def _eval_expand_basic(self, **hints):
summand = self.function.expand(**hints)
if summand.is_Add and summand.is_commutative:
return Add(*[ self.func(i, *self.limits) for i in summand.args ])
elif summand.is_Matrix:
return Matrix._new(summand.rows, summand.cols,
[self.func(i, *self.limits) for i in summand._mat])
elif summand != self.function:
return self.func(summand, *self.limits)
return self
def _eval_expand_basic(self, **hints):
summand = self.function.expand(**hints)
if summand.is_Add and summand.is_commutative:
return Add(*[self.func(i, *self.limits) for i in summand.args])
elif summand.is_Matrix:
return Matrix._new(summand.rows, summand.cols,
[self.func(i, *self.limits) for i in summand._mat])
elif summand != self.function:
return self.func(summand, *self.limits)
return self
def diag(*values, **kwargs):
"""Create a sparse, diagonal matrix from a list of diagonal values.
Notes
=====
When arguments are matrices they are fitted in resultant matrix.
The returned matrix is a mutable, dense matrix. To make it a different
type, send the desired class for keyword ``cls``.
Examples
========
>>> from sympy.matrices import diag, Matrix, ones
>>> diag(1, 2, 3)
Matrix([
[1, 0, 0],
[0, 2, 0],
[0, 0, 3]])
>>> diag(*[1, 2, 3])
Matrix([
[1, 0, 0],
[0, 2, 0],
[0, 0, 3]])
The diagonal elements can be matrices; diagonal filling will
continue on the diagonal from the last element of the matrix:
>>> from sympy.abc import x, y, z
>>> a = Matrix([x, y, z])
>>> b = Matrix([[1, 2], [3, 4]])
>>> c = Matrix([[5, 6]])
>>> diag(a, 7, b, c)
Matrix([
[x, 0, 0, 0, 0, 0],
[y, 0, 0, 0, 0, 0],
[z, 0, 0, 0, 0, 0],
[0, 7, 0, 0, 0, 0],
[0, 0, 1, 2, 0, 0],
[0, 0, 3, 4, 0, 0],
[0, 0, 0, 0, 5, 6]])
When diagonal elements are lists, they will be treated as arguments
to Matrix:
>>> diag([1, 2, 3], 4)
Matrix([
[1, 0],
[2, 0],
[3, 0],
[0, 4]])
>>> diag([[1, 2, 3]], 4)
Matrix([
[1, 2, 3, 0],
[0, 0, 0, 4]])
A given band off the diagonal can be made by padding with a
vertical or horizontal "kerning" vector:
>>> hpad = ones(0, 2)
>>> vpad = ones(2, 0)
>>> diag(vpad, 1, 2, 3, hpad) + diag(hpad, 4, 5, 6, vpad)
Matrix([
[0, 0, 4, 0, 0],
[0, 0, 0, 5, 0],
[1, 0, 0, 0, 6],
[0, 2, 0, 0, 0],
[0, 0, 3, 0, 0]])
The type is mutable by default but can be made immutable by setting
the ``mutable`` flag to False:
>>> type(diag(1))
<class 'sympy.matrices.dense.MutableDenseMatrix'>
>>> from sympy.matrices import ImmutableMatrix
>>> type(diag(1, cls=ImmutableMatrix))
<class 'sympy.matrices.immutable.ImmutableMatrix'>
See Also
========
eye
"""
from .sparse import MutableSparseMatrix
cls = kwargs.pop('cls', None)
if cls is None:
from .dense import Matrix as cls
if kwargs:
raise ValueError('unrecognized keyword%s: %s' % (
's' if len(kwargs) > 1 else '',
', '.join(kwargs.keys())))
rows = 0
cols = 0
values = list(values)
for i in range(len(values)):
m = values[i]
if isinstance(m, MatrixBase):
rows += m.rows
cols += m.cols
elif is_sequence(m):
m = values[i] = Matrix(m)
rows += m.rows
cols += m.cols
else:
rows += 1
cols += 1
res = MutableSparseMatrix.zeros(rows, cols)
i_row = 0
i_col = 0
for m in values:
if isinstance(m, MatrixBase):
res[i_row:i_row + m.rows, i_col:i_col + m.cols] = m
i_row += m.rows
i_col += m.cols
else:
res[i_row, i_col] = m
i_row += 1
i_col += 1
return cls._new(res)
def diag(*values, **kwargs):
"""Create a sparse, diagonal matrix from a list of diagonal values.
