# ndarray.contrib¶

Contrib NDArray API of MXNet.

Functions

 rand_zipfian(true_classes, num_sampled, …) Draw random samples from an approximately log-uniform or Zipfian distribution. foreach(body, data, init_states) Run a for loop with user-defined computation over NDArrays on dimension 0. while_loop(cond, func, loop_vars[, …]) Run a while loop with user-defined computation and loop condition. cond(pred, then_func, else_func) Run an if-then-else using user-defined condition and computation isinf(data) Performs an element-wise check to determine if the NDArray contains an infinite element or not. isfinite(data) Performs an element-wise check to determine if the NDArray contains an infinite element or not. isnan(data) Performs an element-wise check to determine if the NDArray contains a NaN element or not. AdaptiveAvgPooling2D([data, output_size, …]) Applies a 2D adaptive average pooling over a 4D input with the shape of (NCHW). BatchNormWithReLU([data, gamma, beta, …]) Batch normalization with ReLU fusion. BilinearResize2D([data, like, height, …]) Perform 2D resizing (upsampling or downsampling) for 4D input using bilinear interpolation. CTCLoss([data, label, data_lengths, …]) Connectionist Temporal Classification Loss. DeformableConvolution([data, offset, …]) Compute 2-D deformable convolution on 4-D input. DeformablePSROIPooling([data, rois, trans, …]) Performs deformable position-sensitive region-of-interest pooling on inputs. ModulatedDeformableConvolution([data, …]) Compute 2-D modulated deformable convolution on 4-D input. MultiBoxDetection([cls_prob, loc_pred, …]) Convert multibox detection predictions. MultiBoxPrior([data, sizes, ratios, clip, …]) Generate prior(anchor) boxes from data, sizes and ratios. MultiBoxTarget([anchor, label, cls_pred, …]) Compute Multibox training targets MultiProposal([cls_prob, bbox_pred, …]) Generate region proposals via RPN PSROIPooling([data, rois, spatial_scale, …]) Performs region-of-interest pooling on inputs. Proposal([cls_prob, bbox_pred, im_info, …]) Generate region proposals via RPN ROIAlign([data, rois, pooled_size, …]) This operator takes a 4D feature map as an input array and region proposals as rois, then align the feature map over sub-regions of input and produces a fixed-sized output array. RROIAlign([data, rois, pooled_size, …]) Performs Rotated ROI Align on the input array. SyncBatchNorm([data, gamma, beta, …]) Batch normalization. allclose([a, b, rtol, atol, equal_nan, out, …]) This operators implements the numpy.allclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False) arange_like([data, start, step, repeat, …]) Return an array with evenly spaced values. backward_gradientmultiplier([data, scalar, …]) param data source input backward_hawkesll([out, name]) param out The output NDArray to hold the result. backward_index_copy([out, name]) param out The output NDArray to hold the result. backward_quadratic([out, name]) param out The output NDArray to hold the result. bipartite_matching([data, is_ascend, …]) Compute bipartite matching. boolean_mask([data, index, axis, out, name]) Given an n-d NDArray data, and a 1-d NDArray index, the operator produces an un-predeterminable shaped n-d NDArray out, which stands for the rows in x where the corresonding element in index is non-zero. box_decode([data, anchors, std0, std1, …]) Decode bounding boxes training target with normalized center offsets. box_encode([samples, matches, anchors, …]) Encode bounding boxes training target with normalized center offsets. box_iou([lhs, rhs, format, out, name]) Bounding box overlap of two arrays. box_nms([data, overlap_thresh, …]) Apply non-maximum suppression to input. box_non_maximum_suppression([data, …]) Apply non-maximum suppression to input. calibrate_entropy([hist, hist_edges, …]) Provide calibrated min/max for input histogram. count_sketch([data, h, s, out_dim, …]) Apply CountSketch to input: map a d-dimension data to k-dimension data” ctc_loss([data, label, data_lengths, …]) Connectionist Temporal Classification Loss. dequantize([data, min_range, max_range, …]) Dequantize the input tensor into a float tensor. dgl_adjacency([data, out, name]) This operator converts a CSR matrix whose values are edge Ids to an adjacency matrix whose values are ones. This operator samples sub-graph from a csr graph via an non-uniform probability. This operator samples sub-graphs from a csr graph via an uniform probability. dgl_graph_compact(*graph_data, **kwargs) This operator compacts a CSR matrix generated by dgl_csr_neighbor_uniform_sample and dgl_csr_neighbor_non_uniform_sample. dgl_subgraph(*data, **kwargs) This operator constructs an induced subgraph for a given set of vertices from a graph. div_sqrt_dim([data, out, name]) Rescale the input by the square root of the channel dimension. edge_id([data, u, v, out, name]) This operator implements the edge_id function for a graph stored in a CSR matrix (the value of the CSR stores the edge Id of the graph). fft([data, compute_size, out, name]) Apply 1D FFT to input” getnnz([data, axis, out, name]) Number of stored values for a sparse tensor, including explicit zeros. gradientmultiplier([data, scalar, is_int, …]) This operator implements the gradient multiplier function. group_adagrad_update([weight, grad, …]) Update function for Group AdaGrad optimizer. hawkesll([lda, alpha, beta, state, lags, …]) Computes the log likelihood of a univariate Hawkes process. index_array([data, axes, out, name]) Returns an array of indexes of the input array. index_copy([old_tensor, index_vector, …]) Copies the elements of a new_tensor into the old_tensor. interleaved_matmul_encdec_qk([queries, …]) Compute the matrix multiplication between the projections of queries and keys in multihead attention use as encoder-decoder. Compute the matrix multiplication between the projections of values and the attention weights in multihead attention use as encoder-decoder. Compute the matrix multiplication between the projections of queries and keys in multihead attention use as self attention. Compute the matrix multiplication between the projections of values and the attention weights in multihead attention use as self attention. quadratic([data, a, b, c, out, name]) This operators implements the quadratic function. quantize([data, min_range, max_range, …]) Quantize a input tensor from float to out_type, with user-specified min_range and max_range. quantize_v2([data, out_type, …]) Quantize a input tensor from float to out_type, with user-specified min_calib_range and max_calib_range or the input range collected at runtime. quantized_act([data, min_data, max_data, …]) Activation operator for input and output data type of int8. quantized_batch_norm([data, gamma, beta, …]) BatchNorm operator for input and output data type of int8. quantized_concat(*data, **kwargs) Joins input arrays along a given axis. quantized_conv([data, weight, bias, …]) Convolution operator for input, weight and bias data type of int8, and accumulates in type int32 for the output. quantized_elemwise_add([lhs, rhs, lhs_min, …]) elemwise_add operator for input dataA and input dataB data type of int8, quantized_elemwise_mul([lhs, rhs, lhs_min, …]) Multiplies arguments int8 element-wise. quantized_embedding([data, weight, …]) Maps integer indices to int8 vector representations (embeddings). quantized_flatten([data, min_data, …]) param data A ndarray/symbol of type float32 quantized_fully_connected([data, weight, …]) Fully Connected operator for input, weight and bias data type of int8, and accumulates in type int32 for the output. quantized_pooling([data, min_data, …]) Pooling operator for input and output data type of int8. requantize([data, min_range, max_range, …]) Given data that is quantized in int32 and the corresponding thresholds, requantize the data into int8 using min and max thresholds either calculated at runtime or from calibration. round_ste([data, out, name]) Straight-through-estimator of round(). sign_ste([data, out, name]) Straight-through-estimator of sign().
mxnet.ndarray.contrib.rand_zipfian(true_classes, num_sampled, range_max, ctx=None)[source]

Draw random samples from an approximately log-uniform or Zipfian distribution.

This operation randomly samples num_sampled candidates the range of integers [0, range_max). The elements of sampled_candidates are drawn with replacement from the base distribution.

The base distribution for this operator is an approximately log-uniform or Zipfian distribution:

P(class) = (log(class + 2) - log(class + 1)) / log(range_max + 1)

This sampler is useful when the true classes approximately follow such a distribution. For example, if the classes represent words in a lexicon sorted in decreasing order of frequency. If your classes are not ordered by decreasing frequency, do not use this op.

Additionaly, it also returns the number of times each of the true classes and the sampled classes is expected to occur.

Parameters
• true_classes (NDArray) – A 1-D NDArray of the target classes.

• num_sampled (int) – The number of classes to randomly sample.

• range_max (int) – The number of possible classes.

• ctx (Context) – Device context of output. Default is current context.

Returns

• samples (NDArray) – The sampled candidate classes in 1-D int64 dtype.

• expected_count_true (NDArray) – The expected count for true classes in 1-D float64 dtype.

• expected_count_sample (NDArray) – The expected count for sampled candidates in 1-D float64 dtype.

Examples

>>> true_cls = mx.nd.array([3])
>>> samples, exp_count_true, exp_count_sample = mx.nd.contrib.rand_zipfian(true_cls, 4, 5)
>>> samples
[1 3 3 3]
<NDArray 4 @cpu(0)>
>>> exp_count_true
[ 0.12453879]
<NDArray 1 @cpu(0)>
>>> exp_count_sample
[ 0.22629439  0.12453879  0.12453879  0.12453879]
<NDArray 4 @cpu(0)>

mxnet.ndarray.contrib.foreach(body, data, init_states)[source]

Run a for loop with user-defined computation over NDArrays on dimension 0.

This operator simulates a for loop and body has the computation for an iteration of the for loop. It runs the computation in body on each slice from the input NDArrays.

body takes two arguments as input and outputs a tuple of two elements, as illustrated below:

out, states = body(data1, states)


data1 can be either an NDArray or a list of NDArrays. If data is an NDArray, data1 is an NDArray. Otherwise, data1 is a list of NDArrays and has the same size as data. states is a list of NDArrays and have the same size as init_states. Similarly, out can be either an NDArray or a list of NDArrays, which are concatenated as the first output of foreach; states from the last execution of body are the second output of foreach.

The computation done by this operator is equivalent to the pseudo code below when the input data is NDArray:

states = init_states
outs = []
for i in data.shape[0]:
s = data[i]
out, states = body(s, states)
outs.append(out)
outs = stack(*outs)

Parameters
• body (a Python function.) – Define computation in an iteration.

• data (an NDArray or a list of NDArrays.) – The input data.

• init_states (an NDArray or nested lists of NDArrays.) – The initial values of the loop states.

• name (string.) – The name of the operator.

Returns

• outputs (an NDArray or nested lists of NDArrays.) – The output data concatenated from the output of all iterations.

• states (an NDArray or nested lists of NDArrays.) – The loop states in the last iteration.

Examples

>>> step = lambda data, states: (data + states[0], [states[0] * 2])
>>> data = mx.nd.random.uniform(shape=(2, 10))
>>> states = [mx.nd.random.uniform(shape=(10))]
>>> outs, states = mx.nd.contrib.foreach(step, data, states)

mxnet.ndarray.contrib.while_loop(cond, func, loop_vars, max_iterations=None)[source]

Run a while loop with user-defined computation and loop condition.

This operator simulates a while loop which iterately does customized computation as long as the condition is satisfied.

loop_vars is a list of NDArrays on which the computation uses.

cond is a user-defined function, used as the loop condition. It consumes loop_vars, and produces a scalar MXNet NDArray, indicating the termination of the loop. The loop ends when cond returns false (zero). The cond is variadic, and its signature should be cond(*loop_vars) => NDArray.

func is a user-defined function, used as the loop body. It also consumes loop_vars, and produces step_output and new_loop_vars at each step. In each step, step_output should contain the same number elements. Through all steps, the i-th element of step_output should have the same shape and dtype. Also, new_loop_vars should contain the same number of elements as loop_vars, and the corresponding element should have the same shape and dtype. The func is variadic, and its signature should be func(*loop_vars) => (NDArray or nested List[NDArray] step_output, NDArray or nested List[NDArray] new_loop_vars).

max_iterations is a scalar that defines the maximum number of iterations allowed.

This function returns two lists. The first list has the length of |step_output|, in which the i-th element are all i-th elements of step_output from all steps, stacked along axis 0. The second list has the length of |loop_vars|, which represents final states of loop variables.

Warning

For now, the axis 0 of all NDArrays in the first list are max_iterations, due to lack of dynamic shape inference.

Warning

When cond is never satisfied, we assume step_output is empty, because it cannot be inferred. This is different from the symbolic version.

Parameters
• cond (a Python function.) – The loop condition.

• func (a Python function.) – The loop body.

• loop_vars (an NDArray or nested lists of NDArrays.) – The initial values of the loop variables.

• max_iterations (a python int.) – Maximum number of iterations.

