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The following activation functions are supported: - `relu`: Rectified Linear Unit, :math:`y = max(x, 0)` - `sigmoid`: :math:`y = \frac{1}{1 + exp(-x)}` - `tanh`: Hyperbolic tangent, :math:`y = \frac{exp(x) - exp(-x)}{exp(x) + exp(-x)}` - `softrelu`: Soft ReLU, or SoftPlus, :math:`y = log(1 + exp(x))` - `softsign`: :math:`y = \frac{x}{1 + abs(x)}` Defined in src/operator/nn/activation.cc:L147 Parameters ---------- data : NDArray The input array. 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 : NDArray or list of NDArrays The output of this function. i(i((tdatatact_typetouttnametkwargs((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt ActivationscKsdS(sJ Batch normalization. Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as well as offset ``beta``. Assume the input has more than one dimension and we normalize along axis 1. We first compute the mean and variance along this axis: .. math:: data\_mean[i] = mean(data[:,i,:,...]) \\ data\_var[i] = var(data[:,i,:,...]) Then compute the normalized output, which has the same shape as input, as following: .. math:: out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i] Both *mean* and *var* returns a scalar by treating the input as a vector. Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta`` have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and the inverse of ``data_var``, which are needed for the backward pass. Note that gradient of these two outputs are blocked. Besides the inputs and the outputs, this operator accepts two auxiliary states, ``moving_mean`` and ``moving_var``, which are *k*-length vectors. They are global statistics for the whole dataset, which are updated by:: moving_mean = moving_mean * momentum + data_mean * (1 - momentum) moving_var = moving_var * momentum + data_var * (1 - momentum) If ``use_global_stats`` is set to be true, then ``moving_mean`` and ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute the output. It is often used during inference. The parameter ``axis`` specifies which axis of the input shape denotes the 'channel' (separately normalized groups). The default is 1. Specifying -1 sets the channel axis to be the last item in the input shape. Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true, then set ``gamma`` to 1 and its gradient to 0. Note:: When fix_gamma is set to True, no sparse support is provided. If fix_gamma is set to False, the sparse tensors will fallback. Defined in src/operator/nn/batch_norm.cc:L575 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=0.001 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=0.9 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 out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((Rtgammatbetat moving_meant moving_vartepstmomentumt fix_gammatuse_global_statstoutput_mean_vartaxist cudnn_offRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt BatchNorm&sZc KsdS(s¾ Batch normalization. This operator is DEPRECATED. Perform BatchNorm on the input. Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as well as offset ``beta``. Assume the input has more than one dimension and we normalize along axis 1. We first compute the mean and variance along this axis: .. math:: data\_mean[i] = mean(data[:,i,:,...]) \\ data\_var[i] = var(data[:,i,:,...]) Then compute the normalized output, which has the same shape as input, as following: .. math:: out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i] Both *mean* and *var* returns a scalar by treating the input as a vector. Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta`` have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and ``data_var`` as well, which are needed for the backward pass. Besides the inputs and the outputs, this operator accepts two auxiliary states, ``moving_mean`` and ``moving_var``, which are *k*-length vectors. They are global statistics for the whole dataset, which are updated by:: moving_mean = moving_mean * momentum + data_mean * (1 - momentum) moving_var = moving_var * momentum + data_var * (1 - momentum) If ``use_global_stats`` is set to be true, then ``moving_mean`` and ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute the output. It is often used during inference. Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true, then set ``gamma`` to 1 and its gradient to 0. There's no sparse support for this operator, and it will exhibit problematic behavior if used with sparse tensors. Defined in src/operator/batch_norm_v1.cc:L95 Parameters ---------- data : NDArray Input data to batch normalization gamma : NDArray gamma array beta : NDArray beta array eps : float, optional, default=0.001 Epsilon to prevent div 0 momentum : float, optional, default=0.9 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 out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( RRR R R RRRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt BatchNorm_v1‚sMcKsdS(so Applies bilinear sampling to input feature map. Bilinear Sampling is the key of [NIPS2015] \"Spatial Transformer Networks\". The usage of the operator is very similar to remap function in OpenCV, except that the operator has the backward pass. Given :math:`data` and :math:`grid`, then the output is computed by .. math:: x_{src} = grid[batch, 0, y_{dst}, x_{dst}] \\ y_{src} = grid[batch, 1, y_{dst}, x_{dst}] \\ output[batch, channel, y_{dst}, x_{dst}] = G(data[batch, channel, y_{src}, x_{src}) :math:`x_{dst}`, :math:`y_{dst}` enumerate all spatial locations in :math:`output`, and :math:`G()` denotes the bilinear interpolation kernel. The out-boundary points will be padded with zeros.The shape of the output will be (data.shape[0], data.shape[1], grid.shape[2], grid.shape[3]). The operator assumes that :math:`data` has 'NCHW' layout and :math:`grid` has been normalized to [-1, 1]. BilinearSampler often cooperates with GridGenerator which generates sampling grids for BilinearSampler. GridGenerator supports two kinds of transformation: ``affine`` and ``warp``. If users want to design a CustomOp to manipulate :math:`grid`, please firstly refer to the code of GridGenerator. Example 1:: ## Zoom out data two times data = array([[[[1, 4, 3, 6], [1, 8, 8, 9], [0, 4, 1, 5], [1, 0, 1, 3]]]]) affine_matrix = array([[2, 0, 0], [0, 2, 0]]) affine_matrix = reshape(affine_matrix, shape=(1, 6)) grid = GridGenerator(data=affine_matrix, transform_type='affine', target_shape=(4, 4)) out = BilinearSampler(data, grid) out [[[[ 0, 0, 0, 0], [ 0, 3.5, 6.5, 0], [ 0, 1.25, 2.5, 0], [ 0, 0, 0, 0]]] Example 2:: ## shift data horizontally by -1 pixel data = array([[[[1, 4, 3, 6], [1, 8, 8, 9], [0, 4, 1, 5], [1, 0, 1, 3]]]]) warp_maxtrix = array([[[[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]], [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]]]) grid = GridGenerator(data=warp_matrix, transform_type='warp') out = BilinearSampler(data, grid) out [[[[ 4, 3, 6, 0], [ 8, 8, 9, 0], [ 4, 1, 5, 0], [ 0, 1, 3, 0]]] Defined in src/operator/bilinear_sampler.cc:L256 Parameters ---------- data : NDArray Input data to the BilinearsamplerOp. grid : NDArray Input grid to the BilinearsamplerOp.grid has two channels: x_src, y_src cudnn_off : boolean or None, optional, default=None whether to turn cudnn off out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RtgridRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytBilinearSamplerŃs]cKsdS(sōStops gradient computation. Stops the accumulated gradient of the inputs from flowing through this operator in the backward direction. In other words, this operator prevents the contribution of its inputs to be taken into account for computing gradients. Example:: v1 = [1, 2] v2 = [0, 1] a = Variable('a') b = Variable('b') b_stop_grad = stop_gradient(3 * b) loss = MakeLoss(b_stop_grad + a) executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2)) executor.forward(is_train=True, a=v1, b=v2) executor.outputs [ 1. 5.] executor.backward() executor.grad_arrays [ 0. 0.] [ 1. 1.] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L267 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt BlockGrad0s+c KsdS(s7Connectionist Temporal Classification Loss. 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:L97 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 : NDArray or list of NDArrays The output of this function. i(i(( Rtlabelt data_lengthst label_lengthstuse_data_lengthstuse_label_lengthst blank_labelRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytCTCLoss]sHcKsdS(sģCasts all elements of the input to a new type. .. note:: ``Cast`` is deprecated. Use ``cast`` instead. Example:: cast([0.9, 1.3], dtype='int32') = [0, 1] cast([1e20, 11.1], dtype='float16') = [inf, 11.09375] cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594 Parameters ---------- data : NDArray The input. dtype : {'float16', 'float32', 'float64', 'int32', 'int64', 'int8', 'uint8'}, required Output data type. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RtdtypeRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytCast§scOsdS(sˆJoins input arrays along a given axis. .. note:: `Concat` is deprecated. Use `concat` instead. The dimensions of the input arrays should be the same except the axis along which they will be concatenated. The dimension of the output array along the concatenated axis will be equal to the sum of the corresponding dimensions of the input arrays. The storage type of ``concat`` output depends on storage types of inputs - concat(csr, csr, ..., csr, dim=0) = csr - otherwise, ``concat`` generates output with default storage Example:: x = [[1,1],[2,2]] y = [[3,3],[4,4],[5,5]] z = [[6,6], [7,7],[8,8]] concat(x,y,z,dim=0) = [[ 1., 1.], [ 2., 2.], [ 3., 3.], [ 4., 4.], [ 5., 5.], [ 6., 6.], [ 7., 7.], [ 8., 8.]] Note that you cannot concat x,y,z along dimension 1 since dimension 0 is not the same for all the input arrays. concat(y,z,dim=1) = [[ 3., 3., 6., 6.], [ 4., 4., 7., 7.], [ 5., 5., 8., 8.]] Defined in src/operator/nn/concat.cc:L365 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 : NDArray or list of NDArrays The output of this function. i(i((RR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytConcatĒs8cKsdS(säCompute *N*-D convolution on *(N+2)*-D input. In the 2-D convolution, given input data with shape *(batch_size, channel, height, width)*, the output is computed by .. math:: out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star weight[i,j,:,:] where :math:`\star` is the 2-D cross-correlation operator. For general 2-D convolution, the shapes are - **data**: *(batch_size, channel, height, width)* - **weight**: *(num_filter, channel, kernel[0], kernel[1])* - **bias**: *(num_filter,)* - **out**: *(batch_size, num_filter, out_height, out_width)*. Define:: f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1 then we have:: out_height=f(height, kernel[0], pad[0], stride[0], dilate[0]) out_width=f(width, kernel[1], pad[1], stride[1], dilate[1]) If ``no_bias`` is set to be true, then the ``bias`` term is ignored. The default data ``layout`` is *NCHW*, namely *(batch_size, channel, height, width)*. We can choose other layouts such as *NWC*. If ``num_group`` is larger than 1, denoted by *g*, then split the input ``data`` evenly into *g* parts along the channel axis, and also evenly split ``weight`` along the first dimension. Next compute the convolution on the *i*-th part of the data with the *i*-th weight part. The output is obtained by concatenating all the *g* results. 1-D convolution does not have *height* dimension but only *width* in space. - **data**: *(batch_size, channel, width)* - **weight**: *(num_filter, channel, kernel[0])* - **bias**: *(num_filter,)* - **out**: *(batch_size, num_filter, out_width)*. 3-D convolution adds an additional *depth* dimension besides *height* and *width*. The shapes are - **data**: *(batch_size, channel, depth, height, width)* - **weight**: *(num_filter, channel, kernel[0], kernel[1], kernel[2])* - **bias**: *(num_filter,)* - **out**: *(batch_size, num_filter, out_depth, out_height, out_width)*. Both ``weight`` and ``bias`` are learnable parameters. There are other options to tune the performance. - **cudnn_tune**: enable this option leads to higher startup time but may give faster speed. Options are - **off**: no tuning - **limited_workspace**:run test and pick the fastest algorithm that doesn't exceed workspace limit. - **fastest**: pick the fastest algorithm and ignore workspace limit. - **None** (default): the behavior is determined by environment variable ``MXNET_CUDNN_AUTOTUNE_DEFAULT``. 0 for off, 1 for limited workspace (default), 2 for fastest. - **workspace**: A large number leads to more (GPU) memory usage but may improve the performance. Defined in src/operator/nn/convolution.cc:L461 Parameters ---------- data : NDArray Input data to the ConvolutionOp. weight : NDArray Weight matrix. bias : NDArray Bias parameter. 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 : NDArray or list of NDArrays The output of this function. i(i((Rtweighttbiastkerneltstridetdilatetpadt num_filtert num_groupt workspacetno_biast cudnn_tuneRtlayoutRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt ConvolutionsucKsdS(sš This operator is DEPRECATED. Apply convolution to input then add a bias. Parameters ---------- data : NDArray Input data to the ConvolutionV1Op. 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) dilate : Shape(tuple), optional, default=[] convolution dilate: (h, w) or (d, h, w) pad : Shape(tuple), optional, default=[] pad for convolution: (h, w) or (d, h, w) num_filter : int (non-negative), required convolution filter(channel) number num_group : int (non-negative), optional, default=1 Number of group partitions. Equivalent to slicing input into num_group partitions, apply convolution on each, then concatenate the results workspace : long (non-negative), optional, default=1024 Maximum temporary workspace allowed for convolution (MB).This parameter determines the effective batch size of the convolution kernel, which may be smaller than the given batch size. Also, the workspace will be automatically enlarged to make sure that we can run the kernel with batch_size=1 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. Leads to higher startup time but may give faster speed. Options are: 'off': no tuning 'limited_workspace': run test and pick the fastest algorithm that doesn't exceed workspace limit. 'fastest': pick the fastest algorithm and ignore workspace limit. If set to None (default), behavior is determined by environment variable MXNET_CUDNN_AUTOTUNE_DEFAULT: 0 for off, 1 for limited workspace (default), 2 for fastest. cudnn_off : boolean, optional, default=0 Turn off cudnn for this layer. layout : {None, 'NCDHW', 'NCHW', 'NDHWC', 'NHWC'},optional, default='None' Set layout for input, output and weight. Empty for default layout: NCHW for 2d and NCDHW for 3d. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR"R#R$R%R&R'R(R)R*R+R,RR-RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytConvolution_v1xs3c KsdS(s Applies correlation to inputs. The correlation layer performs multiplicative patch comparisons between two feature maps. Given two multi-channel feature maps :math:`f_{1}, f_{2}`, with :math:`w`, :math:`h`, and :math:`c` being their width, height, and number of channels, the correlation layer lets the network compare each patch from :math:`f_{1}` with each patch from :math:`f_{2}`. For now we consider only a single comparison of two patches. The 'correlation' of two patches centered at :math:`x_{1}` in the first map and :math:`x_{2}` in the second map is then defined as: .. math:: c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]} for a square patch of size :math:`K:=2k+1`. Note that the equation above is identical to one step of a convolution in neural networks, but instead of convolving data with a filter, it convolves data with other data. For this reason, it has no training weights. Computing :math:`c(x_{1}, x_{2})` involves :math:`c * K^{2}` multiplications. Comparing all patch combinations involves :math:`w^{2}*h^{2}` such computations. Given a maximum displacement :math:`d`, for each location :math:`x_{1}` it computes correlations :math:`c(x_{1}, x_{2})` only in a neighborhood of size :math:`D:=2d+1`, by limiting the range of :math:`x_{2}`. We use strides :math:`s_{1}, s_{2}`, to quantize :math:`x_{1}` globally and to quantize :math:`x_{2}` within the neighborhood centered around :math:`x_{1}`. The final output is defined by the following expression: .. math:: out[n, q, i, j] = c(x_{i, j}, x_{q}) where :math:`i` and :math:`j` enumerate spatial locations in :math:`f_{1}`, and :math:`q` denotes the :math:`q^{th}` neighborhood of :math:`x_{i,j}`. Defined in src/operator/correlation.cc:L198 Parameters ---------- data1 : NDArray Input data1 to the correlation. data2 : NDArray Input data2 to the correlation. kernel_size : int (non-negative), optional, default=1 kernel size for Correlation must be an odd number max_displacement : int (non-negative), optional, default=1 Max displacement of Correlation stride1 : int (non-negative), optional, default=1 stride1 quantize data1 globally stride2 : int (non-negative), optional, default=1 stride2 quantize data2 within the neighborhood centered around data1 pad_size : int (non-negative), optional, default=0 pad for Correlation is_multiply : boolean, optional, default=1 operation type is either multiplication or subduction out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( tdata1tdata2t kernel_sizetmax_displacementtstride1tstride2tpad_sizet is_multiplyRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt Correlation­s?cOsdS(s .. note:: `Crop` is deprecated. Use `slice` instead. Crop the 2nd and 3rd dim of input data, with the corresponding size of h_w or with width and height of the second input symbol, i.e., with one input, we need h_w to specify the crop height and width, otherwise the second input symbol's size will be used Defined in src/operator/crop.cc:L50 Parameters ---------- data : Symbol or Symbol[] Tensor or List of Tensors, the second input will be used as crop_like shape reference offset : Shape(tuple), optional, default=[0,0] crop offset coordinate: (y, x) h_w : Shape(tuple), optional, default=[0,0] crop height and width: (h, w) center_crop : boolean, optional, default=0 If set to true, then it will use be the center_crop,or it will crop using the shape of crop_like out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytCropīscOsdS(s©Apply a custom operator implemented in a frontend language (like Python). Custom operators should override required methods like `forward` and `backward`. The custom operator must be registered before it can be used. Please check the tutorial here: http://mxnet.io/faq/new_op.html. Defined in src/operator/custom/custom.cc:L547 Parameters ---------- data : NDArray[] Input data for the custom operator. op_type : string Name of the custom operator. This is the name that is passed to `mx.operator.register` to register the operator. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. Example ------- Applies a custom operator named `my_custom_operator` to `input`. >>> output = mx.symbol.Custom(op_type='my_custom_operator', data=input) i(i((RR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytCustoms cKsdS(s$ Computes 1D or 2D transposed convolution (aka fractionally strided convolution) of the input tensor. This operation can be seen as the gradient of Convolution operation with respect to its input. Convolution usually reduces the size of the input. Transposed convolution works the other way, going from a smaller input to a larger output while preserving the connectivity pattern. Parameters ---------- data : NDArray Input tensor to the deconvolution operation. weight : NDArray Weights representing the kernel. bias : NDArray Bias added to the result after the deconvolution operation. kernel : Shape(tuple), required Deconvolution kernel size: (w,), (h, w) or (d, h, w). This is same as the kernel size used for the corresponding convolution stride : Shape(tuple), optional, default=[] The stride used for the corresponding convolution: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension. dilate : Shape(tuple), optional, default=[] Dilation factor for each dimension of the input: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension. pad : Shape(tuple), optional, default=[] The amount of implicit zero padding added during convolution for each dimension of the input: (w,), (h, w) or (d, h, w). ``(kernel-1)/2`` is usually a good choice. If `target_shape` is set, `pad` will be ignored and a padding that will generate the target shape will be used. Defaults to no padding. adj : Shape(tuple), optional, default=[] Adjustment for output shape: (w,), (h, w) or (d, h, w). If `target_shape` is set, `adj` will be ignored and computed accordingly. target_shape : Shape(tuple), optional, default=[] Shape of the output tensor: (w,), (h, w) or (d, h, w). num_filter : int (non-negative), required Number of output filters. num_group : int (non-negative), optional, default=1 Number of groups partition. workspace : long (non-negative), optional, default=512 Maximum temporary workspace allowed (MB) in deconvolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the deconvolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when `limited_workspace` strategy is used. no_bias : boolean, optional, default=1 Whether to disable bias parameter. cudnn_tune : {None, 'fastest', 'limited_workspace', 'off'},optional, default='None' Whether to pick convolution algorithm 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 : NDArray or list of NDArrays The output of this function. i(i((RR"R#R$R%R&R'tadjt target_shapeR(R)R*R+R,RR-RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt Deconvolution1s.cKsdS(sŪApplies dropout operation to input array. - During training, each element of the input is set to zero with probability p. The whole array is rescaled by :math:`1/(1-p)` to keep the expected sum of the input unchanged. - During testing, this operator does not change the input if mode is 'training'. If mode is 'always', the same computaion as during training will be applied. Example:: random.seed(998) input_array = array([[3., 0.5, -0.5, 2., 7.], [2., -0.4, 7., 3., 0.2]]) a = symbol.Variable('a') dropout = symbol.Dropout(a, p = 0.2) executor = dropout.simple_bind(a = input_array.shape) ## If training executor.forward(is_train = True, a = input_array) executor.outputs [[ 3.75 0.625 -0. 2.5 8.75 ] [ 2.5 -0.5 8.75 3.75 0. ]] ## If testing executor.forward(is_train = False, a = input_array) executor.outputs [[ 3. 0.5 -0.5 2. 7. ] [ 2. -0.4 7. 3. 0.2 ]] Defined in src/operator/nn/dropout.cc:L76 Parameters ---------- data : NDArray Input array to which dropout will be applied. p : float, optional, default=0.5 Fraction of the input that gets dropped out during training time. mode : {'always', 'training'},optional, default='training' Whether to only turn on dropout during training or to also turn on for inference. axes : Shape(tuple), optional, default=[] Axes for variational dropout kernel. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RtptmodetaxesRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytDropoutas5cOsdS(sxAdds all input arguments element-wise. .. math:: add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n ``add_n`` is potentially more efficient than calling ``add`` by `n` times. The storage type of ``add_n`` output depends on storage types of inputs - add_n(row_sparse, row_sparse, ..) = row_sparse - add_n(default, csr, default) = default - add_n(any input combinations longer than 4 (>4) with at least one default type) = default - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage Defined in src/operator/tensor/elemwise_sum.cc:L156 Parameters ---------- args : NDArray[] Positional input arguments out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((targsR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytElementWiseSum˜s c KsdS(s± Maps integer indices to vector representations (embeddings). This operator maps words to real-valued vectors in a high-dimensional space, called word embeddings. These embeddings can capture semantic and syntactic properties of the words. For example, it has been noted that in the learned embedding spaces, similar words tend to be close to each other and dissimilar words far apart. For an input array of shape (d1, ..., dK), the shape of an output array is (d1, ..., dK, output_dim). All the input values should be integers in the range [0, input_dim). If the input_dim is ip0 and output_dim is op0, then shape of the embedding weight matrix must be (ip0, op0). By default, if any index mentioned is too large, it is replaced by the index that addresses the last vector in an embedding matrix. Examples:: input_dim = 4 output_dim = 5 // Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3) y = [[ 0., 1., 2., 3., 4.], [ 5., 6., 7., 8., 9.], [ 10., 11., 12., 13., 14.], [ 15., 16., 17., 18., 19.]] // Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)] x = [[ 1., 3.], [ 0., 2.]] // Mapped input x to its vector representation y. Embedding(x, y, 4, 5) = [[[ 5., 6., 7., 8., 9.], [ 15., 16., 17., 18., 19.]], [[ 0., 1., 2., 3., 4.], [ 10., 11., 12., 13., 14.]]] The storage type of weight can be either row_sparse or default. .. Note:: If "sparse_grad" is set to True, the storage type of gradient w.r.t weights will be "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad and Adam. Note that by default lazy updates is turned on, which may perform differently from standard updates. For more details, please check the Optimization API at: https://mxnet.incubator.apache.org/api/python/optimization/optimization.html Defined in src/operator/tensor/indexing_op.cc:L267 Parameters ---------- data : NDArray The input array to the embedding operator. weight : NDArray The embedding weight matrix. input_dim : int, required Vocabulary size of the input indices. output_dim : int, required Dimension of the embedding vectors. dtype : {'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 : NDArray or list of NDArrays The output of this function. i(i(( RR"t input_dimt output_dimRt sparse_gradRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt EmbeddingŗsNcKsdS(s#Flattens the input array into a 2-D array by collapsing the higher dimensions. .. note:: `Flatten` is deprecated. Use `flatten` instead. For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes the input array into an output array of shape ``(d1, d2*...