:math:`(d_1, d_2, ..., d_n)`.
- If `preserve_shape` is ``true``, the softmax function will be computed along
the last axis (`axis` = ``-1``).
- If `multi_output` is ``true``, the softmax function will be computed along
the second axis (`axis` = ``1``).
- During backward propagation, the gradient of cross-entropy loss w.r.t softmax
The provided label can be a one-hot label array or a probability label array.
- If the parameter `use_ignore` is ``true``, `ignore_label` can specify input
with a particular label to be ignored during backward propagation. **This has
softmax `output` has same shape as `label`**.
Example::
data = [[1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4]]
label = [1,0,2,3]
ignore_label = 1
SoftmaxOutput(data=data, label = label,\
multi_output=true, use_ignore=true,\
ignore_label=ignore_label)
## forward softmax output
[[ 0.0320586 0.08714432 0.23688284 0.64391428]
[ 0.25 0.25 0.25 0.25 ]
[ 0.25 0.25 0.25 0.25 ]
[ 0.25 0.25 0.25 0.25 ]]
## backward gradient output
[[ 0. 0. 0. 0. ]
[-0.75 0.25 0.25 0.25]
[ 0.25 0.25 -0.75 0.25]
[ 0.25 0.25 0.25 -0.75]]
## notice that the first row is all 0 because label[0] is 1, which is equal to
- The parameter `grad_scale` can be used to rescale the gradient, which is
give each loss function different weights.
- This operator also supports various ways to normalize the gradient by
The `normalization` is applied if softmax output has different shape than the
The `normalization` mode can be set to the followings:
- ``'null'``: do nothing.
- ``'batch'``: divide the gradient by the batch size.
- ``'valid'``: divide the gradient by the number of instances which are not
Defined in src/operator/softmax_output.cc:L123
| symbol_name | name of the resulting symbol |
| data | Input array. |
| label | Ground truth label. |
| grad_scale | Scales the gradient by a float factor. |
| ignore_label | The instances whose labels == ignore_label will be ignored |
| multi_output | If set to true, the softmax function will be computed along axis 1. This is applied when the shape of input array differs from the |
| use_ignore | If set to true, the ignore_label value will not contribute to |
| preserve_shape | If set to true, the softmax function will be computed along |
| normalization | Normalizes the gradient. |
| out_grad | Multiplies gradient with output gradient element-wise. |
| smooth_alpha | Constant for computing a label smoothed version of cross-entropyfor the backwards pass. This constant gets subtracted from theone-hot encoding of the gold label and distributed uniformly toall other |
|
inline |
Computes the gradient of cross entropy loss with respect to softmax output.
- This operator computes the gradient in two steps.
The cross entropy loss does not actually need to be computed.
- Applies softmax function on the input array.
- Computes and returns the gradient of cross entropy loss w.r.t. the softmax
- The softmax function, cross entropy loss and gradient is given by:
- Softmax Function:
.. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}
- Cross Entropy Function:
.. math:: \text{CE(label, output)} = - \sum_i \text{label}_i
- The gradient of cross entropy loss w.r.t softmax output:
.. math:: \text{gradient} = \text{output} - \text{label}
- During forward propagation, the softmax function is computed for each
For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The
:math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters
and `multi_output` to specify the way to compute softmax:
- By default, `preserve_shape` is ``false``. This operator will reshape the
into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the
each row in the reshaped array, and afterwards reshape it back to the original
:math:`(d_1, d_2, ..., d_n)`.
- If `preserve_shape` is ``true``, the softmax function will be computed along
the last axis (`axis` = ``-1``).
- If `multi_output` is ``true``, the softmax function will be computed along
the second axis (`axis` = ``1``).
- During backward propagation, the gradient of cross-entropy loss w.r.t softmax
The provided label can be a one-hot label array or a probability label array.
- If the parameter `use_ignore` is ``true``, `ignore_label` can specify input
with a particular label to be ignored during backward propagation. **This has
softmax `output` has same shape as `label`**.
