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