switching to high quality piper tts and added label translations

2026-01-29 23:48:19 +01:00
commit d80c619df9
3934 changed files with 1451600 additions and 0 deletions
@@ -0,0 +1,112 @@
+from sympy.core.sympify import _sympify
+from sympy.core import S, Basic
+
+from sympy.matrices.exceptions import NonSquareMatrixError
+from sympy.matrices.expressions.matpow import MatPow
+
+
+class Inverse(MatPow):
+    """
+    The multiplicative inverse of a matrix expression
+
+    This is a symbolic object that simply stores its argument without
+    evaluating it. To actually compute the inverse, use the ``.inverse()``
+    method of matrices.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, Inverse
+    >>> A = MatrixSymbol('A', 3, 3)
+    >>> B = MatrixSymbol('B', 3, 3)
+    >>> Inverse(A)
+    A**(-1)
+    >>> A.inverse() == Inverse(A)
+    True
+    >>> (A*B).inverse()
+    B**(-1)*A**(-1)
+    >>> Inverse(A*B)
+    (A*B)**(-1)
+
+    """
+    is_Inverse = True
+    exp = S.NegativeOne
+
+    def __new__(cls, mat, exp=S.NegativeOne):
+        # exp is there to make it consistent with
+        # inverse.func(*inverse.args) == inverse
+        mat = _sympify(mat)
+        exp = _sympify(exp)
+        if not mat.is_Matrix:
+            raise TypeError("mat should be a matrix")
+        if mat.is_square is False:
+            raise NonSquareMatrixError("Inverse of non-square matrix %s" % mat)
+        return Basic.__new__(cls, mat, exp)
+
+    @property
+    def arg(self):
+        return self.args[0]
+
+    @property
+    def shape(self):
+        return self.arg.shape
+
+    def _eval_inverse(self):
+        return self.arg
+
+    def _eval_transpose(self):
+        return Inverse(self.arg.transpose())
+
+    def _eval_adjoint(self):
+        return Inverse(self.arg.adjoint())
+
+    def _eval_conjugate(self):
+        return Inverse(self.arg.conjugate())
+
+    def _eval_determinant(self):
+        from sympy.matrices.expressions.determinant import det
+        return 1/det(self.arg)
+
+    def doit(self, **hints):
+        if 'inv_expand' in hints and hints['inv_expand'] == False:
+            return self
+
+        arg = self.arg
+        if hints.get('deep', True):
+            arg = arg.doit(**hints)
+
+        return arg.inverse()
+
+    def _eval_derivative_matrix_lines(self, x):
+        arg = self.args[0]
+        lines = arg._eval_derivative_matrix_lines(x)
+        for line in lines:
+            line.first_pointer *= -self.T
+            line.second_pointer *= self
+        return lines
+
+
+from sympy.assumptions.ask import ask, Q
+from sympy.assumptions.refine import handlers_dict
+
+
+def refine_Inverse(expr, assumptions):
+    """
+    >>> from sympy import MatrixSymbol, Q, assuming, refine
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> X.I
+    X**(-1)
+    >>> with assuming(Q.orthogonal(X)):
+    ...     print(refine(X.I))
+    X.T
+    """
+    if ask(Q.orthogonal(expr), assumptions):
+        return expr.arg.T
+    elif ask(Q.unitary(expr), assumptions):
+        return expr.arg.conjugate()
+    elif ask(Q.singular(expr), assumptions):
+        raise ValueError("Inverse of singular matrix %s" % expr.arg)
+
+    return expr
+
+handlers_dict['Inverse'] = refine_Inverse