Overview¶

This document lists the routines of the n-dimensional sparse array package:

The CSRNDArray and RowSparseNDArray API, defined in the ndarray.sparse package, provides imperative sparse tensor operations.

An CSRNDArray inherits from NDArray, and represents a two-dimensional, fixed-size array in compressed sparse row format.

>>> x = mx.nd.array([[1, 0], [0, 0], [2, 3]])
>>> csr = x.tostype('csr')
>>> type(csr)

>>> csr.shape
(3, 2)
>>> csr.data.asnumpy()
array([ 1.  2.  3.], dtype=float32)
>>> csr.indices.asnumpy()
array([0, 0, 1])
>>> csr.indptr.asnumpy()
array([0, 1, 1, 3])
>>> csr.stype
'csr'

A detailed tutorial is available at CSRNDArray - NDArray in Compressed Sparse Row Storage Format.

An RowSparseNDArray inherits from NDArray, and represents a multi-dimensional, fixed-size array in row sparse format.

>>> x = mx.nd.array([[1, 0], [0, 0], [2, 3]])
>>> row_sparse = x.tostype('row_sparse')
>>> type(row_sparse)

>>> row_sparse.data.asnumpy()
array([[ 1.  0.],
       [ 2.  3.]], dtype=float32)
>>> row_sparse.indices.asnumpy()
array([0, 2])
>>> row_sparse.stype
'row_sparse'

A detailed tutorial is available at RowSparseNDArray - NDArray for Sparse Gradient Updates.

In the rest of this document, we first overview the methods provided by the ndarray.sparse.CSRNDArray class and the ndarray.sparse.RowSparseNDArray class, and then list other routines provided by the ndarray.sparse package.

The ndarray.sparse package provides several classes:

We summarize the interface for each class in the following sections.

The CSRNDArray class¶

The RowSparseNDArray class¶

Array creation routines¶

Array manipulation routines¶

Mathematical functions¶

Neural network¶

API Reference¶

class mxnet.ndarray.sparse.CSRNDArray(handle, writable=True)[source]¶

A sparse representation of 2D NDArray in the Compressed Sparse Row format.

A CSRNDArray represents an NDArray as three separate arrays: data, indptr and indices. It uses the CSR representation where the column indices for row i are stored in indices[indptr[i]:indptr[i+1]] and their corresponding values are stored in data[indptr[i]:indptr[i+1]].

The column indices for a given row are expected to be sorted in ascending order. Duplicate column entries for the same row are not allowed.

Example

>>> a = mx.nd.array([[0, 1, 0], [2, 0, 0], [0, 0, 0], [0, 0, 3]])
>>> a = a.tostype('csr')
>>> a.data.asnumpy()
array([ 1.,  2.,  3.], dtype=float32)
>>> a.indices.asnumpy()
array([1, 0, 2])
>>> a.indptr.asnumpy()
array([0, 1, 2, 2, 3])

See also

csr_matrix

Several ways to construct a CSRNDArray

__getitem__(key)[source]¶

x.__getitem__(i) <=> x[i]

Returns a newly created NDArray based on the indexing key.

Parameters:	key (int or mxnet.ndarray.NDArray.slice) – Indexing key.

Examples

>>> indptr = np.array([0, 2, 3, 6])
>>> indices = np.array([0, 2, 2, 0, 1, 2])
>>> data = np.array([1, 2, 3, 4, 5, 6])
>>> a = mx.nd.sparse.csr_matrix((data, indices, indptr), shape=(3, 3))
>>> a.asnumpy()
array([[ 1.,  0.,  2.],
       [ 0.,  0.,  3.],
       [ 4.,  5.,  6.]], dtype=float32)
>>> a[1:2].asnumpy()
array([[ 0.,  0.,  3.]], dtype=float32)
>>> a[1].asnumpy()
array([[ 0.,  0.,  3.]], dtype=float32)
>>> a[-1].asnumpy()
array([[ 4.,  5.,  6.]], dtype=float32)

__setitem__(key, value)[source]¶

x.__setitem__(i, y) <=> x[i]=y

Set self[key] to value. Only slice key [:] is supported.

Parameters:	key (mxnet.ndarray.NDArray.slice) – The indexing key. value (NDArray or CSRNDArray or numpy.ndarray) – The value to set.

Examples

>>> src = mx.nd.sparse.zeros('csr', (3,3))
>>> src.asnumpy()
array([[ 0.,  0.,  0.],
       [ 0.,  0.,  0.],
       [ 0.,  0.,  0.]], dtype=float32)
>>> # assign CSRNDArray with same storage type
>>> x = mx.nd.ones((3,3)).tostype('csr')
>>> x[:] = src
>>> x.asnumpy()
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.],
       [ 1.,  1.,  1.]], dtype=float32)
>>> # assign NDArray to CSRNDArray
>>> x[:] = mx.nd.ones((3,3)) * 2
>>> x.asnumpy()
array([[ 2.,  2.,  2.],
       [ 2.,  2.,  2.],
       [ 2.,  2.,  2.]], dtype=float32)

indices¶

A deep copy NDArray of the indices array of the CSRNDArray. This generates a deep copy of the column indices of the current csr matrix.

Returns:	This CSRNDArray’s indices array.
Return type:	NDArray

indptr¶

A deep copy NDArray of the indptr array of the CSRNDArray. This generates a deep copy of the indptr of the current csr matrix.

Returns:	This CSRNDArray’s indptr array.
Return type:	NDArray

data¶

A deep copy NDArray of the data array of the CSRNDArray. This generates a deep copy of the data of the current csr matrix.

