SymbolBase
Related Doc:
package mxnet
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) + 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:L167
org.apache.mxnet.Symbol
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 following: .. math:: out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[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_mean`` and the inverse of ``data_var``, which are needed for the backward pass. Note that gradient of these 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 sets the channel axis to be the last item in the input shape. Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true, 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`` set to False, the sparse tensors will fallback. Defined in src/operator/nn/batch_norm.cc:L572
org.apache.mxnet.Symbol
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 following: .. math:: out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[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_mean`` and ``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 true, then set ``gamma`` to 1 and its gradient to 0. There's no sparse support for this operator, and it will exhibit problematic behavior if used with sparse tensors. Defined in src/operator/batch_norm_v1.cc:L95
org.apache.mxnet.Symbol
Applies bilinear sampling to input feature map.
Bilinear Sampling is the key of [NIPS2015] \"Spatial Transformer Networks\". The usage of the operator is very similar to remap function in OpenCV,
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}, x_{src})
:math:`x_{dst}`, :math:`y_{dst}` enumerate all spatial locations in :math:`output`, and :math:`G()` denotes the bilinear interpolation kernel.
The out-boundary points will be padded with zeros.The shape of the output will be (data.shape[0], data.shape[1], grid.shape[2], grid.shape[3]).
The operator assumes that :math:`data` has 'NCHW' layout and :math:`grid` has been normalized to [-1, 1].
BilinearSampler often cooperates with GridGenerator which generates sampling grids for BilinearSampler.
GridGenerator supports two kinds of transformation: ``affine`` and ``warp``.
If users want to design a CustomOp to manipulate :math:`grid`, please firstly refer to the code of GridGenerator.
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', target_shape=(4, 4))
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:L256org.apache.mxnet.Symbol
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 contribution 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:L299
org.apache.mxnet.Symbol
Connectionist Temporal Classification Loss. .. note:: The existing alias ``contrib_CTCLoss`` is deprecated. The shapes of the inputs and outputs: - **data**: `(sequence_length, batch_size, alphabet_size)` - **label**: `(batch_size, label_sequence_length)` - **out**: `(batch_size)` The `data` tensor consists of sequences of activation vectors (without applying softmax), with i-th channel in the last dimension corresponding to i-th label for i between 0 and alphabet_size-1 (i.e always 0-indexed). Alphabet size should include one additional value reserved for blank label. When `blank_label` is ``"first"``, the ``0``-th channel is be reserved for activation of blank label, or otherwise if it is "last", ``(alphabet_size-1)``-th channel should be reserved for blank label. ``label`` is an index matrix of integers. When `blank_label` is ``"first"``, the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise, when `blank_label` is ``"last"``, the value `(alphabet_size-1)` is reserved for blank label. If a sequence of labels is shorter than *label_sequence_length*, use the special padding value at the end of the sequence to conform it to the correct length. The padding value is `0` when `blank_label` is ``"first"``, and `-1` otherwise. For example, suppose the vocabulary is `[a, b, c]`, and in one batch we have three sequences 'ba', 'cbb', and 'abac'. When `blank_label` is ``"first"``, we can index the labels as `{'a': 1, 'b': 2, 'c': 3}`, and we reserve the 0-th channel for blank label in data tensor. The resulting `label` tensor should be padded to be:: `[ [2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3] ] When `blank_label` is ``"last"``, we can index the labels as `{'a': 0, 'b': 1, 'c': 2}`, and we reserve the channel index 3 for blank label in data tensor. The resulting `label` tensor should be padded to be:: `[ [1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2] ] ``out`` is a list of CTC loss values, one per example in the batch. See *Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks*, A. Graves *et al*. for more information on the definition and the algorithm. Defined in src/operator/nn/ctc_loss.cc:L100
org.apache.mxnet.Symbol
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:L634
org.apache.mxnet.Symbol
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:L371
org.apache.mxnet.Symbol
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 all 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:L472
org.apache.mxnet.Symbol
This operator is DEPRECATED. Apply convolution to input then add a bias.
org.apache.mxnet.Symbol
Applies correlation to inputs.
The correlation layer performs multiplicative patch comparisons between two feature maps.
Given two multi-channel feature maps :math:`f_{1}, f_{2}`, with :math:`w`, :math:`h`, and :math:`c` being their width, height, and number of channels,
the correlation layer lets the network compare each patch from :math:`f_{1}` with each patch from :math:`f_{2}`.
For now we consider only a single comparison of two patches. The 'correlation' of two patches centered at :math:`x_{1}` in the first map and
: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), f_{2}(x_{2} + 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 with other
data. For this reason, it has no training weights.
Computing :math:`c(x_{1}, x_{2})` involves :math:`c * K^{2}` multiplications. Comparing all patch combinations involves :math:`w^{2}*h^{2}` such computations.
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 :math:`D:=2d+1`,
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 neighborhood
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 :math:`q` denotes the :math:`q^{th}` neighborhood of :math:`x_{i,j}`.
Defined in src/operator/correlation.cc:L198org.apache.mxnet.Symbol
.. 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 h_w to specify the crop height and width, otherwise the second input symbol's size will be used Defined in src/operator/crop.cc:L50
org.apache.mxnet.Symbol
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: http://mxnet.io/faq/new_op.html. Defined in src/operator/custom/custom.cc:L546
org.apache.mxnet.Symbol
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 input to a larger output while preserving the connectivity pattern.
org.apache.mxnet.Symbol
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:L95
org.apache.mxnet.Symbol
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 type) = default - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage Defined in src/operator/tensor/elemwise_sum.cc:L155
org.apache.mxnet.Symbol
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 properties of the words. For example, it has been noted that in the learned embedding spaces, similar words tend 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 weight matrix must be (ip0, op0). By default, if any index mentioned is too large, it is replaced by the index that addresses 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 will be "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad and Adam. Note that by default lazy updates is turned on, which may perform differently from standard updates. For more details, please check the Optimization API at: https://mxnet.incubator.apache.org/api/python/optimization/optimization.html Defined in src/operator/tensor/indexing_op.cc:L519
org.apache.mxnet.Symbol
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 reshapes 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:L291
org.apache.mxnet.Symbol
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 `row_sparse` weight and bias, where the length of `weight.indices` and `bias.indices` must be equal to `num_hidden`. This could be useful for model inference with `row_sparse` weights trained with importance sampling or noise contrastive estimation. To compute linear transformation with 'csr' sparse data, sparse.dot is recommended instead of sparse.FullyConnected. Defined in src/operator/nn/fully_connected.cc:L277
org.apache.mxnet.Symbol
Generates 2D sampling grid for bilinear sampling.
org.apache.mxnet.Symbol
Apply a sparse regularization to the output a sigmoid activation function.
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
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 multidimensional 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 norm.:: 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 position 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, indices=i, axis=dim) ** 2) + eps) -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:L196
org.apache.mxnet.Symbol
Applies local response normalization to the input. The local response normalization layer performs "lateral inhibition" by normalizing over local input regions. If :math:`a_{x,y}^{i}` is the activity of a neuron computed by applying kernel :math:`i` at position :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, i-\frac{n}{2})}^{min(N-1, i+\frac{n}{2})} (a_{x,y}^{j})^{2}}\Bigg)^{\beta}} where the sum runs over :math:`n` "adjacent" kernel maps at the same spatial position, and :math:`N` is the total number of kernels in the layer. Defined in src/operator/nn/lrn.cc:L164
org.apache.mxnet.Symbol
Layer normalization. Normalizes the channels of the input tensor 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 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 + beta Both ``gamma`` and ``beta`` are learnable parameters. Unlike BatchNorm and InstanceNorm, the *mean* and *var* are computed along the channel dimension. 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_mean`` and ``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 the channel axis to be the last item in the input shape. Defined in src/operator/nn/layer_norm.cc:L155
org.apache.mxnet.Symbol
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 * (exp(x) - 1))` where *lambda = 1.0507009873554804934193349852946* and *alpha = 1.6732632423543772848170429916717*. - *leaky*: Leaky ReLU. `y = x > 0 ? x : slope * x` - *prelu*: Parametric ReLU. This is same as *leaky* except that `slope` is learnt during training. - *rrelu*: Randomized ReLU. same as *leaky* but the `slope` is uniformly and randomly chosen from *[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
org.apache.mxnet.Symbol
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` is the corresponding target value, then the squared loss estimated over :math:`n` samples is defined as :math:`\text{SquaredLoss}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_2` .. note:: Use the LinearRegressionOutput as the final output layer of a net. The storage type of ``label`` can be ``default`` or ``csr`` - LinearRegressionOutput(default, default) = default - LinearRegressionOutput(default, csr) = default By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example. The parameter `grad_scale` can be used to change this scale to `grad_scale/m`. Defined in src/operator/regression_output.cc:L92
org.apache.mxnet.Symbol
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 probability.
