566 lines
18 KiB
Python
566 lines
18 KiB
Python
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"""Sparse DIAgonal format"""
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__docformat__ = "restructuredtext en"
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__all__ = ['dia_array', 'dia_matrix', 'isspmatrix_dia']
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import numpy as np
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from .._lib._util import copy_if_needed
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from ._matrix import spmatrix
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from ._base import issparse, _formats, _spbase, sparray
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from ._data import _data_matrix
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from ._sputils import (
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isshape, upcast_char, getdtype, get_sum_dtype, validateaxis, check_shape
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)
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from ._sparsetools import dia_matvec
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class _dia_base(_data_matrix):
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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 issparse(arg1):
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if arg1.format == "dia":
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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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else:
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if arg1.format == self.format 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 = self._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 as e:
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message = 'unrecognized form for dia_array constructor'
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raise ValueError(message) from e
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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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if not copy:
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copy = copy_if_needed
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self.data = np.atleast_2d(np.array(arg1[0], dtype=dtype, copy=copy))
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offsets = np.array(arg1[1],
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dtype=self._get_index_dtype(maxval=max(shape)),
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copy=copy)
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self.offsets = np.atleast_1d(offsets)
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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 as e:
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raise ValueError("unrecognized form for"
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" %s_matrix constructor" % self.format) from e
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if isinstance(self, sparray) and arg1.ndim != 2:
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raise ValueError(f"DIA arrays don't support {arg1.ndim}D input. Use 2D")
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A = self._coo_container(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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_, fmt = _formats[self.format]
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sparse_cls = 'array' if isinstance(self, sparray) else 'matrix'
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shape_str = 'x'.join(str(x) for x in self.shape)
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ndiag = self.data.shape[0]
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return (
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f"<{shape_str} sparse {sparse_cls} of type '{self.dtype.type}'\n"
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f"\twith {self.nnz} stored elements ({ndiag} diagonals) in {fmt} format>"
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)
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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__ = _spbase._getnnz.__doc__
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count_nonzero.__doc__ = _spbase.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 = self._ascontainer(res, dtype=res_dtype)
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else:
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row_sums = np.zeros((num_rows, 1), 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 = self._ascontainer(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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ret = self._ascontainer(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__ = _spbase.sum.__doc__
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def _add_sparse(self, other):
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# Check if other is also of type dia_array
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if not isinstance(other, type(self)):
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# If other is not of type dia_array, default to
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# converting to csr_matrix, as is done in the _add_sparse
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# method of parent class _spbase
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return self.tocsr()._add_sparse(other)
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# The task is to compute m = self + other
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# Start by making a copy of self, of the datatype
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# that should result from adding self and other
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dtype = np.promote_types(self.dtype, other.dtype)
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m = self.astype(dtype, copy=True)
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# Then, add all the stored diagonals of other.
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for d in other.offsets:
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# Check if the diagonal has already been added.
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if d in m.offsets:
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# If the diagonal is already there, we need to take
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# the sum of the existing and the new
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m.setdiag(m.diagonal(d) + other.diagonal(d), d)
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else:
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m.setdiag(other.diagonal(d), d)
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return m
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def _matmul_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,
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x.ravel(), y.ravel())
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return y
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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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data_rows, data_cols = self.data.shape
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if k in self.offsets:
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if max_index > data_cols:
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data = np.zeros((data_rows, max_index), dtype=self.data.dtype)
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data[:, :data_cols] = self.data
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self.data = data
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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, data_cols)
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data = np.zeros((data_rows + 1, m), dtype=self.data.dtype)
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data[:-1, :data_cols] = 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__ = _spbase.todia.__doc__
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def transpose(self, axes=None, copy=False):
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if axes is not None and axes != (1, 0):
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raise ValueError("Sparse arrays/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 self._dia_container((data, offsets), shape=(
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num_cols, num_rows), copy=copy)
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transpose.__doc__ = _spbase.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 = max(0, k)
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last_col = min(rows + k, cols)
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result_size = last_col - first_col
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if idx.size == 0:
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return np.zeros(result_size, dtype=self.data.dtype)
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result = self.data[idx[0], first_col:last_col]
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padding = result_size - len(result)
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if padding > 0:
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result = np.pad(result, (0, padding), mode='constant')
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return result
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diagonal.__doc__ = _spbase.diagonal.__doc__
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def tocsc(self, copy=False):
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if self.nnz == 0:
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return self._csc_container(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 = self._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)[:num_cols])
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if offset_len < num_cols:
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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 self._csc_container((data, indices, indptr), shape=self.shape,
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dtype=self.dtype)
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tocsc.__doc__ = _spbase.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]
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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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row = row[mask]
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col = np.tile(offset_inds, num_offsets)[mask.ravel()]
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idx_dtype = self._get_index_dtype(
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arrays=(self.offsets,), maxval=max(self.shape)
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)
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row = row.astype(idx_dtype, copy=False)
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col = col.astype(idx_dtype, copy=False)
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data = self.data[mask]
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# Note: this cannot set has_canonical_format=True, because despite the
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# lack of duplicates, we do not generate sorted indices.