Returns:	This CSRNDArray’s data array.
Return type:	NDArray

tostype(stype)[source]¶

Return a copy of the array with chosen storage type.

Returns:	A copy of the array with the chosen storage stype
Return type:	NDArray or CSRNDArray

copyto(other)[source]¶

Copies the value of this array to another array.

If other is a NDArray or CSRNDArray object, then other.shape and self.shape should be the same. This function copies the value from self to other.

If other is a context, a new CSRNDArray will be first created on the target context, and the value of self is copied.

Parameters:	other (NDArray or CSRNDArray or Context) – The destination array or context.
Returns:	The copied array. If other is an NDArray or CSRNDArray, then the return value and other will point to the same NDArray or CSRNDArray.
Return type:	NDArray or CSRNDArray

asscipy()[source]¶

Returns a scipy.sparse.csr.csr_matrix object with value copied from this array

Examples

>>> x = mx.nd.sparse.zeros('csr', (2,3))
>>> y = x.asscipy()
>>> type(y)

>>> y
<2x3 sparse matrix of type ''
with 0 stored elements in Compressed Sparse Row format>

__neg__()¶

x.__neg__(y) <=> -x

abs(*args, **kwargs)¶

Convenience fluent method for abs().

The arguments are the same as for abs(), with this array as data.

arcsin(*args, **kwargs)¶

Convenience fluent method for arcsin().

The arguments are the same as for arcsin(), with this array as data.

arcsinh(*args, **kwargs)¶

Convenience fluent method for arcsinh().

The arguments are the same as for arcsinh(), with this array as data.

arctan(*args, **kwargs)¶

Convenience fluent method for arctan().

The arguments are the same as for arctan(), with this array as data.

arctanh(*args, **kwargs)¶

Convenience fluent method for arctanh().

The arguments are the same as for arctanh(), with this array as data.

as_in_context(context)¶

Returns an array on the target device with the same value as this array.

If the target context is the same as self.context, then self is returned. Otherwise, a copy is made.

Parameters:	context (Context) – The target context.
Returns:	The target array.
Return type:	NDArray, CSRNDArray or RowSparseNDArray

Examples

>>> x = mx.nd.ones((2,3))
>>> y = x.as_in_context(mx.cpu())
>>> y is x
True
>>> z = x.as_in_context(mx.gpu(0))
>>> z is x
False

asnumpy()¶

Return a dense numpy.ndarray object with value copied from this array

asscalar()¶

Returns a scalar whose value is copied from this array.

This function is equivalent to self.asnumpy()[0]. This NDArray must have shape (1,).

Examples

>>> x = mx.nd.ones((1,), dtype='int32')
>>> x.asscalar()
1
>>> type(x.asscalar())

astype(dtype, copy=True)¶

Return a copy of the array after casting to a specified type.

Parameters:	dtype (numpy.dtype or str) – The type of the returned array. copy (bool) – Default True. By default, astype always returns a newly allocated ndarray on the same context. If this is set to False, and the dtype requested is the same as the ndarray’s dtype, the ndarray is returned instead of a copy.

Examples

>>> x = mx.nd.sparse.zeros('row_sparse', (2,3), dtype='float32')
>>> y = x.astype('int32')
>>> y.dtype

ceil(*args, **kwargs)¶

Convenience fluent method for ceil().

The arguments are the same as for ceil(), with this array as data.

check_format(full_check=True)¶

Check whether the NDArray format is valid.

Parameters:	full_check (bool, optional) – If True, rigorous check, O(N) operations. Otherwise basic check, O(1) operations (default True).

clip(*args, **kwargs)¶

Convenience fluent method for clip().

The arguments are the same as for clip(), with this array as data.

context¶

Device context of the array.

Examples

>>> x = mx.nd.array([1, 2, 3, 4])
>>> x.context
cpu(0)
>>> type(x.context)

>>> y = mx.nd.zeros((2,3), mx.gpu(0))
>>> y.context
gpu(0)

copy()¶

Makes a copy of this NDArray, keeping the same context.

Returns:	The copied array
Return type:	NDArray, CSRNDArray or RowSparseNDArray

Examples

>>> x = mx.nd.ones((2,3))
>>> y = x.copy()
>>> y.asnumpy()
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.]], dtype=float32)

degrees(*args, **kwargs)¶

Convenience fluent method for degrees().

The arguments are the same as for degrees(), with this array as data.

dtype¶

Data-type of the array’s elements.

Returns:	This NDArray’s data type.
Return type:	numpy.dtype

Examples

>>> x = mx.nd.zeros((2,3))
>>> x.dtype

>>> y = mx.nd.zeros((2,3), dtype='int32')
>>> y.dtype

expm1(*args, **kwargs)¶

Convenience fluent method for expm1().

The arguments are the same as for expm1(), with this array as data.

fix(*args, **kwargs)¶

Convenience fluent method for fix().

The arguments are the same as for fix(), with this array as data.

floor(*args, **kwargs)¶

Convenience fluent method for floor().

The arguments are the same as for floor(), with this array as data.

log1p(*args, **kwargs)¶

Convenience fluent method for log1p().

The arguments are the same as for log1p(), with this array as data.

mean(*args, **kwargs)¶

Convenience fluent method for mean().

The arguments are the same as for mean(), with this array as data.

norm(*args, **kwargs)¶

Convenience fluent method for norm().

The arguments are the same as for norm(), with this array as data.

radians(*args, **kwargs)¶

Convenience fluent method for radians().

