432 lines
14 KiB
Python
432 lines
14 KiB
Python
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"""Sparse DIAgonal format"""
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__docformat__ = "restructuredtext en"
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__all__ = ['dia_matrix', 'isspmatrix_dia']
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import numpy as np
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from .base import isspmatrix, _formats, spmatrix
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from .data import _data_matrix
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from .sputils import (isshape, upcast_char, getdtype, get_index_dtype,
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get_sum_dtype, validateaxis, check_shape, matrix)
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from ._sparsetools import dia_matvec
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class dia_matrix(_data_matrix):
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"""Sparse matrix with DIAgonal storage
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This can be instantiated in several ways:
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dia_matrix(D)
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with a dense matrix
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dia_matrix(S)
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with another sparse matrix S (equivalent to S.todia())
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dia_matrix((M, N), [dtype])
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to construct an empty matrix with shape (M, N),
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dtype is optional, defaulting to dtype='d'.
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dia_matrix((data, offsets), shape=(M, N))
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where the ``data[k,:]`` stores the diagonal entries for
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diagonal ``offsets[k]`` (See example below)
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Attributes
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----------
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dtype : dtype
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Data type of the matrix
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shape : 2-tuple
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Shape of the matrix
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ndim : int
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Number of dimensions (this is always 2)
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nnz
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Number of stored values, including explicit zeros
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data
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DIA format data array of the matrix
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offsets
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DIA format offset array of the matrix
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Notes
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-----
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Sparse matrices can be used in arithmetic operations: they support
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addition, subtraction, multiplication, division, and matrix power.
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Examples
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--------
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>>> import numpy as np
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>>> from scipy.sparse import dia_matrix
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>>> dia_matrix((3, 4), dtype=np.int8).toarray()
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array([[0, 0, 0, 0],
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[0, 0, 0, 0],
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[0, 0, 0, 0]], dtype=int8)
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>>> data = np.array([[1, 2, 3, 4]]).repeat(3, axis=0)
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>>> offsets = np.array([0, -1, 2])
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>>> dia_matrix((data, offsets), shape=(4, 4)).toarray()
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array([[1, 0, 3, 0],
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[1, 2, 0, 4],
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[0, 2, 3, 0],
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[0, 0, 3, 4]])
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>>> from scipy.sparse import dia_matrix
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>>> n = 10
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>>> ex = np.ones(n)
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>>> data = np.array([ex, 2 * ex, ex])
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>>> offsets = np.array([-1, 0, 1])
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>>> dia_matrix((data, offsets), shape=(n, n)).toarray()
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array([[2., 1., 0., ..., 0., 0., 0.],
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[1., 2., 1., ..., 0., 0., 0.],
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[0., 1., 2., ..., 0., 0., 0.],
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...,
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[0., 0., 0., ..., 2., 1., 0.],
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[0., 0., 0., ..., 1., 2., 1.],
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[0., 0., 0., ..., 0., 1., 2.]])
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"""
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format = 'dia'
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def __init__(self, arg1, shape=None, dtype=None, copy=False):
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_data_matrix.__init__(self)
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if isspmatrix_dia(arg1):
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if copy:
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arg1 = arg1.copy()
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self.data = arg1.data
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self.offsets = arg1.offsets
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self._shape = check_shape(arg1.shape)
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elif isspmatrix(arg1):
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if isspmatrix_dia(arg1) and copy:
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A = arg1.copy()
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else:
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A = arg1.todia()
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self.data = A.data
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self.offsets = A.offsets
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self._shape = check_shape(A.shape)
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elif isinstance(arg1, tuple):
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if isshape(arg1):
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# It's a tuple of matrix dimensions (M, N)
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# create empty matrix
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self._shape = check_shape(arg1)
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self.data = np.zeros((0,0), getdtype(dtype, default=float))
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idx_dtype = get_index_dtype(maxval=max(self.shape))
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self.offsets = np.zeros((0), dtype=idx_dtype)
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else:
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try:
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# Try interpreting it as (data, offsets)
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data, offsets = arg1
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except Exception:
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raise ValueError('unrecognized form for dia_matrix constructor')
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else:
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if shape is None:
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raise ValueError('expected a shape argument')
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self.data = np.atleast_2d(np.array(arg1[0], dtype=dtype, copy=copy))
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self.offsets = np.atleast_1d(np.array(arg1[1],
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dtype=get_index_dtype(maxval=max(shape)),
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copy=copy))
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self._shape = check_shape(shape)
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else:
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#must be dense, convert to COO first, then to DIA
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try:
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arg1 = np.asarray(arg1)
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except Exception:
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raise ValueError("unrecognized form for"
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" %s_matrix constructor" % self.format)
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from .coo import coo_matrix
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A = coo_matrix(arg1, dtype=dtype, shape=shape).todia()
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self.data = A.data
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self.offsets = A.offsets
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self._shape = check_shape(A.shape)
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if dtype is not None:
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self.data = self.data.astype(dtype)
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#check format
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if self.offsets.ndim != 1:
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raise ValueError('offsets array must have rank 1')
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if self.data.ndim != 2:
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raise ValueError('data array must have rank 2')
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if self.data.shape[0] != len(self.offsets):
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raise ValueError('number of diagonals (%d) '
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'does not match the number of offsets (%d)'
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% (self.data.shape[0], len(self.offsets)))
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if len(np.unique(self.offsets)) != len(self.offsets):
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raise ValueError('offset array contains duplicate values')
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def __repr__(self):
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format = _formats[self.getformat()][1]
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return "<%dx%d sparse matrix of type '%s'\n" \
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"\twith %d stored elements (%d diagonals) in %s format>" % \
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(self.shape + (self.dtype.type, self.nnz, self.data.shape[0],
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format))
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def _data_mask(self):
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"""Returns a mask of the same shape as self.data, where
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mask[i,j] is True when data[i,j] corresponds to a stored element."""
