# ndarray¶

NDArray API of MXNet.

Classes

 CachedOp(sym[, flags]) Cached operator handle. NDArray(handle[, writable]) An array object representing a multidimensional, homogeneous array of fixed-size items.

Functions

 Activation([data, act_type, out, name]) Applies an activation function element-wise to the input. BatchNorm([data, gamma, beta, moving_mean, …]) Batch normalization. BatchNorm_v1([data, gamma, beta, eps, …]) Batch normalization. BilinearSampler([data, grid, cudnn_off, …]) Applies bilinear sampling to input feature map. BlockGrad([data, out, name]) Stops gradient computation. CTCLoss([data, label, data_lengths, …]) Connectionist Temporal Classification Loss. Cast([data, dtype, out, name]) Casts all elements of the input to a new type. Concat(*data, **kwargs) Joins input arrays along a given axis. Convolution([data, weight, bias, kernel, …]) Compute N-D convolution on (N+2)-D input. Convolution_v1([data, weight, bias, kernel, …]) This operator is DEPRECATED. Correlation([data1, data2, kernel_size, …]) Applies correlation to inputs. Crop(*data, **kwargs) Note Crop is deprecated. Use slice instead. Custom(*data, **kwargs) Apply a custom operator implemented in a frontend language (like Python). Deconvolution([data, weight, bias, kernel, …]) Computes 1D or 2D transposed convolution (aka fractionally strided convolution) of the input tensor. Dropout([data, p, mode, axes, cudnn_off, …]) Applies dropout operation to input array. ElementWiseSum(*args, **kwargs) Adds all input arguments element-wise. Embedding([data, weight, input_dim, …]) Maps integer indices to vector representations (embeddings). Flatten([data, out, name]) Flattens the input array into a 2-D array by collapsing the higher dimensions. FullyConnected([data, weight, bias, …]) Applies a linear transformation: $$Y = XW^T + b$$. GridGenerator([data, transform_type, …]) Generates 2D sampling grid for bilinear sampling. GroupNorm([data, gamma, beta, num_groups, …]) Group normalization. IdentityAttachKLSparseReg([data, …]) Apply a sparse regularization to the output a sigmoid activation function. InstanceNorm([data, gamma, beta, eps, out, name]) Applies instance normalization to the n-dimensional input array. L2Normalization([data, eps, mode, out, name]) Normalize the input array using the L2 norm. LRN([data, alpha, beta, knorm, nsize, out, name]) Applies local response normalization to the input. LayerNorm([data, gamma, beta, axis, eps, …]) Layer normalization. LeakyReLU([data, gamma, act_type, slope, …]) Applies Leaky rectified linear unit activation element-wise to the input. LinearRegressionOutput([data, label, …]) Computes and optimizes for squared loss during backward propagation. LogisticRegressionOutput([data, label, …]) Applies a logistic function to the input. MAERegressionOutput([data, label, …]) Computes mean absolute error of the input. MakeLoss([data, grad_scale, valid_thresh, …]) Make your own loss function in network construction. Pad([data, mode, pad_width, constant_value, …]) Pads an input array with a constant or edge values of the array. Pooling([data, kernel, pool_type, …]) Performs pooling on the input. Pooling_v1([data, kernel, pool_type, …]) This operator is DEPRECATED. RNN([data, parameters, state, state_cell, …]) Applies recurrent layers to input data. ROIPooling([data, rois, pooled_size, …]) Performs region of interest(ROI) pooling on the input array. Reshape([data, shape, reverse, …]) Reshapes the input array. SVMOutput([data, label, margin, …]) Computes support vector machine based transformation of the input. SequenceLast([data, sequence_length, …]) Takes the last element of a sequence. SequenceMask([data, sequence_length, …]) Sets all elements outside the sequence to a constant value. SequenceReverse([data, sequence_length, …]) Reverses the elements of each sequence. SliceChannel([data, num_outputs, axis, …]) Splits an array along a particular axis into multiple sub-arrays. Softmax([data, label, grad_scale, …]) Computes the gradient of cross entropy loss with respect to softmax output. SoftmaxActivation([data, mode, out, name]) Applies softmax activation to input. SoftmaxOutput([data, label, grad_scale, …]) Computes the gradient of cross entropy loss with respect to softmax output. SpatialTransformer([data, loc, …]) Applies a spatial transformer to input feature map. SwapAxis([data, dim1, dim2, out, name]) Interchanges two axes of an array. UpSampling(*data, **kwargs) Upsamples the given input data. abs([data, out, name]) Returns element-wise absolute value of the input. adam_update([weight, grad, mean, var, lr, …]) Update function for Adam optimizer. add_n(*args, **kwargs) Adds all input arguments element-wise. all_finite([data, init_output, out, name]) Check if all the float numbers in the array are finite (used for AMP) amp_cast([data, dtype, out, name]) Cast function between low precision float/FP32 used by AMP. amp_multicast(*data, **kwargs) Cast function used by AMP, that casts its inputs to the common widest type. arccos([data, out, name]) Returns element-wise inverse cosine of the input array. arccosh([data, out, name]) Returns the element-wise inverse hyperbolic cosine of the input array, computed element-wise. arcsin([data, out, name]) Returns element-wise inverse sine of the input array. arcsinh([data, out, name]) Returns the element-wise inverse hyperbolic sine of the input array, computed element-wise. arctan([data, out, name]) Returns element-wise inverse tangent of the input array. arctanh([data, out, name]) Returns the element-wise inverse hyperbolic tangent of the input array, computed element-wise. argmax([data, axis, keepdims, out, name]) Returns indices of the maximum values along an axis. argmax_channel([data, out, name]) Returns argmax indices of each channel from the input array. argmin([data, axis, keepdims, out, name]) Returns indices of the minimum values along an axis. argsort([data, axis, is_ascend, dtype, out, …]) Returns the indices that would sort an input array along the given axis. batch_dot([lhs, rhs, transpose_a, …]) Batchwise dot product. batch_take([a, indices, out, name]) Takes elements from a data batch. broadcast_add([lhs, rhs, out, name]) Returns element-wise sum of the input arrays with broadcasting. broadcast_axes([data, axis, size, out, name]) Broadcasts the input array over particular axes. broadcast_axis([data, axis, size, out, name]) Broadcasts the input array over particular axes. broadcast_div([lhs, rhs, out, name]) Returns element-wise division of the input arrays with broadcasting. broadcast_equal([lhs, rhs, out, name]) Returns the result of element-wise equal to (==) comparison operation with broadcasting. broadcast_greater([lhs, rhs, out, name]) Returns the result of element-wise greater than (>) comparison operation with broadcasting. broadcast_greater_equal([lhs, rhs, out, name]) Returns the result of element-wise greater than or equal to (>=) comparison operation with broadcasting. broadcast_hypot([lhs, rhs, out, name]) Returns the hypotenuse of a right angled triangle, given its “legs” with broadcasting. broadcast_lesser([lhs, rhs, out, name]) Returns the result of element-wise lesser than (<) comparison operation with broadcasting. broadcast_lesser_equal([lhs, rhs, out, name]) Returns the result of element-wise lesser than or equal to (<=) comparison operation with broadcasting. broadcast_like([lhs, rhs, lhs_axes, …]) Broadcasts lhs to have the same shape as rhs. broadcast_logical_and([lhs, rhs, out, name]) Returns the result of element-wise logical and with broadcasting. broadcast_logical_or([lhs, rhs, out, name]) Returns the result of element-wise logical or with broadcasting. broadcast_logical_xor([lhs, rhs, out, name]) Returns the result of element-wise logical xor with broadcasting. broadcast_maximum([lhs, rhs, out, name]) Returns element-wise maximum of the input arrays with broadcasting. broadcast_minimum([lhs, rhs, out, name]) Returns element-wise minimum of the input arrays with broadcasting. broadcast_minus([lhs, rhs, out, name]) Returns element-wise difference of the input arrays with broadcasting. broadcast_mod([lhs, rhs, out, name]) Returns element-wise modulo of the input arrays with broadcasting. broadcast_mul([lhs, rhs, out, name]) Returns element-wise product of the input arrays with broadcasting. broadcast_not_equal([lhs, rhs, out, name]) Returns the result of element-wise not equal to (!=) comparison operation with broadcasting. broadcast_plus([lhs, rhs, out, name]) Returns element-wise sum of the input arrays with broadcasting. broadcast_power([lhs, rhs, out, name]) Returns result of first array elements raised to powers from second array, element-wise with broadcasting. broadcast_sub([lhs, rhs, out, name]) Returns element-wise difference of the input arrays with broadcasting. broadcast_to([data, shape, out, name]) Broadcasts the input array to a new shape. cast([data, dtype, out, name]) Casts all elements of the input to a new type. cast_storage([data, stype, out, name]) Casts tensor storage type to the new type. cbrt([data, out, name]) Returns element-wise cube-root value of the input. ceil([data, out, name]) Returns element-wise ceiling of the input. choose_element_0index([data, index, axis, …]) Picks elements from an input array according to the input indices along the given axis. clip([data, a_min, a_max, out, name]) Clips (limits) the values in an array. col2im([data, output_size, kernel, stride, …]) Combining the output column matrix of im2col back to image array. concat(*data, **kwargs) Joins input arrays along a given axis. cos([data, out, name]) Computes the element-wise cosine of the input array. cosh([data, out, name]) Returns the hyperbolic cosine of the input array, computed element-wise. crop([data, begin, end, step, out, name]) Slices a region of the array. ctc_loss([data, label, data_lengths, …]) Connectionist Temporal Classification Loss. cumsum([a, axis, dtype, out, name]) Return the cumulative sum of the elements along a given axis. degrees([data, out, name]) Converts each element of the input array from radians to degrees. depth_to_space([data, block_size, out, name]) Rearranges(permutes) data from depth into blocks of spatial data. diag([data, k, axis1, axis2, out, name]) Extracts a diagonal or constructs a diagonal array. dot([lhs, rhs, transpose_a, transpose_b, …]) Dot product of two arrays. elemwise_add([lhs, rhs, out, name]) Adds arguments element-wise. elemwise_div([lhs, rhs, out, name]) Divides arguments element-wise. elemwise_mul([lhs, rhs, out, name]) Multiplies arguments element-wise. elemwise_sub([lhs, rhs, out, name]) Subtracts arguments element-wise. erf([data, out, name]) Returns element-wise gauss error function of the input. erfinv([data, out, name]) Returns element-wise inverse gauss error function of the input. exp([data, out, name]) Returns element-wise exponential value of the input. expand_dims([data, axis, out, name]) 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). expm1([data, out, name]) Returns exp(x) - 1 computed element-wise on the input. fill_element_0index([lhs, mhs, rhs, out, name]) Fill one element of each line(row for python, column for R/Julia) in lhs according to index indicated by rhs and values indicated by mhs. fix([data, out, name]) Returns element-wise rounded value to the nearest integer towards zero of the input. flatten([data, out, name]) Flattens the input array into a 2-D array by collapsing the higher dimensions. flip([data, axis, out, name]) Reverses the order of elements along given axis while preserving array shape. floor([data, out, name]) Returns element-wise floor of the input. ftml_update([weight, grad, d, v, z, lr, …]) The FTML optimizer described in FTML - Follow the Moving Leader in Deep Learning, available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf. ftrl_update([weight, grad, z, n, lr, …]) Update function for Ftrl optimizer. gamma([data, out, name]) Returns the gamma function (extension of the factorial function to the reals), computed element-wise on the input array. gammaln([data, out, name]) Returns element-wise log of the absolute value of the gamma function of the input. gather_nd([data, indices, out, name]) Gather elements or slices from data and store to a tensor whose shape is defined by indices. hard_sigmoid([data, alpha, beta, out, name]) Computes hard sigmoid of x element-wise. identity([data, out, name]) Returns a copy of the input. im2col([data, kernel, stride, dilate, pad, …]) Extract sliding blocks from input array. khatri_rao(*args, **kwargs) Computes the Khatri-Rao product of the input matrices. lamb_update_phase1([weight, grad, mean, …]) Phase I of lamb update it performs the following operations and returns g:. lamb_update_phase2([weight, g, r1, r2, lr, …]) Phase II of lamb update it performs the following operations and updates grad. linalg_det([A, out, name]) Compute the determinant of a matrix. linalg_extractdiag([A, offset, out, name]) Extracts the diagonal entries of a square matrix. linalg_extracttrian([A, offset, lower, out, …]) Extracts a triangular sub-matrix from a square matrix. linalg_gelqf([A, out, name]) LQ factorization for general matrix. linalg_gemm([A, B, C, transpose_a, …]) Performs general matrix multiplication and accumulation. linalg_gemm2([A, B, transpose_a, …]) Performs general matrix multiplication. linalg_inverse([A, out, name]) Compute the inverse of a matrix. linalg_makediag([A, offset, out, name]) Constructs a square matrix with the input as diagonal. linalg_maketrian([A, offset, lower, out, name]) Constructs a square matrix with the input representing a specific triangular sub-matrix. linalg_potrf([A, out, name]) Performs Cholesky factorization of a symmetric positive-definite matrix. linalg_potri([A, out, name]) Performs matrix inversion from a Cholesky factorization. linalg_slogdet([A, out, name]) Compute the sign and log of the determinant of a matrix. linalg_sumlogdiag([A, out, name]) Computes the sum of the logarithms of the diagonal elements of a square matrix. linalg_syrk([A, transpose, alpha, out, name]) Multiplication of matrix with its transpose. linalg_trmm([A, B, transpose, rightside, …]) Performs multiplication with a lower triangular matrix. linalg_trsm([A, B, transpose, rightside, …]) Solves matrix equation involving a lower triangular matrix. log([data, out, name]) Returns element-wise Natural logarithmic value of the input. log10([data, out, name]) Returns element-wise Base-10 logarithmic value of the input. log1p([data, out, name]) Returns element-wise log(1 + x) value of the input. log2([data, out, name]) Returns element-wise Base-2 logarithmic value of the input. log_softmax([data, axis, temperature, …]) Computes the log softmax of the input. logical_not([data, out, name]) Returns the result of logical NOT (!) function make_loss([data, out, name]) Make your own loss function in network construction. max([data, axis, keepdims, exclude, out, name]) Computes the max of array elements over given axes. max_axis([data, axis, keepdims, exclude, …]) Computes the max of array elements over given axes. mean([data, axis, keepdims, exclude, out, name]) Computes the mean of array elements over given axes. min([data, axis, keepdims, exclude, out, name]) Computes the min of array elements over given axes. min_axis([data, axis, keepdims, exclude, …]) Computes the min of array elements over given axes. moments([data, axes, keepdims, out, name]) Calculate the mean and variance of data. mp_lamb_update_phase1([weight, grad, mean, …]) Mixed Precision version of Phase I of lamb update it performs the following operations and returns g:. mp_lamb_update_phase2([weight, g, r1, r2, …]) Mixed Precision version Phase II of lamb update it performs the following operations and updates grad. mp_nag_mom_update([weight, grad, mom, …]) Update function for multi-precision Nesterov Accelerated Gradient( NAG) optimizer. mp_sgd_mom_update([weight, grad, mom, …]) Updater function for multi-precision sgd optimizer mp_sgd_update([weight, grad, weight32, lr, …]) Updater function for multi-precision sgd optimizer multi_all_finite(*data, **kwargs) Check if all the float numbers in all the arrays are finite (used for AMP) multi_lars([lrs, weights_sum_sq, …]) Compute the LARS coefficients of multiple weights and grads from their sums of square” multi_mp_sgd_mom_update(*data, **kwargs) Momentum update function for multi-precision Stochastic Gradient Descent (SGD) optimizer. multi_mp_sgd_update(*data, **kwargs) Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer. multi_sgd_mom_update(*data, **kwargs) Momentum update function for Stochastic Gradient Descent (SGD) optimizer. multi_sgd_update(*data, **kwargs) Update function for Stochastic Gradient Descent (SDG) optimizer. multi_sum_sq(*data, **kwargs) Compute the sums of squares of multiple arrays nag_mom_update([weight, grad, mom, lr, …]) Update function for Nesterov Accelerated Gradient( NAG) optimizer. nanprod([data, axis, keepdims, exclude, …]) Computes the product of array elements over given axes treating Not a Numbers (NaN) as one. nansum([data, axis, keepdims, exclude, out, …]) Computes the sum of array elements over given axes treating Not a Numbers (NaN) as zero. negative([data, out, name]) Numerical negative of the argument, element-wise. norm([data, ord, axis, out_dtype, keepdims, …]) Computes the norm on an NDArray. normal([loc, scale, shape, ctx, dtype, out, …]) Draw random samples from a normal (Gaussian) distribution. one_hot([indices, depth, on_value, …]) Returns a one-hot array. ones_like([data, out, name]) Return an array of ones with the same shape and type as the input array. pad([data, mode, pad_width, constant_value, …]) Pads an input array with a constant or edge values of the array. pick([data, index, axis, keepdims, mode, …]) Picks elements from an input array according to the input indices along the given axis. Momentum update function for multi-precision Stochastic Gradient Descent (SGD) optimizer. preloaded_multi_mp_sgd_update(*data, **kwargs) Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer. preloaded_multi_sgd_mom_update(*data, **kwargs) Momentum update function for Stochastic Gradient Descent (SGD) optimizer. preloaded_multi_sgd_update(*data, **kwargs) Update function for Stochastic Gradient Descent (SDG) optimizer. prod([data, axis, keepdims, exclude, out, name]) Computes the product of array elements over given axes. radians([data, out, name]) Converts each element of the input array from degrees to radians. random_exponential([lam, shape, ctx, dtype, …]) Draw random samples from an exponential distribution. random_gamma([alpha, beta, shape, ctx, …]) Draw random samples from a gamma distribution. Draw random samples from a generalized negative binomial distribution. random_negative_binomial([k, p, shape, ctx, …]) Draw random samples from a negative binomial distribution. random_normal([loc, scale, shape, ctx, …]) Draw random samples from a normal (Gaussian) distribution. random_pdf_dirichlet([sample, alpha, …]) Computes the value of the PDF of sample of Dirichlet distributions with parameter alpha. random_pdf_exponential([sample, lam, …]) Computes the value of the PDF of sample of exponential distributions with parameters lam (rate). random_pdf_gamma([sample, alpha, beta, …]) Computes the value of the PDF of sample of gamma distributions with parameters alpha (shape) and beta (rate). Computes the value of the PDF of sample of generalized negative binomial distributions with parameters mu (mean) and alpha (dispersion). random_pdf_negative_binomial([sample, k, p, …]) Computes the value of the PDF of samples of negative binomial distributions with parameters k (failure limit) and p (failure probability). random_pdf_normal([sample, mu, sigma, …]) Computes the value of the PDF of sample of normal distributions with parameters mu (mean) and sigma (standard deviation). random_pdf_poisson([sample, lam, is_log, …]) Computes the value of the PDF of sample of Poisson distributions with parameters lam (rate). random_pdf_uniform([sample, low, high, …]) Computes the value of the PDF of sample of uniform distributions on the intervals given by [low,high). random_poisson([lam, shape, ctx, dtype, …]) Draw random samples from a Poisson distribution. random_randint([low, high, shape, ctx, …]) Draw random samples from a discrete uniform distribution. random_uniform([low, high, shape, ctx, …]) Draw random samples from a uniform distribution. ravel_multi_index([data, shape, out, name]) Converts a batch of index arrays into an array of flat indices. rcbrt([data, out, name]) Returns element-wise inverse cube-root value of the input. reciprocal([data, out, name]) Returns the reciprocal of the argument, element-wise. relu([data, out, name]) Computes rectified linear activation. repeat([data, repeats, axis, out, name]) Repeats elements of an array. reset_arrays(*data, **kwargs) Set to zero multiple arrays reshape([data, shape, reverse, …]) Reshapes the input array. reshape_like([lhs, rhs, lhs_begin, lhs_end, …]) Reshape some or all dimensions of lhs to have the same shape as some or all dimensions of rhs. reverse([data, axis, out, name]) Reverses the order of elements along given axis while preserving array shape. rint([data, out, name]) Returns element-wise rounded value to the nearest integer of the input. rmsprop_update([weight, grad, n, lr, …]) Update function for RMSProp optimizer. rmspropalex_update([weight, grad, n, g, …]) Update function for RMSPropAlex optimizer. round([data, out, name]) Returns element-wise rounded value to the nearest integer of the input. rsqrt([data, out, name]) Returns element-wise inverse square-root value of the input. sample_exponential([lam, shape, dtype, out, …]) Concurrent sampling from multiple exponential distributions with parameters lambda (rate). sample_gamma([alpha, beta, shape, dtype, …]) Concurrent sampling from multiple gamma distributions with parameters alpha (shape) and beta (scale). Concurrent sampling from multiple generalized negative binomial distributions with parameters mu (mean) and alpha (dispersion). sample_multinomial([data, shape, get_prob, …]) Concurrent sampling from multiple multinomial distributions. sample_negative_binomial([k, p, shape, …]) Concurrent sampling from multiple negative binomial distributions with parameters k (failure limit) and p (failure probability). sample_normal([mu, sigma, shape, dtype, …]) Concurrent sampling from multiple normal distributions with parameters mu (mean) and sigma (standard deviation). sample_poisson([lam, shape, dtype, out, name]) Concurrent sampling from multiple Poisson distributions with parameters lambda (rate). sample_uniform([low, high, shape, dtype, …]) Concurrent sampling from multiple uniform distributions on the intervals given by [low,high). scatter_nd([data, indices, shape, out, name]) Scatters data into a new tensor according to indices. sgd_mom_update([weight, grad, mom, lr, …]) Momentum update function for Stochastic Gradient Descent (SGD) optimizer. sgd_update([weight, grad, lr, wd, …]) Update function for Stochastic Gradient Descent (SGD) optimizer. shape_array([data, out, name]) Returns a 1D int64 array containing the shape of data. shuffle([data, out, name]) Randomly shuffle the elements. sigmoid([data, out, name]) Computes sigmoid of x element-wise. sign([data, out, name]) Returns element-wise sign of the input. signsgd_update([weight, grad, lr, wd, …]) Update function for SignSGD optimizer. signum_update([weight, grad, mom, lr, …]) SIGN momentUM (Signum) optimizer. sin([data, out, name]) Computes the element-wise sine of the input array. sinh([data, out, name]) Returns the hyperbolic sine of the input array, computed element-wise. size_array([data, out, name]) Returns a 1D int64 array containing the size of data. slice([data, begin, end, step, out, name]) Slices a region of the array. slice_axis([data, axis, begin, end, out, name]) Slices along a given axis. slice_like([data, shape_like, axes, out, name]) Slices a region of the array like the shape of another array. smooth_l1([data, scalar, out, name]) Calculate Smooth L1 Loss(lhs, scalar) by summing softmax([data, length, axis, temperature, …]) Applies the softmax function. softmax_cross_entropy([data, label, out, name]) Calculate cross entropy of softmax output and one-hot label. softmin([data, axis, temperature, dtype, …]) Applies the softmin function. softsign([data, out, name]) Computes softsign of x element-wise. sort([data, axis, is_ascend, out, name]) Returns a sorted copy of an input array along the given axis. space_to_depth([data, block_size, out, name]) Rearranges(permutes) blocks of spatial data into depth. split([data, num_outputs, axis, …]) Splits an array along a particular axis into multiple sub-arrays. sqrt([data, out, name]) Returns element-wise square-root value of the input. square([data, out, name]) Returns element-wise squared value of the input. squeeze([data, axis, out, name]) Remove single-dimensional entries from the shape of an array. stack(*data, **kwargs) Join a sequence of arrays along a new axis. stop_gradient([data, out, name]) Stops gradient computation. sum([data, axis, keepdims, exclude, out, name]) Computes the sum of array elements over given axes. sum_axis([data, axis, keepdims, exclude, …]) Computes the sum of array elements over given axes. swapaxes([data, dim1, dim2, out, name]) Interchanges two axes of an array. take([a, indices, axis, mode, out, name]) Takes elements from an input array along the given axis. tan([data, out, name]) Computes the element-wise tangent of the input array. tanh([data, out, name]) Returns the hyperbolic tangent of the input array, computed element-wise. tile([data, reps, out, name]) Repeats the whole array multiple times. topk([data, axis, k, ret_typ, is_ascend, …]) Returns the indices of the top k elements in an input array along the given axis (by default). transpose([data, axes, out, name]) Permutes the dimensions of an array. trunc([data, out, name]) Return the element-wise truncated value of the input. uniform([low, high, shape, ctx, dtype, out, …]) Draw random samples from a uniform distribution. unravel_index([data, shape, out, name]) Converts an array of flat indices into a batch of index arrays. where([condition, x, y, out, name]) Return the elements, either from x or y, depending on the condition. zeros_like([data, out, name]) Return an array of zeros with the same shape, type and storage type as the input array. concatenate(arrays[, axis, always_copy]) DEPRECATED, use concat instead ones(shape[, ctx, dtype]) Returns a new array filled with all ones, with the given shape and type. add(lhs, rhs) Returns element-wise sum of the input arrays with broadcasting. arange(start[, stop, step, repeat, …]) Returns evenly spaced values within a given interval. linspace(start, stop, num[, endpoint, ctx, …]) Return evenly spaced numbers within a specified interval. eye(N[, M, k, ctx, dtype]) Return a 2-D array with ones on the diagonal and zeros elsewhere. divide(lhs, rhs) Returns element-wise division of the input arrays with broadcasting. equal(lhs, rhs) Returns the result of element-wise equal to (==) comparison operation with broadcasting. full(shape, val[, ctx, dtype, out]) Returns a new array of given shape and type, filled with the given value val. greater(lhs, rhs) Returns the result of element-wise greater than (>) comparison operation with broadcasting. greater_equal(lhs, rhs) Returns the result of element-wise greater than or equal to (>=) comparison operation with broadcasting. imdecode(str_img[, clip_rect, out, index, …]) DEPRECATED, use mx.img instead lesser(lhs, rhs) Returns the result of element-wise lesser than (<) comparison operation with broadcasting. lesser_equal(lhs, rhs) Returns the result of element-wise lesser than or equal to (<=) comparison operation with broadcasting. logical_and(lhs, rhs) Returns the result of element-wise logical and comparison operation with broadcasting. logical_or(lhs, rhs) Returns the result of element-wise logical or comparison operation with broadcasting. logical_xor(lhs, rhs) Returns the result of element-wise logical xor comparison operation with broadcasting. maximum(lhs, rhs) Returns element-wise maximum of the input arrays with broadcasting. minimum(lhs, rhs) Returns element-wise minimum of the input arrays with broadcasting. moveaxis(tensor, source, destination) Moves the source axis into the destination position modulo(lhs, rhs) Returns element-wise modulo of the input arrays with broadcasting. multiply(lhs, rhs) Returns element-wise product of the input arrays with broadcasting. not_equal(lhs, rhs) Returns the result of element-wise not equal to (!=) comparison operation with broadcasting. onehot_encode(indices, out) One-hot encoding indices into matrix out. power(base, exp) Returns result of first array elements raised to powers from second array, element-wise with broadcasting. subtract(lhs, rhs) Returns element-wise difference of the input arrays with broadcasting. true_divide(lhs, rhs) This function is similar to divide(). Wait for all async operations to finish in MXNet. histogram(a[, bins, range]) Compute the histogram of the input data. split_v2(ary, indices_or_sections[, axis, …]) Split an array into multiple sub-arrays. Returns a reference view of NDArray that represents as DLManagedTensor until all previous write operations on the current array are finished. Returns a reference view of NDArray that represents as DLManagedTensor until all previous read/write operations on the current array are finished. from_dlpack(dlpack) Returns a NDArray backed by a dlpack tensor. from_numpy(ndarray[, zero_copy, array_cls]) Returns an MXNet’s ndarray backed by numpy’s ndarray. zeros(shape[, ctx, dtype, stype]) Return a new array of given shape and type, filled with zeros. indexing_key_expand_implicit_axes(key, shape) Make implicit axes explicit by adding slice(None) and convert boolean array to integer array through nonzero. Returns a dispatch code for calling basic or advanced indexing functions. get_oshape_of_gather_nd_op(dshape, ishape) Given data and index shapes, get the output NDArray shape. zeros(shape[, ctx, dtype, stype]) Return a new array of given shape and type, filled with zeros. empty(shape[, ctx, dtype, stype]) Returns a new array of given shape and type, without initializing entries. array(source_array[, ctx, dtype]) Creates an array from any object exposing the array interface. load(fname) Loads an array from file. Loads an array dictionary or list from a buffer save(fname, data) Saves a list of arrays or a dict of str->array to file.
class mxnet.ndarray.CachedOp(sym, flags=())[source]