Returns

• outputs (an NDArray or nested lists of NDArrays) – stacked output from each step

• states (an NDArray or nested lists of NDArrays) – final state

Examples

>>> cond = lambda i, s: i <= 5
>>> func = lambda i, s: ([i + s], [i + 1, s + i])
>>> loop_vars = (mx.nd.array([0], dtype="int64"), mx.nd.array([1], dtype="int64"))
>>> outputs, states = mx.nd.contrib.while_loop(cond, func, loop_vars, max_iterations=10)
>>> outputs
[
[[ 1]
[ 2]
[ 4]
[ 7]
[11]
[16]
[...]  # undefined value
[...]
[...]
[...]]
<NDArray 6x1 @cpu(0)>]
>>> states
[
[6]
<NDArray 1 @cpu(0)>,
[16]
<NDArray 1 @cpu(0)>]

mxnet.ndarray.contrib.cond(pred, then_func, else_func)[source]

Run an if-then-else using user-defined condition and computation

This operator simulates a if-like branch which chooses to do one of the two customized computations according to the specified condition.

pred is a scalar MXNet NDArray, indicating which branch of computation should be used.

then_func is a user-defined function, used as computation of the then branch. It produces outputs, which is a list of NDArrays. The signature of then_func should be then_func() => NDArray or nested List[NDArray].

else_func is a user-defined function, used as computation of the else branch. It produces outputs, which is a list of NDArrays. The signature of else_func should be else_func() => NDArray or nested List[NDArray].

The outputs produces by then_func and else_func should have the same number of elements, all of which should be in the same shape, of the same dtype and stype.

This function returns a list of symbols, representing the computation result.

Parameters
• pred (a MXNet NDArray representing a scalar.) – The branch condition.

• then_func (a Python function.) – The computation to be executed if pred is true.

• else_func (a Python function.) – The computation to be executed if pred is false.

Returns

outputs

Return type

an NDArray or nested lists of NDArrays, representing the result of computation.

Examples

>>> a, b = mx.nd.array([1]), mx.nd.array([2])
>>> pred = a * b < 5
>>> then_func = lambda: (a + 5) * (b + 5)
>>> else_func = lambda: (a - 5) * (b - 5)
>>> outputs = mx.nd.contrib.cond(pred, then_func, else_func)
>>> outputs[0]
[42.]
<NDArray 1 @cpu(0)>

mxnet.ndarray.contrib.isinf(data)[source]

Performs an element-wise check to determine if the NDArray contains an infinite element or not.

Parameters

input (NDArray) – An N-D NDArray.

Returns

output – The output NDarray, with same shape as input, where 1 indicates the array element is equal to positive or negative infinity and 0 otherwise.

Return type

NDArray

Examples

>>> data = mx.nd.array([np.inf, -np.inf, np.NINF, -1])
>>> output = mx.nd.contrib.isinf(data)
>>> output
[1. 1. 1. 0.]
<NDArray 4 @cpu(0)>

mxnet.ndarray.contrib.isfinite(data)[source]

Performs an element-wise check to determine if the NDArray contains an infinite element or not.

Parameters

input (NDArray) – An N-D NDArray.

Returns

output – The output NDarray, with same shape as input, where 1 indicates the array element is finite i.e. not equal to positive or negative infinity and 0 in places where it is positive or negative infinity.

Return type

NDArray

Examples

>>> data = mx.nd.array([np.inf, -np.inf, np.NINF, -1])
>>> output = mx.nd.contrib.isfinite(data)
>>> output
[0. 0. 0. 1.]
<NDArray 4 @cpu(0)>

mxnet.ndarray.contrib.isnan(data)[source]

Performs an element-wise check to determine if the NDArray contains a NaN element or not.

Parameters

input (NDArray) – An N-D NDArray.

Returns

output – The output NDarray, with same shape as input, where 1 indicates the array element is NaN i.e. Not a Number and 0 otherwise.

Return type

NDArray

Examples

>>> data = mx.nd.array([np.nan, -1])
>>> output = mx.nd.contrib.isnan(data)
>>> output
[1. 0.]
<NDArray 2 @cpu(0)>

mxnet.ndarray.contrib.AdaptiveAvgPooling2D(data=None, output_size=_Null, out=None, name=None, **kwargs)

Applies a 2D adaptive average pooling over a 4D input with the shape of (NCHW). The pooling kernel and stride sizes are automatically chosen for desired output sizes.

• If a single integer is provided for output_size, the output size is (N x C x output_size x output_size) for any input (NCHW).

• If a tuple of integers (height, width) are provided for output_size, the output size is (N x C x height x width) for any input (NCHW).

Parameters
• data (NDArray) – Input data

• output_size (Shape(tuple), optional, default=[]) – int (output size) or a tuple of int for output (height, width).

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.BatchNormWithReLU(data=None, gamma=None, beta=None, moving_mean=None, moving_var=None, eps=_Null, momentum=_Null, fix_gamma=_Null, use_global_stats=_Null, output_mean_var=_Null, axis=_Null, cudnn_off=_Null, min_calib_range=_Null, max_calib_range=_Null, out=None, name=None, **kwargs)

Batch normalization with ReLU fusion.

An extented operator of Batch normalization which can fuse ReLU activation.

Defined in src/operator/contrib/batch_norm_relu.cc:L248

Parameters
• data (NDArray) – Input data to batch normalization

• gamma (NDArray) – gamma array

• beta (NDArray) – beta array

• moving_mean (NDArray) – running mean of input

• moving_var (NDArray) – running variance of input

• eps (double, optional, default=0.0010000000474974513) – Epsilon to prevent div 0. Must be no less than CUDNN_BN_MIN_EPSILON defined in cudnn.h when using cudnn (usually 1e-5)

• momentum (float, optional, default=0.899999976) – Momentum for moving average

• fix_gamma (boolean, optional, default=1) – Fix gamma while training

• use_global_stats (boolean, optional, default=0) – Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator.

• output_mean_var (boolean, optional, default=0) – Output the mean and inverse std

• axis (int, optional, default='1') – Specify which shape axis the channel is specified

• cudnn_off (boolean, optional, default=0) – Do not select CUDNN operator, if available

• min_calib_range (float or None, optional, default=None) – The minimum scalar value in the form of float32 obtained through calibration. If present, it will be used to by quantized batch norm op to calculate primitive scale.Note: this calib_range is to calib bn output.

• max_calib_range (float or None, optional, default=None) – The maximum scalar value in the form of float32 obtained through calibration. If present, it will be used to by quantized batch norm op to calculate primitive scale.Note: this calib_range is to calib bn output.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.BilinearResize2D(data=None, like=None, height=_Null, width=_Null, scale_height=_Null, scale_width=_Null, mode=_Null, align_corners=_Null, out=None, name=None, **kwargs)

Perform 2D resizing (upsampling or downsampling) for 4D input using bilinear interpolation.

Expected input is a 4 dimensional NDArray (NCHW) and the output with the shape of (N x C x height x width). The key idea of bilinear interpolation is to perform linear interpolation first in one direction, and then again in the other direction. See the wikipedia of Bilinear interpolation for more details.

Defined in src/operator/contrib/bilinear_resize.cc:L220

Parameters
• data (NDArray) – Input data

• like (NDArray) – Resize data to it’s shape

• height (int, optional, default='1') – output height (required, but ignored if scale_height is defined or mode is not “size”)

• width (int, optional, default='1') – output width (required, but ignored if scale_width is defined or mode is not “size”)

• scale_height (float or None, optional, default=None) – sampling scale of the height (optional, used in modes “scale” and “odd_scale”)

• scale_width (float or None, optional, default=None) – sampling scale of the width (optional, used in modes “scale” and “odd_scale”)

• mode ({'like', 'odd_scale', 'size', 'to_even_down', 'to_even_up', 'to_odd_down', 'to_odd_up'},optional, default='size') – resizing mode. “simple” - output height equals parameter “height” if “scale_height” parameter is not defined or input height multiplied by “scale_height” otherwise. Same for width;”odd_scale” - if original height or width is odd, then result height is calculated like result_h = (original_h - 1) * scale + 1; for scale > 1 the result shape would be like if we did deconvolution with kernel = (1, 1) and stride = (height_scale, width_scale); and for scale < 1 shape would be like we did convolution with kernel = (1, 1) and stride = (int(1 / height_scale), int( 1/ width_scale);”like” - resize first input to the height and width of second input; “to_even_down” - resize input to nearest lower even height and width (if original height is odd then result height = original height - 1);”to_even_up” - resize input to nearest bigger even height and width (if original height is odd then result height = original height + 1);”to_odd_down” - resize input to nearest odd height and width (if original height is odd then result height = original height - 1);”to_odd_up” - resize input to nearest odd height and width (if original height is odd then result height = original height + 1);

• align_corners (boolean, optional, default=1) – With align_corners = True, the interpolating doesn’t proportionally align theoutput and input pixels, and thus the output values can depend on the input size.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.CTCLoss(data=None, label=None, data_lengths=None, label_lengths=None, use_data_lengths=_Null, use_label_lengths=_Null, blank_label=_Null, out=None, name=None, **kwargs)

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

Parameters
• data (NDArray) – Input ndarray

• label (NDArray) – Ground-truth labels for the loss.

• data_lengths (NDArray) – Lengths of data for each of the samples. Only required when use_data_lengths is true.

• label_lengths (NDArray) – Lengths of labels for each of the samples. Only required when use_label_lengths is true.

• use_data_lengths (boolean, optional, default=0) – Whether the data lenghts are decided by data_lengths. If false, the lengths are equal to the max sequence length.

• use_label_lengths (boolean, optional, default=0) – Whether the label lenghts are decided by label_lengths, or derived from padding_mask. If false, the lengths are derived from the first occurrence of the value of padding_mask. The value of padding_mask is 0 when first CTC label is reserved for blank, and -1 when last label is reserved for blank. See blank_label.

• blank_label ({'first', 'last'},optional, default='first') – Set the label that is reserved for blank label.If “first”, 0-th label is reserved, and label values for tokens in the vocabulary are between 1 and alphabet_size-1, and the padding mask is -1. If “last”, last label value alphabet_size-1 is reserved for blank label instead, and label values for tokens in the vocabulary are between 0 and alphabet_size-2, and the padding mask is 0.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.DeformableConvolution(data=None, offset=None, weight=None, bias=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, num_filter=_Null, num_group=_Null, num_deformable_group=_Null, workspace=_Null, no_bias=_Null, layout=_Null, out=None, name=None, **kwargs)

Compute 2-D deformable convolution on 4-D input.

The deformable convolution operation is described in https://arxiv.org/abs/1703.06211

For 2-D deformable convolution, the shapes are

• data: (batch_size, channel, height, width)

• offset: (batch_size, num_deformable_group * kernel[0] * kernel[1] * 2, 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])


If no_bias is set to be true, then the bias term is ignored.

The default data layout is NCHW, namely (batch_size, channle, height, width).

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 concating all the g results.

If num_deformable_group is larger than 1, denoted by dg, then split the input offset evenly into dg parts along the channel axis, and also evenly split data into dg parts along the channel axis. Next compute the deformable convolution, apply the i-th part of the offset on the i-th part of the data.

Both weight and bias are learnable parameters.

Defined in src/operator/contrib/deformable_convolution.cc:L100

Parameters
• data (NDArray) – Input data to the DeformableConvolutionOp.

• offset (NDArray) – Input offset to the DeformableConvolutionOp.

• weight (NDArray) – Weight matrix.

• bias (NDArray) – Bias parameter.

• kernel (Shape(tuple), required) – Convolution kernel size: (h, w) or (d, h, w)

• stride (Shape(tuple), optional, default=[]) – Convolution stride: (h, w) or (d, h, w). Defaults to 1 for each dimension.

• dilate (Shape(tuple), optional, default=[]) – Convolution dilate: (h, w) or (d, h, w). Defaults to 1 for each dimension.

• pad (Shape(tuple), optional, default=[]) – Zero pad for convolution: (h, w) or (d, h, w). Defaults to no padding.

• num_filter (int, required) – Convolution filter(channel) number

• num_group (int, optional, default='1') – Number of group partitions.

• num_deformable_group (int, optional, default='1') – Number of deformable group partitions.

• workspace (long (non-negative), optional, default=1024) – Maximum temperal workspace allowed for convolution (MB).

• no_bias (boolean, optional, default=0) – Whether to disable bias parameter.

