NAME

AI::MXNet::NDArray::Sparse - Sparse NDArray API of MXNet

DESCRIPTION

The base class of an NDArray stored in a sparse storage format.
See AI::MXNet::NDArray::CSR and AI::MXNet::NDArray::RowSparse for more details.

aspdl

Return a dense PDL object with value copied from this array

astype

Returns a copy of the array after casting to a specified type.
Parameters
----------
dtype : Dtype
    The type of the returned array.
Examples
--------
>>> $x = mx->nd->sparse->zeros('row_sparse', [2,3], dtype=>'float32')
>>> $y = $x->astype('int32')
>>> $y->dtype
<type 'int32'>

copyto

Copies the value of this array to another array.

Parameters
----------
other : NDArray or NDArray::CSR or NDArray::RowSparse or Context
    The destination array or context.

Returns
-------
NDArray or CSRNDArray::CSR or NDArray::RowSparse
    The copied array.

check_format

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).

_data

A deep copy NDArray of the data array associated with the BaseSparseNDArray.

This function blocks. Do not use it in performance critical code.

_aux_data

Get a deep copy NDArray of the i-th aux data array associated with the
AI::MXNet::NDArray::Sparse

This function blocks. Do not use it in performance critical code.

NAME

AI::MXNet::NDArray::CSR - A sparse representation of 2D NDArray in the Compressed Sparse Row format.

DESCRIPTION

A AI::MXNet::NDArray::CSR represents an AI::MXNet::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->aspdl;
[ 1  2  3]
>>> $a->indices->aspdl
[1 0 2]
>>> $a->indptr->aspdl
[0 1 2 2 3]

See Also
--------
csr_matrix: Several ways to construct a CSRNDArray

slice

Returns a newly created array based on the indexing key.

Parameters
----------
key : int or array ref
    Indexing key.

Examples
--------
>>> $indptr = [0, 2, 3, 6];
>>> $indices = [0, 2, 2, 0, 1, 2];
>>> $data = [1, 2, 3, 4, 5, 6];
>>> $a = mx->nd->sparse->csr_matrix([$data, $indices, $indptr], shape=>[3, 3])
>>> $a->aspdl
    [[ 1  0  2]
     [ 0  0  3]
     [ 4  5  6]]
>>> $a->slice([1,2])->aspdl
[[ 0  0  3]]
>>> $a->slice(1)->aspdl
[[ 0  0  3]]
>>> $a->[-1]->aspdl
[[ 4  5  6]]

set

Set self to value. Also usable as overloaded .=

Parameters
----------
value : AI::MXNet::NDArray or AI::MXNet::NDArray::CSR
        or PDL/PDL::CCS::Nd/perl array ref in PDL constructor format
    The value to set.

Examples
--------
>>> $src = mx->nd->sparse->zeros('csr', [3,3])
>>> $src->aspdl
      [[ 0  0  0]
       [ 0  0  0]
       [ 0  0  0]]
>>> # AI::MXNet::NDArray::CSR with same storage type
>>> $x = mx->nd->ones('row_sparse', [3,3])->tostype('csr')
>>> $x .= $src
>>> $x->aspdl
      [[ 1  1  1]
       [ 1  1  1]
       [ 1  1  1]]
>>> # assign NDArray to AI::MXNet::NDArray::CSR
>>> $x .= mx->nd->ones([3,3]) * 2
>>> $x->aspdl
      [[ 2  2  2]
       [ 2  2  2]
       [ 2  2  2]]

indices

A deep copy NDArray of the indices array of the AI::MXNet::NDArray::CSR.
This generates a deep copy of the column indices of the current `csr` matrix.

Returns
-------
NDArray
    This AI::MXNet::NDArray::CSR indices array.

indptr

A deep copy NDArray of the inptr array of the AI::MXNet::NDArray::CSR.
This generates a deep copy of the indptr of the current `csr` matrix.

Returns
-------
NDArray
    This AI::MXNet::NDArray::CSR indptr array.

data

A deep copy NDArray of the data array of the AI::MXNet::NDArray::CSR.
This generates a deep copy of the data of the current `csr` matrix.

Returns
-------
NDArray
    This AI::MXNet::NDArray::CSR data array.

tostype

Return a copy of the array with chosen storage type.

Returns
-------
NDArray or AI::MXNet::NDArray::CSR 
    A copy of the array with the chosen storage stype

copyto

Copies the value of this array to another array.

If $other is a AI::MXNet::NDArray or AI::MXNet::NDArray::CSR 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 AI::MXNet::NDArray::CSR will be first created on
the target context, and the value of $self is copied.

Parameters
----------
$other : AI::MXNet::NDArray or AI::MXNet::NDArray::CSR or AI::MXNet::Context
    The destination array or context.

Returns
-------
AI::MXNet::NDArray or AI::MXNet::NDArray::CSR

Returns a PDL::CCS::Nd object with value copied from this array

NAME

AI::MXNet::NDArray::RowSparse - A sparse representation of a set of NDArray row slices at given indices.

