def test_maxdeg(dim, degrees, basis):
if basis == "power": MultiX = MultiPower
else: MultiX = MultiCheb
for deg in degrees:
coeffs = rand_coeffs(dim, deg, 1)[0]
polys = [MultiX(coeff) for coeff in coeffs]
t = timer()
solve(polys)
print(f"dim {dim}/deg {deg}: time = {timer()-t}")
def run_test(polys):
try:
t = timer()
roots = solve(polys)
t = timer() - t
res = np.abs([poly(roots) for poly in polys])
logres = np.log10(res, out=-16 * np.ones_like(res), where=(res != 0))
return np.array([logres.max(), logres.mean(), t, 0], dtype='float64')
except ConditioningError:
return np.array([0, 0, 0, 1], dtype='float64')
def correctZeros(original_polys, new_polys, transform, MSmatrix):
'''
A helper function for polyroots tests. Takes in polynomials, find their common zeros using polyroots, and calculates
how many of the zeros are correct.
In this function it asserts that the number of zeros is equal to the product of the degrees, which is only valid if
the polynomials are random and upper triangular, and that at least 95% of the zeros are correct (so it will pass even
on bad random runs)
'''
zeros = transform(pr.solve(new_polys, MSmatrix=MSmatrix))
correct = 0
outOfRange = 0
for zero in zeros:
good = True
for poly in original_polys:
if not np.isclose(0, poly(zero), atol=1.e-3):
good = False
if (np.abs(zero) > 1).any():
outOfRange += 1
break
if good:
correct += 1
assert (100 * correct / (len(zeros) - outOfRange) > 95)
def test_paper_example():
#Power form of the polys
p1 = MultiPower(np.array([[1, -4, 0], [0, 3, 0], [1, 0,
0]])) #y^2 + 3xy - 4x +1
p2 = MultiPower(np.array([[3, 0, -2], [6, -6, 0],
[0, 0, 0]])) #-6xy -2x^2 + 6y +3
#Cheb form of the polys
c1 = MultiCheb(np.array([[2, 0, -1], [6, -6, 0], [0, 0,
0]])) #p1 in Cheb form
c2 = MultiCheb(np.array([[1.5, -4, 0], [0, 3, 0], [.5, 0,
0]])) #p2 in Cheb form
right_number_of_roots = 4
#~ ~ ~ Power Form, Mx Matrix ~ ~ ~
power_mult_roots = pr.solve([p1, p2], MSmatrix=1)
assert len(power_mult_roots) == right_number_of_roots
for root in power_mult_roots:
assert np.isclose(0, p1(root), atol=1.e-8)
assert np.isclose(0, p2(root), atol=1.e-8)
#~ ~ ~ Cheb Form, Mx Matrix ~ ~ ~
cheb_mult_roots = pr.solve([c1, c2], MSmatrix=1)
assert len(cheb_mult_roots) == right_number_of_roots
for root in cheb_mult_roots:
assert np.isclose(0, c1(root), atol=1.e-8)
assert np.isclose(0, c1(root), atol=1.e-8)
#~ ~ ~ Power Form, My Matrix ~ ~ ~
power_multR_roots = pr.solve([p1, p2], MSmatrix=2)
assert len(power_multR_roots) == right_number_of_roots
for root in power_multR_roots:
assert np.isclose(0, p1(root), atol=1.e-8)
assert np.isclose(0, p2(root), atol=1.e-8)
#~ ~ ~ Cheb Form, My Matrix ~ ~ ~
cheb_multR_roots = pr.solve([c1, c2], MSmatrix=2)
assert len(cheb_multR_roots) == right_number_of_roots
for root in cheb_multR_roots:
assert np.isclose(0, c1(root), atol=1.e-8)
assert np.isclose(0, c1(root), atol=1.e-8)
#~ ~ ~ Power Form, Pseudorandom Multiplication Matrix ~ ~ ~
power_multrand_roots = pr.solve([p1, p2], MSmatrix=0)
assert len(power_multrand_roots) == right_number_of_roots
for root in power_multrand_roots:
assert np.isclose(0, p1(root), atol=1.e-8)
assert np.isclose(0, p2(root), atol=1.e-8)
#~ ~ ~ Cheb Form, Pseudorandom Multiplication Matrix ~ ~ ~
cheb_multrand_roots = pr.solve([c1, c2], MSmatrix=0)
assert len(cheb_multrand_roots) == right_number_of_roots
for root in cheb_multrand_roots:
assert np.isclose(0, c1(root), atol=1.e-8)
assert np.isclose(0, c1(root), atol=1.e-8)
#~ ~ ~ Power Form, Division Matrix ~ ~ ~
power_div_roots = pr.solve([p1, p2], MSmatrix=-1)
assert len(power_div_roots) == right_number_of_roots
for root in power_div_roots:
assert np.isclose(0, p1(root), atol=1.e-8)
assert np.isclose(0, p2(root), atol=1.e-8)
#~ ~ ~ Cheb Form, Division Matrix ~ ~ ~
cheb_div_roots = pr.solve([c1, c2], MSmatrix=-1)
assert len(cheb_div_roots) == right_number_of_roots
for root in cheb_div_roots:
assert np.isclose(0, c1(root), atol=1.e-8)
assert np.isclose(0, c2(root), atol=1.e-8)