Example::
data = [[1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4]]
label = [1,0,2,3]
ignore_label = 1
SoftmaxOutput(data=data, label = label,\
multi_output=true, use_ignore=true,\
ignore_label=ignore_label)
## forward softmax output
[[ 0.0320586 0.08714432 0.23688284 0.64391428]
[ 0.25 0.25 0.25 0.25 ]
[ 0.25 0.25 0.25 0.25 ]
[ 0.25 0.25 0.25 0.25 ]]
## backward gradient output
[[ 0. 0. 0. 0. ]
[-0.75 0.25 0.25 0.25]
[ 0.25 0.25 -0.75 0.25]
[ 0.25 0.25 0.25 -0.75]]
## notice that the first row is all 0 because label[0] is 1, which is equal to
- The parameter `grad_scale` can be used to rescale the gradient, which is
give each loss function different weights.
- This operator also supports various ways to normalize the gradient by
The `normalization` is applied if softmax output has different shape than the
The `normalization` mode can be set to the followings:
- ``'null'``: do nothing.
- ``'batch'``: divide the gradient by the batch size.
- ``'valid'``: divide the gradient by the number of instances which are not
Defined in src/operator/softmax_output.cc:L123
| data | Input array. |
| label | Ground truth label. |
| grad_scale | Scales the gradient by a float factor. |
| ignore_label | The instances whose labels == ignore_label will be ignored |
| multi_output | If set to true, the softmax function will be computed along axis 1. This is applied when the shape of input array differs from the |
| use_ignore | If set to true, the ignore_label value will not contribute to |
| preserve_shape | If set to true, the softmax function will be computed along |
| normalization | Normalizes the gradient. |
| out_grad | Multiplies gradient with output gradient element-wise. |
| smooth_alpha | Constant for computing a label smoothed version of cross-entropyfor the backwards pass. This constant gets subtracted from theone-hot encoding of the gold label and distributed uniformly toall other |
Computes softsign of x element-wise.
.. math:: y = x / (1 + abs(x)) The storage type of ``softsign`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L145
| symbol_name | name of the resulting symbol |
| data | The input array. |
Computes softsign of x element-wise.
.. math:: y = x / (1 + abs(x)) The storage type of ``softsign`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L145
| data | The input array. |
|
inline |
Returns a sorted copy of an input array along the given axis.
Examples:: x = [[ 1, 4], [ 3, 1]] // sorts along the last axis sort(x) = [[ 1., 4.], [ 1., 3.]] // flattens and then sorts sort(x) = [ 1., 1., 3., 4.] // sorts along the first axis sort(x, axis=0) = [[ 1., 1.], [ 3., 4.]] // in a descend order sort(x, is_ascend=0) = [[ 4., 1.], [ 3., 1.]] Defined in src/operator/tensor/ordering_op.cc:L127
| symbol_name | name of the resulting symbol |
| data | The input array |
| axis | Axis along which to choose sort the input tensor. If not given, the |
| is_ascend | Whether to sort in ascending or descending order. |
|
inline |
Returns a sorted copy of an input array along the given axis.
Examples:: x = [[ 1, 4], [ 3, 1]] // sorts along the last axis sort(x) = [[ 1., 4.], [ 1., 3.]] // flattens and then sorts sort(x) = [ 1., 1., 3., 4.] // sorts along the first axis sort(x, axis=0) = [[ 1., 1.], [ 3., 4.]] // in a descend order sort(x, is_ascend=0) = [[ 4., 1.], [ 3., 1.]] Defined in src/operator/tensor/ordering_op.cc:L127
| data | The input array |
| axis | Axis along which to choose sort the input tensor. If not given, the |
| is_ascend | Whether to sort in ascending or descending order. |
|
inline |
Rearranges(permutes) blocks of spatial data into depth. Similar to ONNX SpaceToDepth operator: https://github.com/onnx/onnx/blob/master/docs/Operators.md#SpaceToDepth
The output is a new tensor where the values from height and width dimension are moved to the depth dimension. The reverse of this operation is
.. math::
{gather*} x = reshape(x, [N, C, H / block_size, block_size, W / block_size, x = transpose(x , [0, 3, 5, 1, 2, 4]) \ y = reshape(x , [N, C * (block_size ^ 2), H / block_size, W / {gather*}
where :math:x is an input tensor with default layout as :math:[N, C, H, W]: and :math:y is the output tensor of layout :math:`[N, C * (block_size ^ 2),
Example::
x = [[[[0, 6, 1, 7, 2, 8], [12, 18, 13, 19, 14, 20], [3, 9, 4, 10, 5, 11], [15, 21, 16, 22, 17, 23]]]]
space_to_depth(x, 2) = [[[[0, 1, 2], [3, 4, 5]], [[6, 7, 8], [9, 10, 11]], [[12, 13, 14], [15, 16, 17]], [[18, 19, 20], [21, 22, 23]]]] Defined in src/operator/tensor/matrix_op.cc:L999
