You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
221 lines
6.2 KiB
221 lines
6.2 KiB
from sympy.core.sympify import _sympify
|
|
|
|
from sympy.matrices.expressions import MatrixExpr
|
|
from sympy.core import S, Eq, Ge
|
|
from sympy.core.mul import Mul
|
|
from sympy.functions.special.tensor_functions import KroneckerDelta
|
|
|
|
|
|
class DiagonalMatrix(MatrixExpr):
|
|
"""DiagonalMatrix(M) will create a matrix expression that
|
|
behaves as though all off-diagonal elements,
|
|
`M[i, j]` where `i != j`, are zero.
|
|
|
|
Examples
|
|
========
|
|
|
|
>>> from sympy import MatrixSymbol, DiagonalMatrix, Symbol
|
|
>>> n = Symbol('n', integer=True)
|
|
>>> m = Symbol('m', integer=True)
|
|
>>> D = DiagonalMatrix(MatrixSymbol('x', 2, 3))
|
|
>>> D[1, 2]
|
|
0
|
|
>>> D[1, 1]
|
|
x[1, 1]
|
|
|
|
The length of the diagonal -- the lesser of the two dimensions of `M` --
|
|
is accessed through the `diagonal_length` property:
|
|
|
|
>>> D.diagonal_length
|
|
2
|
|
>>> DiagonalMatrix(MatrixSymbol('x', n + 1, n)).diagonal_length
|
|
n
|
|
|
|
When one of the dimensions is symbolic the other will be treated as
|
|
though it is smaller:
|
|
|
|
>>> tall = DiagonalMatrix(MatrixSymbol('x', n, 3))
|
|
>>> tall.diagonal_length
|
|
3
|
|
>>> tall[10, 1]
|
|
0
|
|
|
|
When the size of the diagonal is not known, a value of None will
|
|
be returned:
|
|
|
|
>>> DiagonalMatrix(MatrixSymbol('x', n, m)).diagonal_length is None
|
|
True
|
|
|
|
"""
|
|
arg = property(lambda self: self.args[0])
|
|
|
|
shape = property(lambda self: self.arg.shape) # type:ignore
|
|
|
|
@property
|
|
def diagonal_length(self):
|
|
r, c = self.shape
|
|
if r.is_Integer and c.is_Integer:
|
|
m = min(r, c)
|
|
elif r.is_Integer and not c.is_Integer:
|
|
m = r
|
|
elif c.is_Integer and not r.is_Integer:
|
|
m = c
|
|
elif r == c:
|
|
m = r
|
|
else:
|
|
try:
|
|
m = min(r, c)
|
|
except TypeError:
|
|
m = None
|
|
return m
|
|
|
|
def _entry(self, i, j, **kwargs):
|
|
if self.diagonal_length is not None:
|
|
if Ge(i, self.diagonal_length) is S.true:
|
|
return S.Zero
|
|
elif Ge(j, self.diagonal_length) is S.true:
|
|
return S.Zero
|
|
eq = Eq(i, j)
|
|
if eq is S.true:
|
|
return self.arg[i, i]
|
|
elif eq is S.false:
|
|
return S.Zero
|
|
return self.arg[i, j]*KroneckerDelta(i, j)
|
|
|
|
|
|
class DiagonalOf(MatrixExpr):
|
|
"""DiagonalOf(M) will create a matrix expression that
|
|
is equivalent to the diagonal of `M`, represented as
|
|
a single column matrix.