The arguments are the same as for radians(), with this array as data.

rint(*args, **kwargs)¶

Convenience fluent method for rint().

The arguments are the same as for rint(), with this array as data.

round(*args, **kwargs)¶

Convenience fluent method for round().

The arguments are the same as for round(), with this array as data.

shape¶

Tuple of array dimensions.

Examples

>>> x = mx.nd.array([1, 2, 3, 4])
>>> x.shape
(4L,)
>>> y = mx.nd.zeros((2, 3, 4))
>>> y.shape
(2L, 3L, 4L)

sign(*args, **kwargs)¶

Convenience fluent method for sign().

The arguments are the same as for sign(), with this array as data.

sin(*args, **kwargs)¶

Convenience fluent method for sin().

The arguments are the same as for sin(), with this array as data.

sinh(*args, **kwargs)¶

Convenience fluent method for sinh().

The arguments are the same as for sinh(), with this array as data.

slice(*args, **kwargs)¶

Convenience fluent method for slice().

The arguments are the same as for slice(), with this array as data.

sqrt(*args, **kwargs)¶

Convenience fluent method for sqrt().

The arguments are the same as for sqrt(), with this array as data.

square(*args, **kwargs)¶

Convenience fluent method for square().

The arguments are the same as for square(), with this array as data.

square(*args, **kwargs)

Convenience fluent method for square().

The arguments are the same as for square(), with this array as data.

stype¶

Storage-type of the array.

sum(*args, **kwargs)¶

Convenience fluent method for sum().

The arguments are the same as for sum(), with this array as data.

tan(*args, **kwargs)¶

Convenience fluent method for tan().

The arguments are the same as for tan(), with this array as data.

tanh(*args, **kwargs)¶

Convenience fluent method for tanh().

The arguments are the same as for tanh(), with this array as data.

trunc(*args, **kwargs)¶

Convenience fluent method for trunc().

The arguments are the same as for trunc(), with this array as data.

wait_to_read()¶

Waits until all previous write operations on the current array are finished.

This method guarantees that all previous write operations that pushed into the backend engine for execution are actually finished.

Examples

>>> import time
>>> tic = time.time()
>>> a = mx.nd.ones((1000,1000))
>>> b = mx.nd.dot(a, a)
>>> print(time.time() - tic) 
0.003854036331176758
>>> b.wait_to_read()
>>> print(time.time() - tic) 
0.0893700122833252

zeros_like(*args, **kwargs)¶

Convenience fluent method for zeros_like().

The arguments are the same as for zeros_like(), with this array as data.

class mxnet.ndarray.sparse.RowSparseNDArray(handle, writable=True)[source]¶

A sparse representation of a set of NDArray row slices at given indices.

A RowSparseNDArray represents a multidimensional NDArray using two separate arrays: data and indices. The number of dimensions has to be at least 2.

• data: an NDArray of any dtype with shape [D0, D1, ..., Dn].
• indices: a 1-D int64 NDArray with shape [D0] with values sorted in ascending order.

The indices stores the indices of the row slices with non-zeros, while the values are stored in data. The corresponding NDArray dense represented by RowSparseNDArray rsp has

dense[rsp.indices[i], :, :, :, ...] = rsp.data[i, :, :, :, ...]

>>> dense.asnumpy()
array([[ 1.,  2., 3.],
       [ 0.,  0., 0.],
       [ 4.,  0., 5.],
       [ 0.,  0., 0.],
       [ 0.,  0., 0.]], dtype=float32)
>>> rsp = dense.tostype('row_sparse')
>>> rsp.indices.asnumpy()
array([0, 2], dtype=int64)
>>> rsp.data.asnumpy()
array([[ 1.,  2., 3.],
       [ 4.,  0., 5.]], dtype=float32)

A RowSparseNDArray is typically used to represent non-zero row slices of a large NDArray of shape [LARGE0, D1, .. , Dn] where LARGE0 >> D0 and most row slices are zeros.

RowSparseNDArray is used principally in the definition of gradients for operations that have sparse gradients (e.g. sparse dot and sparse embedding).

See also

row_sparse_array

Several ways to construct a RowSparseNDArray

__getitem__(key)[source]¶

x.__getitem__(i) <=> x[i]

Returns a sliced view of this array.

Parameters:	key (mxnet.ndarray.NDArray.slice) – Indexing key.

Examples

>>> x = mx.nd.sparse.zeros('row_sparse', (2, 3))
>>> x[:].asnumpy()
array([[ 0.,  0.,  0.],
       [ 0.,  0.,  0.]], dtype=float32)

__setitem__(key, value)[source]¶

x.__setitem__(i, y) <=> x[i]=y

Set self[key] to value. Only slice key [:] is supported.

Parameters:	key (mxnet.ndarray.NDArray.slice) – The indexing key. value (NDArray or numpy.ndarray) – The value to set.

Examples

>>> src = mx.nd.row_sparse([[1, 0, 2], [4, 5, 6]], [0, 2], (3,3))
>>> src.asnumpy()
array([[ 1.,  0.,  2.],
       [ 0.,  0.,  0.],
       [ 4.,  5.,  6.]], dtype=float32)
>>> # assign RowSparseNDArray with same storage type
>>> x = mx.nd.sparse.zeros('row_sparse', (3,3))
>>> x[:] = src
>>> x.asnumpy()
array([[ 1.,  0.,  2.],
       [ 0.,  0.,  0.],
       [ 4.,  5.,  6.]], dtype=float32)
>>> # assign NDArray to RowSparseNDArray
>>> x[:] = mx.nd.ones((3,3))
>>> x.asnumpy()
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.],
       [ 1.,  1.,  1.]], dtype=float32)

indices¶

A deep copy NDArray of the indices array of the RowSparseNDArray. This generates a deep copy of the row indices of the current row_sparse matrix.

