def check_gl_quad_chunks_extra_dims2(n):
"""check that gl_quad integrates polynomial of degree 3*n+1 (even) and
3*n+2 (odd)exactly, with multiple intervals with function that returns
extra dims.
This test is not rigorous because the polynomials formed can be fairly well
approximated using lower order schemes
"""
#a, b = (-0.9, 1.3)
a = np.array([-0.9, -0.4, .5])
b = np.array([-0.4, 0.5, 1.3])
coeff = np.arange(1, 3 * n + 1 + (n % 2))
coeff[::2] = coeff[::2] * -1.0
f = np.poly1d(coeff)
def g(x):
out = f(x) * np.arange(1, 9)
return out
g_ = g #np.vectorize(g)
F = f.integ()
exact = np.sum(F(b) - F(a)) * np.arange(1, 9)
assert_allclose(gl_quad(g_, a, b, n=n, sum_intervals=True),
exact,
rtol=1e-3,
atol=0)
def check_gl_quad(n):
"""check that gl_quad integrates polynomial of degree 2*n-1 'exactly'
This test is not rigorous because the ploynmials formed can be fairly well
approximated using lower order schemes"""
a, b = (-0.9, 1.3)
coeff = np.arange(1, 2*n+1)
coeff[::2] =coeff[::2]*-1.0
f = np.poly1d(coeff)
F = f.integ()
exact = F(b) - F(a)
assert_allclose(gl_quad(f,a,b, n=n), exact, rtol=1e-14,atol=0)
def check_gl_quad(n):
"""check that gl_quad integrates polynomial of degree 2*n-1 'exactly'
This test is not rigorous because the polynomials formed can be fairly well
approximated using lower order schemes"""
a, b = (-0.9, 1.3)
coeff = np.arange(1, 2 * n + 1)
coeff[::2] = coeff[::2] * -1.0
f = np.poly1d(coeff)
F = f.integ()
exact = F(b) - F(a)
assert_allclose(gl_quad(f, a, b, n=n), exact, rtol=1e-14, atol=0)
def check_gl_quad_chunks(n):
"""check that gk_quad integrates polynomial of degree 3*n+1 (even) and
3*n+2 (odd)exactly, with multiple intervals
This test is not rigorous because the polynomials formed can be fairly well
approximated using lower order schemes
"""
#a, b = (-0.9, 1.3)
a = np.array([-0.9, -0.4, .5])
b = np.array([-0.4, 0.5, 1.3])
coeff = np.arange(1, 3*n + 1 + (n%2))
coeff[::2] =coeff[::2]*-1.0
f = np.poly1d(coeff)
F = f.integ()
exact = np.sum(F(b) - F(a))
assert_allclose(gl_quad(f,a,b, n=n, sum_intervals=True), exact, rtol=1e-3,atol=0)
def check_gl_quad_chunks(n):
"""check that gk_quad integrates polynomial of degree 3*n+1 (even) and
3*n+2 (odd)exactly, with multiple intervals
This test is not rigorous because the polynomials formed can be fairly well
approximated using lower order schemes
"""
#a, b = (-0.9, 1.3)
a = np.array([-0.9, -0.4, .5])
b = np.array([-0.4, 0.5, 1.3])
coeff = np.arange(1, 3 * n + 1 + (n % 2))
coeff[::2] = coeff[::2] * -1.0
f = np.poly1d(coeff)
F = f.integ()
exact = np.sum(F(b) - F(a))
assert_allclose(gl_quad(f, a, b, n=n, sum_intervals=True),
exact,
rtol=1e-3,
atol=0)
def check_gl_quad_chunks_extra_dims2(n):
"""check that gl_quad integrates polynomial of degree 3*n+1 (even) and
3*n+2 (odd)exactly, with multiple intervals with function that returns
extra dims.
This test is not rigorous because the polynomials formed can be fairly well
approximated using lower order schemes
"""
#a, b = (-0.9, 1.3)
a = np.array([-0.9, -0.4, .5])
b = np.array([-0.4, 0.5, 1.3])
coeff = np.arange(1, 3*n + 1 + (n%2))
coeff[::2] =coeff[::2]*-1.0
f = np.poly1d(coeff)
def g(x):
out = f(x)*np.arange(1,9)
return out
g_ = g#np.vectorize(g)
F = f.integ()
exact = np.sum(F(b) - F(a)) * np.arange(1,9)
assert_allclose(gl_quad(g_,a,b, n=n, sum_intervals=True), exact, rtol=1e-3,atol=0)