Bases: object

Cached operator handle.

mxnet.ndarray.Activation(data=None, act_type=_Null, out=None, name=None, **kwargs)

Applies an activation function element-wise to the input.

The following activation functions are supported:

• relu: Rectified Linear Unit, $$y = max(x, 0)$$

• sigmoid: $$y = \frac{1}{1 + exp(-x)}$$

• tanh: Hyperbolic tangent, $$y = \frac{exp(x) - exp(-x)}{exp(x) + exp(-x)}$$

• softrelu: Soft ReLU, or SoftPlus, $$y = log(1 + exp(x))$$

• softsign: $$y = \frac{x}{1 + abs(x)}$$

Defined in src/operator/nn/activation.cc:L165

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 – The output of this function.

Return type

NDArray or list of NDArrays

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

Batch normalization.

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:

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

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

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

Both mean and var returns a scalar by treating the input as a vector.

Assume the input has size k on axis 1, then both gamma and beta have shape (k,). If output_mean_var is set to be true, then outputs both data_mean and 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:L591

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

• gamma (NDArray) – gamma array

• beta (NDArray) – beta array

• moving_mean (NDArray) – running mean of input

• moving_var (NDArray) – running variance of input

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

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

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

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

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

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

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

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

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

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.BatchNorm_v1(data=None, gamma=None, beta=None, eps=_Null, momentum=_Null, fix_gamma=_Null, use_global_stats=_Null, output_mean_var=_Null, out=None, name=None, **kwargs)

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:

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

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

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

Both mean and var returns a scalar by treating the input as a vector.

Assume the input has size k on axis 1, then both gamma and beta have shape (k,). If output_mean_var is set to be true, then outputs both data_mean and data_var as well, which are needed for the backward pass.

Besides the inputs and the outputs, this operator accepts two auxiliary states, moving_mean and moving_var, which are k-length vectors. They are global statistics for the whole dataset, which are updated by:

moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
moving_var = moving_var * momentum + data_var * (1 - momentum)


If use_global_stats is set to be true, then moving_mean and moving_var are used instead of data_mean and data_var to compute the output. It is often used during inference.

Both gamma and beta are learnable parameters. But if fix_gamma is true, then set gamma to 1 and its gradient to 0.

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=0.00100000005) – Epsilon to prevent div 0

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

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

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

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

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.BilinearSampler(data=None, grid=None, cudnn_off=_Null, out=None, name=None, **kwargs)

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 $$data$$ and $$grid$$, then the output is computed by

$\begin{split}x_{src} = grid[batch, 0, y_{dst}, x_{dst}] \\ y_{src} = grid[batch, 1, y_{dst}, x_{dst}] \\ output[batch, channel, y_{dst}, x_{dst}] = G(data[batch, channel, y_{src}, x_{src})\end{split}$

$$x_{dst}$$, $$y_{dst}$$ enumerate all spatial locations in $$output$$, and $$G()$$ 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 $$data$$ has ‘NCHW’ layout and $$grid$$ 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 $$grid$$, 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 – The output of this function.

Return type

NDArray or list of NDArrays

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

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')

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()
[ 0.  0.]
[ 1.  1.]


Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L325

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Connectionist Temporal Classification Loss.

Note

The existing alias contrib_CTCLoss is deprecated.

The shapes of the inputs and outputs:

• data: (sequence_length, batch_size, alphabet_size)

• label: (batch_size, label_sequence_length)

• out: (batch_size)

The data tensor consists of sequences of activation vectors (without applying softmax), with i-th channel in the last dimension corresponding to i-th label for i between 0 and alphabet_size-1 (i.e always 0-indexed). Alphabet size should include one additional value reserved for blank label. When blank_label is "first", the 0-th channel is be reserved for activation of blank label, or otherwise if it is “last”, (alphabet_size-1)-th channel should be reserved for blank label.

label is an index matrix of integers. When blank_label is "first", the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise, when blank_label is "last", the value (alphabet_size-1) is reserved for blank label.

If a sequence of labels is shorter than label_sequence_length, use the special padding value at the end of the sequence to conform it to the correct length. The padding value is 0 when blank_label is "first", and -1 otherwise.

For example, suppose the vocabulary is [a, b, c], and in one batch we have three sequences ‘ba’, ‘cbb’, and ‘abac’. When blank_label is "first", we can index the labels as {‘a’: 1, ‘b’: 2, ‘c’: 3}, and we reserve the 0-th channel for blank label in data tensor. The resulting label tensor should be padded to be:

[[2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3]]


When blank_label is "last", we can index the labels as {‘a’: 0, ‘b’: 1, ‘c’: 2}, and we reserve the channel index 3 for blank label in data tensor. The resulting label tensor should be padded to be:

[[1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2]]


out is a list of CTC loss values, one per example in the batch.

See Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks, A. Graves et al. for more information on the definition and the algorithm.