| symbol_name | name of the resulting symbol |
| data | Input ndarray |
| block_size | Blocks of [block_size. block_size] are moved |
Rearranges(permutes) blocks of spatial data into depth. Similar to ONNX SpaceToDepth operator: https://github.com/onnx/onnx/blob/master/docs/Operators.md#SpaceToDepth
The output is a new tensor where the values from height and width dimension are moved to the depth dimension. The reverse of this operation is
.. math::
{gather*} x = reshape(x, [N, C, H / block_size, block_size, W / block_size, x = transpose(x , [0, 3, 5, 1, 2, 4]) \ y = reshape(x , [N, C * (block_size ^ 2), H / block_size, W / {gather*}
where :math:x is an input tensor with default layout as :math:[N, C, H, W]: and :math:y is the output tensor of layout :math:`[N, C * (block_size ^ 2),
Example::
x = [[[[0, 6, 1, 7, 2, 8], [12, 18, 13, 19, 14, 20], [3, 9, 4, 10, 5, 11], [15, 21, 16, 22, 17, 23]]]]
space_to_depth(x, 2) = [[[[0, 1, 2], [3, 4, 5]], [[6, 7, 8], [9, 10, 11]], [[12, 13, 14], [15, 16, 17]], [[18, 19, 20], [21, 22, 23]]]] Defined in src/operator/tensor/matrix_op.cc:L999
| data | Input ndarray |
| block_size | Blocks of [block_size. block_size] are moved |
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Applies a spatial transformer to input feature map.
| symbol_name | name of the resulting symbol |
| data | Input data to the SpatialTransformerOp. |
| loc | localisation net, the output dim should be 6 when transform_type is affine. |
| transform_type | transformation type |
| sampler_type | sampling type |
| target_shape | output shape(h, w) of spatial transformer: (y, x) |
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Applies a spatial transformer to input feature map.
| data | Input data to the SpatialTransformerOp. |
| loc | localisation net, the output dim should be 6 when transform_type is affine. |
| transform_type | transformation type |
| sampler_type | sampling type |
| target_shape | output shape(h, w) of spatial transformer: (y, x) |
Returns element-wise square-root value of the input.
.. math::
\textrm{sqrt}(x) = \sqrt{x}
Example::
sqrt([4, 9, 16]) = [2, 3, 4]
The storage type of ``sqrt`` output depends upon the input storage type:
- sqrt(default) = default
- sqrt(row_sparse) = row_sparse
- sqrt(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L846
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise square-root value of the input.
.. math::
\textrm{sqrt}(x) = \sqrt{x}
Example::
sqrt([4, 9, 16]) = [2, 3, 4]
The storage type of ``sqrt`` output depends upon the input storage type:
- sqrt(default) = default
- sqrt(row_sparse) = row_sparse
- sqrt(csr) = csr
Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L846
| data | The input array. |
Returns element-wise squared value of the input.
.. math:: square(x) = x^2 Example:: square([2, 3, 4]) = [4, 9, 16] The storage type of ``square`` output depends upon the input storage type: - square(default) = default - square(row_sparse) = row_sparse - square(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L823
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns element-wise squared value of the input.
.. math:: square(x) = x^2 Example:: square([2, 3, 4]) = [4, 9, 16] The storage type of ``square`` output depends upon the input storage type: - square(default) = default - square(row_sparse) = row_sparse - square(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L823
| data | The input array. |
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Remove single-dimensional entries from the shape of an array. Same behavior of defining the output tensor shape as numpy.squeeze for the most See the following note for exception.
Examples::
data = [[[0], [1], [2]]] squeeze(data) = [0, 1, 2] squeeze(data, axis=0) = [[0], [1], [2]] squeeze(data, axis=2) = [[0, 1, 2]] squeeze(data, axis=(0, 2)) = [0, 1, 2]
.. Note:: The output of this operator will keep at least one dimension not removed. For squeeze([[[4]]]) = [4], while in numpy.squeeze, the output will become a scalar.
| symbol_name | name of the resulting symbol |
| data | data to squeeze |
| axis | Selects a subset of the single-dimensional entries in the shape. If an |
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Remove single-dimensional entries from the shape of an array. Same behavior of defining the output tensor shape as numpy.squeeze for the most See the following note for exception.
