dia.py
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"""Sparse DIAgonal format"""
__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]])
>>> 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):
if isspmatrix_dia(arg1) and copy:
A = arg1.copy()
else:
A = arg1.todia()
self.data = A.data
self.offsets = A.offsets
self._shape = check_shape(A.shape)
elif isinstance(arg1, tuple):
if isshape(arg1):
# It's a tuple of matrix dimensions (M, N)
# create empty matrix
self._shape = check_shape(arg1)
self.data = np.zeros((0,0), getdtype(dtype, default=float))
idx_dtype = get_index_dtype(maxval=max(self.shape))
self.offsets = np.zeros((0), dtype=idx_dtype)
else:
try:
# Try interpreting it as (data, offsets)
data, offsets = arg1
except Exception:
raise ValueError('unrecognized form for dia_matrix constructor')
else:
if shape is None:
raise ValueError('expected a shape argument')
self.data = np.atleast_2d(np.array(arg1[0], dtype=dtype, copy=copy))
self.offsets = np.atleast_1d(np.array(arg1[1],
dtype=get_index_dtype(maxval=max(shape)),
copy=copy))
self._shape = check_shape(shape)
else:
#must be dense, convert to COO first, then to DIA
try:
arg1 = np.asarray(arg1)
except Exception:
raise ValueError("unrecognized form for"
" %s_matrix constructor" % self.format)
from .coo import coo_matrix
A = coo_matrix(arg1, dtype=dtype, shape=shape).todia()
self.data = A.data
self.offsets = A.offsets
self._shape = check_shape(A.shape)
if dtype is not None:
self.data = self.data.astype(dtype)
#check format
if self.offsets.ndim != 1:
raise ValueError('offsets array must have rank 1')
if self.data.ndim != 2:
raise ValueError('data array must have rank 2')
if self.data.shape[0] != len(self.offsets):
raise ValueError('number of diagonals (%d) '
'does not match the number of offsets (%d)'
% (self.data.shape[0], len(self.offsets)))
if len(np.unique(self.offsets)) != len(self.offsets):
raise ValueError('offset array contains duplicate values')
def __repr__(self):
format = _formats[self.getformat()][1]
return "<%dx%d sparse matrix of type '%s'\n" \
"\twith %d stored elements (%d diagonals) in %s format>" % \
(self.shape + (self.dtype.type, self.nnz, self.data.shape[0],
format))
def _data_mask(self):
"""Returns a mask of the same shape as self.data, where
mask[i,j] is True when data[i,j] corresponds to a stored element."""
num_rows, num_cols = self.shape
offset_inds = np.arange(self.data.shape[1])
row = offset_inds - self.offsets[:,None]
mask = (row >= 0)
mask &= (row < num_rows)
mask &= (offset_inds < num_cols)
return mask
def count_nonzero(self):
mask = self._data_mask()
return np.count_nonzero(self.data[mask])
def getnnz(self, axis=None):
if axis is not None:
raise NotImplementedError("getnnz over an axis is not implemented "
"for DIA format")
M,N = self.shape
nnz = 0
for k in self.offsets:
if k > 0:
nnz += min(M,N-k)
else:
nnz += min(M+k,N)
return int(nnz)
getnnz.__doc__ = spmatrix.getnnz.__doc__
count_nonzero.__doc__ = spmatrix.count_nonzero.__doc__
def sum(self, axis=None, dtype=None, out=None):
validateaxis(axis)
if axis is not None and axis < 0:
axis += 2
res_dtype = get_sum_dtype(self.dtype)
num_rows, num_cols = self.shape
ret = None
if axis == 0:
mask = self._data_mask()
x = (self.data * mask).sum(axis=0)
if x.shape[0] == num_cols:
res = x
else:
res = np.zeros(num_cols, dtype=x.dtype)
res[:x.shape[0]] = x
ret = matrix(res, dtype=res_dtype)
else:
row_sums = np.zeros(num_rows, dtype=res_dtype)
one = np.ones(num_cols, dtype=res_dtype)
dia_matvec(num_rows, num_cols, len(self.offsets),
self.data.shape[1], self.offsets, self.data, one, row_sums)
