def xspline_integrate():
import numpy as np
import scipy.integrate as integrate
from xspline.__init__ import xspline
ok = True
# setup test problem
# -------------------------------------------------------------------------
knots = np.linspace(0.0, 1.0, 5)
degree = 1
bs = xspline(knots, degree, l_linear=True, r_linear=True)
# test integrate function
# -------------------------------------------------------------------------
N = 3
x = np.linspace(-1.0, 2.0, N)
a = np.repeat(-1.0, N)
my_If = bs.splineIF(a, x, 0, 2)
def func(x):
return bs.splineIF(-1.0, x, 0, 1)
tr_If = np.array([integrate.quad(func, a[i], x[i])[0] for i in range(N)])
tol = 1e-8
ok = ok and np.linalg.norm(my_If - tr_If) < tol
if not ok:
print('tr_If', tr_If)
print('my_If', my_If)
return ok
def xspline_intgLinear():
import numpy as np
from xspline.__init__ import xspline
ok = True
# setup test problem
# -------------------------------------------------------------------------
knots = np.linspace(0.0, 1.0, 3)
degree = 1
bs = xspline(knots, degree)
# test intgLinear function
# -------------------------------------------------------------------------
a = np.random.rand(20)
x = a + 1.0
slope = 2.0
intercept_at_0 = 1.0
my_if = bs.intgLinear(a, x, 1, 0.0, intercept_at_0, slope)
tr_if = 0.5*slope*(x**2 - a**2) + intercept_at_0*(x - a)
tol = 1e-10
ok = ok and np.linalg.norm(my_if - tr_if) < tol
if not ok:
print('tr_if', tr_if)
print('my_if', my_if)
return ok
def xspline_lastDMat():
import numpy as np
from xspline.__init__ import xspline
ok = True
# setup test problem
# -------------------------------------------------------------------------
knots = np.linspace(0.0, 1.0, 5)
degree = 3
bs = xspline(knots, degree, l_linear=True, r_linear=True)
# test lastDMat function
# -------------------------------------------------------------------------
my_dmat = bs.lastDMat()
x = np.array(
[0.5 * (knots[i] + knots[i + 1]) for i in range(bs.num_knots - 1)])
tr_dmat = bs.designDMat(x[1:-1], degree)
tr_dmat = np.vstack((bs.designDMat(x[0:1], 1), tr_dmat))
tr_dmat = np.vstack((tr_dmat, bs.designDMat(x[-1:], 1)))
tol = 1e-10
ok = ok and np.linalg.norm(my_dmat - tr_dmat) < tol
return ok
def xspline_designIMat():
import numpy as np
from xspline.__init__ import xspline
ok = True
# setup test problem
# -------------------------------------------------------------------------
knots = np.linspace(0.0, 1.0, 3)
degree = 1
tol = 1e-10
# test designIMat function left linear
# -------------------------------------------------------------------------
bs = xspline(knots, degree, l_linear=True)
a = np.zeros(201)
x = np.linspace(0.0, 1.0, 201)
my_imat = bs.designIMat(a, x, 1)
tr_imat = np.zeros((x.size, 2))
tr_imat[:, 0] = 1.0 - (x - 1.0)**2
tr_imat[:, 1] = x**2 - x
ok = ok and np.linalg.norm(my_imat - tr_imat) < tol
if not ok:
print('xspline_designIMat: l_linear error.')
# test designIMat function right linear
# -------------------------------------------------------------------------
bs = xspline(knots, degree, r_linear=True)
a = np.zeros(201)
x = np.linspace(0.0, 1.0, 201)
my_imat = bs.designIMat(a, x, 1)
tr_imat = np.zeros((x.size, 2))
tr_imat[:, 0] = x - x**2
tr_imat[:, 1] = x**2
ok = ok and np.linalg.norm(my_imat - tr_imat) < tol
if not ok:
print('xspline_designIMat: r_linear error.')
return ok
def xspline_splineDF():
import numpy as np
from xspline.__init__ import xspline
ok = True
# setup test problem
# -------------------------------------------------------------------------
knots = np.linspace(0.0, 1.0, 3)
degree = 1
tol = 1e-10
# test splineDF function left linear without extrapolation
# -------------------------------------------------------------------------
bs = xspline(knots, degree, l_linear=True)
x = np.linspace(-1.0, 1.0, 201)
my_Df = bs.splineDF(x, 0, 1, l_extra=False)
valid_index = (x >= bs.knots[0]) & (x <= bs.knots[-1])
tr_Df = np.zeros(x.size)
tr_Df[valid_index] = -2.0
ok = ok and np.linalg.norm(my_Df - tr_Df) < tol
if not ok:
print('xspline_splineDF: l_linear error.')
# test splineDF function left linear extrapolation
# -------------------------------------------------------------------------
x = np.linspace(-1.0, 0.0, 101)
my_Df = bs.splineDF(x, 0, 1, l_extra=True)
tr_Df = -2.0 * np.ones(x.size)
ok = ok and np.linalg.norm(my_Df - tr_Df) < tol
if not ok:
print('xspline_splineDF: l_linear and l_extra error.')
# test splineDF function right linear without extrapolation
# -------------------------------------------------------------------------
bs = xspline(knots, degree, r_linear=True)
x = np.linspace(0.0, 2.0, 201)
my_Df = bs.splineDF(x, 1, 1, r_extra=False)
valid_index = (x >= bs.knots[0]) & (x <= bs.knots[-1])
tr_Df = np.zeros(x.size)
tr_Df[valid_index] = 2.0
ok = ok and np.linalg.norm(my_Df - tr_Df) < tol
if not ok:
print('xspline_splineDF: r_linear error.')
# test splineDF function right linear extrapolation
# -------------------------------------------------------------------------
x = np.linspace(1.0, 2.0, 101)
my_Df = bs.splineDF(x, 1, 1, r_extra=True)
tr_Df = 2.0 * np.ones(x.size)
ok = ok and np.linalg.norm(my_Df - tr_Df) < tol
if not ok:
print('xspline_splineDF: r_linear and r_extra error.')
return ok