Examples::
data = [[[0], [1], [2]]] squeeze(data) = [0, 1, 2] squeeze(data, axis=0) = [[0], [1], [2]] squeeze(data, axis=2) = [[0, 1, 2]] squeeze(data, axis=(0, 2)) = [0, 1, 2]
.. Note:: The output of this operator will keep at least one dimension not removed. For squeeze([[[4]]]) = [4], while in numpy.squeeze, the output will become a scalar.
| data | data to squeeze |
| axis | Selects a subset of the single-dimensional entries in the shape. If an |
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Join a sequence of arrays along a new axis.
The axis parameter specifies the index of the new axis in the dimensions of the result. For example, if axis=0 it will be the first dimension and if axis=-1 it will be the last dimension. Examples:: x = [1, 2] y = [3, 4] stack(x, y) = [[1, 2], [3, 4]] stack(x, y, axis=1) = [[1, 3], [2, 4]]
| symbol_name | name of the resulting symbol |
| data | List of arrays to stack |
| num_args | Number of inputs to be stacked. |
| axis | The axis in the result array along which the input arrays are stacked. |
Join a sequence of arrays along a new axis.
The axis parameter specifies the index of the new axis in the dimensions of the result. For example, if axis=0 it will be the first dimension and if axis=-1 it will be the last dimension. Examples:: x = [1, 2] y = [3, 4] stack(x, y) = [[1, 2], [3, 4]] stack(x, y, axis=1) = [[1, 3], [2, 4]]
| data | List of arrays to stack |
| num_args | Number of inputs to be stacked. |
| axis | The axis in the result array along which the input arrays are stacked. |
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Computes the sum of array elements over given axes.
.. Note:: `sum` and `sum_axis` are equivalent. For ndarray of csr storage type summation along axis 0 and axis 1 is supported. Setting keepdims or exclude to True will cause a fallback to dense operator. Example:: data = [[[1, 2], [2, 3], [1, 3]], [[1, 4], [4, 3], [5, 2]], [[7, 1], [7, 2], [7, 3]]] sum(data, axis=1) [[ 4. 8.] [ 10. 9.] [ 21. 6.]] sum(data, axis=[1,2]) [ 12. 19. 27.] data = [[1, 2, 0], [3, 0, 1], [4, 1, 0]] csr = cast_storage(data, 'csr') sum(csr, axis=0) [ 8. 3. 1.] sum(csr, axis=1) [ 3. 4. 5.] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L115
| symbol_name | name of the resulting symbol |
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
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Computes the sum of array elements over given axes.
.. Note:: `sum` and `sum_axis` are equivalent. For ndarray of csr storage type summation along axis 0 and axis 1 is supported. Setting keepdims or exclude to True will cause a fallback to dense operator. Example:: data = [[[1, 2], [2, 3], [1, 3]], [[1, 4], [4, 3], [5, 2]], [[7, 1], [7, 2], [7, 3]]] sum(data, axis=1) [[ 4. 8.] [ 10. 9.] [ 21. 6.]] sum(data, axis=[1,2]) [ 12. 19. 27.] data = [[1, 2, 0], [3, 0, 1], [4, 1, 0]] csr = cast_storage(data, 'csr') sum(csr, axis=0) [ 8. 3. 1.] sum(csr, axis=1) [ 3. 4. 5.] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L115
| data | The input |
| axis | The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. |
| keepdims | If this is set to True, the reduced axes are left in the result as |
| exclude | Whether to perform reduction on axis that are NOT in axis instead. |
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Computes support vector machine based transformation of the input.
This tutorial demonstrates using SVM as output layer for classification instead https://github.com/dmlc/mxnet/tree/master/example/svm_mnist.
| symbol_name | name of the resulting symbol |
| data | Input data for SVM transformation. |
| label | Class label for the input data. |
| margin | The loss function penalizes outputs that lie outside this margin. |
| regularization_coefficient | Regularization parameter for the SVM. This balances |
| use_linear | Whether to use L1-SVM objective. L2-SVM objective is used by default. |
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Computes support vector machine based transformation of the input.