DESCRIPTION

A AI::MXNet::NDArray::RowSparse 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 AI::MXNet::NDArray::RowSparse ``rsp`` has

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

    >>> $dense->aspdl
          [[ 1  2  3 ]
           [ 0  0  0 ]
           [ 4  0  5 ]
           [ 0  0  0 ]
           [ 0  0  0 ]]
    >>> $rsp = $dense->tostype('row_sparse');
    >>> $rsp->indices->aspdl
          [ 0 2 ]
    >>> $rsp->data->aspdl
          [[ 1  2 3 ]
           [ 4  0 5 ]]

A AI::MXNet::NDArray::RowSparse 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.

AI::MXNet::NDArray::RowSparse 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 AI::MXNet::NDArray::RowSparse

set

Set self to value. Also usable as overloaded .=

Parameters
----------
value : AI::MXNet::NDArray or AI::MXNet::NDArray::CSR
        or PDL/PDL::CCS::Nd/perl array ref in PDL constructor format
    The value to set.

Examples
--------
>>> $src = mx->nd->sparse->zeros('raw_sparse', [3,3])
>>> $src->aspdl
      [[ 0  0  0]
       [ 0  0  0]
       [ 0  0  0]]
>>> # AI::MXNet::NDArray::RowSparse with same storage type
>>> $x = mx->nd->ones('row_sparse', [3,3])
>>> $src .= $x
>>> $src->aspdl
      [[ 1  1  1]
       [ 1  1  1]
       [ 1  1  1]]
>>> # assign NDArray to AI::MXNet::NDArray::RowSparse
>>> $x .= mx->nd->ones([3,3]) * 2
>>> $x->aspdl
      [[ 2  2  2]
       [ 2  2  2]
       [ 2  2  2]]

data

A deep copy NDArray of the data array of the AI::MXNet::NDArray::RowSparse.
This generates a deep copy of the data of the current `row_sparse` matrix.

Returns
-------
NDArray
    This AI::MXNet::NDArray::RowSparse data array.

indices

A deep copy NDArray of the indices array of the AI::MXNet::NDArray::RowSparse.
This generates a deep copy of the column indices of the current `row_sparse` matrix.

Returns
-------
NDArray
    This AI::MXNet::NDArray::RowSparse indices array.

data

A deep copy NDArray of the data array of the AI::MXNet::NDArray::RowSparse.
This generates a deep copy of the data of the current `row_sparse` matrix.

Returns
-------
NDArray
    This AI::MXNet::NDArray::RowSparse data array.

tostype

Return a copy of the array with chosen storage type.

Returns
-------
NDArray or RowSparseNDArray
    A copy of the array with the chosen storage stype

copyto

Copies the value of this array to another array.

If $other is a AI::MXNet::NDArray or AI::MXNet::NDArray::RawSparse 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 AI::MXNet::NDArray::RawSparse will be first created on
the target context, and the value of $self is copied.

Parameters
----------
$other : AI::MXNet::NDArray or AI::MXNet::NDArray::RawSparse or AI::MXNet::Context
    The destination array or context.

Returns
-------
AI::MXNet::NDArray or AI::MXNet::NDArray::RawSparse

csr_matrix

Creates a AI::MXNet::NDArray::CSR, an 2D array with compressed sparse row (CSR) format.

The AI::MXNet::NDArray::CSR can be instantiated in several ways:

- csr_matrix($arg1, Maybe[AI::MXNet::Context] :$ctx=, Maybe[Shape] :$shape, Maybe [Dtype] :$dtype=)
    $ctx, $shape, $dtype are optional
    $arg1 can be given in following variants

- to construct a AI::MXNet::NDArray::CSR with a dense 2D array $arg1
        - $arg1 is in AI::MXNet::NDArray::array input format

- to construct a AI::MXNet::NDArray::CSR with a sparse 2D array $arg1
        $arg1 is AI::MXNet::NDArray::CSR or PDL::CCS::Nd - A sparse matrix.
        PDL::CCS::Nd is expected to be converted internally into CSR format
        AI::MXNet injects 'tocsr' method into PDL and PDL::CCS::Nd modules for this purpose.

- to construct an empty AI::MXNet::NDArray::CSR with shape $arg1 = [$M, $N]
        -  $M - Number of rows in the matrix
        -  $N - Number of columns in the matrix

- to construct a AI::MXNet::NDArray::CSR 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.
    In this case $arg1 = [$data, $indices, $indptr]
        $data, $indices, $indptr must be given in the AI::MXNet::NDArray::array input format
        - $data - holds all the non-zero entries of the matrix in row-major order.
        - $indices - stores the column index for each non-zero element in $data.
        stores the column index for each non-zero element in $data.
        - $indptr  - stores the offset into $data of the first non-zero element number of each
        row of the matrix.

    to construct a AI::MXNet::NDArray::CSR 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.
    In this case $arg1 = [$data, [$row, $col]]
        $data, $row, $col must be given in the AI::MXNet::NDArray::array input format
        $data - holds all the non-zero entries of the matrix in COO format.
        $row - stores the row index for each non zero element in $data.
        - **col** (*array_like*) - An object exposing the array interface, which
        $col - stores the col index for each non zero element in $data.