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 regression outputs of a training example.
The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
Defined in src/operator/regression_output.cc:L152org.apache.mxnet.Symbol
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` is the corresponding target value,
then the mean absolute error (MAE) estimated over :math:`n` samples is defined as
:math:`\text{MAE}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_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 is the number of regression outputs of a training example.
The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
Defined in src/operator/regression_output.cc:L120org.apache.mxnet.Symbol
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 data. For example, if you are a making a cross entropy loss function. Assume ``out`` is the predicted output and ``label`` is the true label, then the cross entropy can be defined as:: 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 we want to combine multiple loss functions. Also we may want to stop some variables' gradients 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
org.apache.mxnet.Symbol
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 padding applied 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`. `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 length ``2*N`` where ``N`` is the number of dimensions of the array. For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values 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
org.apache.mxnet.Symbol
Performs pooling on the input. The shapes for 1-D pooling are - **data** and **out**: *(batch_size, channel, width)* (NCW layout) or *(batch_size, width, channel)* (NWC layout), The shapes for 2-D pooling are - **data** and **out**: *(batch_size, channel, height, width)* (NCHW layout) or *(batch_size, height, width, channel)* (NHWC layout), 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 and output will have shape *(batch_size, channel, depth, height, width)* (NCDHW layout) or *(batch_size, depth, height, width, channel)* (NDHWC layout). Notes on Lp pooling: Lp pooling was first introduced by this paper: https://arxiv.org/pdf/1204.3968.pdf. 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 common value for p is 2. 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:L416
org.apache.mxnet.Symbol
This operator is DEPRECATED. Perform pooling on the input. The shapes for 2-D pooling is - **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 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
org.apache.mxnet.Symbol
Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are implemented, with both multi-layer and bidirectional support. When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use pseudo-float16 precision (float32 math with float16 I/O) precision in order to use Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups. **Vanilla RNN** Applies a single-gate recurrent layer to input X. Two kinds of activation function are supported: 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 = \tanh(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. http://www.bioinf.jku.at/publications/older/2604.pdf .. math:: \begin{array}{ll} i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\ f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \\ o_t = \mathrm{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 * \tanh(c_t) \end{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 CUDNN. .. math:: \begin{array}{ll} r_t = \mathrm{sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\ z_t = \mathrm{sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\ n_t = \tanh(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)} \\ \end{array} Defined in src/operator/rnn.cc:L690
org.apache.mxnet.Symbol
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 fixed and region of interest is a parameter. Its purpose is to perform max pooling on the inputs of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a neural-net 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 `rois`, 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 fixed size output indicated by a `pooled_size` parameter. batch_size will change to the number of region 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
org.apache.mxnet.Symbol
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 new shape. The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array. 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, -3, -4}. The significance of each is explained below: - ``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 input dimensions 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 the output dimension. 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 to -4 in shape (can contain -1). 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 from right to left. Example:: - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5) - with reverse=1, output shape will be (50,4). Defined in src/operator/tensor/matrix_op.cc:L202
org.apache.mxnet.Symbol
Computes support vector machine based transformation of the input. This tutorial demonstrates using SVM as output layer for classification instead of softmax: https://github.com/dmlc/mxnet/tree/master/example/svm_mnist.
org.apache.mxnet.Symbol
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 (n-1)-dimensional array of the form [batch_size, other_feature_dims]. Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` 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. .. 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:L100
org.apache.mxnet.Symbol
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 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 [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 and 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:L186
org.apache.mxnet.Symbol
Reverses the elements of each sequence. This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] 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 [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. 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:L122
org.apache.mxnet.Symbol
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 arrays. **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] == num_outputs``. Example:: z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1) z = `[ [ 1.] [ 2.] ] `[ [ 3.] [ 4.] ] `[ [ 5.] [ 6.] ] z[0].shape = (2 ,1 ) Defined in src/operator/slice_channel.cc:L107
org.apache.mxnet.Symbol
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 output. - 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 \log(\text{output}_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 instance in the input array. For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The size is :math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters `preserve_shape` and `multi_output` to specify the way to compute softmax: - By default, `preserve_shape` is ``false``. This operator will reshape the input array into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the softmax function for each row in the reshaped array, and afterwards reshape it back to the original shape :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 output array is computed. 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 instances with a particular label to be ignored during backward propagation. **This has no effect when 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 ignore_label. - The parameter `grad_scale` can be used to rescale the gradient, which is often used to give each loss function different weights. - This operator also supports various ways to normalize the gradient by `normalization`, The `normalization` is applied if softmax output has different shape than the labels. 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 ignored. Defined in src/operator/softmax_output.cc:L230
org.apache.mxnet.Symbol
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 instance in the batch. This is the default mode. If `mode` = ``channel``, this operator will compute a k-class softmax at each position of each instance, where `k` = ``num_channel``. This mode can only be used when the input array 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 9.73605454e-01] [ 6.56221947e-03 5.95310994e-04 9.73919690e-01 1.78379621e-02 1.08472735e-03] ] Defined in src/operator/nn/softmax_activation.cc:L59
org.apache.mxnet.Symbol
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 output. - 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 \log(\text{output}_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 instance in the input array. For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The size is :math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters `preserve_shape` and `multi_output` to specify the way to compute softmax: - By default, `preserve_shape` is ``false``. This operator will reshape the input array into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the softmax function for each row in the reshaped array, and afterwards reshape it back to the original shape :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 output array is computed. 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 instances with a particular label to be ignored during backward propagation. **This has no effect when 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 ignore_label. - The parameter `grad_scale` can be used to rescale the gradient, which is often used to give each loss function different weights. - This operator also supports various ways to normalize the gradient by `normalization`, The `normalization` is applied if softmax output has different shape than the labels. 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 ignored. Defined in src/operator/softmax_output.cc:L230
org.apache.mxnet.Symbol
Applies a spatial transformer to input feature map.