|
|
|
|
Examples
|
|
========
|
|
|
|
>>> from sympy import MatrixSymbol, DiagonalOf, Symbol
|
|
>>> n = Symbol('n', integer=True)
|
|
>>> m = Symbol('m', integer=True)
|
|
>>> x = MatrixSymbol('x', 2, 3)
|
|
>>> diag = DiagonalOf(x)
|
|
>>> diag.shape
|
|
(2, 1)
|
|
|
|
The diagonal can be addressed like a matrix or vector and will
|
|
return the corresponding element of the original matrix:
|
|
|
|
>>> diag[1, 0] == diag[1] == x[1, 1]
|
|
True
|
|
|
|
The length of the diagonal -- the lesser of the two dimensions of `M` --
|
|
is accessed through the `diagonal_length` property:
|
|
|
|
>>> diag.diagonal_length
|
|
2
|
|
>>> DiagonalOf(MatrixSymbol('x', n + 1, n)).diagonal_length
|
|
n
|
|
|
|
When only one of the dimensions is symbolic the other will be
|
|
treated as though it is smaller:
|
|
|
|
>>> dtall = DiagonalOf(MatrixSymbol('x', n, 3))
|
|
>>> dtall.diagonal_length
|
|
3
|
|
|
|
When the size of the diagonal is not known, a value of None will
|
|
be returned:
|
|
|
|
>>> DiagonalOf(MatrixSymbol('x', n, m)).diagonal_length is None
|
|
True
|
|
|
|
"""
|
|
arg = property(lambda self: self.args[0])
|
|
@property
|
|
def shape(self):
|
|
r, c = self.arg.shape
|
|
if r.is_Integer and c.is_Integer:
|
|
m = min(r, c)
|
|
elif r.is_Integer and not c.is_Integer:
|
|
m = r
|
|
elif c.is_Integer and not r.is_Integer:
|
|
m = c
|
|
elif r == c:
|
|
m = r
|
|
else:
|
|
try:
|
|
m = min(r, c)
|
|
except TypeError:
|
|
m = None
|
|
return m, S.One
|
|
|
|
@property
|
|
def diagonal_length(self):
|
|
return self.shape[0]
|
|
|
|
def _entry(self, i, j, **kwargs):
|
|
return self.arg._entry(i, i, **kwargs)
|
|
|
|
|
|
class DiagMatrix(MatrixExpr):
|
|
"""
|
|
Turn a vector into a diagonal matrix.
|
|
"""
|
|
def __new__(cls, vector):
|
|
vector = _sympify(vector)
|
|
obj = MatrixExpr.__new__(cls, vector)
|
|
shape = vector.shape
|
|
dim = shape[1] if shape[0] == 1 else shape[0]
|
|
if vector.shape[0] != 1:
|
|
obj._iscolumn = True
|
|
else:
|
|
obj._iscolumn = False
|
|
obj._shape = (dim, dim)
|
|
obj._vector = vector
|
|
return obj
|
|
|
|
@property
|
|
def shape(self):
|
|
return self._shape
|
|
|
|
def _entry(self, i, j, **kwargs):
|
|
if self._iscolumn:
|
|
result = self._vector._entry(i, 0, **kwargs)
|
|
else:
|
|
result = self._vector._entry(0, j, **kwargs)
|
|
if i != j:
|
|
result *= KroneckerDelta(i, j)
|
|
return result
|
|
|
|
def _eval_transpose(self):
|
|
return self
|
|
|
|
def as_explicit(self):
|
|
from sympy.matrices.dense import diag
|
|
return diag(*list(self._vector.as_explicit()))
|
|
|
|
def doit(self, **hints):
|
|
from sympy.assumptions import ask, Q
|
|
from sympy.matrices.expressions.matmul import MatMul
|
|
from sympy.matrices.expressions.transpose import Transpose
|
|
from sympy.matrices.dense import eye
|
|
from sympy.matrices.matrices import MatrixBase
|
|
vector = self._vector
|
|
# This accounts for shape (1, 1) and identity matrices, among others:
|
|
if ask(Q.diagonal(vector)):
|
|
return vector
|
|
if isinstance(vector, MatrixBase):
|
|
ret = eye(max(vector.shape))
|
|
for i in range(ret.shape[0]):
|
|
ret[i, i] = vector[i]
|
|
return type(vector)(ret)
|
|
if vector.is_MatMul:
|
|
matrices = [arg for arg in vector.args if arg.is_Matrix]
|
|
scalars = [arg for arg in vector.args if arg not in matrices]
|
|
if scalars:
|
|
return Mul.fromiter(scalars)*DiagMatrix(MatMul.fromiter(matrices).doit()).doit()
|
|
if isinstance(vector, Transpose):
|
|
vector = vector.arg
|
|
return DiagMatrix(vector)
|
|
|
|
|
|
def diagonalize_vector(vector):
|
|
return DiagMatrix(vector).doit()
|