def op(i, j, x, y):
# scaling = "monic"
scaling = "classical"
iterator = orthopy.c1.jacobi.Eval((x - y) / (x + y), scaling, 0, 0)
val1 = get_nth(iterator, i)
# val1 = numpy.polyval(scipy.special.jacobi(i, 0, 0), (x - y) / (x + y))
# treat x==0, y==0 separately
if isinstance(val1, numpy.ndarray):
idx = numpy.where(numpy.logical_and(x == 0, y == 0))[0]
val1[idx] = numpy.polyval(scipy.special.jacobi(i, 0, 0), 0.0)
else:
if numpy.isnan(val1):
val1 = numpy.polyval(scipy.special.jacobi(i, 0, 0), 0.0)
iterator = orthopy.c1.jacobi.Eval(1 - 2 * (x + y), scaling, 2 * i + 1, 0)
val2 = get_nth(iterator, j)
# val2 = numpy.polyval(scipy.special.jacobi(j, 2*i+1, 0), 1-2*(x+y))
flt = numpy.vectorize(float)
return flt(
numpy.sqrt(2 * i + 1) * val1 * (x + y)**i *
numpy.sqrt(2 * j + 2 * i + 2) * val2)
def test_chebyshev2_normal(n, y):
x = numpy.array([0, S(1) / 2, 1])
scaling = "normal"
y0 = get_nth(orthopy.c1.chebyshev2.Eval(x[0], scaling, symbolic=True), n)
assert y0 == y[0]
val = get_nth(orthopy.c1.chebyshev2.Eval(x, scaling, symbolic=True), n)
assert all(val == y)
def test_chebyshev1_monic(n, y):
x = numpy.array([0, Rational(1, 2), 1])
# Test evaluation of one value
y0 = get_nth(orthopy.c1.chebyshev1.Eval(x[0], "monic", symbolic=True), n)
assert y0 == y[0]
# Test evaluation of multiple values
val = get_nth(orthopy.c1.chebyshev1.Eval(x, "monic", symbolic=True), n)
assert all(val == y)
def test_legendre_monic(scaling, n, y):
x = numpy.array([0, S(1) / 2, 1])
# Test evaluation of one value
y0 = get_nth(orthopy.c1.legendre.Eval(x[0], scaling, symbolic=True), n)
assert y0 == y[0]
# Test evaluation of multiple values
val = get_nth(orthopy.c1.legendre.Eval(x, scaling, symbolic=True), n)
assert all(val == y)
def test_gegenbauer_monic(n, y):
x = numpy.array([0, Rational(1, 2), 1])
lmbda = -Rational(1, 2)
# Test evaluation of one value
y0 = get_nth(
orthopy.c1.gegenbauer.Eval(x[0], "monic", lmbda, symbolic=True), n)
assert y0 == y[0]
# Test evaluation of multiple values
val = get_nth(orthopy.c1.gegenbauer.Eval(x, "monic", lmbda, symbolic=True),
n)
assert all(val == y)
def test_chebyshev2_p11(n, y):
x = numpy.array([0, Rational(1, 2), 1])
scaling = "classical"
y0 = get_nth(orthopy.c1.chebyshev2.Eval(x[0], scaling, symbolic=True), n)
assert y0 == y[0]
alpha = Rational(1, 2)
assert sympy.binomial(n + alpha, n) == y[2]
val = get_nth(orthopy.c1.chebyshev2.Eval(x, scaling, symbolic=True), n)
assert all(val == y)
def test_jacobi_monic(scaling, n, y):
x = numpy.array([0, S(1) / 2, 1])
alpha = 3
beta = 2
y2 = get_nth(
orthopy.c1.jacobi.Eval(x[2], scaling, alpha, beta, symbolic=True), n)
assert y2 == y[2]
val = get_nth(
orthopy.c1.jacobi.Eval(x, scaling, alpha, beta, symbolic=True), n)
assert all(val == y)
def test_eval(t, ref, tol=1.0e-14):
n = 5
value = get_nth(orthopy.c1.legendre.Eval(t, "monic", symbolic=True), n)
assert numpy.all(value == ref)
# Evaluating the Legendre polynomial in this way is rather unstable, so don't go too
# far with n.
approx_ref = numpy.polyval(scipy.special.legendre(n, monic=True), t)
assert numpy.all(numpy.abs(value - approx_ref) < tol)
def test_eval(t, ref):
n = 5
value = get_nth(orthopy.c1.chebyshev2.Eval(t, "monic", symbolic=True), n)
assert numpy.all(value == ref)
def test_eval(t, ref, tol=1.0e-14):
n = 5
value = get_nth(orthopy.c1.chebyshev1.Eval(t, "monic"), n)
assert numpy.all(value == ref)