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
Upsamples the given input data. Two algorithms (``sample_type``) are available for upsampling: - Nearest Neighbor - Bilinear **Nearest Neighbor Upsampling** Input data is expected to be NCHW. Example:: x = `[ [`[ [1. 1. 1.] [1. 1. 1.] [1. 1. 1.] ] ] ] UpSampling(x, scale=2, sample_type='nearest') = `[ [`[ [1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1.] ] ] ] **Bilinear Upsampling** Uses `deconvolution` algorithm under the hood. You need provide both input data and the kernel. Input data is expected to be NCHW. `num_filter` is expected to be same as the number of channels. Example:: x = `[ [`[ [1. 1. 1.] [1. 1. 1.] [1. 1. 1.] ] ] ] w = `[ [`[ [1. 1. 1. 1.] [1. 1. 1. 1.] [1. 1. 1. 1.] [1. 1. 1. 1.] ] ] ] UpSampling(x, w, scale=2, sample_type='bilinear', num_filter=1) = `[ [`[ [1. 2. 2. 2. 2. 1.] [2. 4. 4. 4. 4. 2.] [2. 4. 4. 4. 4. 2.] [2. 4. 4. 4. 4. 2.] [2. 4. 4. 4. 4. 2.] [1. 2. 2. 2. 2. 1.] ] ] ] Defined in src/operator/nn/upsampling.cc:L173
org.apache.mxnet.Symbol
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:L708
org.apache.mxnet.Symbol
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, v are 1st and 2nd order moment estimates (mean and variance). .. math:: g_t = \nabla J(W_{t-1})\\ m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\ v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\ W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon } 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 the storage 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 and v):: 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:L686
org.apache.mxnet.Symbol
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 type) = default - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage Defined in src/operator/tensor/elemwise_sum.cc:L155
org.apache.mxnet.Symbol
Check if all the float numbers in the array are finite (used for AMP) Defined in src/operator/contrib/all_finite.cc:L101
org.apache.mxnet.Symbol
Cast function between low precision float/FP32 used by AMP. It casts only between low precision float/FP32 and does not do anything for other types. Defined in src/operator/tensor/amp_cast.cc:L37
org.apache.mxnet.Symbol
Cast function used by AMP, that casts its inputs to the common widest type. It casts only between low precision float/FP32 and does not do anything for other types. Defined in src/operator/tensor/amp_cast.cc:L71
org.apache.mxnet.Symbol
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:L179
org.apache.mxnet.Symbol
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:L320org.apache.mxnet.Symbol
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:L160
org.apache.mxnet.Symbol
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: - arcsinh(default) = default - arcsinh(row_sparse) = row_sparse - arcsinh(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L306
org.apache.mxnet.Symbol
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:L200
org.apache.mxnet.Symbol
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: - arctanh(default) = default - arctanh(row_sparse) = row_sparse - arctanh(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L337
org.apache.mxnet.Symbol
Returns indices of the maximum values along an axis. In the case of multiple occurrences of maximum values, the indices corresponding to the first occurrence 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
org.apache.mxnet.Symbol
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 corresponding to the first occurrence 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
org.apache.mxnet.Symbol
Returns indices of the minimum values along an axis. In the case of multiple occurrences of minimum values, the indices corresponding to the first occurrence 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
org.apache.mxnet.Symbol
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 indices having same shape 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
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
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 result will be 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:L753
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
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:L238
org.apache.mxnet.Symbol
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:L238
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
Returns the result of element-wise **equal to** (==) comparison operation with broadcasting. 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
org.apache.mxnet.Symbol
Returns the result of element-wise **greater than** (>) comparison operation with broadcasting. 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
org.apache.mxnet.Symbol
Returns the result of element-wise **greater than or equal to** (>=) comparison operation with broadcasting. 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
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
Returns the result of element-wise **lesser than** (<) comparison operation with broadcasting. 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
org.apache.mxnet.Symbol
Returns the result of element-wise **lesser than or equal to** (<=) comparison operation with broadcasting. 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
org.apache.mxnet.Symbol
Broadcasts lhs to have the same shape as rhs. Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations with arrays of different shapes efficiently without creating multiple copies of arrays. Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_ for more explanation. 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.] ]) broadcast_like([9], [1,2,3,4,5], lhs_axes=(0,), rhs_axes=(-1,)) = [9,9,9,9,9] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L315
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
Returns element-wise maximum of the input arrays with broadcasting. This function compares two input arrays and returns a new array having the element-wise maxima. 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
org.apache.mxnet.Symbol
Returns element-wise minimum of the input arrays with broadcasting. This function compares two input arrays and returns a new array having the element-wise minima. 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
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
Returns the result of element-wise **not equal to** (!=) comparison operation with broadcasting. 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
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
Returns result of first array elements raised to powers from second array, element-wise with broadcasting. 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
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
Broadcasts the input array to a new shape. Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations with arrays of different shapes efficiently without creating multiple copies of arrays. Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_ for more explanation. 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 means copy the original value. 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:L262
org.apache.mxnet.Symbol
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:L634
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
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:L950
org.apache.mxnet.Symbol
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:L786
org.apache.mxnet.Symbol
Picks elements from an input array according to the input indices along the given axis. Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be 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 that addresses 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:L154
org.apache.mxnet.Symbol
Clips (limits) the values in an array.
Given an interval, values outside the interval are clipped to the interval edges.
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 a_min, a_max \
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:L723org.apache.mxnet.Symbol
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:L371
org.apache.mxnet.Symbol
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:L89
org.apache.mxnet.Symbol
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:L272
org.apache.mxnet.Symbol
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:L506
org.apache.mxnet.Symbol
Connectionist Temporal Classification Loss. .. note:: The existing alias ``contrib_CTCLoss`` is deprecated. The shapes of the inputs and outputs: - **data**: `(sequence_length, batch_size, alphabet_size)` - **label**: `(batch_size, label_sequence_length)` - **out**: `(batch_size)` The `data` tensor consists of sequences of activation vectors (without applying softmax), with i-th channel in the last dimension corresponding to i-th label for i between 0 and alphabet_size-1 (i.e always 0-indexed). Alphabet size should include one additional value reserved for blank label. When `blank_label` is ``"first"``, the ``0``-th channel is be reserved for activation of blank label, or otherwise if it is "last", ``(alphabet_size-1)``-th channel should be reserved for blank label. ``label`` is an index matrix of integers. When `blank_label` is ``"first"``, the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise, when `blank_label` is ``"last"``, the value `(alphabet_size-1)` is reserved for blank label. If a sequence of labels is shorter than *label_sequence_length*, use the special padding value at the end of the sequence to conform it to the correct length. The padding value is `0` when `blank_label` is ``"first"``, and `-1` otherwise. For example, suppose the vocabulary is `[a, b, c]`, and in one batch we have three sequences 'ba', 'cbb', and 'abac'. When `blank_label` is ``"first"``, we can index the labels as `{'a': 1, 'b': 2, 'c': 3}`, and we reserve the 0-th channel for blank label in data tensor. The resulting `label` tensor should be padded to be:: `[ [2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3] ] When `blank_label` is ``"last"``, we can index the labels as `{'a': 0, 'b': 1, 'c': 2}`, and we reserve the channel index 3 for blank label in data tensor. The resulting `label` tensor should be padded to be:: `[ [1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2] ] ``out`` is a list of CTC loss values, one per example in the batch. See *Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks*, A. Graves *et al*. for more information on the definition and the algorithm. Defined in src/operator/nn/ctc_loss.cc:L100
org.apache.mxnet.Symbol
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:L219
org.apache.mxnet.Symbol
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 spatial blocks to height and width dimension. The reverse of this operation is ``space_to_depth``. .. math:: \begin{gather*} x \prime = reshape(x, [N, block\_size, block\_size, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \\ x \prime \prime = transpose(x \prime, [0, 3, 4, 1, 5, 2]) \\ y = reshape(x \prime \prime, [N, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \end{gather*} where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width] and :math:`y` is the output tensor of layout :math:`[N, C / (block\_size ^ 2), H * block\_size, W * block\_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] ] ] ] 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:L1050
org.apache.mxnet.Symbol
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 elements are zero. - N-D arrays: extracts the diagonals of the sub-arrays with axes specified by ``axis1`` and ``axis2``. The output shape would be decided by removing the axes numbered ``axis1`` and ``axis2`` from the input shape and appending to the result a new axis with the size of the diagonals in question. For example, when the input shape is `(2, 3, 4, 5)`, ``axis1`` and ``axis2`` are 0 and 2 respectively and ``k`` is 0, the resulting shape would be `(3, 5, 2)`. 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] ] x = `[ `[ [1, 2], [3, 4] ], `[ [5, 6], [7, 8] ] ] diag(x) = `[ [1, 7], [2, 8] ] diag(x, k=1) = `[ [3], [4] ] diag(x, axis1=-2, axis2=-1) = `[ [1, 4], [5, 8] ] Defined in src/operator/tensor/diag_op.cc:L87
org.apache.mxnet.Symbol
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 `(k,r,s)`, the 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, transpose option and forward_stype option for output storage type. Implemented sparse operations include: - dot(default, default, transpose_a=True/False, transpose_b=True/False) = default - 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 of the 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 will be "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad and Adam. Note that by default lazy updates is turned on, which may perform differently from standard updates. For more details, please check the Optimization API at: https://mxnet.incubator.apache.org/api/python/optimization/optimization.html Defined in src/operator/tensor/dot.cc:L77
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
Divides arguments element-wise.
