def check_2(self,
f=f1,
per=0,
s=0,
a=0,
b=2 * pi,
N=20,
xb=None,
xe=None,
ia=0,
ib=2 * pi,
dx=0.2 * pi):
if xb is None:
xb = a
if xe is None:
xe = b
x = a + (b - a) * arange(N + 1, dtype=float) / float(N) # nodes
v = f(x)
def err_est(k, d):
# Assume f has all derivatives < 1
h = 1.0 / float(N)
tol = 5 * h**(.75 * (k - d))
if s > 0:
tol += 1e5 * s
return tol
nk = []
for k in range(1, 6):
tck = splrep(x, v, s=s, per=per, k=k, xe=xe)
nk.append([splint(ia, ib, tck), spalde(dx, tck)])
put("\nf = %s s=S_k(x;t,c) x in [%s, %s] > [%s, %s]" %
(f(None), repr(round(xb, 3)), repr(round(xe, 3)), repr(round(
a, 3)), repr(round(b, 3))))
put(" per=%d s=%s N=%d [a, b] = [%s, %s] dx=%s" %
(per, repr(s), N, repr(round(ia, 3)), repr(round(
ib, 3)), repr(round(dx, 3))))
put(" k : int(s,[a,b]) Int.Error Rel. error of s^(d)(dx) d = 0, .., k"
)
k = 1
for r in nk:
if r[0] < 0:
sr = '-'
else:
sr = ' '
put(" %d %s%.8f %.1e " %
(k, sr, abs(r[0]), abs(r[0] - (f(ib, -1) - f(ia, -1)))))
d = 0
for dr in r[1]:
err = abs(1 - dr / f(dx, d))
tol = err_est(k, d)
assert_(err < tol, (k, d))
put(" %.1e %.1e" % (err, tol))
d = d + 1
put("\n")
k = k + 1
def test_new_uniform_cubic1(self):
# create the knot and control point vectors
knots = numpy.array([-2.0, -1.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0])
cp = numpy.array([0.0, 10.0, 2.0, 30.0, 4.0, 50.0])
cpa = numpy.array([cp])
aspl = asrl_splines.UniformCubicBSpline(cpa,1.0,knots[3]);
fspl = (knots,cp,3)
for i in numpy.arange(2.0,4.0,0.1):
print "Eval at %f\n" % (i)
f = fp.spalde(float(i),fspl)
for j in range(0,3):
a = aspl.evalD(i,j)
assert abs(a - f[j]) < 1e-10, "spline (D%d) evaluated at %f (%f != %f) was not right" % (j,float(i),a,f[j])
def check_2(self, f=f1, per=0, s=0, a=0, b=2 * pi, N=20, xb=None, xe=None, ia=0, ib=2 * pi, dx=0.2 * pi):
if xb is None:
xb = a
if xe is None:
xe = b
x = a + (b - a) * arange(N + 1, dtype=float) / float(N) # nodes
v = f(x)
def err_est(k, d):
# Assume f has all derivatives < 1
h = 1.0 / float(N)
tol = 5 * h ** (0.75 * (k - d))
if s > 0:
tol += 1e5 * s
return tol
nk = []
for k in range(1, 6):
tck = splrep(x, v, s=s, per=per, k=k, xe=xe)
nk.append([splint(ia, ib, tck), spalde(dx, tck)])
put(
"\nf = %s s=S_k(x;t,c) x in [%s, %s] > [%s, %s]"
% (f(None), repr(round(xb, 3)), repr(round(xe, 3)), repr(round(a, 3)), repr(round(b, 3)))
)
put(
" per=%d s=%s N=%d [a, b] = [%s, %s] dx=%s"
% (per, repr(s), N, repr(round(ia, 3)), repr(round(ib, 3)), repr(round(dx, 3)))
)
put(" k : int(s,[a,b]) Int.Error Rel. error of s^(d)(dx) d = 0, .., k")
k = 1
for r in nk:
if r[0] < 0:
sr = "-"
else:
sr = " "
put(" %d %s%.8f %.1e " % (k, sr, abs(r[0]), abs(r[0] - (f(ib, -1) - f(ia, -1)))))
d = 0
for dr in r[1]:
err = abs(1 - dr / f(dx, d))
tol = err_est(k, d)
assert_(err < tol, (k, d))
put(" %.1e %.1e" % (err, tol))
d = d + 1
put("\n")
k = k + 1
def test_random(self):
numpy.random.seed(3)
for order in range(2, 10):
aspl = aslam_splines.OptEuclideanBSpline(order, 1)
kr = aspl.numKnotsRequired(3)
kc = aspl.numCoefficientsRequired(3)
knots = numpy.random.random([kr]) * 10
knots.sort()
cp = numpy.random.random([kc])
cpa = numpy.array([cp])
aspl.initWithKnotsAndControlVertices(knots, cpa)
fspl = (knots, cp, order - 1)
for i in numpy.linspace(aspl.getMinTime(), aspl.getMaxTime(), 10):
f = fp.spalde(float(i), fspl)
a = aspl.eval(i)
for j in range(0, f.shape[0]):
a = aspl.evalD(i, j)
self.assertAlmostEqual(a, f[j])
def test_random(self):
numpy.random.seed(3)
for order in range(2,10):
aspl = bsplines.EuclideanBSpline(order, 1)
kr = aspl.numKnotsRequired(3)
kc = aspl.numCoefficientsRequired(3);
knots = numpy.random.random([kr]) * 10
knots.sort()
cp = numpy.random.random([kc])
cpa = numpy.array([cp])
aspl.initWithKnotsAndControlVertices(knots, cpa)
fspl = (knots,cp,order-1)
for i in numpy.linspace(aspl.getMinTime(),aspl.getMaxTime(),10):
f = fp.spalde(float(i),fspl)
a = aspl.eval(i)
for j in range(0,f.shape[0]):
a = aspl.evalD(i,j)
self.assertAlmostEqual(a, f[j])
def test_random(self):
numpy.random.seed(3)
for order in range(2, 10):
aspl = bsplines.BSpline(order)
kr = aspl.numKnotsRequired(3)
kc = aspl.numCoefficientsRequired(3)
knots = numpy.random.random([kr]) * 10
knots.sort()
cp = numpy.random.random([kc])
cpa = numpy.array([cp])
aspl.setKnotVectorAndCoefficients(knots, cpa)
fspl = (knots, cp, order - 1)
for i in numpy.linspace(aspl.t_min(), aspl.t_max(), 10):
f = fp.spalde(float(i), fspl)
a = aspl.eval(i)
for j in range(0, f.shape[0]):
a = aspl.evalD(i, j)
self.assertAlmostEqual(a, f[j])
def test_uniform(self):
numpy.random.seed(1)
for order in range(2,10):
aspl = aslam_splines.OptEuclideanBSpline(order, 1)
kr = aspl.numKnotsRequired(3)
kc = aspl.numCoefficientsRequired(3);
