<commit_before>"""Sparse DIAgonal format"""

from __future__ import division, print_function, absolute_import

__docformat__ = "restructuredtext en"

__all__ = ['dia_matrix', 'isspmatrix_dia']

import numpy as np

from .base import isspmatrix, _formats, spmatrix
from .data import _data_matrix
from .sputils import (isshape, upcast_char, getdtype, get_index_dtype,
                      get_sum_dtype, validateaxis, check_shape, matrix)
from ._sparsetools import dia_matvec


class dia_matrix(_data_matrix):
    """Sparse matrix with DIAgonal storage

    This can be instantiated in several ways:
        dia_matrix(D)
            with a dense matrix

        dia_matrix(S)
            with another sparse matrix S (equivalent to S.todia())

        dia_matrix((M, N), [dtype])
            to construct an empty matrix with shape (M, N),
            dtype is optional, defaulting to dtype='d'.

        dia_matrix((data, offsets), shape=(M, N))
            where the ``data[k,:]`` stores the diagonal entries for
            diagonal ``offsets[k]`` (See example below)

    Attributes
    ----------
    dtype : dtype
        Data type of the matrix
    shape : 2-tuple
        Shape of the matrix
    ndim : int
        Number of dimensions (this is always 2)
    nnz
        Number of stored values, including explicit zeros
    data
        DIA format data array of the matrix
    offsets
        DIA format offset array of the matrix

    Notes
    -----

    Sparse matrices can be used in arithmetic operations: they support
    addition, subtraction, multiplication, division, and matrix power.

    Examples
    --------

    >>> import numpy as np
    >>> from scipy.sparse import dia_matrix
    >>> dia_matrix((3, 4), dtype=np.int8).toarray()
    array([[0, 0, 0, 0],
           [0, 0, 0, 0],
           [0, 0, 0, 0]], dtype=int8)

    >>> data = np.array([[1, 2, 3, 4]]).repeat(3, axis=0)
    >>> offsets = np.array([0, -1, 2])
    >>> dia_matrix((data, offsets), shape=(4, 4)).toarray()
    array([[1, 0, 3, 0],
           [1, 2, 0, 4],
           [0, 2, 3, 0],
           [0, 0, 3, 4]])

    >>> n= 10000
    >>> ex = np.ones(n)
    >>> data = np.array([ex, 2 * ex, ex])
    >>> offsets = np.array([-1, 0, 1])
    >>> dia_matrix((data, offsets), shape=(n, n)).toarray()

    array([[2., 1., 0., ..., 0., 0., 0.],
           [1., 2., 1., ..., 0., 0., 0.],
           [0., 1., 2., ..., 0., 0., 0.],
           ...,
           [0., 0., 0., ..., 2., 1., 0.],
           [0., 0., 0., ..., 1., 2., 1.],
           [0., 0., 0., ..., 0., 1., 2.]])
    """
    format = 'dia'

    def __init__(self, arg1, shape=None, dtype=None, copy=False):
        _data_matrix.__init__(self)

        if isspmatrix_dia(arg1):
            if copy:
                arg1 = arg1.copy()
            self.data = arg1.data
            self.offsets = arg1.offsets
            self._shape = check_shape(arg1.shape)
        elif isspmatrix(arg1):<commit_msg>fix explicit import and pick a smaller n<commit_after>"""Sparse DIAgonal format"""

from __future__ import division, print_function, absolute_import

__docformat__ = "restructuredtext en"

__all__ = ['dia_matrix', 'isspmatrix_dia']

import numpy as np

from .base import isspmatrix, _formats, spmatrix
from .data import _data_matrix
from .sputils import (isshape, upcast_char, getdtype, get_index_dtype,
                      get_sum_dtype, validateaxis, check_shape, matrix)
from ._sparsetools import dia_matvec


class dia_matrix(_data_matrix):
    """Sparse matrix with DIAgonal storage

    This can be instantiated in several ways:
        dia_matrix(D)
            with a dense matrix

        dia_matrix(S)
            with another sparse matrix S (equivalent to S.todia())

        dia_matrix((M, N), [dtype])
            to construct an empty matrix with shape (M, N),
            dtype is optional, defaulting to dtype='d'.

        dia_matrix((data, offsets), shape=(M, N))
            where the ``data[k,:]`` stores the diagonal entries for
            diagonal ``offsets[k]`` (See example below)

    Attributes
    ----------
    dtype : dtype
        Data type of the matrix
    shape : 2-tuple
        Shape of the matrix
    ndim : int
        Number of dimensions (this is always 2)
    nnz
        Number of stored values, including explicit zeros
    data
        DIA format data array of the matrix
    offsets
        DIA format offset array of the matrix

    Notes
    -----

    Sparse matrices can be used in arithmetic operations: they support
    addition, subtraction, multiplication, division, and matrix power.

    Examples
    --------

    >>> import numpy as np
    >>> from scipy.sparse import dia_matrix
    >>> dia_matrix((3, 4), dtype=np.int8).toarray()
    array([[0, 0, 0, 0],
           [0, 0, 0, 0],
           [0, 0, 0, 0]], dtype=int8)

    >>> data = np.array([[1, 2, 3, 4]]).repeat(3, axis=0)
    >>> offsets = np.array([0, -1, 2])
    >>> dia_matrix((data, offsets), shape=(4, 4)).toarray()
    array([[1, 0, 3, 0],
           [1, 2, 0, 4],
           [0, 2, 3, 0],
           [0, 0, 3, 4]])

    >>> import numpy as np
    >>> from scipy.sparse import dia_matrix
    >>> n= 10
    >>> ex = np.ones(n)
    >>> data = np.array([ex, 2 * ex, ex])
    >>> offsets = np.array([-1, 0, 1])
    >>> dia_matrix((data, offsets), shape=(n, n)).toarray()

    array([[2., 1., 0., ..., 0., 0., 0.],
           [1., 2., 1., ..., 0., 0., 0.],
           [0., 1., 2., ..., 0., 0., 0.],
           ...,
           [0., 0., 0., ..., 2., 1., 0.],
           [0., 0., 0., ..., 1., 2., 1.],
           [0., 0., 0., ..., 0., 1., 2.]])
    """
    format = 'dia'

    def __init__(self, arg1, shape=None, dtype=None, copy=False):
        _data_matrix.__init__(self)

        if isspmatrix_dia(arg1):
            if copy:
                arg1 = arg1.copy()
            self.data = arg1.data
            self.offsets = arg1.offsets
            self._shape = check_shape(arg1.shape)
        elif isspmatrix(arg1):
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