The storage type of ``elemwise_div`` output is always denseorg.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
Returns element-wise gauss error function of the input. Example:: erf([0, -1., 10.]) = [0., -0.8427, 1.] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L964
org.apache.mxnet.Symbol
Returns element-wise inverse gauss error function of the input. Example:: erfinv([0, 0.5., -1.]) = [0., 0.4769, -inf] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L985
org.apache.mxnet.Symbol
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:L1044
org.apache.mxnet.Symbol
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:L416
org.apache.mxnet.Symbol
Returns ``exp(x) - 1`` computed element-wise on the input. This function provides greater precision than ``exp(x) - 1`` for small values of ``x``. 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:L1189
org.apache.mxnet.Symbol
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 assume rhs uses 0-based index.
org.apache.mxnet.Symbol
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: - fix(default) = default - fix(row_sparse) = row_sparse - fix(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L843
org.apache.mxnet.Symbol
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 reshapes 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:L291
org.apache.mxnet.Symbol
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:L898
org.apache.mxnet.Symbol
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:L805
org.apache.mxnet.Symbol
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 = \nabla J(W_{t-1})\\ v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\ d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon) \sigma_t = d_t - \beta_1 d_{t-1} z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1} W_t = - \frac{ z_t }{ d_t } Defined in src/operator/optimizer_op.cc:L638
org.apache.mxnet.Symbol
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 / learning_rate n += rescaled_grad**2 w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1) 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 and n):: 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) - sqrt(n[row])) * weight[row] / learning_rate n[row] += rescaled_grad[row]**2 w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1) Defined in src/operator/optimizer_op.cc:L874
org.apache.mxnet.Symbol
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 denseorg.apache.mxnet.Symbol
Returns element-wise log of the absolute value of the gamma function \
of the input.
The storage type of ``gammaln`` output is always denseorg.apache.mxnet.Symbol
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, ..., X_{N-1})`, where `M <= N`. If `M == 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, ..., y_{K-1}], ..., 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] ]
org.apache.mxnet.Symbol
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:L133
org.apache.mxnet.Symbol
Returns a copy of the input.
From:src/operator/tensor/elemwise_unary_op_basic.cc:218org.apache.mxnet.Symbol
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:L108org.apache.mxnet.Symbol
Extracts the diagonal entries of a square matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, then *A* represents a single square matrix which diagonal elements get extracted as a 1-dimensional tensor. If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted diagonals are returned as an *n-1*-dimensional tensor. .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix diagonal extraction A = `[ [1.0, 2.0], [3.0, 4.0] ] extractdiag(A) = [1.0, 4.0] extractdiag(A, 1) = [2.0] // Batch matrix diagonal extraction A = `[ `[ [1.0, 2.0], [3.0, 4.0] ], `[ [5.0, 6.0], [7.0, 8.0] ] ] extractdiag(A) = `[ [1.0, 4.0], [5.0, 8.0] ] Defined in src/operator/tensor/la_op.cc:L495
org.apache.mxnet.Symbol
Extracts a triangular sub-matrix from a square matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, then *A* represents a single square matrix from which a triangular sub-matrix is extracted as a 1-dimensional tensor. If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted triangular sub-matrices are returned as an *n-1*-dimensional tensor. The *offset* and *lower* parameters determine the triangle to be extracted: - When *offset = 0* either the lower or upper triangle with respect to the main diagonal is extracted depending on the value of parameter *lower*. - When *offset = k > 0* the upper triangle with respect to the k-th diagonal above the main diagonal is extracted. - When *offset = k < 0* the lower triangle with respect to the k-th diagonal below the main diagonal is extracted. .. note:: The operator supports float32 and float64 data types only. Examples:: // Single triagonal extraction A = `[ [1.0, 2.0], [3.0, 4.0] ] extracttrian(A) = [1.0, 3.0, 4.0] extracttrian(A, lower=False) = [1.0, 2.0, 4.0] extracttrian(A, 1) = [2.0] extracttrian(A, -1) = [3.0] // Batch triagonal extraction A = `[ `[ [1.0, 2.0], [3.0, 4.0] ], `[ [5.0, 6.0], [7.0, 8.0] ] ] extracttrian(A) = `[ [1.0, 3.0, 4.0], [5.0, 7.0, 8.0] ] Defined in src/operator/tensor/la_op.cc:L605
org.apache.mxnet.Symbol
LQ factorization for general matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, we compute the LQ factorization (LAPACK *gelqf*, followed by *orglq*). *A* must have shape *(x, y)* with *x <= y*, and must have full rank *=x*. The LQ factorization consists of *L* with shape *(x, x)* and *Q* with shape *(x, y)*, so that: *A* = *L* \* *Q* Here, *L* is lower triangular (upper triangle equal to zero) with nonzero diagonal, and *Q* is row-orthonormal, meaning that *Q* \* *Q*\ :sup:`T` is equal to the identity matrix of shape *(x, x)*. If *n>2*, *gelqf* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: // Single LQ factorization A = `[ [1., 2., 3.], [4., 5., 6.] ] Q, L = gelqf(A) Q = `[ [-0.26726124, -0.53452248, -0.80178373], [0.87287156, 0.21821789, -0.43643578] ] L = `[ [-3.74165739, 0.], [-8.55235974, 1.96396101] ] // Batch LQ factorization A = `[ `[ [1., 2., 3.], [4., 5., 6.] ], `[ [7., 8., 9.], [10., 11., 12.] ] ] Q, L = gelqf(A) Q = `[ `[ [-0.26726124, -0.53452248, -0.80178373], [0.87287156, 0.21821789, -0.43643578] ], `[ [-0.50257071, -0.57436653, -0.64616234], [0.7620735, 0.05862104, -0.64483142] ] ] L = `[ `[ [-3.74165739, 0.], [-8.55235974, 1.96396101] ], `[ [-13.92838828, 0.], [-19.09768702, 0.52758934] ] ] Defined in src/operator/tensor/la_op.cc:L798
org.apache.mxnet.Symbol
Performs general matrix multiplication and accumulation. Input are tensors *A*, *B*, *C*, each of dimension *n >= 2* and having the same shape on the leading *n-2* dimensions. If *n=2*, the BLAS3 function *gemm* is performed: *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*) + *beta* \* *C* Here, *alpha* and *beta* are scalar parameters, and *op()* is either the identity or matrix transposition (depending on *transpose_a*, *transpose_b*). If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis* parameter. By default, the trailing two dimensions will be used for matrix encoding. For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes calls. For example let *A*, *B*, *C* be 5 dimensional tensors. Then gemm(*A*, *B*, *C*, axis=1) is equivalent to the following without the overhead of the additional swapaxis operations:: A1 = swapaxes(A, dim1=1, dim2=3) B1 = swapaxes(B, dim1=1, dim2=3) C = swapaxes(C, dim1=1, dim2=3) C = gemm(A1, B1, C) C = swapaxis(C, dim1=1, dim2=3) When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use pseudo-float16 precision (float32 math with float16 I/O) precision in order to use Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups. .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix multiply-add A = `[ [1.0, 1.0], [1.0, 1.0] ] B = `[ [1.0, 1.0], [1.0, 1.0], [1.0, 1.0] ] C = `[ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ] gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0) = `[ [14.0, 14.0, 14.0], [14.0, 14.0, 14.0] ] // Batch matrix multiply-add A = `[ `[ [1.0, 1.0] ], `[ [0.1, 0.1] ] ] B = `[ `[ [1.0, 1.0] ], `[ [0.1, 0.1] ] ] C = `[ `[ [10.0] ], `[ [0.01] ] ] gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0) = `[ `[ [104.0] ], `[ [0.14] ] ] Defined in src/operator/tensor/la_op.cc:L89
org.apache.mxnet.Symbol
Performs general matrix multiplication. Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape on the leading *n-2* dimensions. If *n=2*, the BLAS3 function *gemm* is performed: *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*) Here *alpha* is a scalar parameter and *op()* is either the identity or the matrix transposition (depending on *transpose_a*, *transpose_b*). If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis* parameter. By default, the trailing two dimensions will be used for matrix encoding. For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes calls. For example let *A*, *B* be 5 dimensional tensors. Then gemm(*A*, *B*, axis=1) is equivalent to the following without the overhead of the additional swapaxis operations:: A1 = swapaxes(A, dim1=1, dim2=3) B1 = swapaxes(B, dim1=1, dim2=3) C = gemm2(A1, B1) C = swapaxis(C, dim1=1, dim2=3) When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use pseudo-float16 precision (float32 math with float16 I/O) precision in order to use Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups. .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix multiply A = `[ [1.0, 1.0], [1.0, 1.0] ] B = `[ [1.0, 1.0], [1.0, 1.0], [1.0, 1.0] ] gemm2(A, B, transpose_b=True, alpha=2.0) = `[ [4.0, 4.0, 4.0], [4.0, 4.0, 4.0] ] // Batch matrix multiply A = `[ `[ [1.0, 1.0] ], `[ [0.1, 0.1] ] ] B = `[ `[ [1.0, 1.0] ], `[ [0.1, 0.1] ] ] gemm2(A, B, transpose_b=True, alpha=2.0) = `[ `[ [4.0] ], `[ [0.04 ] ] ] Defined in src/operator/tensor/la_op.cc:L163
