def test_fwht_ifwht():
assert all(tf(ls) == ls for tf in (fwht, ifwht) \
for ls in ([], [S(7)/4]))
ls = [213, 321, 43235, 5325, 312, 53]
fls = [49459, 38061, -47661, -37759, 48729, 37543, -48391, -38277]
assert fwht(ls) == fls
assert ifwht(fls) == ls + [S.Zero] * 2
ls = [
S(1) / 2 + 2 * I,
S(3) / 7 + 4 * I,
S(5) / 6 + 6 * I,
S(7) / 3,
S(9) / 4
]
ifls = [
S(533) / 672 + 3 * I / 2,
S(23) / 224 + I / 2,
S(1) / 672,
S(107) / 224 - I,
S(155) / 672 + 3 * I / 2, -S(103) / 224 + I / 2, -S(377) / 672,
-S(19) / 224 - I
]
assert ifwht(ls) == ifls
assert fwht(ifls) == ls + [S.Zero] * 3
x, y = symbols('x y')
raises(TypeError, lambda: fwht(x))
ls = [x, 2 * x, 3 * x**2, 4 * x**3]
ifls = [
x**3 + 3 * x**2 / 4 + 3 * x / 4, -x**3 + 3 * x**2 / 4 - x / 4,
-x**3 - 3 * x**2 / 4 + 3 * x / 4, x**3 - 3 * x**2 / 4 - x / 4
]
assert ifwht(ls) == ifls
assert fwht(ifls) == ls
ls = [x, y, x**2, y**2, x * y]
fls = [
x**2 + x * y + x + y**2 + y, x**2 + x * y + x - y**2 - y,
-x**2 + x * y + x - y**2 + y, -x**2 + x * y + x + y**2 - y,
x**2 - x * y + x + y**2 + y, x**2 - x * y + x - y**2 - y,
-x**2 - x * y + x - y**2 + y, -x**2 - x * y + x + y**2 - y
]
assert fwht(ls) == fls
assert ifwht(fls) == ls + [S.Zero] * 3
ls = list(range(6))
assert fwht(ls) == [x * 8 for x in ifwht(ls)]
def test_fwht_ifwht():
assert all(tf(ls) == ls for tf in (fwht, ifwht) \
for ls in ([], [S(7)/4]))
ls = [213, 321, 43235, 5325, 312, 53]
fls = [49459, 38061, -47661, -37759, 48729, 37543, -48391, -38277]
assert fwht(ls) == fls
assert ifwht(fls) == ls + [S.Zero]*2
ls = [S(1)/2 + 2*I, S(3)/7 + 4*I, S(5)/6 + 6*I, S(7)/3, S(9)/4]
ifls = [S(533)/672 + 3*I/2, S(23)/224 + I/2, S(1)/672, S(107)/224 - I,
S(155)/672 + 3*I/2, -S(103)/224 + I/2, -S(377)/672, -S(19)/224 - I]
assert ifwht(ls) == ifls
assert fwht(ifls) == ls + [S.Zero]*3
x, y = symbols('x y')
raises(TypeError, lambda: fwht(x))
ls = [x, 2*x, 3*x**2, 4*x**3]
ifls = [x**3 + 3*x**2/4 + 3*x/4,
-x**3 + 3*x**2/4 - x/4,
-x**3 - 3*x**2/4 + 3*x/4,
x**3 - 3*x**2/4 - x/4]
assert ifwht(ls) == ifls
assert fwht(ifls) == ls
ls = [x, y, x**2, y**2, x*y]
fls = [x**2 + x*y + x + y**2 + y,
x**2 + x*y + x - y**2 - y,
-x**2 + x*y + x - y**2 + y,
-x**2 + x*y + x + y**2 - y,
x**2 - x*y + x + y**2 + y,
x**2 - x*y + x - y**2 - y,
-x**2 - x*y + x - y**2 + y,
-x**2 - x*y + x + y**2 - y]
assert fwht(ls) == fls
assert ifwht(fls) == ls + [S.Zero]*3
ls = list(range(6))
assert fwht(ls) == [x*8 for x in ifwht(ls)]
def test_fwht_ifwht():
assert all(tf(ls) == ls for tf in (fwht, ifwht) \
for ls in ([], [Rational(7, 4)]))
ls = [213, 321, 43235, 5325, 312, 53]
fls = [49459, 38061, -47661, -37759, 48729, 37543, -48391, -38277]
assert fwht(ls) == fls
assert ifwht(fls) == ls + [S.Zero]*2
ls = [S.Half + 2*I, Rational(3, 7) + 4*I, Rational(5, 6) + 6*I, Rational(7, 3), Rational(9, 4)]
ifls = [Rational(533, 672) + I*3/2, Rational(23, 224) + I/2, Rational(1, 672), Rational(107, 224) - I,
Rational(155, 672) + I*3/2, Rational(-103, 224) + I/2, Rational(-377, 672), Rational(-19, 224) - I]
assert ifwht(ls) == ifls
assert fwht(ifls) == ls + [S.Zero]*3
x, y = symbols('x y')
raises(TypeError, lambda: fwht(x))
ls = [x, 2*x, 3*x**2, 4*x**3]
ifls = [x**3 + 3*x**2/4 + x*Rational(3, 4),
-x**3 + 3*x**2/4 - x/4,
-x**3 - 3*x**2/4 + x*Rational(3, 4),
x**3 - 3*x**2/4 - x/4]
assert ifwht(ls) == ifls
assert fwht(ifls) == ls
ls = [x, y, x**2, y**2, x*y]
fls = [x**2 + x*y + x + y**2 + y,
x**2 + x*y + x - y**2 - y,
-x**2 + x*y + x - y**2 + y,
-x**2 + x*y + x + y**2 - y,
x**2 - x*y + x + y**2 + y,
x**2 - x*y + x - y**2 - y,
-x**2 - x*y + x - y**2 + y,
-x**2 - x*y + x + y**2 - y]
assert fwht(ls) == fls
assert ifwht(fls) == ls + [S.Zero]*3
ls = list(range(6))
assert fwht(ls) == [x*8 for x in ifwht(ls)]