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
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+from sympy.core.sympify import _sympify
+from sympy.matrices.expressions import MatrixExpr
+from sympy.core.numbers import I
+from sympy.core.singleton import S
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+
+
+class DFT(MatrixExpr):
+    r"""
+    Returns a discrete Fourier transform matrix. The matrix is scaled
+    with :math:`\frac{1}{\sqrt{n}}` so that it is unitary.
+
+    Parameters
+    ==========
+
+    n : integer or Symbol
+        Size of the transform.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import n
+    >>> from sympy.matrices.expressions.fourier import DFT
+    >>> DFT(3)
+    DFT(3)
+    >>> DFT(3).as_explicit()
+    Matrix([
+    [sqrt(3)/3,                sqrt(3)/3,                sqrt(3)/3],
+    [sqrt(3)/3, sqrt(3)*exp(-2*I*pi/3)/3,  sqrt(3)*exp(2*I*pi/3)/3],
+    [sqrt(3)/3,  sqrt(3)*exp(2*I*pi/3)/3, sqrt(3)*exp(-2*I*pi/3)/3]])
+    >>> DFT(n).shape
+    (n, n)
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/DFT_matrix
+
+    """
+
+    def __new__(cls, n):
+        n = _sympify(n)
+        cls._check_dim(n)
+
+        obj = super().__new__(cls, n)
+        return obj
+
+    n = property(lambda self: self.args[0])  # type: ignore
+    shape = property(lambda self: (self.n, self.n))  # type: ignore
+
+    def _entry(self, i, j, **kwargs):
+        w = exp(-2*S.Pi*I/self.n)
+        return w**(i*j) / sqrt(self.n)
+
+    def _eval_inverse(self):
+        return IDFT(self.n)
+
+
+class IDFT(DFT):
+    r"""
+    Returns an inverse discrete Fourier transform matrix. The matrix is scaled
+    with :math:`\frac{1}{\sqrt{n}}` so that it is unitary.
+
+    Parameters
+    ==========
+
+    n : integer or Symbol
+        Size of the transform
+
+    Examples
+    ========
+
+    >>> from sympy.matrices.expressions.fourier import DFT, IDFT
+    >>> IDFT(3)
+    IDFT(3)
+    >>> IDFT(4)*DFT(4)
+    I
+
+    See Also
+    ========
+
+    DFT
+
+    """
+    def _entry(self, i, j, **kwargs):
+        w = exp(-2*S.Pi*I/self.n)
+        return w**(-i*j) / sqrt(self.n)
+
+    def _eval_inverse(self):
+        return DFT(self.n)