45 lines
1.6 KiB
Python
45 lines
1.6 KiB
Python
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from sympy.assumptions.ask import (Q, ask)
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from sympy.core.numbers import (I, Rational)
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from sympy.core.singleton import S
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from sympy.functions.elementary.complexes import Abs
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from sympy.functions.elementary.exponential import exp
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.simplify.simplify import simplify
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from sympy.core.symbol import symbols
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from sympy.matrices.expressions.fourier import DFT, IDFT
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from sympy.matrices import det, Matrix, Identity
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from sympy.testing.pytest import raises
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def test_dft_creation():
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assert DFT(2)
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assert DFT(0)
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raises(ValueError, lambda: DFT(-1))
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raises(ValueError, lambda: DFT(2.0))
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raises(ValueError, lambda: DFT(2 + 1j))
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n = symbols('n')
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assert DFT(n)
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n = symbols('n', integer=False)
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raises(ValueError, lambda: DFT(n))
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n = symbols('n', negative=True)
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raises(ValueError, lambda: DFT(n))
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def test_dft():
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n, i, j = symbols('n i j')
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assert DFT(4).shape == (4, 4)
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assert ask(Q.unitary(DFT(4)))
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assert Abs(simplify(det(Matrix(DFT(4))))) == 1
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assert DFT(n)*IDFT(n) == Identity(n)
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assert DFT(n)[i, j] == exp(-2*S.Pi*I/n)**(i*j) / sqrt(n)
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def test_dft2():
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assert DFT(1).as_explicit() == Matrix([[1]])
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assert DFT(2).as_explicit() == 1/sqrt(2)*Matrix([[1,1],[1,-1]])
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assert DFT(4).as_explicit() == Matrix([[S.Half, S.Half, S.Half, S.Half],
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[S.Half, -I/2, Rational(-1,2), I/2],
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[S.Half, Rational(-1,2), S.Half, Rational(-1,2)],
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[S.Half, I/2, Rational(-1,2), -I/2]])
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