def test_bspderiv():
numval = 10
maxord = 10
dx = 1e-6
xl = np.linspace(0, 10, numval)
xr = xl + dx
xm = xl + dx/2
for k in range(1, maxord):
# Check k + 1 degree k b-splines.
n = k + 1
t = [0]*n + list(range(1, 10)) + [10]*n
c = np.eye(len(t) - n)
for j in range(n):
msg = "k = %d, j = %d" % (k, j)
spl = bs.BSpline(t, k, c[j])
der = bs.bsplderiv(spl, n=1)
res = bs.bsplval(xm, der)
tgt = (bs.bsplval(xr, spl) - bs.bsplval(xl, spl))/dx
assert_almost_equal(res, tgt, err_msg=msg)
def test_bspderiv():
pass
numval = 10
maxord = 10
dx = 1e-6
xl = np.linspace(0, 10, numval)
xr = xl + dx
xm = xl + dx / 2
for k in range(1, maxord):
# Check k + 1 degree k b-splines.
n = k + 1
t = [0] * n + list(range(1, 10)) + [10] * n
c = np.eye(len(t) - n)
for j in range(n):
msg = "k = %d, j = %d" % (k, j)
tck = bs.Tck(t, c[j], k)
dck = bs.bsplderiv(tck, n=1)
tgt = (bs.bsplval(xr, tck) - bs.bsplval(xl, tck)) / dx
res = bs.bsplval(xm, dck)
assert_almost_equal(res, tgt, err_msg=msg)
def test_bspvander():
numval = 10
maxord = 10
x = np.linspace(0, 10, numval)
for k in range(maxord):
# Check k + 1 degree k b-splines.
n = k + 1
t = [0]*n + list(range(1, 10)) + [10]*n
c = np.eye(len(t) - n)
v = bs.bsplvander(x, t, k)
for j in range(n):
msg = "k = %d, j = %d" % (k, j)
bsp = bs.BSpline(t, k, c[j])
tgt = bs.bsplval(x, bsp)
assert_almost_equal(v[:, j], tgt, err_msg=msg)
def test_bspline_values():
# Test computed b-spline values against Bernstein polynomials.
numval = 10
maxord = 10
x = np.linspace(0, 1, numval)
y = 1 - x
b = np.ones((1, numval))
for k in range(maxord):
# Check k + 1 degree k b-splines.
n = k + 1
t = [0]*n + [1]*n
c = np.eye(n)
for j in range(n):
msg = "k = %d, j = %d" % (k, j)
bsp = bs.BSpline(t, k, c[j])
res = bs.bsplval(x, bsp)
assert_almost_equal(res, b[j], err_msg=msg)
# Prepare next set of Bernstein polynomial values if needed.
if n < maxord:
tmp = b
b = np.zeros((n + 1, numval))
b[:n] += y*tmp
b[1:] += x*tmp