300 lines
7.3 KiB
Python
300 lines
7.3 KiB
Python
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from sympy.assumptions.ask import ask, Q
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from sympy.core.relational import Eq
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from sympy.core.singleton import S
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from sympy.core.sympify import _sympify
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from sympy.functions.special.tensor_functions import KroneckerDelta
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from sympy.matrices.common import NonInvertibleMatrixError
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from .matexpr import MatrixExpr
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class ZeroMatrix(MatrixExpr):
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"""The Matrix Zero 0 - additive identity
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Examples
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========
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>>> from sympy import MatrixSymbol, ZeroMatrix
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>>> A = MatrixSymbol('A', 3, 5)
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>>> Z = ZeroMatrix(3, 5)
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>>> A + Z
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A
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>>> Z*A.T
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0
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"""
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is_ZeroMatrix = True
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def __new__(cls, m, n):
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m, n = _sympify(m), _sympify(n)
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cls._check_dim(m)
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cls._check_dim(n)
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return super().__new__(cls, m, n)
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@property
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def shape(self):
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return (self.args[0], self.args[1])
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def _eval_power(self, exp):
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# exp = -1, 0, 1 are already handled at this stage
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if (exp < 0) == True:
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raise NonInvertibleMatrixError("Matrix det == 0; not invertible")
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return self
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def _eval_transpose(self):
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return ZeroMatrix(self.cols, self.rows)
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def _eval_adjoint(self):
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return ZeroMatrix(self.cols, self.rows)
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def _eval_trace(self):
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return S.Zero
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def _eval_determinant(self):
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return S.Zero
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def _eval_inverse(self):
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raise NonInvertibleMatrixError("Matrix det == 0; not invertible.")
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def _eval_as_real_imag(self):
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return (self, self)
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def _eval_conjugate(self):
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return self
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def _entry(self, i, j, **kwargs):
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return S.Zero
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class GenericZeroMatrix(ZeroMatrix):
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"""
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A zero matrix without a specified shape
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This exists primarily so MatAdd() with no arguments can return something
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meaningful.
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"""
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def __new__(cls):
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# super(ZeroMatrix, cls) instead of super(GenericZeroMatrix, cls)
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# because ZeroMatrix.__new__ doesn't have the same signature
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return super(ZeroMatrix, cls).__new__(cls)
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@property
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def rows(self):
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raise TypeError("GenericZeroMatrix does not have a specified shape")
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@property
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def cols(self):
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raise TypeError("GenericZeroMatrix does not have a specified shape")
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@property
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def shape(self):
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raise TypeError("GenericZeroMatrix does not have a specified shape")
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# Avoid Matrix.__eq__ which might call .shape
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def __eq__(self, other):
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return isinstance(other, GenericZeroMatrix)
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def __ne__(self, other):
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return not (self == other)
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def __hash__(self):
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return super().__hash__()
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class Identity(MatrixExpr):
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"""The Matrix Identity I - multiplicative identity
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Examples
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========
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>>> from sympy import Identity, MatrixSymbol
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>>> A = MatrixSymbol('A', 3, 5)
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>>> I = Identity(3)
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>>> I*A
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A
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"""
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is_Identity = True
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def __new__(cls, n):
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n = _sympify(n)
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cls._check_dim(n)
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return super().__new__(cls, n)
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@property
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def rows(self):
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return self.args[0]
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@property
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def cols(self):
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return self.args[0]
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@property
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def shape(self):
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return (self.args[0], self.args[0])
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@property
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def is_square(self):
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return True
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def _eval_transpose(self):
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return self
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def _eval_trace(self):
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return self.rows
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def _eval_inverse(self):
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return self
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def _eval_as_real_imag(self):
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return (self, ZeroMatrix(*self.shape))
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def _eval_conjugate(self):
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return self
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def _eval_adjoint(self):
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return self
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def _entry(self, i, j, **kwargs):
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eq = Eq(i, j)
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if eq is S.true:
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return S.One
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elif eq is S.false:
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return S.Zero
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return KroneckerDelta(i, j, (0, self.cols-1))
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def _eval_determinant(self):
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return S.One
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def _eval_power(self, exp):
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return self
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class GenericIdentity(Identity):
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"""
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An identity matrix without a specified shape
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This exists primarily so MatMul() with no arguments can return something
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meaningful.
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"""
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def __new__(cls):
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# super(Identity, cls) instead of super(GenericIdentity, cls) because
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# Identity.__new__ doesn't have the same signature
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return super(Identity, cls).__new__(cls)
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@property
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def rows(self):
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raise TypeError("GenericIdentity does not have a specified shape")
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@property
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def cols(self):
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raise TypeError("GenericIdentity does not have a specified shape")
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@property
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def shape(self):
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raise TypeError("GenericIdentity does not have a specified shape")
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@property
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def is_square(self):
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return True
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# Avoid Matrix.__eq__ which might call .shape
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def __eq__(self, other):
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return isinstance(other, GenericIdentity)
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def __ne__(self, other):
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return not (self == other)
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def __hash__(self):
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return super().__hash__()
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class OneMatrix(MatrixExpr):
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"""
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Matrix whose all entries are ones.
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"""
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def __new__(cls, m, n, evaluate=False):
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m, n = _sympify(m), _sympify(n)
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cls._check_dim(m)
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cls._check_dim(n)
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if evaluate:
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condition = Eq(m, 1) & Eq(n, 1)
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if condition == True:
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return Identity(1)
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obj = super().__new__(cls, m, n)
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return obj
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@property
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def shape(self):
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return self._args
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@property
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def is_Identity(self):
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return self._is_1x1() == True
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def as_explicit(self):
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from sympy.matrices.immutable import ImmutableDenseMatrix
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return ImmutableDenseMatrix.ones(*self.shape)
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def doit(self, **hints):
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args = self.args
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if hints.get('deep', True):
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args = [a.doit(**hints) for a in args]
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return self.func(*args, evaluate=True)
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def _eval_power(self, exp):
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# exp = -1, 0, 1 are already handled at this stage
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if self._is_1x1() == True:
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return Identity(1)
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if (exp < 0) == True:
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raise NonInvertibleMatrixError("Matrix det == 0; not invertible")
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if ask(Q.integer(exp)):
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return self.shape[0] ** (exp - 1) * OneMatrix(*self.shape)
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return super()._eval_power(exp)
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def _eval_transpose(self):
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return OneMatrix(self.cols, self.rows)
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def _eval_adjoint(self):
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return OneMatrix(self.cols, self.rows)
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def _eval_trace(self):
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return S.One*self.rows
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def _is_1x1(self):
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"""Returns true if the matrix is known to be 1x1"""
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shape = self.shape
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return Eq(shape[0], 1) & Eq(shape[1], 1)
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def _eval_determinant(self):
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condition = self._is_1x1()
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if condition == True:
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return S.One
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elif condition == False:
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return S.Zero
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else:
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from sympy.matrices.expressions.determinant import Determinant
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return Determinant(self)
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def _eval_inverse(self):
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condition = self._is_1x1()
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if condition == True:
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return Identity(1)
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elif condition == False:
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raise NonInvertibleMatrixError("Matrix det == 0; not invertible.")
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else:
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from .inverse import Inverse
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return Inverse(self)
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def _eval_as_real_imag(self):
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return (self, ZeroMatrix(*self.shape))
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def _eval_conjugate(self):
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return self
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def _entry(self, i, j, **kwargs):
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return S.One
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