org.apache.mxnet.Symbol
Compute the inverse of a matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, *A* is a square matrix. We compute: *out* = *A*\ :sup:`-1` If *n>2*, *inverse* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix inversion A = `[ [1., 4.], [2., 3.] ] inverse(A) = `[ [-0.6, 0.8], [0.4, -0.2] ] // Batch matrix inversion A = `[ `[ [1., 4.], [2., 3.] ], `[ [1., 3.], [2., 4.] ] ] inverse(A) = `[ `[ [-0.6, 0.8], [0.4, -0.2] ], `[ [-2., 1.5], [1., -0.5] ] ] Defined in src/operator/tensor/la_op.cc:L917
org.apache.mxnet.Symbol
Constructs a square matrix with the input as diagonal. Input is a tensor *A* of dimension *n >= 1*. If *n=1*, then *A* represents the diagonal entries of a single square matrix. This matrix will be returned as a 2-dimensional tensor. If *n>1*, then *A* represents a batch of diagonals of square matrices. The batch of diagonal matrices will be returned as an *n+1*-dimensional tensor. .. note:: The operator supports float32 and float64 data types only. Examples:: // Single diagonal matrix construction A = [1.0, 2.0] makediag(A) = `[ [1.0, 0.0], [0.0, 2.0] ] makediag(A, 1) = `[ [0.0, 1.0, 0.0], [0.0, 0.0, 2.0], [0.0, 0.0, 0.0] ] // Batch diagonal matrix construction A = `[ [1.0, 2.0], [3.0, 4.0] ] makediag(A) = `[ `[ [1.0, 0.0], [0.0, 2.0] ], `[ [3.0, 0.0], [0.0, 4.0] ] ] Defined in src/operator/tensor/la_op.cc:L547
org.apache.mxnet.Symbol
Constructs a square matrix with the input representing a specific triangular sub-matrix. This is basically the inverse of *linalg.extracttrian*. Input is a tensor *A* of dimension *n >= 1*. If *n=1*, then *A* represents the entries of a triangular matrix which is lower triangular if *offset<0* or *offset=0*, *lower=true*. The resulting matrix is derived by first constructing the square matrix with the entries outside the triangle set to zero and then adding *offset*-times an additional diagonal with zero entries to the square matrix. If *n>1*, then *A* represents a batch of triangular sub-matrices. The batch of corresponding square matrices is returned as an *n+1*-dimensional tensor. .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix construction A = [1.0, 2.0, 3.0] maketrian(A) = `[ [1.0, 0.0], [2.0, 3.0] ] maketrian(A, lower=false) = `[ [1.0, 2.0], [0.0, 3.0] ] maketrian(A, offset=1) = `[ [0.0, 1.0, 2.0], [0.0, 0.0, 3.0], [0.0, 0.0, 0.0] ] maketrian(A, offset=-1) = `[ [0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [2.0, 3.0, 0.0] ] // Batch matrix construction A = `[ [1.0, 2.0, 3.0], [4.0, 5.0, 6.0] ] maketrian(A) = `[ `[ [1.0, 0.0], [2.0, 3.0] ], `[ [4.0, 0.0], [5.0, 6.0] ] ] maketrian(A, offset=1) = `[ `[ [0.0, 1.0, 2.0], [0.0, 0.0, 3.0], [0.0, 0.0, 0.0] ], `[ [0.0, 4.0, 5.0], [0.0, 0.0, 6.0], [0.0, 0.0, 0.0] ] ] Defined in src/operator/tensor/la_op.cc:L673
org.apache.mxnet.Symbol
Performs Cholesky factorization of a symmetric positive-definite matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, the Cholesky factor *B* of the symmetric, positive definite matrix *A* is computed. *B* is triangular (entries of upper or lower triangle are all zero), has positive diagonal entries, and: *A* = *B* \* *B*\ :sup:`T` if *lower* = *true* *A* = *B*\ :sup:`T` \* *B* if *lower* = *false* If *n>2*, *potrf* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix factorization A = `[ [4.0, 1.0], [1.0, 4.25] ] potrf(A) = `[ [2.0, 0], [0.5, 2.0] ] // Batch matrix factorization A = `[ `[ [4.0, 1.0], [1.0, 4.25] ], `[ [16.0, 4.0], [4.0, 17.0] ] ] potrf(A) = `[ `[ [2.0, 0], [0.5, 2.0] ], `[ [4.0, 0], [1.0, 4.0] ] ] Defined in src/operator/tensor/la_op.cc:L214
org.apache.mxnet.Symbol
Performs matrix inversion from a Cholesky factorization. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, *A* is a triangular matrix (entries of upper or lower triangle are all zero) with positive diagonal. We compute: *out* = *A*\ :sup:`-T` \* *A*\ :sup:`-1` if *lower* = *true* *out* = *A*\ :sup:`-1` \* *A*\ :sup:`-T` if *lower* = *false* In other words, if *A* is the Cholesky factor of a symmetric positive definite matrix *B* (obtained by *potrf*), then *out* = *B*\ :sup:`-1` If *n>2*, *potri* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. .. note:: Use this operator only if you are certain you need the inverse of *B*, and cannot use the Cholesky factor *A* (*potrf*), together with backsubstitution (*trsm*). The latter is numerically much safer, and also cheaper. Examples:: // Single matrix inverse A = `[ [2.0, 0], [0.5, 2.0] ] potri(A) = `[ [0.26563, -0.0625], [-0.0625, 0.25] ] // Batch matrix inverse A = `[ `[ [2.0, 0], [0.5, 2.0] ], `[ [4.0, 0], [1.0, 4.0] ] ] potri(A) = `[ `[ [0.26563, -0.0625], [-0.0625, 0.25] ], `[ [0.06641, -0.01562], [-0.01562, 0,0625] ] ] Defined in src/operator/tensor/la_op.cc:L275
org.apache.mxnet.Symbol
Computes the sum of the logarithms of the diagonal elements of a square matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, *A* must be square with positive diagonal entries. We sum the natural logarithms of the diagonal elements, the result has shape (1,). If *n>2*, *sumlogdiag* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix reduction A = `[ [1.0, 1.0], [1.0, 7.0] ] sumlogdiag(A) = [1.9459] // Batch matrix reduction A = `[ `[ [1.0, 1.0], [1.0, 7.0] ], `[ [3.0, 0], [0, 17.0] ] ] sumlogdiag(A) = [1.9459, 3.9318] Defined in src/operator/tensor/la_op.cc:L445
org.apache.mxnet.Symbol
Multiplication of matrix with its transpose. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, the operator performs the BLAS3 function *syrk*: *out* = *alpha* \* *A* \* *A*\ :sup:`T` if *transpose=False*, or *out* = *alpha* \* *A*\ :sup:`T` \ \* *A* if *transpose=True*. If *n>2*, *syrk* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix multiply A = `[ [1., 2., 3.], [4., 5., 6.] ] syrk(A, alpha=1., transpose=False) = `[ [14., 32.], [32., 77.] ] syrk(A, alpha=1., transpose=True) = `[ [17., 22., 27.], [22., 29., 36.], [27., 36., 45.] ] // Batch matrix multiply A = `[ `[ [1., 1.] ], `[ [0.1, 0.1] ] ] syrk(A, alpha=2., transpose=False) = `[ `[ [4.] ], `[ [0.04] ] ] Defined in src/operator/tensor/la_op.cc:L730
org.apache.mxnet.Symbol
Performs multiplication with a lower triangular matrix. Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape on the leading *n-2* dimensions. If *n=2*, *A* must be triangular. The operator performs the BLAS3 function *trmm*: *out* = *alpha* \* *op*\ (*A*) \* *B* if *rightside=False*, or *out* = *alpha* \* *B* \* *op*\ (*A*) if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the identity or the matrix transposition (depending on *transpose*). If *n>2*, *trmm* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: // Single triangular matrix multiply A = `[ [1.0, 0], [1.0, 1.0] ] B = `[ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ] trmm(A, B, alpha=2.0) = `[ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ] // Batch triangular matrix multiply A = `[ `[ [1.0, 0], [1.0, 1.0] ], `[ [1.0, 0], [1.0, 1.0] ] ] B = `[ `[ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ], `[ [0.5, 0.5, 0.5], [0.5, 0.5, 0.5] ] ] trmm(A, B, alpha=2.0) = `[ `[ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ], `[ [1.0, 1.0, 1.0], [2.0, 2.0, 2.0] ] ] Defined in src/operator/tensor/la_op.cc:L333
org.apache.mxnet.Symbol
Solves matrix equation involving a lower triangular matrix. Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape on the leading *n-2* dimensions. If *n=2*, *A* must be triangular. The operator performs the BLAS3 function *trsm*, solving for *out* in: *op*\ (*A*) \* *out* = *alpha* \* *B* if *rightside=False*, or *out* \* *op*\ (*A*) = *alpha* \* *B* if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the identity or the matrix transposition (depending on *transpose*). If *n>2*, *trsm* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix solve A = `[ [1.0, 0], [1.0, 1.0] ] B = `[ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ] trsm(A, B, alpha=0.5) = `[ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ] // Batch matrix solve A = `[ `[ [1.0, 0], [1.0, 1.0] ], `[ [1.0, 0], [1.0, 1.0] ] ] B = `[ `[ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ], `[ [4.0, 4.0, 4.0], [8.0, 8.0, 8.0] ] ] trsm(A, B, alpha=0.5) = `[ `[ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ], `[ [2.0, 2.0, 2.0], [2.0, 2.0, 2.0] ] ] Defined in src/operator/tensor/la_op.cc:L396
org.apache.mxnet.Symbol
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:L1057org.apache.mxnet.Symbol
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:L1074
org.apache.mxnet.Symbol
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:L1171
org.apache.mxnet.Symbol
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:L1086
org.apache.mxnet.Symbol
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)
org.apache.mxnet.Symbol
Returns the result of logical NOT (!) function Example: logical_not([-2., 0., 1.]) = [0., 1., 0.]