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num_rows, num_cols = self.shape
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offset_inds = np.arange(self.data.shape[1])
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row = offset_inds - self.offsets[:,None]
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mask = (row >= 0)
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mask &= (row < num_rows)
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mask &= (offset_inds < num_cols)
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return mask
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def count_nonzero(self):
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mask = self._data_mask()
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return np.count_nonzero(self.data[mask])
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def getnnz(self, axis=None):
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if axis is not None:
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raise NotImplementedError("getnnz over an axis is not implemented "
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"for DIA format")
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M,N = self.shape
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nnz = 0
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for k in self.offsets:
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if k > 0:
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nnz += min(M,N-k)
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else:
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nnz += min(M+k,N)
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return int(nnz)
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getnnz.__doc__ = spmatrix.getnnz.__doc__
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count_nonzero.__doc__ = spmatrix.count_nonzero.__doc__
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def sum(self, axis=None, dtype=None, out=None):
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validateaxis(axis)
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if axis is not None and axis < 0:
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axis += 2
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res_dtype = get_sum_dtype(self.dtype)
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num_rows, num_cols = self.shape
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ret = None
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if axis == 0:
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mask = self._data_mask()
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x = (self.data * mask).sum(axis=0)
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if x.shape[0] == num_cols:
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res = x
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else:
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res = np.zeros(num_cols, dtype=x.dtype)
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res[:x.shape[0]] = x
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ret = matrix(res, dtype=res_dtype)
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else:
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row_sums = np.zeros(num_rows, dtype=res_dtype)
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one = np.ones(num_cols, dtype=res_dtype)
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dia_matvec(num_rows, num_cols, len(self.offsets),
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self.data.shape[1], self.offsets, self.data, one, row_sums)
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row_sums = matrix(row_sums)
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if axis is None:
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return row_sums.sum(dtype=dtype, out=out)
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if axis is not None:
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row_sums = row_sums.T
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ret = matrix(row_sums.sum(axis=axis))
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if out is not None and out.shape != ret.shape:
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raise ValueError("dimensions do not match")
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return ret.sum(axis=(), dtype=dtype, out=out)
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sum.__doc__ = spmatrix.sum.__doc__
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def _mul_vector(self, other):
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x = other
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y = np.zeros(self.shape[0], dtype=upcast_char(self.dtype.char,
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x.dtype.char))
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L = self.data.shape[1]
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M,N = self.shape
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dia_matvec(M,N, len(self.offsets), L, self.offsets, self.data, x.ravel(), y.ravel())
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return y
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def _mul_multimatrix(self, other):
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return np.hstack([self._mul_vector(col).reshape(-1,1) for col in other.T])
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def _setdiag(self, values, k=0):
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M, N = self.shape
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if values.ndim == 0:
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# broadcast
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values_n = np.inf
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else:
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values_n = len(values)
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if k < 0:
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n = min(M + k, N, values_n)
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min_index = 0
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max_index = n
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else:
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n = min(M, N - k, values_n)
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min_index = k
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max_index = k + n
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if values.ndim != 0:
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# allow also longer sequences
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values = values[:n]
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if k in self.offsets:
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self.data[self.offsets == k, min_index:max_index] = values
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else:
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self.offsets = np.append(self.offsets, self.offsets.dtype.type(k))
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m = max(max_index, self.data.shape[1])
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data = np.zeros((self.data.shape[0]+1, m), dtype=self.data.dtype)
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data[:-1,:self.data.shape[1]] = self.data
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data[-1, min_index:max_index] = values
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self.data = data
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def todia(self, copy=False):
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if copy:
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return self.copy()
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else:
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return self
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todia.__doc__ = spmatrix.todia.__doc__
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def transpose(self, axes=None, copy=False):
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if axes is not None:
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raise ValueError(("Sparse matrices do not support "
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"an 'axes' parameter because swapping "
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"dimensions is the only logical permutation."))
