def test_convolution():
# fft
a = [1, S(5) / 3, sqrt(3), S(7) / 5]
b = [9, 5, 5, 4, 3, 2]
c = [3, 5, 3, 7, 8]
d = [1422, 6572, 3213, 5552]
assert convolution(a, b, fft=True) == convolution_fft(a, b)
assert convolution(a, b, dps=9, fft=True) == convolution_fft(a, b, dps=9)
assert convolution(a, d, fft=True, dps=7) == convolution_fft(d, a, dps=7)
assert convolution(a, d[1:], dps=3) == convolution_fft(d[1:], a, dps=3)
# prime moduli of the form (m*2**k + 1), sequence length
# should be a divisor of 2**k
p = 7 * 17 * 2**23 + 1
q = 19 * 2**10 + 1
# ntt
assert convolution(d, b, ntt=True, prime=q) == convolution_ntt(b,
d,
prime=q)
assert convolution(c, b, prime=p) == convolution_ntt(b, c, prime=p)
assert convolution(d, c, prime=p, ntt=True) == convolution_ntt(c,
d,
prime=p)
raises(TypeError, lambda: convolution(b, d, ntt=True))
raises(TypeError, lambda: convolution(b, d, ntt=True, cycle=0))
raises(TypeError, lambda: convolution(b, d, dps=5, prime=q))
raises(TypeError, lambda: convolution(b, d, dps=6, ntt=True, prime=q))
raises(TypeError,
lambda: convolution(b, d, fft=True, dps=7, ntt=True, prime=q))
# ntt is a specialized variant of fft, TypeError should not be raised
assert convolution(b, d, fft=True, ntt=True, prime=q) == \
convolution_ntt(b, d, prime=q)
# fwht
assert convolution(a, b, dyadic=True) == convolution_fwht(a, b)
assert convolution(a, b, dyadic=False) == convolution(a, b)
raises(TypeError, lambda: convolution(b, d, fft=True, dps=2, dyadic=True))
raises(TypeError,
lambda: convolution(b, d, ntt=True, prime=p, dyadic=True))
raises(TypeError, lambda: convolution(b, d, fft=True, dyadic=True))
raises(TypeError, lambda: convolution(a, b, dps=2, dyadic=True))
raises(TypeError, lambda: convolution(b, c, prime=p, dyadic=True))
# subset
assert convolution(a, b, subset=True) == convolution_subset(a, b) == \
convolution(a, b, subset=True, dyadic=False) == \
convolution(a, b, subset=True, fft=False) == \
convolution(a, b, subset=True, fft=False, ntt=False)
assert convolution(a, b, subset=False) == convolution(a, b)
raises(TypeError, lambda: convolution(a, b, subset=True, dyadic=True))
raises(TypeError, lambda: convolution(b, c, subset=True, fft=True))
raises(TypeError, lambda: convolution(c, d, subset=True, dps=6))
raises(TypeError, lambda: convolution(a, c, subset=True, prime=q))
def test_convolution_subset():
assert convolution_subset([], []) == []
assert convolution_subset([], [S(1) / 3]) == []
assert convolution_subset([6 + 3 * I / 7], [S(2) / 3]) == [4 + 2 * I / 7]
a = [1, S(5) / 3, sqrt(3), 4 + 5 * I]
b = [64, 71, 55, 47, 33, 29, 15]
c = [3 + 2 * I / 3, 5 + 7 * I, 7, S(7) / 5, 9]
assert convolution_subset(a, b) == [
64, 533 / S(3), 55 + 64 * sqrt(3),
71 * sqrt(3) + 1184 / S(3) + 320 * I, 33, 84, 15 + 33 * sqrt(3),
29 * sqrt(3) + 157 + 165 * I
]
assert convolution_subset(b, c) == [
192 + 128 * I / 3, 533 + 1486 * I / 3, 613 + 110 * I / 3,
5013 / 5 + 1249 * I / 3, 675 + 22 * I, 891 + 751 * I / 3, 771 + 10 * I,
3736 / 5 + 105 * I
]
assert convolution_subset(a, c) == convolution_subset(c, a)
assert convolution_subset(a[:2], b) == \
[64, 533/S(3), 55, 416/S(3), 33, 84, 15, 25]
assert convolution_subset(a[:2], c) == \
[3 + 2*I/3, 10 + 73*I/9, 7, 196/S(15), 9, 15, 0, 0]
u, v, w, x, y, z = symbols('u v w x y z')
assert convolution_subset([u, v, w],
[x, y]) == [u * x, u * y + v * x, w * x, w * y]
assert convolution_subset([u, v, w, x], [y, z]) == \
[u*y, u*z + v*y, w*y, w*z + x*y]
assert convolution_subset([u, v], [x, y, z]) == \
convolution_subset([x, y, z], [u, v])
raises(TypeError, lambda: convolution_subset(x, z))
raises(TypeError, lambda: convolution_subset(S(7) / 3, u))