• layout ({None, 'NCDHW', 'NCHW', 'NCW'},optional, default='None') – Set layout for input, output and weight. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.DeformablePSROIPooling(data=None, rois=None, trans=None, spatial_scale=_Null, output_dim=_Null, group_size=_Null, pooled_size=_Null, part_size=_Null, sample_per_part=_Null, trans_std=_Null, no_trans=_Null, out=None, name=None, **kwargs)

Performs deformable position-sensitive region-of-interest pooling on inputs. The DeformablePSROIPooling operation is described in https://arxiv.org/abs/1703.06211 .batch_size will change to the number of region bounding boxes after DeformablePSROIPooling

Parameters
• data (Symbol) – Input data to the pooling operator, a 4D Feature maps

• rois (Symbol) – Bounding box coordinates, a 2D array of [[batch_index, x1, y1, x2, y2]]. (x1, y1) and (x2, y2) are top left and down right corners of designated region of interest. batch_index indicates the index of corresponding image in the input data

• trans (Symbol) – transition parameter

• spatial_scale (float, required) – Ratio of input feature map height (or w) to raw image height (or w). Equals the reciprocal of total stride in convolutional layers

• output_dim (int, required) – fix output dim

• group_size (int, required) – fix group size

• pooled_size (int, required) – fix pooled size

• part_size (int, optional, default='0') – fix part size

• sample_per_part (int, optional, default='1') – fix samples per part

• trans_std (float, optional, default=0) – fix transition std

• no_trans (boolean, optional, default=0) – Whether to disable trans parameter.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.ModulatedDeformableConvolution(data=None, offset=None, mask=None, weight=None, bias=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, num_filter=_Null, num_group=_Null, num_deformable_group=_Null, workspace=_Null, no_bias=_Null, im2col_step=_Null, layout=_Null, out=None, name=None, **kwargs)

Compute 2-D modulated deformable convolution on 4-D input.

The modulated deformable convolution operation is described in https://arxiv.org/abs/1811.11168

For 2-D modulated deformable convolution, the shapes are

• data: (batch_size, channel, height, width)

• offset: (batch_size, num_deformable_group * kernel[0] * kernel[1] * 2, height, width)

• mask: (batch_size, num_deformable_group * kernel[0] * kernel[1], 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])


If no_bias is set to be true, then the bias term is ignored.

The default data layout is NCHW, namely (batch_size, channle, height, width).

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 concating all the g results.

If num_deformable_group is larger than 1, denoted by dg, then split the input offset evenly into dg parts along the channel axis, and also evenly split out evenly into dg parts along the channel axis. Next compute the deformable convolution, apply the i-th part of the offset part on the i-th out.

Both weight and bias are learnable parameters.

Defined in src/operator/contrib/modulated_deformable_convolution.cc:L102

Parameters
• data (NDArray) – Input data to the ModulatedDeformableConvolutionOp.

• offset (NDArray) – Input offset to ModulatedDeformableConvolutionOp.

• weight (NDArray) – Weight matrix.

• bias (NDArray) – Bias parameter.

• kernel (Shape(tuple), required) – Convolution kernel size: (h, w) or (d, h, w)

• stride (Shape(tuple), optional, default=[]) – Convolution stride: (h, w) or (d, h, w). Defaults to 1 for each dimension.

• dilate (Shape(tuple), optional, default=[]) – Convolution dilate: (h, w) or (d, h, w). Defaults to 1 for each dimension.

• pad (Shape(tuple), optional, default=[]) – Zero pad for convolution: (h, w) or (d, h, w). Defaults to no padding.

• num_filter (int (non-negative), required) – Convolution filter(channel) number

• num_group (int (non-negative), optional, default=1) – Number of group partitions.

• num_deformable_group (int (non-negative), optional, default=1) – Number of deformable group partitions.

• workspace (long (non-negative), optional, default=1024) – Maximum temperal workspace allowed for convolution (MB).

• no_bias (boolean, optional, default=0) – Whether to disable bias parameter.

• im2col_step (int (non-negative), optional, default=64) – Maximum number of images per im2col computation; The total batch size should be divisable by this value or smaller than this value; if you face out of memory problem, you can try to use a smaller value here.

• layout ({None, 'NCDHW', 'NCHW', 'NCW'},optional, default='None') – Set layout for input, output and weight. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.MultiBoxDetection(cls_prob=None, loc_pred=None, anchor=None, clip=_Null, threshold=_Null, background_id=_Null, nms_threshold=_Null, force_suppress=_Null, variances=_Null, nms_topk=_Null, out=None, name=None, **kwargs)

Convert multibox detection predictions.

Parameters
• cls_prob (NDArray) – Class probabilities.

• loc_pred (NDArray) – Location regression predictions.

• anchor (NDArray) – Multibox prior anchor boxes

• clip (boolean, optional, default=1) – Clip out-of-boundary boxes.

• threshold (float, optional, default=0.00999999978) – Threshold to be a positive prediction.

• background_id (int, optional, default='0') – Background id.

• nms_threshold (float, optional, default=0.5) – Non-maximum suppression threshold.

• force_suppress (boolean, optional, default=0) – Suppress all detections regardless of class_id.

• variances (tuple of <float>, optional, default=[0.1,0.1,0.2,0.2]) – Variances to be decoded from box regression output.

• nms_topk (int, optional, default='-1') – Keep maximum top k detections before nms, -1 for no limit.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.MultiBoxPrior(data=None, sizes=_Null, ratios=_Null, clip=_Null, steps=_Null, offsets=_Null, out=None, name=None, **kwargs)

Generate prior(anchor) boxes from data, sizes and ratios.

Parameters
• data (NDArray) – Input data.

• sizes (tuple of <float>, optional, default=[1]) – List of sizes of generated MultiBoxPriores.

• ratios (tuple of <float>, optional, default=[1]) – List of aspect ratios of generated MultiBoxPriores.

• clip (boolean, optional, default=0) – Whether to clip out-of-boundary boxes.

• steps (tuple of <float>, optional, default=[-1,-1]) – Priorbox step across y and x, -1 for auto calculation.

• offsets (tuple of <float>, optional, default=[0.5,0.5]) – Priorbox center offsets, y and x respectively

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.MultiBoxTarget(anchor=None, label=None, cls_pred=None, overlap_threshold=_Null, ignore_label=_Null, negative_mining_ratio=_Null, negative_mining_thresh=_Null, minimum_negative_samples=_Null, variances=_Null, out=None, name=None, **kwargs)

Compute Multibox training targets

Parameters
• anchor (NDArray) – Generated anchor boxes.

• label (NDArray) – Object detection labels.

• cls_pred (NDArray) – Class predictions.

• overlap_threshold (float, optional, default=0.5) – Anchor-GT overlap threshold to be regarded as a positive match.

• ignore_label (float, optional, default=-1) – Label for ignored anchors.

• negative_mining_ratio (float, optional, default=-1) – Max negative to positive samples ratio, use -1 to disable mining

• negative_mining_thresh (float, optional, default=0.5) – Threshold used for negative mining.

• minimum_negative_samples (int, optional, default='0') – Minimum number of negative samples.

• variances (tuple of <float>, optional, default=[0.1,0.1,0.2,0.2]) – Variances to be encoded in box regression target.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.MultiProposal(cls_prob=None, bbox_pred=None, im_info=None, rpn_pre_nms_top_n=_Null, rpn_post_nms_top_n=_Null, threshold=_Null, rpn_min_size=_Null, scales=_Null, ratios=_Null, feature_stride=_Null, output_score=_Null, iou_loss=_Null, out=None, name=None, **kwargs)

Generate region proposals via RPN

Parameters
• cls_prob (NDArray) – Score of how likely proposal is object.

• bbox_pred (NDArray) – BBox Predicted deltas from anchors for proposals

• im_info (NDArray) – Image size and scale.

• rpn_pre_nms_top_n (int, optional, default='6000') – Number of top scoring boxes to keep before applying NMS to RPN proposals

• rpn_post_nms_top_n (int, optional, default='300') – Number of top scoring boxes to keep after applying NMS to RPN proposals

• threshold (float, optional, default=0.699999988) – NMS value, below which to suppress.

• rpn_min_size (int, optional, default='16') – Minimum height or width in proposal

• scales (tuple of <float>, optional, default=[4,8,16,32]) – Used to generate anchor windows by enumerating scales

• ratios (tuple of <float>, optional, default=[0.5,1,2]) – Used to generate anchor windows by enumerating ratios

• feature_stride (int, optional, default='16') – The size of the receptive field each unit in the convolution layer of the rpn,for example the product of all stride’s prior to this layer.

• output_score (boolean, optional, default=0) – Add score to outputs

• iou_loss (boolean, optional, default=0) – Usage of IoU Loss

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.PSROIPooling(data=None, rois=None, spatial_scale=_Null, output_dim=_Null, pooled_size=_Null, group_size=_Null, out=None, name=None, **kwargs)

Performs region-of-interest pooling on inputs. Resize bounding box coordinates by spatial_scale and crop input feature maps accordingly. The cropped feature maps are pooled by max pooling to a fixed size output indicated by pooled_size. batch_size will change to the number of region bounding boxes after PSROIPooling

Parameters
• data (Symbol) – Input data to the pooling operator, a 4D Feature maps

• rois (Symbol) – Bounding box coordinates, a 2D array of [[batch_index, x1, y1, x2, y2]]. (x1, y1) and (x2, y2) are top left and down right corners of designated region of interest. batch_index indicates the index of corresponding image in the input data

• spatial_scale (float, required) – Ratio of input feature map height (or w) to raw image height (or w). Equals the reciprocal of total stride in convolutional layers

• output_dim (int, required) – fix output dim

• pooled_size (int, required) – fix pooled size

• group_size (int, optional, default='0') – fix group size

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.Proposal(cls_prob=None, bbox_pred=None, im_info=None, rpn_pre_nms_top_n=_Null, rpn_post_nms_top_n=_Null, threshold=_Null, rpn_min_size=_Null, scales=_Null, ratios=_Null, feature_stride=_Null, output_score=_Null, iou_loss=_Null, out=None, name=None, **kwargs)

Generate region proposals via RPN

Parameters
• cls_prob (NDArray) – Score of how likely proposal is object.

• bbox_pred (NDArray) – BBox Predicted deltas from anchors for proposals

• im_info (NDArray) – Image size and scale.

• rpn_pre_nms_top_n (int, optional, default='6000') – Number of top scoring boxes to keep before applying NMS to RPN proposals

• rpn_post_nms_top_n (int, optional, default='300') – Number of top scoring boxes to keep after applying NMS to RPN proposals

• threshold (float, optional, default=0.699999988) – NMS value, below which to suppress.

• rpn_min_size (int, optional, default='16') – Minimum height or width in proposal

• scales (tuple of <float>, optional, default=[4,8,16,32]) – Used to generate anchor windows by enumerating scales

• ratios (tuple of <float>, optional, default=[0.5,1,2]) – Used to generate anchor windows by enumerating ratios

• feature_stride (int, optional, default='16') – The size of the receptive field each unit in the convolution layer of the rpn,for example the product of all stride’s prior to this layer.

• output_score (boolean, optional, default=0) – Add score to outputs

• iou_loss (boolean, optional, default=0) – Usage of IoU Loss

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.ROIAlign(data=None, rois=None, pooled_size=_Null, spatial_scale=_Null, sample_ratio=_Null, position_sensitive=_Null, aligned=_Null, out=None, name=None, **kwargs)

This operator takes a 4D feature map as an input array and region proposals as rois, then align the feature map over sub-regions of input and produces a fixed-sized output array. This operator is typically used in Faster R-CNN & Mask R-CNN networks. If roi batchid is less than 0, it will be ignored, and the corresponding output will be set to 0.

Different from ROI pooling, ROI Align removes the harsh quantization, properly aligning the extracted features with the input. RoIAlign computes the value of each sampling point by bilinear interpolation from the nearby grid points on the feature map. No quantization is performed on any coordinates involved in the RoI, its bins, or the sampling points. Bilinear interpolation is used to compute the exact values of the input features at four regularly sampled locations in each RoI bin. Then the feature map can be aggregated by avgpooling.

References

He, Kaiming, et al. “Mask R-CNN.” ICCV, 2017

Defined in src/operator/contrib/roi_align.cc:L559

Parameters
• data (NDArray) – Input data to the pooling operator, a 4D Feature maps

• rois (NDArray) – Bounding box coordinates, a 2D array, if batchid is less than 0, it will be ignored.

• pooled_size (Shape(tuple), required) – ROI Align output roi feature map height and width: (h, w)

• spatial_scale (float, required) – Ratio of input feature map height (or w) to raw image height (or w). Equals the reciprocal of total stride in convolutional layers

• sample_ratio (int, optional, default='-1') – Optional sampling ratio of ROI align, using adaptive size by default.

• position_sensitive (boolean, optional, default=0) – Whether to perform position-sensitive RoI pooling. PSRoIPooling is first proposaled by R-FCN and it can reduce the input channels by ph*pw times, where (ph, pw) is the pooled_size

• aligned (boolean, optional, default=0) – Center-aligned ROIAlign introduced in Detectron2. To enable, set aligned to True.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.RROIAlign(data=None, rois=None, pooled_size=_Null, spatial_scale=_Null, sampling_ratio=_Null, out=None, name=None, **kwargs)

Performs Rotated ROI Align on the input array.

This operator takes a 4D feature map as an input array and region proposals as rois, then align the feature map over sub-regions of input and produces a fixed-sized output array.

Different from ROI Align, RROI Align uses rotated rois, which is suitable for text detection. RRoIAlign computes the value of each sampling point by bilinear interpolation from the nearby grid points on the rotated feature map. No quantization is performed on any coordinates involved in the RoI, its bins, or the sampling points. Bilinear interpolation is used to compute the exact values of the input features at four regularly sampled locations in each RoI bin. Then the feature map can be aggregated by avgpooling.