Returns
-------
AI::MXNet::NDArray::CSR
    A AI::MXNet::NDArray::CSR with the 'csr' storage representation.

Example
-------
>>> $a = mx->nd->sparse->csr_matrix([[1, 2, 3], [1, 0, 2], [0, 1, 2, 2, 3]], shape => [4, 3])
>>> $a->aspdl
      [[ 0  1  0]
       [ 2  0  0]
       [ 0  0  0]
       [ 0  0  3]]

See Also
--------
CSRNDArray : MXNet NDArray in compressed sparse row format.

row_sparse_array

Creates a AI::MXNet::NDArray::RowSparse, a multidimensional row sparse array with a set of
tensor slices at given indices.

The AI::MXNet::NDArray::RowSparse can be instantiated in several ways:

- row_sparse_array($arg1, Maybe[AI::MXNet::Context] :$ctx=, Maybe[Shape] :$shape, Maybe [Dtype] :$dtype=)
    $ctx, $shape, $dtype are optional
    $arg1 can be given in following variants

- to construct a AI::MXNet::NDArray::RowSparse with a dense array $arg1
        - $arg1 is in AI::MXNet::NDArray::array input format

- to construct a AI::MXNet::NDArray::RowSparse with a sparse array $arg1
        $arg1 is AI::MXNet::NDArray::RowSparse

- to construct an empty AI::MXNet::NDArray::RowSparse with shape $arg1 = [$D1, $D1, ...$DN]

- 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 RowSparse rsp has
    dense[rsp.indices[i], :, :, :, ...] = rsp.data[i, :, :, :, ...]
    The row indices for are expected to be **sorted in ascending order.
    $arg1 = [$data, $indices]
        $data, $indices must be given in the AI::MXNet::NDArray::array input format

Returns
-------
AI::MXNet::NDArray::RowSparse
    A AI::MXNet::NDArray::RowSparse with the 'row_sparse' storage representation.

Example
-------
>>> $a = mx->nd->sparse->row_sparse_array([[[1, 2], [3, 4]], [1, 4]], shape=>[6, 2])
>>> $a->aspdl
      [[ 0  0]
       [ 1  2]
       [ 0  0]
       [ 0  0]
       [ 3  4]
       [ 0  0]]

zeros

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

Parameters
----------
$stype: string
    The storage type of the empty array, such as 'row_sparse', 'csr', etc
shape : int or array ref of int
    The shape of the empty array
:$ctx : AI::MXNet::Context, optional
    An optional device context (default is the current default context)
:$dtype : Dtype, optional
    An optional value type (default is `float32`)

Returns
-------
AI::MXNet::NDArray::RowSparse or AI::MXNet::NDArray::CSR
    A created array
Examples
--------
>>> mx->nd->sparse->zeros('csr', [1,2])
<AI::MXNet::NDArray::CSR 1x2 @cpu(0)>
>>> mx->nd->sparse->zeros('row_sparse', [1,2], ctx=>mx->cpu(), dtype=>'float16')->aspdl
[[ 0  0]]

empty

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 array ref of int
    The shape of the empty array.
ctx : Context, optional
    An optional device context (default is the current default context).
dtype : Dtype, optional
    An optional value type (default is `float32`).

Returns
-------
AI::MXNet::NDArray::CSR or AI::MXNet::NDArray::RowSparse
    A created array.

array

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

Parameters
----------
$source_array : AI::MXNet::NDArray::RowSparse, AI::MXNet::NDArray::CSR or PDL::CCS::Nd
    The source sparse array
:$ctx : Context, optional
    The default context is $source_array->context if $source_array is an NDArray.
    The current default context otherwise.
:$dtype : Dtype, optional
    The data type of the output array. The default dtype is $source_array->dtype
    if $source_array is an AI::MXNet::NDArray, PDL or PDL::CCS::Nd
    'float32' otherwise.

Returns
-------
AI::MXNet::NDArray::RowSparse or AI::MXNet::NDArray::CSR
    An array with the same contents as the $source_array.

Examples
--------
>>> use PDL; use PDL::CCS::Nd
>>> $csr = zeros([100, 2])->tocsr
>>> mx->nd->sparse->array($csr)
<AI::MXNet::NDArray::CSR 2x100 @cpu(0)>
>>> mx->nd->sparse->array(mx->nd->sparse->zeros('csr', [3, 2]))
<AI::MXNet::NDArray::CSR 3x2 @cpu(0)>
>>> mx->nd->sparse->array(mx->nd->sparse->zeros('row_sparse', [3, 2]))
<AI::MXNet::NDArray::RowSparse 3x2 @cpu(0)>