Notes
=====
When arguments are matrices they are fitted in resultant matrix.
The returned matrix is a mutable, dense matrix. To make it a different
type, send the desired class for keyword ``cls``.
Examples
========
>>> from sympy.matrices import diag, Matrix, ones
>>> diag(1, 2, 3)
Matrix([
[1, 0, 0],
[0, 2, 0],
[0, 0, 3]])
>>> diag(*[1, 2, 3])
Matrix([
[1, 0, 0],
[0, 2, 0],
[0, 0, 3]])
The diagonal elements can be matrices; diagonal filling will
continue on the diagonal from the last element of the matrix:
>>> from sympy.abc import x, y, z
>>> a = Matrix([x, y, z])
>>> b = Matrix([[1, 2], [3, 4]])
>>> c = Matrix([[5, 6]])
>>> diag(a, 7, b, c)
Matrix([
[x, 0, 0, 0, 0, 0],
[y, 0, 0, 0, 0, 0],
[z, 0, 0, 0, 0, 0],
[0, 7, 0, 0, 0, 0],
[0, 0, 1, 2, 0, 0],
[0, 0, 3, 4, 0, 0],
[0, 0, 0, 0, 5, 6]])
When diagonal elements are lists, they will be treated as arguments
to Matrix:
>>> diag([1, 2, 3], 4)
Matrix([
[1, 0],
[2, 0],
[3, 0],
[0, 4]])
>>> diag([[1, 2, 3]], 4)
Matrix([
[1, 2, 3, 0],
[0, 0, 0, 4]])
A given band off the diagonal can be made by padding with a
vertical or horizontal "kerning" vector:
>>> hpad = ones(0, 2)
>>> vpad = ones(2, 0)
>>> diag(vpad, 1, 2, 3, hpad) + diag(hpad, 4, 5, 6, vpad)
Matrix([
[0, 0, 4, 0, 0],
[0, 0, 0, 5, 0],
[1, 0, 0, 0, 6],
[0, 2, 0, 0, 0],
[0, 0, 3, 0, 0]])
The type is mutable by default but can be made immutable by setting
the ``mutable`` flag to False:
>>> type(diag(1))
<class 'sympy.matrices.dense.MutableDenseMatrix'>
>>> from sympy.matrices import ImmutableMatrix
>>> type(diag(1, cls=ImmutableMatrix))
<class 'sympy.matrices.immutable.ImmutableMatrix'>
See Also
========
eye
"""
from .sparse import MutableSparseMatrix
cls = kwargs.pop('cls', None)
if cls is None:
from .dense import Matrix as cls
if kwargs:
raise ValueError('unrecognized keyword%s: %s' % (
's' if len(kwargs) > 1 else '',
', '.join(kwargs.keys())))
rows = 0
cols = 0
values = list(values)
for i in range(len(values)):
m = values[i]
if isinstance(m, MatrixBase):
rows += m.rows
cols += m.cols
elif is_sequence(m):
m = values[i] = Matrix(m)
rows += m.rows
cols += m.cols
else:
rows += 1
cols += 1
res = MutableSparseMatrix.zeros(rows, cols)
i_row = 0
i_col = 0
for m in values:
if isinstance(m, MatrixBase):
res[i_row:i_row + m.rows, i_col:i_col + m.cols] = m
i_row += m.rows
i_col += m.cols
else:
res[i_row, i_col] = m
i_row += 1
i_col += 1
return cls._new(res)