This tutorial demonstrates using SVM as output layer for classification instead https://github.com/dmlc/mxnet/tree/master/example/svm_mnist.
| data | Input data for SVM transformation. |
| label | Class label for the input data. |
| margin | The loss function penalizes outputs that lie outside this margin. |
| regularization_coefficient | Regularization parameter for the SVM. This balances |
| use_linear | Whether to use L1-SVM objective. L2-SVM objective is used by default. |
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Interchanges two axes of an array.
Examples:: x = [[1, 2, 3]]) swapaxes(x, 0, 1) = [[ 1], [ 2], [ 3]] x = [[[ 0, 1], [ 2, 3]], [[ 4, 5], [ 6, 7]]] // (2,2,2) array swapaxes(x, 0, 2) = [[[ 0, 4], [ 2, 6]], [[ 1, 5], [ 3, 7]]] Defined in src/operator/swapaxis.cc:L70
| symbol_name | name of the resulting symbol |
| data | Input array. |
| dim1 | the first axis to be swapped. |
| dim2 | the second axis to be swapped. |
Interchanges two axes of an array.
Examples:: x = [[1, 2, 3]]) swapaxes(x, 0, 1) = [[ 1], [ 2], [ 3]] x = [[[ 0, 1], [ 2, 3]], [[ 4, 5], [ 6, 7]]] // (2,2,2) array swapaxes(x, 0, 2) = [[[ 0, 4], [ 2, 6]], [[ 1, 5], [ 3, 7]]] Defined in src/operator/swapaxis.cc:L70
| data | Input array. |
| dim1 | the first axis to be swapped. |
| dim2 | the second axis to be swapped. |
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Takes elements from an input array along the given axis.
This function slices the input array along a particular axis with the provided Given data tensor of rank r >= 1, and indices tensor of rank q, gather entries dimension of data (by default outer-most one as axis=0) indexed by indices, and in an output tensor of rank q + (r - 1). Examples:: x = [4. 5. 6.] // Trivial case, take the second element along the first axis. take(x, [1]) = [ 5. ] // The other trivial case, axis=-1, take the third element along the first axis take(x, [3], axis=-1, mode='clip') = [ 6. ] x = [[ 1., 2.], [ 3., 4.], [ 5., 6.]] // In this case we will get rows 0 and 1, then 1 and 2. Along axis 0 take(x, [[0,1],[1,2]]) = [[[ 1., 2.], [ 3., 4.]], [[ 3., 4.], [ 5., 6.]]] // In this case we will get rows 0 and 1, then 1 and 2 (calculated by wrapping // Along axis 1 take(x, [[0, 3], [-1, -2]], axis=1, mode='wrap') = [[[ 1., 2.], [ 3., 4.]], [[ 3., 4.], [ 5., 6.]]] Defined in src/operator/tensor/indexing_op.cc:L434
| symbol_name | name of the resulting symbol |
| a | The input array. |
| indices | The indices of the values to be extracted. |
| axis | The axis of input array to be taken.For input tensor of rank r, it could |
| mode | Specify how out-of-bound indices bahave. Default is "clip". "clip" means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis. "wrap" |
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Takes elements from an input array along the given axis.
This function slices the input array along a particular axis with the provided Given data tensor of rank r >= 1, and indices tensor of rank q, gather entries dimension of data (by default outer-most one as axis=0) indexed by indices, and in an output tensor of rank q + (r - 1). Examples:: x = [4. 5. 6.] // Trivial case, take the second element along the first axis. take(x, [1]) = [ 5. ] // The other trivial case, axis=-1, take the third element along the first axis take(x, [3], axis=-1, mode='clip') = [ 6. ] x = [[ 1., 2.], [ 3., 4.], [ 5., 6.]] // In this case we will get rows 0 and 1, then 1 and 2. Along axis 0 take(x, [[0,1],[1,2]]) = [[[ 1., 2.], [ 3., 4.]], [[ 3., 4.], [ 5., 6.]]] // In this case we will get rows 0 and 1, then 1 and 2 (calculated by wrapping // Along axis 1 take(x, [[0, 3], [-1, -2]], axis=1, mode='wrap') = [[[ 1., 2.], [ 3., 4.]], [[ 3., 4.], [ 5., 6.]]] Defined in src/operator/tensor/indexing_op.cc:L434
| a | The input array. |
| indices | The indices of the values to be extracted. |
| axis | The axis of input array to be taken.For input tensor of rank r, it could |
| mode | Specify how out-of-bound indices bahave. Default is "clip". "clip" means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis. "wrap" |
Computes the element-wise tangent of the input array.