References

Ma, Jianqi, et al. “Arbitrary-Oriented Scene Text Detection via Rotation Proposals.” IEEE Transactions on Multimedia, 2018.

Defined in src/operator/contrib/rroi_align.cc:L274

Parameters
• data (NDArray) – Input data to the pooling operator, a 4D Feature maps

• rois (NDArray) – Bounding box coordinates, a 2D array

• pooled_size (Shape(tuple), required) – RROI align output shape (h,w)

• spatial_scale (float, required) – Ratio of input feature map height (or width) to raw image height (or width). Equals the reciprocal of total stride in convolutional layers

• sampling_ratio (int, optional, default='-1') – Optional sampling ratio of RROI align, using adaptive size by default.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.SyncBatchNorm(data=None, gamma=None, beta=None, moving_mean=None, moving_var=None, eps=_Null, momentum=_Null, fix_gamma=_Null, use_global_stats=_Null, output_mean_var=_Null, ndev=_Null, key=_Null, out=None, name=None, **kwargs)

Batch normalization.

Normalizes a data batch by mean and variance, and applies a scale gamma as well as offset beta. Standard BN 1 implementation only normalize the data within each device. SyncBN normalizes the input within the whole mini-batch. We follow the sync-onece implmentation described in the paper 2.

Assume the input has more than one dimension and we normalize along axis 1. We first compute the mean and variance along this axis:

$\begin{split}data\_mean[i] = mean(data[:,i,:,...]) \\ data\_var[i] = var(data[:,i,:,...])\end{split}$

Then compute the normalized output, which has the same shape as input, as following:

$out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]$

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.

Reference:
1

Ioffe, Sergey, and Christian Szegedy. “Batch normalization: Accelerating deep network training by reducing internal covariate shift.” ICML 2015

2

Hang Zhang, Kristin Dana, Jianping Shi, Zhongyue Zhang, Xiaogang Wang, Ambrish Tyagi, and Amit Agrawal. “Context Encoding for Semantic Segmentation.” CVPR 2018

Defined in src/operator/contrib/sync_batch_norm.cc:L97

Parameters
• data (NDArray) – Input data to batch normalization

• gamma (NDArray) – gamma array

• beta (NDArray) – beta array

• moving_mean (NDArray) – running mean of input

• moving_var (NDArray) – running variance of input

• eps (float, optional, default=0.00100000005) – Epsilon to prevent div 0

• momentum (float, optional, default=0.899999976) – Momentum for moving average

• fix_gamma (boolean, optional, default=1) – Fix gamma while training

• use_global_stats (boolean, optional, default=0) – Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator.

• output_mean_var (boolean, optional, default=0) – Output All,normal mean and var

• ndev (int, optional, default='1') – The count of GPU devices

• key (string, required) – Hash key for synchronization, please set the same hash key for same layer, Block.prefix is typically used as in gluon.nn.contrib.SyncBatchNorm.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.allclose(a=None, b=None, rtol=_Null, atol=_Null, equal_nan=_Null, out=None, name=None, **kwargs)

This operators implements the numpy.allclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False)

$f(x) = |a-b|<=atol+rtol|b|$

where $$a, b$$ are the input tensors of equal types an shapes $$atol, rtol$$ the values of absolute and relative tolerance (by default, rtol=1e-05, atol=1e-08)

Examples:

a = [1e10, 1e-7],
b = [1.00001e10, 1e-8]
y = allclose(a, b)
y = False

a = [1e10, 1e-8],
b = [1.00001e10, 1e-9]
y = allclose(a, b)
y = True


Defined in src/operator/contrib/allclose_op.cc:L55

Parameters
• a (NDArray) – Input array a

• b (NDArray) – Input array b

• rtol (float, optional, default=9.99999975e-06) – Relative tolerance.

• atol (float, optional, default=9.99999994e-09) – Absolute tolerance.

• equal_nan (boolean, optional, default=1) – Whether to compare NaN’s as equal. If True, NaN’s in A will be considered equal to NaN’s in B in the output array.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.arange_like(data=None, start=_Null, step=_Null, repeat=_Null, ctx=_Null, axis=_Null, out=None, name=None, **kwargs)

Return an array with evenly spaced values. If axis is not given, the output will have the same shape as the input array. Otherwise, the output will be a 1-D array with size of the specified axis in input shape.

Examples:

x = [[0.14883883 0.7772398  0.94865847 0.7225052 ]
[0.23729339 0.6112595  0.66538996 0.5132841 ]
[0.30822644 0.9912457  0.15502319 0.7043658 ]]
<NDArray 3x4 @cpu(0)>

out = mx.nd.contrib.arange_like(x, start=0)

[[ 0.  1.  2.  3.]
[ 4.  5.  6.  7.]
[ 8.  9. 10. 11.]]
<NDArray 3x4 @cpu(0)>

out = mx.nd.contrib.arange_like(x, start=0, axis=-1)

[0. 1. 2. 3.]
<NDArray 4 @cpu(0)>

Parameters
• data (NDArray) – The input

• start (double, optional, default=0) – Start of interval. The interval includes this value. The default start value is 0.

• step (double, optional, default=1) – Spacing between values.

• repeat (int, optional, default='1') – The repeating time of all elements. E.g repeat=3, the element a will be repeated three times –> a, a, a.

• ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n).Only used for imperative calls.

• axis (int or None, optional, default='None') – Arange elements according to the size of a certain axis of input array. The negative numbers are interpreted counting from the backward. If not provided, will arange elements according to the input shape.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.backward_gradientmultiplier(data=None, scalar=_Null, is_int=_Null, out=None, name=None, **kwargs)
Parameters
• data (NDArray) – source input

• scalar (double, optional, default=1) – Scalar input value

• is_int (boolean, optional, default=1) – Indicate whether scalar input is int type

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.backward_hawkesll(out=None, name=None, **kwargs)
Parameters

out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.backward_index_copy(out=None, name=None, **kwargs)
Parameters

out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.backward_quadratic(out=None, name=None, **kwargs)
Parameters

out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.bipartite_matching(data=None, is_ascend=_Null, threshold=_Null, topk=_Null, out=None, name=None, **kwargs)
Compute bipartite matching.

The matching is performed on score matrix with shape [B, N, M] - B: batch_size - N: number of rows to match - M: number of columns as reference to be matched against.

Returns: x : matched column indices. -1 indicating non-matched elements in rows. y : matched row indices.

Note:

Zero gradients are back-propagated in this op for now.


Example:

s = [[0.5, 0.6], [0.1, 0.2], [0.3, 0.4]]
x, y = bipartite_matching(x, threshold=1e-12, is_ascend=False)
x = [1, -1, 0]
y = [2, 0]


Defined in src/operator/contrib/bounding_box.cc:L183

Parameters
• data (NDArray) – The input

• is_ascend (boolean, optional, default=0) – Use ascend order for scores instead of descending. Please set threshold accordingly.

• threshold (float, required) – Ignore matching when score < thresh, if is_ascend=false, or ignore score > thresh, if is_ascend=true.

• topk (int, optional, default='-1') – Limit the number of matches to topk, set -1 for no limit

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.boolean_mask(data=None, index=None, axis=_Null, out=None, name=None, **kwargs)

Given an n-d NDArray data, and a 1-d NDArray index, the operator produces an un-predeterminable shaped n-d NDArray out, which stands for the rows in x where the corresonding element in index is non-zero.

>>> data = mx.nd.array([[1, 2, 3],[4, 5, 6],[7, 8, 9]])
>>> index = mx.nd.array([0, 1, 0])
>>> out


[[4. 5. 6.]] <NDArray 1x3 @cpu(0)>

Parameters
• data (NDArray) – Data

• axis (int, optional, default='0') – An integer that represents the axis in NDArray to mask from.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.box_decode(data=None, anchors=None, std0=_Null, std1=_Null, std2=_Null, std3=_Null, clip=_Null, format=_Null, out=None, name=None, **kwargs)
Decode bounding boxes training target with normalized center offsets.

Input bounding boxes are using corner type: x_{min}, y_{min}, x_{max}, y_{max} or center type: x, y, width, height.) array

Defined in src/operator/contrib/bounding_box.cc:L234

Parameters
• data (NDArray) – (B, N, 4) predicted bbox offset

• anchors (NDArray) – (1, N, 4) encoded in corner or center

• std0 (float, optional, default=1) – value to be divided from the 1st encoded values

• std1 (float, optional, default=1) – value to be divided from the 2nd encoded values

• std2 (float, optional, default=1) – value to be divided from the 3rd encoded values

• std3 (float, optional, default=1) – value to be divided from the 4th encoded values

• clip (float, optional, default=-1) – If larger than 0, bounding box target will be clipped to this value.

• format ({'center', 'corner'},optional, default='center') – The box encoding type. “corner” means boxes are encoded as [xmin, ymin, xmax, ymax], “center” means boxes are encodes as [x, y, width, height].

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.box_encode(samples=None, matches=None, anchors=None, refs=None, means=None, stds=None, out=None, name=None, **kwargs)
Encode bounding boxes training target with normalized center offsets.

Input bounding boxes are using corner type: x_{min}, y_{min}, x_{max}, y_{max}.) array

Defined in src/operator/contrib/bounding_box.cc:L211

Parameters
• samples (NDArray) – (B, N) value +1 (positive), -1 (negative), 0 (ignore)

• matches (NDArray) – (B, N) value range [0, M)

• anchors (NDArray) – (B, N, 4) encoded in corner

• refs (NDArray) – (B, M, 4) encoded in corner

• means (NDArray) – (4,) Mean value to be subtracted from encoded values

• stds (NDArray) – (4,) Std value to be divided from encoded values

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.box_iou(lhs=None, rhs=None, format=_Null, out=None, name=None, **kwargs)
Bounding box overlap of two arrays.

The overlap is defined as Intersection-over-Union, aka, IOU. - lhs: (a_1, a_2, …, a_n, 4) array - rhs: (b_1, b_2, …, b_n, 4) array - output: (a_1, a_2, …, a_n, b_1, b_2, …, b_n) array

Note:

Zero gradients are back-propagated in this op for now.


Example:

x = [[0.5, 0.5, 1.0, 1.0], [0.0, 0.0, 0.5, 0.5]]
y = [[0.25, 0.25, 0.75, 0.75]]
box_iou(x, y, format='corner') = [[0.1428], [0.1428]]


Defined in src/operator/contrib/bounding_box.cc:L137

Parameters
• lhs (NDArray) – The first input

• rhs (NDArray) – The second input

• format ({'center', 'corner'},optional, default='corner') – The box encoding type. “corner” means boxes are encoded as [xmin, ymin, xmax, ymax], “center” means boxes are encodes as [x, y, width, height].

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.box_nms(data=None, overlap_thresh=_Null, valid_thresh=_Null, topk=_Null, coord_start=_Null, score_index=_Null, id_index=_Null, background_id=_Null, force_suppress=_Null, in_format=_Null, out_format=_Null, out=None, name=None, **kwargs)

Apply non-maximum suppression to input.

The output will be sorted in descending order according to score. Boxes with overlaps larger than overlap_thresh, smaller scores and background boxes will be removed and filled with -1, the corresponding position will be recorded for backward propogation.

During back-propagation, the gradient will be copied to the original position according to the input index. For positions that have been suppressed, the in_grad will be assigned 0. In summary, gradients are sticked to its boxes, will either be moved or discarded according to its original index in input.

Input requirements:

1. Input tensor have at least 2 dimensions, (n, k), any higher dims will be regarded
as batch, e.g. (a, b, c, d, n, k) == (a*b*c*d, n, k)
2. n is the number of boxes in each batch
3. k is the width of each box item.


By default, a box is [id, score, xmin, ymin, xmax, ymax, …], additional elements are allowed.

• id_index: optional, use -1 to ignore, useful if force_suppress=False, which means we will skip highly overlapped boxes if one is apple while the other is car.

• background_id: optional, default=-1, class id for background boxes, useful when id_index >= 0 which means boxes with background id will be filtered before nms.

• coord_start: required, default=2, the starting index of the 4 coordinates. Two formats are supported:

• corner: [xmin, ymin, xmax, ymax]

• center: [x, y, width, height]

• score_index: required, default=1, box score/confidence. When two boxes overlap IOU > overlap_thresh, the one with smaller score will be suppressed.

• in_format and out_format: default=’corner’, specify in/out box formats.