Defined in src/operator/nn/ctc_loss.cc:L100

Parameters
• data (NDArray) – Input ndarray

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

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

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

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

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

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

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.Cast(data=None, dtype=_Null, out=None, name=None, **kwargs)

Casts all elements of the input to a new type.

Note

Cast is deprecated. Use cast instead.

Example:

cast([0.9, 1.3], dtype='int32') = [0, 1]
cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]


Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L664

Parameters
• data (NDArray) – The input.

• dtype ({'bfloat16', 'bool', 'float16', 'float32', 'float64', 'int32', 'int64', 'int8', 'uint8'}, required) – Output data type.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.Concat(*data, **kwargs)

Joins input arrays along a given axis.

Note

Concat is deprecated. Use concat instead.

The dimensions of the input arrays should be the same except the axis along which they will be concatenated. The dimension of the output array along the concatenated axis will be equal to the sum of the corresponding dimensions of the input arrays.

The storage type of concat output depends on storage types of inputs

• concat(csr, csr, …, csr, dim=0) = csr

• otherwise, concat generates output with default storage

Example:

x = [[1,1],[2,2]]
y = [[3,3],[4,4],[5,5]]
z = [[6,6], [7,7],[8,8]]

concat(x,y,z,dim=0) = [[ 1.,  1.],
[ 2.,  2.],
[ 3.,  3.],
[ 4.,  4.],
[ 5.,  5.],
[ 6.,  6.],
[ 7.,  7.],
[ 8.,  8.]]

Note that you cannot concat x,y,z along dimension 1 since dimension
0 is not the same for all the input arrays.

concat(y,z,dim=1) = [[ 3.,  3.,  6.,  6.],
[ 4.,  4.,  7.,  7.],
[ 5.,  5.,  8.,  8.]]


Defined in src/operator/nn/concat.cc:L385

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

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

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.Convolution(data=None, weight=None, bias=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, num_filter=_Null, num_group=_Null, workspace=_Null, no_bias=_Null, cudnn_tune=_Null, cudnn_off=_Null, layout=_Null, out=None, name=None, **kwargs)

Compute N-D convolution on (N+2)-D input.

In the 2-D convolution, given input data with shape (batch_size, channel, height, width), the output is computed by

$out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star weight[i,j,:,:]$

where $$\star$$ 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])


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:L469

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.Convolution_v1(data=None, weight=None, bias=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, num_filter=_Null, num_group=_Null, workspace=_Null, no_bias=_Null, cudnn_tune=_Null, cudnn_off=_Null, layout=_Null, out=None, name=None, **kwargs)

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.Correlation(data1=None, data2=None, kernel_size=_Null, max_displacement=_Null, stride1=_Null, stride2=_Null, pad_size=_Null, is_multiply=_Null, out=None, name=None, **kwargs)

Applies correlation to inputs.

The correlation layer performs multiplicative patch comparisons between two feature maps.

Given two multi-channel feature maps $$f_{1}, f_{2}$$, with $$w$$, $$h$$, and $$c$$ being their width, height, and number of channels, the correlation layer lets the network compare each patch from $$f_{1}$$ with each patch from $$f_{2}$$.

For now we consider only a single comparison of two patches. The ‘correlation’ of two patches centered at $$x_{1}$$ in the first map and $$x_{2}$$ in the second map is then defined as:

$c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]} <f_{1}(x_{1} + o), f_{2}(x_{2} + o)>$

for a square patch of size $$K:=2k+1$$.

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 $$c(x_{1}, x_{2})$$ involves $$c * K^{2}$$ multiplications. Comparing all patch combinations involves $$w^{2}*h^{2}$$ such computations.

Given a maximum displacement $$d$$, for each location $$x_{1}$$ it computes correlations $$c(x_{1}, x_{2})$$ only in a neighborhood of size $$D:=2d+1$$, by limiting the range of $$x_{2}$$. We use strides $$s_{1}, s_{2}$$, to quantize $$x_{1}$$ globally and to quantize $$x_{2}$$ within the neighborhood centered around $$x_{1}$$.

The final output is defined by the following expression:

$out[n, q, i, j] = c(x_{i, j}, x_{q})$

where $$i$$ and $$j$$ enumerate spatial locations in $$f_{1}$$, and $$q$$ denotes the $$q^{th}$$ neighborhood of $$x_{i,j}$$.

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

• 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.Crop(*data, **kwargs)

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.Custom(*data, **kwargs)

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: https://mxnet.incubator.apache.org/api/faq/new_op

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 – The output of this function.

Return type

NDArray or list of NDArrays

Example

Applies a custom operator named my_custom_operator to input.

>>> output = mx.symbol.Custom(op_type='my_custom_operator', data=input)

mxnet.ndarray.Deconvolution(data=None, weight=None, bias=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, adj=_Null, target_shape=_Null, num_filter=_Null, num_group=_Null, workspace=_Null, no_bias=_Null, cudnn_tune=_Null, cudnn_off=_Null, layout=_Null, out=None, name=None, **kwargs)

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.Dropout(data=None, p=_Null, mode=_Null, axes=_Null, cudnn_off=_Null, out=None, name=None, **kwargs)

Applies dropout operation to input array.

• During training, each element of the input is set to zero with probability p. The whole array is rescaled by $$1/(1-p)$$ 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:L96

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.

• cudnn_off (boolean or None, optional, default=0) – Whether to turn off cudnn in dropout operator. This option is ignored if axes is specified.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.ElementWiseSum(*args, **kwargs)

$add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n$

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.Embedding(data=None, weight=None, input_dim=_Null, output_dim=_Null, dtype=_Null, sparse_grad=_Null, out=None, name=None, **kwargs)

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).

When “sparse_grad” is False, if any index mentioned is too large, it is replaced by the index that addresses the last vector in an embedding matrix. When “sparse_grad” is True, an error will be raised if invalid indices are found.

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:L598

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

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

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

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 behavior 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:L250

Parameters
• data (NDArray) – Input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.FullyConnected(data=None, weight=None, bias=None, num_hidden=_Null, no_bias=_Null, flatten=_Null, out=None, name=None, **kwargs)

Applies a linear transformation: $$Y = XW^T + b$$.

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:L287

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.GridGenerator(data=None, transform_type=_Null, target_shape=_Null, out=None, name=None, **kwargs)

Generates 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.GroupNorm(data=None, gamma=None, beta=None, num_groups=_Null, eps=_Null, output_mean_var=_Null, out=None, name=None, **kwargs)

Group normalization.

The input channels are separated into num_groups groups, each containing num_channels / num_groups channels. The mean and standard-deviation are calculated separately over the each group.

$data = data.reshape((N, num_groups, C // num_groups, ...)) out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta$

Both gamma and beta are learnable parameters.

Defined in src/operator/nn/group_norm.cc:L77

Parameters
• data (NDArray) – Input data

• gamma (NDArray) – gamma array

• beta (NDArray) – beta array

• num_groups (int, optional, default='1') – Total number of groups.

• eps (float, optional, default=9.99999975e-06) – 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.IdentityAttachKLSparseReg(data=None, sparseness_target=_Null, penalty=_Null, momentum=_Null, out=None, name=None, **kwargs)

Apply a sparse regularization to the output a sigmoid activation function.

Parameters
• data (NDArray) – Input data.

• sparseness_target (float, optional, default=0.100000001) – The sparseness target

• penalty (float, optional, default=0.00100000005) – The tradeoff parameter for the sparseness penalty

• momentum (float, optional, default=0.899999976) – The momentum for running average

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.InstanceNorm(data=None, gamma=None, beta=None, eps=_Null, out=None, name=None, **kwargs)

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:

$out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta$

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 this paper 1

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=0.00100000005) – An epsilon parameter to prevent division by 0.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.L2Normalization(data=None, eps=_Null, mode=_Null, out=None, name=None, **kwargs)

Normalize the input array using the L2 norm.

For 1-D NDArray, it computes:

out = data / sqrt(sum(data ** 2) + eps)


For N-D NDArray, if the input array has shape (N, N, …, N),

with mode = instance, it normalizes each instance in the multidimensional array by its L2 norm.:

for i in 0...N
out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps)


with mode = channel, it normalizes each channel in the array by its L2 norm.:

for i in 0...N
out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps)


with mode = spatial, it normalizes the cross channel norm for each position in the array by its L2 norm.:

for dim in 2...N
for i in 0...N
out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps)
-dim-


Example:

x = [[[1,2],
[3,4]],
[[2,2],
[5,6]]]

L2Normalization(x, mode='instance')
=[[[ 0.18257418  0.36514837]
[ 0.54772252  0.73029673]]
[[ 0.24077171  0.24077171]
[ 0.60192931  0.72231513]]]

L2Normalization(x, mode='channel')
=[[[ 0.31622776  0.44721359]
[ 0.94868326  0.89442718]]
[[ 0.37139067  0.31622776]
[ 0.92847669  0.94868326]]]

L2Normalization(x, mode='spatial')
=[[[ 0.44721359  0.89442718]
[ 0.60000002  0.80000001]]
[[ 0.70710677  0.70710677]
[ 0.6401844   0.76822126]]]


Defined in src/operator/l2_normalization.cc:L196

Parameters
• data (NDArray) – Input array to normalize.

• eps (float, optional, default=1.00000001e-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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.LRN(data=None, alpha=_Null, beta=_Null, knorm=_Null, nsize=_Null, out=None, name=None, **kwargs)

Applies local response normalization to the input.

The local response normalization layer performs “lateral inhibition” by normalizing over local input regions.

If $$a_{x,y}^{i}$$ is the activity of a neuron computed by applying kernel $$i$$ at position $$(x, y)$$ and then applying the ReLU nonlinearity, the response-normalized activity $$b_{x,y}^{i}$$ is given by the expression:

$b_{x,y}^{i} = \frac{a_{x,y}^{i}}{\Bigg({k + \frac{\alpha}{n} \sum_{j=max(0, i-\frac{n}{2})}^{min(N-1, i+\frac{n}{2})} (a_{x,y}^{j})^{2}}\Bigg)^{\beta}}$

where the sum runs over $$n$$ “adjacent” kernel maps at the same spatial position, and $$N$$ is the total number of kernels in the layer.

Defined in src/operator/nn/lrn.cc:L158

Parameters
• data (NDArray) – Input data to LRN

• alpha (float, optional, default=9.99999975e-05) – The variance scaling parameter $$lpha$$ in the LRN expression.

• beta (float, optional, default=0.75) – The power parameter $$eta$$ in the LRN expression.

• knorm (float, optional, default=2) – The parameter $$k$$ 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.LayerNorm(data=None, gamma=None, beta=None, axis=_Null, eps=_Null, output_mean_var=_Null, out=None, name=None, **kwargs)

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:

$out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta$

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:L158

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=9.99999975e-06) – 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.LeakyReLU(data=None, gamma=None, act_type=_Null, slope=_Null, lower_bound=_Null, upper_bound=_Null, out=None, name=None, **kwargs)

Applies Leaky rectified linear unit activation element-wise to the input.

Leaky ReLUs attempt to fix the “dying ReLU” problem by allowing a small slope when the input is negative and has a slope of one when input is positive.

The following modified ReLU Activation functions are supported:

• elu: Exponential Linear Unit. y = x > 0 ? x : slope * (exp(x)-1)

• selu: Scaled Exponential Linear Unit. y = lambda * (x > 0 ? x : alpha * (exp(x) - 1)) where lambda = 1.0507009873554804934193349852946 and alpha = 1.6732632423543772848170429916717.

• leaky: Leaky ReLU. y = x > 0 ? x : slope * x

• prelu: Parametric ReLU. This is same as leaky except that slope is learnt during training.

• rrelu: Randomized ReLU. same as leaky but the slope is uniformly and randomly chosen from [lower_bound, upper_bound) for training, while fixed to be (lower_bound+upper_bound)/2 for inference.

Defined in src/operator/leaky_relu.cc:L161

Parameters
• data (NDArray) – Input data to activation function.

• gamma (NDArray) – Input data to activation function.

• act_type ({'elu', 'gelu', '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=0.333999991) – Upper bound of random slope. (For rrelu only)

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.LinearRegressionOutput(data=None, label=None, grad_scale=_Null, out=None, name=None, **kwargs)

Computes and optimizes for squared loss during backward propagation. Just outputs data during forward propagation.

If $$\hat{y}_i$$ is the predicted value of the i-th sample, and $$y_i$$ is the corresponding target value, then the squared loss estimated over $$n$$ samples is defined as

$$\text{SquaredLoss}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_2$$

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.LogisticRegressionOutput(data=None, label=None, grad_scale=_Null, out=None, name=None, **kwargs)

Applies a logistic function to the input.

The logistic function, also known as the sigmoid function, is computed as $$\frac{1}{1+exp(-\textbf{x})}$$.

Commonly, the sigmoid is used to squash the real-valued output of a linear model $$wTx+b$$ 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:

$$-{(y\log(p) + (1 - y)\log(1 - p))}$$

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.MAERegressionOutput(data=None, label=None, grad_scale=_Null, out=None, name=None, **kwargs)

Computes mean absolute error of the input.

MAE is a risk metric corresponding to the expected value of the absolute error.

If $$\hat{y}_i$$ is the predicted value of the i-th sample, and $$y_i$$ is the corresponding target value, then the mean absolute error (MAE) estimated over $$n$$ samples is defined as

$$\text{MAE}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_1$$

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.MakeLoss(data=None, grad_scale=_Null, valid_thresh=_Null, normalization=_Null, out=None, name=None, **kwargs)

Make your own loss function in network construction.

This operator accepts a customized loss function symbol as a terminal loss and the symbol should be an operator with no backward dependency. The output of this function is the gradient of loss with respect to the input data.

For example, if you are a making a cross entropy loss function. Assume out is the predicted output and label is the true label, then the cross entropy can be defined as:

cross_entropy = label * log(out) + (1 - label) * log(1 - out)
loss = MakeLoss(cross_entropy)


We will need to use MakeLoss when we are creating our own loss function or we want to combine multiple loss functions. Also we may want to stop some variables’ gradients from backpropagation. See more detail in BlockGrad or stop_gradient.

In addition, we can give a scale to the loss by setting grad_scale, so that the gradient of the loss will be rescaled in the backpropagation.

Note

This operator should be used as a Symbol instead of NDArray.

Defined in src/operator/make_loss.cc:L71

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.Pad(data=None, mode=_Null, pad_width=_Null, constant_value=_Null, out=None, name=None, **kwargs)

Pads an input array with a constant or edge values of the array.

Note

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.]]]]

[[[[  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.]]]]

[[[[  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.]]]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

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

Performs pooling on the input.

The shapes for 1-D pooling are

• data and out: (batch_size, channel, width) (NCW layout) or (batch_size, width, channel) (NWC layout),

The shapes for 2-D pooling are

• data and out: (batch_size, channel, height, width) (NCHW layout) or (batch_size, height, width, channel) (NHWC layout),

out_height = f(height, kernel[0], pad[0], stride[0]) out_width = f(width, kernel[1], pad[1], stride[1])

The definition of f depends on pooling_convention, which has two options:

• valid (default):

f(x, k, p, s) = floor((x+2*p-k)/s)+1

• full, which is compatible with Caffe:

f(x, k, p, s) = ceil((x+2*p-k)/s)+1


When global_pool is set to be true, then global pooling is performed. It will reset kernel=(height, width) and set the appropiate padding to 0.

Three pooling options are supported by pool_type:

• avg: average pooling

• max: max pooling

• sum: sum pooling

• lp: Lp pooling

For 3-D pooling, an additional depth dimension is added before height. Namely the input data and output will have shape (batch_size, channel, depth, height, width) (NCDHW layout) or (batch_size, depth, height, width, channel) (NDHWC layout).

Notes on Lp pooling:

Lp pooling was first introduced by this paper: https://arxiv.org/pdf/1204.3968.pdf. L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling. We can see that Lp pooling stands between those two, in practice the most common value for p is 2.

For each window X, the mathematical expression for Lp pooling is:

$$f(X) = \sqrt[p]{\sum_{x}^{X} x^p}$$

Defined in src/operator/nn/pooling.cc:L414

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.

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

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.Pooling_v1(data=None, kernel=_Null, pool_type=_Null, global_pool=_Null, pooling_convention=_Null, stride=_Null, pad=_Null, out=None, name=None, **kwargs)

This operator is DEPRECATED. Perform pooling on the input.

The shapes for 2-D pooling is

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

• out: (batch_size, num_filter, out_height, out_width), with:

out_height = f(height, kernel[0], pad[0], stride[0])
out_width = f(width, kernel[1], pad[1], stride[1])


The definition of f depends on pooling_convention, which has two options:

• valid (default):

f(x, k, p, s) = floor((x+2*p-k)/s)+1

• full, which is compatible with Caffe:

f(x, k, p, s) = ceil((x+2*p-k)/s)+1


But global_pool is set to be true, then do a global pooling, namely reset kernel=(height, width).