The input should be in radians (:math:`2\pi` rad equals 360 degrees). .. math:: tan([0, \pi/4, \pi/2]) = [0, 1, -inf] The storage type of ``tan`` output depends upon the input storage type: - tan(default) = default - tan(row_sparse) = row_sparse - tan(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L83
| symbol_name | name of the resulting symbol |
| data | The input array. |
Computes the element-wise tangent of the input array.
The input should be in radians (:math:`2\pi` rad equals 360 degrees). .. math:: tan([0, \pi/4, \pi/2]) = [0, 1, -inf] The storage type of ``tan`` output depends upon the input storage type: - tan(default) = default - tan(row_sparse) = row_sparse - tan(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L83
| data | The input array. |
Returns the hyperbolic tangent of the input array, computed element-wise.
.. math:: tanh(x) = sinh(x) / cosh(x) The storage type of ``tanh`` output depends upon the input storage type: - tanh(default) = default - tanh(row_sparse) = row_sparse - tanh(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L234
| symbol_name | name of the resulting symbol |
| data | The input array. |
Returns the hyperbolic tangent of the input array, computed element-wise.
.. math:: tanh(x) = sinh(x) / cosh(x) The storage type of ``tanh`` output depends upon the input storage type: - tanh(default) = default - tanh(row_sparse) = row_sparse - tanh(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L234
| data | The input array. |
Repeats the whole array multiple times.
If ``reps`` has length *d*, and input array has dimension of *n*. There are three cases: - **n=d**. Repeat *i*-th dimension of the input by ``reps[i]`` times:: x = [[1, 2], [3, 4]] tile(x, reps=(2,3)) = [[ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.], [ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.]] - **n>d**. ``reps`` is promoted to length *n* by pre-pending 1's to it. Thus for an input shape ``(2,3)``, ``repos=(2,)`` is treated as ``(1,2)``:: tile(x, reps=(2,)) = [[ 1., 2., 1., 2.], [ 3., 4., 3., 4.]] - **n<d**. The input is promoted to be d-dimensional by prepending new axes. So shape ``(2,2)`` array is promoted to ``(1,2,2)`` for 3-D replication:: tile(x, reps=(2,2,3)) = [[[ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.], [ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.]], [[ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.], [ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.]]] Defined in src/operator/tensor/matrix_op.cc:L752
| symbol_name | name of the resulting symbol |
| data | Input data array |
| reps | The number of times for repeating the tensor a. Each dim size of reps must be a positive integer. If reps has length d, the result will have dimension of max(d, a.ndim); If a.ndim < d, a is promoted to be d-dimensional by prepending |
Repeats the whole array multiple times.
If ``reps`` has length *d*, and input array has dimension of *n*. There are three cases: - **n=d**. Repeat *i*-th dimension of the input by ``reps[i]`` times:: x = [[1, 2], [3, 4]] tile(x, reps=(2,3)) = [[ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.], [ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.]] - **n>d**. ``reps`` is promoted to length *n* by pre-pending 1's to it. Thus for an input shape ``(2,3)``, ``repos=(2,)`` is treated as ``(1,2)``:: tile(x, reps=(2,)) = [[ 1., 2., 1., 2.], [ 3., 4., 3., 4.]] - **n<d**. The input is promoted to be d-dimensional by prepending new axes. So shape ``(2,2)`` array is promoted to ``(1,2,2)`` for 3-D replication:: tile(x, reps=(2,2,3)) = [[[ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.], [ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.]], [[ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.], [ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.]]] Defined in src/operator/tensor/matrix_op.cc:L752
| data | Input data array |
| reps | The number of times for repeating the tensor a. Each dim size of reps must be a positive integer. If reps has length d, the result will have dimension of max(d, a.ndim); If a.ndim < d, a is promoted to be d-dimensional by prepending |
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Returns the top k elements in an input array along the given axis. The returned elements will be sorted.
Examples::
x = [[ 0.3, 0.2, 0.4], [ 0.1, 0.3, 0.2]]
// returns an index of the largest element on last axis topk(x) = [[ 2.], [ 1.]]