Examples:

x = [[0, 0.5, 0.1, 0.1, 0.2, 0.2], [1, 0.4, 0.1, 0.1, 0.2, 0.2],
[0, 0.3, 0.1, 0.1, 0.14, 0.14], [2, 0.6, 0.5, 0.5, 0.7, 0.8]]
box_nms(x, overlap_thresh=0.1, coord_start=2, score_index=1, id_index=0,
force_suppress=True, in_format='corner', out_typ='corner') =
[[2, 0.6, 0.5, 0.5, 0.7, 0.8], [0, 0.5, 0.1, 0.1, 0.2, 0.2],
[-1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1]]
out_grad = [[0.1, 0.1, 0.1, 0.1, 0.1, 0.1], [0.2, 0.2, 0.2, 0.2, 0.2, 0.2],
[0.3, 0.3, 0.3, 0.3, 0.3, 0.3], [0.4, 0.4, 0.4, 0.4, 0.4, 0.4]]
# exe.backward
in_grad = [[0.2, 0.2, 0.2, 0.2, 0.2, 0.2], [0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0], [0.1, 0.1, 0.1, 0.1, 0.1, 0.1]]


Defined in src/operator/contrib/bounding_box.cc:L95

Parameters
• data (NDArray) – The input

• overlap_thresh (float, optional, default=0.5) – Overlapping(IoU) threshold to suppress object with smaller score.

• valid_thresh (float, optional, default=0) – Filter input boxes to those whose scores greater than valid_thresh.

• topk (int, optional, default='-1') – Apply nms to topk boxes with descending scores, -1 to no restriction.

• coord_start (int, optional, default='2') – Start index of the consecutive 4 coordinates.

• score_index (int, optional, default='1') – Index of the scores/confidence of boxes.

• id_index (int, optional, default='-1') – Optional, index of the class categories, -1 to disable.

• background_id (int, optional, default='-1') – Optional, id of the background class which will be ignored in nms.

• force_suppress (boolean, optional, default=0) – Optional, if set false and id_index is provided, nms will only apply to boxes belongs to the same category

• in_format ({'center', 'corner'},optional, default='corner') – The input box encoding type. “corner” means boxes are encoded as [xmin, ymin, xmax, ymax], “center” means boxes are encodes as [x, y, width, height].

• out_format ({'center', 'corner'},optional, default='corner') – The output box encoding type. “corner” means boxes are encoded as [xmin, ymin, xmax, ymax], “center” means boxes are encodes as [x, y, width, height].

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.box_non_maximum_suppression(data=None, overlap_thresh=_Null, valid_thresh=_Null, topk=_Null, coord_start=_Null, score_index=_Null, id_index=_Null, background_id=_Null, force_suppress=_Null, in_format=_Null, out_format=_Null, out=None, name=None, **kwargs)

Apply non-maximum suppression to input.

The output will be sorted in descending order according to score. Boxes with overlaps larger than overlap_thresh, smaller scores and background boxes will be removed and filled with -1, the corresponding position will be recorded for backward propogation.

During back-propagation, the gradient will be copied to the original position according to the input index. For positions that have been suppressed, the in_grad will be assigned 0. In summary, gradients are sticked to its boxes, will either be moved or discarded according to its original index in input.

Input requirements:

1. Input tensor have at least 2 dimensions, (n, k), any higher dims will be regarded
as batch, e.g. (a, b, c, d, n, k) == (a*b*c*d, n, k)
2. n is the number of boxes in each batch
3. k is the width of each box item.


By default, a box is [id, score, xmin, ymin, xmax, ymax, …], additional elements are allowed.

• id_index: optional, use -1 to ignore, useful if force_suppress=False, which means we will skip highly overlapped boxes if one is apple while the other is car.

• background_id: optional, default=-1, class id for background boxes, useful when id_index >= 0 which means boxes with background id will be filtered before nms.

• coord_start: required, default=2, the starting index of the 4 coordinates. Two formats are supported:

• corner: [xmin, ymin, xmax, ymax]

• center: [x, y, width, height]

• score_index: required, default=1, box score/confidence. When two boxes overlap IOU > overlap_thresh, the one with smaller score will be suppressed.

• in_format and out_format: default=’corner’, specify in/out box formats.

Examples:

x = [[0, 0.5, 0.1, 0.1, 0.2, 0.2], [1, 0.4, 0.1, 0.1, 0.2, 0.2],
[0, 0.3, 0.1, 0.1, 0.14, 0.14], [2, 0.6, 0.5, 0.5, 0.7, 0.8]]
box_nms(x, overlap_thresh=0.1, coord_start=2, score_index=1, id_index=0,
force_suppress=True, in_format='corner', out_typ='corner') =
[[2, 0.6, 0.5, 0.5, 0.7, 0.8], [0, 0.5, 0.1, 0.1, 0.2, 0.2],
[-1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1]]
out_grad = [[0.1, 0.1, 0.1, 0.1, 0.1, 0.1], [0.2, 0.2, 0.2, 0.2, 0.2, 0.2],
[0.3, 0.3, 0.3, 0.3, 0.3, 0.3], [0.4, 0.4, 0.4, 0.4, 0.4, 0.4]]
# exe.backward
in_grad = [[0.2, 0.2, 0.2, 0.2, 0.2, 0.2], [0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0], [0.1, 0.1, 0.1, 0.1, 0.1, 0.1]]


Defined in src/operator/contrib/bounding_box.cc:L95

Parameters
• data (NDArray) – The input

• overlap_thresh (float, optional, default=0.5) – Overlapping(IoU) threshold to suppress object with smaller score.

• valid_thresh (float, optional, default=0) – Filter input boxes to those whose scores greater than valid_thresh.

• topk (int, optional, default='-1') – Apply nms to topk boxes with descending scores, -1 to no restriction.

• coord_start (int, optional, default='2') – Start index of the consecutive 4 coordinates.

• score_index (int, optional, default='1') – Index of the scores/confidence of boxes.

• id_index (int, optional, default='-1') – Optional, index of the class categories, -1 to disable.

• background_id (int, optional, default='-1') – Optional, id of the background class which will be ignored in nms.

• force_suppress (boolean, optional, default=0) – Optional, if set false and id_index is provided, nms will only apply to boxes belongs to the same category

• in_format ({'center', 'corner'},optional, default='corner') – The input box encoding type. “corner” means boxes are encoded as [xmin, ymin, xmax, ymax], “center” means boxes are encodes as [x, y, width, height].

• out_format ({'center', 'corner'},optional, default='corner') – The output box encoding type. “corner” means boxes are encoded as [xmin, ymin, xmax, ymax], “center” means boxes are encodes as [x, y, width, height].

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.calibrate_entropy(hist=None, hist_edges=None, num_quantized_bins=_Null, out=None, name=None, **kwargs)

Provide calibrated min/max for input histogram.

Note

This operator only supports forward propagation. DO NOT use it in training.

Defined in src/operator/quantization/calibrate.cc:L197

Parameters
• hist (NDArray) – A ndarray/symbol of type float32

• hist_edges (NDArray) – A ndarray/symbol of type float32

• num_quantized_bins (int, optional, default='255') – The number of quantized bins.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.count_sketch(data=None, h=None, s=None, out_dim=_Null, processing_batch_size=_Null, out=None, name=None, **kwargs)

Apply CountSketch to input: map a d-dimension data to k-dimension data”

Note

count_sketch is only available on GPU.

Assume input data has shape (N, d), sign hash table s has shape (N, d), index hash table h has shape (N, d) and mapping dimension out_dim = k, each element in s is either +1 or -1, each element in h is random integer from 0 to k-1. Then the operator computs:

$out[h[i]] += data[i] * s[i]$

Example:

out_dim = 5
x = [[1.2, 2.5, 3.4],[3.2, 5.7, 6.6]]
h = [[0, 3, 4]]
s = [[1, -1, 1]]
mx.contrib.ndarray.count_sketch(data=x, h=h, s=s, out_dim = 5) = [[1.2, 0, 0, -2.5, 3.4],
[3.2, 0, 0, -5.7, 6.6]]


Defined in src/operator/contrib/count_sketch.cc:L67

Parameters
• data (NDArray) – Input data to the CountSketchOp.

• h (NDArray) – The index vector

• s (NDArray) – The sign vector

• out_dim (int, required) – The output dimension.

• processing_batch_size (int, optional, default='32') – How many sketch vectors to process at one time.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.ctc_loss(data=None, label=None, data_lengths=None, label_lengths=None, use_data_lengths=_Null, use_label_lengths=_Null, blank_label=_Null, out=None, name=None, **kwargs)

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

Parameters
• data (NDArray) – Input ndarray

• label (NDArray) – Ground-truth labels for the loss.

• data_lengths (NDArray) – Lengths of data for each of the samples. Only required when use_data_lengths is true.

• label_lengths (NDArray) – Lengths of labels for each of the samples. Only required when use_label_lengths is true.

• use_data_lengths (boolean, optional, default=0) – Whether the data lenghts are decided by data_lengths. If false, the lengths are equal to the max sequence length.

• use_label_lengths (boolean, optional, default=0) – Whether the label lenghts are decided by label_lengths, or derived from padding_mask. If false, the lengths are derived from the first occurrence of the value of padding_mask. The value of padding_mask is 0 when first CTC label is reserved for blank, and -1 when last label is reserved for blank. See blank_label.

• blank_label ({'first', 'last'},optional, default='first') – Set the label that is reserved for blank label.If “first”, 0-th label is reserved, and label values for tokens in the vocabulary are between 1 and alphabet_size-1, and the padding mask is -1. If “last”, last label value alphabet_size-1 is reserved for blank label instead, and label values for tokens in the vocabulary are between 0 and alphabet_size-2, and the padding mask is 0.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.dequantize(data=None, min_range=None, max_range=None, out_type=_Null, out=None, name=None, **kwargs)

Dequantize the input tensor into a float tensor. min_range and max_range are scalar floats that specify the range for the output data.

When input data type is uint8, the output is calculated using the following equation:

out[i] = in[i] * (max_range - min_range) / 255.0,

When input data type is int8, the output is calculate using the following equation by keep zero centered for the quantized value:

out[i] = in[i] * MaxAbs(min_range, max_range) / 127.0,

Note

This operator only supports forward propogation. DO NOT use it in training.

Defined in src/operator/quantization/dequantize.cc:L81

Parameters
• data (NDArray) – A ndarray/symbol of type uint8

• min_range (NDArray) – The minimum scalar value possibly produced for the input in float32

• max_range (NDArray) – The maximum scalar value possibly produced for the input in float32

• out_type ({'float32'},optional, default='float32') – Output data type.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.dgl_adjacency(data=None, out=None, name=None, **kwargs)

This operator converts a CSR matrix whose values are edge Ids to an adjacency matrix whose values are ones. The output CSR matrix always has the data value of float32.

Example

x = [[ 1, 0, 0 ],
[ 0, 2, 0 ],
[ 0, 0, 3 ]]
[[ 1, 0, 0 ],
[ 0, 1, 0 ],
[ 0, 0, 1 ]]


Defined in src/operator/contrib/dgl_graph.cc:L1424

Parameters
• data (NDArray) – Input ndarray

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.dgl_csr_neighbor_non_uniform_sample(*seed_arrays, **kwargs)

This operator samples sub-graph from a csr graph via an non-uniform probability. The operator is designed for DGL.

The operator outputs four sets of NDArrays to represent the sampled results (the number of NDArrays in each set is the same as the number of seed NDArrays): 1) a set of 1D NDArrays containing the sampled vertices, 2) a set of CSRNDArrays representing the sampled edges, 3) a set of 1D NDArrays with the probability that vertices are sampled, 4) a set of 1D NDArrays indicating the layer where a vertex is sampled. The first set of 1D NDArrays have a length of max_num_vertices+1. The last element in an NDArray indicate the acutal number of vertices in a subgraph. The third and fourth set of NDArrays have a length of max_num_vertices, and the valid number of vertices is the same as the ones in the first set.

Example

shape = (5, 5)
prob = mx.nd.array([0.9, 0.8, 0.2, 0.4, 0.1], dtype=np.float32)
data_np = np.array([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20], dtype=np.int64)
indices_np = np.array([1,2,3,4,0,2,3,4,0,1,3,4,0,1,2,4,0,1,2,3], dtype=np.int64)
indptr_np = np.array([0,4,8,12,16,20], dtype=np.int64)
a = mx.nd.sparse.csr_matrix((data_np, indices_np, indptr_np), shape=shape)
seed = mx.nd.array([0,1,2,3,4], dtype=np.int64)
out = mx.nd.contrib.dgl_csr_neighbor_non_uniform_sample(a, prob, seed, num_args=3, num_hops=1, num_neighbor=2, max_num_vertices=5)

out[0]
[0 1 2 3 4 5]
<NDArray 6 @cpu(0)>

out[1].asnumpy()
array([[ 0,  1,  2,  0,  0],
[ 5,  0,  6,  0,  0],
[ 9, 10,  0,  0,  0],
[13, 14,  0,  0,  0],
[ 0, 18, 19,  0,  0]])

out[2]
[0.9 0.8 0.2 0.4 0.1]
<NDArray 5 @cpu(0)>

out[3]
[0 0 0 0 0]
<NDArray 5 @cpu(0)>


Defined in src/operator/contrib/dgl_graph.cc:L911

Parameters
• csr_matrix (NDArray) – csr matrix

• probability (NDArray) – probability vector

• seed_arrays (NDArray[]) – seed vertices

• num_hops (long, optional, default=1) – Number of hops.

