def spdiags(data, diags, m, n, format=None):
"""
Return a sparse matrix from diagonals.
Parameters
----------
data : array_like
matrix diagonals stored row-wise
diags : diagonals to set
- k = 0 the main diagonal
- k > 0 the k-th upper diagonal
- k < 0 the k-th lower diagonal
m, n : int
shape of the result
format : format of the result (e.g. "csr")
By default (format=None) an appropriate sparse matrix
format is returned. This choice is subject to change.
See Also
--------
dia_matrix : the sparse DIAgonal format.
Examples
--------
>>> data = array([[1,2,3,4],[1,2,3,4],[1,2,3,4]])
>>> diags = array([0,-1,2])
>>> spdiags(data, diags, 4, 4).todense()
matrix([[1, 0, 3, 0],
[1, 2, 0, 4],
[0, 2, 3, 0],
[0, 0, 3, 4]])
"""
return dia_matrix((data, diags), shape=(m, n)).asformat(format)
def spdiags(data, diags, m, n, format=None):
"""
Return a sparse matrix from diagonals.
Parameters
----------
data : array_like
matrix diagonals stored row-wise
diags : diagonals to set
- k = 0 the main diagonal
- k > 0 the k-th upper diagonal
- k < 0 the k-th lower diagonal
m, n : int
shape of the result
format : format of the result (e.g. "csr")
By default (format=None) an appropriate sparse matrix
format is returned. This choice is subject to change.
See Also
--------
dia_matrix : the sparse DIAgonal format.
Examples
--------
>>> data = array([[1,2,3,4],[1,2,3,4],[1,2,3,4]])
>>> diags = array([0,-1,2])
>>> spdiags(data, diags, 4, 4).todense()
matrix([[1, 0, 3, 0],
[1, 2, 0, 4],
[0, 2, 3, 0],
[0, 0, 3, 4]])
"""
return dia_matrix((data, diags), shape=(m,n)).asformat(format)
def todia(self):
from dia import dia_matrix
ks = self.col - self.row #the diagonal for each nonzero
diags = np.unique(ks)
if len(diags) > 100:
#probably undesired, should we do something?
#should todia() have a maxdiags parameter?
pass
#initialize and fill in data array
data = np.zeros( (len(diags), self.col.max()+1), dtype=self.dtype)
data[ np.searchsorted(diags,ks), self.col ] = self.data
return dia_matrix((data,diags), shape=self.shape)
def todia(self):
from dia import dia_matrix
ks = self.col - self.row #the diagonal for each nonzero
diags = np.unique(ks)
if len(diags) > 100:
#probably undesired, should we do something?
#should todia() have a maxdiags parameter?
pass
#initialize and fill in data array
data = np.zeros((len(diags), self.col.max() + 1), dtype=self.dtype)
data[np.searchsorted(diags, ks), self.col] = self.data
return dia_matrix((data, diags), shape=self.shape)
def identity(n, dtype='d', format=None):
"""Identity matrix in sparse format
Returns an identity matrix with shape (n,n) using a given
sparse format and dtype.
Parameters
----------
n : integer
Shape of the identity matrix.
dtype :
Data type of the matrix
format : string
Sparse format of the result, e.g. format="csr", etc.
Examples
--------
>>> identity(3).todense()
matrix([[ 1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]])
>>> identity(3, dtype='int8', format='dia')
<3x3 sparse matrix of type '<type 'numpy.int8'>'
with 3 stored elements (1 diagonals) in DIAgonal format>
"""
if format in ['csr', 'csc']:
indptr = np.arange(n + 1, dtype=np.intc)
indices = np.arange(n, dtype=np.intc)
data = np.ones(n, dtype=dtype)
cls = eval('%s_matrix' % format)
return cls((data, indices, indptr), (n, n))
elif format == 'coo':
row = np.arange(n, dtype=np.intc)
col = np.arange(n, dtype=np.intc)
data = np.ones(n, dtype=dtype)
return coo_matrix((data, (row, col)), (n, n))
elif format == 'dia':
data = np.ones(n, dtype=dtype)
diags = [0]
return dia_matrix((data, diags), shape=(n, n))
else:
return identity(n, dtype=dtype, format='csr').asformat(format)
def identity(n, dtype='d', format=None):
"""Identity matrix in sparse format
Returns an identity matrix with shape (n,n) using a given
sparse format and dtype.