row_sums = matrix(row_sums)
if axis is None:
return row_sums.sum(dtype=dtype, out=out)
if axis is not None:
row_sums = row_sums.T
ret = matrix(row_sums.sum(axis=axis))
if out is not None and out.shape != ret.shape:
raise ValueError("dimensions do not match")
return ret.sum(axis=(), dtype=dtype, out=out)
sum.__doc__ = spmatrix.sum.__doc__
def _mul_vector(self, other):
x = other
y = np.zeros(self.shape[0], dtype=upcast_char(self.dtype.char,
x.dtype.char))
L = self.data.shape[1]
M,N = self.shape
dia_matvec(M,N, len(self.offsets), L, self.offsets, self.data, x.ravel(), y.ravel())
return y
def _mul_multimatrix(self, other):
return np.hstack([self._mul_vector(col).reshape(-1,1) for col in other.T])
def _setdiag(self, values, k=0):
M, N = self.shape
if values.ndim == 0:
# broadcast
values_n = np.inf
else:
values_n = len(values)
if k < 0:
n = min(M + k, N, values_n)
min_index = 0
max_index = n
else:
n = min(M, N - k, values_n)
min_index = k
max_index = k + n
if values.ndim != 0:
# allow also longer sequences
values = values[:n]
if k in self.offsets:
self.data[self.offsets == k, min_index:max_index] = values
else:
self.offsets = np.append(self.offsets, self.offsets.dtype.type(k))
m = max(max_index, self.data.shape[1])
data = np.zeros((self.data.shape[0]+1, m), dtype=self.data.dtype)
data[:-1,:self.data.shape[1]] = self.data
data[-1, min_index:max_index] = values
self.data = data
def todia(self, copy=False):
if copy:
return self.copy()
else:
return self
todia.__doc__ = spmatrix.todia.__doc__
def transpose(self, axes=None, copy=False):
if axes is not None:
raise ValueError(("Sparse matrices do not support "
"an 'axes' parameter because swapping "
"dimensions is the only logical permutation."))
num_rows, num_cols = self.shape
max_dim = max(self.shape)
# flip diagonal offsets
offsets = -self.offsets
# re-align the data matrix
r = np.arange(len(offsets), dtype=np.intc)[:, None]
c = np.arange(num_rows, dtype=np.intc) - (offsets % max_dim)[:, None]
pad_amount = max(0, max_dim-self.data.shape[1])
data = np.hstack((self.data, np.zeros((self.data.shape[0], pad_amount),
dtype=self.data.dtype)))
data = data[r, c]
return dia_matrix((data, offsets), shape=(
num_cols, num_rows), copy=copy)
transpose.__doc__ = spmatrix.transpose.__doc__
def diagonal(self, k=0):
rows, cols = self.shape
if k <= -rows or k >= cols:
return np.empty(0, dtype=self.data.dtype)
idx, = np.nonzero(self.offsets == k)
first_col, last_col = max(0, k), min(rows + k, cols)
if idx.size == 0:
return np.zeros(last_col - first_col, dtype=self.data.dtype)
return self.data[idx[0], first_col:last_col]
diagonal.__doc__ = spmatrix.diagonal.__doc__
def tocsc(self, copy=False):
from .csc import csc_matrix
if self.nnz == 0:
return csc_matrix(self.shape, dtype=self.dtype)
num_rows, num_cols = self.shape
num_offsets, offset_len = self.data.shape
offset_inds = np.arange(offset_len)
row = offset_inds - self.offsets[:,None]
mask = (row >= 0)
mask &= (row < num_rows)
mask &= (offset_inds < num_cols)
mask &= (self.data != 0)
idx_dtype = get_index_dtype(maxval=max(self.shape))
indptr = np.zeros(num_cols + 1, dtype=idx_dtype)
indptr[1:offset_len+1] = np.cumsum(mask.sum(axis=0))
indptr[offset_len+1:] = indptr[offset_len]
indices = row.T[mask.T].astype(idx_dtype, copy=False)
data = self.data.T[mask.T]
return csc_matrix((data, indices, indptr), shape=self.shape,
dtype=self.dtype)
tocsc.__doc__ = spmatrix.tocsc.__doc__
def tocoo(self, copy=False):
num_rows, num_cols = self.shape
num_offsets, offset_len = self.data.shape
offset_inds = np.arange(offset_len)
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)