• num_neighbor (long, optional, default=2) – Number of neighbor.

• max_num_vertices (long, optional, default=100) – Max number of vertices.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.dgl_csr_neighbor_uniform_sample(*seed_arrays, **kwargs)

This operator samples sub-graphs from a csr graph via an uniform probability. The operator is designed for DGL.

The operator outputs three sets of NDArrays to represent the sampled results (the number of NDArrays in each set is the same as the number of seed NDArrays): 1) a set of 1D NDArrays containing the sampled vertices, 2) a set of CSRNDArrays representing the sampled edges, 3) a set of 1D NDArrays indicating the layer where a vertex is sampled. The first set of 1D NDArrays have a length of max_num_vertices+1. The last element in an NDArray indicate the acutal number of vertices in a subgraph. The third set of NDArrays have a length of max_num_vertices, and the valid number of vertices is the same as the ones in the first set.

Example

shape = (5, 5)
data_np = np.array([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20], dtype=np.int64)
indices_np = np.array([1,2,3,4,0,2,3,4,0,1,3,4,0,1,2,4,0,1,2,3], dtype=np.int64)
indptr_np = np.array([0,4,8,12,16,20], dtype=np.int64)
a = mx.nd.sparse.csr_matrix((data_np, indices_np, indptr_np), shape=shape)
a.asnumpy()
seed = mx.nd.array([0,1,2,3,4], dtype=np.int64)
out = mx.nd.contrib.dgl_csr_neighbor_uniform_sample(a, seed, num_args=2, num_hops=1, num_neighbor=2, max_num_vertices=5)

out[0]
[0 1 2 3 4 5]
<NDArray 6 @cpu(0)>

out[1].asnumpy()
array([[ 0,  1,  0,  3,  0],
[ 5,  0,  0,  7,  0],
[ 9,  0,  0, 11,  0],
[13,  0, 15,  0,  0],
[17,  0, 19,  0,  0]])

out[2]
[0 0 0 0 0]
<NDArray 5 @cpu(0)>


Defined in src/operator/contrib/dgl_graph.cc:L801

Parameters
• csr_matrix (NDArray) – csr matrix

• seed_arrays (NDArray[]) – seed vertices

• num_hops (long, optional, default=1) – Number of hops.

• num_neighbor (long, optional, default=2) – Number of neighbor.

• max_num_vertices (long, optional, default=100) – Max number of vertices.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.dgl_graph_compact(*graph_data, **kwargs)

This operator compacts a CSR matrix generated by dgl_csr_neighbor_uniform_sample and dgl_csr_neighbor_non_uniform_sample. The CSR matrices generated by these two operators may have many empty rows at the end and many empty columns. This operator removes these empty rows and empty columns.

Example

shape = (5, 5)
data_np = np.array([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20], dtype=np.int64)
indices_np = np.array([1,2,3,4,0,2,3,4,0,1,3,4,0,1,2,4,0,1,2,3], dtype=np.int64)
indptr_np = np.array([0,4,8,12,16,20], dtype=np.int64)
a = mx.nd.sparse.csr_matrix((data_np, indices_np, indptr_np), shape=shape)
seed = mx.nd.array([0,1,2,3,4], dtype=np.int64)
out = mx.nd.contrib.dgl_csr_neighbor_uniform_sample(a, seed, num_args=2, num_hops=1,
num_neighbor=2, max_num_vertices=6)
subg_v = out[0]
subg = out[1]
compact = mx.nd.contrib.dgl_graph_compact(subg, subg_v,
graph_sizes=(subg_v[-1].asnumpy()[0]), return_mapping=False)

compact.asnumpy()
array([[0, 0, 0, 1, 0],
[2, 0, 3, 0, 0],
[0, 4, 0, 0, 5],
[0, 6, 0, 0, 7],
[8, 9, 0, 0, 0]])


Defined in src/operator/contrib/dgl_graph.cc:L1613

Parameters
• graph_data (NDArray[]) – Input graphs and input vertex Ids.

• return_mapping (boolean, required) – Return mapping of vid and eid between the subgraph and the parent graph.

• graph_sizes (tuple of <long>, required) – the number of vertices in each graph.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.dgl_subgraph(*data, **kwargs)

This operator constructs an induced subgraph for a given set of vertices from a graph. The operator accepts multiple sets of vertices as input. For each set of vertices, it returns a pair of CSR matrices if return_mapping is True: the first matrix contains edges with new edge Ids, the second matrix contains edges with the original edge Ids.

Example

x=[[1, 0, 0, 2],
[3, 0, 4, 0],
[0, 5, 0, 0],
[0, 6, 7, 0]]
v = [0, 1, 2]
dgl_subgraph(x, v, return_mapping=True) =
[[1, 0, 0],
[2, 0, 3],
[0, 4, 0]],
[[1, 0, 0],
[3, 0, 4],
[0, 5, 0]]


Defined in src/operator/contrib/dgl_graph.cc:L1171

Parameters
• graph (NDArray) – Input graph where we sample vertices.

• data (NDArray[]) – The input arrays that include data arrays and states.

• return_mapping (boolean, required) – Return mapping of vid and eid between the subgraph and the parent graph.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.div_sqrt_dim(data=None, out=None, name=None, **kwargs)

Rescale the input by the square root of the channel dimension.

out = data / sqrt(data.shape[-1])

Defined in src/operator/contrib/transformer.cc:L840

Parameters
• data (NDArray) – The input array.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.edge_id(data=None, u=None, v=None, out=None, name=None, **kwargs)

This operator implements the edge_id function for a graph stored in a CSR matrix (the value of the CSR stores the edge Id of the graph). output[i] = input[u[i], v[i]] if there is an edge between u[i] and v[i]], otherwise output[i] will be -1. Both u and v should be 1D vectors.

Example

x = [[ 1, 0, 0 ],
[ 0, 2, 0 ],
[ 0, 0, 3 ]]
u = [ 0, 0, 1, 1, 2, 2 ]
v = [ 0, 1, 1, 2, 0, 2 ]
edge_id(x, u, v) = [ 1, -1, 2, -1, -1, 3 ]

The storage type of edge_id output depends on storage types of inputs
• edge_id(csr, default, default) = default

• default and rsp inputs are not supported

Defined in src/operator/contrib/dgl_graph.cc:L1352

Parameters
• data (NDArray) – Input ndarray

• u (NDArray) – u ndarray

• v (NDArray) – v ndarray

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.fft(data=None, compute_size=_Null, out=None, name=None, **kwargs)

Apply 1D FFT to input”

Note

fft is only available on GPU.

Currently accept 2 input data shapes: (N, d) or (N1, N2, N3, d), data can only be real numbers. The output data has shape: (N, 2*d) or (N1, N2, N3, 2*d). The format is: [real0, imag0, real1, imag1, …].

Example:

data = np.random.normal(0,1,(3,4))
out = mx.contrib.ndarray.fft(data = mx.nd.array(data,ctx = mx.gpu(0)))


Defined in src/operator/contrib/fft.cc:L56

Parameters
• data (NDArray) – Input data to the FFTOp.

• compute_size (int, optional, default='128') – Maximum size of sub-batch to be forwarded at one time

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.getnnz(data=None, axis=_Null, out=None, name=None, **kwargs)

Number of stored values for a sparse tensor, including explicit zeros.

This operator only supports CSR matrix on CPU.

Defined in src/operator/contrib/nnz.cc:L177

Parameters
• data (NDArray) – Input

• axis (int or None, optional, default='None') – Select between the number of values across the whole matrix, in each column, or in each row.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.gradientmultiplier(data=None, scalar=_Null, is_int=_Null, out=None, name=None, **kwargs)

This operator implements the gradient multiplier function. In forward pass it acts as an identity transform. During backpropagation it multiplies the gradient from the subsequent level by a scalar factor lambda and passes it to the preceding layer.

Parameters
• data (NDArray) – The input array.

• scalar (double, optional, default=1) – Scalar input value

• is_int (boolean, optional, default=1) – Indicate whether scalar input is int type

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.group_adagrad_update(weight=None, grad=None, history=None, lr=_Null, rescale_grad=_Null, clip_gradient=_Null, epsilon=_Null, out=None, name=None, **kwargs)

Referenced from Adaptive Subgradient Methods for Online Learning and Stochastic Optimization, and available at http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf but uses only a single learning rate for every row of the parameter array.

grad = clip(grad * rescale_grad, clip_gradient)
div = grad / (sqrt(history) + epsilon)
weight -= div * lr


Weights are updated lazily if the gradient is sparse.

Note that non-zero values for the weight decay option are not supported.

Defined in src/operator/contrib/optimizer_op.cc:L71

Parameters
• weight (NDArray) – Weight

• history (NDArray) – History

• lr (float, required) – Learning rate

• epsilon (float, optional, default=9.99999975e-06) – Epsilon for numerical stability

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.hawkesll(lda=None, alpha=None, beta=None, state=None, lags=None, marks=None, valid_length=None, max_time=None, out=None, name=None, **kwargs)

Computes the log likelihood of a univariate Hawkes process.

The log likelihood is calculated on point process observations represented as ragged matrices for lags (interarrival times w.r.t. the previous point), and marks (identifiers for the process ID). Note that each mark is considered independent, i.e., computes the joint likelihood of a set of Hawkes processes determined by the conditional intensity:

$\lambda_k^*(t) = \lambda_k + \alpha_k \sum_{\{t_i < t, y_i = k\}} \beta_k \exp(-\beta_k (t - t_i))$

where $$\lambda_k$$ specifies the background intensity lda, $$\alpha_k$$ specifies the branching ratio or alpha, and $$\beta_k$$ the delay density parameter beta.

lags and marks are two NDArrays of shape (N, T) and correspond to the representation of the point process observation, the first dimension corresponds to the batch index, and the second to the sequence. These are “left-aligned” ragged matrices (the first index of the second dimension is the beginning of every sequence. The length of each sequence is given by valid_length, of shape (N,) where valid_length[i] corresponds to the number of valid points in lags[i, :] and marks[i, :].

max_time is the length of the observation period of the point process. That is, specifying max_time[i] = 5 computes the likelihood of the i-th sample as observed on the time interval $$(0, 5]$$. Naturally, the sum of all valid lags[i, :valid_length[i]] must be less than or equal to 5.

The input state specifies the memory of the Hawkes process. Invoking the memoryless property of exponential decays, we compute the memory as

$s_k(t) = \sum_{t_i < t} \exp(-\beta_k (t - t_i)).$

The state to be provided is $$s_k(0)$$ and carries the added intensity due to past events before the current batch. $$s_k(T)$$ is returned from the function where $$T$$ is max_time[T].

Example:

# define the Hawkes process parameters
lda = nd.array([1.5, 2.0, 3.0]).tile((N, 1))
alpha = nd.array([0.2, 0.3, 0.4])  # branching ratios should be < 1
beta = nd.array([1.0, 2.0, 3.0])

# the "data", or observations
ia_times = nd.array([[6, 7, 8, 9], [1, 2, 3, 4], [3, 4, 5, 6], [8, 9, 10, 11]])
marks = nd.zeros((N, T)).astype(np.int32)

# starting "state" of the process
states = nd.zeros((N, K))

valid_length = nd.array([1, 2, 3, 4])  # number of valid points in each sequence
max_time = nd.ones((N,)) * 100.0  # length of the observation period

A = nd.contrib.hawkesll(
lda, alpha, beta, states, ia_times, marks, valid_length, max_time
)


References:

• Bacry, E., Mastromatteo, I., & Muzy, J. F. (2015). Hawkes processes in finance. Market Microstructure and Liquidity , 1(01), 1550005.

Defined in src/operator/contrib/hawkes_ll.cc:L84

Parameters
• lda (NDArray) – Shape (N, K) The intensity for each of the K processes, for each sample

• alpha (NDArray) – Shape (K,) The infectivity factor (branching ratio) for each process

• beta (NDArray) – Shape (K,) The decay parameter for each process

• state (NDArray) – Shape (N, K) the Hawkes state for each process

• lags (NDArray) – Shape (N, T) the interarrival times

• marks (NDArray) – Shape (N, T) the marks (process ids)

• valid_length (NDArray) – The number of valid points in the process

• max_time (NDArray) – the length of the interval where the processes were sampled

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.index_array(data=None, axes=_Null, out=None, name=None, **kwargs)

Returns an array of indexes of the input array.

For an input array with shape $$(d_1, d_2, ..., d_n)$$, index_array returns a $$(d_1, d_2, ..., d_n, n)$$ array idx, where $$idx[i_1, i_2, ..., i_n, :] = [i_1, i_2, ..., i_n]$$.

Additionally, when the parameter axes is specified, idx will be a $$(d_1, d_2, ..., d_n, m)$$ array where m is the length of axes, and the following equality will hold: $$idx[i_1, i_2, ..., i_n, j] = i_{axes[j]}$$.