Returns:	This RowSparseNDArray’s indices array.
Return type:	NDArray

data¶

A deep copy NDArray of the data array of the RowSparseNDArray. This generates a deep copy of the data of the current row_sparse matrix.

Returns:	This RowSparseNDArray’s data array.
Return type:	NDArray

tostype(stype)[source]¶

Return a copy of the array with chosen storage type.

Returns:	A copy of the array with the chosen storage stype
Return type:	NDArray or RowSparseNDArray

copyto(other)[source]¶

Copies the value of this array to another array.

If other is a NDArray or RowSparseNDArray object, then other.shape and self.shape should be the same. This function copies the value from self to other.

If other is a context, a new RowSparseNDArray will be first created on the target context, and the value of self is copied.

Parameters:	other (NDArray or RowSparseNDArray or Context) – The destination array or context.
Returns:	The copied array. If other is an NDArray or RowSparseNDArray, then the return value and other will point to the same NDArray or RowSparseNDArray.
Return type:	NDArray or RowSparseNDArray

retain(*args, **kwargs)[source]¶

Convenience fluent method for retain().

The arguments are the same as for retain(), with this array as data.

abs(*args, **kwargs)¶

Convenience fluent method for abs().

The arguments are the same as for abs(), with this array as data.

arcsin(*args, **kwargs)¶

Convenience fluent method for arcsin().

The arguments are the same as for arcsin(), with this array as data.

arcsinh(*args, **kwargs)¶

Convenience fluent method for arcsinh().

The arguments are the same as for arcsinh(), with this array as data.

arctan(*args, **kwargs)¶

Convenience fluent method for arctan().

The arguments are the same as for arctan(), with this array as data.

arctanh(*args, **kwargs)¶

Convenience fluent method for arctanh().

The arguments are the same as for arctanh(), with this array as data.

as_in_context(context)¶

Returns an array on the target device with the same value as this array.

If the target context is the same as self.context, then self is returned. Otherwise, a copy is made.

Parameters:	context (Context) – The target context.
Returns:	The target array.
Return type:	NDArray, CSRNDArray or RowSparseNDArray

Examples

>>> x = mx.nd.ones((2,3))
>>> y = x.as_in_context(mx.cpu())
>>> y is x
True
>>> z = x.as_in_context(mx.gpu(0))
>>> z is x
False

asnumpy()¶

Return a dense numpy.ndarray object with value copied from this array

asscalar()¶

Returns a scalar whose value is copied from this array.

This function is equivalent to self.asnumpy()[0]. This NDArray must have shape (1,).

Examples

>>> x = mx.nd.ones((1,), dtype='int32')
>>> x.asscalar()
1
>>> type(x.asscalar())

astype(dtype, copy=True)¶

Return a copy of the array after casting to a specified type.

Parameters:	dtype (numpy.dtype or str) – The type of the returned array. copy (bool) – Default True. By default, astype always returns a newly allocated ndarray on the same context. If this is set to False, and the dtype requested is the same as the ndarray’s dtype, the ndarray is returned instead of a copy.

Examples

>>> x = mx.nd.sparse.zeros('row_sparse', (2,3), dtype='float32')
>>> y = x.astype('int32')
>>> y.dtype

ceil(*args, **kwargs)¶

Convenience fluent method for ceil().

The arguments are the same as for ceil(), with this array as data.

check_format(full_check=True)¶

Check whether the NDArray format is valid.

Parameters:	full_check (bool, optional) – If True, rigorous check, O(N) operations. Otherwise basic check, O(1) operations (default True).

clip(*args, **kwargs)¶

Convenience fluent method for clip().

The arguments are the same as for clip(), with this array as data.

context¶

Device context of the array.

Examples

>>> x = mx.nd.array([1, 2, 3, 4])
>>> x.context
cpu(0)
>>> type(x.context)

>>> y = mx.nd.zeros((2,3), mx.gpu(0))
>>> y.context
gpu(0)

copy()¶

Makes a copy of this NDArray, keeping the same context.

Returns:	The copied array
Return type:	NDArray, CSRNDArray or RowSparseNDArray

Examples

>>> x = mx.nd.ones((2,3))
>>> y = x.copy()
>>> y.asnumpy()
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.]], dtype=float32)

degrees(*args, **kwargs)¶

Convenience fluent method for degrees().

The arguments are the same as for degrees(), with this array as data.

dtype¶

Data-type of the array’s elements.

Returns:	This NDArray’s data type.
Return type:	numpy.dtype

Examples

>>> x = mx.nd.zeros((2,3))
>>> x.dtype

>>> y = mx.nd.zeros((2,3), dtype='int32')
>>> y.dtype

expm1(*args, **kwargs)¶

Convenience fluent method for expm1().

The arguments are the same as for expm1(), with this array as data.

fix(*args, **kwargs)¶

Convenience fluent method for fix().

The arguments are the same as for fix(), with this array as data.

floor(*args, **kwargs)¶

Convenience fluent method for floor().

The arguments are the same as for floor(), with this array as data.

log1p(*args, **kwargs)¶

Convenience fluent method for log1p().

The arguments are the same as for log1p(), with this array as data.

norm(*args, **kwargs)¶

Convenience fluent method for norm().

The arguments are the same as for norm(), with this array as data.

radians(*args, **kwargs)¶

Convenience fluent method for radians().