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num_rows, num_cols = self.shape
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max_dim = max(self.shape)
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# flip diagonal offsets
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offsets = -self.offsets
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# re-align the data matrix
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r = np.arange(len(offsets), dtype=np.intc)[:, None]
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c = np.arange(num_rows, dtype=np.intc) - (offsets % max_dim)[:, None]
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pad_amount = max(0, max_dim-self.data.shape[1])
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data = np.hstack((self.data, np.zeros((self.data.shape[0], pad_amount),
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dtype=self.data.dtype)))
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data = data[r, c]
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return dia_matrix((data, offsets), shape=(
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num_cols, num_rows), copy=copy)
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transpose.__doc__ = spmatrix.transpose.__doc__
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def diagonal(self, k=0):
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rows, cols = self.shape
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if k <= -rows or k >= cols:
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return np.empty(0, dtype=self.data.dtype)
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idx, = np.nonzero(self.offsets == k)
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first_col, last_col = max(0, k), min(rows + k, cols)
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if idx.size == 0:
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return np.zeros(last_col - first_col, dtype=self.data.dtype)
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return self.data[idx[0], first_col:last_col]
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diagonal.__doc__ = spmatrix.diagonal.__doc__
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def tocsc(self, copy=False):
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from .csc import csc_matrix
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if self.nnz == 0:
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return csc_matrix(self.shape, dtype=self.dtype)
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num_rows, num_cols = self.shape
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num_offsets, offset_len = self.data.shape
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offset_inds = np.arange(offset_len)
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row = offset_inds - self.offsets[:,None]
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mask = (row >= 0)
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mask &= (row < num_rows)
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mask &= (offset_inds < num_cols)
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mask &= (self.data != 0)
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idx_dtype = get_index_dtype(maxval=max(self.shape))
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indptr = np.zeros(num_cols + 1, dtype=idx_dtype)
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indptr[1:offset_len+1] = np.cumsum(mask.sum(axis=0))
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indptr[offset_len+1:] = indptr[offset_len]
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indices = row.T[mask.T].astype(idx_dtype, copy=False)
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data = self.data.T[mask.T]
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return csc_matrix((data, indices, indptr), shape=self.shape,
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dtype=self.dtype)
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tocsc.__doc__ = spmatrix.tocsc.__doc__
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def tocoo(self, copy=False):
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num_rows, num_cols = self.shape
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num_offsets, offset_len = self.data.shape
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offset_inds = np.arange(offset_len)
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|
|
row = offset_inds - self.offsets[:,None]
|
||
|
|
mask = (row >= 0)
|
||
|
|
mask &= (row < num_rows)
|
||
|
|
mask &= (offset_inds < num_cols)
|
||
|
|
mask &= (self.data != 0)
|
||
|
|
row = row[mask]
|
||
|
|
col = np.tile(offset_inds, num_offsets)[mask.ravel()]
|
||
|
|
data = self.data[mask]
|
||
|
|
|
||
|
|
from .coo import coo_matrix
|
||
|
|
A = coo_matrix((data,(row,col)), shape=self.shape, dtype=self.dtype)
|
||
|
|
A.has_canonical_format = True
|
||
|
|
return A
|
||
|
|
|
||
|
|
tocoo.__doc__ = spmatrix.tocoo.__doc__
|
||
|
|
|
||
|
|
# needed by _data_matrix
|
||
|
|
def _with_data(self, data, copy=True):
|
||
|
|
"""Returns a matrix with the same sparsity structure as self,
|
||
|
|
but with different data. By default the structure arrays are copied.
|
||
|
|
"""
|
||
|
|
if copy:
|
||
|
|
return dia_matrix((data, self.offsets.copy()), shape=self.shape)
|
||
|
|
else:
|
||
|
|
return dia_matrix((data,self.offsets), shape=self.shape)
|
||
|
|
|
||
|
|
def resize(self, *shape):
|
||
|
|
shape = check_shape(shape)
|
||
|
|
M, N = shape
|
||
|
|
# we do not need to handle the case of expanding N
|
||
|
|
self.data = self.data[:, :N]
|
||
|
|
|
||
|
|
if (M > self.shape[0] and
|
||
|
|
np.any(self.offsets + self.shape[0] < self.data.shape[1])):
|
||
|
|
# explicitly clear values that were previously hidden
|
||
|
|
mask = (self.offsets[:, None] + self.shape[0] <=
|
||
|
|
np.arange(self.data.shape[1]))
|
||
|
|
self.data[mask] = 0
|
||
|
|
|
||
|
|
self._shape = shape
|
||
|
|
|
||
|
|
resize.__doc__ = spmatrix.resize.__doc__
|
||
|
|
|
||
|
|
|
||
|
|
def isspmatrix_dia(x):
|
||
|
|
"""Is x of dia_matrix type?
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
x
|
||
|
|
object to check for being a dia matrix
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
bool
|
||
|
|
True if x is a dia matrix, False otherwise
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from scipy.sparse import dia_matrix, isspmatrix_dia
|
||
|
|
>>> isspmatrix_dia(dia_matrix([[5]]))
|
||
|
|
True
|
||
|
|
|
||
|
|
>>> from scipy.sparse import dia_matrix, csr_matrix, isspmatrix_dia
|
||
|
|
>>> isspmatrix_dia(csr_matrix([[5]]))
|
||
|
|
False
|
||
|
|
"""
|
||
|
|
return isinstance(x, dia_matrix)
|