Three pooling options are supported by pool_type:

• avg: average pooling

• max: max pooling

• sum: sum pooling

1-D pooling is special case of 2-D pooling with weight=1 and kernel[1]=1.

For 3-D pooling, an additional depth dimension is added before height. Namely the input data will have shape (batch_size, channel, depth, height, width).

Defined in src/operator/pooling_v1.cc:L104

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.RNN(data=None, parameters=None, state=None, state_cell=None, sequence_length=None, state_size=_Null, num_layers=_Null, bidirectional=_Null, mode=_Null, p=_Null, state_outputs=_Null, projection_size=_Null, lstm_state_clip_min=_Null, lstm_state_clip_max=_Null, lstm_state_clip_nan=_Null, use_sequence_length=_Null, out=None, name=None, **kwargs)

Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are implemented, with both multi-layer and bidirectional support.

When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use pseudo-float16 precision (float32 math with float16 I/O) precision in order to use Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.

Vanilla RNN

Applies a single-gate recurrent layer to input X. Two kinds of activation function are supported: ReLU and Tanh.

With ReLU activation function:

$h_t = relu(W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh})$

With Tanh activtion function:

$h_t = \tanh(W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh})$

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

$\begin{split}\begin{array}{ll} i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\ f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \\ o_t = \mathrm{sigmoid}(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\ c_t = f_t * c_{(t-1)} + i_t * g_t \\ h_t = o_t * \tanh(c_t) \end{array}\end{split}$

With the projection size being set, LSTM could use the projection feature to reduce the parameters size and give some speedups without significant damage to the accuracy.

Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognition - Sak et al. 2014. https://arxiv.org/abs/1402.1128

$\begin{split}\begin{array}{ll} i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{ri} r_{(t-1)} + b_{ri}) \\ f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{rf} r_{(t-1)} + b_{rf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{rc} r_{(t-1)} + b_{rg}) \\ o_t = \mathrm{sigmoid}(W_{io} x_t + b_{o} + W_{ro} r_{(t-1)} + b_{ro}) \\ c_t = f_t * c_{(t-1)} + i_t * g_t \\ h_t = o_t * \tanh(c_t) r_t = W_{hr} h_t \end{array}\end{split}$

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.

$\begin{split}\begin{array}{ll} r_t = \mathrm{sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\ z_t = \mathrm{sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\ n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \\ h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \\ \end{array}\end{split}$

Defined in src/operator/rnn.cc:L368

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)

• sequence_length (NDArray) – Vector of valid sequence lengths for each element in batch. (Only used if use_sequence_length kwarg is True)

• 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) – drop rate of the dropout on the outputs of each RNN layer, except the last layer.

• state_outputs (boolean, optional, default=0) – Whether to have the states as symbol outputs.

• projection_size (int or None, optional, default='None') – size of project size

• lstm_state_clip_min (double or None, optional, default=None) – Minimum clip value of LSTM states. This option must be used together with lstm_state_clip_max.

• lstm_state_clip_max (double or None, optional, default=None) – Maximum clip value of LSTM states. This option must be used together with lstm_state_clip_min.

• lstm_state_clip_nan (boolean, optional, default=0) – Whether to stop NaN from propagating in state by clipping it to min/max. If clipping range is not specified, this option is ignored.

• 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

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

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:L225

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.Reshape(data=None, shape=_Null, reverse=_Null, target_shape=_Null, keep_highest=_Null, out=None, name=None, **kwargs)

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:L175

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 – The output of this function.

Return type

NDArray or list of NDArrays

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)

mxnet.ndarray.SVMOutput(data=None, label=None, margin=_Null, regularization_coefficient=_Null, use_linear=_Null, out=None, name=None, **kwargs)

Computes support vector machine based transformation of the input.

This tutorial demonstrates using SVM as output layer for classification instead of softmax: https://github.com/dmlc/mxnet/tree/master/example/svm_mnist.

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.SequenceLast(data=None, sequence_length=None, use_sequence_length=_Null, axis=_Null, out=None, name=None, **kwargs)

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:L106

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.SequenceMask(data=None, sequence_length=None, use_sequence_length=_Null, value=_Null, axis=_Null, out=None, name=None, **kwargs)

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
[[[  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
[[[  1.,   2.,   3.],
[  4.,   5.,   6.]],

[[  7.,   8.,   9.],
[  10.,  11.,  12.]],

[[   1.,   1.,   1.],
[  16.,  17.,  18.]]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.SequenceReverse(data=None, sequence_length=None, use_sequence_length=_Null, axis=_Null, out=None, name=None, **kwargs)

Reverses the elements of each sequence.

This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape.

Parameter sequence_length is used to handle variable-length sequences. sequence_length should be an input array of positive ints of dimension [batch_size]. To use this parameter, set use_sequence_length to True, otherwise each example in the batch is assumed to have the max sequence length.

Example:

x = [[[  1.,   2.,   3.],
[  4.,   5.,   6.]],

[[  7.,   8.,   9.],
[ 10.,  11.,  12.]],

[[ 13.,  14.,   15.],
[ 16.,  17.,   18.]]]

// Batch 1
B1 = [[  1.,   2.,   3.],
[  7.,   8.,   9.],
[ 13.,  14.,  15.]]

// Batch 2
B2 = [[  4.,   5.,   6.],
[ 10.,  11.,  12.],
[ 16.,  17.,  18.]]

// returns reverse sequence when sequence_length parameter is not used
SequenceReverse(x) = [[[ 13.,  14.,   15.],
[ 16.,  17.,   18.]],

[[  7.,   8.,   9.],
[ 10.,  11.,  12.]],

[[  1.,   2.,   3.],
[  4.,   5.,   6.]]]

// sequence_length [2,2] means 2 rows of
// both batch B1 and B2 will be reversed.
SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) =
[[[  7.,   8.,   9.],
[ 10.,  11.,  12.]],

[[  1.,   2.,   3.],
[  4.,   5.,   6.]],

[[ 13.,  14.,   15.],
[ 16.,  17.,   18.]]]

// sequence_length [2,3] means 2 of batch B2 and 3 of batch B3
// will be reversed.
SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) =
[[[  7.,   8.,   9.],
[ 16.,  17.,  18.]],

[[  1.,   2.,   3.],
[ 10.,  11.,  12.]],

[[ 13.,  14,   15.],
[  4.,   5.,   6.]]]


Defined in src/operator/sequence_reverse.cc:L122

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.SliceChannel(data=None, num_outputs=_Null, axis=_Null, squeeze_axis=_Null, out=None, name=None, **kwargs)

Splits an array along a particular axis into multiple sub-arrays.

Note

SliceChannel is deprecated. Use split instead.

Note that num_outputs should evenly divide the length of the axis along which to split the array.

Example:

x  = [[[ 1.]
[ 2.]]
[[ 3.]
[ 4.]]
[[ 5.]
[ 6.]]]
x.shape = (3, 2, 1)

y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1)
y = [[[ 1.]]
[[ 3.]]
[[ 5.]]]

[[[ 2.]]
[[ 4.]]
[[ 6.]]]

y[0].shape = (3, 1, 1)

z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1)
z = [[[ 1.]
[ 2.]]]

[[[ 3.]
[ 4.]]]

[[[ 5.]
[ 6.]]]

z[0].shape = (1, 2, 1)


squeeze_axis=1 removes the axis with length 1 from the shapes of the output arrays. Note that setting squeeze_axis to 1 removes axis with length 1 only along the axis which it is split. Also squeeze_axis can be set to true only if input.shape[axis] == num_outputs.

Example:

z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1)
z = [[ 1.]
[ 2.]]

[[ 3.]
[ 4.]]

[[ 5.]
[ 6.]]
z[0].shape = (2 ,1 )


Defined in src/operator/slice_channel.cc:L107

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.Softmax(data=None, label=None, grad_scale=_Null, ignore_label=_Null, multi_output=_Null, use_ignore=_Null, preserve_shape=_Null, normalization=_Null, out_grad=_Null, smooth_alpha=_Null, out=None, name=None, **kwargs)

Computes the gradient of cross entropy loss with respect to softmax output.

• This operator computes the gradient in two steps. The cross entropy loss does not actually need to be computed.

• Applies softmax function on the input array.

• Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.

• The softmax function, cross entropy loss and gradient is given by:

• Softmax Function:

$\text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}$
• Cross Entropy Function:

$\text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)$
• The gradient of cross entropy loss w.r.t softmax output:

$\text{gradient} = \text{output} - \text{label}$
• During forward propagation, the softmax function is computed for each instance in the input array.

For general N-D input arrays with shape $$(d_1, d_2, ..., d_n)$$. The size is $$s=d_1 \cdot d_2 \cdot \cdot \cdot d_n$$. 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 $$(d_1, \frac{s}{d_1})$$ and then compute the softmax function for each row in the reshaped array, and afterwards reshape it back to the original shape $$(d_1, d_2, ..., d_n)$$.

• 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      ]]
[[ 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:L231

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.

• 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.SoftmaxActivation(data=None, mode=_Null, out=None, name=None, **kwargs)

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.SoftmaxOutput(data=None, label=None, grad_scale=_Null, ignore_label=_Null, multi_output=_Null, use_ignore=_Null, preserve_shape=_Null, normalization=_Null, out_grad=_Null, smooth_alpha=_Null, out=None, name=None, **kwargs)

Computes the gradient of cross entropy loss with respect to softmax output.

• This operator computes the gradient in two steps. The cross entropy loss does not actually need to be computed.

• Applies softmax function on the input array.

• Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.

• The softmax function, cross entropy loss and gradient is given by:

• Softmax Function:

$\text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}$
• Cross Entropy Function:

$\text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)$
• The gradient of cross entropy loss w.r.t softmax output:

$\text{gradient} = \text{output} - \text{label}$
• During forward propagation, the softmax function is computed for each instance in the input array.

For general N-D input arrays with shape $$(d_1, d_2, ..., d_n)$$. The size is $$s=d_1 \cdot d_2 \cdot \cdot \cdot d_n$$. 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 $$(d_1, \frac{s}{d_1})$$ and then compute the softmax function for each row in the reshaped array, and afterwards reshape it back to the original shape $$(d_1, d_2, ..., d_n)$$.

• 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      ]]
[[ 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:L231

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.

• 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.SpatialTransformer(data=None, loc=None, target_shape=_Null, transform_type=_Null, sampler_type=_Null, cudnn_off=_Null, out=None, name=None, **kwargs)

Applies 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.SwapAxis(data=None, dim1=_Null, dim2=_Null, out=None, name=None, **kwargs)

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, optional, default='0') – the first axis to be swapped.

• dim2 (int, optional, default='0') – the second axis to be swapped.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.UpSampling(*data, **kwargs)

Upsamples the given input data.

Two algorithms (sample_type) are available for upsampling:

• Nearest Neighbor

• Bilinear

Nearest Neighbor Upsampling

Input data is expected to be NCHW.

Example:

x = [[[[1. 1. 1.]
[1. 1. 1.]
[1. 1. 1.]]]]

UpSampling(x, scale=2, sample_type='nearest') = [[[[1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.]]]]


Bilinear Upsampling

Uses deconvolution algorithm under the hood. You need provide both input data and the kernel.

Input data is expected to be NCHW.

num_filter is expected to be same as the number of channels.

Example:

x = [[[[1. 1. 1.]
[1. 1. 1.]
[1. 1. 1.]]]]

w = [[[[1. 1. 1. 1.]
[1. 1. 1. 1.]
[1. 1. 1. 1.]
[1. 1. 1. 1.]]]]

UpSampling(x, w, scale=2, sample_type='bilinear', num_filter=1) = [[[[1. 2. 2. 2. 2. 1.]
[2. 4. 4. 4. 4. 2.]
[2. 4. 4. 4. 4. 2.]
[2. 4. 4. 4. 4. 2.]
[2. 4. 4. 4. 4. 2.]
[1. 2. 2. 2. 2. 1.]]]]


Defined in src/operator/nn/upsampling.cc:L173

Parameters
• data (NDArray[]) – Array of tensors to upsample. For bilinear upsampling, there should be 2 inputs - 1 data and 1 weight.

• scale (int, required) – Up sampling scale

• num_filter (int, optional, default='0') – Input filter. Only used by bilinear sample_type.Since bilinear upsampling uses deconvolution, num_filters is set to the number of channels.

• 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 – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns element-wise absolute value of the input.

Example:

abs([-2, 0, 3]) = [2, 0, 3]


The storage type of abs output depends upon the input storage type:

• abs(default) = default

• abs(row_sparse) = row_sparse

• abs(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L720

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.adam_update(weight=None, grad=None, mean=None, var=None, lr=_Null, beta1=_Null, beta2=_Null, epsilon=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, lazy_update=_Null, out=None, name=None, **kwargs)

Adam update consists of the following steps, where g represents gradient and m, v are 1st and 2nd order moment estimates (mean and variance).

$\begin{split}g_t = \nabla J(W_{t-1})\\ m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\ v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\ W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon }\end{split}$

m = beta1*m + (1-beta1)*grad
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:
w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)


Defined in src/operator/optimizer_op.cc:L688

Parameters
• weight (NDArray) – Weight

• mean (NDArray) – Moving mean

• var (NDArray) – Moving variance

• lr (float, required) – Learning rate

• beta1 (float, optional, default=0.899999976) – The decay rate for the 1st moment estimates.

• beta2 (float, optional, default=0.999000013) – The decay rate for the 2nd moment estimates.

• epsilon (float, optional, default=9.99999994e-09) – 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.

• 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.add_n(*args, **kwargs)

$add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n$

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.all_finite(data=None, init_output=_Null, out=None, name=None, **kwargs)

Check if all the float numbers in the array are finite (used for AMP)

Defined in src/operator/contrib/all_finite.cc:L101

Parameters
• data (NDArray) – Array

• init_output (boolean, optional, default=1) – Initialize output to 1.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.amp_cast(data=None, dtype=_Null, out=None, name=None, **kwargs)

Cast function between low precision float/FP32 used by AMP.

It casts only between low precision float/FP32 and does not do anything for other types.

Defined in src/operator/tensor/amp_cast.cc:L121

Parameters
• data (NDArray) – The input.

• dtype ({'bfloat16', 'float16', 'float32', 'float64', 'int32', 'int64', 'int8', 'uint8'}, required) – Output data type.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.amp_multicast(*data, **kwargs)

Cast function used by AMP, that casts its inputs to the common widest type.

It casts only between low precision float/FP32 and does not do anything for other types.

Defined in src/operator/tensor/amp_cast.cc:L165

Parameters
• data (NDArray[]) – Weights

• num_outputs (int, required) – Number of input/output pairs to be casted to the widest type.

• cast_narrow (boolean, optional, default=0) – Whether to cast to the narrowest type

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns element-wise inverse cosine of the input array.

The input should be in range [-1, 1]. The output is in the closed interval $$[0, \pi]$$

$arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0]$

The storage type of arccos output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L233

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns the element-wise inverse hyperbolic cosine of the input array, computed element-wise.

The storage type of arccosh output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L535

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

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 [$$-\pi/2$$, $$\pi/2$$].

$arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2]$

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:L187

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns the element-wise inverse hyperbolic sine of the input array, computed element-wise.

The storage type of arcsinh output depends upon the input storage type:

• arcsinh(default) = default

• arcsinh(row_sparse) = row_sparse

• arcsinh(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L494

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns element-wise inverse tangent of the input array.

The output is in the closed interval $$[-\pi/2, \pi/2]$$

$arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4]$

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:L282

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns the element-wise inverse hyperbolic tangent of the input array, computed element-wise.

The storage type of arctanh output depends upon the input storage type:

• arctanh(default) = default

• arctanh(row_sparse) = row_sparse

• arctanh(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L579

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.argmax(data=None, axis=_Null, keepdims=_Null, out=None, name=None, **kwargs)

Returns indices of the maximum values along an axis.

In the case of multiple occurrences of maximum values, the indices corresponding to the first occurrence are returned.

Examples:

x = [[ 0.,  1.,  2.],
[ 3.,  4.,  5.]]

// argmax along axis 0
argmax(x, axis=0) = [ 1.,  1.,  1.]

// argmax along axis 1
argmax(x, axis=1) = [ 2.,  2.]

// argmax along axis 1 keeping same dims as an input array
argmax(x, axis=1, keepdims=True) = [[ 2.],
[ 2.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns argmax indices of each channel from the input array.

The result will be an NDArray of shape (num_channel,).

In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence are returned.

Examples:

x = [[ 0.,  1.,  2.],
[ 3.,  4.,  5.]]

argmax_channel(x) = [ 2.,  2.]