The arguments are the same as for radians(), with this array as data.

rint(*args, **kwargs)¶

Convenience fluent method for rint().

The arguments are the same as for rint(), with this array as data.

round(*args, **kwargs)¶

Convenience fluent method for round().

The arguments are the same as for round(), with this array as data.

shape¶

Tuple of array dimensions.

Examples

>>> x = mx.nd.array([1, 2, 3, 4])
>>> x.shape
(4L,)
>>> y = mx.nd.zeros((2, 3, 4))
>>> y.shape
(2L, 3L, 4L)

sign(*args, **kwargs)¶

Convenience fluent method for sign().

The arguments are the same as for sign(), with this array as data.

sin(*args, **kwargs)¶

Convenience fluent method for sin().

The arguments are the same as for sin(), with this array as data.

sinh(*args, **kwargs)¶

Convenience fluent method for sinh().

The arguments are the same as for sinh(), with this array as data.

sqrt(*args, **kwargs)¶

Convenience fluent method for sqrt().

The arguments are the same as for sqrt(), with this array as data.

square(*args, **kwargs)¶

Convenience fluent method for square().

The arguments are the same as for square(), with this array as data.

stype¶

Storage-type of the array.

tan(*args, **kwargs)¶

Convenience fluent method for tan().

The arguments are the same as for tan(), with this array as data.

tanh(*args, **kwargs)¶

Convenience fluent method for tanh().

The arguments are the same as for tanh(), with this array as data.

trunc(*args, **kwargs)¶

Convenience fluent method for trunc().

The arguments are the same as for trunc(), with this array as data.

wait_to_read()¶

Waits until all previous write operations on the current array are finished.

This method guarantees that all previous write operations that pushed into the backend engine for execution are actually finished.

Examples

>>> import time
>>> tic = time.time()
>>> a = mx.nd.ones((1000,1000))
>>> b = mx.nd.dot(a, a)
>>> print(time.time() - tic) 
0.003854036331176758
>>> b.wait_to_read()
>>> print(time.time() - tic) 
0.0893700122833252

zeros_like(*args, **kwargs)¶

Convenience fluent method for zeros_like().

The arguments are the same as for zeros_like(), with this array as data.

Sparse NDArray API of MXNet.

mxnet.ndarray.sparse.csr_matrix(arg1, shape=None, ctx=None, dtype=None)[source]¶

Creates a CSRNDArray, an 2D array with compressed sparse row (CSR) format.

The CSRNDArray can be instantiated in several ways:

• csr_matrix(D):

  to construct a CSRNDArray with a dense 2D array D

  • D (array_like) - An object exposing the array interface, an object whose __array__ method returns an array, or any (nested) sequence.
  • ctx (Context, optional) - Device context (default is the current default context).
  • dtype (str or numpy.dtype, optional) - The data type of the output array. The default dtype is D.dtype if D is an NDArray or numpy.ndarray, float32 otherwise.

• csr_matrix(S)

  to construct a CSRNDArray with a sparse 2D array S

  • S (CSRNDArray or scipy.sparse.csr.csr_matrix) - A sparse matrix.
  • ctx (Context, optional) - Device context (default is the current default context).
  • dtype (str or numpy.dtype, optional) - The data type of the output array. The default dtype is S.dtype.

• csr_matrix((M, N))

  to construct an empty CSRNDArray with shape (M, N)

  • M (int) - Number of rows in the matrix
  • N (int) - Number of columns in the matrix
  • ctx (Context, optional) - Device context (default is the current default context).
  • dtype (str or numpy.dtype, optional) - The data type of the output array. The default dtype is float32.

• csr_matrix((data, indices, indptr))

  to construct a CSRNDArray based on the definition of compressed sparse row format using three separate arrays, where the column indices for row i are stored in indices[indptr[i]:indptr[i+1]] and their corresponding values are stored in data[indptr[i]:indptr[i+1]]. The column indices for a given row are expected to be sorted in ascending order. Duplicate column entries for the same row are not allowed.

  • data (array_like) - An object exposing the array interface, which holds all the non-zero entries of the matrix in row-major order.
  • indices (array_like) - An object exposing the array interface, which stores the column index for each non-zero element in data.
  • indptr (array_like) - An object exposing the array interface, which stores the offset into data of the first non-zero element number of each row of the matrix.
  • shape (tuple of int, optional) - The shape of the array. The default shape is inferred from the indices and indptr arrays.
  • ctx (Context, optional) - Device context (default is the current default context).
  • dtype (str or numpy.dtype, optional) - The data type of the output array. The default dtype is data.dtype if data is an NDArray or numpy.ndarray, float32 otherwise.

• csr_matrix((data, (row, col)))

  to construct a CSRNDArray based on the COOrdinate format using three seperate arrays, where row[i] is the row index of the element, col[i] is the column index of the element and data[i] is the data corresponding to the element. All the missing elements in the input are taken to be zeroes.

  • data (array_like) - An object exposing the array interface, which holds all the non-zero entries of the matrix in COO format.
  • row (array_like) - An object exposing the array interface, which stores the row index for each non zero element in data.
  • col (array_like) - An object exposing the array interface, which stores the col index for each non zero element in data.
  • shape (tuple of int, optional) - The shape of the array. The default shape is inferred from the row and col arrays.
  • ctx (Context, optional) - Device context (default is the current default context).
  • dtype (str or numpy.dtype, optional) - The data type of the output array. The default dtype is float32.

Parameters:	arg1 (tuple of int, tuple of array_like, array_like, CSRNDArray, scipy.sparse.csr_matrix, scipy.sparse.coo_matrix, tuple of int or tuple of array_like) – The argument to help instantiate the csr matrix. See above for further details. shape (tuple of int, optional) – The shape of the csr matrix. ctx (Context, optional) – Device context (default is the current default context). dtype (str or numpy.dtype, optional) – The data type of the output array.
Returns:	A CSRNDArray with the csr storage representation.
Return type:	CSRNDArray

Example

>>> a = mx.nd.sparse.csr_matrix(([1, 2, 3], [1, 0, 2], [0, 1, 2, 2, 3]), shape=(4, 3))
>>> a.asnumpy()
array([[ 0.,  1.,  0.],
       [ 2.,  0.,  0.],
       [ 0.,  0.,  0.],
       [ 0.,  0.,  3.]], dtype=float32)

See also

CSRNDArray()

MXNet NDArray in compressed sparse row format.

mxnet.ndarray.sparse.row_sparse_array(arg1, shape=None, ctx=None, dtype=None)[source]¶

Creates a RowSparseNDArray, a multidimensional row sparse array with a set of tensor slices at given indices.

The RowSparseNDArray can be instantiated in several ways:

• row_sparse_array(D):

  to construct a RowSparseNDArray with a dense ndarray D - D (array_like) - An object exposing the array interface, an object whose __array__ method returns an array, or any (nested) sequence. - ctx (Context, optional) - Device context (default is the current default context). - dtype (str or numpy.dtype, optional) - The data type of the output array. The default dtype is D.dtype if D is an NDArray or numpy.ndarray, float32 otherwise.

• row_sparse_array(S)

  to construct a RowSparseNDArray with a sparse ndarray S - S (RowSparseNDArray) - A sparse ndarray. - ctx (Context, optional) - Device context (default is the current default context). - dtype (str or numpy.dtype, optional) - The data type of the output array. The default dtype is S.dtype.

• row_sparse_array((D0, D1 .. Dn))

  to construct an empty RowSparseNDArray with shape (D0, D1, ... Dn) - D0, D1 .. Dn (int) - The shape of the ndarray - ctx (Context, optional) - Device context (default is the current default context). - dtype (str or numpy.dtype, optional) - The data type of the output array. The default dtype is float32.

• row_sparse_array((data, indices))

  to construct a RowSparseNDArray based on the definition of row sparse format using two separate arrays, where the indices stores the indices of the row slices with non-zeros, while the values are stored in data. The corresponding NDArray dense represented by RowSparseNDArray rsp has dense[rsp.indices[i], :, :, :, ...] = rsp.data[i, :, :, :, ...] The row indices for are expected to be sorted in ascending order. - data (array_like) - An object exposing the array interface, which holds all the non-zero row slices of the array. - indices (array_like) - An object exposing the array interface, which stores the row index for each row slice with non-zero elements. - shape (tuple of int, optional) - The shape of the array. The default shape is inferred from the indices and indptr arrays. - ctx (Context, optional) - Device context (default is the current default context). - dtype (str or numpy.dtype, optional) - The data type of the output array. The default dtype is float32.

Parameters:	arg1 (NDArray, numpy.ndarray, RowSparseNDArray, tuple of int or tuple of array_like) – The argument to help instantiate the row sparse ndarray. See above for further details. shape (tuple of int, optional) – The shape of the row sparse ndarray. (Default value = None) ctx (Context, optional) – Device context (default is the current default context). dtype (str or numpy.dtype, optional) – The data type of the output array. (Default value = None)
Returns:	An RowSparseNDArray with the row_sparse storage representation.
Return type:	RowSparseNDArray

Examples

>>> a = mx.nd.sparse.row_sparse_array(([[1, 2], [3, 4]], [1, 4]), shape=(6, 2))
>>> a.asnumpy()
array([[ 0.,  0.],
       [ 1.,  2.],
       [ 0.,  0.],
       [ 0.,  0.],
       [ 3.,  4.],
       [ 0.,  0.]], dtype=float32)

See also

RowSparseNDArray()

MXNet NDArray in row sparse format.

mxnet.ndarray.sparse.add(lhs, rhs)[source]¶

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

Equivalent to lhs + rhs, mx.nd.broadcast_add(lhs, rhs) and mx.nd.broadcast_plus(lhs, rhs) when shapes of lhs and rhs do not match. If lhs.shape == rhs.shape, this is equivalent to mx.nd.elemwise_add(lhs, rhs)

Note

If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.abs

Parameters:	lhs (scalar or mxnet.ndarray.sparse.array) – First array to be added. rhs (scalar or mxnet.ndarray.sparse.array) – Second array to be added. If lhs.shape != rhs.shape, they must be broadcastable to a common shape.
Returns:	The element-wise sum of the input arrays.
Return type:	NDArray

Examples

>>> a = mx.nd.ones((2,3)).tostype('csr')
>>> b = mx.nd.ones((2,3)).tostype('csr')
>>> a.asnumpy()
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.]], dtype=float32)
>>> b.asnumpy()
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.]], dtype=float32)
>>> (a+b).asnumpy()
array([[ 2.,  2.,  2.],
       [ 2.,  2.,  2.]], dtype=float32)
>>> c = mx.nd.ones((2,3)).tostype('row_sparse')
>>> d = mx.nd.ones((2,3)).tostype('row_sparse')
>>> c.asnumpy()
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.]], dtype=float32)
>>> d.asnumpy()
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.]], dtype=float32)
>>> (c+d).asnumpy()
array([[ 2.,  2.,  2.],
       [ 2.,  2.,  2.]], dtype=float32)

mxnet.ndarray.sparse.subtract(lhs, rhs)[source]¶

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

Equivalent to lhs - rhs, mx.nd.broadcast_sub(lhs, rhs) and mx.nd.broadcast_minus(lhs, rhs) when shapes of lhs and rhs do not match. If lhs.shape == rhs.shape, this is equivalent to mx.nd.elemwise_sub(lhs, rhs)

Note

If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.

Parameters:	lhs (scalar or mxnet.ndarray.sparse.array) – First array to be subtracted. rhs (scalar or mxnet.ndarray.sparse.array) – Second array to be subtracted. If lhs.shape != rhs.shape, they must be broadcastable to a common shape.__spec__
Returns:	The element-wise difference of the input arrays.
Return type:	NDArray

Examples

>>> a = mx.nd.ones((2,3)).tostype('csr')
>>> b = mx.nd.ones((2,3)).tostype('csr')
>>> a.asnumpy()
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.]], dtype=float32)
>>> b.asnumpy()
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.]], dtype=float32)
>>> (a-b).asnumpy()
array([[ 0.,  0.,  0.],
       [ 0.,  0.,  0.]], dtype=float32)
>>> c = mx.nd.ones((2,3)).tostype('row_sparse')
>>> d = mx.nd.ones((2,3)).tostype('row_sparse')
>>> c.asnumpy()
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.]], dtype=float32)
>>> d.asnumpy()
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.]], dtype=float32)
>>> (c-d).asnumpy()
array([[ 0.,  0.,  0.],
       [ 0.,  0.,  0.]], dtype=float32)

mxnet.ndarray.sparse.multiply(lhs, rhs)[source]¶

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

Equivalent to lhs * rhs and mx.nd.broadcast_mul(lhs, rhs) when shapes of lhs and rhs do not match. If lhs.shape == rhs.shape, this is equivalent to mx.nd.elemwise_mul(lhs, rhs)

Note

If the corresponding dimensions of two arrays have the same size or one of them has size 1, then the arrays are broadcastable to a common shape.

Parameters:	lhs (scalar or mxnet.ndarray.sparse.array) – First array to be multiplied. rhs (scalar or mxnet.ndarray.sparse.array) – Second array to be multiplied. If lhs.shape != rhs.shape, they must be broadcastable to a common shape.
Returns:	The element-wise multiplication of the input arrays.
Return type:	NDArray

Examples

>>> x = mx.nd.ones((2,3)).tostype('csr')
>>> y = mx.nd.arange(2).reshape((2,1))
>>> z = mx.nd.arange(3)
>>> x.asnumpy()
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.]], dtype=float32)
>>> y.asnumpy()
array([[ 0.],
       [ 1.]], dtype=float32)
>>> z.asnumpy()
array([ 0.,  1.,  2.], dtype=float32)
>>> (x*2).asnumpy()
array([[ 2.,  2.,  2.],
       [ 2.,  2.,  2.]], dtype=float32)
>>> (x*y).asnumpy()
array([[ 0.,  0.,  0.],
       [ 1.,  1.,  1.]], dtype=float32)
>>> mx.nd.sparse.multiply(x, y).asnumpy()
array([[ 0.,  0.,  0.],
       [ 1.,  1.,  1.]], dtype=float32)
>>> (x*z).asnumpy()
array([[ 0.,  1.,  2.],
       [ 0.,  1.,  2.]], dtype=float32)
>>> mx.nd.sparse.multiply(x, z).asnumpy()
array([[ 0.,  1.,  2.],
       [ 0.,  1.,  2.]], dtype=float32)
>>> z = z.reshape((1, 3))
>>> z.asnumpy()
array([[ 0.,  1.,  2.]], dtype=float32)
>>> (x*z).asnumpy()
array([[ 0.,  1.,  2.],
       [ 0.,  1.,  2.]], dtype=float32)
>>> mx.nd.sparse.multiply(x, z).asnumpy()
array([[ 0.,  1.,  2.],
       [ 0.,  1.,  2.]], dtype=float32)

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

Adds all input arguments element-wise.

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

add_n is potentially more efficient than calling add by n times.

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

• add_n(row_sparse, row_sparse, ..) = row_sparse
• add_n(default, csr, default) = default
• add_n(any input combinations longer than 4 (>4) with at least one default type) = default
• otherwise, add_n falls all inputs back to default storage and generates default storage

Defined in src/operator/tensor/elemwise_sum.cc:L155

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.sparse.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).

By default, if any index mentioned is too large, it is replaced by the index that addresses the last vector in an embedding matrix.

Examples:

input_dim = 4
output_dim = 5

// Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3)
y = [[  0.,   1.,   2.,   3.,   4.],
     [  5.,   6.,   7.,   8.,   9.],
     [ 10.,  11.,  12.,  13.,  14.],
     [ 15.,  16.,  17.,  18.,  19.]]

// Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)]
x = [[ 1.,  3.],
     [ 0.,  2.]]

// Mapped input x to its vector representation y.
Embedding(x, y, 4, 5) = [[[  5.,   6.,   7.,   8.,   9.],
                          [ 15.,  16.,  17.,  18.,  19.]],

                         [[  0.,   1.,   2.,   3.,   4.],
                          [ 10.,  11.,  12.,  13.,  14.]]]

The storage type of weight can be either row_sparse or default.

Note

If “sparse_grad” is set to True, the storage type of gradient w.r.t weights will be “row_sparse”. Only a subset of optimizers support sparse gradients, including SGD, AdaGrad and Adam. Note that by default lazy updates is turned on, which may perform differently from standard updates. For more details, please check the Optimization API at: /api/python/optimization/optimization.html

Defined in src/operator/tensor/indexing_op.cc:L519

Parameters:	data (NDArray) – The input array to the embedding operator. weight (NDArray) – The embedding weight matrix. input_dim (int, required) – Vocabulary size of the input indices. output_dim (int, required) – Dimension of the embedding vectors. dtype ({'float16', 'float32', 'float64', 'int32', 'int64', 'int8', 'uint8'},optional, default='float32') – Data type of weight. sparse_grad (boolean, optional, default=0) – Compute row sparse gradient in the backward calculation. If set to True, the grad’s storage type is row_sparse. out (NDArray, optional) – The output NDArray to hold the result.
Returns:	out – The output of this function.
Return type:	NDArray or list of NDArrays

mxnet.ndarray.sparse.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:L277

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.sparse.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.sparse.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.sparse.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.sparse.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:L708

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.sparse.adagrad_update(weight=None, grad=None, history=None, lr=_Null, epsilon=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, out=None, name=None, **kwargs)¶

Update function for AdaGrad optimizer.

Referenced from Adaptive Subgradient Methods for Online Learning and Stochastic Optimization, and available at http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf.

Updates are applied by:

rescaled_grad = clip(grad * rescale_grad, clip_gradient)
history = history + square(rescaled_grad)
w = w - learning_rate * rescaled_grad / sqrt(history + epsilon)

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

Defined in src/operator/optimizer_op.cc:L907

Parameters:	weight (NDArray) – Weight grad (NDArray) – Gradient history (NDArray) – History lr (float, required) – Learning rate epsilon (float, optional, default=1.00000001e-07) – epsilon wd (float, optional, default=0) – weight decay rescale_grad (float, optional, default=1) – Rescale gradient to grad = rescale_grad*grad. clip_gradient (float, optional, default=-1) – Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). out (NDArray, optional) – The output NDArray to hold the result.
Returns:	out – The output of this function.
Return type:	NDArray or list of NDArrays

mxnet.ndarray.sparse.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)¶

Update function for Adam optimizer. Adam is seen as a generalization of AdaGrad.

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

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

It updates the weights using:

m = beta1*m + (1-beta1)*grad
v = beta2*v + (1-beta2)*(grad**2)
w += - learning_rate * m / (sqrt(v) + epsilon)

However, if grad’s storage type is row_sparse, lazy_update is True and the storage type of weight is the same as those of m and v, only the row slices whose indices appear in grad.indices are updated (for w, m and v):

for row in grad.indices:
    m[row] = beta1*m[row] + (1-beta1)*grad[row]
    v[row] = beta2*v[row] + (1-beta2)*(grad[row]**2)
    w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)

Defined in src/operator/optimizer_op.cc:L686

Parameters:	weight (NDArray) – Weight grad (NDArray) – Gradient mean (NDArray) – Moving mean var (NDArray) – Moving variance lr (float, required) – Learning rate beta1 (float, optional, default=0.899999976) – 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. rescale_grad (float, optional, default=1) – Rescale gradient to grad = rescale_grad*grad. clip_gradient (float, optional, default=-1) – Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). lazy_update (boolean, optional, default=1) – If true, lazy updates are applied if gradient’s stype is row_sparse and all of w, m and v have the same stype out (NDArray, optional) – The output NDArray to hold the result.
Returns:	out – The output of this function.
Return type:	NDArray or list of NDArrays

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

Adds all input arguments element-wise.

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

add_n is potentially more efficient than calling add by n times.

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

• add_n(row_sparse, row_sparse, ..) = row_sparse
• add_n(default, csr, default) = default
• add_n(any input combinations longer than 4 (>4) with at least one default type) = default
• otherwise, add_n falls all inputs back to default storage and generates default storage

Defined in src/operator/tensor/elemwise_sum.cc:L155

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.sparse.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:L179

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.sparse.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:L320

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.sparse.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:L160

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.sparse.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:L306

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.sparse.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:L200

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.sparse.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:L337

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.sparse.broadcast_add(lhs=None, rhs=None, out=None, name=None, **kwargs)¶

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

broadcast_plus is an alias to the function broadcast_add.

Example:

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

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

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

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

Supported sparse operations:

broadcast_add(csr, dense(1D)) = dense broadcast_add(dense(1D), csr) = dense

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58

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.sparse.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:

broadcast_div(csr, dense(1D)) = csr

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L187

Parameters:	lhs (NDArray) – First input to the function rhs (NDArray) – Second input to the function out (NDArray, optional) – The output NDArray to hold the result.
Returns:	out – The output of this function.
Return type:	NDArray or list of NDArrays

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

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

broadcast_minus is an alias to the function broadcast_sub.

Example:

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

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

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

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

Supported sparse operations:

broadcast_sub/minus(csr, dense(1D)) = dense broadcast_sub/minus(dense(1D), csr) = dense

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106

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.sparse.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:

broadcast_mul(csr, dense(1D)) = csr

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L146

Parameters:	lhs (NDArray) – First input to the function rhs (NDArray) – Second input to the function out (NDArray, optional) – The output NDArray to hold the result.
Returns:	out – The output of this function.
Return type:	NDArray or list of NDArrays

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

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

broadcast_plus is an alias to the function broadcast_add.

Example:

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

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

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

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

Supported sparse operations:

broadcast_add(csr, dense(1D)) = dense broadcast_add(dense(1D), csr) = dense

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58

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