org.apache.mxnet.Symbol
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 data. For example, if you are a making a cross entropy loss function. Assume ``out`` is the predicted output and ``label`` is the true label, then the cross entropy can be defined as:: 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 we want to combine multiple loss functions. Also we may want to stop some variables' gradients 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:L332
org.apache.mxnet.Symbol
Computes the max of array elements over given axes. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191
org.apache.mxnet.Symbol
Computes the max of array elements over given axes. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191
org.apache.mxnet.Symbol
Computes the mean of array elements over given axes. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L132
org.apache.mxnet.Symbol
Computes the min of array elements over given axes. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205
org.apache.mxnet.Symbol
Computes the min of array elements over given axes. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205
org.apache.mxnet.Symbol
Calculate the mean and variance of `data`. The mean and variance are calculated by aggregating the contents of data across axes. If x is 1-D and axes = [0] this is just the mean and variance of a vector. Example: x = `[ [1, 2, 3], [4, 5, 6] ] mean, var = moments(data=x, axes=[0]) mean = [2.5, 3.5, 4.5] var = [2.25, 2.25, 2.25] mean, var = moments(data=x, axes=[1]) mean = [2.0, 5.0] var = [0.66666667, 0.66666667] mean, var = moments(data=x, axis=[0, 1]) mean = [3.5] var = [2.9166667] Defined in src/operator/nn/moments.cc:L54
org.apache.mxnet.Symbol
Update function for multi-precision Nesterov Accelerated Gradient( NAG) optimizer.
Defined in src/operator/optimizer_op.cc:L743org.apache.mxnet.Symbol
Updater function for multi-precision sgd optimizerorg.apache.mxnet.Symbol
Updater function for multi-precision sgd optimizerorg.apache.mxnet.Symbol
Check if all the float numbers in all the arrays are finite (used for AMP) Defined in src/operator/contrib/all_finite.cc:L133
org.apache.mxnet.Symbol
Momentum update function for multi-precision Stochastic Gradient Descent (SGD) optimizer. Momentum update has better convergence rates on neural networks. Mathematically it looks 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 each epoch. Defined in src/operator/optimizer_op.cc:L470
org.apache.mxnet.Symbol
Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.
It updates the weights using::
weight = weight - learning_rate * (gradient + wd * weight)
Defined in src/operator/optimizer_op.cc:L415org.apache.mxnet.Symbol
Momentum update function for Stochastic Gradient Descent (SGD) optimizer. Momentum update has better convergence rates on neural networks. Mathematically it looks 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 each epoch. Defined in src/operator/optimizer_op.cc:L372
org.apache.mxnet.Symbol
Update function for Stochastic Gradient Descent (SDG) optimizer.
It updates the weights using::
weight = weight - learning_rate * (gradient + wd * weight)
Defined in src/operator/optimizer_op.cc:L327org.apache.mxnet.Symbol
Update function for Nesterov Accelerated Gradient( NAG) optimizer. It updates the weights using the following formula, .. math:: v_t = \gamma v_{t-1} + \eta * \nabla J(W_{t-1} - \gamma v_{t-1})\\ W_t = W_{t-1} - v_t Where :math:`\eta` is the learning rate of the optimizer :math:`\gamma` is the decay rate of the momentum estimate :math:`\v_t` is the update vector at time step `t` :math:`\W_t` is the weight vector at time step `t` Defined in src/operator/optimizer_op.cc:L724
org.apache.mxnet.Symbol
Computes the product of array elements over given axes treating Not a Numbers (``NaN``) as one. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L177
org.apache.mxnet.Symbol
Computes the sum of array elements over given axes treating Not a Numbers (``NaN``) as zero. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L162
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
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 entire 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:L350
org.apache.mxnet.Symbol
Draw random samples from a normal (Gaussian) distribution. .. note:: The existing alias ``normal`` is deprecated. Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation). Example:: normal(loc=0, scale=1, shape=(2,2)) = `[ [ 1.89171135, -1.16881478], [-1.23474145, 1.55807114] ] Defined in src/operator/random/sample_op.cc:L113
org.apache.mxnet.Symbol
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`` would result 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:L799
org.apache.mxnet.Symbol
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.] ]
org.apache.mxnet.Symbol
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 padding applied 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`. `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 length ``2*N`` where ``N`` is the number of dimensions of the array. For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values 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
org.apache.mxnet.Symbol
Picks elements from an input array according to the input indices along the given axis. Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be 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 that addresses 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:L154
org.apache.mxnet.Symbol
Computes the product of array elements over given axes. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L147
org.apache.mxnet.Symbol
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:L238
org.apache.mxnet.Symbol
Draw random samples from an exponential distribution. Samples are distributed according to an exponential distribution parametrized by *lambda* (rate). Example:: exponential(lam=4, shape=(2,2)) = `[ [ 0.0097189 , 0.08999364], [ 0.04146638, 0.31715935] ] Defined in src/operator/random/sample_op.cc:L137
org.apache.mxnet.Symbol
Draw random samples from a gamma distribution. Samples are distributed according to a gamma distribution parametrized by *alpha* (shape) and *beta* (scale). Example:: gamma(alpha=9, beta=0.5, shape=(2,2)) = `[ [ 7.10486984, 3.37695289], [ 3.91697288, 3.65933681] ] Defined in src/operator/random/sample_op.cc:L125
org.apache.mxnet.Symbol
Draw random samples from a generalized negative binomial distribution. Samples are distributed according to a generalized negative binomial distribution parametrized by *mu* (mean) and *alpha* (dispersion). *alpha* is defined as *1/k* where *k* is the failure limit of the number of unsuccessful experiments (generalized to real numbers). Samples will always be returned as a floating point data type. Example:: generalized_negative_binomial(mu=2.0, alpha=0.3, shape=(2,2)) = `[ [ 2., 1.], [ 6., 4.] ] Defined in src/operator/random/sample_op.cc:L179
org.apache.mxnet.Symbol
Draw random samples from a negative binomial distribution. Samples are distributed according to a negative binomial distribution parametrized by *k* (limit of unsuccessful experiments) and *p* (failure probability in each experiment). Samples will always be returned as a floating point data type. Example:: negative_binomial(k=3, p=0.4, shape=(2,2)) = `[ [ 4., 7.], [ 2., 5.] ] Defined in src/operator/random/sample_op.cc:L164
org.apache.mxnet.Symbol
Draw random samples from a normal (Gaussian) distribution. .. note:: The existing alias ``normal`` is deprecated. Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation). Example:: normal(loc=0, scale=1, shape=(2,2)) = `[ [ 1.89171135, -1.16881478], [-1.23474145, 1.55807114] ] Defined in src/operator/random/sample_op.cc:L113
org.apache.mxnet.Symbol
Draw random samples from a Poisson distribution. Samples are distributed according to a Poisson distribution parametrized by *lambda* (rate). Samples will always be returned as a floating point data type. Example:: poisson(lam=4, shape=(2,2)) = `[ [ 5., 2.], [ 4., 6.] ] Defined in src/operator/random/sample_op.cc:L150
org.apache.mxnet.Symbol
Draw random samples from a discrete uniform distribution. Samples are uniformly distributed over the half-open interval *[low, high)* (includes *low*, but excludes *high*). Example:: randint(low=0, high=5, shape=(2,2)) = `[ [ 0, 2], [ 3, 1] ] Defined in src/operator/random/sample_op.cc:L193
org.apache.mxnet.Symbol
Draw random samples from a uniform distribution. .. note:: The existing alias ``uniform`` is deprecated. Samples are uniformly distributed over the half-open interval *[low, high)* (includes *low*, but excludes *high*). Example:: uniform(low=0, high=1, shape=(2,2)) = `[ [ 0.60276335, 0.85794562], [ 0.54488319, 0.84725171] ] Defined in src/operator/random/sample_op.cc:L96
org.apache.mxnet.Symbol
Converts a batch of index arrays into an array of flat indices. The operator follows numpy conventions so a single multi index is given by a column of the input matrix. The leading dimension may be left unspecified by using -1 as placeholder. Examples:: A = `[ [3,6,6],[4,5,1] ] ravel(A, shape=(7,6)) = [22,41,37] ravel(A, shape=(-1,6)) = [22,41,37] Defined in src/operator/tensor/ravel.cc:L42
org.apache.mxnet.Symbol
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:L1004
org.apache.mxnet.Symbol
Returns the reciprocal of the argument, element-wise. Calculates 1/x. Example:: reciprocal([-2, 1, 3, 1.6.0, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L686
org.apache.mxnet.Symbol
Computes rectified linear activation. .. 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