# Choose a uniform knot sequence.
knots = numpy.linspace(0.0,kr*1.0, kr)
cp = numpy.random.random([kc])
cpa = numpy.array([cp])
aspl.initWithKnotsAndControlVertices(knots, cpa)
fspl = (knots,cp,order-1)
for i in numpy.linspace(aspl.getMinTime(),aspl.getMaxTime()-1e-15,10):
f = fp.spalde(float(i),fspl)
a = aspl.eval(i)
for j in range(0,f.shape[0]):
a = aspl.evalD(i,j)
self.assertAlmostEqual(a, f[j])
def test_random(self):
numpy.random.seed(3)
for order in range(2,10):
aspl = bsplines.BSpline(order)
kr = aspl.numKnotsRequired(3)
kc = aspl.numCoefficientsRequired(3);
knots = numpy.random.random([kr]) * 10
knots.sort()
cp = numpy.random.random([kc])
cpa = numpy.array([cp])
aspl.setKnotVectorAndCoefficients(knots, cpa)
fspl = (knots,cp,order-1)
for i in numpy.linspace(aspl.t_min(),aspl.t_max(),10):
f = fp.spalde(float(i),fspl)
a = aspl.eval(i)
for j in range(0,f.shape[0]):
a = aspl.evalD(i,j)
self.assertAlmostEqual(a, f[j])
def test_uniform(self):
numpy.random.seed(1)
for order in range(2, 10):
aspl = bsplines.EuclideanBSpline(order, 1)
kr = aspl.numKnotsRequired(3)
kc = aspl.numCoefficientsRequired(3)
# Choose a uniform knot sequence.
knots = numpy.linspace(0.0, kr * 1.0, kr)
cp = numpy.random.random([kc])
cpa = numpy.array([cp])
aspl.initWithKnotsAndControlVertices(knots, cpa)
fspl = (knots, cp, order - 1)
for i in numpy.linspace(aspl.getMinTime(),
aspl.getMaxTime() - 1e-15, 10):
f = fp.spalde(float(i), fspl)
a = aspl.eval(i)
for j in range(0, f.shape[0]):
a = aspl.evalD(i, j)
self.assertAlmostEqual(a, f[j])
def test_repeated(self):
numpy.random.seed(2)
for order in range(2, 10):
aspl = bsplines.BSpline(order)
kr = aspl.numKnotsRequired(3)
kc = aspl.numCoefficientsRequired(3)
# Make a knot sequence that is all zeros at one end and all ones at the other.
knots = numpy.zeros(kr)
for i in range(0, knots.size):
if i >= knots.size * 0.5:
knots[i] = 1.0
cp = numpy.random.random([kc])
cpa = numpy.array([cp])
aspl.setKnotVectorAndCoefficients(knots, cpa)
fspl = (knots, cp, order - 1)
for i in numpy.linspace(aspl.t_min(), aspl.t_max() - 1e-15, 10):
f = fp.spalde(float(i), fspl)
a = aspl.eval(i)
for j in range(0, f.shape[0]):
a = aspl.evalD(i, j)
self.assertAlmostEqual(a, f[j])
def test_repeated(self):
numpy.random.seed(2)
for order in range(2,10):
aspl = bsplines.BSpline(order)
kr = aspl.numKnotsRequired(3)
kc = aspl.numCoefficientsRequired(3);
# Make a knot sequence that is all zeros at one end and all ones at the other.
knots = numpy.zeros(kr)
for i in range(0,knots.size):
if i >= knots.size * 0.5:
knots[i] = 1.0
cp = numpy.random.random([kc])
cpa = numpy.array([cp])
aspl.setKnotVectorAndCoefficients(knots, cpa)
fspl = (knots,cp,order-1)
for i in numpy.linspace(aspl.t_min(),aspl.t_max()-1e-15,10):
f = fp.spalde(float(i),fspl)
a = aspl.eval(i)
for j in range(0,f.shape[0]):
a = aspl.evalD(i,j)
self.assertAlmostEqual(a, f[j])