Parameters
----------
n : integer
Shape of the identity matrix.
dtype :
Data type of the matrix
format : string
Sparse format of the result, e.g. format="csr", etc.
Examples
--------
>>> identity(3).todense()
matrix([[ 1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]])
>>> identity(3, dtype='int8', format='dia')
<3x3 sparse matrix of type '<type 'numpy.int8'>'
with 3 stored elements (1 diagonals) in DIAgonal format>
"""
if format in ['csr','csc']:
indptr = np.arange(n+1, dtype=np.intc)
indices = np.arange(n, dtype=np.intc)
data = np.ones(n, dtype=dtype)
cls = eval('%s_matrix' % format)
return cls((data,indices,indptr),(n,n))
elif format == 'coo':
row = np.arange(n, dtype=np.intc)
col = np.arange(n, dtype=np.intc)
data = np.ones(n, dtype=dtype)
return coo_matrix((data,(row,col)),(n,n))
elif format == 'dia':
data = np.ones(n, dtype=dtype)
diags = [0]
return dia_matrix((data,diags), shape=(n,n))
else:
return identity(n, dtype=dtype, format='csr').asformat(format)
def diags(diagonals, offsets, shape=None, format=None, dtype=None):
"""
Construct a sparse matrix from diagonals.
.. versionadded:: 0.11
Parameters
----------
diagonals : sequence of array_like
Sequence of arrays containing the matrix diagonals,
corresponding to `offsets`.
offsets : sequence of int
Diagonals to set:
- k = 0 the main diagonal
- k > 0 the k-th upper diagonal
- k < 0 the k-th lower diagonal
shape : tuple of int, optional
Shape of the result. If omitted, a square matrix large enough
to contain the diagonals is returned.
format : {"dia", "csr", "csc", "lil", ...}, optional
Matrix format of the result. By default (format=None) an
appropriate sparse matrix format is returned. This choice is
subject to change.
dtype : dtype, optional
Data type of the matrix.
See Also
--------
spdiags : construct matrix from diagonals
Notes
-----
This function differs from `spdiags` in the way it handles
off-diagonals.
The result from `diags` is the sparse equivalent of::
np.diag(diagonals[0], offsets[0])
+ ...
+ np.diag(diagonals[k], offsets[k])
Repeated diagonal offsets are disallowed.
Examples
--------
>>> diagonals = [[1,2,3,4], [1,2,3], [1,2]]
>>> diags(diagonals, [0, -1, 2]).todense()
matrix([[1, 0, 1, 0],
[1, 2, 0, 2],
[0, 2, 3, 0],
[0, 0, 3, 4]])
Broadcasting of scalars is supported (but shape needs to be
specified):
>>> diags([1, -2, 1], [-1, 0, 1], shape=(4, 4)).todense()
matrix([[-2., 1., 0., 0.],
[ 1., -2., 1., 0.],
[ 0., 1., -2., 1.],
[ 0., 0., 1., -2.]])
"""
offsets = np.atleast_1d(offsets)
diagonals = map(np.atleast_1d, diagonals)
# Basic check
if len(diagonals) != len(offsets):
raise ValueError("Different number of diagonals and offsets.")