*dk)``. Note that the bahavior of this function is different from numpy.ndarray.flatten, which behaves similar to mxnet.ndarray.reshape((-1,)). Example:: x = [[ [1,2,3], [4,5,6], [7,8,9] ], [ [1,2,3], [4,5,6], [7,8,9] ]], flatten(x) = [[ 1., 2., 3., 4., 5., 6., 7., 8., 9.], [ 1., 2., 3., 4., 5., 6., 7., 8., 9.]] Defined in src/operator/tensor/matrix_op.cc:L259 Parameters ---------- data : NDArray Input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytFlatten s+c KsdS(s;Applies a linear transformation: :math:`Y = XW^T + b`. If ``flatten`` is set to be true, then the shapes are: - **data**: `(batch_size, x1, x2, ..., xn)` - **weight**: `(num_hidden, x1 * x2 * ... * xn)` - **bias**: `(num_hidden,)` - **out**: `(batch_size, num_hidden)` If ``flatten`` is set to be false, then the shapes are: - **data**: `(x1, x2, ..., xn, input_dim)` - **weight**: `(num_hidden, input_dim)` - **bias**: `(num_hidden,)` - **out**: `(x1, x2, ..., xn, num_hidden)` The learnable parameters include both ``weight`` and ``bias``. If ``no_bias`` is set to be true, then the ``bias`` term is ignored. .. Note:: The sparse support for FullyConnected is limited to forward evaluation with `row_sparse` weight and bias, where the length of `weight.indices` and `bias.indices` must be equal to `num_hidden`. This could be useful for model inference with `row_sparse` weights trained with importance sampling or noise contrastive estimation. To compute linear transformation with 'csr' sparse data, sparse.dot is recommended instead of sparse.FullyConnected. Defined in src/operator/nn/fully_connected.cc:L271 Parameters ---------- data : NDArray Input data. weight : NDArray Weight matrix. bias : NDArray Bias parameter. 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 : NDArray or list of NDArrays The output of this function. i(i(( RR"R#t num_hiddenR+tflattenRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytFullyConnected7s:cKsdS(sūGenerates 2D sampling grid for bilinear sampling. Parameters ---------- data : NDArray Input data to the function. transform_type : {'affine', 'warp'}, required The type of transformation. For `affine`, input data should be an affine matrix of size (batch, 6). For `warp`, input data should be an optical flow of size (batch, 2, h, w). target_shape : Shape(tuple), optional, default=[0,0] Specifies the output shape (H, W). This is required if transformation type is `affine`. If transformation type is `warp`, this parameter is ignored. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((Rttransform_typeR<RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt GridGeneratorsscKsdS(sTApply a sparse regularization to the output a sigmoid activation function. Parameters ---------- data : NDArray Input data. sparseness_target : float, optional, default=0.1 The sparseness target penalty : float, optional, default=0.001 The tradeoff parameter for the sparseness penalty momentum : float, optional, default=0.9 The momentum for running average out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((Rtsparseness_targettpenaltyR RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytIdentityAttachKLSparseReg‰scKsdS(s'Applies instance normalization to the n-dimensional input array. This operator takes an n-dimensional input array where (n>2) and normalizes the input using the following formula: .. math:: out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta This layer is similar to batch normalization layer (`BatchNorm`) with two differences: first, the normalization is carried out per example (instance), not over a batch. Second, the same normalization is applied both at test and train time. This operation is also known as `contrast normalization`. If the input data is of shape [batch, channel, spacial_dim1, spacial_dim2, ...], `gamma` and `beta` parameters must be vectors of shape [channel]. This implementation is based on paper: .. [1] Instance Normalization: The Missing Ingredient for Fast Stylization, D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2). Examples:: // Input of shape (2,1,2) x = [[[ 1.1, 2.2]], [[ 3.3, 4.4]]] // gamma parameter of length 1 gamma = [1.5] // beta parameter of length 1 beta = [0.5] // Instance normalization is calculated with the above formula InstanceNorm(x,gamma,beta) = [[[-0.997527 , 1.99752665]], [[-0.99752653, 1.99752724]]] Defined in src/operator/instance_norm.cc:L95 Parameters ---------- data : NDArray An n-dimensional input array (n > 2) of the form [batch, channel, spatial_dim1, spatial_dim2, ...]. gamma : NDArray A vector of length 'channel', which multiplies the normalized input. beta : NDArray A vector of length 'channel', which is added to the product of the normalized input and the weight. eps : float, optional, default=0.001 An `epsilon` parameter to prevent division by 0. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR R RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt InstanceNorm”s?cKsdS(sKNormalize the input array using the L2 norm. For 1-D NDArray, it computes:: out = data / sqrt(sum(data ** 2) + eps) For N-D NDArray, if the input array has shape (N, N, ..., N), with ``mode`` = ``instance``, it normalizes each instance in the multidimensional array by its L2 norm.:: for i in 0...N out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps) with ``mode`` = ``channel``, it normalizes each channel in the array by its L2 norm.:: for i in 0...N out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps) with ``mode`` = ``spatial``, it normalizes the cross channel norm for each position in the array by its L2 norm.:: for dim in 2...N for i in 0...N out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps) -dim- Example:: x = [[[1,2], [3,4]], [[2,2], [5,6]]] L2Normalization(x, mode='instance') =[[[ 0.18257418 0.36514837] [ 0.54772252 0.73029673]] [[ 0.24077171 0.24077171] [ 0.60192931 0.72231513]]] L2Normalization(x, mode='channel') =[[[ 0.31622776 0.44721359] [ 0.94868326 0.89442718]] [[ 0.37139067 0.31622776] [ 0.92847669 0.94868326]]] L2Normalization(x, mode='spatial') =[[[ 0.44721359 0.89442718] [ 0.60000002 0.80000001]] [[ 0.70710677 0.70710677] [ 0.6401844 0.76822126]]] Defined in src/operator/l2_normalization.cc:L98 Parameters ---------- data : NDArray Input array to normalize. eps : float, optional, default=1e-10 A small constant for numerical stability. mode : {'channel', 'instance', 'spatial'},optional, default='instance' Specify the dimension along which to compute L2 norm. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR R?RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytL2NormalizationāsJcKsdS(s“Applies local response normalization to the input. The local response normalization layer performs "lateral inhibition" by normalizing over local input regions. If :math:`a_{x,y}^{i}` is the activity of a neuron computed by applying kernel :math:`i` at position :math:`(x, y)` and then applying the ReLU nonlinearity, the response-normalized activity :math:`b_{x,y}^{i}` is given by the expression: .. math:: b_{x,y}^{i} = \frac{a_{x,y}^{i}}{\Bigg({k + \frac{\alpha}{n} \sum_{j=max(0, i-\frac{n}{2})}^{min(N-1, i+\frac{n}{2})} (a_{x,y}^{j})^{2}}\Bigg)^{\beta}} where the sum runs over :math:`n` "adjacent" kernel maps at the same spatial position, and :math:`N` is the total number of kernels in the layer. Defined in src/operator/nn/lrn.cc:L164 Parameters ---------- data : NDArray Input data to LRN alpha : float, optional, default=0.0001 The variance scaling parameter :math:`lpha` in the LRN expression. beta : float, optional, default=0.75 The power parameter :math:`eta` in the LRN expression. knorm : float, optional, default=2 The parameter :math:`k` in the LRN expression. nsize : int (non-negative), required normalization window width in elements. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RtalphaR tknormtnsizeRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytLRN.s)c KsdS(s”Layer normalization. Normalizes the channels of the input tensor by mean and variance, and applies a scale ``gamma`` as well as offset ``beta``. Assume the input has more than one dimension and we normalize along axis 1. We first compute the mean and variance along this axis and then compute the normalized output, which has the same shape as input, as following: .. math:: out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta Both ``gamma`` and ``beta`` are learnable parameters. Unlike BatchNorm and InstanceNorm, the *mean* and *var* are computed along the channel dimension. Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta`` have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and ``data_std``. Note that no gradient will be passed through these two outputs. The parameter ``axis`` specifies which axis of the input shape denotes the 'channel' (separately normalized groups). The default is -1, which sets the channel axis to be the last item in the input shape. Defined in src/operator/nn/layer_norm.cc:L94 Parameters ---------- data : NDArray Input data to layer normalization gamma : NDArray gamma array beta : NDArray beta array axis : int, optional, default='-1' The axis to perform layer normalization. Usually, this should be be axis of the channel dimension. Negative values means indexing from right to left. eps : float, optional, default=1e-05 An `epsilon` parameter to prevent division by 0. output_mean_var : boolean, optional, default=0 Output the mean and std calculated along the given axis. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( RRR RR RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt LayerNormYs5c KsdS(stApplies Leaky rectified linear unit activation element-wise to the input. Leaky ReLUs attempt to fix the "dying ReLU" problem by allowing a small `slope` when the input is negative and has a slope of one when input is positive. The following modified ReLU Activation functions are supported: - *elu*: Exponential Linear Unit. `y = x > 0 ? x : slope * (exp(x)-1)` - *selu*: Scaled Exponential Linear Unit. `y = lambda * (x > 0 ? x : alpha * (exp(x) - 1))` where *lambda = 1.0507009873554804934193349852946* and *alpha = 1.6732632423543772848170429916717*. - *leaky*: Leaky ReLU. `y = x > 0 ? x : slope * x` - *prelu*: Parametric ReLU. This is same as *leaky* except that `slope` is learnt during training. - *rrelu*: Randomized ReLU. same as *leaky* but the `slope` is uniformly and randomly chosen from *[lower_bound, upper_bound)* for training, while fixed to be *(lower_bound+upper_bound)/2* for inference. Defined in src/operator/leaky_relu.cc:L65 Parameters ---------- data : NDArray Input data to activation function. gamma : NDArray Slope parameter for PReLU. Only required when act_type is 'prelu'. It should be either a vector of size 1, or the same size as the second dimension of data. act_type : {'elu', 'leaky', 'prelu', 'rrelu', 'selu'},optional, default='leaky' Activation function to be applied. slope : float, optional, default=0.25 Init slope for the activation. (For leaky and elu only) lower_bound : float, optional, default=0.125 Lower bound of random slope. (For rrelu only) upper_bound : float, optional, default=0.334 Upper bound of random slope. (For rrelu only) out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( RRRtslopet lower_boundt upper_boundRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt LeakyReLUs,cKsdS(sŽComputes and optimizes for squared loss during backward propagation. Just outputs ``data`` during forward propagation. If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i` is the corresponding target value, then the squared loss estimated over :math:`n` samples is defined as :math:`\text{SquaredLoss}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_2` .. note:: Use the LinearRegressionOutput as the final output layer of a net. The storage type of ``label`` can be ``default`` or ``csr`` - LinearRegressionOutput(default, default) = default - LinearRegressionOutput(default, csr) = default By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example. The parameter `grad_scale` can be used to change this scale to `grad_scale/m`. Defined in src/operator/regression_output.cc:L92 Parameters ---------- data : NDArray Input data to the function. label : NDArray Input label to the function. grad_scale : float, optional, default=1 Scale the gradient by a float factor out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRt grad_scaleRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytLinearRegressionOutput¾s)cKsdS(sVApplies a logistic function to the input. The logistic function, also known as the sigmoid function, is computed as :math:`\frac{1}{1+exp(-\textbf{x})}`. Commonly, the sigmoid is used to squash the real-valued output of a linear model :math:`wTx+b` into the [0,1] range so that it can be interpreted as a probability. It is suitable for binary classification or probability prediction tasks. .. note:: Use the LogisticRegressionOutput as the final output layer of a net. The storage type of ``label`` can be ``default`` or ``csr`` - LogisticRegressionOutput(default, default) = default - LogisticRegressionOutput(default, csr) = default The loss function used is the Binary Cross Entropy Loss: :math:`-{(y\log(p) + (1 - y)\log(1 - p))}` Where `y` is the ground truth probability of positive outcome for a given example, and `p` the probability predicted by the model. By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example. The parameter `grad_scale` can be used to change this scale to `grad_scale/m`. Defined in src/operator/regression_output.cc:L152 Parameters ---------- data : NDArray Input data to the function. label : NDArray Input label to the function. grad_scale : float, optional, default=1 Scale the gradient by a float factor out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR\RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytLogisticRegressionOutputés.cKsdS(sŽComputes mean absolute error of the input. MAE is a risk metric corresponding to the expected value of the absolute error. If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i` is the corresponding target value, then the mean absolute error (MAE) estimated over :math:`n` samples is defined as :math:`\text{MAE}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_1` .. note:: Use the MAERegressionOutput as the final output layer of a net. The storage type of ``label`` can be ``default`` or ``csr`` - MAERegressionOutput(default, default) = default - MAERegressionOutput(default, csr) = default By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example. The parameter `grad_scale` can be used to change this scale to `grad_scale/m`. Defined in src/operator/regression_output.cc:L120 Parameters ---------- data : NDArray Input data to the function. label : NDArray Input label to the function. grad_scale : float, optional, default=1 Scale the gradient by a float factor out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR\RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytMAERegressionOutputs*cKsdS(sŲMake your own loss function in network construction. This operator accepts a customized loss function symbol as a terminal loss and the symbol should be an operator with no backward dependency. The output of this function is the gradient of loss with respect to the input data. For example, if you are a making a cross entropy loss function. Assume ``out`` is the predicted output and ``label`` is the true label, then the cross entropy can be defined as:: cross_entropy = label * log(out) + (1 - label) * log(1 - out) loss = MakeLoss(cross_entropy) We will need to use ``MakeLoss`` when we are creating our own loss function or we want to combine multiple loss functions. Also we may want to stop some variables' gradients from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``. In addition, we can give a scale to the loss by setting ``grad_scale``, so that the gradient of the loss will be rescaled in the backpropagation. .. note:: This operator should be used as a Symbol instead of NDArray. Defined in src/operator/make_loss.cc:L71 Parameters ---------- data : NDArray Input array. grad_scale : float, optional, default=1 Gradient scale as a supplement to unary and binary operators valid_thresh : float, optional, default=0 clip each element in the array to 0 when it is less than ``valid_thresh``. This is used when ``normalization`` is set to ``'valid'``. normalization : {'batch', 'null', 'valid'},optional, default='null' If this is set to null, the output gradient will not be normalized. If this is set to batch, the output gradient will be divided by the batch size. If this is set to valid, the output gradient will be divided by the number of valid input elements. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR\t valid_thresht normalizationRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytMakeLossEs-cKsdS(sPads an input array with a constant or edge values of the array. .. note:: `Pad` is deprecated. Use `pad` instead. .. note:: Current implementation only supports 4D and 5D input arrays with padding applied only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero. This operation pads an input array with either a `constant_value` or edge values along each axis of the input array. The amount of padding is specified by `pad_width`. `pad_width` is a tuple of integer padding widths for each axis of the format ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of length ``2*N`` where ``N`` is the number of dimensions of the array. For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values to add before and after the elements of the array along dimension ``N``. The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``, ``after_2`` must be 0. Example:: x = [[[[ 1. 2. 3.] [ 4. 5. 6.]] [[ 7. 8. 9.] [ 10. 11. 12.]]] [[[ 11. 12. 13.] [ 14. 15. 16.]] [[ 17. 18. 19.] [ 20. 21. 22.]]]] pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) = [[[[ 1. 1. 2. 3. 3.] [ 1. 1. 2. 3. 3.] [ 4. 4. 5. 6. 6.] [ 4. 4. 5. 6. 6.]] [[ 7. 7. 8. 9. 9.] [ 7. 7. 8. 9. 9.] [ 10. 10. 11. 12. 12.] [ 10. 10. 11. 12. 12.]]] [[[ 11. 11. 12. 13. 13.] [ 11. 11. 12. 13. 13.] [ 14. 14. 15. 16. 16.] [ 14. 14. 15. 16. 16.]] [[ 17. 17. 18. 19. 19.] [ 17. 17. 18. 19. 19.] [ 20. 20. 21. 22. 22.] [ 20. 20. 21. 22. 22.]]]] pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) = [[[[ 0. 0. 0. 0. 0.] [ 0. 1. 2. 3. 0.] [ 0. 4. 5. 6. 0.] [ 0. 0. 0. 0. 0.]] [[ 0. 0. 0. 0. 0.] [ 0. 7. 8. 9. 0.] [ 0. 10. 11. 12. 0.] [ 0. 0. 0. 0. 0.]]] [[[ 0. 0. 0. 0. 0.] [ 0. 11. 12. 13. 0.] [ 0. 14. 15. 16. 0.] [ 0. 0. 0. 0. 0.]] [[ 0. 0. 0. 0. 0.] [ 0. 17. 18. 19. 0.] [ 0. 20. 21. 22. 0.] [ 0. 0. 0. 0. 0.]]]] Defined in src/operator/pad.cc:L766 Parameters ---------- data : NDArray An n-dimensional input array. mode : {'constant', 'edge', 'reflect'}, required Padding type to use. "constant" pads with `constant_value` "edge" pads using the edge values of the input array "reflect" pads by reflecting values with respect to the edges. pad_width : Shape(tuple), required Widths of the padding regions applied to the edges of each axis. It is a tuple of integer padding widths for each axis of the format ``(before_1, after_1, ... , before_N, after_N)``. It should be of length ``2*N`` where ``N`` is the number of dimensions of the array.This is equivalent to pad_width in numpy.pad, but flattened. constant_value : double, optional, default=0 The value used for padding when `mode` is "constant". out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR?t pad_widthtconstant_valueRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytPadtsic KsdS(s Performs pooling on the input. The shapes for 1-D pooling are - **data**: *(batch_size, channel, width)*, - **out**: *(batch_size, num_filter, out_width)*. The shapes for 2-D pooling are - **data**: *(batch_size, channel, height, width)* - **out**: *(batch_size, num_filter, out_height, out_width)*, with:: out_height = f(height, kernel[0], pad[0], stride[0]) out_width = f(width, kernel[1], pad[1], stride[1]) The definition of *f* depends on ``pooling_convention``, which has two options: - **valid** (default):: f(x, k, p, s) = floor((x+2*p-k)/s)+1 - **full**, which is compatible with Caffe:: f(x, k, p, s) = ceil((x+2*p-k)/s)+1 But ``global_pool`` is set to be true, then do a global pooling, namely reset ``kernel=(height, width)``. Three pooling options are supported by ``pool_type``: - **avg**: average pooling - **max**: max pooling - **sum**: sum pooling - **lp**: Lp pooling For 3-D pooling, an additional *depth* dimension is added before *height*. Namely the input data will have shape *(batch_size, channel, depth, height, width)*. Notes on Lp pooling: Lp pooling was first introduced by this paper: https://arxiv.org/pdf/1204.3968.pdf. L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling. We can see that Lp pooling stands between those two, in practice the most common value for p is 2. For each window ``X``, the mathematical expression for Lp pooling is: :math:`f(X) = \sqrt[p]{\sum_{x}^{X} x^p}` Defined in src/operator/nn/pooling.cc:L379 Parameters ---------- data : NDArray Input data to the pooling operator. 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. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( RR$t pool_typet global_poolRtpooling_conventionR%R'tp_valuetcount_include_padRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytPoolingßsUc KsdS(sThis operator is DEPRECATED. Perform pooling on the input. The shapes for 2-D pooling is - **data**: *(batch_size, channel, height, width)* - **out**: *(batch_size, num_filter, out_height, out_width)*, with:: out_height = f(height, kernel[0], pad[0], stride[0]) out_width = f(width, kernel[1], pad[1], stride[1]) The definition of *f* depends on ``pooling_convention``, which has two options: - **valid** (default):: f(x, k, p, s) = floor((x+2*p-k)/s)+1 - **full**, which is compatible with Caffe:: f(x, k, p, s) = ceil((x+2*p-k)/s)+1 But ``global_pool`` is set to be true, then do a global pooling, namely reset ``kernel=(height, width)``. Three pooling options are supported by ``pool_type``: - **avg**: average pooling - **max**: max pooling - **sum**: sum pooling 1-D pooling is special case of 2-D pooling with *weight=1* and *kernel[1]=1*. For 3-D pooling, an additional *depth* dimension is added before *height*. Namely the input data will have shape *(batch_size, channel, depth, height, width)*. Defined in src/operator/pooling_v1.cc:L104 Parameters ---------- data : NDArray Input data to the pooling operator. kernel : Shape(tuple), optional, default=[] pooling kernel size: (y, x) or (d, y, x) pool_type : {'avg', '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. pooling_convention : {'full', 'valid'},optional, default='valid' Pooling convention to be applied. stride : Shape(tuple), optional, default=[] stride: for pooling (y, x) or (d, y, x) pad : Shape(tuple), optional, default=[] pad for pooling: (y, x) or (d, y, x) out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( RR$RfRgRhR%R'RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt Pooling_v16sCc KsdS(sv Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are implemented, with both multi-layer and bidirectional support. **Vanilla RNN** Applies a single-gate recurrent layer to input X. Two kinds of activation function are supported: ReLU and Tanh. With ReLU activation function: .. math:: h_t = relu(W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh}) With Tanh activtion function: .. math:: h_t = \tanh(W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh}) Reference paper: Finding structure in time - Elman, 1988. https://crl.ucsd.edu/~elman/Papers/fsit.pdf **LSTM** Long Short-Term Memory - Hochreiter, 1997. http://www.bioinf.jku.at/publications/older/2604.pdf .. math:: \begin{array}{ll} i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\ f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \\ o_t = \mathrm{sigmoid}(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\ c_t = f_t * c_{(t-1)} + i_t * g_t \\ h_t = o_t * \tanh(c_t) \end{array} **GRU** Gated Recurrent Unit - Cho et al. 2014. http://arxiv.org/abs/1406.1078 The definition of GRU here is slightly different from paper but compatible with CUDNN. .. math:: \begin{array}{ll} r_t = \mathrm{sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\ z_t = \mathrm{sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\ n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \\ h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \\ \end{array} Parameters ---------- data : NDArray Input data to RNN parameters : NDArray Vector of all RNN trainable parameters concatenated state : NDArray initial hidden state of the RNN state_cell : NDArray initial cell state for LSTM networks (only for LSTM) state_size : int (non-negative), required size of the state for each layer num_layers : int (non-negative), required number of stacked layers bidirectional : boolean, optional, default=0 whether to use bidirectional recurrent layers mode : {'gru', 'lstm', 'rnn_relu', 'rnn_tanh'}, required the type of RNN to compute p : float, optional, default=0 Dropout probability, fraction of the input that gets dropped out at training time state_outputs : boolean, optional, default=0 Whether to have the states as symbol outputs. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( Rt parameterststatet state_cellt state_sizet num_layerst bidirectionalR?R>t state_outputsRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytRNN{sQcKsdS(s^ Performs region of interest(ROI) pooling on the input array. ROI pooling is a variant of a max pooling layer, in which the output size is fixed and region of interest is a parameter. Its purpose is to perform max pooling on the inputs of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a neural-net layer mostly used in training a `Fast R-CNN` network for object detection. This operator takes a 4D feature map as an input array and region proposals as `rois`, then it pools over sub-regions of input and produces a fixed-sized output array regardless of the ROI size. To crop the feature map accordingly, you can resize the bounding box coordinates by changing the parameters `rois` and `spatial_scale`. The cropped feature maps are pooled by standard max pooling operation to a fixed size output indicated by a `pooled_size` parameter. batch_size will change to the number of region bounding boxes after `ROIPooling`. The size of each region of interest doesn't have to be perfectly divisible by the number of pooling sections(`pooled_size`). Example:: x = [[[[ 0., 1., 2., 3., 4., 5.], [ 6., 7., 8., 9., 10., 11.], [ 12., 13., 14., 15., 16., 17.], [ 18., 19., 20., 21., 22., 23.], [ 24., 25., 26., 27., 28., 29.], [ 30., 31., 32., 33., 34., 35.], [ 36., 37., 38., 39., 40., 41.], [ 42., 43., 44., 45., 46., 47.]]]] // region of interest i.e. bounding box coordinates. y = [[0,0,0,4,4]] // returns array of shape (2,2) according to the given roi with max pooling. ROIPooling(x, y, (2,2), 1.0) = [[[[ 14., 16.], [ 26., 28.]]]] // region of interest is changed due to the change in `spacial_scale` parameter. ROIPooling(x, y, (2,2), 0.7) = [[[[ 7., 9.], [ 19., 21.]]]] Defined in src/operator/roi_pooling.cc:L295 Parameters ---------- data : NDArray The input array to the pooling operator, a 4D Feature maps rois : NDArray Bounding box coordinates, a 2D array of [[batch_index, x1, y1, x2, y2]], where (x1, y1) and (x2, y2) are top left and bottom right corners of designated region of interest. `batch_index` indicates the index of corresponding image in the input array pooled_size : Shape(tuple), required ROI pooling output shape (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 out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((Rtroist pooled_sizet spatial_scaleRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt ROIPoolingĪsCcKsdS(s…Reshapes the input array. .. note:: ``Reshape`` is deprecated, use ``reshape`` Given an array and a shape, this function returns a copy of the array in the new shape. The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array. Example:: reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]] Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below: - ``0`` copy this dimension from the input to the output shape. Example:: - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2) - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4) - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions keeping the size of the new array same as that of the input array. At most one dimension of shape can be -1. Example:: - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4) - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8) - input shape = (2,3,4), shape=(-1,), output shape = (24,) - ``-2`` copy all/remainder of the input dimensions to the output shape. Example:: - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4) - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4) - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1) - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension. Example:: - input shape = (2,3,4), shape = (-3,4), output shape = (6,4) - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20) - input shape = (2,3,4), shape = (0,-3), output shape = (2,12) - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4) - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1). Example:: - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4) - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4) If the argument `reverse` is set to 1, then the special values are inferred from right to left. Example:: - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5) - with reverse=1, output shape will be (50,4). Defined in src/operator/tensor/matrix_op.cc:L169 Parameters ---------- data : NDArray Input data to reshape. shape : Shape(tuple), optional, default=[] The target shape reverse : boolean, optional, default=0 If true then the special values are inferred from right to left target_shape : Shape(tuple), optional, default=[] (Deprecated! Use ``shape`` instead.) Target new shape. One and only one dim can be 0, in which case it will be inferred from the rest of dims keep_highest : boolean, optional, default=0 (Deprecated! Use ``shape`` instead.) Whether keep the highest dim unchanged.If set to true, then the first dim in target_shape is ignored,and always fixed as input out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. Examples -------- Reshapes the input array into a new shape. >>> x = mx.nd.array([1, 2, 3, 4]) >>> y = mx.nd.reshape(x, shape=(2, 2)) >>> x.shape (4L,) >>> y.shape (2L, 2L) >>> y.asnumpy() array([[ 1., 2.], [ 3., 4.]], dtype=float32) You can use ``0`` to copy a particular dimension from the input to the output shape and '-1' to infer the dimensions of the output. >>> x = mx.nd.ones((2, 3, 4)) >>> x.shape (2L, 3L, 4L) >>> y = mx.nd.reshape(x, shape=(4, 0, -1)) >>> y.shape (4L, 3L, 2L) i(i((RtshapetreverseR<t keep_highestRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytReshapesocKsdS(sąComputes support vector machine based transformation of the input. This tutorial demonstrates using SVM as output layer for classification instead of softmax: https://github.com/dmlc/mxnet/tree/master/example/svm_mnist. Parameters ---------- data : NDArray Input data for SVM transformation. label : NDArray Class label for the input data. margin : float, optional, default=1 The loss function penalizes outputs that lie outside this margin. Default margin is 1. regularization_coefficient : float, optional, default=1 Regularization parameter for the SVM. This balances the tradeoff between coefficient size and error. use_linear : boolean, optional, default=0 Whether to use L1-SVM objective. L2-SVM objective is used by default. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRtmargintregularization_coefficientt use_linearRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt SVMOutput„scKsdS(sg Takes the last element of a sequence. This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns a (n-1)-dimensional array of the form [batch_size, other_feature_dims]. Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be an input array of positive ints of dimension [batch_size]. To use this parameter, set `use_sequence_length` to `True`, otherwise each example in the batch is assumed to have the max sequence length. .. note:: Alternatively, you can also use `take` operator. Example:: x = [[[ 1., 2., 3.], [ 4., 5., 6.], [ 7., 8., 9.]], [[ 10., 11., 12.], [ 13., 14., 15.], [ 16., 17., 18.]], [[ 19., 20., 21.], [ 22., 23., 24.], [ 25., 26., 27.]]] // returns last sequence when sequence_length parameter is not used SequenceLast(x) = [[ 19., 20., 21.], [ 22., 23., 24.], [ 25., 26., 27.]] // sequence_length is used SequenceLast(x, sequence_length=[1,1,1], use_sequence_length=True) = [[ 1., 2., 3.], [ 4., 5., 6.], [ 7., 8., 9.]] // sequence_length is used SequenceLast(x, sequence_length=[1,2,3], use_sequence_length=True) = [[ 1., 2., 3.], [ 13., 14., 15.], [ 25., 26., 27.]] Defined in src/operator/sequence_last.cc:L92 Parameters ---------- data : NDArray n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] where n>2 sequence_length : NDArray vector of sequence lengths of the form [batch_size] use_sequence_length : boolean, optional, default=0 If set to true, this layer takes in an extra input parameter `sequence_length` to specify variable length sequence axis : int, optional, default='0' The sequence axis. Only values of 0 and 1 are currently supported. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((Rtsequence_lengthtuse_sequence_lengthRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt SequenceLast£sDcKsdS(s‘ Sets all elements outside the sequence to a constant value. This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape. Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be an input array of positive ints of dimension [batch_size]. To use this parameter, set `use_sequence_length` to `True`, otherwise each example in the batch is assumed to have the max sequence length and this operator works as the `identity` operator. Example:: x = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // Batch 1 B1 = [[ 1., 2., 3.], [ 7., 8., 9.], [ 13., 14., 15.]] // Batch 2 B2 = [[ 4., 5., 6.], [ 10., 11., 12.], [ 16., 17., 18.]] // works as identity operator when sequence_length parameter is not used SequenceMask(x) = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // sequence_length [1,1] means 1 of each batch will be kept // and other rows are masked with default mask value = 0 SequenceMask(x, sequence_length=[1,1], use_sequence_length=True) = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 0., 0., 0.], [ 0., 0., 0.]], [[ 0., 0., 0.], [ 0., 0., 0.]]] // sequence_length [2,3] means 2 of batch B1 and 3 of batch B2 will be kept // and other rows are masked with value = 1 SequenceMask(x, sequence_length=[2,3], use_sequence_length=True, value=1) = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 1., 1., 1.], [ 16., 17., 18.]]] Defined in src/operator/sequence_mask.cc:L114 Parameters ---------- data : NDArray n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] where n>2 sequence_length : NDArray vector of sequence lengths of the form [batch_size] use_sequence_length : boolean, optional, default=0 If set to true, this layer takes in an extra input parameter `sequence_length` to specify variable length sequence value : float, optional, default=0 The value to be used as a mask. axis : int, optional, default='0' The sequence axis. Only values of 0 and 1 are currently supported. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR‚tvalueRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt SequenceMaskés\cKsdS(sŽ Reverses the elements of each sequence. This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape. Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be an input array of positive ints of dimension [batch_size]. To use this parameter, set `use_sequence_length` to `True`, otherwise each example in the batch is assumed to have the max sequence length. Example:: x = [[[ 1., 2., 3.], [ 4., 5., 6.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // Batch 1 B1 = [[ 1., 2., 3.], [ 7., 8., 9.], [ 13., 14., 15.]] // Batch 2 B2 = [[ 4., 5., 6.], [ 10., 11., 12.], [ 16., 17., 18.]] // returns reverse sequence when sequence_length parameter is not used SequenceReverse(x) = [[[ 13., 14., 15.], [ 16., 17., 18.]], [[ 7., 8., 9.], [ 10., 11., 12.]], [[ 1., 2., 3.], [ 4., 5., 6.]]] // sequence_length [2,2] means 2 rows of // both batch B1 and B2 will be reversed. SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) = [[[ 7., 8., 9.], [ 10., 11., 12.]], [[ 1., 2., 3.], [ 4., 5., 6.]], [[ 13., 14., 15.], [ 16., 17., 18.]]] // sequence_length [2,3] means 2 of batch B2 and 3 of batch B3 // will be reversed. SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) = [[[ 7., 8., 9.], [ 16., 17., 18.]], [[ 1., 2., 3.], [ 10., 11., 12.]], [[ 13., 14, 15.], [ 4., 5., 6.]]] Defined in src/operator/sequence_reverse.cc:L113 Parameters ---------- data : NDArray n-dimensional input array of the form [max_sequence_length, batch_size, other dims] where n>2 sequence_length : NDArray vector of sequence lengths of the form [batch_size] use_sequence_length : boolean, optional, default=0 If set to true, this layer takes in an extra input parameter `sequence_length` to specify variable length sequence axis : int, optional, default='0' The sequence axis. Only 0 is currently supported. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR‚RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytSequenceReverseG sYcKsdS(sńSplits an array along a particular axis into multiple sub-arrays. .. note:: ``SliceChannel`` is deprecated. Use ``split`` instead. **Note** that `num_outputs` should evenly divide the length of the axis along which to split the array. Example:: x = [[[ 1.] [ 2.]] [[ 3.] [ 4.]] [[ 5.] [ 6.]]] x.shape = (3, 2, 1) y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1) y = [[[ 1.]] [[ 3.]] [[ 5.]]] [[[ 2.]] [[ 4.]] [[ 6.]]] y[0].shape = (3, 1, 1) z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1) z = [[[ 1.] [ 2.]]] [[[ 3.] [ 4.]]] [[[ 5.] [ 6.]]] z[0].shape = (1, 2, 1) `squeeze_axis=1` removes the axis with length 1 from the shapes of the output arrays. **Note** that setting `squeeze_axis` to ``1`` removes axis with length 1 only along the `axis` which it is split. Also `squeeze_axis` can be set to true only if ``input.shape[axis] == num_outputs``. Example:: z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1) z = [[ 1.] [ 2.]] [[ 3.] [ 4.]] [[ 5.] [ 6.]] z[0].shape = (2 ,1 ) Defined in src/operator/slice_channel.cc:L107 Parameters ---------- data : NDArray The input num_outputs : int, required Number of splits. Note that this should evenly divide the length of the `axis`. axis : int, optional, default='1' Axis along which to split. squeeze_axis : boolean, optional, default=0 If true, Removes the axis with length 1 from the shapes of the output arrays. **Note** that setting `squeeze_axis` to ``true`` removes axis with length 1 only along the `axis` which it is split. Also `squeeze_axis` can be set to ``true`` only if ``input.shape[axis] == num_outputs``. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((Rt num_outputsRt squeeze_axisRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt SliceChannel¢ sRc KsdS(sPlease use `SoftmaxOutput`. .. note:: This operator has been renamed to `SoftmaxOutput`, which computes the gradient of cross-entropy loss w.r.t softmax output. To just compute softmax output, use the `softmax` operator. Defined in src/operator/softmax_output.cc:L138 Parameters ---------- data : NDArray Input array. grad_scale : float, optional, default=1 Scales the gradient by a float factor. ignore_label : float, optional, default=-1 The instances whose `labels` == `ignore_label` will be ignored during backward, if `use_ignore` is set to ``true``). multi_output : boolean, optional, default=0 If set to ``true``, the softmax function will be computed along axis ``1``. This is applied when the shape of input array differs from the shape of label array. use_ignore : boolean, optional, default=0 If set to ``true``, the `ignore_label` value will not contribute to the backward gradient. preserve_shape : boolean, optional, default=0 If set to ``true``, the softmax function will be computed along the last axis (``-1``). normalization : {'batch', 'null', 'valid'},optional, default='null' Normalizes the gradient. out_grad : boolean, optional, default=0 Multiplies gradient with output gradient element-wise. smooth_alpha : float, optional, default=0 Constant for computing a label smoothed version of cross-entropyfor the backwards pass. This constant gets subtracted from theone-hot encoding of the gold label and distributed uniformly toall other labels. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( RR\t ignore_labelt multi_outputt use_ignoretpreserve_shapeRatout_gradt smooth_alphaRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytSoftmaxö s*cKsdS(s@Applies softmax activation to input. This is intended for internal layers. .. note:: This operator has been deprecated, please use `softmax`. If `mode` = ``instance``, this operator will compute a softmax for each instance in the batch. This is the default mode. If `mode` = ``channel``, this operator will compute a k-class softmax at each position of each instance, where `k` = ``num_channel``. This mode can only be used when the input array has at least 3 dimensions. This can be used for `fully convolutional network`, `image segmentation`, etc. Example:: >>> input_array = mx.nd.array([[3., 0.5, -0.5, 2., 7.], >>> [2., -.4, 7., 3., 0.2]]) >>> softmax_act = mx.nd.SoftmaxActivation(input_array) >>> print softmax_act.asnumpy() [[ 1.78322066e-02 1.46375655e-03 5.38485940e-04 6.56010211e-03 9.73605454e-01] [ 6.56221947e-03 5.95310994e-04 9.73919690e-01 1.78379621e-02 1.08472735e-03]] Defined in src/operator/nn/softmax_activation.cc:L59 Parameters ---------- data : NDArray The input array. mode : {'channel', 'instance'},optional, default='instance' Specifies how to compute the softmax. If set to ``instance``, it computes softmax for each instance. If set to ``channel``, It computes cross channel softmax for each position of each instance. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR?RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytSoftmaxActivation" s+c KsdS(sdComputes the gradient of cross entropy loss with respect to softmax output. - This operator computes the gradient in two steps. The cross entropy loss does not actually need to be computed. - Applies softmax function on the input array. - Computes and returns the gradient of cross entropy loss w.r.t. the softmax output. - The softmax function, cross entropy loss and gradient is given by: - Softmax Function: .. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)} - Cross Entropy Function: .. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i) - The gradient of cross entropy loss w.r.t softmax output: .. math:: \text{gradient} = \text{output} - \text{label} - During forward propagation, the softmax function is computed for each instance in the input array. For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The size is :math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters `preserve_shape` and `multi_output` to specify the way to compute softmax: - By default, `preserve_shape` is ``false``. This operator will reshape the input array into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the softmax function for each row in the reshaped array, and afterwards reshape it back to the original shape :math:`(d_1, d_2, ..., d_n)`. - If `preserve_shape` is ``true``, the softmax function will be computed along the last axis (`axis` = ``-1``). - If `multi_output` is ``true``, the softmax function will be computed along the second axis (`axis` = ``1``). - During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed. The provided label can be a one-hot label array or a probability label array. - If the parameter `use_ignore` is ``true``, `ignore_label` can specify input instances with a particular label to be ignored during backward propagation. **This has no effect when softmax `output` has same shape as `label`**. Example:: data = [[1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4]] label = [1,0,2,3] ignore_label = 1 SoftmaxOutput(data=data, label = label,\ multi_output=true, use_ignore=true,\ ignore_label=ignore_label) ## forward softmax output [[ 0.0320586 0.08714432 0.23688284 0.64391428] [ 0.25 0.25 0.25 0.25 ] [ 0.25 0.25 0.25 0.25 ] [ 0.25 0.25 0.25 0.25 ]] ## backward gradient output [[ 0. 0. 0. 0. ] [-0.75 0.25 0.25 0.25] [ 0.25 0.25 -0.75 0.25] [ 0.25 0.25 0.25 -0.75]] ## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label. - The parameter `grad_scale` can be used to rescale the gradient, which is often used to give each loss function different weights. - This operator also supports various ways to normalize the gradient by `normalization`, The `normalization` is applied if softmax output has different shape than the labels. The `normalization` mode can be set to the followings: - ``'null'``: do nothing. - ``'batch'``: divide the gradient by the batch size. - ``'valid'``: divide the gradient by the number of instances which are not ignored. Defined in src/operator/softmax_output.cc:L123 Parameters ---------- data : NDArray Input array. label : NDArray Ground truth label. grad_scale : float, optional, default=1 Scales the gradient by a float factor. ignore_label : float, optional, default=-1 The instances whose `labels` == `ignore_label` will be ignored during backward, if `use_ignore` is set to ``true``). multi_output : boolean, optional, default=0 If set to ``true``, the softmax function will be computed along axis ``1``. This is applied when the shape of input array differs from the shape of label array. use_ignore : boolean, optional, default=0 If set to ``true``, the `ignore_label` value will not contribute to the backward gradient. preserve_shape : boolean, optional, default=0 If set to ``true``, the softmax function will be computed along the last axis (``-1``). normalization : {'batch', 'null', 'valid'},optional, default='null' Normalizes the gradient. out_grad : boolean, optional, default=0 Multiplies gradient with output gradient element-wise. smooth_alpha : float, optional, default=0 Constant for computing a label smoothed version of cross-entropyfor the backwards pass. This constant gets subtracted from theone-hot encoding of the gold label and distributed uniformly toall other labels. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( RRR\RŠR‹RŒRRaRŽRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt SoftmaxOutputO soc KsdS(sDApplies a spatial transformer to input feature map. Parameters ---------- data : NDArray Input data to the SpatialTransformerOp. loc : NDArray localisation net, the output dim should be 6 when transform_type is affine. You shold initialize the weight and bias with identity tranform. target_shape : Shape(tuple), optional, default=[0,0] output shape(h, w) of spatial transformer: (y, x) transform_type : {'affine'}, required transformation type sampler_type : {'bilinear'}, required sampling type cudnn_off : boolean or None, optional, default=None whether to turn cudnn off out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( RtlocR<RLt sampler_typeRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytSpatialTransformerĄ scKsdS(s†Interchanges two axes of an array. Examples:: x = [[1, 2, 3]]) swapaxes(x, 0, 1) = [[ 1], [ 2], [ 3]] x = [[[ 0, 1], [ 2, 3]], [[ 4, 5], [ 6, 7]]] // (2,2,2) array swapaxes(x, 0, 2) = [[[ 0, 4], [ 2, 6]], [[ 1, 5], [ 3, 7]]] Defined in src/operator/swapaxis.cc:L70 Parameters ---------- data : NDArray Input array. dim1 : int (non-negative), optional, default=0 the first axis to be swapped. dim2 : int (non-negative), optional, default=0 the second axis to be swapped. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((Rtdim1tdim2RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytSwapAxisÜ s(cOsdS(sšPerforms nearest neighbor/bilinear up sampling to inputs. Parameters ---------- data : NDArray[] Array of tensors to upsample scale : int, required Up sampling scale num_filter : int, optional, default='0' Input filter. Only used by bilinear sample_type. sample_type : {'bilinear', 'nearest'}, required upsampling method multi_input_mode : {'concat', 'sum'},optional, default='concat' How to handle multiple input. concat means concatenate upsampled images along the channel dimension. sum means add all images together, only available for nearest neighbor upsampling. workspace : long (non-negative), optional, default=512 Tmp workspace for deconvolution (MB) out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt UpSampling scKsdS(sVReturns element-wise absolute value of the input. Example:: abs([-2, 0, 3]) = [2, 0, 3] The storage type of ``abs`` output depends upon the input storage type: - abs(default) = default - abs(row_sparse) = row_sparse - abs(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L660 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytabs" scKsdS(sŁ Update function for Adam optimizer. Adam is seen as a generalization of AdaGrad. Adam update consists of the following steps, where g represents gradient and m, v are 1st and 2nd order moment estimates (mean and variance). .. math:: g_t = \nabla J(W_{t-1})\\ m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\ v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\ W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon } It updates the weights using:: m = beta1*m + (1-beta1)*grad v = beta2*v + (1-beta2)*(grad**2) w += - learning_rate * m / (sqrt(v) + epsilon) However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and the storage type of weight is the same as those of m and v, only the row slices whose indices appear in grad.indices are updated (for w, m and v):: for row in grad.indices: m[row] = beta1*m[row] + (1-beta1)*grad[row] v[row] = beta2*v[row] + (1-beta2)*(grad[row]**2) w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon) Defined in src/operator/optimizer_op.cc:L495 Parameters ---------- weight : NDArray Weight grad : NDArray Gradient mean : NDArray Moving mean var : NDArray Moving variance lr : float, required Learning rate beta1 : float, optional, default=0.9 The decay rate for the 1st moment estimates. beta2 : float, optional, default=0.999 The decay rate for the 2nd moment estimates. epsilon : float, optional, default=1e-08 A small constant for numerical stability. wd : float, optional, default=0 Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. rescale_grad : float, optional, default=1 Rescale gradient to grad = rescale_grad*grad. clip_gradient : float, optional, default=-1 Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). lazy_update : boolean, optional, default=1 If true, lazy updates are applied if gradient's stype is row_sparse and all of w, m and v have the same stype out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R"tgradtmeantvartlrtbeta1tbeta2tepsilontwdt rescale_gradt clip_gradientt lazy_updateRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt adam_updateB sDcOsdS(sxAdds all input arguments element-wise. .. math:: add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n ``add_n`` is potentially more efficient than calling ``add`` by `n` times. The storage type of ``add_n`` output depends on storage types of inputs - add_n(row_sparse, row_sparse, ..) = row_sparse - add_n(default, csr, default) = default - add_n(any input combinations longer than 4 (>4) with at least one default type) = default - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage Defined in src/operator/tensor/elemwise_sum.cc:L156 Parameters ---------- args : NDArray[] Positional input arguments out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RBR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytadd_nˆ s cKsdS(suReturns element-wise inverse cosine of the input array. The input should be in range `[-1, 1]`. The output is in the closed interval :math:`[0, \pi]` .. math:: arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0] The storage type of ``arccos`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L123 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytarccosŖ scKsdS(säReturns the element-wise inverse hyperbolic cosine of the input array, \ computed element-wise. The storage type of ``arccosh`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L264 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytarccoshČ scKsdS(s Returns element-wise inverse sine of the input array. The input should be in the range `[-1, 1]`. The output is in the closed interval of [:math:`-\pi/2`, :math:`\pi/2`]. .. math:: arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2] The storage type of ``arcsin`` output depends upon the input storage type: - arcsin(default) = default - arcsin(row_sparse) = row_sparse - arcsin(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L104 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytarcsinį s cKsdS(sbReturns the element-wise inverse hyperbolic sine of the input array, \ computed element-wise. The storage type of ``arcsinh`` output depends upon the input storage type: - arcsinh(default) = default - arcsinh(row_sparse) = row_sparse - arcsinh(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L250 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytarcsinh scKsdS(sµReturns element-wise inverse tangent of the input array. The output is in the closed interval :math:`[-\pi/2, \pi/2]` .. math:: arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4] The storage type of ``arctan`` output depends upon the input storage type: - arctan(default) = default - arctan(row_sparse) = row_sparse - arctan(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L144 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytarctan scKsdS(seReturns the element-wise inverse hyperbolic tangent of the input array, \ computed element-wise. The storage type of ``arctanh`` output depends upon the input storage type: - arctanh(default) = default - arctanh(row_sparse) = row_sparse - arctanh(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L281 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytarctanhA scKsdS(sėReturns indices of the maximum values along an axis. In the case of multiple occurrences of maximum values, the indices corresponding to the first occurrence are returned. Examples:: x = [[ 0., 1., 2.], [ 3., 4., 5.]] // argmax along axis 0 argmax(x, axis=0) = [ 1., 1., 1.] // argmax along axis 1 argmax(x, axis=1) = [ 2., 2.] // argmax along axis 1 keeping same dims as an input array argmax(x, axis=1, keepdims=True) = [[ 2.], [ 2.]] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L52 Parameters ---------- data : NDArray The input axis : int or None, optional, default='None' The axis along which to perform the reduction. Negative values means indexing from right to left. ``Requires axis to be set as int, because global reduction is not supported yet.`` keepdims : boolean, optional, default=0 If this is set to `True`, the reduced axis is left in the result as dimension with size one. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRtkeepdimsRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytargmax^ s*cKsdS(s­Returns argmax indices of each channel from the input array. The result will be an NDArray of shape (num_channel,). In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence are returned. Examples:: x = [[ 0., 1., 2.], [ 3., 4., 5.]] argmax_channel(x) = [ 2., 2.] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L97 Parameters ---------- data : NDArray The input array out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytargmax_channelŠ s cKsdS(sėReturns indices of the minimum values along an axis. In the case of multiple occurrences of minimum values, the indices corresponding to the first occurrence are returned. Examples:: x = [[ 0., 1., 2.], [ 3., 4., 5.]] // argmin along axis 0 argmin(x, axis=0) = [ 0., 0., 0.] // argmin along axis 1 argmin(x, axis=1) = [ 0., 0.] // argmin along axis 1 keeping same dims as an input array argmin(x, axis=1, keepdims=True) = [[ 0.], [ 0.]] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L77 Parameters ---------- data : NDArray The input axis : int or None, optional, default='None' The axis along which to perform the reduction. Negative values means indexing from right to left. ``Requires axis to be set as int, because global reduction is not supported yet.`` keepdims : boolean, optional, default=0 If this is set to `True`, the reduced axis is left in the result as dimension with size one. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR®RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytargmin¬ s*cKsdS(s³Returns the indices that would sort an input array along the given axis. This function performs sorting along the given axis and returns an array of indices having same shape as an input array that index data in sorted order. Examples:: x = [[ 0.3, 0.2, 0.4], [ 0.1, 0.3, 0.2]] // sort along axis -1 argsort(x) = [[ 1., 0., 2.], [ 0., 2., 1.]] // sort along axis 0 argsort(x, axis=0) = [[ 1., 0., 1.] [ 0., 1., 0.]] // flatten and then sort argsort(x) = [ 3., 1., 5., 0., 4., 2.] Defined in src/operator/tensor/ordering_op.cc:L177 Parameters ---------- data : NDArray The input array axis : int or None, optional, default='-1' Axis along which to sort the input tensor. If not given, the flattened array is used. Default is -1. is_ascend : boolean, optional, default=1 Whether to sort in ascending or descending order. dtype : {'float16', 'float32', 'float64', 'int32', 'uint8'},optional, default='float32' DType of the output indices. It is only valid when ret_typ is "indices" or "both". An error will be raised if the selected data type cannot precisely represent the indices. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRt is_ascendRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytargsortŲ s,cKsdS(s?Batchwise dot product. ``batch_dot`` is used to compute dot product of ``x`` and ``y`` when ``x`` and ``y`` are data in batch, namely 3D arrays in shape of `(batch_size, :, :)`. For example, given ``x`` with shape `(batch_size, n, m)` and ``y`` with shape `(batch_size, m, k)`, the result array will have shape `(batch_size, n, k)`, which is computed by:: batch_dot(x,y)[i,:,:] = dot(x[i,:,:], y[i,:,:]) Defined in src/operator/tensor/dot.cc:L125 Parameters ---------- lhs : NDArray The first input rhs : NDArray The second input transpose_a : boolean, optional, default=0 If true then transpose the first input before dot. transpose_b : boolean, optional, default=0 If true then transpose the second input before dot. forward_stype : {None, 'csr', 'default', 'row_sparse'},optional, default='None' The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still produce an output of the desired storage type. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((tlhstrhst transpose_at transpose_bt forward_stypeRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt batch_dot s%cKsdS(s6Takes elements from a data batch. .. note:: `batch_take` is deprecated. Use `pick` instead. Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be an output array of shape ``(i0,)`` with:: output[i] = input[i, indices[i]] Examples:: x = [[ 1., 2.], [ 3., 4.], [ 5., 6.]] // takes elements with specified indices batch_take(x, [0,1,0]) = [ 1. 4. 5.] Defined in src/operator/tensor/indexing_op.cc:L490 Parameters ---------- a : NDArray The input array indices : NDArray The index array out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((tatindicesRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt batch_take- s'cKsdS(sĮReturns element-wise sum of the input arrays with broadcasting. `broadcast_plus` is an alias to the function `broadcast_add`. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_add(x, y) = [[ 1., 1., 1.], [ 2., 2., 2.]] broadcast_plus(x, y) = [[ 1., 1., 1.], [ 2., 2., 2.]] Supported sparse operations: broadcast_add(csr, dense(1D)) = dense broadcast_add(dense(1D), csr) = dense Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt broadcast_addV s+cKsdS(sżBroadcasts the input array over particular axes. Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. Example:: // given x of shape (1,2,1) x = [[[ 1.], [ 2.]]] // broadcast x on on axis 2 broadcast_axis(x, axis=2, size=3) = [[[ 1., 1., 1.], [ 2., 2., 2.]]] // broadcast x on on axes 0 and 2 broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1., 1., 1.], [ 2., 2., 2.]], [[ 1., 1., 1.], [ 2., 2., 2.]]] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L238 Parameters ---------- data : NDArray The input axis : Shape(tuple), optional, default=[] The axes to perform the broadcasting. size : Shape(tuple), optional, default=[] Target sizes of the broadcasting axes. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRtsizeRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_axesƒ s)cKsdS(sżBroadcasts the input array over particular axes. Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. Example:: // given x of shape (1,2,1) x = [[[ 1.], [ 2.]]] // broadcast x on on axis 2 broadcast_axis(x, axis=2, size=3) = [[[ 1., 1., 1.], [ 2., 2., 2.]]] // broadcast x on on axes 0 and 2 broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1., 1., 1.], [ 2., 2., 2.]], [[ 1., 1., 1.], [ 2., 2., 2.]]] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L238 Parameters ---------- data : NDArray The input axis : Shape(tuple), optional, default=[] The axes to perform the broadcasting. size : Shape(tuple), optional, default=[] Target sizes of the broadcasting axes. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR¾RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_axis® s)cKsdS(sōReturns element-wise division of the input arrays with broadcasting. Example:: x = [[ 6., 6., 6.], [ 6., 6., 6.]] y = [[ 2.], [ 3.]] broadcast_div(x, y) = [[ 3., 3., 3.], [ 2., 2., 2.]] Supported sparse operations: broadcast_div(csr, dense(1D)) = csr Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L187 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt broadcast_divŁ s%cKsdS(sĮReturns the result of element-wise **equal to** (==) comparison operation with broadcasting. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_equal(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L46 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_equals!cKsdS(sČReturns the result of element-wise **greater than** (>) comparison operation with broadcasting. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_greater(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L82 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_greater#s!cKsdS(sāReturns the result of element-wise **greater than or equal to** (>=) comparison operation with broadcasting. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_greater_equal(x, y) = [[ 1., 1., 1.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L100 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_greater_equalFs!cKsdS(sm Returns the hypotenuse of a right angled triangle, given its "legs" with broadcasting. It is equivalent to doing :math:`sqrt(x_1^2 + x_2^2)`. Example:: x = [[ 3., 3., 3.]] y = [[ 4.], [ 4.]] broadcast_hypot(x, y) = [[ 5., 5., 5.], [ 5., 5., 5.]] z = [[ 0.], [ 4.]] broadcast_hypot(x, z) = [[ 3., 3., 3.], [ 5., 5., 5.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L156 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_hypotis)cKsdS(sĘReturns the result of element-wise **lesser than** (<) comparison operation with broadcasting. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_lesser(x, y) = [[ 0., 0., 0.], [ 0., 0., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L118 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_lesser”s!cKsdS(sßReturns the result of element-wise **lesser than or equal to** (<=) comparison operation with broadcasting. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_lesser_equal(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L136 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_lesser_equal·s!cKsdS(s(Broadcasts lhs to have the same shape as rhs. Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations with arrays of different shapes efficiently without creating multiple copies of arrays. Also see, `Broadcasting `_ for more explanation. Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. For example:: broadcast_like([[1,2,3]], [[5,6,7],[7,8,9]]) = [[ 1., 2., 3.], [ 1., 2., 3.]]) broadcast_like([9], [1,2,3,4,5], lhs_axes=(0,), rhs_axes=(-1,)) = [9,9,9,9,9] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L315 Parameters ---------- lhs : NDArray First input. rhs : NDArray Second input. lhs_axes : Shape or None, optional, default=None Axes to perform broadcast on in the first input array rhs_axes : Shape or None, optional, default=None Axes to copy from the second input array out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“Rµtlhs_axestrhs_axesRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_likeŚs(cKsdS(s·Returns the result of element-wise **logical and** with broadcasting. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_logical_and(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L154 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_logical_ands!cKsdS(s“Returns the result of element-wise **logical or** with broadcasting. Example:: x = [[ 1., 1., 0.], [ 1., 1., 0.]] y = [[ 1.], [ 0.]] broadcast_logical_or(x, y) = [[ 1., 1., 1.], [ 1., 1., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L172 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_logical_or's!cKsdS(s·Returns the result of element-wise **logical xor** with broadcasting. Example:: x = [[ 1., 1., 0.], [ 1., 1., 0.]] y = [[ 1.], [ 0.]] broadcast_logical_xor(x, y) = [[ 0., 0., 1.], [ 1., 1., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L190 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_logical_xorJs!cKsdS(sReturns element-wise maximum of the input arrays with broadcasting. This function compares two input arrays and returns a new array having the element-wise maxima. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_maximum(x, y) = [[ 1., 1., 1.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L80 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_maximumms#cKsdS(sReturns element-wise minimum of the input arrays with broadcasting. This function compares two input arrays and returns a new array having the element-wise minima. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_maximum(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L115 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_minimum’s#cKsdS(sŲReturns element-wise difference of the input arrays with broadcasting. `broadcast_minus` is an alias to the function `broadcast_sub`. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_sub(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] broadcast_minus(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] Supported sparse operations: broadcast_sub/minus(csr, dense(1D)) = dense broadcast_sub/minus(dense(1D), csr) = dense Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_minus·s+cKsdS(s¤Returns element-wise modulo of the input arrays with broadcasting. Example:: x = [[ 8., 8., 8.], [ 8., 8., 8.]] y = [[ 2.], [ 3.]] broadcast_mod(x, y) = [[ 0., 0., 0.], [ 2., 2., 2.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L222 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt broadcast_modäs!cKsdS(sóReturns element-wise product of the input arrays with broadcasting. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_mul(x, y) = [[ 0., 0., 0.], [ 1., 1., 1.]] Supported sparse operations: broadcast_mul(csr, dense(1D)) = csr Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L146 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt broadcast_muls%cKsdS(sĶReturns the result of element-wise **not equal to** (!=) comparison operation with broadcasting. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_not_equal(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L64 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_not_equal.s!cKsdS(sĮReturns element-wise sum of the input arrays with broadcasting. `broadcast_plus` is an alias to the function `broadcast_add`. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_add(x, y) = [[ 1., 1., 1.], [ 2., 2., 2.]] broadcast_plus(x, y) = [[ 1., 1., 1.], [ 2., 2., 2.]] Supported sparse operations: broadcast_add(csr, dense(1D)) = dense broadcast_add(dense(1D), csr) = dense Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_plusQs+cKsdS(sŅReturns result of first array elements raised to powers from second array, element-wise with broadcasting. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_power(x, y) = [[ 2., 2., 2.], [ 4., 4., 4.]] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L45 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytbroadcast_power~s!cKsdS(sŲReturns element-wise difference of the input arrays with broadcasting. `broadcast_minus` is an alias to the function `broadcast_sub`. Example:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] y = [[ 0.], [ 1.]] broadcast_sub(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] broadcast_minus(x, y) = [[ 1., 1., 1.], [ 0., 0., 0.]] Supported sparse operations: broadcast_sub/minus(csr, dense(1D)) = dense broadcast_sub/minus(dense(1D), csr) = dense Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106 Parameters ---------- lhs : NDArray First input to the function rhs : NDArray Second input to the function out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt broadcast_sub”s+cKsdS(s}Broadcasts the input array to a new shape. Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations with arrays of different shapes efficiently without creating multiple copies of arrays. Also see, `Broadcasting `_ for more explanation. Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. For example:: broadcast_to([[1,2,3]], shape=(2,3)) = [[ 1., 2., 3.], [ 1., 2., 3.]]) The dimension which you do not want to change can also be kept as `0` which means copy the original value. So with `shape=(2,0)`, we will obtain the same result as in the above example. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L262 Parameters ---------- data : NDArray The input shape : Shape(tuple), optional, default=[] The shape of the desired array. We can set the dim to zero if it's same as the original. E.g `A = broadcast_to(B, shape=(10, 0, 0))` has the same meaning as `A = broadcast_axis(B, axis=0, size=10)`. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRyRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt broadcast_toĪs%cKsdS(sģCasts all elements of the input to a new type. .. note:: ``Cast`` is deprecated. Use ``cast`` instead. Example:: cast([0.9, 1.3], dtype='int32') = [0, 1] cast([1e20, 11.1], dtype='float16') = [inf, 11.09375] cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594 Parameters ---------- data : NDArray The input. dtype : {'float16', 'float32', 'float64', 'int32', 'int64', 'int8', 'uint8'}, required Output data type. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytcastõscKsdS(s&Casts tensor storage type to the new type. When an NDArray with default storage type is cast to csr or row_sparse storage, the result is compact, which means: - for csr, zero values will not be retained - for row_sparse, row slices of all zeros will not be retained The storage type of ``cast_storage`` output depends on stype parameter: - cast_storage(csr, 'default') = default - cast_storage(row_sparse, 'default') = default - cast_storage(default, 'csr') = csr - cast_storage(default, 'row_sparse') = row_sparse - cast_storage(csr, 'csr') = csr - cast_storage(row_sparse, 'row_sparse') = row_sparse Example:: dense = [[ 0., 1., 0.], [ 2., 0., 3.], [ 0., 0., 0.], [ 0., 0., 0.]] # cast to row_sparse storage type rsp = cast_storage(dense, 'row_sparse') rsp.indices = [0, 1] rsp.values = [[ 0., 1., 0.], [ 2., 0., 3.]] # cast to csr storage type csr = cast_storage(dense, 'csr') csr.indices = [1, 0, 2] csr.values = [ 1., 2., 3.] csr.indptr = [0, 1, 3, 3, 3] Defined in src/operator/tensor/cast_storage.cc:L71 Parameters ---------- data : NDArray The input. stype : {'csr', 'default', 'row_sparse'}, required Output storage type. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RtstypeRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt cast_storages8cKsdS(s‹Returns element-wise cube-root value of the input. .. math:: cbrt(x) = \sqrt[3]{x} Example:: cbrt([1, 8, -125]) = [1, 2, -5] The storage type of ``cbrt`` output depends upon the input storage type: - cbrt(default) = default - cbrt(row_sparse) = row_sparse - cbrt(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L881 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytcbrtOs!cKsdS(sĄReturns element-wise ceiling of the input. The ceil of the scalar x is the smallest integer i, such that i >= x. Example:: ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1., 2., 2., 3.] The storage type of ``ceil`` output depends upon the input storage type: - ceil(default) = default - ceil(row_sparse) = row_sparse - ceil(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L738 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytceilrs cKsdS(sćChoose one element from each line(row for python, column for R/Julia) in lhs according to index indicated by rhs. This function assume rhs uses 0-based index. Parameters ---------- lhs : NDArray Left operand to the function. rhs : NDArray Right operand to the function. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytchoose_element_0index”scKsdS(sźClips (limits) the values in an array. Given an interval, values outside the interval are clipped to the interval edges. Clipping ``x`` between `a_min` and `a_x` would be:: clip(x, a_min, a_max) = max(min(x, a_max), a_min)) Example:: x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] clip(x,1,8) = [ 1., 1., 2., 3., 4., 5., 6., 7., 8., 8.] The storage type of ``clip`` output depends on storage types of inputs and the a_min, a_max \ parameter values: - clip(default) = default - clip(row_sparse, a_min <= 0, a_max >= 0) = row_sparse - clip(csr, a_min <= 0, a_max >= 0) = csr - clip(row_sparse, a_min < 0, a_max < 0) = default - clip(row_sparse, a_min > 0, a_max > 0) = default - clip(csr, a_min < 0, a_max < 0) = csr - clip(csr, a_min > 0, a_max > 0) = csr Defined in src/operator/tensor/matrix_op.cc:L619 Parameters ---------- data : NDArray Input array. a_min : float, required Minimum value a_max : float, required Maximum value out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((Rta_minta_maxRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytclipØs.cOsdS(sˆJoins input arrays along a given axis. .. note:: `Concat` is deprecated. Use `concat` instead. The dimensions of the input arrays should be the same except the axis along which they will be concatenated. The dimension of the output array along the concatenated axis will be equal to the sum of the corresponding dimensions of the input arrays. The storage type of ``concat`` output depends on storage types of inputs - concat(csr, csr, ..., csr, dim=0) = csr - otherwise, ``concat`` generates output with default storage Example:: x = [[1,1],[2,2]] y = [[3,3],[4,4],[5,5]] z = [[6,6], [7,7],[8,8]] concat(x,y,z,dim=0) = [[ 1., 1.], [ 2., 2.], [ 3., 3.], [ 4., 4.], [ 5., 5.], [ 6., 6.], [ 7., 7.], [ 8., 8.]] Note that you cannot concat x,y,z along dimension 1 since dimension 0 is not the same for all the input arrays. concat(y,z,dim=1) = [[ 3., 3., 6., 6.], [ 4., 4., 7., 7.], [ 5., 5., 8., 8.]] Defined in src/operator/nn/concat.cc:L365 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 : NDArray or list of NDArrays The output of this function. i(i((RR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytconcatŲs8cKsdS(s8Computes the element-wise cosine of the input array. The input should be in radians (:math:`2\pi` rad equals 360 degrees). .. math:: cos([0, \pi/4, \pi/2]) = [1, 0.707, 0] The storage type of ``cos`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L63 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytcosscKsdS(sReturns the hyperbolic cosine of the input array, computed element-wise. .. math:: cosh(x) = 0.5\times(exp(x) + exp(-x)) The storage type of ``cosh`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L216 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytcosh/scKsdS(s¼ Slices a region of the array. .. note:: ``crop`` is deprecated. Use ``slice`` instead. This function returns a sliced array between the indices given by `begin` and `end` with the corresponding `step`. For an input array of ``shape=(d_0, d_1, ..., d_n-1)``, slice operation with ``begin=(b_0, b_1...b_m-1)``, ``end=(e_0, e_1, ..., e_m-1)``, and ``step=(s_0, s_1, ..., s_m-1)``, where m <= n, results in an array with the shape ``(|e_0-b_0|/|s_0|, ..., |e_m-1-b_m-1|/|s_m-1|, d_m, ..., d_n-1)``. The resulting array's *k*-th dimension contains elements from the *k*-th dimension of the input array starting from index ``b_k`` (inclusive) with step ``s_k`` until reaching ``e_k`` (exclusive). If the *k*-th elements are `None` in the sequence of `begin`, `end`, and `step`, the following rule will be used to set default values. If `s_k` is `None`, set `s_k=1`. If `s_k > 0`, set `b_k=0`, `e_k=d_k`; else, set `b_k=d_k-1`, `e_k=-1`. The storage type of ``slice`` output depends on storage types of inputs - slice(csr) = csr - otherwise, ``slice`` generates output with default storage .. note:: When input data storage type is csr, it only supports step=(), or step=(None,), or step=(1,) to generate a csr output. For other step parameter values, it falls back to slicing a dense tensor. Example:: x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice(x, begin=(0,1), end=(2,4)) = [[ 2., 3., 4.], [ 6., 7., 8.]] slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = [[9., 11.], [5., 7.], [1., 3.]] Defined in src/operator/tensor/matrix_op.cc:L414 Parameters ---------- data : NDArray Source input begin : Shape(tuple), required starting indices for the slice operation, supports negative indices. end : Shape(tuple), required ending indices for the slice operation, supports negative indices. step : Shape(tuple), optional, default=[] step for the slice operation, supports negative values. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RtbegintendtstepRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytcropJsDc KsdS(s7Connectionist Temporal Classification Loss. 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:L97 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 : NDArray or list of NDArrays The output of this function. i(i(( RRRRRRRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytctc_losssHcKsdS(s˜Converts each element of the input array from radians to degrees. .. math:: degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360] The storage type of ``degrees`` output depends upon the input storage type: - degrees(default) = default - degrees(row_sparse) = row_sparse - degrees(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L163 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytdegreesŚscKsdS(s Rearranges(permutes) data from depth into blocks of spatial data. Similar to ONNX DepthToSpace operator: https://github.com/onnx/onnx/blob/master/docs/Operators.md#DepthToSpace. The output is a new tensor where the values from depth dimension are moved in spatial blocks to height and width dimension. The reverse of this operation is ``space_to_depth``. .. math:: \begin{gather*} x \prime = reshape(x, [N, block\_size, block\_size, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \\ x \prime \prime = transpose(x \prime, [0, 3, 4, 1, 5, 2]) \\ y = reshape(x \prime \prime, [N, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \end{gather*} where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width] and :math:`y` is the output tensor of layout :math:`[N, C / (block\_size ^ 2), H * block\_size, W * block\_size]` Example:: x = [[[[0, 1, 2], [3, 4, 5]], [[6, 7, 8], [9, 10, 11]], [[12, 13, 14], [15, 16, 17]], [[18, 19, 20], [21, 22, 23]]]] depth_to_space(x, 2) = [[[[0, 6, 1, 7, 2, 8], [12, 18, 13, 19, 14, 20], [3, 9, 4, 10, 5, 11], [15, 21, 16, 22, 17, 23]]]] Defined in src/operator/tensor/matrix_op.cc:L946 Parameters ---------- data : NDArray Input ndarray block_size : int, required Blocks of [block_size. block_size] are moved out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((Rt block_sizeRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytdepth_to_spacełs4cKsdS(s½Extracts a diagonal or constructs a diagonal array. ``diag``'s behavior depends on the input array dimensions: - 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero. - N-D arrays: extracts the diagonals of the sub-arrays with axes specified by ``axis1`` and ``axis2``. The output shape would be decided by removing the axes numbered ``axis1`` and ``axis2`` from the input shape and appending to the result a new axis with the size of the diagonals in question. For example, when the input shape is `(2, 3, 4, 5)`, ``axis1`` and ``axis2`` are 0 and 2 respectively and ``k`` is 0, the resulting shape would be `(3, 5, 2)`. Examples:: x = [[1, 2, 3], [4, 5, 6]] diag(x) = [1, 5] diag(x, k=1) = [2, 6] diag(x, k=-1) = [4] x = [1, 2, 3] diag(x) = [[1, 0, 0], [0, 2, 0], [0, 0, 3]] diag(x, k=1) = [[0, 1, 0], [0, 0, 2], [0, 0, 0]] diag(x, k=-1) = [[0, 0, 0], [1, 0, 0], [0, 2, 0]] x = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]] diag(x) = [[1, 7], [2, 8]] diag(x, k=1) = [[3], [4]] diag(x, axis1=-2, axis2=-1) = [[1, 4], [5, 8]] Defined in src/operator/tensor/diag_op.cc:L87 Parameters ---------- data : NDArray Input ndarray k : int, optional, default='0' Diagonal in question. The default is 0. Use k>0 for diagonals above the main diagonal, and k<0 for diagonals below the main diagonal. If input has shape (S0 S1) k must be between -S0 and S1 axis1 : int, optional, default='0' The first axis of the sub-arrays of interest. Ignored when the input is a 1-D array. axis2 : int, optional, default='1' The second axis of the sub-arrays of interest. Ignored when the input is a 1-D array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((Rtktaxis1taxis2RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytdiag/sLcKsdS(sC Dot product of two arrays. ``dot``'s behavior depends on the input array dimensions: - 1-D arrays: inner product of vectors - 2-D arrays: matrix multiplication - N-D arrays: a sum product over the last axis of the first input and the first axis of the second input For example, given 3-D ``x`` with shape `(n,m,k)` and ``y`` with shape `(k,r,s)`, the result array will have shape `(n,m,r,s)`. It is computed by:: dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b]) Example:: x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2)) y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2)) dot(x,y)[0,0,1,1] = 0 sum(x[0,0,:]*y[:,1,1]) = 0 The storage type of ``dot`` output depends on storage types of inputs, transpose option and forward_stype option for output storage type. Implemented sparse operations include: - dot(default, default, transpose_a=True/False, transpose_b=True/False) = default - dot(csr, default, transpose_a=True) = default - dot(csr, default, transpose_a=True) = row_sparse - dot(csr, default) = default - dot(csr, row_sparse) = default - dot(default, csr) = csr (CPU only) - dot(default, csr, forward_stype='default') = default - dot(default, csr, transpose_b=True, forward_stype='default') = default If the combination of input storage types and forward_stype does not match any of the above patterns, ``dot`` will fallback and generate output with default storage. .. Note:: If the storage type of the lhs is "csr", the storage type of gradient w.r.t rhs will be "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad and Adam. Note that by default lazy updates is turned on, which may perform differently from standard updates. For more details, please check the Optimization API at: https://mxnet.incubator.apache.org/api/python/optimization/optimization.html Defined in src/operator/tensor/dot.cc:L77 Parameters ---------- lhs : NDArray The first input rhs : NDArray The second input transpose_a : boolean, optional, default=0 If true then transpose the first input before dot. transpose_b : boolean, optional, default=0 If true then transpose the second input before dot. forward_stype : {None, 'csr', 'default', 'row_sparse'},optional, default='None' The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still produce an output of the desired storage type. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµR¶R·RøRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytdot}sFcKsdS(sąAdds arguments element-wise. The storage type of ``elemwise_add`` output depends on storage types of inputs - elemwise_add(row_sparse, row_sparse) = row_sparse - elemwise_add(csr, csr) = csr - elemwise_add(default, csr) = default - elemwise_add(csr, default) = default - elemwise_add(default, rsp) = default - elemwise_add(rsp, default) = default - otherwise, ``elemwise_add`` generates output with default storage Parameters ---------- lhs : NDArray first input rhs : NDArray second input out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. Example ------- >>> x = mx.nd.array([1, 2, 3, 4]) >>> y = mx.nd.array([1.1, 2.1, 3.1, 4.1]) >>> mx.nd.elemwise_add(x, y).asnumpy() array([ 2.0999999 , 4.0999999 , 6.0999999 , 8.10000038], dtype=float32) i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt elemwise_addÅs&cKsdS(sƒDivides arguments element-wise. The storage type of ``elemwise_div`` output is always dense Parameters ---------- lhs : NDArray first input rhs : NDArray second input out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt elemwise_divķscKsdS(sčMultiplies arguments element-wise. The storage type of ``elemwise_mul`` output depends on storage types of inputs - elemwise_mul(default, default) = default - elemwise_mul(row_sparse, row_sparse) = row_sparse - elemwise_mul(default, row_sparse) = row_sparse - elemwise_mul(row_sparse, default) = row_sparse - elemwise_mul(csr, csr) = csr - otherwise, ``elemwise_mul`` generates output with default storage Parameters ---------- lhs : NDArray first input rhs : NDArray second input out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt elemwise_mulscKsdS(sżSubtracts arguments element-wise. The storage type of ``elemwise_sub`` output depends on storage types of inputs - elemwise_sub(row_sparse, row_sparse) = row_sparse - elemwise_sub(csr, csr) = csr - elemwise_sub(default, csr) = default - elemwise_sub(csr, default) = default - elemwise_sub(default, rsp) = default - elemwise_sub(rsp, default) = default - otherwise, ``elemwise_sub`` generates output with default storage Parameters ---------- lhs : NDArray first input rhs : NDArray second input out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt elemwise_sub$scKsdS(s*Returns element-wise exponential value of the input. .. math:: exp(x) = e^x \approx 2.718^x Example:: exp([0, 1, 2]) = [1., 2.71828175, 7.38905621] The storage type of ``exp`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L921 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytexpDscKsdS(s§Inserts a new axis of size 1 into the array shape For example, given ``x`` with shape ``(2,3,4)``, then ``expand_dims(x, axis=1)`` will return a new array with shape ``(2,1,3,4)``. Defined in src/operator/tensor/matrix_op.cc:L348 Parameters ---------- data : NDArray Source input axis : int, required Position where new axis is to be inserted. Suppose that the input `NDArray`'s dimension is `ndim`, the range of the inserted axis is `[-ndim, ndim]` out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt expand_dimscscKsdS(s’Returns ``exp(x) - 1`` computed element-wise on the input. This function provides greater precision than ``exp(x) - 1`` for small values of ``x``. The storage type of ``expm1`` output depends upon the input storage type: - expm1(default) = default - expm1(row_sparse) = row_sparse - expm1(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1000 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytexpm1~scKsdS(s5Fill one element of each line(row for python, column for R/Julia) in lhs according to index indicated by rhs and values indicated by mhs. This function assume rhs uses 0-based index. Parameters ---------- lhs : NDArray Left operand to the function. mhs : NDArray Middle operand to the function. rhs : NDArray Right operand to the function. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“tmhsRµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytfill_element_0indexœscKsdS(s•Returns element-wise rounded value to the nearest \ integer towards zero of the input. Example:: fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1., 1., 2.] The storage type of ``fix`` output depends upon the input storage type: - fix(default) = default - fix(row_sparse) = row_sparse - fix(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L795 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytfix²scKsdS(s#Flattens the input array into a 2-D array by collapsing the higher dimensions. .. note:: `Flatten` is deprecated. Use `flatten` instead. For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes the input array into an output array of shape ``(d1, d2*...*dk)``. Note that the bahavior of this function is different from numpy.ndarray.flatten, which behaves similar to mxnet.ndarray.reshape((-1,)). Example:: x = [[ [1,2,3], [4,5,6], [7,8,9] ], [ [1,2,3], [4,5,6], [7,8,9] ]], flatten(x) = [[ 1., 2., 3., 4., 5., 6., 7., 8., 9.], [ 1., 2., 3., 4., 5., 6., 7., 8., 9.]] Defined in src/operator/tensor/matrix_op.cc:L259 Parameters ---------- data : NDArray Input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyRJÓs+cKsdS(scReverses the order of elements along given axis while preserving array shape. Note: reverse and flip are equivalent. We use reverse in the following examples. Examples:: x = [[ 0., 1., 2., 3., 4.], [ 5., 6., 7., 8., 9.]] reverse(x, axis=0) = [[ 5., 6., 7., 8., 9.], [ 0., 1., 2., 3., 4.]] reverse(x, axis=1) = [[ 4., 3., 2., 1., 0.], [ 9., 8., 7., 6., 5.]] Defined in src/operator/tensor/matrix_op.cc:L794 Parameters ---------- data : NDArray Input data array axis : Shape(tuple), required The axis which to reverse elements. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytflips"cKsdS(sĆReturns element-wise floor of the input. The floor of the scalar x is the largest integer i, such that i <= x. Example:: floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2., 1., 1., 2.] The storage type of ``floor`` output depends upon the input storage type: - floor(default) = default - floor(row_sparse) = row_sparse - floor(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L757 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytfloor$s cKsdS(s(The FTML optimizer described in *FTML - Follow the Moving Leader in Deep Learning*, available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf. .. math:: g_t = \nabla J(W_{t-1})\\ v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\ d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon) \sigma_t = d_t - \beta_1 d_{t-1} z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1} W_t = - \frac{ z_t }{ d_t } Defined in src/operator/optimizer_op.cc:L447 Parameters ---------- weight : NDArray Weight grad : NDArray Gradient d : NDArray Internal state ``d_t`` v : NDArray Internal state ``v_t`` z : NDArray Internal state ``z_t`` lr : float, required Learning rate. beta1 : float, optional, default=0.6 Generally close to 0.5. beta2 : float, optional, default=0.999 Generally close to 1. epsilon : double, optional, default=1e-08 Epsilon to prevent div 0. t : int, required Number of update. wd : float, optional, default=0 Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. rescale_grad : float, optional, default=1 Rescale gradient to grad = rescale_grad*grad. clip_grad : float, optional, default=-1 Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R"R›tdtvtzRžRŸR R”ttR¢R£t clip_gradRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt ftml_updateFs7c KsdS(sUpdate function for Ftrl optimizer. Referenced from *Ad Click Prediction: a View from the Trenches*, available at http://dl.acm.org/citation.cfm?id=2488200. It updates the weights using:: rescaled_grad = clip(grad * rescale_grad, clip_gradient) z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate n += rescaled_grad**2 w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1) If w, z and n are all of ``row_sparse`` storage type, only the row slices whose indices appear in grad.indices are updated (for w, z and n):: for row in grad.indices: rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient) z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate n[row] += rescaled_grad[row]**2 w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1) Defined in src/operator/optimizer_op.cc:L632 Parameters ---------- weight : NDArray Weight grad : NDArray Gradient z : NDArray z n : NDArray Square of grad lr : float, required Learning rate lamda1 : float, optional, default=0.01 The L1 regularization coefficient. beta : float, optional, default=1 Per-Coordinate Learning Rate beta. wd : float, optional, default=0 Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. rescale_grad : float, optional, default=1 Rescale gradient to grad = rescale_grad*grad. clip_gradient : float, optional, default=-1 Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( R"R›R’tnRžtlamda1R R¢R£R¤RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt ftrl_updates8cKsdS(sŗReturns the gamma function (extension of the factorial function \ to the reals), computed element-wise on the input array. The storage type of ``gamma`` output is always dense Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyR¹scKsdS(s–Returns element-wise log of the absolute value of the gamma function \ of the input. The storage type of ``gammaln`` output is always dense Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytgammalnŠscKsdS(sGather elements or slices from `data` and store to a tensor whose shape is defined by `indices`. Given `data` with shape `(X_0, X_1, ..., X_{N-1})` and indices with shape `(M, Y_0, ..., Y_{K-1})`, the output will have shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})`, where `M <= N`. If `M == N`, output shape will simply be `(Y_0, ..., Y_{K-1})`. The elements in output is defined as follows:: output[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] = data[indices[0, y_0, ..., y_{K-1}], ..., indices[M-1, y_0, ..., y_{K-1}], x_M, ..., x_{N-1}] Examples:: data = [[0, 1], [2, 3]] indices = [[1, 1, 0], [0, 1, 0]] gather_nd(data, indices) = [2, 3, 0] data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]] indices = [[0, 1], [1, 0]] gather_nd(data, indices) = [[3, 4], [5, 6]] Parameters ---------- data : NDArray data indices : NDArray indices out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR»RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt gather_ndēs*cKsdS(s6Computes hard sigmoid of x element-wise. .. math:: y = max(0, min(1, alpha * x + beta)) Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L115 Parameters ---------- data : NDArray The input array. alpha : float, optional, default=0.2 Slope of hard sigmoid beta : float, optional, default=0.5 Bias of hard sigmoid. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRSR RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt hard_sigmoidscKsdS(sYReturns a copy of the input. From:src/operator/tensor/elemwise_unary_op_basic.cc:200 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytidentity0scOsdS(sšComputes the Khatri-Rao product of the input matrices. Given a collection of :math:`n` input matrices, .. math:: A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N}, the (column-wise) Khatri-Rao product is defined as the matrix, .. math:: X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N}, where the :math:`k` th column is equal to the column-wise outer product :math:`{A_1}_k \otimes \cdots \otimes {A_n}_k` where :math:`{A_i}_k` is the kth column of the ith matrix. Example:: >>> A = mx.nd.array([[1, -1], >>> [2, -3]]) >>> B = mx.nd.array([[1, 4], >>> [2, 5], >>> [3, 6]]) >>> C = mx.nd.khatri_rao(A, B) >>> print(C.asnumpy()) [[ 1. -4.] [ 2. -5.] [ 3. -6.] [ 2. -12.] [ 4. -15.] [ 6. -18.]] Defined in src/operator/contrib/krprod.cc:L108 Parameters ---------- args : NDArray[] Positional input matrices out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RBR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt khatri_raoDs2cKsdS(soLQ factorization for general matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, we compute the LQ factorization (LAPACK *gelqf*, followed by *orglq*). *A* must have shape *(x, y)* with *x <= y*, and must have full rank *=x*. The LQ factorization consists of *L* with shape *(x, x)* and *Q* with shape *(x, y)*, so that: *A* = *L* \* *Q* Here, *L* is lower triangular (upper triangle equal to zero) with nonzero diagonal, and *Q* is row-orthonormal, meaning that *Q* \* *Q*\ :sup:`T` is equal to the identity matrix of shape *(x, x)*. If *n>2*, *gelqf* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: // Single LQ factorization A = [[1., 2., 3.], [4., 5., 6.]] Q, L = gelqf(A) Q = [[-0.26726124, -0.53452248, -0.80178373], [0.87287156, 0.21821789, -0.43643578]] L = [[-3.74165739, 0.], [-8.55235974, 1.96396101]] // Batch LQ factorization A = [[[1., 2., 3.], [4., 5., 6.]], [[7., 8., 9.], [10., 11., 12.]]] Q, L = gelqf(A) Q = [[[-0.26726124, -0.53452248, -0.80178373], [0.87287156, 0.21821789, -0.43643578]], [[-0.50257071, -0.57436653, -0.64616234], [0.7620735, 0.05862104, -0.64483142]]] L = [[[-3.74165739, 0.], [-8.55235974, 1.96396101]], [[-13.92838828, 0.], [-19.09768702, 0.52758934]]] Defined in src/operator/tensor/la_op.cc:L552 Parameters ---------- A : NDArray Tensor of input matrices to be factorized out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((tARRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt linalg_gelqfxs>c KsdS(s¹ Performs general matrix multiplication and accumulation. Input are tensors *A*, *B*, *C*, each of dimension *n >= 2* and having the same shape on the leading *n-2* dimensions. If *n=2*, the BLAS3 function *gemm* is performed: *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*) + *beta* \* *C* Here, *alpha* and *beta* are scalar parameters, and *op()* is either the identity or matrix transposition (depending on *transpose_a*, *transpose_b*). If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis* parameter. By default, the trailing two dimensions will be used for matrix encoding. For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes calls. For example let *A*, *B*, *C* be 5 dimensional tensors. Then gemm(*A*, *B*, *C*, axis=1) is equivalent to A1 = swapaxes(A, dim1=1, dim2=3) B1 = swapaxes(B, dim1=1, dim2=3) C = swapaxes(C, dim1=1, dim2=3) C = gemm(A1, B1, C) C = swapaxis(C, dim1=1, dim2=3) without the overhead of the additional swapaxis operations. .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix multiply-add A = [[1.0, 1.0], [1.0, 1.0]] B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]] C = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]] gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0) = [[14.0, 14.0, 14.0], [14.0, 14.0, 14.0]] // Batch matrix multiply-add A = [[[1.0, 1.0]], [[0.1, 0.1]]] B = [[[1.0, 1.0]], [[0.1, 0.1]]] C = [[[10.0]], [[0.01]]] gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0) = [[[104.0]], [[0.14]]] Defined in src/operator/tensor/la_op.cc:L81 Parameters ---------- A : NDArray Tensor of input matrices B : NDArray Tensor of input matrices C : NDArray Tensor of input matrices transpose_a : boolean, optional, default=0 Multiply with transposed of first input (A). transpose_b : boolean, optional, default=0 Multiply with transposed of second input (B). alpha : double, optional, default=1 Scalar factor multiplied with A*B. beta : double, optional, default=1 Scalar factor multiplied with C. axis : int, optional, default='-2' Axis corresponding to the matrix rows. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( R tBtCR¶R·RSR RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt linalg_gemmøsKc KsdS(sf Performs general matrix multiplication. Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape on the leading *n-2* dimensions. If *n=2*, the BLAS3 function *gemm* is performed: *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*) Here *alpha* is a scalar parameter and *op()* is either the identity or the matrix transposition (depending on *transpose_a*, *transpose_b*). If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis* parameter. By default, the trailing two dimensions will be used for matrix encoding. For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes calls. For example let *A*, *B* be 5 dimensional tensors. Then gemm(*A*, *B*, axis=1) is equivalent to A1 = swapaxes(A, dim1=1, dim2=3) B1 = swapaxes(B, dim1=1, dim2=3) C = gemm2(A1, B1) C = swapaxis(C, dim1=1, dim2=3) without the overhead of the additional swapaxis operations. .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix multiply A = [[1.0, 1.0], [1.0, 1.0]] B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]] gemm2(A, B, transpose_b=True, alpha=2.0) = [[4.0, 4.0, 4.0], [4.0, 4.0, 4.0]] // Batch matrix multiply A = [[[1.0, 1.0]], [[0.1, 0.1]]] B = [[[1.0, 1.0]], [[0.1, 0.1]]] gemm2(A, B, transpose_b=True, alpha=2.0) = [[[4.0]], [[0.04 ]]] Defined in src/operator/tensor/la_op.cc:L151 Parameters ---------- A : NDArray Tensor of input matrices B : NDArray Tensor of input matrices transpose_a : boolean, optional, default=0 Multiply with transposed of first input (A). transpose_b : boolean, optional, default=0 Multiply with transposed of second input (B). alpha : double, optional, default=1 Scalar factor multiplied with A*B. axis : int, optional, default='-2' Axis corresponding to the matrix row indices. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( R R R¶R·RSRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt linalg_gemm2sDcKsdS(sŸPerforms Cholesky factorization of a symmetric positive-definite matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, the Cholesky factor *L* of the symmetric, positive definite matrix *A* is computed. *L* is lower triangular (entries of upper triangle are all zero), has positive diagonal entries, and: *A* = *L* \* *L*\ :sup:`T` If *n>2*, *potrf* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix factorization A = [[4.0, 1.0], [1.0, 4.25]] potrf(A) = [[2.0, 0], [0.5, 2.0]] // Batch matrix factorization A = [[[4.0, 1.0], [1.0, 4.25]], [[16.0, 4.0], [4.0, 17.0]]] potrf(A) = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]] Defined in src/operator/tensor/la_op.cc:L201 Parameters ---------- A : NDArray Tensor of input matrices to be decomposed out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt linalg_potrfKs)cKsdS(sPerforms matrix inversion from a Cholesky factorization. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, *A* is a lower triangular matrix (entries of upper triangle are all zero) with positive diagonal. We compute: *out* = *A*\ :sup:`-T` \* *A*\ :sup:`-1` In other words, if *A* is the Cholesky factor of a symmetric positive definite matrix *B* (obtained by *potrf*), then *out* = *B*\ :sup:`-1` If *n>2*, *potri* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. .. note:: Use this operator only if you are certain you need the inverse of *B*, and cannot use the Cholesky factor *A* (*potrf*), together with backsubstitution (*trsm*). The latter is numerically much safer, and also cheaper. Examples:: // Single matrix inverse A = [[2.0, 0], [0.5, 2.0]] potri(A) = [[0.26563, -0.0625], [-0.0625, 0.25]] // Batch matrix inverse A = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]] potri(A) = [[[0.26563, -0.0625], [-0.0625, 0.25]], [[0.06641, -0.01562], [-0.01562, 0,0625]]] Defined in src/operator/tensor/la_op.cc:L259 Parameters ---------- A : NDArray Tensor of lower triangular matrices out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt linalg_potrivs2cKsdS(sComputes the sum of the logarithms of the diagonal elements of a square matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, *A* must be square with positive diagonal entries. We sum the natural logarithms of the diagonal elements, the result has shape (1,). If *n>2*, *sumlogdiag* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix reduction A = [[1.0, 1.0], [1.0, 7.0]] sumlogdiag(A) = [1.9459] // Batch matrix reduction A = [[[1.0, 1.0], [1.0, 7.0]], [[3.0, 0], [0, 17.0]]] sumlogdiag(A) = [1.9459, 3.9318] Defined in src/operator/tensor/la_op.cc:L428 Parameters ---------- A : NDArray Tensor of square matrices out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytlinalg_sumlogdiagŖs&cKsdS(s±Multiplication of matrix with its transpose. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, the operator performs the BLAS3 function *syrk*: *out* = *alpha* \* *A* \* *A*\ :sup:`T` if *transpose=False*, or *out* = *alpha* \* *A*\ :sup:`T` \ \* *A* if *transpose=True*. If *n>2*, *syrk* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix multiply A = [[1., 2., 3.], [4., 5., 6.]] syrk(A, alpha=1., transpose=False) = [[14., 32.], [32., 77.]] syrk(A, alpha=1., transpose=True) = [[17., 22., 27.], [22., 29., 36.], [27., 36., 45.]] // Batch matrix multiply A = [[[1., 1.]], [[0.1, 0.1]]] syrk(A, alpha=2., transpose=False) = [[[4.]], [[0.04]]] Defined in src/operator/tensor/la_op.cc:L484 Parameters ---------- A : NDArray Tensor of input matrices transpose : boolean, optional, default=0 Use transpose of input matrix. alpha : double, optional, default=1 Scalar factor to be applied to the result. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R t transposeRSRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt linalg_syrkŅs7cKsdS(s’Performs multiplication with a lower triangular matrix. Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape on the leading *n-2* dimensions. If *n=2*, *A* must be lower triangular. The operator performs the BLAS3 function *trmm*: *out* = *alpha* \* *op*\ (*A*) \* *B* if *rightside=False*, or *out* = *alpha* \* *B* \* *op*\ (*A*) if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the identity or the matrix transposition (depending on *transpose*). If *n>2*, *trmm* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: // Single triangular matrix multiply A = [[1.0, 0], [1.0, 1.0]] B = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]] trmm(A, B, alpha=2.0) = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]] // Batch triangular matrix multiply A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]] B = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], [[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]]] trmm(A, B, alpha=2.0) = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]], [[1.0, 1.0, 1.0], [2.0, 2.0, 2.0]]] Defined in src/operator/tensor/la_op.cc:L316 Parameters ---------- A : NDArray Tensor of lower triangular matrices B : NDArray Tensor of matrices transpose : boolean, optional, default=0 Use transposed of the triangular matrix rightside : boolean, optional, default=0 Multiply triangular matrix from the right to non-triangular one. alpha : double, optional, default=1 Scalar factor to be applied to the result. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R R Rt rightsideRSRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt linalg_trmm s= 2* and having the same shape on the leading *n-2* dimensions. If *n=2*, *A* must be lower triangular. The operator performs the BLAS3 function *trsm*, solving for *out* in: *op*\ (*A*) \* *out* = *alpha* \* *B* if *rightside=False*, or *out* \* *op*\ (*A*) = *alpha* \* *B* if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the identity or the matrix transposition (depending on *transpose*). If *n>2*, *trsm* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: // Single matrix solve A = [[1.0, 0], [1.0, 1.0]] B = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]] trsm(A, B, alpha=0.5) = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]] // Batch matrix solve A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]] B = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]], [[4.0, 4.0, 4.0], [8.0, 8.0, 8.0]]] trsm(A, B, alpha=0.5) = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], [[2.0, 2.0, 2.0], [2.0, 2.0, 2.0]]] Defined in src/operator/tensor/la_op.cc:L379 Parameters ---------- A : NDArray Tensor of lower triangular matrices B : NDArray Tensor of matrices transpose : boolean, optional, default=0 Use transposed of the triangular matrix rightside : boolean, optional, default=0 Multiply triangular matrix from the right to non-triangular one. alpha : double, optional, default=1 Scalar factor to be applied to the result. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R R RRRSRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt linalg_trsmIs>> x = mx.nd.array([1, 2, .1]) >>> mx.nd.log_softmax(x).asnumpy() array([-1.41702998, -0.41702995, -2.31702995], dtype=float32) >>> x = mx.nd.array( [[1, 2, .1],[.1, 2, 1]] ) >>> mx.nd.log_softmax(x, axis=0).asnumpy() array([[-0.34115392, -0.69314718, -1.24115396], [-1.24115396, -0.69314718, -0.34115392]], dtype=float32) Parameters ---------- data : NDArray The input array. axis : int, optional, default='-1' The axis along which to compute softmax. temperature : double or None, optional, default=None Temperature parameter in softmax out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRt temperatureRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt log_softmaxōs#cKsdS(snReturns the result of logical NOT (!) function Example: logical_not([-2., 0., 1.]) = [0., 1., 0.] Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt logical_notscKsdS(s>Make your own loss function in network construction. This operator accepts a customized loss function symbol as a terminal loss and the symbol should be an operator with no backward dependency. The output of this function is the gradient of loss with respect to the input data. For example, if you are a making a cross entropy loss function. Assume ``out`` is the predicted output and ``label`` is the true label, then the cross entropy can be defined as:: cross_entropy = label * log(out) + (1 - label) * log(1 - out) loss = make_loss(cross_entropy) We will need to use ``make_loss`` when we are creating our own loss function or we want to combine multiple loss functions. Also we may want to stop some variables' gradients from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``. The storage type of ``make_loss`` output depends upon the input storage type: - make_loss(default) = default - make_loss(row_sparse) = row_sparse Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L300 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt make_loss0s'cKsdS(sĢComputes the max of array elements over given axes. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191 Parameters ---------- data : NDArray The input axis : Shape or None, optional, default=None The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims : boolean, optional, default=0 If this is set to `True`, the reduced axes are left in the result as dimension with size one. exclude : boolean, optional, default=0 Whether to perform reduction on axis that are NOT in axis instead. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR®texcludeRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytmaxYs%cKsdS(sĢComputes the max of array elements over given axes. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191 Parameters ---------- data : NDArray The input axis : Shape or None, optional, default=None The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims : boolean, optional, default=0 If this is set to `True`, the reduced axes are left in the result as dimension with size one. exclude : boolean, optional, default=0 Whether to perform reduction on axis that are NOT in axis instead. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR®R!RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytmax_axis€s%cKsdS(sĶComputes the mean of array elements over given axes. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L132 Parameters ---------- data : NDArray The input axis : Shape or None, optional, default=None The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims : boolean, optional, default=0 If this is set to `True`, the reduced axes are left in the result as dimension with size one. exclude : boolean, optional, default=0 Whether to perform reduction on axis that are NOT in axis instead. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR®R!RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyRœ§s%cKsdS(sĢComputes the min of array elements over given axes. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205 Parameters ---------- data : NDArray The input axis : Shape or None, optional, default=None The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims : boolean, optional, default=0 If this is set to `True`, the reduced axes are left in the result as dimension with size one. exclude : boolean, optional, default=0 Whether to perform reduction on axis that are NOT in axis instead. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR®R!RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytminĪs%cKsdS(sĢComputes the min of array elements over given axes. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205 Parameters ---------- data : NDArray The input axis : Shape or None, optional, default=None The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims : boolean, optional, default=0 If this is set to `True`, the reduced axes are left in the result as dimension with size one. exclude : boolean, optional, default=0 Whether to perform reduction on axis that are NOT in axis instead. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR®R!RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytmin_axisõs%c KsdS(sųUpdater function for multi-precision sgd optimizer Parameters ---------- weight : NDArray Weight grad : NDArray Gradient mom : NDArray Momentum weight32 : NDArray Weight32 lr : float, required Learning rate momentum : float, optional, default=0 The decay rate of momentum estimates at each epoch. wd : float, optional, default=0 Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. rescale_grad : float, optional, default=1 Rescale gradient to grad = rescale_grad*grad. clip_gradient : float, optional, default=-1 Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). lazy_update : boolean, optional, default=1 If true, lazy updates are applied if gradient's stype is row_sparse and both weight and momentum have the same stype out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( R"R›tmomtweight32RžR R¢R£R¤R„RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytmp_sgd_mom_updates"c KsdS(s?Updater function for multi-precision sgd optimizer Parameters ---------- weight : NDArray Weight grad : NDArray gradient weight32 : NDArray Weight32 lr : float, required Learning rate wd : float, optional, default=0 Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. rescale_grad : float, optional, default=1 Rescale gradient to grad = rescale_grad*grad. clip_gradient : float, optional, default=-1 Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). lazy_update : boolean, optional, default=1 If true, lazy updates are applied if gradient's stype is row_sparse. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( R"R›R'RžR¢R£R¤R„RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt mp_sgd_update@scKsdS(sśComputes the product of array elements over given axes treating Not a Numbers (``NaN``) as one. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L177 Parameters ---------- data : NDArray The input axis : Shape or None, optional, default=None The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims : boolean, optional, default=0 If this is set to `True`, the reduced axes are left in the result as dimension with size one. exclude : boolean, optional, default=0 Whether to perform reduction on axis that are NOT in axis instead. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR®R!RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytnanprod`s'cKsdS(s÷Computes the sum of array elements over given axes treating Not a Numbers (``NaN``) as zero. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L162 Parameters ---------- data : NDArray The input axis : Shape or None, optional, default=None The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims : boolean, optional, default=0 If this is set to `True`, the reduced axes are left in the result as dimension with size one. exclude : boolean, optional, default=0 Whether to perform reduction on axis that are NOT in axis instead. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR®R!RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytnansum‰s'cKsdS(sóNumerical negative of the argument, element-wise. The storage type of ``negative`` output depends upon the input storage type: - negative(default) = default - negative(row_sparse) = row_sparse - negative(csr) = csr Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytnegative²scKsdS(s²Computes the norm on an NDArray. This operator computes the norm on an NDArray with the specified axis, depending on the value of the ord parameter. By default, it computes the L2 norm on the entire array. Currently only ord=2 supports sparse ndarrays. Examples:: x = [[[1, 2], [3, 4]], [[2, 2], [5, 6]]] norm(x, ord=2, axis=1) = [[3.1622777 4.472136 ] [5.3851647 6.3245554]] norm(x, ord=1, axis=1) = [[4., 6.], [7., 8.]] rsp = x.cast_storage('row_sparse') norm(rsp) = [5.47722578] csr = x.cast_storage('csr') norm(csr) = [5.47722578] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L350 Parameters ---------- data : NDArray The input ord : int, optional, default='2' Order of the norm. Currently ord=1 and ord=2 is supported. axis : Shape or None, optional, default=None The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. keepdims : boolean, optional, default=0 If this is set to `True`, the reduced axis is left in the result as dimension with size one. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RtordRR®RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytnormĢs8cKsdS(sĪDraw random samples from a normal (Gaussian) distribution. .. note:: The existing alias ``normal`` is deprecated. Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation). Example:: normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478], [-1.23474145, 1.55807114]] Defined in src/operator/random/sample_op.cc:L85 Parameters ---------- loc : float, optional, default=0 Mean of the distribution. scale : float, optional, default=1 Standard deviation of the distribution. shape : Shape(tuple), optional, default=[] Shape of the output. ctx : string, optional, default='' Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“tscaleRytctxRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytnormals$cKsdS(sjReturns a one-hot array. The locations represented by `indices` take value `on_value`, while all other locations take value `off_value`. `one_hot` operation with `indices` of shape ``(i0, i1)`` and `depth` of ``d`` would result in an output array of shape ``(i0, i1, d)`` with:: output[i,j,:] = off_value output[i,j,indices[i,j]] = on_value Examples:: one_hot([1,0,2,0], 3) = [[ 0. 1. 0.] [ 1. 0. 0.] [ 0. 0. 1.] [ 1. 0. 0.]] one_hot([1,0,2,0], 3, on_value=8, off_value=1, dtype='int32') = [[1 8 1] [8 1 1] [1 1 8] [8 1 1]] one_hot([[1,0],[1,0],[2,0]], 3) = [[[ 0. 1. 0.] [ 1. 0. 0.]] [[ 0. 1. 0.] [ 1. 0. 0.]] [[ 0. 0. 1.] [ 1. 0. 0.]]] Defined in src/operator/tensor/indexing_op.cc:L536 Parameters ---------- indices : NDArray array of locations where to set on_value depth : int, required Depth of the one hot dimension. on_value : double, optional, default=1 The value assigned to the locations represented by indices. off_value : double, optional, default=0 The value assigned to the locations not represented by indices. dtype : {'float16', 'float32', 'float64', 'int32', 'int64', 'int8', 'uint8'},optional, default='float32' DType of the output out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R»tdepthton_valuet off_valueRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytone_hot,s:cKsdS(sßReturn an array of ones with the same shape and type as the input array. Examples:: x = [[ 0., 0., 0.], [ 0., 0., 0.]] ones_like(x) = [[ 1., 1., 1.], [ 1., 1., 1.]] Parameters ---------- data : NDArray The input out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt ones_likehscKsdS(sPads an input array with a constant or edge values of the array. .. note:: `Pad` is deprecated. Use `pad` instead. .. note:: Current implementation only supports 4D and 5D input arrays with padding applied only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero. This operation pads an input array with either a `constant_value` or edge values along each axis of the input array. The amount of padding is specified by `pad_width`. `pad_width` is a tuple of integer padding widths for each axis of the format ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of length ``2*N`` where ``N`` is the number of dimensions of the array. For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values to add before and after the elements of the array along dimension ``N``. The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``, ``after_2`` must be 0. Example:: x = [[[[ 1. 2. 3.] [ 4. 5. 6.]] [[ 7. 8. 9.] [ 10. 11. 12.]]] [[[ 11. 12. 13.] [ 14. 15. 16.]] [[ 17. 18. 19.] [ 20. 21. 22.]]]] pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) = [[[[ 1. 1. 2. 3. 3.] [ 1. 1. 2. 3. 3.] [ 4. 4. 5. 6. 6.] [ 4. 4. 5. 6. 6.]] [[ 7. 7. 8. 9. 9.] [ 7. 7. 8. 9. 9.] [ 10. 10. 11. 12. 12.] [ 10. 10. 11. 12. 12.]]] [[[ 11. 11. 12. 13. 13.] [ 11. 11. 12. 13. 13.] [ 14. 14. 15. 16. 16.] [ 14. 14. 15. 16. 16.]] [[ 17. 17. 18. 19. 19.] [ 17. 17. 18. 19. 19.] [ 20. 20. 21. 22. 22.] [ 20. 20. 21. 22. 22.]]]] pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) = [[[[ 0. 0. 0. 0. 0.] [ 0. 1. 2. 3. 0.] [ 0. 4. 5. 6. 0.] [ 0. 0. 0. 0. 0.]] [[ 0. 0. 0. 0. 0.] [ 0. 7. 8. 9. 0.] [ 0. 10. 11. 12. 0.] [ 0. 0. 0. 0. 0.]]] [[[ 0. 0. 0. 0. 0.] [ 0. 11. 12. 13. 0.] [ 0. 14. 15. 16. 0.] [ 0. 0. 0. 0. 0.]] [[ 0. 0. 0. 0. 0.] [ 0. 17. 18. 19. 0.] [ 0. 20. 21. 22. 0.] [ 0. 0. 0. 0. 0.]]]] Defined in src/operator/pad.cc:L766 Parameters ---------- data : NDArray An n-dimensional input array. mode : {'constant', 'edge', 'reflect'}, required Padding type to use. "constant" pads with `constant_value` "edge" pads using the edge values of the input array "reflect" pads by reflecting values with respect to the edges. pad_width : Shape(tuple), required Widths of the padding regions applied to the edges of each axis. It is a tuple of integer padding widths for each axis of the format ``(before_1, after_1, ... , before_N, after_N)``. It should be of length ``2*N`` where ``N`` is the number of dimensions of the array.This is equivalent to pad_width in numpy.pad, but flattened. constant_value : double, optional, default=0 The value used for padding when `mode` is "constant". out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR?RcRdRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyR'…sicKsdS(sW Picks elements from an input array according to the input indices along the given axis. Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be an output array of shape ``(i0,)`` with:: output[i] = input[i, indices[i]] By default, if any index mentioned is too large, it is replaced by the index that addresses the last element along an axis (the `clip` mode). This function supports n-dimensional input and (n-1)-dimensional indices arrays. Examples:: x = [[ 1., 2.], [ 3., 4.], [ 5., 6.]] // picks elements with specified indices along axis 0 pick(x, y=[0,1], 0) = [ 1., 4.] // picks elements with specified indices along axis 1 pick(x, y=[0,1,0], 1) = [ 1., 4., 5.] y = [[ 1.], [ 0.], [ 2.]] // picks elements with specified indices along axis 1 using 'wrap' mode // to place indicies that would normally be out of bounds pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1., 4., 5.] y = [[ 1.], [ 0.], [ 2.]] // picks elements with specified indices along axis 1 and dims are maintained pick(x,y, 1, keepdims=True) = [[ 2.], [ 3.], [ 6.]] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L153 Parameters ---------- data : NDArray The input array index : NDArray The index array axis : int or None, optional, default='-1' int or None. The axis to picking the elements. Negative values means indexing from right to left. If is `None`, the elements in the index w.r.t the flattened input will be picked. keepdims : boolean, optional, default=0 If true, the axis where we pick the elements is left in the result as dimension with size one. mode : {'clip', 'wrap'},optional, default='clip' Specify how out-of-bound indices behave. Default is "clip". "clip" means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis. "wrap" means to wrap around. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RtindexRR®R?RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytpickšsCcKsdS(sŠComputes the product of array elements over given axes. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L147 Parameters ---------- data : NDArray The input axis : Shape or None, optional, default=None The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims : boolean, optional, default=0 If this is set to `True`, the reduced axes are left in the result as dimension with size one. exclude : boolean, optional, default=0 Whether to perform reduction on axis that are NOT in axis instead. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR®R!RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytprod5s%cKsdS(s˜Converts each element of the input array from degrees to radians. .. math:: radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi] The storage type of ``radians`` output depends upon the input storage type: - radians(default) = default - radians(row_sparse) = row_sparse - radians(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L182 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytradians\scKsdS(s6Draw random samples from an exponential distribution. Samples are distributed according to an exponential distribution parametrized by *lambda* (rate). Example:: exponential(lam=4, shape=(2,2)) = [[ 0.0097189 , 0.08999364], [ 0.04146638, 0.31715935]] Defined in src/operator/random/sample_op.cc:L115 Parameters ---------- lam : float, optional, default=1 Lambda parameter (rate) of the exponential distribution. shape : Shape(tuple), optional, default=[] Shape of the output. ctx : string, optional, default='' Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((tlamRyR0RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytrandom_exponential{s cKsdS(s£Draw random samples from a gamma distribution. Samples are distributed according to a gamma distribution parametrized by *alpha* (shape) and *beta* (scale). Example:: gamma(alpha=9, beta=0.5, shape=(2,2)) = [[ 7.10486984, 3.37695289], [ 3.91697288, 3.65933681]] Defined in src/operator/random/sample_op.cc:L100 Parameters ---------- alpha : float, optional, default=1 Alpha parameter (shape) of the gamma distribution. beta : float, optional, default=1 Beta parameter (scale) of the gamma distribution. shape : Shape(tuple), optional, default=[] Shape of the output. ctx : string, optional, default='' Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RSR RyR0RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt random_gammas"cKsdS(s½Draw random samples from a generalized negative binomial distribution. Samples are distributed according to a generalized negative binomial distribution parametrized by *mu* (mean) and *alpha* (dispersion). *alpha* is defined as *1/k* where *k* is the failure limit of the number of unsuccessful experiments (generalized to real numbers). Samples will always be returned as a floating point data type. Example:: generalized_negative_binomial(mu=2.0, alpha=0.3, shape=(2,2)) = [[ 2., 1.], [ 6., 4.]] Defined in src/operator/random/sample_op.cc:L168 Parameters ---------- mu : float, optional, default=1 Mean of the negative binomial distribution. alpha : float, optional, default=1 Alpha (dispersion) parameter of the negative binomial distribution. shape : Shape(tuple), optional, default=[] Shape of the output. ctx : string, optional, default='' Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((tmuRSRyR0RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt$random_generalized_negative_binomialĮs%cKsdS(sDraw random samples from a negative binomial distribution. Samples are distributed according to a negative binomial distribution parametrized by *k* (limit of unsuccessful experiments) and *p* (failure probability in each experiment). Samples will always be returned as a floating point data type. Example:: negative_binomial(k=3, p=0.4, shape=(2,2)) = [[ 4., 7.], [ 2., 5.]] Defined in src/operator/random/sample_op.cc:L149 Parameters ---------- k : int, optional, default='1' Limit of unsuccessful experiments. p : float, optional, default=1 Failure probability in each experiment. shape : Shape(tuple), optional, default=[] Shape of the output. ctx : string, optional, default='' Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RģR>RyR0RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytrandom_negative_binomialčs$cKsdS(sĪDraw random samples from a normal (Gaussian) distribution. .. note:: The existing alias ``normal`` is deprecated. Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation). Example:: normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478], [-1.23474145, 1.55807114]] Defined in src/operator/random/sample_op.cc:L85 Parameters ---------- loc : float, optional, default=0 Mean of the distribution. scale : float, optional, default=1 Standard deviation of the distribution. shape : Shape(tuple), optional, default=[] Shape of the output. ctx : string, optional, default='' Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“R/RyR0RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt random_normals$cKsdS(sCDraw random samples from a Poisson distribution. Samples are distributed according to a Poisson distribution parametrized by *lambda* (rate). Samples will always be returned as a floating point data type. Example:: poisson(lam=4, shape=(2,2)) = [[ 5., 2.], [ 4., 6.]] Defined in src/operator/random/sample_op.cc:L132 Parameters ---------- lam : float, optional, default=1 Lambda parameter (rate) of the Poisson distribution. shape : Shape(tuple), optional, default=[] Shape of the output. ctx : string, optional, default='' Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R;RyR0RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytrandom_poisson4s!cKsdS(sĀDraw random samples from a uniform distribution. .. note:: The existing alias ``uniform`` is deprecated. Samples are uniformly distributed over the half-open interval *[low, high)* (includes *low*, but excludes *high*). Example:: uniform(low=0, high=1, shape=(2,2)) = [[ 0.60276335, 0.85794562], [ 0.54488319, 0.84725171]] Defined in src/operator/random/sample_op.cc:L66 Parameters ---------- low : float, optional, default=0 Lower bound of the distribution. high : float, optional, default=1 Upper bound of the distribution. shape : Shape(tuple), optional, default=[] Shape of the output. ctx : string, optional, default='' Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((tlowthighRyR0RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytrandom_uniformWs&cKsdS(s«Converts a batch of index arrays into an array of flat indices. The operator follows numpy conventions so a single multi index is given by a column of the input matrix. Examples:: A = [[3,6,6],[4,5,1]] ravel(A, shape=(7,6)) = [22,41,37] Defined in src/operator/tensor/ravel.cc:L41 Parameters ---------- data : NDArray Batch of multi-indices shape : Shape(tuple), optional, default=[] Shape of the array into which the multi-indices apply. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRyRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytravel_multi_indexscKsdS(sėReturns element-wise inverse cube-root value of the input. .. math:: rcbrt(x) = 1/\sqrt[3]{x} Example:: rcbrt([1,8,-125]) = [1.0, 0.5, -0.2] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L898 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytrcbrtœscKsdS(sļReturns the reciprocal of the argument, element-wise. Calculates 1/x. Example:: reciprocal([-2, 1, 3, 1.6, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L638 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt reciprocal¹scKsdS(s6Computes rectified linear. .. math:: max(features, 0) The storage type of ``relu`` output depends upon the input storage type: - relu(default) = default - relu(row_sparse) = row_sparse - relu(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L85 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytreluÕscKsdS(soRepeats elements of an array. By default, ``repeat`` flattens the input array into 1-D and then repeats the elements:: x = [[ 1, 2], [ 3, 4]] repeat(x, repeats=2) = [ 1., 1., 2., 2., 3., 3., 4., 4.] The parameter ``axis`` specifies the axis along which to perform repeat:: repeat(x, repeats=2, axis=1) = [[ 1., 1., 2., 2.], [ 3., 3., 4., 4.]] repeat(x, repeats=2, axis=0) = [[ 1., 2.], [ 1., 2.], [ 3., 4.], [ 3., 4.]] repeat(x, repeats=2, axis=-1) = [[ 1., 1., 2., 2.], [ 3., 3., 4., 4.]] Defined in src/operator/tensor/matrix_op.cc:L692 Parameters ---------- data : NDArray Input data array repeats : int, required The number of repetitions for each element. axis : int or None, optional, default='None' The axis along which to repeat values. The negative numbers are interpreted counting from the backward. By default, use the flattened input array, and return a flat output array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RtrepeatsRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytrepeatōs-cKsdS(sC Reshapes the input array. .. note:: ``Reshape`` is deprecated, use ``reshape`` Given an array and a shape, this function returns a copy of the array in the new shape. The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array. Example:: reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]] Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below: - ``0`` copy this dimension from the input to the output shape. Example:: - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2) - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4) - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions keeping the size of the new array same as that of the input array. At most one dimension of shape can be -1. Example:: - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4) - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8) - input shape = (2,3,4), shape=(-1,), output shape = (24,) - ``-2`` copy all/remainder of the input dimensions to the output shape. Example:: - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4) - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4) - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1) - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension. Example:: - input shape = (2,3,4), shape = (-3,4), output shape = (6,4) - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20) - input shape = (2,3,4), shape = (0,-3), output shape = (2,12) - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4) - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1). Example:: - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4) - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4) If the argument `reverse` is set to 1, then the special values are inferred from right to left. Example:: - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5) - with reverse=1, output shape will be (50,4). Defined in src/operator/tensor/matrix_op.cc:L169 Parameters ---------- data : NDArray Input data to reshape. shape : Shape(tuple), optional, default=[] The target shape reverse : boolean, optional, default=0 If true then the special values are inferred from right to left target_shape : Shape(tuple), optional, default=[] (Deprecated! Use ``shape`` instead.) Target new shape. One and only one dim can be 0, in which case it will be inferred from the rest of dims keep_highest : boolean, optional, default=0 (Deprecated! Use ``shape`` instead.) Whether keep the highest dim unchanged.If set to true, then the first dim in target_shape is ignored,and always fixed as input out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRyRzR<R{RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytreshape#sWcKsdS(sįReshape some or all dimensions of `lhs` to have the same shape as some or all dimensions of `rhs`. Returns a **view** of the `lhs` array with a new shape without altering any data. Example:: x = [1, 2, 3, 4, 5, 6] y = [[0, -4], [3, 2], [2, 2]] reshape_like(x, y) = [[1, 2], [3, 4], [5, 6]] More precise control over how dimensions are inherited is achieved by specifying \ slices over the `lhs` and `rhs` array dimensions. Only the sliced `lhs` dimensions \ are reshaped to the `rhs` sliced dimensions, with the non-sliced `lhs` dimensions staying the same. Examples:: - lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, rhs_begin=0, rhs_end=2, output shape = (15,2,7) - lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, rhs_begin=1, rhs_end=2, output shape = (15) Negative indices are supported, and `None` can be used for either `lhs_end` or `rhs_end` to indicate the end of the range. Example:: - lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, rhs_begin=1, rhs_end=None, output shape = (30, 2, 2, 3) Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L455 Parameters ---------- lhs : NDArray First input. rhs : NDArray Second input. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R“RµRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt reshape_like|s-cKsdS(scReverses the order of elements along given axis while preserving array shape. Note: reverse and flip are equivalent. We use reverse in the following examples. Examples:: x = [[ 0., 1., 2., 3., 4.], [ 5., 6., 7., 8., 9.]] reverse(x, axis=0) = [[ 5., 6., 7., 8., 9.], [ 0., 1., 2., 3., 4.]] reverse(x, axis=1) = [[ 4., 3., 2., 1., 0.], [ 9., 8., 7., 6., 5.]] Defined in src/operator/tensor/matrix_op.cc:L794 Parameters ---------- data : NDArray Input data array axis : Shape(tuple), required The axis which to reverse elements. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyRz«s"cKsdS(s>Returns element-wise rounded value to the nearest integer of the input. .. note:: - For input ``n.5`` ``rint`` returns ``n`` while ``round`` returns ``n+1``. - For input ``-n.5`` both ``rint`` and ``round`` returns ``-n-1``. Example:: rint([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2., 1., -2., 2., 2.] The storage type of ``rint`` output depends upon the input storage type: - rint(default) = default - rint(row_sparse) = row_sparse - rint(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L719 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytrintĻs"c KsdS(s½ Update function for `RMSProp` optimizer. `RMSprop` is a variant of stochastic gradient descent where the gradients are divided by a cache which grows with the sum of squares of recent gradients? `RMSProp` is similar to `AdaGrad`, a popular variant of `SGD` which adaptively tunes the learning rate of each parameter. `AdaGrad` lowers the learning rate for each parameter monotonically over the course of training. While this is analytically motivated for convex optimizations, it may not be ideal for non-convex problems. `RMSProp` deals with this heuristically by allowing the learning rates to rebound as the denominator decays over time. Define the Root Mean Square (RMS) error criterion of the gradient as :math:`RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}`, where :math:`g` represents gradient and :math:`E[g^2]_t` is the decaying average over past squared gradient. The :math:`E[g^2]_t` is given by: .. math:: E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2 The update step is .. math:: \theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t The RMSProp code follows the version in http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf Tieleman & Hinton, 2012. Hinton suggests the momentum term :math:`\gamma` to be 0.9 and the learning rate :math:`\eta` to be 0.001. Defined in src/operator/optimizer_op.cc:L553 Parameters ---------- weight : NDArray Weight grad : NDArray Gradient n : NDArray n lr : float, required Learning rate gamma1 : float, optional, default=0.95 The decay rate of momentum estimates. epsilon : float, optional, default=1e-08 A small constant for numerical stability. wd : float, optional, default=0 Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. rescale_grad : float, optional, default=1 Rescale gradient to grad = rescale_grad*grad. clip_gradient : float, optional, default=-1 Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). clip_weights : float, optional, default=-1 Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, clip_weights), -clip_weights). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( R"R›RRžtgamma1R”R¢R£R¤t clip_weightsRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytrmsprop_updateósEcKsdS(sžUpdate function for RMSPropAlex optimizer. `RMSPropAlex` is non-centered version of `RMSProp`. Define :math:`E[g^2]_t` is the decaying average over past squared gradient and :math:`E[g]_t` is the decaying average over past gradient. .. math:: E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\ E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\ \Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 + \epsilon}} g_t\\ The update step is .. math:: \theta_{t+1} = \theta_t + \Delta_t The RMSPropAlex code follows the version in http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013. Graves suggests the momentum term :math:`\gamma_1` to be 0.95, :math:`\gamma_2` to be 0.9 and the learning rate :math:`\eta` to be 0.0001. Defined in src/operator/optimizer_op.cc:L592 Parameters ---------- weight : NDArray Weight grad : NDArray Gradient n : NDArray n g : NDArray g delta : NDArray delta lr : float, required Learning rate gamma1 : float, optional, default=0.95 Decay rate. gamma2 : float, optional, default=0.9 Decay rate. epsilon : float, optional, default=1e-08 A small constant for numerical stability. wd : float, optional, default=0 Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. rescale_grad : float, optional, default=1 Rescale gradient to grad = rescale_grad*grad. clip_gradient : float, optional, default=-1 Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). clip_weights : float, optional, default=-1 Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, clip_weights), -clip_weights). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R"R›RtgtdeltaRžROtgamma2R”R¢R£R¤RPRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytrmspropalex_update:s@cKsdS(s”Returns element-wise rounded value to the nearest integer of the input. Example:: round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2., 2., -2., 2., 2.] The storage type of ``round`` output depends upon the input storage type: - round(default) = default - round(row_sparse) = row_sparse - round(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L698 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytround|scKsdS(s)Returns element-wise inverse square-root value of the input. .. math:: rsqrt(x) = 1/\sqrt{x} Example:: rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25] The storage type of ``rsqrt`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L858 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytrsqrtœscKsdS(s6Concurrent sampling from multiple exponential distributions with parameters lambda (rate). The parameters of the distributions are provided as an input array. Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input array, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input value at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input array. Examples:: lam = [ 1.0, 8.5 ] // Draw a single sample for each distribution sample_exponential(lam) = [ 0.51837951, 0.09994757] // Draw a vector containing two samples for each distribution sample_exponential(lam, shape=(2)) = [[ 0.51837951, 0.19866663], [ 0.09994757, 0.50447971]] Defined in src/operator/random/multisample_op.cc:L284 Parameters ---------- lam : NDArray Lambda (rate) parameters of the distributions. shape : Shape(tuple), optional, default=[] Shape to be sampled from each random distribution. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R;RyRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsample_exponential»s.cKsdS(sµConcurrent sampling from multiple gamma distributions with parameters *alpha* (shape) and *beta* (scale). The parameters of the distributions are provided as input arrays. Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays. Examples:: alpha = [ 0.0, 2.5 ] beta = [ 1.0, 0.7 ] // Draw a single sample for each distribution sample_gamma(alpha, beta) = [ 0. , 2.25797319] // Draw a vector containing two samples for each distribution sample_gamma(alpha, beta, shape=(2)) = [[ 0. , 0. ], [ 2.25797319, 1.70734084]] Defined in src/operator/random/multisample_op.cc:L282 Parameters ---------- alpha : NDArray Alpha (shape) parameters of the distributions. shape : Shape(tuple), optional, default=[] Shape to be sampled from each random distribution. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). beta : NDArray Beta (scale) parameters of the distributions. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RSR RyRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt sample_gammaės1cKsdS(sConcurrent sampling from multiple generalized negative binomial distributions with parameters *mu* (mean) and *alpha* (dispersion). The parameters of the distributions are provided as input arrays. Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays. Samples will always be returned as a floating point data type. Examples:: mu = [ 2.0, 2.5 ] alpha = [ 1.0, 0.1 ] // Draw a single sample for each distribution sample_generalized_negative_binomial(mu, alpha) = [ 0., 3.] // Draw a vector containing two samples for each distribution sample_generalized_negative_binomial(mu, alpha, shape=(2)) = [[ 0., 3.], [ 3., 1.]] Defined in src/operator/random/multisample_op.cc:L293 Parameters ---------- mu : NDArray Means of the distributions. shape : Shape(tuple), optional, default=[] Shape to be sampled from each random distribution. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). alpha : NDArray Alpha (dispersion) parameters of the distributions. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R>RSRyRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt$sample_generalized_negative_binomial s3cKsdS(sŖConcurrent sampling from multiple multinomial distributions. *data* is an *n* dimensional array whose last dimension has length *k*, where *k* is the number of possible outcomes of each multinomial distribution. This operator will draw *shape* samples from each distribution. If shape is empty one sample will be drawn from each distribution. If *get_prob* is true, a second array containing log likelihood of the drawn samples will also be returned. This is usually used for reinforcement learning where you can provide reward as head gradient for this array to estimate gradient. Note that the input distribution must be normalized, i.e. *data* must sum to 1 along its last axis. Examples:: probs = [[0, 0.1, 0.2, 0.3, 0.4], [0.4, 0.3, 0.2, 0.1, 0]] // Draw a single sample for each distribution sample_multinomial(probs) = [3, 0] // Draw a vector containing two samples for each distribution sample_multinomial(probs, shape=(2)) = [[4, 2], [0, 0]] // requests log likelihood sample_multinomial(probs, get_prob=True) = [2, 1], [0.2, 0.3] Parameters ---------- data : NDArray Distribution probabilities. Must sum to one on the last axis. shape : Shape(tuple), optional, default=[] Shape to be sampled from each random distribution. get_prob : boolean, optional, default=0 Whether to also return the log probability of sampled result. This is usually used for differentiating through stochastic variables, e.g. in reinforcement learning. dtype : {'float16', 'float32', 'float64', 'int32', 'uint8'},optional, default='int32' DType of the output in case this can't be inferred. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRytget_probRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsample_multinomialS s2cKsdS(sÜConcurrent sampling from multiple negative binomial distributions with parameters *k* (failure limit) and *p* (failure probability). The parameters of the distributions are provided as input arrays. Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays. Samples will always be returned as a floating point data type. Examples:: k = [ 20, 49 ] p = [ 0.4 , 0.77 ] // Draw a single sample for each distribution sample_negative_binomial(k, p) = [ 15., 16.] // Draw a vector containing two samples for each distribution sample_negative_binomial(k, p, shape=(2)) = [[ 15., 50.], [ 16., 12.]] Defined in src/operator/random/multisample_op.cc:L289 Parameters ---------- k : NDArray Limits of unsuccessful experiments. shape : Shape(tuple), optional, default=[] Shape to be sampled from each random distribution. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). p : NDArray Failure probabilities in each experiment. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RģR>RyRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsample_negative_binomial‡ s3cKsdS(s¢Concurrent sampling from multiple normal distributions with parameters *mu* (mean) and *sigma* (standard deviation). The parameters of the distributions are provided as input arrays. Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays. Examples:: mu = [ 0.0, 2.5 ] sigma = [ 1.0, 3.7 ] // Draw a single sample for each distribution sample_normal(mu, sigma) = [-0.56410581, 0.95934606] // Draw a vector containing two samples for each distribution sample_normal(mu, sigma, shape=(2)) = [[-0.56410581, 0.2928229 ], [ 0.95934606, 4.48287058]] Defined in src/operator/random/multisample_op.cc:L279 Parameters ---------- mu : NDArray Means of the distributions. shape : Shape(tuple), optional, default=[] Shape to be sampled from each random distribution. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). sigma : NDArray Standard deviations of the distributions. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R>tsigmaRyRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt sample_normal¼ s1cKsdS(s@Concurrent sampling from multiple Poisson distributions with parameters lambda (rate). The parameters of the distributions are provided as an input array. Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input array, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input value at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input array. Samples will always be returned as a floating point data type. Examples:: lam = [ 1.0, 8.5 ] // Draw a single sample for each distribution sample_poisson(lam) = [ 0., 13.] // Draw a vector containing two samples for each distribution sample_poisson(lam, shape=(2)) = [[ 0., 4.], [ 13., 8.]] Defined in src/operator/random/multisample_op.cc:L286 Parameters ---------- lam : NDArray Lambda (rate) parameters of the distributions. shape : Shape(tuple), optional, default=[] Shape to be sampled from each random distribution. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((R;RyRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsample_poissonļ s0cKsdS(sConcurrent sampling from multiple uniform distributions on the intervals given by *[low,high)*. The parameters of the distributions are provided as input arrays. Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays. Examples:: low = [ 0.0, 2.5 ] high = [ 1.0, 3.7 ] // Draw a single sample for each distribution sample_uniform(low, high) = [ 0.40451524, 3.18687344] // Draw a vector containing two samples for each distribution sample_uniform(low, high, shape=(2)) = [[ 0.40451524, 0.18017688], [ 3.18687344, 3.68352246]] Defined in src/operator/random/multisample_op.cc:L277 Parameters ---------- low : NDArray Lower bounds of the distributions. shape : Shape(tuple), optional, default=[] Shape to be sampled from each random distribution. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). high : NDArray Upper bounds of the distributions. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RCRDRyRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsample_uniform!!s1cKsdS(s’Scatters data into a new tensor according to indices. Given `data` with shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})` and indices with shape `(M, Y_0, ..., Y_{K-1})`, the output will have shape `(X_0, X_1, ..., X_{N-1})`, where `M <= N`. If `M == N`, data shape should simply be `(Y_0, ..., Y_{K-1})`. The elements in output is defined as follows:: output[indices[0, y_0, ..., y_{K-1}], ..., indices[M-1, y_0, ..., y_{K-1}], x_M, ..., x_{N-1}] = data[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] all other entries in output are 0. .. warning:: If the indices have duplicates, the result will be non-deterministic and the gradient of `scatter_nd` will not be correct!! Examples:: data = [2, 3, 0] indices = [[1, 1, 0], [0, 1, 0]] shape = (2, 2) scatter_nd(data, indices, shape) = [[0, 0], [2, 3]] data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]] indices = [[0, 1], [1, 1]] shape = (2, 2, 2, 2) scatter_nd(data, indices, shape) = [[[[0, 0], [0, 0]], [[1, 2], [3, 4]]], [[[0, 0], [0, 0]], [[5, 6], [7, 8]]]] Parameters ---------- data : NDArray data indices : NDArray indices shape : Shape(tuple), required Shape of output. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR»RyRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt scatter_ndT!s?c KsdS(sfMomentum update function for Stochastic Gradient Descent (SGD) optimizer. Momentum update has better convergence rates on neural networks. Mathematically it looks like below: .. math:: v_1 = \alpha * \nabla J(W_0)\\ v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\ W_t = W_{t-1} + v_t It updates the weights using:: v = momentum * v - learning_rate * gradient weight += v Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch. However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and weight's storage type is the same as momentum's storage type, only the row slices whose indices appear in grad.indices are updated (for both weight and momentum):: for row in gradient.indices: v[row] = momentum[row] * v[row] - learning_rate * gradient[row] weight[row] += v[row] Defined in src/operator/optimizer_op.cc:L372 Parameters ---------- weight : NDArray Weight grad : NDArray Gradient mom : NDArray Momentum lr : float, required Learning rate momentum : float, optional, default=0 The decay rate of momentum estimates at each epoch. wd : float, optional, default=0 Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. rescale_grad : float, optional, default=1 Rescale gradient to grad = rescale_grad*grad. clip_gradient : float, optional, default=-1 Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). lazy_update : boolean, optional, default=1 If true, lazy updates are applied if gradient's stype is row_sparse and both weight and momentum have the same stype out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( R"R›R&RžR R¢R£R¤R„RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsgd_mom_update•!s 0`, set `b_k=0`, `e_k=d_k`; else, set `b_k=d_k-1`, `e_k=-1`. The storage type of ``slice`` output depends on storage types of inputs - slice(csr) = csr - otherwise, ``slice`` generates output with default storage .. note:: When input data storage type is csr, it only supports step=(), or step=(None,), or step=(1,) to generate a csr output. For other step parameter values, it falls back to slicing a dense tensor. Example:: x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice(x, begin=(0,1), end=(2,4)) = [[ 2., 3., 4.], [ 6., 7., 8.]] slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = [[9., 11.], [5., 7.], [1., 3.]] Defined in src/operator/tensor/matrix_op.cc:L414 Parameters ---------- data : NDArray Source input begin : Shape(tuple), required starting indices for the slice operation, supports negative indices. end : Shape(tuple), required ending indices for the slice operation, supports negative indices. step : Shape(tuple), optional, default=[] step for the slice operation, supports negative values. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRäRåRęRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytslice-#sDcKsdS(s{Slices along a given axis. Returns an array slice along a given `axis` starting from the `begin` index to the `end` index. Examples:: x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice_axis(x, axis=0, begin=1, end=3) = [[ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] slice_axis(x, axis=1, begin=0, end=2) = [[ 1., 2.], [ 5., 6.], [ 9., 10.]] slice_axis(x, axis=1, begin=-3, end=-1) = [[ 2., 3.], [ 6., 7.], [ 10., 11.]] Defined in src/operator/tensor/matrix_op.cc:L501 Parameters ---------- data : NDArray Source input axis : int, required Axis along which to be sliced, supports negative indexes. begin : int, required The beginning index along the axis to be sliced, supports negative indexes. end : int or None, required The ending index along the axis to be sliced, supports negative indexes. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRäRåRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt slice_axiss#s-cKsdS(sÖ Slices a region of the array like the shape of another array. This function is similar to ``slice``, however, the `begin` are always `0`s and `end` of specific axes are inferred from the second input `shape_like`. Given the second `shape_like` input of ``shape=(d_0, d_1, ..., d_n-1)``, a ``slice_like`` operator with default empty `axes`, it performs the following operation: `` out = slice(input, begin=(0, 0, ..., 0), end=(d_0, d_1, ..., d_n-1))``. When `axes` is not empty, it is used to speficy which axes are being sliced. Given a 4-d input data, ``slice_like`` operator with ``axes=(0, 2, -1)`` will perform the following operation: `` out = slice(input, begin=(0, 0, 0, 0), end=(d_0, None, d_2, d_3))``. Note that it is allowed to have first and second input with different dimensions, however, you have to make sure the `axes` are specified and not exceeding the dimension limits. For example, given `input_1` with ``shape=(2,3,4,5)`` and `input_2` with ``shape=(1,2,3)``, it is not allowed to use: `` out = slice_like(a, b)`` because ndim of `input_1` is 4, and ndim of `input_2` is 3. The following is allowed in this situation: `` out = slice_like(a, b, axes=(0, 2))`` Example:: x = [[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.]] y = [[ 0., 0., 0.], [ 0., 0., 0.]] slice_like(x, y) = [[ 1., 2., 3.] [ 5., 6., 7.]] slice_like(x, y, axes=(0, 1)) = [[ 1., 2., 3.] [ 5., 6., 7.]] slice_like(x, y, axes=(0)) = [[ 1., 2., 3., 4.] [ 5., 6., 7., 8.]] slice_like(x, y, axes=(-1)) = [[ 1., 2., 3.] [ 5., 6., 7.] [ 9., 10., 11.]] Defined in src/operator/tensor/matrix_op.cc:L570 Parameters ---------- data : NDArray Source input shape_like : NDArray Shape like input axes : Shape(tuple), optional, default=[] List of axes on which input data will be sliced according to the corresponding size of the second input. By default will slice on all axes. Negative axes are supported. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((Rt shape_likeR@RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt slice_like¢#sHcKsdS(s+Calculate Smooth L1 Loss(lhs, scalar) by summing .. math:: f(x) = \begin{cases} (\sigma x)^2/2,& \text{if }x < 1/\sigma^2\\ |x|-0.5/\sigma^2,& \text{otherwise} \end{cases} where :math:`x` is an element of the tensor *lhs* and :math:`\sigma` is the scalar. Example:: smooth_l1([1, 2, 3, 4]) = [0.5, 1.5, 2.5, 3.5] smooth_l1([1, 2, 3, 4], scalar=1) = [0.5, 1.5, 2.5, 3.5] Defined in src/operator/tensor/elemwise_binary_scalar_op_extended.cc:L104 Parameters ---------- data : NDArray source input scalar : float scalar input out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RtscalarRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt smooth_l1ģ#s%cKsdS(siApplies the softmax function. The resulting array contains elements in the range (0,1) and the elements along the given axis sum up to 1. .. math:: softmax(\mathbf{z/t})_j = \frac{e^{z_j/t}}{\sum_{k=1}^K e^{z_k/t}} for :math:`j = 1, ..., K` t is the temperature parameter in softmax function. By default, t equals 1.0 Example:: x = [[ 1. 1. 1.] [ 1. 1. 1.]] softmax(x,axis=0) = [[ 0.5 0.5 0.5] [ 0.5 0.5 0.5]] softmax(x,axis=1) = [[ 0.33333334, 0.33333334, 0.33333334], [ 0.33333334, 0.33333334, 0.33333334]] Defined in src/operator/nn/softmax.cc:L93 Parameters ---------- data : NDArray The input array. axis : int, optional, default='-1' The axis along which to compute softmax. temperature : double or None, optional, default=None Temperature parameter in softmax out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsoftmax$s,cKsdS(s§Calculate cross entropy of softmax output and one-hot label. - This operator computes the cross entropy in two steps: - Applies softmax function on the input array. - Computes and returns the cross entropy loss between the softmax output and the labels. - The softmax function and cross entropy loss is given by: - Softmax Function: .. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)} - Cross Entropy Function: .. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i) Example:: x = [[1, 2, 3], [11, 7, 5]] label = [2, 0] softmax(x) = [[0.09003057, 0.24472848, 0.66524094], [0.97962922, 0.01794253, 0.00242826]] softmax_cross_entropy(data, label) = - log(0.66524084) - log(0.97962922) = 0.4281871 Defined in src/operator/loss_binary_op.cc:L59 Parameters ---------- data : NDArray Input data label : NDArray Input label out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsoftmax_cross_entropyA$s0cKsdS(s‘Applies the softmin function. The resulting array contains elements in the range (0,1) and the elements along the given axis sum up to 1. .. math:: softmin(\mathbf{z/t})_j = \frac{e^{-z_j/t}}{\sum_{k=1}^K e^{-z_k/t}} for :math:`j = 1, ..., K` t is the temperature parameter in softmax function. By default, t equals 1.0 Example:: x = [[ 1. 2. 3.] [ 3. 2. 1.]] softmin(x,axis=0) = [[ 0.88079703, 0.5, 0.11920292], [ 0.11920292, 0.5, 0.88079703]] softmin(x,axis=1) = [[ 0.66524094, 0.24472848, 0.09003057], [ 0.09003057, 0.24472848, 0.66524094]] Defined in src/operator/nn/softmax.cc:L137 Parameters ---------- data : NDArray The input array. axis : int, optional, default='-1' The axis along which to compute softmax. temperature : double or None, optional, default=None Temperature parameter in softmax out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsoftmins$s-cKsdS(sŅComputes softsign of x element-wise. .. math:: y = x / (1 + abs(x)) The storage type of ``softsign`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L145 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsoftsign¢$scKsdS(s>Returns a sorted copy of an input array along the given axis. Examples:: x = [[ 1, 4], [ 3, 1]] // sorts along the last axis sort(x) = [[ 1., 4.], [ 1., 3.]] // flattens and then sorts sort(x) = [ 1., 1., 3., 4.] // sorts along the first axis sort(x, axis=0) = [[ 1., 1.], [ 3., 4.]] // in a descend order sort(x, is_ascend=0) = [[ 4., 1.], [ 3., 1.]] Defined in src/operator/tensor/ordering_op.cc:L127 Parameters ---------- data : NDArray The input array axis : int or None, optional, default='-1' Axis along which to choose sort the input tensor. If not given, the flattened array is used. Default is -1. is_ascend : boolean, optional, default=1 Whether to sort in ascending or descending order. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR²RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsort½$s,cKsdS(s2Rearranges(permutes) blocks of spatial data into depth. Similar to ONNX SpaceToDepth operator: https://github.com/onnx/onnx/blob/master/docs/Operators.md#SpaceToDepth The output is a new tensor where the values from height and width dimension are moved to the depth dimension. The reverse of this operation is ``depth_to_space``. .. math:: \begin{gather*} x \prime = reshape(x, [N, C, H / block\_size, block\_size, W / block\_size, block\_size]) \\ x \prime \prime = transpose(x \prime, [0, 3, 5, 1, 2, 4]) \\ y = reshape(x \prime \prime, [N, C * (block\_size ^ 2), H / block\_size, W / block\_size]) \end{gather*} where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width] and :math:`y` is the output tensor of layout :math:`[N, C * (block\_size ^ 2), H / block\_size, W / block\_size]` Example:: x = [[[[0, 6, 1, 7, 2, 8], [12, 18, 13, 19, 14, 20], [3, 9, 4, 10, 5, 11], [15, 21, 16, 22, 17, 23]]]] space_to_depth(x, 2) = [[[[0, 1, 2], [3, 4, 5]], [[6, 7, 8], [9, 10, 11]], [[12, 13, 14], [15, 16, 17]], [[18, 19, 20], [21, 22, 23]]]] Defined in src/operator/tensor/matrix_op.cc:L1000 Parameters ---------- data : NDArray Input ndarray block_size : int, required Blocks of [block_size. block_size] are moved out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRźRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytspace_to_depthė$s6cKsdS(sńSplits an array along a particular axis into multiple sub-arrays. .. note:: ``SliceChannel`` is deprecated. Use ``split`` instead. **Note** that `num_outputs` should evenly divide the length of the axis along which to split the array. Example:: x = [[[ 1.] [ 2.]] [[ 3.] [ 4.]] [[ 5.] [ 6.]]] x.shape = (3, 2, 1) y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1) y = [[[ 1.]] [[ 3.]] [[ 5.]]] [[[ 2.]] [[ 4.]] [[ 6.]]] y[0].shape = (3, 1, 1) z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1) z = [[[ 1.] [ 2.]]] [[[ 3.] [ 4.]]] [[[ 5.] [ 6.]]] z[0].shape = (1, 2, 1) `squeeze_axis=1` removes the axis with length 1 from the shapes of the output arrays. **Note** that setting `squeeze_axis` to ``1`` removes axis with length 1 only along the `axis` which it is split. Also `squeeze_axis` can be set to true only if ``input.shape[axis] == num_outputs``. Example:: z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1) z = [[ 1.] [ 2.]] [[ 3.] [ 4.]] [[ 5.] [ 6.]] z[0].shape = (2 ,1 ) Defined in src/operator/slice_channel.cc:L107 Parameters ---------- data : NDArray The input num_outputs : int, required Number of splits. Note that this should evenly divide the length of the `axis`. axis : int, optional, default='1' Axis along which to split. squeeze_axis : boolean, optional, default=0 If true, Removes the axis with length 1 from the shapes of the output arrays. **Note** that setting `squeeze_axis` to ``true`` removes axis with length 1 only along the `axis` which it is split. Also `squeeze_axis` can be set to ``true`` only if ``input.shape[axis] == num_outputs``. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR‡RRˆRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsplit#%sRcKsdS(sReturns element-wise square-root value of the input. .. math:: \textrm{sqrt}(x) = \sqrt{x} Example:: sqrt([4, 9, 16]) = [2, 3, 4] The storage type of ``sqrt`` output depends upon the input storage type: - sqrt(default) = default - sqrt(row_sparse) = row_sparse - sqrt(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L838 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsqrtw%s!cKsdS(sŠReturns element-wise squared value of the input. .. math:: square(x) = x^2 Example:: square([2, 3, 4]) = [4, 9, 16] The storage type of ``square`` output depends upon the input storage type: - square(default) = default - square(row_sparse) = row_sparse - square(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L815 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsquareš%s!cOsdS(s'Remove single-dimensional entries from the shape of an array. Same behavior of defining the output tensor shape as numpy.squeeze for the most of cases. See the following note for exception. Examples:: data = [[[0], [1], [2]]] squeeze(data) = [0, 1, 2] squeeze(data, axis=0) = [[0], [1], [2]] squeeze(data, axis=2) = [[0, 1, 2]] squeeze(data, axis=(0, 2)) = [0, 1, 2] .. Note:: The output of this operator will keep at least one dimension not removed. For example, squeeze([[[4]]]) = [4], while in numpy.squeeze, the output will become a scalar. Parameters ---------- data : NDArray[] data to squeeze axis : Shape or None, optional, default=None Selects a subset of the single-dimensional entries in the shape. If an axis is selected with shape entry greater than one, an error is raised. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsqueeze½%s!cOsdS(s+Join a sequence of arrays along a new axis. The axis parameter specifies the index of the new axis in the dimensions of the result. For example, if axis=0 it will be the first dimension and if axis=-1 it will be the last dimension. Examples:: x = [1, 2] y = [3, 4] stack(x, y) = [[1, 2], [3, 4]] stack(x, y, axis=1) = [[1, 3], [2, 4]] Parameters ---------- data : NDArray[] List of arrays to stack axis : int, optional, default='0' The axis in the result array along which the input arrays are stacked. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytstacką%s!cKsdS(sōStops gradient computation. Stops the accumulated gradient of the inputs from flowing through this operator in the backward direction. In other words, this operator prevents the contribution of its inputs to be taken into account for computing gradients. Example:: v1 = [1, 2] v2 = [0, 1] a = Variable('a') b = Variable('b') b_stop_grad = stop_gradient(3 * b) loss = MakeLoss(b_stop_grad + a) executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2)) executor.forward(is_train=True, a=v1, b=v2) executor.outputs [ 1. 5.] executor.backward() executor.grad_arrays [ 0. 0.] [ 1. 1.] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L267 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt stop_gradient&s+cKsdS(sŒComputes the sum of array elements over given axes. .. Note:: `sum` and `sum_axis` are equivalent. For ndarray of csr storage type summation along axis 0 and axis 1 is supported. Setting keepdims or exclude to True will cause a fallback to dense operator. Example:: data = [[[1, 2], [2, 3], [1, 3]], [[1, 4], [4, 3], [5, 2]], [[7, 1], [7, 2], [7, 3]]] sum(data, axis=1) [[ 4. 8.] [ 10. 9.] [ 21. 6.]] sum(data, axis=[1,2]) [ 12. 19. 27.] data = [[1, 2, 0], [3, 0, 1], [4, 1, 0]] csr = cast_storage(data, 'csr') sum(csr, axis=0) [ 8. 3. 1.] sum(csr, axis=1) [ 3. 4. 5.] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L116 Parameters ---------- data : NDArray The input axis : Shape or None, optional, default=None The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims : boolean, optional, default=0 If this is set to `True`, the reduced axes are left in the result as dimension with size one. exclude : boolean, optional, default=0 Whether to perform reduction on axis that are NOT in axis instead. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR®R!RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsum0&sGcKsdS(sŒComputes the sum of array elements over given axes. .. Note:: `sum` and `sum_axis` are equivalent. For ndarray of csr storage type summation along axis 0 and axis 1 is supported. Setting keepdims or exclude to True will cause a fallback to dense operator. Example:: data = [[[1, 2], [2, 3], [1, 3]], [[1, 4], [4, 3], [5, 2]], [[7, 1], [7, 2], [7, 3]]] sum(data, axis=1) [[ 4. 8.] [ 10. 9.] [ 21. 6.]] sum(data, axis=[1,2]) [ 12. 19. 27.] data = [[1, 2, 0], [3, 0, 1], [4, 1, 0]] csr = cast_storage(data, 'csr') sum(csr, axis=0) [ 8. 3. 1.] sum(csr, axis=1) [ 3. 4. 5.] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L116 Parameters ---------- data : NDArray The input axis : Shape or None, optional, default=None The axis or axes along which to perform the reduction. The default, `axis=()`, will compute over all elements into a scalar array with shape `(1,)`. If `axis` is int, a reduction is performed on a particular axis. If `axis` is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If `exclude` is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims : boolean, optional, default=0 If this is set to `True`, the reduced axes are left in the result as dimension with size one. exclude : boolean, optional, default=0 Whether to perform reduction on axis that are NOT in axis instead. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRR®R!RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytsum_axisy&sGcKsdS(s†Interchanges two axes of an array. Examples:: x = [[1, 2, 3]]) swapaxes(x, 0, 1) = [[ 1], [ 2], [ 3]] x = [[[ 0, 1], [ 2, 3]], [[ 4, 5], [ 6, 7]]] // (2,2,2) array swapaxes(x, 0, 2) = [[[ 0, 4], [ 2, 6]], [[ 1, 5], [ 3, 7]]] Defined in src/operator/swapaxis.cc:L70 Parameters ---------- data : NDArray Input array. dim1 : int (non-negative), optional, default=0 the first axis to be swapped. dim2 : int (non-negative), optional, default=0 the second axis to be swapped. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR–R—RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytswapaxesĀ&s(cKsdS(sžTakes elements from an input array along the given axis. This function slices the input array along a particular axis with the provided indices. Given data tensor of rank r >= 1, and indices tensor of rank q, gather entries of the axis dimension of data (by default outer-most one as axis=0) indexed by indices, and concatenates them in an output tensor of rank q + (r - 1). Examples:: x = [4. 5. 6.] // Trivial case, take the second element along the first axis. take(x, [1]) = [ 5. ] // The other trivial case, axis=-1, take the third element along the first axis take(x, [3], axis=-1, mode='clip') = [ 6. ] x = [[ 1., 2.], [ 3., 4.], [ 5., 6.]] // In this case we will get rows 0 and 1, then 1 and 2. Along axis 0 take(x, [[0,1],[1,2]]) = [[[ 1., 2.], [ 3., 4.]], [[ 3., 4.], [ 5., 6.]]] // In this case we will get rows 0 and 1, then 1 and 2 (calculated by wrapping around). // Along axis 1 take(x, [[0, 3], [-1, -2]], axis=1, mode='wrap') = [[[ 1., 2.], [ 3., 4.]], [[ 3., 4.], [ 5., 6.]]] Defined in src/operator/tensor/indexing_op.cc:L434 Parameters ---------- a : NDArray The input array. indices : NDArray The indices of the values to be extracted. axis : int, optional, default='0' The axis of input array to be taken.For input tensor of rank r, it could be in the range of [-r, r-1] mode : {'clip', 'raise', 'wrap'},optional, default='clip' Specify how out-of-bound indices bahave. Default is "clip". "clip" means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis. "wrap" means to wrap around. "raise" means to raise an error, not supported yet. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RŗR»RR?RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyttakeģ&s@cKsdS(s¬Computes the element-wise tangent of the input array. The input should be in radians (:math:`2\pi` rad equals 360 degrees). .. math:: tan([0, \pi/4, \pi/2]) = [0, 1, -inf] The storage type of ``tan`` output depends upon the input storage type: - tan(default) = default - tan(row_sparse) = row_sparse - tan(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L83 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyttan.'scKsdS(spReturns the hyperbolic tangent of the input array, computed element-wise. .. math:: tanh(x) = sinh(x) / cosh(x) The storage type of ``tanh`` output depends upon the input storage type: - tanh(default) = default - tanh(row_sparse) = row_sparse - tanh(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L234 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyttanhO'scKsdS(sVRepeats the whole array multiple times. If ``reps`` has length *d*, and input array has dimension of *n*. There are three cases: - **n=d**. Repeat *i*-th dimension of the input by ``reps[i]`` times:: x = [[1, 2], [3, 4]] tile(x, reps=(2,3)) = [[ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.], [ 1., 2., 1., 2., 1., 2.], [ 3., 4., 3., 4., 3., 4.]] - **n>d**. ``reps`` is promoted to length *n* by pre-pending 1's to it. Thus for an input shape ``(2,3)``, ``repos=(2,)`` is treated as ``(1,2)``:: tile(x, reps=(2,)) = [[ 1., 2., 1., 2.], [ 3., 4., 3., 4.]] - **n d, reps is promoted to a.ndim by pre-pending 1's to it. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RtrepsRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyttilen's6c KsdS(s¹ Returns the top *k* elements in an input array along the given axis. The returned elements will be sorted. Examples:: x = [[ 0.3, 0.2, 0.4], [ 0.1, 0.3, 0.2]] // returns an index of the largest element on last axis topk(x) = [[ 2.], [ 1.]] // returns the value of top-2 largest elements on last axis topk(x, ret_typ='value', k=2) = [[ 0.4, 0.3], [ 0.3, 0.2]] // returns the value of top-2 smallest elements on last axis topk(x, ret_typ='value', k=2, is_ascend=1) = [[ 0.2 , 0.3], [ 0.1 , 0.2]] // returns the value of top-2 largest elements on axis 0 topk(x, axis=0, ret_typ='value', k=2) = [[ 0.3, 0.3, 0.4], [ 0.1, 0.2, 0.2]] // flattens and then returns list of both values and indices topk(x, ret_typ='both', k=2) = [[[ 0.4, 0.3], [ 0.3, 0.2]] , [[ 2., 0.], [ 1., 2.]]] Defined in src/operator/tensor/ordering_op.cc:L64 Parameters ---------- data : NDArray The input array axis : int or None, optional, default='-1' Axis along which to choose the top k indices. If not given, the flattened array is used. Default is -1. k : int, optional, default='1' Number of top elements to select, should be always smaller than or equal to the element number in the given axis. A global sort is performed if set k < 1. ret_typ : {'both', 'indices', 'mask', 'value'},optional, default='indices' The return type. "value" means to return the top k values, "indices" means to return the indices of the top k values, "mask" means to return a mask array containing 0 and 1. 1 means the top k values. "both" means to return a list of both values and indices of top k elements. is_ascend : boolean, optional, default=0 Whether to choose k largest or k smallest elements. Top K largest elements will be chosen if set to false. dtype : {'float16', 'float32', 'float64', 'int32', 'uint8'},optional, default='float32' DType of the output indices when ret_typ is "indices" or "both". An error will be raised if the selected data type cannot precisely represent the indices. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i(( RRRģtret_typR²RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyttopk¦'s8cKsdS(sPermutes the dimensions of an array. Examples:: x = [[ 1, 2], [ 3, 4]] transpose(x) = [[ 1., 3.], [ 2., 4.]] x = [[[ 1., 2.], [ 3., 4.]], [[ 5., 6.], [ 7., 8.]]] transpose(x) = [[[ 1., 5.], [ 3., 7.]], [[ 2., 6.], [ 4., 8.]]] transpose(x, axes=(1,0,2)) = [[[ 1., 2.], [ 5., 6.]], [[ 3., 4.], [ 7., 8.]]] Defined in src/operator/tensor/matrix_op.cc:L312 Parameters ---------- data : NDArray Source input axes : Shape(tuple), optional, default=[] Target axis order. By default the axes will be inverted. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RR@RRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyRą's/cKsdS(s1Return the element-wise truncated value of the input. The truncated value of the scalar x is the nearest integer i which is closer to zero than x is. In short, the fractional part of the signed number x is discarded. Example:: trunc([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1., 1., 1., 2.] The storage type of ``trunc`` output depends upon the input storage type: - trunc(default) = default - trunc(row_sparse) = row_sparse - trunc(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L777 Parameters ---------- data : NDArray The input array. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyttrunc(s!cKsdS(sĀDraw random samples from a uniform distribution. .. note:: The existing alias ``uniform`` is deprecated. Samples are uniformly distributed over the half-open interval *[low, high)* (includes *low*, but excludes *high*). Example:: uniform(low=0, high=1, shape=(2,2)) = [[ 0.60276335, 0.85794562], [ 0.54488319, 0.84725171]] Defined in src/operator/random/sample_op.cc:L66 Parameters ---------- low : float, optional, default=0 Lower bound of the distribution. high : float, optional, default=1 Upper bound of the distribution. shape : Shape(tuple), optional, default=[] Shape of the output. ctx : string, optional, default='' Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype : {'None', 'float16', 'float32', 'float64'},optional, default='None' DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None). out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RCRDRyR0RRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytuniform4(s&cKsdS(s©Converts an array of flat indices into a batch of index arrays. The operator follows numpy conventions so a single multi index is given by a column of the output matrix. Examples:: A = [22,41,37] unravel(A, shape=(7,6)) = [[3,6,6],[4,5,1]] Defined in src/operator/tensor/ravel.cc:L65 Parameters ---------- data : NDArray Array of flat indices shape : Shape(tuple), optional, default=[] Shape of the array into which the multi-indices apply. out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((RRyRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pyt unravel_index\(scKsdS(sLReturn the elements, either from x or y, depending on the condition. Given three ndarrays, condition, x, and y, return an ndarray with the elements from x or y, depending on the elements from condition are true or false. x and y must have the same shape. If condition has the same shape as x, each element in the output array is from x if the corresponding element in the condition is true, and from y if false. If condition does not have the same shape as x, it must be a 1D array whose size is the same as x's first dimension size. Each row of the output array is from x's row if the corresponding element from condition is true, and from y's row if false. Note that all non-zero values are interpreted as ``True`` in condition. Examples:: x = [[1, 2], [3, 4]] y = [[5, 6], [7, 8]] cond = [[0, 1], [-1, 0]] where(cond, x, y) = [[5, 2], [3, 8]] csr_cond = cast_storage(cond, 'csr') where(csr_cond, x, y) = [[5, 2], [3, 8]] Defined in src/operator/tensor/control_flow_op.cc:L57 Parameters ---------- condition : NDArray condition array x : NDArray y : NDArray out : NDArray, optional The output NDArray to hold the result. Returns ------- out : NDArray or list of NDArrays The output of this function. i(i((t conditiontxtyRRR((sT/usr/local/lib/python2.7/site-packages/mxnet-1.3.1-py2.7.egg/mxnet/ndarray/gen_op.pytwherey(s-cKsdS(s³Return an array of zeros with the same shape, type and storage type as the input array. The storage type of ``zeros_like`` output depends on the storage type of the input - zeros_like(row_sparse) = row_sparse - zeros_like(csr) = csr - zeros_like(default) = default Examples:: x = [[ 1., 1., 1.], [ 1., 1., 1.]] zeros_like(x) = [[ 0., 0., 0.], [ 0., 0., 0.]] Parameters ---------- data : NDArray The input out : NDArray, optional The output NDArray to hold the result. 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