// returns the value of top-2 largest elements on last axis topk(x, ret_typ='value', k=2) = [[ 0.4, 0.3], [ 0.3, 0.2]]
// returns the value of top-2 smallest elements on last axis topk(x, ret_typ='value', k=2, is_ascend=1) = [[ 0.2 , 0.3], [ 0.1 , 0.2]]
// returns the value of top-2 largest elements on axis 0 topk(x, axis=0, ret_typ='value', k=2) = [[ 0.3, 0.3, 0.4], [ 0.1, 0.2, 0.2]]
// flattens and then returns list of both values and indices topk(x, ret_typ='both', k=2) = [[[ 0.4, 0.3], [ 0.3, 0.2]] , [[ 2., 0.], [
Defined in src/operator/tensor/ordering_op.cc:L64
| symbol_name | name of the resulting symbol |
| data | The input array |
| axis | Axis along which to choose the top k indices. If not given, the flattened |
| k | Number of top elements to select, should be always smaller than or equal to |
| ret_typ | The return type. "value" means to return the top k values, "indices" means to return the indices of the top k values, "mask" means to return a mask array containing 0 and 1. 1 means the top k values. "both" means to return a list of both values and |
| is_ascend | Whether to choose k largest or k smallest elements. Top K largest |
| dtype | DType of the output indices when ret_typ is "indices" or "both". An error |
|
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Returns the top k elements in an input array along the given axis. The returned elements will be sorted.
Examples::
x = [[ 0.3, 0.2, 0.4], [ 0.1, 0.3, 0.2]]
// returns an index of the largest element on last axis topk(x) = [[ 2.], [ 1.]]
// returns the value of top-2 largest elements on last axis topk(x, ret_typ='value', k=2) = [[ 0.4, 0.3], [ 0.3, 0.2]]
// returns the value of top-2 smallest elements on last axis topk(x, ret_typ='value', k=2, is_ascend=1) = [[ 0.2 , 0.3], [ 0.1 , 0.2]]
// returns the value of top-2 largest elements on axis 0 topk(x, axis=0, ret_typ='value', k=2) = [[ 0.3, 0.3, 0.4], [ 0.1, 0.2, 0.2]]
// flattens and then returns list of both values and indices topk(x, ret_typ='both', k=2) = [[[ 0.4, 0.3], [ 0.3, 0.2]] , [[ 2., 0.], [
Defined in src/operator/tensor/ordering_op.cc:L64
| data | The input array |
| axis | Axis along which to choose the top k indices. If not given, the flattened |
| k | Number of top elements to select, should be always smaller than or equal to |
| ret_typ | The return type. "value" means to return the top k values, "indices" means to return the indices of the top k values, "mask" means to return a mask array containing 0 and 1. 1 means the top k values. "both" means to return a list of both values and |
| is_ascend | Whether to choose k largest or k smallest elements. Top K largest |
| dtype | DType of the output indices when ret_typ is "indices" or "both". An error |
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Permutes the dimensions of an array.
Examples:: x = [[ 1, 2], [ 3, 4]] transpose(x) = [[ 1., 3.], [ 2., 4.]] x = [[[ 1., 2.], [ 3., 4.]], [[ 5., 6.], [ 7., 8.]]] transpose(x) = [[[ 1., 5.], [ 3., 7.]], [[ 2., 6.], [ 4., 8.]]] transpose(x, axes=(1,0,2)) = [[[ 1., 2.], [ 5., 6.]], [[ 3., 4.], [ 7., 8.]]] Defined in src/operator/tensor/matrix_op.cc:L311
| symbol_name | name of the resulting symbol |
| data | Source input |
| axes | Target axis order. By default the axes will be inverted. |
Permutes the dimensions of an array.
Examples:: x = [[ 1, 2], [ 3, 4]] transpose(x) = [[ 1., 3.], [ 2., 4.]] x = [[[ 1., 2.], [ 3., 4.]], [[ 5., 6.], [ 7., 8.]]] transpose(x) = [[[ 1., 5.], [ 3., 7.]], [[ 2., 6.], [ 4., 8.]]] transpose(x, axes=(1,0,2)) = [[[ 1., 2.], [ 5., 6.]], [[ 3., 4.], [ 7., 8.]]] Defined in src/operator/tensor/matrix_op.cc:L311
| data | Source input |
| axes | Target axis order. By default the axes will be inverted. |
Return the element-wise truncated value of the input.
The truncated value of the scalar x is the nearest integer i which is closer to zero than x is. In short, the fractional part of the signed number x is Example:: trunc([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1., 1., 1., 2.] The storage type of ``trunc`` output depends upon the input storage type: - trunc(default) = default - trunc(row_sparse) = row_sparse - trunc(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L785
| symbol_name | name of the resulting symbol |
| data | The input array. |
Return the element-wise truncated value of the input.