# Determine shape, if omitted
if shape is None:
m = len(diagonals[0]) + abs(int(offsets[0]))
shape = (m, m)
# Determine data type, if omitted
if dtype is None:
dtype = np.common_type(*diagonals)
# Construct data array
m, n = shape
M = max([min(m + offset, n - offset) + max(0, offset)
for offset in offsets])
M = max(0, M)
data_arr = np.zeros((len(offsets), M), dtype=dtype)
for j, diagonal in enumerate(diagonals):
offset = offsets[j]
k = max(0, offset)
length = min(m + offset, n - offset)
if length <= 0:
raise ValueError("Offset %d (index %d) out of bounds" % (offset, j))
try:
data_arr[j, k:k+length] = diagonal
except ValueError:
if len(diagonal) != length and len(diagonal) != 1:
raise ValueError(
"Diagonal length (index %d: %d at offset %d) does not "
"agree with matrix size (%d, %d)." % (
j, len(diagonal), offset, m, n))
raise
return dia_matrix((data_arr, offsets), shape=(m, n)).asformat(format)
def diags(diagonals, offsets, shape=None, format=None, dtype=None):
"""
Construct a sparse matrix from diagonals.
.. versionadded:: 0.11
Parameters
----------
diagonals : sequence of array_like
Sequence of arrays containing the matrix diagonals,
corresponding to `offsets`.
offsets : sequence of int
Diagonals to set:
- k = 0 the main diagonal
- k > 0 the k-th upper diagonal
- k < 0 the k-th lower diagonal
shape : tuple of int, optional
Shape of the result. If omitted, a square matrix large enough
to contain the diagonals is returned.
format : {"dia", "csr", "csc", "lil", ...}, optional
Matrix format of the result. By default (format=None) an
appropriate sparse matrix format is returned. This choice is
subject to change.
dtype : dtype, optional
Data type of the matrix.
See Also
--------
spdiags : construct matrix from diagonals
Notes
-----
This function differs from `spdiags` in the way it handles
off-diagonals.
The result from `diags` is the sparse equivalent of::
np.diag(diagonals[0], offsets[0])
+ ...
+ np.diag(diagonals[k], offsets[k])
Repeated diagonal offsets are disallowed.
Examples
--------
>>> diagonals = [[1,2,3,4], [1,2,3], [1,2]]
>>> diags(diagonals, [0, -1, 2]).todense()
matrix([[1, 0, 1, 0],
[1, 2, 0, 2],
[0, 2, 3, 0],
[0, 0, 3, 4]])
Broadcasting of scalars is supported (but shape needs to be
specified):
>>> diags([1, -2, 1], [-1, 0, 1], shape=(4, 4)).todense()
matrix([[-2., 1., 0., 0.],
[ 1., -2., 1., 0.],
[ 0., 1., -2., 1.],
[ 0., 0., 1., -2.]])
"""
offsets = np.atleast_1d(offsets)
diagonals = map(np.atleast_1d, diagonals)
# Basic check
if len(diagonals) != len(offsets):
raise ValueError("Different number of diagonals and offsets.")
# Determine shape, if omitted
if shape is None:
m = len(diagonals[0]) + abs(int(offsets[0]))
shape = (m, m)
# Determine data type, if omitted
if dtype is None:
dtype = np.common_type(*diagonals)
# Construct data array
m, n = shape
M = max(
[min(m + offset, n - offset) + max(0, offset) for offset in offsets])
M = max(0, M)
data_arr = np.zeros((len(offsets), M), dtype=dtype)
for j, diagonal in enumerate(diagonals):
offset = offsets[j]
k = max(0, offset)
length = min(m + offset, n - offset)
if length <= 0:
raise ValueError("Offset %d (index %d) out of bounds" %
(offset, j))
try:
data_arr[j, k:k + length] = diagonal
except ValueError:
if len(diagonal) != length and len(diagonal) != 1:
raise ValueError(
"Diagonal length (index %d: %d at offset %d) does not "
"agree with matrix size (%d, %d)." %
(j, len(diagonal), offset, m, n))
raise
return dia_matrix((data_arr, offsets), shape=(m, n)).asformat(format)