org.apache.mxnet.Symbol
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:L796
org.apache.mxnet.Symbol
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 new shape. The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array. 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, -3, -4}. The significance of each is explained below: - ``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 input dimensions 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 the output dimension. 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 to -4 in shape (can contain -1). 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 from right to left. Example:: - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5) - with reverse=1, output shape will be (50,4). Defined in src/operator/tensor/matrix_op.cc:L202
org.apache.mxnet.Symbol
Reshape some or all dimensions of `lhs` to have the same shape as some or all dimensions of `rhs`. Returns a **view** of the `lhs` array with a new shape without altering any data. 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 specifying \ slices over the `lhs` and `rhs` array dimensions. Only the sliced `lhs` dimensions \ are reshaped to the `rhs` sliced dimensions, with the non-sliced `lhs` dimensions staying the same. Examples:: - lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, rhs_begin=0, rhs_end=2, output shape = (15,2,7) - lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, rhs_begin=1, rhs_end=2, output shape = (15) Negative indices are supported, and `None` can be used for either `lhs_end` or `rhs_end` to indicate the end of the range. Example:: - lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, rhs_begin=1, rhs_end=None, output shape = (30, 2, 2, 3) Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L485
org.apache.mxnet.Symbol
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:L898
org.apache.mxnet.Symbol
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:L767
org.apache.mxnet.Symbol
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 for each parameter monotonically over the course of training. While this is analytically motivated for convex optimizations, it may not be ideal 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 gradient. 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:L795
org.apache.mxnet.Symbol
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 + \epsilon}} g_t\\ 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:L834
org.apache.mxnet.Symbol
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:L746
org.apache.mxnet.Symbol
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:L927
org.apache.mxnet.Symbol
Concurrent sampling from multiple exponential distributions with parameters lambda (rate). The parameters of the distributions are provided as an input array. Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input array, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input value at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input array. Examples:: lam = [ 1.0, 8.5 ] // Draw a single sample for each distribution sample_exponential(lam) = [ 0.51837951, 0.09994757] // Draw a vector containing two samples for each distribution sample_exponential(lam, shape=(2)) = `[ [ 0.51837951, 0.19866663], [ 0.09994757, 0.50447971] ] Defined in src/operator/random/multisample_op.cc:L284
org.apache.mxnet.Symbol
Concurrent sampling from multiple gamma distributions with parameters *alpha* (shape) and *beta* (scale). The parameters of the distributions are provided as input arrays. Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays. Examples:: alpha = [ 0.0, 2.5 ] beta = [ 1.0, 0.7 ] // Draw a single sample for each distribution sample_gamma(alpha, beta) = [ 0. , 2.25797319] // Draw a vector containing two samples for each distribution sample_gamma(alpha, beta, shape=(2)) = `[ [ 0. , 0. ], [ 2.25797319, 1.70734084] ] Defined in src/operator/random/multisample_op.cc:L282
org.apache.mxnet.Symbol
Concurrent sampling from multiple generalized negative binomial distributions with parameters *mu* (mean) and *alpha* (dispersion). The parameters of the distributions are provided as input arrays. Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays. Samples will always be returned as a floating point data type. Examples:: mu = [ 2.0, 2.5 ] alpha = [ 1.0, 0.1 ] // Draw a single sample for each distribution sample_generalized_negative_binomial(mu, alpha) = [ 0., 3.] // Draw a vector containing two samples for each distribution sample_generalized_negative_binomial(mu, alpha, shape=(2)) = `[ [ 0., 3.], [ 3., 1.] ] Defined in src/operator/random/multisample_op.cc:L293
org.apache.mxnet.Symbol
Concurrent sampling from multiple multinomial distributions. *data* is an *n* dimensional array whose last dimension has length *k*, where *k* is the number of possible outcomes of each multinomial distribution. This operator will draw *shape* samples from each distribution. If shape is empty one sample will be drawn from each distribution. If *get_prob* is true, a second array containing log likelihood of the drawn samples will also be returned. This is usually used for reinforcement learning where you can provide reward as head gradient for this array to estimate gradient. Note that the input distribution must be normalized, i.e. *data* must sum to 1 along its last axis. Examples:: probs = `[ [0, 0.1, 0.2, 0.3, 0.4], [0.4, 0.3, 0.2, 0.1, 0] ] // Draw a single sample for each distribution sample_multinomial(probs) = [3, 0] // Draw a vector containing two samples for each distribution sample_multinomial(probs, shape=(2)) = `[ [4, 2], [0, 0] ] // requests log likelihood sample_multinomial(probs, get_prob=True) = [2, 1], [0.2, 0.3]
org.apache.mxnet.Symbol
Concurrent sampling from multiple negative binomial distributions with parameters *k* (failure limit) and *p* (failure probability). The parameters of the distributions are provided as input arrays. Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays. Samples will always be returned as a floating point data type. Examples:: k = [ 20, 49 ] p = [ 0.4 , 0.77 ] // Draw a single sample for each distribution sample_negative_binomial(k, p) = [ 15., 16.] // Draw a vector containing two samples for each distribution sample_negative_binomial(k, p, shape=(2)) = `[ [ 15., 50.], [ 16., 12.] ] Defined in src/operator/random/multisample_op.cc:L289
org.apache.mxnet.Symbol
Concurrent sampling from multiple normal distributions with parameters *mu* (mean) and *sigma* (standard deviation). The parameters of the distributions are provided as input arrays. Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays. Examples:: mu = [ 0.0, 2.5 ] sigma = [ 1.0, 3.7 ] // Draw a single sample for each distribution sample_normal(mu, sigma) = [-0.56410581, 0.95934606] // Draw a vector containing two samples for each distribution sample_normal(mu, sigma, shape=(2)) = `[ [-0.56410581, 0.2928229 ], [ 0.95934606, 4.48287058] ] Defined in src/operator/random/multisample_op.cc:L279
org.apache.mxnet.Symbol
Concurrent sampling from multiple Poisson distributions with parameters lambda (rate). The parameters of the distributions are provided as an input array. Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input array, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input value at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input array. Samples will always be returned as a floating point data type. Examples:: lam = [ 1.0, 8.5 ] // Draw a single sample for each distribution sample_poisson(lam) = [ 0., 13.] // Draw a vector containing two samples for each distribution sample_poisson(lam, shape=(2)) = `[ [ 0., 4.], [ 13., 8.] ] Defined in src/operator/random/multisample_op.cc:L286
org.apache.mxnet.Symbol
Concurrent sampling from multiple uniform distributions on the intervals given by *[low,high)*. The parameters of the distributions are provided as input arrays. Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays. Examples:: low = [ 0.0, 2.5 ] high = [ 1.0, 3.7 ] // Draw a single sample for each distribution sample_uniform(low, high) = [ 0.40451524, 3.18687344] // Draw a vector containing two samples for each distribution sample_uniform(low, high, shape=(2)) = `[ [ 0.40451524, 0.18017688], [ 3.18687344, 3.68352246] ] Defined in src/operator/random/multisample_op.cc:L277
org.apache.mxnet.Symbol
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 with shape `(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] ] ] ]
org.apache.mxnet.Symbol
Momentum update function for Stochastic Gradient Descent (SGD) optimizer. Momentum update has better convergence rates on neural networks. Mathematically it looks 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 each epoch. However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and weight's storage type is the same as momentum's storage type, only the row slices whose indices appear in grad.indices are updated (for both weight and momentum):: 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:L563
org.apache.mxnet.Symbol
Update function for Stochastic Gradient Descent (SGD) 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 True, 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:L522
org.apache.mxnet.Symbol
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:L544
org.apache.mxnet.Symbol
Randomly shuffle the elements. This shuffles the array along the first axis. The order of the elements in each subarray does not change. For example, if a 2D array is given, the order of the rows randomly changes, but the order of the elements in each row does not change.