Parameters
• data (NDArray) – The input array

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.argmin(data=None, axis=_Null, keepdims=_Null, out=None, name=None, **kwargs)

Returns indices of the minimum values along an axis.

In the case of multiple occurrences of minimum values, the indices corresponding to the first occurrence are returned.

Examples:

x = [[ 0.,  1.,  2.],
[ 3.,  4.,  5.]]

// argmin along axis 0
argmin(x, axis=0) = [ 0.,  0.,  0.]

// argmin along axis 1
argmin(x, axis=1) = [ 0.,  0.]

// argmin along axis 1 keeping same dims as an input array
argmin(x, axis=1, keepdims=True) = [[ 0.],
[ 0.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.argsort(data=None, axis=_Null, is_ascend=_Null, dtype=_Null, out=None, name=None, **kwargs)

Returns the indices that would sort an input array along the given axis.

This function performs sorting along the given axis and returns an array of indices having same shape as an input array that index data in sorted order.

Examples:

x = [[ 0.3,  0.2,  0.4],
[ 0.1,  0.3,  0.2]]

// sort along axis -1
argsort(x) = [[ 1.,  0.,  2.],
[ 0.,  2.,  1.]]

// sort along axis 0
argsort(x, axis=0) = [[ 1.,  0.,  1.]
[ 0.,  1.,  0.]]

// flatten and then sort
argsort(x, axis=None) = [ 3.,  1.,  5.,  0.,  4.,  2.]


Defined in src/operator/tensor/ordering_op.cc:L185

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', 'int64', '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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.batch_dot(lhs=None, rhs=None, transpose_a=_Null, transpose_b=_Null, forward_stype=_Null, out=None, name=None, **kwargs)

Batchwise dot product.

batch_dot is used to compute dot product of x and y when x and y are data in batch, namely N-D (N >= 3) arrays in shape of (B0, …, B_i, :, :).

For example, given x with shape (B_0, …, B_i, N, M) and y with shape (B_0, …, B_i, M, K), the result array will have shape (B_0, …, B_i, N, K), which is computed by:

batch_dot(x,y)[b_0, ..., b_i, :, :] = dot(x[b_0, ..., b_i, :, :], y[b_0, ..., b_i, :, :])


Defined in src/operator/tensor/dot.cc:L127

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.batch_take(a=None, indices=None, out=None, name=None, **kwargs)

Takes elements from a data batch.

Note

batch_take is deprecated. Use pick instead.

Given an input array of shape (d0, d1) and indices of shape (i0,), the result will be an output array of shape (i0,) with:

output[i] = input[i, indices[i]]


Examples:

x = [[ 1.,  2.],
[ 3.,  4.],
[ 5.,  6.]]

// takes elements with specified indices
batch_take(x, [0,1,0]) = [ 1.  4.  5.]


Defined in src/operator/tensor/indexing_op.cc:L836

Parameters
• a (NDArray) – The input array

• indices (NDArray) – The index array

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_add(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns element-wise sum of the input arrays with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

[ 2.,  2.,  2.]]

broadcast_plus(x, y) = [[ 1.,  1.,  1.],
[ 2.,  2.,  2.]]


Supported sparse operations:

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_axes(data=None, axis=_Null, size=_Null, out=None, name=None, **kwargs)

Broadcasts the input array over particular axes.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to (2,8,3,9). Elements will be duplicated on the broadcasted axes.

Example:

// given x of shape (1,2,1)
x = [[[ 1.],
[ 2.]]]

// broadcast x on on axis 2
broadcast_axis(x, axis=2, size=3) = [[[ 1.,  1.,  1.],
[ 2.,  2.,  2.]]]
// broadcast x on on axes 0 and 2
broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1.,  1.,  1.],
[ 2.,  2.,  2.]],
[[ 1.,  1.,  1.],
[ 2.,  2.,  2.]]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_axis(data=None, axis=_Null, size=_Null, out=None, name=None, **kwargs)

Broadcasts the input array over particular axes.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to (2,8,3,9). Elements will be duplicated on the broadcasted axes.

Example:

// given x of shape (1,2,1)
x = [[[ 1.],
[ 2.]]]

// broadcast x on on axis 2
broadcast_axis(x, axis=2, size=3) = [[[ 1.,  1.,  1.],
[ 2.,  2.,  2.]]]
// broadcast x on on axes 0 and 2
broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1.,  1.,  1.],
[ 2.,  2.,  2.]],
[[ 1.,  1.,  1.],
[ 2.,  2.,  2.]]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_div(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns element-wise division of the input arrays with broadcasting.

Example:

x = [[ 6.,  6.,  6.],
[ 6.,  6.,  6.]]

y = [[ 2.],
[ 3.]]

broadcast_div(x, y) = [[ 3.,  3.,  3.],
[ 2.,  2.,  2.]]


Supported sparse operations:

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_equal(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns the result of element-wise equal to (==) comparison operation with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_equal(x, y) = [[ 0.,  0.,  0.],
[ 1.,  1.,  1.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_greater(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns the result of element-wise greater than (>) comparison operation with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_greater(x, y) = [[ 1.,  1.,  1.],
[ 0.,  0.,  0.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_greater_equal(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns the result of element-wise greater than or equal to (>=) comparison operation with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_greater_equal(x, y) = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_hypot(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns the hypotenuse of a right angled triangle, given its “legs” with broadcasting.

It is equivalent to doing $$sqrt(x_1^2 + x_2^2)$$.

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.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_lesser(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns the result of element-wise lesser than (<) comparison operation with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_lesser(x, y) = [[ 0.,  0.,  0.],
[ 0.,  0.,  0.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_lesser_equal(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns the result of element-wise lesser than or equal to (<=) comparison operation with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_lesser_equal(x, y) = [[ 0.,  0.,  0.],
[ 1.,  1.,  1.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_like(lhs=None, rhs=None, lhs_axes=_Null, rhs_axes=_Null, out=None, name=None, **kwargs)

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]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_logical_and(lhs=None, rhs=None, out=None, name=None, **kwargs)

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.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_logical_or(lhs=None, rhs=None, out=None, name=None, **kwargs)

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.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_logical_xor(lhs=None, rhs=None, out=None, name=None, **kwargs)

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.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_maximum(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns element-wise maximum of the input arrays with broadcasting.

This function compares two input arrays and returns a new array having the element-wise maxima.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_maximum(x, y) = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_minimum(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns element-wise minimum of the input arrays with broadcasting.

This function compares two input arrays and returns a new array having the element-wise minima.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_maximum(x, y) = [[ 0.,  0.,  0.],
[ 1.,  1.,  1.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_minus(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns element-wise difference of the input arrays with broadcasting.

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:

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_mod(lhs=None, rhs=None, out=None, name=None, **kwargs)

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.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_mul(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns element-wise product of the input arrays with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_mul(x, y) = [[ 0.,  0.,  0.],
[ 1.,  1.,  1.]]


Supported sparse operations:

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_not_equal(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns the result of element-wise not equal to (!=) comparison operation with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_not_equal(x, y) = [[ 1.,  1.,  1.],
[ 0.,  0.,  0.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_plus(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns element-wise sum of the input arrays with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

[ 2.,  2.,  2.]]

broadcast_plus(x, y) = [[ 1.,  1.,  1.],
[ 2.,  2.,  2.]]


Supported sparse operations:

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_power(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns result of first array elements raised to powers from second array, element-wise with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_power(x, y) = [[ 2.,  2.,  2.],
[ 4.,  4.,  4.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_sub(lhs=None, rhs=None, out=None, name=None, **kwargs)

Returns element-wise difference of the input arrays with broadcasting.

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:

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.broadcast_to(data=None, shape=_Null, out=None, name=None, **kwargs)

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.

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.cast(data=None, dtype=_Null, out=None, name=None, **kwargs)

Casts all elements of the input to a new type.

Note

Cast is deprecated. Use cast instead.

Example:

cast([0.9, 1.3], dtype='int32') = [0, 1]
cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]


Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L664

Parameters
• data (NDArray) – The input.

• dtype ({'bfloat16', 'bool', 'float16', 'float32', 'float64', 'int32', 'int64', 'int8', 'uint8'}, required) – Output data type.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.cast_storage(data=None, stype=_Null, out=None, name=None, **kwargs)

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 – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns element-wise cube-root value of the input.

$cbrt(x) = \sqrt[3]{x}$

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_pow.cc:L270

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns element-wise ceiling of the input.

The ceil of the scalar x is the smallest integer i, such that i >= x.

Example:

ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  2.,  2.,  3.]


The storage type of ceil output depends upon the input storage type:

• ceil(default) = default

• ceil(row_sparse) = row_sparse

• ceil(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L817

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.choose_element_0index(data=None, index=None, axis=_Null, keepdims=_Null, mode=_Null, out=None, name=None, **kwargs)

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.]

// 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.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.clip(data=None, a_min=_Null, a_max=_Null, out=None, name=None, **kwargs)

Clips (limits) the values in an array. Given an interval, values outside the interval are clipped to the interval edges. Clipping x between a_min and a_max would be:: .. math:

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:L677

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.col2im(data=None, output_size=_Null, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, out=None, name=None, **kwargs)

Combining the output column matrix of im2col back to image array.

Like im2col, this operator is also used in the vanilla convolution implementation. Despite the name, col2im is not the reverse operation of im2col. Since there may be overlaps between neighbouring sliding blocks, the column elements cannot be directly put back into image. Instead, they are accumulated (i.e., summed) in the input image just like the gradient computation, so col2im is the gradient of im2col and vice versa.

Using the notation in im2col, given an input column array of shape $$(N, C \times \prod(\text{kernel}), W)$$, this operator accumulates the column elements into output array of shape $$(N, C, \text{output_size}[0], \text{output_size}[1], \dots)$$. Only 1-D, 2-D and 3-D of spatial dimension is supported in this operator.

Defined in src/operator/nn/im2col.cc:L182

Parameters
• data (NDArray) – Input array to combine sliding blocks.

• output_size (Shape(tuple), required) – The spatial dimension of image array: (w,), (h, w) or (d, h, w).

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

• stride (Shape(tuple), optional, default=[]) – The stride between adjacent sliding blocks in spatial dimension: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.

• dilate (Shape(tuple), optional, default=[]) – The spacing between adjacent kernel points: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.

• pad (Shape(tuple), optional, default=[]) – The zero-value padding size on both sides of spatial dimension: (w,), (h, w) or (d, h, w). Defaults to no padding.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.concat(*data, **kwargs)

Joins input arrays along a given axis.

Note

Concat is deprecated. Use concat instead.

The dimensions of the input arrays should be the same except the axis along which they will be concatenated. The dimension of the output array along the concatenated axis will be equal to the sum of the corresponding dimensions of the input arrays.

The storage type of concat output depends on storage types of inputs

• concat(csr, csr, …, csr, dim=0) = csr

• otherwise, concat generates output with default storage

Example:

x = [[1,1],[2,2]]
y = [[3,3],[4,4],[5,5]]
z = [[6,6], [7,7],[8,8]]

concat(x,y,z,dim=0) = [[ 1.,  1.],
[ 2.,  2.],
[ 3.,  3.],
[ 4.,  4.],
[ 5.,  5.],
[ 6.,  6.],
[ 7.,  7.],
[ 8.,  8.]]

Note that you cannot concat x,y,z along dimension 1 since dimension
0 is not the same for all the input arrays.

concat(y,z,dim=1) = [[ 3.,  3.,  6.,  6.],
[ 4.,  4.,  7.,  7.],
[ 5.,  5.,  8.,  8.]]


Defined in src/operator/nn/concat.cc:L385

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

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

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Computes the element-wise cosine of the input array.

The input should be in radians ($$2\pi$$ rad equals 360 degrees).

$cos([0, \pi/4, \pi/2]) = [1, 0.707, 0]$

The storage type of cos output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L90

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns the hyperbolic cosine of the input array, computed element-wise.

$cosh(x) = 0.5\times(exp(x) + exp(-x))$

The storage type of cosh output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L409

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.crop(data=None, begin=_Null, end=_Null, step=_Null, out=None, name=None, **kwargs)

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:L482

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 – The output of this function.

Return type

NDArray or list of NDArrays

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

Connectionist Temporal Classification Loss.

Note

The existing alias contrib_CTCLoss is deprecated.

The shapes of the inputs and outputs:

• data: (sequence_length, batch_size, alphabet_size)

• label: (batch_size, label_sequence_length)

• out: (batch_size)

The data tensor consists of sequences of activation vectors (without applying softmax), with i-th channel in the last dimension corresponding to i-th label for i between 0 and alphabet_size-1 (i.e always 0-indexed). Alphabet size should include one additional value reserved for blank label. When blank_label is "first", the 0-th channel is be reserved for activation of blank label, or otherwise if it is “last”, (alphabet_size-1)-th channel should be reserved for blank label.

label is an index matrix of integers. When blank_label is "first", the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise, when blank_label is "last", the value (alphabet_size-1) is reserved for blank label.

If a sequence of labels is shorter than label_sequence_length, use the special padding value at the end of the sequence to conform it to the correct length. The padding value is 0 when blank_label is "first", and -1 otherwise.

For example, suppose the vocabulary is [a, b, c], and in one batch we have three sequences ‘ba’, ‘cbb’, and ‘abac’. When blank_label is "first", we can index the labels as {‘a’: 1, ‘b’: 2, ‘c’: 3}, and we reserve the 0-th channel for blank label in data tensor. The resulting label tensor should be padded to be:

[[2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3]]


When blank_label is "last", we can index the labels as {‘a’: 0, ‘b’: 1, ‘c’: 2}, and we reserve the channel index 3 for blank label in data tensor. The resulting label tensor should be padded to be:

[[1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2]]


out is a list of CTC loss values, one per example in the batch.

See Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks, A. Graves et al. for more information on the definition and the algorithm.

Defined in src/operator/nn/ctc_loss.cc:L100

Parameters
• data (NDArray) – Input ndarray

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

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

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

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

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

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

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.cumsum(a=None, axis=_Null, dtype=_Null, out=None, name=None, **kwargs)

Return the cumulative sum of the elements along a given axis.

Defined in src/operator/numpy/np_cumsum.cc:L70

Parameters
• a (NDArray) – Input ndarray

• axis (int or None, optional, default='None') – Axis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array.

• dtype ({None, 'float16', 'float32', 'float64', 'int32', 'int64', 'int8'},optional, default='None') – Type of the returned array and of the accumulator in which the elements are summed. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Converts each element of the input array from radians to degrees.

$degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360]$

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:L332

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.depth_to_space(data=None, block_size=_Null, out=None, name=None, **kwargs)

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 $$x$$ is an input tensor with default layout as $$[N, C, H, W]$$: [batch, channels, height, width] and $$y$$ is the output tensor of layout $$[N, C / (block\_size ^ 2), H * block\_size, W * block\_size]$$ 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:L972

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.diag(data=None, k=_Null, axis1=_Null, axis2=_Null, out=None, name=None, **kwargs)

Extracts a diagonal or constructs a diagonal array.

diag’s behavior depends on the input array dimensions:

• 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero.

• N-D arrays: extracts the diagonals of the sub-arrays with axes specified by axis1 and axis2. The output shape would be decided by removing the axes numbered axis1 and axis2 from the input shape and appending to the result a new axis with the size of the diagonals in question.

For example, when the input shape is (2, 3, 4, 5), axis1 and axis2 are 0 and 2 respectively and k is 0, the resulting shape would be (3, 5, 2).

Examples:

x = [[1, 2, 3],
[4, 5, 6]]

diag(x) = [1, 5]

diag(x, k=1) = [2, 6]

diag(x, k=-1) = [4]

x = [1, 2, 3]

diag(x) = [[1, 0, 0],
[0, 2, 0],
[0, 0, 3]]

diag(x, k=1) = [[0, 1, 0],
[0, 0, 2],
[0, 0, 0]]

diag(x, k=-1) = [[0, 0, 0],
[1, 0, 0],
[0, 2, 0]]

x = [[[1, 2],
[3, 4]],

[[5, 6],
[7, 8]]]

diag(x) = [[1, 7],
[2, 8]]

diag(x, k=1) = [[3],
[4]]

diag(x, axis1=-2, axis2=-1) = [[1, 4],
[5, 8]]


Defined in src/operator/tensor/diag_op.cc:L87

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.dot(lhs=None, rhs=None, transpose_a=_Null, transpose_b=_Null, forward_stype=_Null, out=None, name=None, **kwargs)

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.elemwise_add(lhs=None, rhs=None, out=None, name=None, **kwargs)

The storage type of elemwise_add output depends on storage types of inputs

• 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 – The output of this function.