Examples:

x = mx.nd.ones((3, 2))

mx.nd.contrib.index_array(x) = [[[0 0]
[0 1]]

[[1 0]
[1 1]]

[[2 0]
[2 1]]]

x = mx.nd.ones((3, 2, 2))

mx.nd.contrib.index_array(x, axes=(1, 0)) = [[[[0 0]
[0 0]]

[[1 0]
[1 0]]]

[[[0 1]
[0 1]]

[[1 1]
[1 1]]]

[[[0 2]
[0 2]]

[[1 2]
[1 2]]]]


Defined in src/operator/contrib/index_array.cc:L118

Parameters
• data (NDArray) – Input data

• axes (Shape or None, optional, default=None) – The axes to include in the index array. Supports negative values.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.index_copy(old_tensor=None, index_vector=None, new_tensor=None, out=None, name=None, **kwargs)

Copies the elements of a new_tensor into the old_tensor.

This operator copies the elements by selecting the indices in the order given in index. The output will be a new tensor containing the rest elements of old tensor and the copied elements of new tensor. For example, if index[i] == j, then the i th row of new_tensor is copied to the j th row of output.

The index must be a vector and it must have the same size with the 0 th dimension of new_tensor. Also, the 0 th dimension of old_tensor must >= the 0 th dimension of new_tensor, or an error will be raised.

Examples:

x = mx.nd.zeros((5,3))
t = mx.nd.array([[1,2,3],[4,5,6],[7,8,9]])
index = mx.nd.array([0,4,2])

mx.nd.contrib.index_copy(x, index, t)

[[1. 2. 3.]
[0. 0. 0.]
[7. 8. 9.]
[0. 0. 0.]
[4. 5. 6.]]
<NDArray 5x3 @cpu(0)>


Defined in src/operator/contrib/index_copy.cc:L193

Parameters
• old_tensor (NDArray) – Old tensor

• index_vector (NDArray) – Index vector

• new_tensor (NDArray) – New tensor to be copied

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.interleaved_matmul_encdec_qk(queries=None, keys_values=None, heads=_Null, out=None, name=None, **kwargs)

Compute the matrix multiplication between the projections of queries and keys in multihead attention use as encoder-decoder.

the inputs must be a tensor of projections of queries following the layout: (seq_length, batch_size, num_heads * head_dim)

and a tensor of interleaved projections of values and keys following the layout: (seq_length, batch_size, num_heads * head_dim * 2)

the equivalent code would be:

q_proj = mx.nd.transpose(queries, axes=(1, 2, 0, 3))
q_proj = mx.nd.reshape(q_proj, shape=(-1, 0, 0), reverse=True)
q_proj = mx.nd.contrib.div_sqrt_dim(q_proj)
tmp = mx.nd.reshape(keys_values, shape=(0, 0, num_heads, 2, -1))
k_proj = mx.nd.transpose(tmp[:,:,:,0,:], axes=(1, 2, 0, 3))
k_proj = mx.nd.reshap(k_proj, shape=(-1, 0, 0), reverse=True)
output = mx.nd.batch_dot(q_proj, k_proj, transpose_b=True)


Defined in src/operator/contrib/transformer.cc:L760

Parameters
• queries (NDArray) – Queries

• keys_values (NDArray) – Keys and values interleaved

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.interleaved_matmul_encdec_valatt(keys_values=None, attention=None, heads=_Null, out=None, name=None, **kwargs)

Compute the matrix multiplication between the projections of values and the attention weights in multihead attention use as encoder-decoder.

the inputs must be a tensor of interleaved projections of keys and values following the layout: (seq_length, batch_size, num_heads * head_dim * 2)

and the attention weights following the layout: (batch_size, seq_length, seq_length)

the equivalent code would be:

tmp = mx.nd.reshape(queries_keys_values, shape=(0, 0, num_heads, 3, -1))
v_proj = mx.nd.transpose(tmp[:,:,:,1,:], axes=(1, 2, 0, 3))
v_proj = mx.nd.reshape(v_proj, shape=(-1, 0, 0), reverse=True)
output = mx.nd.batch_dot(attention, v_proj, transpose_b=True)
output = mx.nd.reshape(output, shape=(-1, num_heads, 0, 0), reverse=True)
output = mx.nd.transpose(output, axes=(0, 2, 1, 3))
output = mx.nd.reshape(output, shape=(0, 0, -1))


Defined in src/operator/contrib/transformer.cc:L807

Parameters
• keys_values (NDArray) – Keys and values interleaved

• attention (NDArray) – Attention maps

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.interleaved_matmul_selfatt_qk(queries_keys_values=None, heads=_Null, out=None, name=None, **kwargs)

Compute the matrix multiplication between the projections of queries and keys in multihead attention use as self attention.

the input must be a single tensor of interleaved projections of queries, keys and values following the layout: (seq_length, batch_size, num_heads * head_dim * 3)

the equivalent code would be:

tmp = mx.nd.reshape(queries_keys_values, shape=(0, 0, num_heads, 3, -1))
q_proj = mx.nd.transpose(tmp[:,:,:,0,:], axes=(1, 2, 0, 3))
q_proj = mx.nd.reshape(q_proj, shape=(-1, 0, 0), reverse=True)
q_proj = mx.nd.contrib.div_sqrt_dim(q_proj)
k_proj = mx.nd.transpose(tmp[:,:,:,1,:], axes=(1, 2, 0, 3))
k_proj = mx.nd.reshape(k_proj, shape=(-1, 0, 0), reverse=True)
output = mx.nd.batch_dot(q_proj, k_proj, transpose_b=True)


Defined in src/operator/contrib/transformer.cc:L668

Parameters
• queries_keys_values (NDArray) – Interleaved queries, keys and values

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.interleaved_matmul_selfatt_valatt(queries_keys_values=None, attention=None, heads=_Null, out=None, name=None, **kwargs)

Compute the matrix multiplication between the projections of values and the attention weights in multihead attention use as self attention.

the inputs must be a tensor of interleaved projections of queries, keys and values following the layout: (seq_length, batch_size, num_heads * head_dim * 3)

and the attention weights following the layout: (batch_size, seq_length, seq_length)

the equivalent code would be:

tmp = mx.nd.reshape(queries_keys_values, shape=(0, 0, num_heads, 3, -1))
v_proj = mx.nd.transpose(tmp[:,:,:,2,:], axes=(1, 2, 0, 3))
v_proj = mx.nd.reshape(v_proj, shape=(-1, 0, 0), reverse=True)
output = mx.nd.batch_dot(attention, v_proj)
output = mx.nd.reshape(output, shape=(-1, num_heads, 0, 0), reverse=True)
output = mx.nd.transpose(output, axes=(2, 0, 1, 3))
output = mx.nd.reshape(output, shape=(0, 0, -1))


Defined in src/operator/contrib/transformer.cc:L714

Parameters
• queries_keys_values (NDArray) – Queries, keys and values interleaved

• attention (NDArray) – Attention maps

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.quadratic(data=None, a=_Null, b=_Null, c=_Null, out=None, name=None, **kwargs)

This operators implements the quadratic function.

$f(x) = ax^2+bx+c$

where $$x$$ is an input tensor and all operations in the function are element-wise.

Example:

x = [[1, 2], [3, 4]]
y = quadratic(data=x, a=1, b=2, c=3)
y = [[6, 11], [18, 27]]

The storage type of quadratic output depends on storage types of inputs
• quadratic(csr, a, b, 0) = csr

• quadratic(default, a, b, c) = default

Parameters
• data (NDArray) – Input ndarray

• a (float, optional, default=0) – Coefficient of the quadratic term in the quadratic function.

• b (float, optional, default=0) – Coefficient of the linear term in the quadratic function.

• c (float, optional, default=0) – Constant term in the quadratic function.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.quantize(data=None, min_range=None, max_range=None, out_type=_Null, out=None, name=None, **kwargs)

Quantize a input tensor from float to out_type, with user-specified min_range and max_range.

min_range and max_range are scalar floats that specify the range for the input data.

When out_type is uint8, the output is calculated using the following equation:

out[i] = (in[i] - min_range) * range(OUTPUT_TYPE) / (max_range - min_range) + 0.5,

where range(T) = numeric_limits<T>::max() - numeric_limits<T>::min().

When out_type is int8, the output is calculate using the following equation by keep zero centered for the quantized value:

out[i] = sign(in[i]) * min(abs(in[i] * scale + 0.5f, quantized_range),

where quantized_range = MinAbs(max(int8), min(int8)) and scale = quantized_range / MaxAbs(min_range, max_range).

Note

This operator only supports forward propagation. DO NOT use it in training.

Defined in src/operator/quantization/quantize.cc:L74

Parameters
• data (NDArray) – A ndarray/symbol of type float32

• min_range (NDArray) – The minimum scalar value possibly produced for the input

• max_range (NDArray) – The maximum scalar value possibly produced for the input

• out_type ({'int8', 'uint8'},optional, default='uint8') – Output data type.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.quantize_v2(data=None, out_type=_Null, min_calib_range=_Null, max_calib_range=_Null, out=None, name=None, **kwargs)

Quantize a input tensor from float to out_type, with user-specified min_calib_range and max_calib_range or the input range collected at runtime.

Output min_range and max_range are scalar floats that specify the range for the input data.

When out_type is uint8, the output is calculated using the following equation:

out[i] = (in[i] - min_range) * range(OUTPUT_TYPE) / (max_range - min_range) + 0.5,

where range(T) = numeric_limits<T>::max() - numeric_limits<T>::min().

When out_type is int8, the output is calculate using the following equation by keep zero centered for the quantized value:

out[i] = sign(in[i]) * min(abs(in[i] * scale + 0.5f, quantized_range),

where quantized_range = MinAbs(max(int8), min(int8)) and scale = quantized_range / MaxAbs(min_range, max_range).

When out_type is auto, the output type is automatically determined by min_calib_range if presented. If min_calib_range < 0.0f, the output type will be int8, otherwise will be uint8. If min_calib_range isn’t presented, the output type will be int8.

Note

This operator only supports forward propagation. DO NOT use it in training.

Defined in src/operator/quantization/quantize_v2.cc:L92

Parameters
• data (NDArray) – A ndarray/symbol of type float32

• out_type ({'auto', 'int8', 'uint8'},optional, default='int8') – Output data type. auto can be specified to automatically determine output type according to min_calib_range.

• min_calib_range (float or None, optional, default=None) – The minimum scalar value in the form of float32. If present, it will be used to quantize the fp32 data into int8 or uint8.

• max_calib_range (float or None, optional, default=None) – The maximum scalar value in the form of float32. If present, it will be used to quantize the fp32 data into int8 or uint8.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.quantized_act(data=None, min_data=None, max_data=None, act_type=_Null, out=None, name=None, **kwargs)

Activation operator for input and output data type of int8. The input and output data comes with min and max thresholds for quantizing the float32 data into int8.

Note

This operator only supports forward propogation. DO NOT use it in training. This operator only supports relu

Defined in src/operator/quantization/quantized_activation.cc:L91

Parameters
• data (NDArray) – Input data.

• min_data (NDArray) – Minimum value of data.

• max_data (NDArray) – Maximum value of data.

• act_type ({'relu', 'sigmoid', 'softrelu', 'softsign', 'tanh'}, required) – Activation function to be applied.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.quantized_batch_norm(data=None, gamma=None, beta=None, moving_mean=None, moving_var=None, min_data=None, max_data=None, eps=_Null, momentum=_Null, fix_gamma=_Null, use_global_stats=_Null, output_mean_var=_Null, axis=_Null, cudnn_off=_Null, min_calib_range=_Null, max_calib_range=_Null, out=None, name=None, **kwargs)

BatchNorm operator for input and output data type of int8. The input and output data comes with min and max thresholds for quantizing the float32 data into int8.

Note

This operator only supports forward propogation. DO NOT use it in training.

Defined in src/operator/quantization/quantized_batch_norm.cc:L95

Parameters
• data (NDArray) – Input data.

• gamma (NDArray) – gamma.

• beta (NDArray) – beta.

• moving_mean (NDArray) – moving_mean.

• moving_var (NDArray) – moving_var.

• min_data (NDArray) – Minimum value of data.

• max_data (NDArray) – Maximum value of data.

• eps (double, optional, default=0.0010000000474974513) – Epsilon to prevent div 0. Must be no less than CUDNN_BN_MIN_EPSILON defined in cudnn.h when using cudnn (usually 1e-5)

• momentum (float, optional, default=0.899999976) – Momentum for moving average

• fix_gamma (boolean, optional, default=1) – Fix gamma while training

• use_global_stats (boolean, optional, default=0) – Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator.

• output_mean_var (boolean, optional, default=0) – Output the mean and inverse std

• axis (int, optional, default='1') – Specify which shape axis the channel is specified

• cudnn_off (boolean, optional, default=0) – Do not select CUDNN operator, if available

• min_calib_range (float or None, optional, default=None) – The minimum scalar value in the form of float32 obtained through calibration. If present, it will be used to by quantized batch norm op to calculate primitive scale.Note: this calib_range is to calib bn output.