org.apache.mxnet.Symbol
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:L119
org.apache.mxnet.Symbol
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:L727
org.apache.mxnet.Symbol
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:L61
org.apache.mxnet.Symbol
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 each epoch.
.. note::
- sparse ndarray not supported for this optimizer yet.
Defined in src/operator/optimizer_op.cc:L90org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
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:L257
org.apache.mxnet.Symbol
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:L596
org.apache.mxnet.Symbol
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:L506
org.apache.mxnet.Symbol
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:L596
org.apache.mxnet.Symbol
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 dimensions, 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 `input_2` 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:L665
org.apache.mxnet.Symbol
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 scalar.
Example::
smooth_l1([1, 2, 3, 4]) = [0.5, 1.5, 2.5, 3.5]
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:L104org.apache.mxnet.Symbol
Applies the softmax function. The resulting array contains elements in the range (0,1) and the elements along the given axis sum up to 1. .. 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:L93
org.apache.mxnet.Symbol
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 labels. - 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 \log(\text{output}_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) = 0.4281871 Defined in src/operator/loss_binary_op.cc:L59
org.apache.mxnet.Symbol
Applies the softmin function. The resulting array contains elements in the range (0,1) and the elements along the given axis sum up to 1. .. math:: softmin(\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. 2. 3.] [ 3. 2. 1.] ] softmin(x,axis=0) = `[ [ 0.88079703, 0.5, 0.11920292], [ 0.11920292, 0.5, 0.88079703] ] softmin(x,axis=1) = `[ [ 0.66524094, 0.24472848, 0.09003057], [ 0.09003057, 0.24472848, 0.66524094] ] Defined in src/operator/nn/softmax.cc:L153
org.apache.mxnet.Symbol
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:L163
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
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 ``depth_to_space``. .. math:: \begin{gather*} x \prime = reshape(x, [N, C, H / block\_size, block\_size, W / block\_size, block\_size]) \\ x \prime \prime = transpose(x \prime, [0, 3, 5, 1, 2, 4]) \\ y = reshape(x \prime \prime, [N, C * (block\_size ^ 2), H / block\_size, W / block\_size]) \end{gather*} where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width] and :math:`y` is the output tensor of layout :math:`[N, C * (block\_size ^ 2), H / block\_size, W / block\_size]` 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:L1104
org.apache.mxnet.Symbol
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 arrays. **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] == num_outputs``. Example:: z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1) z = `[ [ 1.] [ 2.] ] `[ [ 3.] [ 4.] ] `[ [ 5.] [ 6.] ] z[0].shape = (2 ,1 ) Defined in src/operator/slice_channel.cc:L107
org.apache.mxnet.Symbol
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:L907org.apache.mxnet.Symbol
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:L883
org.apache.mxnet.Symbol
Remove single-dimensional entries from the shape of an array. Same behavior of defining the output tensor shape as numpy.squeeze for the most of cases. 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 example, squeeze(`[ `[ [4] ] ]) = [4], while in numpy.squeeze, the output will become a scalar.
org.apache.mxnet.Symbol
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] ]
org.apache.mxnet.Symbol
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 contribution 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:L299
org.apache.mxnet.Symbol
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:L116
org.apache.mxnet.Symbol
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:L116
org.apache.mxnet.Symbol
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
org.apache.mxnet.Symbol
Takes elements from an input array along the given axis. This function slices the input array along a particular axis with the provided indices. Given data tensor of rank r >= 1, and indices tensor of rank q, gather entries of the axis dimension of data (by default outer-most one as axis=0) indexed by indices, and concatenates them 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 around). // Along axis 1 take(x, `[ [0, 3], [-1, -2] ], axis=1, mode='wrap') = `[ `[ [ 1. 2.] [ 2. 1.] ] `[ [ 3. 4.] [ 4. 3.] ] `[ [ 5. 6.] [ 6. 5.] ] ] The storage type of ``take`` output depends upon the input storage type: - take(default, default) = default - take(csr, default, axis=0) = csr Defined in src/operator/tensor/indexing_op.cc:L695
org.apache.mxnet.Symbol
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:L139
org.apache.mxnet.Symbol
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:L290
org.apache.mxnet.Symbol
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 a
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:L857org.apache.mxnet.Symbol
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.], [ 1., 2.] ] ] Defined in src/operator/tensor/ordering_op.cc:L64
org.apache.mxnet.Symbol
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:L375
org.apache.mxnet.Symbol
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 discarded. 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:L825
org.apache.mxnet.Symbol
Draw random samples from a uniform distribution. .. note:: The existing alias ``uniform`` is deprecated. Samples are uniformly distributed over the half-open interval *[low, high)* (includes *low*, but excludes *high*). Example:: uniform(low=0, high=1, shape=(2,2)) = `[ [ 0.60276335, 0.85794562], [ 0.54488319, 0.84725171] ] Defined in src/operator/random/sample_op.cc:L96
org.apache.mxnet.Symbol
Converts an array of flat indices into a batch of index arrays. The operator follows numpy conventions so a single multi index is given by a column of the output matrix. The leading dimension may be left unspecified by using -1 as placeholder. Examples:: A = [22,41,37] unravel(A, shape=(7,6)) = `[ [3,6,6],[4,5,1] ] unravel(A, shape=(-1,6)) = `[ [3,6,6],[4,5,1] ] Defined in src/operator/tensor/ravel.cc:L67
org.apache.mxnet.Symbol
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 from x or y, depending on the elements from condition are true or false. x and y must have the same shape. If condition has the same shape as x, each element in the output array is from x if the 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 size is the same as x's first dimension size. Each row of the output array is from x's row 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
org.apache.mxnet.Symbol
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 input - zeros_like(row_sparse) = row_sparse - zeros_like(csr) = csr - zeros_like(default) = default Examples:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] zeros_like(x) = `[ [ 0., 0., 0.], [ 0., 0., 0.] ]
org.apache.mxnet.Symbol