Return type

NDArray or list of NDArrays

Example

>>> x = mx.nd.array([1, 2, 3, 4])
>>> y = mx.nd.array([1.1, 2.1, 3.1, 4.1])
array([ 2.0999999 ,  4.0999999 ,  6.0999999 ,  8.10000038], dtype=float32)

mxnet.ndarray.elemwise_div(lhs=None, rhs=None, out=None, name=None, **kwargs)

Divides 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.elemwise_mul(lhs=None, rhs=None, out=None, name=None, **kwargs)

Multiplies arguments element-wise.

The storage type of elemwise_mul output depends on storage types of inputs

• elemwise_mul(default, default) = default

• elemwise_mul(row_sparse, row_sparse) = row_sparse

• elemwise_mul(default, row_sparse) = row_sparse

• elemwise_mul(row_sparse, default) = row_sparse

• elemwise_mul(csr, csr) = csr

• otherwise, elemwise_mul generates output with default storage

Parameters
• lhs (NDArray) – first input

• rhs (NDArray) – second input

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.elemwise_sub(lhs=None, rhs=None, out=None, name=None, **kwargs)

Subtracts arguments element-wise.

The storage type of elemwise_sub output depends on storage types of inputs

• elemwise_sub(row_sparse, row_sparse) = row_sparse

• elemwise_sub(csr, csr) = csr

• elemwise_sub(default, csr) = default

• elemwise_sub(csr, default) = default

• elemwise_sub(default, rsp) = default

• elemwise_sub(rsp, default) = default

• otherwise, elemwise_sub generates output with default storage

Parameters
• lhs (NDArray) – first input

• rhs (NDArray) – second input

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns element-wise gauss error function of the input.

Example:

erf([0, -1., 10.]) = [0., -0.8427, 1.]


Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L886

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns element-wise inverse gauss error function of the input.

Example:

erfinv([0, 0.5., -1.]) = [0., 0.4769, -inf]


Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L908

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns element-wise exponential value of the input.

$exp(x) = e^x \approx 2.718^x$

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_logexp.cc:L64

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

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:L395

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.expm1(data=None, out=None, name=None, **kwargs)

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_logexp.cc:L244

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.fill_element_0index(lhs=None, mhs=None, rhs=None, out=None, name=None, **kwargs)

Fill one element of each line(row for python, column for R/Julia) in lhs according to index indicated by rhs and values indicated by mhs. This function assume rhs uses 0-based index.

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 – The output of this function.

Return type

NDArray or list of NDArrays

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

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:L874

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

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 behavior 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:L250

Parameters
• data (NDArray) – Input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Reverses the order of elements along given axis while preserving array shape. Note: reverse and flip are equivalent. We use reverse in the following examples. Examples:

x = [[ 0.,  1.,  2.,  3.,  4.],
[ 5.,  6.,  7.,  8.,  9.]]
reverse(x, axis=0) = [[ 5.,  6.,  7.,  8.,  9.],
[ 0.,  1.,  2.,  3.,  4.]]
reverse(x, axis=1) = [[ 4.,  3.,  2.,  1.,  0.],
[ 9.,  8.,  7.,  6.,  5.]]


Defined in src/operator/tensor/matrix_op.cc:L832

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 – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns element-wise floor of the input.

The floor of the scalar x is the largest integer i, such that i <= x.

Example:

floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2.,  1.,  1.,  2.]


The storage type of floor output depends upon the input storage type:

• floor(default) = default

• floor(row_sparse) = row_sparse

• floor(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L836

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.ftml_update(weight=None, grad=None, d=None, v=None, z=None, lr=_Null, beta1=_Null, beta2=_Null, epsilon=_Null, t=_Null, wd=_Null, rescale_grad=_Null, clip_grad=_Null, out=None, name=None, **kwargs)

The FTML optimizer described in FTML - Follow the Moving Leader in Deep Learning, available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.

$\begin{split}g_t = \nabla J(W_{t-1})\\ v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\ d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon) \sigma_t = d_t - \beta_1 d_{t-1} z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1} W_t = - \frac{ z_t }{ d_t }\end{split}$

Defined in src/operator/optimizer_op.cc:L640

Parameters
• weight (NDArray) – Weight

• 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=0.600000024) – Generally close to 0.5.

• beta2 (float, optional, default=0.999000013) – Generally close to 1.

• epsilon (double, optional, default=9.9999999392252903e-09) – 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.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.ftrl_update(weight=None, grad=None, z=None, n=None, lr=_Null, lamda1=_Null, beta=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, out=None, name=None, **kwargs)

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.

rescaled_grad = clip(grad * rescale_grad, clip_gradient)
z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate
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:
z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate
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:L876

Parameters
• weight (NDArray) – Weight

• z (NDArray) – z

• n (NDArray) – Square of grad

• lr (float, required) – Learning rate

• lamda1 (float, optional, default=0.00999999978) – 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.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns the gamma function (extension of the factorial function to the reals), computed element-wise on the input array.

The storage type of gamma output is always dense

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.gather_nd(data=None, indices=None, out=None, name=None, **kwargs)

Gather elements or slices from data and store to a tensor whose shape is defined by indices.

Given data with shape (X_0, X_1, …, X_{N-1}) and indices with shape (M, Y_0, …, Y_{K-1}), the output will have shape (Y_0, …, Y_{K-1}, X_M, …, X_{N-1}), where M <= N. If M == N, output shape will simply be (Y_0, …, Y_{K-1}).

The elements in output is defined as follows:

output[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] = data[indices[0, y_0, ..., y_{K-1}],
...,
indices[M-1, y_0, ..., y_{K-1}],
x_M, ..., x_{N-1}]


Examples:

data = [[0, 1], [2, 3]]
indices = [[1, 1, 0], [0, 1, 0]]
gather_nd(data, indices) = [2, 3, 0]

data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]
indices = [[0, 1], [1, 0]]
gather_nd(data, indices) = [[3, 4], [5, 6]]

Parameters
• data (NDArray) – data

• indices (NDArray) – indices

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.hard_sigmoid(data=None, alpha=_Null, beta=_Null, out=None, name=None, **kwargs)

Computes hard sigmoid of x element-wise.

$y = max(0, min(1, alpha * x + beta))$

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L161

Parameters
• data (NDArray) – The input array.

• alpha (float, optional, default=0.200000003) – 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 – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns a copy of the input.

From:src/operator/tensor/elemwise_unary_op_basic.cc:244

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.im2col(data=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, out=None, name=None, **kwargs)

Extract sliding blocks from input array.

This operator is used in vanilla convolution implementation to transform the sliding blocks on image to column matrix, then the convolution operation can be computed by matrix multiplication between column and convolution weight. Due to the close relation between im2col and convolution, the concept of kernel, stride, dilate and pad in this operator are inherited from convolution operation.

Given the input data of shape $$(N, C, *)$$, where $$N$$ is the batch size, $$C$$ is the channel size, and $$*$$ is the arbitrary spatial dimension, the output column array is always with shape $$(N, C \times \prod(\text{kernel}), W)$$, where $$C \times \prod(\text{kernel})$$ is the block size, and $$W$$ is the block number which is the spatial size of the convolution output with same input parameters. Only 1-D, 2-D and 3-D of spatial dimension is supported in this operator.

Defined in src/operator/nn/im2col.cc:L100

Parameters
• data (NDArray) – Input array to extract sliding blocks.

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

• stride (Shape(tuple), optional, default=[]) – The stride between adjacent sliding blocks in spatial dimension: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.

• dilate (Shape(tuple), optional, default=[]) – The spacing between adjacent kernel points: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.

• pad (Shape(tuple), optional, default=[]) – The zero-value padding size on both sides of spatial dimension: (w,), (h, w) or (d, h, w). Defaults to no padding.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.khatri_rao(*args, **kwargs)

Computes the Khatri-Rao product of the input matrices.

Given a collection of $$n$$ input matrices,

$A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N},$

the (column-wise) Khatri-Rao product is defined as the matrix,

$X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N},$

where the $$k$$ th column is equal to the column-wise outer product $${A_1}_k \otimes \cdots \otimes {A_n}_k$$ where $${A_i}_k$$ 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.lamb_update_phase1(weight=None, grad=None, mean=None, var=None, beta1=_Null, beta2=_Null, epsilon=_Null, t=_Null, bias_correction=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, out=None, name=None, **kwargs)

Phase I of lamb update it performs the following operations and returns g:.

\begin{align}\begin{aligned}\begin{gather*} grad = grad * rescale_grad if (grad < -clip_gradient) then grad = -clip_gradient if (grad > clip_gradient) then grad = clip_gradient\\mean = beta1 * mean + (1 - beta1) * grad; variance = beta2 * variance + (1. - beta2) * grad ^ 2;\\if (bias_correction) then mean_hat = mean / (1. - beta1^t); var_hat = var / (1 - beta2^t); g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight; else g = mean / (var_data^(1/2) + epsilon) + wd * weight; \end{gather*}\end{aligned}\end{align}

Defined in src/operator/optimizer_op.cc:L953

Parameters
• weight (NDArray) – Weight

• mean (NDArray) – Moving mean

• var (NDArray) – Moving variance

• beta1 (float, optional, default=0.899999976) – The decay rate for the 1st moment estimates.

• beta2 (float, optional, default=0.999000013) – The decay rate for the 2nd moment estimates.

• epsilon (float, optional, default=9.99999997e-07) – A small constant for numerical stability.

• t (int, required) – Index update count.

• bias_correction (boolean, optional, default=1) – Whether to use bias correction.

• wd (float, required) – 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.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.lamb_update_phase2(weight=None, g=None, r1=None, r2=None, lr=_Null, lower_bound=_Null, upper_bound=_Null, out=None, name=None, **kwargs)

Phase II of lamb update it performs the following operations and updates grad.

\begin{align}\begin{aligned}\begin{gather*} if (lower_bound >= 0) then r1 = max(r1, lower_bound) if (upper_bound >= 0) then r1 = max(r1, upper_bound)\\if (r1 == 0 or r2 == 0) then lr = lr else lr = lr * (r1/r2) weight = weight - lr * g \end{gather*}\end{aligned}\end{align}

Defined in src/operator/optimizer_op.cc:L992

Parameters
• weight (NDArray) – Weight

• g (NDArray) – Output of lamb_update_phase 1

• r1 (NDArray) – r1

• r2 (NDArray) – r2

• lr (float, required) – Learning rate

• lower_bound (float, optional, default=-1) – Lower limit of norm of weight. If lower_bound <= 0, Lower limit is not set

• upper_bound (float, optional, default=-1) – Upper limit of norm of weight. If upper_bound <= 0, Upper limit is not set

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_det(A=None, out=None, name=None, **kwargs)

Compute the determinant of a matrix. Input is a tensor A of dimension n >= 2.

If n=2, A is a square matrix. We compute:

out = det(A)

If n>2, det is performed separately on the trailing two dimensions for all inputs (batch mode).

Note

The operator supports float32 and float64 data types only.

Note

There is no gradient backwarded when A is non-invertible (which is equivalent to det(A) = 0) because zero is rarely hit upon in float point computation and the Jacobi’s formula on determinant gradient is not computationally efficient when A is non-invertible.

Examples:

Single matrix determinant
A = [[1., 4.], [2., 3.]]
det(A) = [-5.]

Batch matrix determinant
A = [[[1., 4.], [2., 3.]],
[[2., 3.], [1., 4.]]]
det(A) = [-5., 5.]


Defined in src/operator/tensor/la_op.cc:L975

Parameters
• A (NDArray) – Tensor of square matrix

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_extractdiag(A=None, offset=_Null, out=None, name=None, **kwargs)

Extracts the diagonal entries of a square matrix. Input is a tensor A of dimension n >= 2.

If n=2, then A represents a single square matrix which diagonal elements get extracted as a 1-dimensional tensor.

If n>2, then A represents a batch of square matrices on the trailing two dimensions. The extracted diagonals are returned as an n-1-dimensional tensor.

Note

The operator supports float32 and float64 data types only.

Examples:

Single matrix diagonal extraction
A = [[1.0, 2.0],
[3.0, 4.0]]

extractdiag(A) = [1.0, 4.0]

extractdiag(A, 1) = [2.0]

Batch matrix diagonal extraction
A = [[[1.0, 2.0],
[3.0, 4.0]],
[[5.0, 6.0],
[7.0, 8.0]]]

extractdiag(A) = [[1.0, 4.0],
[5.0, 8.0]]


Defined in src/operator/tensor/la_op.cc:L495

Parameters
• A (NDArray) – Tensor of square matrices

• offset (int, optional, default='0') – Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_extracttrian(A=None, offset=_Null, lower=_Null, out=None, name=None, **kwargs)

Extracts a triangular sub-matrix from a square matrix. Input is a tensor A of dimension n >= 2.

If n=2, then A represents a single square matrix from which a triangular sub-matrix is extracted as a 1-dimensional tensor.

If n>2, then A represents a batch of square matrices on the trailing two dimensions. The extracted triangular sub-matrices are returned as an n-1-dimensional tensor.

The offset and lower parameters determine the triangle to be extracted:

• When offset = 0 either the lower or upper triangle with respect to the main diagonal is extracted depending on the value of parameter lower.

• When offset = k > 0 the upper triangle with respect to the k-th diagonal above the main diagonal is extracted.

• When offset = k < 0 the lower triangle with respect to the k-th diagonal below the main diagonal is extracted.

Note

The operator supports float32 and float64 data types only.

Examples:

Single triagonal extraction
A = [[1.0, 2.0],
[3.0, 4.0]]

extracttrian(A) = [1.0, 3.0, 4.0]
extracttrian(A, lower=False) = [1.0, 2.0, 4.0]
extracttrian(A, 1) = [2.0]
extracttrian(A, -1) = [3.0]

Batch triagonal extraction
A = [[[1.0, 2.0],
[3.0, 4.0]],
[[5.0, 6.0],
[7.0, 8.0]]]

extracttrian(A) = [[1.0, 3.0, 4.0],
[5.0, 7.0, 8.0]]


Defined in src/operator/tensor/la_op.cc:L605

Parameters
• A (NDArray) – Tensor of square matrices

• offset (int, optional, default='0') – Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.

• lower (boolean, optional, default=1) – Refer to the lower triangular matrix if lower=true, refer to the upper otherwise. Only relevant when offset=0

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_gelqf(A=None, out=None, name=None, **kwargs)

LQ factorization for general matrix. Input is a tensor A of dimension n >= 2.

If n=2, we compute the LQ factorization (LAPACK gelqf, followed by orglq). A must have shape (x, y) with x <= y, and must have full rank =x. The LQ factorization consists of L with shape (x, x) and Q with shape (x, y), so that:

A = L * Q

Here, L is lower triangular (upper triangle equal to zero) with nonzero diagonal, and Q is row-orthonormal, meaning that

Q * QT

is equal to the identity matrix of shape (x, x).

If n>2, gelqf is performed separately on the trailing two dimensions for all inputs (batch mode).

Note

The operator supports float32 and float64 data types only.

Examples:

Single LQ factorization
A = [[1., 2., 3.], [4., 5., 6.]]
Q, L = gelqf(A)
Q = [[-0.26726124, -0.53452248, -0.80178373],
[0.87287156, 0.21821789, -0.43643578]]
L = [[-3.74165739, 0.],
[-8.55235974, 1.96396101]]

Batch LQ factorization
A = [[[1., 2., 3.], [4., 5., 6.]],
[[7., 8., 9.], [10., 11., 12.]]]
Q, L = gelqf(A)
Q = [[[-0.26726124, -0.53452248, -0.80178373],
[0.87287156, 0.21821789, -0.43643578]],
[[-0.50257071, -0.57436653, -0.64616234],
[0.7620735, 0.05862104, -0.64483142]]]
L = [[[-3.74165739, 0.],
[-8.55235974, 1.96396101]],
[[-13.92838828, 0.],
[-19.09768702, 0.52758934]]]


Defined in src/operator/tensor/la_op.cc:L798

Parameters
• A (NDArray) – Tensor of input matrices to be factorized

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_gemm(A=None, B=None, C=None, transpose_a=_Null, transpose_b=_Null, alpha=_Null, beta=_Null, axis=_Null, out=None, name=None, **kwargs)

Performs general matrix multiplication and accumulation. Input are tensors A, B, C, each of dimension n >= 2 and having the same shape on the leading n-2 dimensions.

If n=2, the BLAS3 function gemm is performed:

out = alpha * op(A) * op(B) + beta * C

Here, alpha and beta are scalar parameters, and op() is either the identity or matrix transposition (depending on transpose_a, transpose_b).

If n>2, gemm is performed separately for a batch of matrices. The column indices of the matrices are given by the last dimensions of the tensors, the row indices by the axis specified with the axis parameter. By default, the trailing two dimensions will be used for matrix encoding.