The truncated value of the scalar x is the nearest integer i which is closer to zero than x is. In short, the fractional part of the signed number x is Example:: trunc([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1., 1., 1., 2.] The storage type of ``trunc`` output depends upon the input storage type: - trunc(default) = default - trunc(row_sparse) = row_sparse - trunc(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L785
| data | The input array. |
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Performs nearest neighbor/bilinear up sampling to inputs.
| symbol_name | name of the resulting symbol |
| data | Array of tensors to upsample |
| scale | Up sampling scale |
| sample_type | upsampling method |
| num_args | Number of inputs to be upsampled. For nearest neighbor upsampling, this can be 1-N; the size of output will be(scale*h_0,scale*w_0) and all other inputs will be upsampled to thesame size. For bilinear upsampling this must be |
| num_filter | Input filter. Only used by bilinear sample_type. |
| multi_input_mode | How to handle multiple input. concat means concatenate upsampled images along the channel dimension. sum means add all images |
| workspace | Tmp workspace for deconvolution (MB) |
|
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Performs nearest neighbor/bilinear up sampling to inputs.
| data | Array of tensors to upsample |
| scale | Up sampling scale |
| sample_type | upsampling method |
| num_args | Number of inputs to be upsampled. For nearest neighbor upsampling, this can be 1-N; the size of output will be(scale*h_0,scale*w_0) and all other inputs will be upsampled to thesame size. For bilinear upsampling this must be |
| num_filter | Input filter. Only used by bilinear sample_type. |
| multi_input_mode | How to handle multiple input. concat means concatenate upsampled images along the channel dimension. sum means add all images |
| workspace | Tmp workspace for deconvolution (MB) |
|
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Return the elements, either from x or y, depending on the condition.
Given three ndarrays, condition, x, and y, return an ndarray with the elements depending on the elements from condition are true or false. x and y must have If condition has the same shape as x, each element in the output array is from corresponding element in the condition is true, and from y if false. If condition does not have the same shape as x, it must be a 1D array whose the same as x's first dimension size. Each row of the output array is from x's if the corresponding element from condition is true, and from y's row if false. Note that all non-zero values are interpreted as ``True`` in condition. Examples:: x = [[1, 2], [3, 4]] y = [[5, 6], [7, 8]] cond = [[0, 1], [-1, 0]] where(cond, x, y) = [[5, 2], [3, 8]] csr_cond = cast_storage(cond, 'csr') where(csr_cond, x, y) = [[5, 2], [3, 8]] Defined in src/operator/tensor/control_flow_op.cc:L57
| symbol_name | name of the resulting symbol |
| condition | condition array |
| x | |
| y |
Return the elements, either from x or y, depending on the condition.
Given three ndarrays, condition, x, and y, return an ndarray with the elements depending on the elements from condition are true or false. x and y must have If condition has the same shape as x, each element in the output array is from corresponding element in the condition is true, and from y if false. If condition does not have the same shape as x, it must be a 1D array whose the same as x's first dimension size. Each row of the output array is from x's if the corresponding element from condition is true, and from y's row if false. Note that all non-zero values are interpreted as ``True`` in condition. Examples:: x = [[1, 2], [3, 4]] y = [[5, 6], [7, 8]] cond = [[0, 1], [-1, 0]] where(cond, x, y) = [[5, 2], [3, 8]] csr_cond = cast_storage(cond, 'csr') where(csr_cond, x, y) = [[5, 2], [3, 8]] Defined in src/operator/tensor/control_flow_op.cc:L57
| condition | condition array |
| x | |
| y |
Return an array of zeros with the same shape, type and storage type as the input array.
The storage type of zeros_like output depends on the storage type of the
Examples::
x = [[ 1., 1., 1.], [ 1., 1., 1.]]
zeros_like(x) = [[ 0., 0., 0.], [ 0., 0., 0.]]
| symbol_name | name of the resulting symbol |
| data | The input |
Return an array of zeros with the same shape, type and storage type as the input array.
The storage type of zeros_like output depends on the storage type of the
Examples::
x = [[ 1., 1., 1.], [ 1., 1., 1.]]
zeros_like(x) = [[ 0., 0., 0.], [ 0., 0., 0.]]
| data | The input |
1.8.11