• max_calib_range (float or None, optional, default=None) – The maximum scalar value in the form of float32 obtained through calibration. If present, it will be used to by quantized batch norm op to calculate primitive scale.Note: this calib_range is to calib bn output.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.quantized_concat(*data, **kwargs)

Joins input arrays along a given axis.

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. All inputs with different min/max will be rescaled by using largest [min, max] pairs. If any input holds int8, then the output will be int8. Otherwise output will be uint8.

Defined in src/operator/quantization/quantized_concat.cc:L108

Parameters
• data (NDArray[]) – List of arrays to concatenate

• dim (int, optional, default='1') – the dimension to be concated.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.quantized_conv(data=None, weight=None, bias=None, min_data=None, max_data=None, min_weight=None, max_weight=None, min_bias=None, max_bias=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, num_filter=_Null, num_group=_Null, workspace=_Null, no_bias=_Null, cudnn_tune=_Null, cudnn_off=_Null, layout=_Null, out=None, name=None, **kwargs)

Convolution operator for input, weight and bias data type of int8, and accumulates in type int32 for the output. For each argument, two more arguments of type float32 must be provided representing the thresholds of quantizing argument from data type float32 to int8. The final outputs contain the convolution result in int32, and min and max thresholds representing the threholds for quantizing the float32 output into int32.

Note

This operator only supports forward propogation. DO NOT use it in training.

Defined in src/operator/quantization/quantized_conv.cc:L188

Parameters
• data (NDArray) – Input data.

• weight (NDArray) – weight.

• bias (NDArray) – bias.

• min_data (NDArray) – Minimum value of data.

• max_data (NDArray) – Maximum value of data.

• min_weight (NDArray) – Minimum value of weight.

• max_weight (NDArray) – Maximum value of weight.

• min_bias (NDArray) – Minimum value of bias.

• max_bias (NDArray) – Maximum value of bias.

• kernel (Shape(tuple), required) – Convolution kernel size: (w,), (h, w) or (d, h, w)

• stride (Shape(tuple), optional, default=[]) – Convolution stride: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.

• dilate (Shape(tuple), optional, default=[]) – Convolution dilate: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.

• pad (Shape(tuple), optional, default=[]) – Zero pad for convolution: (w,), (h, w) or (d, h, w). Defaults to no padding.

• num_filter (int (non-negative), required) – Convolution filter(channel) number

• num_group (int (non-negative), optional, default=1) – Number of group partitions.

• workspace (long (non-negative), optional, default=1024) – Maximum temporary workspace allowed (MB) in convolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the convolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when limited_workspace strategy is used.

• no_bias (boolean, optional, default=0) – Whether to disable bias parameter.

• cudnn_tune ({None, 'fastest', 'limited_workspace', 'off'},optional, default='None') – Whether to pick convolution algo by running performance test.

• cudnn_off (boolean, optional, default=0) – Turn off cudnn for this layer.

• layout ({None, 'NCDHW', 'NCHW', 'NCW', 'NDHWC', 'NHWC'},optional, default='None') – Set layout for input, output and weight. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.NHWC and NDHWC are only supported on GPU.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.quantized_elemwise_add(lhs=None, rhs=None, lhs_min=None, lhs_max=None, rhs_min=None, rhs_max=None, out=None, name=None, **kwargs)

elemwise_add operator for input dataA and input dataB data type of int8, and accumulates in type int32 for the output. For each argument, two more arguments of type float32 must be provided representing the thresholds of quantizing argument from data type float32 to int8. The final outputs contain result in int32, and min and max thresholds representing the threholds for quantizing the float32 output into int32.

Note

This operator only supports forward propogation. DO NOT use it in training.

Parameters
• lhs (NDArray) – first input

• rhs (NDArray) – second input

• lhs_min (NDArray) – 3rd input

• lhs_max (NDArray) – 4th input

• rhs_min (NDArray) – 5th input

• rhs_max (NDArray) – 6th input

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.quantized_elemwise_mul(lhs=None, rhs=None, lhs_min=None, lhs_max=None, rhs_min=None, rhs_max=None, min_calib_range=_Null, max_calib_range=_Null, enable_float_output=_Null, out=None, name=None, **kwargs)

Multiplies arguments int8 element-wise.

Defined in src/operator/quantization/quantized_elemwise_mul.cc:L221

Parameters
• lhs (NDArray) – first input

• rhs (NDArray) – second input

• lhs_min (NDArray) – Minimum value of first input.

• lhs_max (NDArray) – Maximum value of first input.

• rhs_min (NDArray) – Minimum value of second input.

• rhs_max (NDArray) – Maximum value of second input.

• min_calib_range (float or None, optional, default=None) – The minimum scalar value in the form of float32 obtained through calibration. If present, it will be used to requantize the int8 output data.

• max_calib_range (float or None, optional, default=None) – The maximum scalar value in the form of float32 obtained through calibration. If present, it will be used to requantize the int8 output data.

• enable_float_output (boolean, optional, default=0) – Whether to enable float32 output

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.quantized_embedding(data=None, weight=None, min_weight=None, max_weight=None, input_dim=_Null, output_dim=_Null, dtype=_Null, sparse_grad=_Null, out=None, name=None, **kwargs)

Maps integer indices to int8 vector representations (embeddings).

Defined in src/operator/quantization/quantized_indexing_op.cc:L134

Parameters
• data (NDArray) – The input array to the embedding operator.

• weight (NDArray) – The embedding weight matrix.

• min_weight (NDArray) – Minimum value of data.

• max_weight (NDArray) – Maximum value of data.

• input_dim (int, required) – Vocabulary size of the input indices.

• output_dim (int, required) – Dimension of the embedding vectors.

• dtype ({'bfloat16', 'float16', 'float32', 'float64', 'int32', 'int64', 'int8', 'uint8'},optional, default='float32') – Data type of weight.

• sparse_grad (boolean, optional, default=0) – Compute row sparse gradient in the backward calculation. If set to True, the grad’s storage type is row_sparse.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.quantized_flatten(data=None, min_data=None, max_data=None, out=None, name=None, **kwargs)
Parameters
• data (NDArray) – A ndarray/symbol of type float32

• min_data (NDArray) – The minimum scalar value possibly produced for the data

• max_data (NDArray) – The maximum scalar value possibly produced for the data

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.quantized_fully_connected(data=None, weight=None, bias=None, min_data=None, max_data=None, min_weight=None, max_weight=None, min_bias=None, max_bias=None, num_hidden=_Null, no_bias=_Null, flatten=_Null, out=None, name=None, **kwargs)

Fully Connected operator for input, weight and bias data type of int8, and accumulates in type int32 for the output. For each argument, two more arguments of type float32 must be provided representing the thresholds of quantizing argument from data type float32 to int8. The final outputs contain the convolution result in int32, and min and max thresholds representing the threholds for quantizing the float32 output into int32.

Note

This operator only supports forward propogation. DO NOT use it in training.

Defined in src/operator/quantization/quantized_fully_connected.cc:L313

Parameters
• data (NDArray) – Input data.

• weight (NDArray) – weight.

• bias (NDArray) – bias.

• min_data (NDArray) – Minimum value of data.

• max_data (NDArray) – Maximum value of data.

• min_weight (NDArray) – Minimum value of weight.

• max_weight (NDArray) – Maximum value of weight.

• min_bias (NDArray) – Minimum value of bias.

• max_bias (NDArray) – Maximum value of bias.

• num_hidden (int, required) – Number of hidden nodes of the output.

• no_bias (boolean, optional, default=0) – Whether to disable bias parameter.

• flatten (boolean, optional, default=1) – Whether to collapse all but the first axis of the input data tensor.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.quantized_pooling(data=None, min_data=None, max_data=None, kernel=_Null, pool_type=_Null, global_pool=_Null, cudnn_off=_Null, pooling_convention=_Null, stride=_Null, pad=_Null, p_value=_Null, count_include_pad=_Null, layout=_Null, out=None, name=None, **kwargs)

Pooling operator for input and output data type of int8. The input and output data comes with min and max thresholds for quantizing the float32 data into int8.

Note

This operator only supports forward propogation. DO NOT use it in training. This operator only supports pool_type of avg or max.

Defined in src/operator/quantization/quantized_pooling.cc:L187

Parameters
• data (NDArray) – Input data.

• min_data (NDArray) – Minimum value of data.

• max_data (NDArray) – Maximum value of data.

• kernel (Shape(tuple), optional, default=[]) – Pooling kernel size: (y, x) or (d, y, x)

• pool_type ({'avg', 'lp', 'max', 'sum'},optional, default='max') – Pooling type to be applied.

• global_pool (boolean, optional, default=0) – Ignore kernel size, do global pooling based on current input feature map.

• cudnn_off (boolean, optional, default=0) – Turn off cudnn pooling and use MXNet pooling operator.

• pooling_convention ({'full', 'same', 'valid'},optional, default='valid') – Pooling convention to be applied.

• stride (Shape(tuple), optional, default=[]) – Stride: for pooling (y, x) or (d, y, x). Defaults to 1 for each dimension.

• pad (Shape(tuple), optional, default=[]) – Pad for pooling: (y, x) or (d, y, x). Defaults to no padding.

• p_value (int or None, optional, default='None') – Value of p for Lp pooling, can be 1 or 2, required for Lp Pooling.

• count_include_pad (boolean or None, optional, default=None) – Only used for AvgPool, specify whether to count padding elements for averagecalculation. For example, with a 5*5 kernel on a 3*3 corner of a image,the sum of the 9 valid elements will be divided by 25 if this is set to true,or it will be divided by 9 if this is set to false. Defaults to true.

• layout ({None, 'NCDHW', 'NCHW', 'NCW', 'NDHWC', 'NHWC', 'NWC'},optional, default='None') – Set layout for input and output. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.requantize(data=None, min_range=None, max_range=None, out_type=_Null, min_calib_range=_Null, max_calib_range=_Null, out=None, name=None, **kwargs)

Given data that is quantized in int32 and the corresponding thresholds, requantize the data into int8 using min and max thresholds either calculated at runtime or from calibration. It’s highly recommended to pre-calucate the min and max thresholds through calibration since it is able to save the runtime of the operator and improve the inference accuracy.

Note

This operator only supports forward propogation. DO NOT use it in training.

Defined in src/operator/quantization/requantize.cc:L60

Parameters
• data (NDArray) – A ndarray/symbol of type int32

• min_range (NDArray) – The original minimum scalar value in the form of float32 used for quantizing data into int32.

• max_range (NDArray) – The original maximum scalar value in the form of float32 used for quantizing data into int32.

• out_type ({'auto', 'int8', 'uint8'},optional, default='int8') – Output data type. auto can be specified to automatically determine output type according to min_calib_range.

• min_calib_range (float or None, optional, default=None) – The minimum scalar value in the form of float32 obtained through calibration. If present, it will be used to requantize the int32 data into int8.

• max_calib_range (float or None, optional, default=None) – The maximum scalar value in the form of float32 obtained through calibration. If present, it will be used to requantize the int32 data into int8.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.round_ste(data=None, out=None, name=None, **kwargs)

Straight-through-estimator of round().

In forward pass, returns element-wise rounded value to the nearest integer of the input (same as round()).

In backward pass, returns gradients of 1 everywhere (instead of 0 everywhere as in round()): $$\frac{d}{dx}{round\_ste(x)} = 1$$ vs. $$\frac{d}{dx}{round(x)} = 0$$. This is useful for quantized training.

Reference: Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation.

Example::

x = round_ste([-1.5, 1.5, -1.9, 1.9, 2.7]) x.backward() x = [-2., 2., -2., 2., 3.] x.grad() = [1., 1., 1., 1., 1.]

The storage type of round_ste output depends upon the input storage type:
• round_ste(default) = default

• round_ste(row_sparse) = row_sparse

• round_ste(csr) = csr

Defined in src/operator/contrib/stes_op.cc:L55

Parameters
• data (NDArray) – The input array.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.contrib.sign_ste(data=None, out=None, name=None, **kwargs)

Straight-through-estimator of sign().

In forward pass, returns element-wise sign of the input (same as sign()).

In backward pass, returns gradients of 1 everywhere (instead of 0 everywhere as in sign()): $$\frac{d}{dx}{sign\_ste(x)} = 1$$ vs. $$\frac{d}{dx}{sign(x)} = 0$$. This is useful for quantized training.

Reference: Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation.

Example::

x = sign_ste([-2, 0, 3]) x.backward() x = [-1., 0., 1.] x.grad() = [1., 1., 1.]

The storage type of sign_ste` output depends upon the input storage type:
• round_ste(default) = default

• round_ste(row_sparse) = row_sparse

• round_ste(csr) = csr

Defined in src/operator/contrib/stes_op.cc:L80

Parameters
• data (NDArray) – The input array.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays