Sparse NDArray API¶

Overview¶

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

mxnet.ndarray.sparse Sparse NDArray API of MXNet.

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

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.

Note

mxnet.ndarray.sparse is similar to mxnet.ndarray in some aspects. But the differences are not negligible. For instance:

Only a subset of operators in mxnet.ndarray have specialized implementations in mxnet.ndarray.sparse. Operators such as Convolution and broadcasting do not have sparse implementations yet.
The storage types (stype) of sparse operators’ outputs depend on the storage types of inputs. By default the operators not available in mxnet.ndarray.sparse infer “default” (dense) storage type for outputs. Please refer to the [API Reference](#api-reference) section for further details on specific operators.
GPU support for mxnet.ndarray.sparse is experimental. Only a few sparse operators are supported on GPU such as sparse.dot.

Note

mxnet.ndarray.sparse.CSRNDArray is similar to scipy.sparse.csr_matrix in some aspects. But they differ in a few aspects:

In MXNet the column indices (CSRNDArray.indices) for a given row are expected to be sorted in ascending order. Duplicate column entries for the same row are not allowed.
CSRNDArray.data, CSRNDArray.indices and CSRNDArray.indptr always create deep copies, while it’s not the case in scipy.sparse.csr_matrix.

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:

`CSRNDArray`	A sparse representation of 2D NDArray in the Compressed Sparse Row format.
`RowSparseNDArray`	A sparse representation of a set of NDArray row slices at given indices.

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

The `CSRNDArray` class¶

Array attributes¶

`CSRNDArray.shape`	Tuple of array dimensions.
`CSRNDArray.context`	Device context of the array.
`CSRNDArray.dtype`	Data-type of the array’s elements.
`CSRNDArray.stype`	Storage-type of the array.
`CSRNDArray.data`	A deep copy NDArray of the data array of the CSRNDArray.
`CSRNDArray.indices`	A deep copy NDArray of the indices array of the CSRNDArray.
`CSRNDArray.indptr`	A deep copy NDArray of the indptr array of the CSRNDArray.

Array conversion¶

`CSRNDArray.copy`	Makes a copy of this `NDArray`, keeping the same context.
`CSRNDArray.copyto`	Copies the value of this array to another array.
`CSRNDArray.as_in_context`	Returns an array on the target device with the same value as this array.
`CSRNDArray.asnumpy`	Return a dense `numpy.ndarray` object with value copied from this array
`CSRNDArray.asscalar`	Returns a scalar whose value is copied from this array.
`CSRNDArray.astype`	Returns a copy of the array after casting to a specified type.
`CSRNDArray.tostype`	Return a copy of the array with chosen storage type.

Array creation¶

CSRNDArray.zeros_like Convenience fluent method for zeros_like().

Indexing¶

`CSRNDArray.__getitem__`	x.__getitem__(i) <=> x[i]
`CSRNDArray.__setitem__`	x.__setitem__(i, y) <=> x[i]=y
`CSRNDArray.slice`	Convenience fluent method for `slice()`.

Lazy evaluation¶

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

The `RowSparseNDArray` class¶

Array attributes¶

`RowSparseNDArray.shape`	Tuple of array dimensions.
`RowSparseNDArray.context`	Device context of the array.
`RowSparseNDArray.dtype`	Data-type of the array’s elements.
`RowSparseNDArray.stype`	Storage-type of the array.
`RowSparseNDArray.data`	A deep copy NDArray of the data array of the RowSparseNDArray.
`RowSparseNDArray.indices`	A deep copy NDArray of the indices array of the RowSparseNDArray.

Array conversion¶

`RowSparseNDArray.copy`	Makes a copy of this `NDArray`, keeping the same context.
`RowSparseNDArray.copyto`	Copies the value of this array to another array.
`RowSparseNDArray.as_in_context`	Returns an array on the target device with the same value as this array.
`RowSparseNDArray.asnumpy`	Return a dense `numpy.ndarray` object with value copied from this array
`RowSparseNDArray.asscalar`	Returns a scalar whose value is copied from this array.
`RowSparseNDArray.astype`	Returns a copy of the array after casting to a specified type.
`RowSparseNDArray.tostype`	Return a copy of the array with chosen storage type.

Array creation¶

RowSparseNDArray.zeros_like Convenience fluent method for zeros_like().

Array rounding¶

`RowSparseNDArray.round`	Convenience fluent method for `round()`.
`RowSparseNDArray.rint`	Convenience fluent method for `rint()`.
`RowSparseNDArray.fix`	Convenience fluent method for `fix()`.
`RowSparseNDArray.floor`	Convenience fluent method for `floor()`.
`RowSparseNDArray.ceil`	Convenience fluent method for `ceil()`.
`RowSparseNDArray.trunc`	Convenience fluent method for `trunc()`.

Indexing¶

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

Lazy evaluation¶

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

Array creation routines¶

`array`	Creates a sparse array from any object exposing the array interface.
`empty`	Returns a new array of given shape and type, without initializing entries.
`zeros`	Return a new array of given shape and type, filled with zeros.
`zeros_like`	Return an array of zeros with the same shape and type as the input array.
`csr_matrix`	Creates a CSRNDArray, an 2D array with compressed sparse row (CSR) format.
`row_sparse_array`	Creates a RowSparseNDArray, a multidimensional row sparse array with a set of tensor slices at given indices.
`mxnet.ndarray.load`	Loads an array from file.
`mxnet.ndarray.save`	Saves a list of arrays or a dict of str->array to file.

Array manipulation routines¶

Changing array storage type¶

cast_storage Casts tensor storage type to the new type.

Indexing routines¶

`slice`	Slices a contiguous region of the array.
`retain`	pick rows specified by user input index array from a row sparse matrix

Mathematical functions¶

Arithmetic operations¶

`elemwise_add`	Adds arguments element-wise.
`elemwise_sub`	Subtracts arguments element-wise.
`elemwise_mul`	Multiplies arguments element-wise.
`negative`	Numerical negative of the argument, element-wise.
`dot`	Dot product of two arrays.
`add_n`	Adds all input arguments element-wise.

Trigonometric functions¶

`sin`	Computes the element-wise sine of the input array.
`tan`	Computes the element-wise tangent of the input array.
`arcsin`	Returns element-wise inverse sine of the input array.
`arctan`	Returns element-wise inverse tangent of the input array.
`degrees`	Converts each element of the input array from radians to degrees.
`radians`	Converts each element of the input array from degrees to radians.

Hyperbolic functions¶

`sinh`	Returns the hyperbolic sine of the input array, computed element-wise.
`tanh`	Returns the hyperbolic tangent of the input array, computed element-wise.
`arcsinh`	Returns the element-wise inverse hyperbolic sine of the input array, computed element-wise.
`arctanh`	Returns the element-wise inverse hyperbolic tangent of the input array, computed element-wise.

Rounding¶

`round`	Returns element-wise rounded value to the nearest integer of the input.
`rint`	Returns element-wise rounded value to the nearest integer of the input.
`fix`	Returns element-wise rounded value to the nearest integer towards zero of the input.
`floor`	Returns element-wise floor of the input.
`ceil`	Returns element-wise ceiling of the input.
`trunc`	Return the element-wise truncated value of the input.

Exponents and logarithms¶

`expm1`	Returns `exp(x) - 1` computed element-wise on the input.
`log1p`	Returns element-wise `log(1 + x)` value of the input.

Powers¶

`sqrt`	Returns element-wise square-root value of the input.
`square`	Returns element-wise squared value of the input.

Miscellaneous¶

`abs`	Returns element-wise absolute value of the input.
`sign`	Returns element-wise sign of the input.

More¶

`make_loss`	Make your own loss function in network construction.
`stop_gradient`	Stops gradient computation.

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 sliced view of this array.

Parameters:	key (int or 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 (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('row_sparse', (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

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)¶

Returns a copy of the array after casting to a specified type. :param dtype: The type of the returned array. :type dtype: numpy.dtype or str

Examples

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

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)

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

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)

slice(*args, **kwargs)¶

Convenience fluent method for slice().

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

stype¶: Storage-type of the array.

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 (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 (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

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)¶

Returns a copy of the array after casting to a specified type. :param dtype: The type of the returned array. :type dtype: numpy.dtype or str

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.

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)

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

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.

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)

stype¶: Storage-type of the array.

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.

Parameters:	arg1 (NDArray, CSRNDArray, numpy.ndarray, scipy.sparse.csr.csr_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. 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:	An RowSparseNDArray with the row_sparse storage representation.
Return type:	RowSparseNDArray

Example

>>> 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.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
otherwise, add_n generates output with default storage

Defined in src/operator/tensor/elemwise_sum.cc:L122

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.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

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L387

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.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
otherwise, add_n generates output with default storage

Defined in src/operator/tensor/elemwise_sum.cc:L122

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:L123

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:L264

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

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L104

Parameters:	data (NDArray) – The input array. out (NDArray, optional) – The output NDArray to hold the result.
Returns:	out – 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

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L250

Parameters:	data (NDArray) – The input array. out (NDArray, optional) – The output NDArray to hold the result.
Returns:	out – 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

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L144

Parameters:	data (NDArray) – The input array. out (NDArray, optional) – The output NDArray to hold the result.
Returns:	out – 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

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L281

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

mxnet.ndarray.sparse.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

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:L69

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.sparse.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

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L464

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.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:L63

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.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:L216

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.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

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

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

mxnet.ndarray.sparse.dot(lhs=None, rhs=None, transpose_a=_Null, transpose_b=_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 and transpose options:

dot(csr, default) = default
dot(csr.T, default) = row_sparse
dot(csr, row_sparse) = default
otherwise, dot generates output with default storage

Defined in src/operator/tensor/dot.cc:L61

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. out (NDArray, 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.elemwise_add(lhs=None, rhs=None, out=None, name=None, **kwargs)¶

Adds arguments element-wise.

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

elemwise_add(row_sparse, row_sparse) = row_sparse

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

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

Divides arguments element-wise.

The storage type of elemwise_dev 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.sparse.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

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.sparse.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

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

mxnet.ndarray.sparse.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_basic.cc:L638

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.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

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L717

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.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

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L518

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.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

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L482

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.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.sparse.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.sparse.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_basic.cc:L650

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.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_basic.cc:L662

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.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

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L699

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.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_basic.cc:L674

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.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:L201

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.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.sparse.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:

radians(default) = default

radians(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L182

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

mxnet.ndarray.sparse.relu(data=None, out=None, name=None, **kwargs)¶

Computes rectified linear.

\[max(features, 0)\]

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

relu(default) = default

relu(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L84

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.retain(data=None, indices=None, out=None, name=None, **kwargs)¶

pick rows specified by user input index array from a row sparse matrix and save them in the output sparse matrix.

Example:

data = [[1, 2], [3, 4], [5, 6]]
indices = [0, 1, 3]
shape = (4, 2)
rsp_in = row_sparse(data, indices)
to_retain = [0, 3]
rsp_out = retain(rsp_in, to_retain)
rsp_out.values = [[1, 2], [5, 6]]
rsp_out.indices = [0, 3]

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

retain(row_sparse, default) = row_sparse
otherwise, retain is not supported

Defined in src/operator/tensor/sparse_retain.cc:L53

Parameters:	data (NDArray) – The input array for sparse_retain operator. indices (NDArray) – The index array of rows ids that will be retained. out (NDArray, 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.rint(data=None, out=None, name=None, **kwargs)¶

Returns element-wise rounded value to the nearest integer of the input.

Note

For input n.5 rint returns n while round returns n+1.
For input -n.5 both rint and round returns -n-1.

Example:

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

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

rint(default) = default

rint(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L446

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.round(data=None, out=None, name=None, **kwargs)¶

Returns element-wise rounded value to the nearest integer of the input.

Example:

round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  2., -2.,  2.,  2.]

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

round(default) = default

round(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L425

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.rsqrt(data=None, out=None, name=None, **kwargs)¶

Returns element-wise inverse square-root value of the input.

\[rsqrt(x) = 1/\sqrt{x}\]

Example:

rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25]

The storage type of rsqrt output is always dense

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L581

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.sigmoid(data=None, out=None, name=None, **kwargs)¶

Computes sigmoid of x element-wise.

\[y = 1 / (1 + exp(-x))\]

The storage type of sigmoid output is always dense

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L104

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.sign(data=None, out=None, name=None, **kwargs)¶

Returns element-wise sign of the input.

Example:

sign([-2, 0, 3]) = [-1, 0, 1]

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

sign(default) = default

sign(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L406

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.sin(data=None, out=None, name=None, **kwargs)¶

Computes the element-wise sine of the input array.

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

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

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

sin(default) = default

sin(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L46

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.sinh(data=None, out=None, name=None, **kwargs)¶

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

\[sinh(x) = 0.5\times(exp(x) - exp(-x))\]

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

sinh(default) = default

sinh(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L201

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.slice(data=None, begin=_Null, end=_Null, out=None, name=None, **kwargs)¶

Slices a contiguous region of the array.

Note

crop is deprecated. Use slice instead.

This function returns a sliced continuous region of the array between the indices given by begin and end.

For an input array of n dimensions, slice operation with begin=(b_0, b_1...b_n-1) indices and end=(e_1, e_2, ... e_n) indices will result in an array with the shape (e_1-b_0, ..., e_n-b_n-1).

The resulting array’s k-th dimension contains elements from the k-th dimension of the input array with the open range [b_k, e_k).

For an input array of non-default storage type(e.g. csr or row_sparse), it only supports slicing on the first dimension.

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.]]

Defined in src/operator/tensor/matrix_op.cc:L278

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. out (NDArray, 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.sqrt(data=None, out=None, name=None, **kwargs)¶

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

\[\textrm{sqrt}(x) = \sqrt{x}\]

Example:

sqrt([4, 9, 16]) = [2, 3, 4]

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

sqrt(default) = default

sqrt(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L561

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.square(data=None, out=None, name=None, **kwargs)¶

Returns element-wise squared value of the input.

\[square(x) = x^2\]

Example:

square([2, 3, 4]) = [4, 9, 16]

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

square(default) = default

square(row_sparse) = row_sparse

square(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L538

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.stop_gradient(data=None, out=None, name=None, **kwargs)¶

Stops gradient computation.

Stops the accumulated gradient of the inputs from flowing through this operator in the backward direction. In other words, this operator prevents the contribution of its inputs to be taken into account for computing gradients.

Example:

v1 = [1, 2]
v2 = [0, 1]
a = Variable('a')
b = Variable('b')
b_stop_grad = stop_gradient(3 * b)
loss = MakeLoss(b_stop_grad + a)

executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2))
executor.forward(is_train=True, a=v1, b=v2)
executor.outputs
[ 1.  5.]

executor.backward()
executor.grad_arrays
[ 0.  0.]
[ 1.  1.]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L168

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.sum(data=None, axis=_Null, keepdims=_Null, exclude=_Null, out=None, name=None, **kwargs)¶

Computes the sum of array elements over given axes.

Note

sum and sum_axis are equivalent. For ndarray of csr storage type summation along axis 0 and axis 1 is supported. Setting keepdims or exclude to True will cause a fallback to dense operator.

Example:

data = [[[1,2],[2,3],[1,3]],
        [[1,4],[4,3],[5,2]],
        [[7,1],[7,2],[7,3]]]

sum(data, axis=1)
[[  4.   8.]
 [ 10.   9.]
 [ 21.   6.]]

sum(data, axis=[1,2])
[ 12.  19.  27.]

data = [[1,2,0],
        [3,0,1],
        [4,1,0]]

csr = cast_storage(data, 'csr')

sum(csr, axis=0)
[ 8.  2.  2.]

sum(csr, axis=1)
[ 3.  4.  5.]

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L84

Parameters:	data (NDArray) – The input axis (Shape(tuple), optional, default=()) – 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.sparse.tan(data=None, out=None, name=None, **kwargs)¶

Computes the element-wise tangent of the input array.

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

\[tan([0, \pi/4, \pi/2]) = [0, 1, -inf]\]

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

tan(default) = default

tan(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L83

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

mxnet.ndarray.sparse.tanh(data=None, out=None, name=None, **kwargs)¶

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

\[tanh(x) = sinh(x) / cosh(x)\]

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

tanh(default) = default

tanh(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L234

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

mxnet.ndarray.sparse.trunc(data=None, out=None, name=None, **kwargs)¶

Return the element-wise truncated value of the input.

The truncated value of the scalar x is the nearest integer i which is closer to zero than x is. In short, the fractional part of the signed number x is discarded.

Example:

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

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

trunc(default) = default

trunc(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L501

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.zeros_like(data=None, out=None, name=None, **kwargs)¶

Return an array of zeros with the same shape and type as the input array.

The storage type of zeros_like output depends on the storage type of the input

zeros_like(row_sparse) = row_sparse
zeros_like(csr) = csr
zeros_like(default) = default

Examples:

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

zeros_like(x) = [[ 0.,  0.,  0.],
                 [ 0.,  0.,  0.]]

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

Sparse NDArray API of MXNet.

mxnet.ndarray.sparse.zeros(stype, shape, ctx=None, dtype=None, **kwargs)[source]¶

Return a new array of given shape and type, filled with zeros.

Parameters:	stype (string) – The storage type of the empty array, such as ‘row_sparse’, ‘csr’, etc shape (int or tuple of int) – The shape of the empty array ctx (Context, optional) – An optional device context (default is the current default context) dtype (str or numpy.dtype, optional) – An optional value type (default is float32)
Returns:	A created array
Return type:	RowSparseNDArray or CSRNDArray

Examples

>>> mx.nd.sparse.zeros('csr', (1,2))

>>> mx.nd.sparse.zeros('row_sparse', (1,2), ctx=mx.cpu(), dtype='float16').asnumpy()
array([[ 0.,  0.]], dtype=float16)

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

Returns a new array of given shape and type, without initializing entries.

Parameters:	stype (string) – The storage type of the empty array, such as ‘row_sparse’, ‘csr’, etc shape (int or tuple of int) – The shape of the empty array. ctx (Context, optional) – An optional device context (default is the current default context). dtype (str or numpy.dtype, optional) – An optional value type (default is float32).
Returns:	A created array.
Return type:	CSRNDArray or RowSparseNDArray

mxnet.ndarray.sparse.array(source_array, ctx=None, dtype=None)[source]¶

Creates a sparse array from any object exposing the array interface.

Parameters:	source_array (RowSparseNDArray, CSRNDArray or scipy.sparse.csr.csr_matrix) – The source sparse array ctx (Context, optional) – The default context is `source_array.context` if `source_array` is an NDArray. The current default context otherwise. dtype (str or numpy.dtype, optional) – The data type of the output array. The default dtype is `source_array.dtype` if source_array is an NDArray, numpy.ndarray or scipy.sparse.csr.csr_matrix, float32 otherwise.
Returns:	An array with the same contents as the source_array.
Return type:	RowSparseNDArray or CSRNDArray

Examples

>>> import scipy.sparse as spsp
>>> csr = spsp.csr_matrix((2, 100))
>>> mx.nd.sparse.array(csr)

>>> mx.nd.sparse.array(mx.nd.sparse.zeros('csr', (3, 2)))

>>> mx.nd.sparse.array(mx.nd.sparse.zeros('row_sparse', (3, 2)))

NDArray API of MXNet.

mxnet.ndarray.load(fname)[source]¶

Loads an array from file.

See more details in save.

Parameters:	fname (str) – The filename.
Returns:	Loaded data.
Return type:	list of NDArray, RowSparseNDArray or CSRNDArray, or dict of str to NDArray, RowSparseNDArray or CSRNDArray

mxnet.ndarray.save(fname, data)[source]¶

Saves a list of arrays or a dict of str->array to file.

Examples of filenames:

/path/to/file
s3://my-bucket/path/to/file (if compiled with AWS S3 supports)
hdfs://path/to/file (if compiled with HDFS supports)

Parameters:	fname (str) – The filename. data (NDArray, RowSparseNDArray or CSRNDArray, or list of NDArray, RowSparseNDArray or CSRNDArray, or dict of str to NDArray, RowSparseNDArray or CSRNDArray) – The data to save.

Examples

>>> x = mx.nd.zeros((2,3))
>>> y = mx.nd.ones((1,4))
>>> mx.nd.save('my_list', [x,y])
>>> mx.nd.save('my_dict', {'x':x, 'y':y})
>>> mx.nd.load('my_list')
[, ]
>>> mx.nd.load('my_dict')
{'y': , 'x': }

Sparse NDArray API¶

Overview¶

The CSRNDArray class¶

Array attributes¶

Array conversion¶

Array creation¶

Indexing¶

Lazy evaluation¶

The RowSparseNDArray class¶

Array attributes¶

Array conversion¶

Array creation¶

Array rounding¶

Indexing¶

Lazy evaluation¶

Array creation routines¶

Array manipulation routines¶

Changing array storage type¶

Indexing routines¶

Mathematical functions¶

Arithmetic operations¶

Trigonometric functions¶

Hyperbolic functions¶

Rounding¶

Exponents and logarithms¶

Powers¶

Miscellaneous¶

More¶

API Reference¶

The `CSRNDArray` class¶

The `RowSparseNDArray` class¶