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return self._coo_container(
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|
|
(data, (row, col)), shape=self.shape, dtype=self.dtype, copy=False
|
||
|
|
)
|
||
|
|
|
||
|
|
tocoo.__doc__ = _spbase.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 self._dia_container(
|
||
|
|
(data, self.offsets.copy()), shape=self.shape
|
||
|
|
)
|
||
|
|
else:
|
||
|
|
return self._dia_container(
|
||
|
|
(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__ = _spbase.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_array, dia_matrix, coo_matrix, isspmatrix_dia
|
||
|
|
>>> isspmatrix_dia(dia_matrix([[5]]))
|
||
|
|
True
|
||
|
|
>>> isspmatrix_dia(dia_array([[5]]))
|
||
|
|
False
|
||
|
|
>>> isspmatrix_dia(coo_matrix([[5]]))
|
||
|
|
False
|
||
|
|
"""
|
||
|
|
return isinstance(x, dia_matrix)
|
||
|
|
|
||
|
|
|
||
|
|
# This namespace class separates array from matrix with isinstance
|
||
|
|
class dia_array(_dia_base, sparray):
|
||
|
|
"""
|
||
|
|
Sparse array with DIAgonal storage.
|
||
|
|
|
||
|
|
This can be instantiated in several ways:
|
||
|
|
dia_array(D)
|
||
|
|
where D is a 2-D ndarray
|
||
|
|
|
||
|
|
dia_array(S)
|
||
|
|
with another sparse array or matrix S (equivalent to S.todia())
|
||
|
|
|
||
|
|
dia_array((M, N), [dtype])
|
||
|
|
to construct an empty array with shape (M, N),
|
||
|
|
dtype is optional, defaulting to dtype='d'.
|
||
|
|
|
||
|
|
dia_array((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 array
|
||
|
|
shape : 2-tuple
|
||
|
|
Shape of the array
|
||
|
|
ndim : int
|
||
|
|
Number of dimensions (this is always 2)
|
||
|
|
nnz
|
||
|
|
size
|
||
|
|
data
|
||
|
|
DIA format data array of the array
|
||
|
|
offsets
|
||
|
|
DIA format offset array of the array
|
||
|
|
T
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
|
||
|
|
Sparse arrays 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_array
|
||
|
|
>>> dia_array((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_array((data, offsets), shape=(4, 4)).toarray()
|
||
|
|
array([[1, 0, 3, 0],
|
||
|
|
[1, 2, 0, 4],
|
||
|
|
[0, 2, 3, 0],
|
||
|
|
[0, 0, 3, 4]])
|
||
|
|
|
||
|
|
>>> from scipy.sparse import dia_array
|
||
|
|
>>> n = 10
|
||
|
|
>>> ex = np.ones(n)
|
||
|
|
>>> data = np.array([ex, 2 * ex, ex])
|
||
|
|
>>> offsets = np.array([-1, 0, 1])
|
||
|
|
>>> dia_array((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.]])
|
||
|
|
"""
|
||
|
|
|
||
|
|
|
||
|
|
class dia_matrix(spmatrix, _dia_base):
|
||
|
|
"""
|
||
|
|
Sparse matrix with DIAgonal storage.
|
||
|
|
|
||
|
|
This can be instantiated in several ways:
|
||
|
|
dia_matrix(D)
|
||
|
|
where D is a 2-D ndarray
|
||
|
|
|
||
|
|
dia_matrix(S)
|
||
|
|
with another sparse array or 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
|
||
|
|
size
|
||
|
|
data
|
||
|
|
DIA format data array of the matrix
|
||
|
|
offsets
|
||
|
|
DIA format offset array of the matrix
|
||
|
|
T
|
||
|
|
|
||
|
|
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]])
|
||
|
|
|
||
|
|
>>> 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.]])
|
||
|
|
"""
|