For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes calls. For example let A, B, C be 5 dimensional tensors. Then gemm(A, B, C, axis=1) is equivalent to the following without the overhead of the additional swapaxis operations:

A1 = swapaxes(A, dim1=1, dim2=3)
B1 = swapaxes(B, dim1=1, dim2=3)
C = swapaxes(C, dim1=1, dim2=3)
C = gemm(A1, B1, C)
C = swapaxis(C, dim1=1, dim2=3)


When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use pseudo-float16 precision (float32 math with float16 I/O) precision in order to use Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.

Note

The operator supports float32 and float64 data types only.

Examples:

Single matrix multiply-add
A = [[1.0, 1.0], [1.0, 1.0]]
B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
C = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0)
= [[14.0, 14.0, 14.0], [14.0, 14.0, 14.0]]

A = [[[1.0, 1.0]], [[0.1, 0.1]]]
B = [[[1.0, 1.0]], [[0.1, 0.1]]]
C = [[[10.0]], [[0.01]]]
gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0)
= [[[104.0]], [[0.14]]]


Defined in src/operator/tensor/la_op.cc:L89

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_gemm2(A=None, B=None, transpose_a=_Null, transpose_b=_Null, alpha=_Null, axis=_Null, out=None, name=None, **kwargs)

Performs general matrix multiplication. Input are tensors A, B, each of dimension n >= 2 and having the same shape on the leading n-2 dimensions.

If n=2, the BLAS3 function gemm is performed:

out = alpha * op(A) * op(B)

Here alpha is a scalar parameter and op() is either the identity or the matrix transposition (depending on transpose_a, transpose_b).

If n>2, gemm is performed separately for a batch of matrices. The column indices of the matrices are given by the last dimensions of the tensors, the row indices by the axis specified with the axis parameter. By default, the trailing two dimensions will be used for matrix encoding.

For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes calls. For example let A, B be 5 dimensional tensors. Then gemm(A, B, axis=1) is equivalent to the following without the overhead of the additional swapaxis operations:

A1 = swapaxes(A, dim1=1, dim2=3)
B1 = swapaxes(B, dim1=1, dim2=3)
C = gemm2(A1, B1)
C = swapaxis(C, dim1=1, dim2=3)


When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use pseudo-float16 precision (float32 math with float16 I/O) precision in order to use Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.

Note

The operator supports float32 and float64 data types only.

Examples:

Single matrix multiply
A = [[1.0, 1.0], [1.0, 1.0]]
B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
gemm2(A, B, transpose_b=True, alpha=2.0)
= [[4.0, 4.0, 4.0], [4.0, 4.0, 4.0]]

Batch matrix multiply
A = [[[1.0, 1.0]], [[0.1, 0.1]]]
B = [[[1.0, 1.0]], [[0.1, 0.1]]]
gemm2(A, B, transpose_b=True, alpha=2.0)
= [[[4.0]], [[0.04 ]]]


Defined in src/operator/tensor/la_op.cc:L163

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_inverse(A=None, out=None, name=None, **kwargs)

Compute the inverse of a matrix. Input is a tensor A of dimension n >= 2.

If n=2, A is a square matrix. We compute:

out = A-1

If n>2, inverse is performed separately on the trailing two dimensions for all inputs (batch mode).

Note

The operator supports float32 and float64 data types only.

Examples:

Single matrix inverse
A = [[1., 4.], [2., 3.]]
inverse(A) = [[-0.6, 0.8], [0.4, -0.2]]

Batch matrix inverse
A = [[[1., 4.], [2., 3.]],
[[1., 3.], [2., 4.]]]
inverse(A) = [[[-0.6, 0.8], [0.4, -0.2]],
[[-2., 1.5], [1., -0.5]]]


Defined in src/operator/tensor/la_op.cc:L920

Parameters
• A (NDArray) – Tensor of square matrix

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_makediag(A=None, offset=_Null, out=None, name=None, **kwargs)

Constructs a square matrix with the input as diagonal. Input is a tensor A of dimension n >= 1.

If n=1, then A represents the diagonal entries of a single square matrix. This matrix will be returned as a 2-dimensional tensor. If n>1, then A represents a batch of diagonals of square matrices. The batch of diagonal matrices will be returned as an n+1-dimensional tensor.

Note

The operator supports float32 and float64 data types only.

Examples:

Single diagonal matrix construction
A = [1.0, 2.0]

makediag(A)    = [[1.0, 0.0],
[0.0, 2.0]]

makediag(A, 1) = [[0.0, 1.0, 0.0],
[0.0, 0.0, 2.0],
[0.0, 0.0, 0.0]]

Batch diagonal matrix construction
A = [[1.0, 2.0],
[3.0, 4.0]]

makediag(A) = [[[1.0, 0.0],
[0.0, 2.0]],
[[3.0, 0.0],
[0.0, 4.0]]]


Defined in src/operator/tensor/la_op.cc:L547

Parameters
• A (NDArray) – Tensor of diagonal entries

• offset (int, optional, default='0') – Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_maketrian(A=None, offset=_Null, lower=_Null, out=None, name=None, **kwargs)

Constructs a square matrix with the input representing a specific triangular sub-matrix. This is basically the inverse of linalg.extracttrian. Input is a tensor A of dimension n >= 1.

If n=1, then A represents the entries of a triangular matrix which is lower triangular if offset<0 or offset=0, lower=true. The resulting matrix is derived by first constructing the square matrix with the entries outside the triangle set to zero and then adding offset-times an additional diagonal with zero entries to the square matrix.

If n>1, then A represents a batch of triangular sub-matrices. The batch of corresponding square matrices is returned as an n+1-dimensional tensor.

Note

The operator supports float32 and float64 data types only.

Examples:

Single  matrix construction
A = [1.0, 2.0, 3.0]

maketrian(A)              = [[1.0, 0.0],
[2.0, 3.0]]

maketrian(A, lower=false) = [[1.0, 2.0],
[0.0, 3.0]]

maketrian(A, offset=1)    = [[0.0, 1.0, 2.0],
[0.0, 0.0, 3.0],
[0.0, 0.0, 0.0]]
maketrian(A, offset=-1)   = [[0.0, 0.0, 0.0],
[1.0, 0.0, 0.0],
[2.0, 3.0, 0.0]]

Batch matrix construction
A = [[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0]]

maketrian(A)           = [[[1.0, 0.0],
[2.0, 3.0]],
[[4.0, 0.0],
[5.0, 6.0]]]

maketrian(A, offset=1) = [[[0.0, 1.0, 2.0],
[0.0, 0.0, 3.0],
[0.0, 0.0, 0.0]],
[[0.0, 4.0, 5.0],
[0.0, 0.0, 6.0],
[0.0, 0.0, 0.0]]]


Defined in src/operator/tensor/la_op.cc:L673

Parameters
• A (NDArray) – Tensor of triangular matrices stored as vectors

• offset (int, optional, default='0') – Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.

• lower (boolean, optional, default=1) – Refer to the lower triangular matrix if lower=true, refer to the upper otherwise. Only relevant when offset=0

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_potrf(A=None, out=None, name=None, **kwargs)

Performs Cholesky factorization of a symmetric positive-definite matrix. Input is a tensor A of dimension n >= 2.

If n=2, the Cholesky factor B of the symmetric, positive definite matrix A is computed. B is triangular (entries of upper or lower triangle are all zero), has positive diagonal entries, and:

A = B * BT if lower = true A = BT * B if lower = false

If n>2, potrf is performed separately on the trailing two dimensions for all inputs (batch mode).

Note

The operator supports float32 and float64 data types only.

Examples:

Single matrix factorization
A = [[4.0, 1.0], [1.0, 4.25]]
potrf(A) = [[2.0, 0], [0.5, 2.0]]

Batch matrix factorization
A = [[[4.0, 1.0], [1.0, 4.25]], [[16.0, 4.0], [4.0, 17.0]]]
potrf(A) = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]


Defined in src/operator/tensor/la_op.cc:L214

Parameters
• A (NDArray) – Tensor of input matrices to be decomposed

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_potri(A=None, out=None, name=None, **kwargs)

Performs matrix inversion from a Cholesky factorization. Input is a tensor A of dimension n >= 2.

If n=2, A is a triangular matrix (entries of upper or lower triangle are all zero) with positive diagonal. We compute:

out = A-T * A-1 if lower = true out = A-1 * A-T if lower = false

In other words, if A is the Cholesky factor of a symmetric positive definite matrix B (obtained by potrf), then

out = B-1

If n>2, potri is performed separately on the trailing two dimensions for all inputs (batch mode).

Note

The operator supports float32 and float64 data types only.

Note

Use this operator only if you are certain you need the inverse of B, and cannot use the Cholesky factor A (potrf), together with backsubstitution (trsm). The latter is numerically much safer, and also cheaper.

Examples:

Single matrix inverse
A = [[2.0, 0], [0.5, 2.0]]
potri(A) = [[0.26563, -0.0625], [-0.0625, 0.25]]

Batch matrix inverse
A = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
potri(A) = [[[0.26563, -0.0625], [-0.0625, 0.25]],
[[0.06641, -0.01562], [-0.01562, 0,0625]]]


Defined in src/operator/tensor/la_op.cc:L275

Parameters
• A (NDArray) – Tensor of lower triangular matrices

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_slogdet(A=None, out=None, name=None, **kwargs)

Compute the sign and log of the determinant of a matrix. Input is a tensor A of dimension n >= 2.

If n=2, A is a square matrix. We compute:

sign = sign(det(A)) logabsdet = log(abs(det(A)))

If n>2, slogdet is performed separately on the trailing two dimensions for all inputs (batch mode).

Note

The operator supports float32 and float64 data types only.

Note

The gradient is not properly defined on sign, so the gradient of it is not backwarded.

Note

No gradient is backwarded when A is non-invertible. Please see the docs of operator det for detail.

Examples:

Single matrix signed log determinant
A = [[2., 3.], [1., 4.]]
sign, logabsdet = slogdet(A)
sign = [1.]
logabsdet = [1.609438]

Batch matrix signed log determinant
A = [[[2., 3.], [1., 4.]],
[[1., 2.], [2., 4.]],
[[1., 2.], [4., 3.]]]
sign, logabsdet = slogdet(A)
sign = [1., 0., -1.]
logabsdet = [1.609438, -inf, 1.609438]


Defined in src/operator/tensor/la_op.cc:L1034

Parameters
• A (NDArray) – Tensor of square matrix

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_sumlogdiag(A=None, out=None, name=None, **kwargs)

Computes the sum of the logarithms of the diagonal elements of a square matrix. Input is a tensor A of dimension n >= 2.

If n=2, A must be square with positive diagonal entries. We sum the natural logarithms of the diagonal elements, the result has shape (1,).

If n>2, sumlogdiag is performed separately on the trailing two dimensions for all inputs (batch mode).

Note

The operator supports float32 and float64 data types only.

Examples:

Single matrix reduction
A = [[1.0, 1.0], [1.0, 7.0]]
sumlogdiag(A) = [1.9459]

Batch matrix reduction
A = [[[1.0, 1.0], [1.0, 7.0]], [[3.0, 0], [0, 17.0]]]
sumlogdiag(A) = [1.9459, 3.9318]


Defined in src/operator/tensor/la_op.cc:L445

Parameters
• A (NDArray) – Tensor of square matrices

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_syrk(A=None, transpose=_Null, alpha=_Null, out=None, name=None, **kwargs)

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 * AT

if transpose=False, or

out = alpha * AT * A

if transpose=True.

If n>2, syrk is performed separately on the trailing two dimensions for all inputs (batch mode).

Note

The operator supports float32 and float64 data types only.

Examples:

Single matrix multiply
A = [[1., 2., 3.], [4., 5., 6.]]
syrk(A, alpha=1., transpose=False)
= [[14., 32.],
[32., 77.]]
syrk(A, alpha=1., transpose=True)
= [[17., 22., 27.],
[22., 29., 36.],
[27., 36., 45.]]

Batch matrix multiply
A = [[[1., 1.]], [[0.1, 0.1]]]
syrk(A, alpha=2., transpose=False) = [[[4.]], [[0.04]]]


Defined in src/operator/tensor/la_op.cc:L730

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_trmm(A=None, B=None, transpose=_Null, rightside=_Null, lower=_Null, alpha=_Null, out=None, name=None, **kwargs)

Performs multiplication with a lower triangular matrix. Input are tensors A, B, each of dimension n >= 2 and having the same shape on the leading n-2 dimensions.

If n=2, A must be triangular. The operator performs the BLAS3 function trmm:

out = alpha * op(A) * B

if rightside=False, or

out = alpha * B * op(A)

if rightside=True. Here, alpha is a scalar parameter, and op() is either the identity or the matrix transposition (depending on transpose).

If n>2, trmm is performed separately on the trailing two dimensions for all inputs (batch mode).

Note

The operator supports float32 and float64 data types only.

Examples:

Single triangular matrix multiply
A = [[1.0, 0], [1.0, 1.0]]
B = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
trmm(A, B, alpha=2.0) = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]

Batch triangular matrix multiply
A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
B = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], [[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]]]
trmm(A, B, alpha=2.0) = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
[[1.0, 1.0, 1.0], [2.0, 2.0, 2.0]]]


Defined in src/operator/tensor/la_op.cc:L333

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.

• lower (boolean, optional, default=1) – True if the triangular matrix is lower triangular, false if it is upper triangular.

• 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.linalg_trsm(A=None, B=None, transpose=_Null, rightside=_Null, lower=_Null, alpha=_Null, out=None, name=None, **kwargs)

Solves matrix equation involving a lower triangular matrix. Input are tensors A, B, each of dimension n >= 2 and having the same shape on the leading n-2 dimensions.

If n=2, A must be triangular. The operator performs the BLAS3 function trsm, solving for out in:

op(A) * out = alpha * B

if rightside=False, or

out * op(A) = alpha * B

if rightside=True. Here, alpha is a scalar parameter, and op() is either the identity or the matrix transposition (depending on transpose).

If n>2, trsm is performed separately on the trailing two dimensions for all inputs (batch mode).

Note

The operator supports float32 and float64 data types only.

Examples:

Single matrix solve
A = [[1.0, 0], [1.0, 1.0]]
B = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]
trsm(A, B, alpha=0.5) = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]

Batch matrix solve
A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
B = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
[[4.0, 4.0, 4.0], [8.0, 8.0, 8.0]]]
trsm(A, B, alpha=0.5) = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]],
[[2.0, 2.0, 2.0], [2.0, 2.0, 2.0]]]


Defined in src/operator/tensor/la_op.cc:L396

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.

• lower (boolean, optional, default=1) – True if the triangular matrix is lower triangular, false if it is upper triangular.

• 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 – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns element-wise Natural logarithmic value of the input.

The natural logarithm is logarithm in base e, so that log(exp(x)) = x

The storage type of log output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L77

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.log10(data=None, out=None, name=None, **kwargs)

Returns element-wise Base-10 logarithmic value of the input.

10**log10(x) = x

The storage type of log10 output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L94

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.log1p(data=None, out=None, name=None, **kwargs)

Returns element-wise log(1 + x) value of the input.

This function is more accurate than log(1 + x) for small x so that $$1+x\approx 1$$

The storage type of log1p output depends upon the input storage type:

• log1p(default) = default

• log1p(row_sparse) = row_sparse

• log1p(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L199

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.log2(data=None, out=None, name=None, **kwargs)

Returns element-wise Base-2 logarithmic value of the input.

2**log2(x) = x

The storage type of log2 output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L106

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.log_softmax(data=None, axis=_Null, temperature=_Null, dtype=_Null, use_length=_Null, out=None, name=None, **kwargs)

Computes the log softmax of the input. This is equivalent to computing softmax followed by log.

Examples:

>>> x = mx.nd.array([1, 2, .1])
>>> mx.nd.log_softmax(x).asnumpy()
array([-1.41702998, -0.41702995, -2.31702995], dtype=float32)

>>> x = mx.nd.array( [[1, 2, .1],[.1, 2, 1]] )
>>> mx.nd.log_softmax(x, axis=0).asnumpy()
array([[-0.34115392, -0.69314718, -1.24115396],
[-1.24115396, -0.69314718, -0.34115392]], dtype=float32)

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

• dtype ({None, 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to the same as input’s dtype if not defined (dtype=None).

• use_length (boolean or None, optional, default=0) – Whether to use the length input as a mask over the data input.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

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

Returns 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 – The output of this function.

Return type

NDArray or list of NDArrays

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

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:L358

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.max(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)

Computes the max of array elements over given axes.

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.max_axis(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)

Computes the max of array elements over given axes.

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.mean(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)

Computes the mean of array elements over given axes.

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.min(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)

Computes the min of array elements over given axes.

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.min_axis(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)

Computes the min of array elements over given axes.

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.moments(data=None, axes=_Null, keepdims=_Null, out=None, name=None, **kwargs)

Calculate the mean and variance of data.

The mean and variance are calculated by aggregating the contents of data across axes. If x is 1-D and axes = [0] this is just the mean and variance of a vector.

Example

x = [[1, 2, 3], [4, 5, 6]] mean, var = moments(data=x, axes=[0]) mean = [2.5, 3.5, 4.5] var = [2.25, 2.25, 2.25] mean, var = moments(data=x, axes=[1]) mean = [2.0, 5.0] var = [0.66666667, 0.66666667] mean, var = moments(data=x, axis=[0, 1]) mean = [3.5] var = [2.9166667]

Defined in src/operator/nn/moments.cc:L54

Parameters
• data (NDArray) – Input ndarray

• axes (Shape or None, optional, default=None) – Array of ints. Axes along which to compute mean and variance.

• keepdims (boolean, optional, default=0) – produce moments with the same dimensionality as the input.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.mp_lamb_update_phase1(weight=None, grad=None, mean=None, var=None, weight32=None, beta1=_Null, beta2=_Null, epsilon=_Null, t=_Null, bias_correction=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, out=None, name=None, **kwargs)

Mixed Precision version of Phase I of lamb update it performs the following operations and returns g:.

\begin{align}\begin{aligned}\begin{gather*} grad32 = grad(float16) * rescale_grad if (grad < -clip_gradient) then grad = -clip_gradient if (grad > clip_gradient) then grad = clip_gradient\\mean = beta1 * mean + (1 - beta1) * grad; variance = beta2 * variance + (1. - beta2) * grad ^ 2;\\if (bias_correction) then mean_hat = mean / (1. - beta1^t); var_hat = var / (1 - beta2^t); g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight32; else g = mean / (var_data^(1/2) + epsilon) + wd * weight32; \end{gather*}\end{aligned}\end{align}

Defined in src/operator/optimizer_op.cc:L1033

Parameters
• weight (NDArray) – Weight

• mean (NDArray) – Moving mean

• var (NDArray) – Moving variance

• weight32 (NDArray) – Weight32

• beta1 (float, optional, default=0.899999976) – The decay rate for the 1st moment estimates.

• beta2 (float, optional, default=0.999000013) – The decay rate for the 2nd moment estimates.

• epsilon (float, optional, default=9.99999997e-07) – A small constant for numerical stability.

• t (int, required) – Index update count.

• bias_correction (boolean, optional, default=1) – Whether to use bias correction.

• wd (float, required) – 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.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.mp_lamb_update_phase2(weight=None, g=None, r1=None, r2=None, weight32=None, lr=_Null, lower_bound=_Null, upper_bound=_Null, out=None, name=None, **kwargs)

Mixed Precision version Phase II of lamb update it performs the following operations and updates grad.

\begin{align}\begin{aligned}\begin{gather*} if (lower_bound >= 0) then r1 = max(r1, lower_bound) if (upper_bound >= 0) then r1 = max(r1, upper_bound)\\if (r1 == 0 or r2 == 0) then lr = lr else lr = lr * (r1/r2) weight32 = weight32 - lr * g weight(float16) = weight32 \end{gather*}\end{aligned}\end{align}

Defined in src/operator/optimizer_op.cc:L1075

Parameters
• weight (NDArray) – Weight

• g (NDArray) – Output of mp_lamb_update_phase 1

• r1 (NDArray) – r1

• r2 (NDArray) – r2

• weight32 (NDArray) – Weight32

• lr (float, required) – Learning rate

• lower_bound (float, optional, default=-1) – Lower limit of norm of weight. If lower_bound <= 0, Lower limit is not set

• upper_bound (float, optional, default=-1) – Upper limit of norm of weight. If upper_bound <= 0, Upper limit is not set

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.mp_nag_mom_update(weight=None, grad=None, mom=None, weight32=None, lr=_Null, momentum=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, out=None, name=None, **kwargs)

Update function for multi-precision Nesterov Accelerated Gradient( NAG) optimizer.

Defined in src/operator/optimizer_op.cc:L745

Parameters
• weight (NDArray) – Weight

• 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.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.mp_sgd_mom_update(weight=None, grad=None, mom=None, weight32=None, lr=_Null, momentum=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, lazy_update=_Null, out=None, name=None, **kwargs)

Updater function for multi-precision sgd optimizer

Parameters
• weight (NDArray) – Weight

• 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.

• 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.mp_sgd_update(weight=None, grad=None, weight32=None, lr=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, lazy_update=_Null, out=None, name=None, **kwargs)

Updater function for multi-precision sgd optimizer

Parameters
• weight (NDArray) – Weight

• 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.

• 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.multi_all_finite(*data, **kwargs)

Check if all the float numbers in all the arrays are finite (used for AMP)

Defined in src/operator/contrib/all_finite.cc:L133

Parameters
• data (NDArray[]) – Arrays

• num_arrays (int, optional, default='1') – Number of arrays.

• init_output (boolean, optional, default=1) – Initialize output to 1.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.multi_lars(lrs=None, weights_sum_sq=None, grads_sum_sq=None, wds=None, eta=_Null, eps=_Null, rescale_grad=_Null, out=None, name=None, **kwargs)

Compute the LARS coefficients of multiple weights and grads from their sums of square”

Defined in src/operator/contrib/multi_lars.cc:L37

Parameters
• lrs (NDArray) – Learning rates to scale by LARS coefficient

• weights_sum_sq (NDArray) – sum of square of weights arrays

• wds (NDArray) – weight decays

• eta (float, required) – LARS eta

• eps (float, required) – LARS eps

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.multi_mp_sgd_mom_update(*data, **kwargs)

Momentum update function for multi-precision Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks like below:

$\begin{split}v_1 = \alpha * \nabla J(W_0)\\ v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\ W_t = W_{t-1} + v_t\end{split}$

v = momentum * v - learning_rate * gradient
weight += v


Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Defined in src/operator/optimizer_op.cc:L472

Parameters
• data (NDArray[]) – Weights

• lrs (tuple of <float>, required) – Learning rates.

• wds (tuple of <float>, required) – 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.

• momentum (float, optional, default=0) – The decay rate of momentum estimates at each epoch.

• num_weights (int, optional, default='1') – Number of updated weights.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.multi_mp_sgd_update(*data, **kwargs)

Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.

weight = weight - learning_rate * (gradient + wd * weight)


Defined in src/operator/optimizer_op.cc:L417

Parameters
• data (NDArray[]) – Weights

• lrs (tuple of <float>, required) – Learning rates.

• wds (tuple of <float>, required) – 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.

• num_weights (int, optional, default='1') – Number of updated weights.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.multi_sgd_mom_update(*data, **kwargs)

Momentum update function for Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks like below:

$\begin{split}v_1 = \alpha * \nabla J(W_0)\\ v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\ W_t = W_{t-1} + v_t\end{split}$

v = momentum * v - learning_rate * gradient
weight += v


Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Defined in src/operator/optimizer_op.cc:L374

Parameters
• data (NDArray[]) – Weights, gradients and momentum

• lrs (tuple of <float>, required) – Learning rates.

• wds (tuple of <float>, required) – 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.

• momentum (float, optional, default=0) – The decay rate of momentum estimates at each epoch.

• num_weights (int, optional, default='1') – Number of updated weights.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.multi_sgd_update(*data, **kwargs)

Update function for Stochastic Gradient Descent (SDG) optimizer.

weight = weight - learning_rate * (gradient + wd * weight)


Defined in src/operator/optimizer_op.cc:L329

Parameters
• data (NDArray[]) – Weights

• lrs (tuple of <float>, required) – Learning rates.

• wds (tuple of <float>, required) – 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.

• num_weights (int, optional, default='1') – Number of updated weights.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.multi_sum_sq(*data, **kwargs)

Compute the sums of squares of multiple arrays

Defined in src/operator/contrib/multi_sum_sq.cc:L36

Parameters
• data (NDArray[]) – Arrays

• num_arrays (int, required) – number of input arrays.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.nag_mom_update(weight=None, grad=None, mom=None, lr=_Null, momentum=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, out=None, name=None, **kwargs)

Update function for Nesterov Accelerated Gradient( NAG) optimizer. It updates the weights using the following formula,

$\begin{split}v_t = \gamma v_{t-1} + \eta * \nabla J(W_{t-1} - \gamma v_{t-1})\\ W_t = W_{t-1} - v_t\end{split}$

Where $$\eta$$ is the learning rate of the optimizer $$\gamma$$ is the decay rate of the momentum estimate $$\v_t$$ is the update vector at time step t $$\W_t$$ is the weight vector at time step t

Defined in src/operator/optimizer_op.cc:L726

Parameters
• weight (NDArray) – Weight

• 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.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.nanprod(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)

Computes the product of array elements over given axes treating Not a Numbers (NaN) as one.

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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.nansum(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)

Computes the sum of array elements over given axes treating Not a Numbers (NaN) as zero.

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 – The output of this function.

Return type

NDArray or list of NDArrays

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

Numerical negative of the argument, element-wise.

The storage type of negative output depends upon the input storage type:

• negative(default) = default

• negative(row_sparse) = row_sparse

• negative(csr) = csr

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.norm(data=None, ord=_Null, axis=_Null, out_dtype=_Null, keepdims=_Null, out=None, name=None, **kwargs)

Computes the norm on an NDArray.

This operator computes the norm on an NDArray with the specified axis, depending on the value of the ord parameter. By default, it computes the L2 norm on the entire array. Currently only ord=2 supports sparse ndarrays.

Examples:

x = [[[1, 2],
[3, 4]],
[[2, 2],
[5, 6]]]

norm(x, ord=2, axis=1) = [[3.1622777 4.472136 ]
[5.3851647 6.3245554]]

norm(x, ord=1, axis=1) = [[4., 6.],
[7., 8.]]

rsp = x.cast_storage('row_sparse')

norm(rsp) = [5.47722578]

csr = x.cast_storage('csr')

norm(csr) = [5.47722578]


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.

• out_dtype ({None, 'float16', 'float32', 'float64', 'int32', 'int64', 'int8'},optional, default='None') – The data type of the output.

• 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.normal(loc=_Null, scale=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)

Draw random samples from a normal (Gaussian) distribution.

Note

The existing alias normal is deprecated.

Samples are distributed according to a normal distribution parametrized by loc (mean) and scale (standard deviation).

Example:

normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
[-1.23474145,  1.55807114]]


Defined in src/operator/random/sample_op.cc:L113

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=None) – 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.one_hot(indices=None, depth=_Null, on_value=_Null, off_value=_Null, dtype=_Null, out=None, name=None, **kwargs)

Returns a one-hot array.

The locations represented by indices take value on_value, while all other locations take value off_value.

one_hot operation with indices of shape (i0, i1) and depth of d would result in an output array of shape (i0, i1, d) with:

output[i,j,:] = off_value
output[i,j,indices[i,j]] = on_value


Examples:

one_hot([1,0,2,0], 3) = [[ 0.  1.  0.]
[ 1.  0.  0.]
[ 0.  0.  1.]
[ 1.  0.  0.]]

one_hot([1,0,2,0], 3, on_value=8, off_value=1,
dtype='int32') = [[1 8 1]
[8 1 1]
[1 1 8]
[8 1 1]]

one_hot([[1,0],[1,0],[2,0]], 3) = [[[ 0.  1.  0.]
[ 1.  0.  0.]]

[[ 0.  1.  0.]
[ 1.  0.  0.]]

[[ 0.  0.  1.]
[ 1.  0.  0.]]]


Defined in src/operator/tensor/indexing_op.cc:L883

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 ({'bfloat16', '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 – The output of this function.

Return type

NDArray or list of NDArrays

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

Return an array of ones with the same shape and type as the input array.

Examples:

x = [[ 0.,  0.,  0.],
[ 0.,  0.,  0.]]

ones_like(x) = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

Parameters
• data (NDArray) – The input

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.pad(data=None, mode=_Null, pad_width=_Null, constant_value=_Null, out=None, name=None, **kwargs)

Pads an input array with a constant or edge values of the array.

Note

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.]]]]

[[[[  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.]]]]

[[[[  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.]]]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.pick(data=None, index=None, axis=_Null, keepdims=_Null, mode=_Null, out=None, name=None, **kwargs)

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.]

// 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.]]


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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.preloaded_multi_mp_sgd_mom_update(*data, **kwargs)

Momentum update function for multi-precision Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks like below:

$\begin{split}v_1 = \alpha * \nabla J(W_0)\\ v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\ W_t = W_{t-1} + v_t\end{split}$

v = momentum * v - learning_rate * gradient
weight += v


Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Parameters
• data (NDArray[]) – Weights, gradients, momentums, learning rates and weight decays

• momentum (float, optional, default=0) – The decay rate of momentum estimates at each epoch.

• num_weights (int, optional, default='1') – Number of updated weights.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.preloaded_multi_mp_sgd_update(*data, **kwargs)

Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.

weight = weight - learning_rate * (gradient + wd * weight)


Parameters
• data (NDArray[]) – Weights, gradients, learning rates and weight decays

• num_weights (int, optional, default='1') – Number of updated weights.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.preloaded_multi_sgd_mom_update(*data, **kwargs)

Momentum update function for Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks like below:

$\begin{split}v_1 = \alpha * \nabla J(W_0)\\ v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\ W_t = W_{t-1} + v_t\end{split}$

v = momentum * v - learning_rate * gradient
weight += v


Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Parameters
• data (NDArray[]) – Weights, gradients, momentum, learning rates and weight decays

• momentum (float, optional, default=0) – The decay rate of momentum estimates at each epoch.

• num_weights (int, optional, default='1') – Number of updated weights.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.preloaded_multi_sgd_update(*data, **kwargs)

Update function for Stochastic Gradient Descent (SDG) optimizer.

weight = weight - learning_rate * (gradient + wd * weight)


Parameters
• data (NDArray[]) – Weights, gradients, learning rates and weight decays

• num_weights (int, optional, default='1') – Number of updated weights.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.prod(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)

Computes the product of array elements over given axes.

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 – The output of this function.

Return type

NDArray or list of NDArrays

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

Converts each element of the input array from degrees to radians.

$radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi]$

The storage type of radians output depends upon the input storage type:

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L351

Parameters
• data (NDArray) – The input array.

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

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.random_exponential(lam=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)

Draw random samples from an exponential distribution.

Samples are distributed according to an exponential distribution parametrized by lambda (rate).

Example:

exponential(lam=4, shape=(2,2)) = [[ 0.0097189 ,  0.08999364],
[ 0.04146638,  0.31715935]]


Defined in src/operator/random/sample_op.cc:L137

Parameters
• lam (float, optional, default=1) – Lambda parameter (rate) of the exponential distribution.

• shape (Shape(tuple), optional, default=None) – 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.random_gamma(alpha=_Null, beta=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)

Draw random samples from a gamma distribution.

Samples are distributed according to a gamma distribution parametrized by alpha (shape) and beta (scale).

Example:

gamma(alpha=9, beta=0.5, shape=(2,2)) = [[ 7.10486984,  3.37695289],
[ 3.91697288,  3.65933681]]


Defined in src/operator/random/sample_op.cc:L125

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=None) – 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.random_generalized_negative_binomial(mu=_Null, alpha=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)

Draw random samples from a generalized negative binomial distribution.

Samples are distributed according to a generalized negative binomial distribution parametrized by mu (mean) and alpha (dispersion). alpha is defined as 1/k where k is the failure limit of the number of unsuccessful experiments (generalized to real numbers). Samples will always be returned as a floating point data type.

Example:

generalized_negative_binomial(mu=2.0, alpha=0.3, shape=(2,2)) = [[ 2.,  1.],
[ 6.,  4.]]


Defined in src/operator/random/sample_op.cc:L179

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=None) – 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.random_negative_binomial(k=_Null, p=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)

Draw random samples from a negative binomial distribution.

Samples are distributed according to a negative binomial distribution parametrized by k (limit of unsuccessful experiments) and p (failure probability in each experiment). Samples will always be returned as a floating point data type.

Example:

negative_binomial(k=3, p=0.4, shape=(2,2)) = [[ 4.,  7.],
[ 2.,  5.]]


Defined in src/operator/random/sample_op.cc:L164

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=None) – 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 – The output of this function.

Return type

NDArray or list of NDArrays

mxnet.ndarray.random_normal(loc=_Null, scale=_Null, shape=_Null, ctx=_Null, dtype=_Null, out=None, name=None, **kwargs)

Draw random samples from a normal (Gaussian) distribution.

Note

The existing alias normal is deprecated.

Samples are distributed according to a normal distribution parametrized by loc (mean) and scale (standard deviation).

Example:

normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
[-1.23474145,  1.55807114]]


Defined in src/operator/random/sample_op.cc:L113

Parameters
• loc (float, optional, default=0) – Mean of the distribution.

• scale (float, optional, default=1) – Standard deviation of the distribution.

• shape (Shape(tuple), opti