def test_integral(self):
for order in range(2, 8, 2):
for dt in numpy.arange(0.1, 2.0, 0.1):
# Create a spline with three segments
aspl = bsplines.BSpline(order)
kr = aspl.numKnotsRequired(4)
kc = aspl.numCoefficientsRequired(4)
# Choose a uniform knot sequence.
knots = numpy.linspace(0.0, (kr - 1) * dt, kr)
cp = numpy.random.random(kc)
cpa = numpy.array([cp])
aspl = bsplines.BSpline(order)
aspl.setKnotVectorAndCoefficients(knots, cpa)
fspl = (knots, cp, order - 1)
for a in numpy.arange(aspl.t_min(),
aspl.t_max() - 1e-15, 0.4 * dt):
for i in numpy.arange(aspl.t_min(),
aspl.t_max() - 1e-15, 0.4 * dt):
print("Eval at %f\n" % (i))
f = fp.splint(a, float(i), fspl)
b = aspl.evalI(a, i)
self.assertAlmostEqual(
b,
f,
msg=
"order %d spline integral evaluated on [%f,%f] (%f != %f) was not right"
% (order, a, i, float(b), f))
def test_integral_non_uniform(self):
for order in range(2, 8, 2):
# Create a spline with three segments
aspl = aslam_splines.OptEuclideanBSpline(order, 1)
kr = aspl.numKnotsRequired(4)
kc = aspl.numCoefficientsRequired(4)
# Choose a non-uniform knot sequence.
knots = numpy.linspace(0.0, (kr - 1), kr)
knots = knots * knots
cp = numpy.random.random(kc)
cpa = numpy.array([cp])
aspl = aslam_splines.OptEuclideanBSpline(order, 1)
aspl.initWithKnotsAndControlVertices(knots, cpa)
fspl = (knots, cp, order - 1)
for a in numpy.arange(aspl.getMinTime(),
aspl.getMaxTime() - 1e-15, 0.4):
for i in numpy.arange(aspl.getMinTime(),
aspl.getMaxTime() - 1e-15, 0.4):
#print "Eval at %f\n" % (i)
f = fp.splint(a, float(i), fspl)
b = aspl.evalI(a, i)
self.assertEqual(b.shape, (1, ))
self.assertAlmostEqual(
b[0],
f,
msg=
"order %d spline integral evaluated on [%f,%f] (%f != %f) was not right"
% (order, a, i, float(b), f))
def test_integral_non_uniform_repeated(self):
for order in range(2,8,2):
# Create a spline with three segments
aspl = bsplines.BSpline(order)
kr = aspl.numKnotsRequired(4)
kc = aspl.numCoefficientsRequired(4);
# Choose a non-uniform knot sequence.
knots = numpy.linspace(0.0, (kr - 1), kr)
knots = knots*knots
for i in range(0,len(knots)):
if i & 1 > 0:
knots[i] = knots[i-1]
cp = numpy.random.random(kc);
cpa = numpy.array([cp])
aspl = bsplines.BSpline(order);
aspl.setKnotVectorAndCoefficients(knots,cpa);
fspl = (knots,cp,order-1)
for a in numpy.arange(aspl.t_min(),aspl.t_max()-1e-15,0.4):
for i in numpy.arange(aspl.t_min(), aspl.t_max()-1e-15, 0.4):
print "Eval at %f\n" % (i)
f = fp.splint(a,float(i),fspl)
b = aspl.evalI(a,i)
self.assertAlmostEqual(b, f, msg="order %d spline integral evaluated on [%f,%f] (%f != %f) was not right" % (order, a,i,float(b),f))
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_splantider_vs_splint(self):
# Check antiderivative vs. FITPACK
spl2 = splantider(self.spl)
# no extrapolation, splint assumes function is zero outside
# range
xx = np.linspace(0, 1, 20)
for x1 in xx:
for x2 in xx:
y1 = splint(x1, x2, self.spl)
y2 = splev(x2, spl2) - splev(x1, spl2)
assert_allclose(y1, y2)
def test_splantider_vs_splint(self):
# Check antiderivative vs. FITPACK
spl2 = splantider(self.spl)
# no extrapolation, splint assumes function is zero outside
# range
xx = np.linspace(0, 1, 20)
for x1 in xx:
for x2 in xx:
y1 = splint(x1, x2, self.spl)
y2 = splev(x2, spl2) - splev(x1, spl2)
assert_allclose(y1, y2)
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_new_uniform_cubicIntegral(self):
# create the knot and control point vectors
cardinalknots = 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])
for dt in numpy.arange(0.1,2.0,0.1):
knots = cardinalknots * dt;
aspl = asrl_splines.UniformCubicBSpline(cpa,dt,knots[3]);
fspl = (knots,cp,3)
for a in numpy.arange(2.0*dt,3.9*dt,0.1*dt):
for i in numpy.arange(2.1*dt,4.0*dt,0.1*dt):
print "Eval at %f\n" % (i)
f = fp.splint(a,float(i),fspl)
b = aspl.evalI(a,i)
assert abs(b - f) < 1e-10, "spline integral evaluated on [%f,%f] (%f != %f) was not right" % (a,i,float(b),f)
def test_integral(self):
for order in range(2,8,2):
for dt in numpy.arange(0.1,2.0,0.1):
# Create a spline with three segments
aspl = aslam_splines.OptEuclideanBSpline(order, 1)
kr = aspl.numKnotsRequired(4)
kc = aspl.numCoefficientsRequired(4);
# Choose a uniform knot sequence.
knots = numpy.linspace(0.0, (kr - 1)*dt, kr)
cp = numpy.random.random(kc);
cpa = numpy.array([cp])
aspl.initWithKnotsAndControlVertices(knots, cpa);
fspl = (knots,cp,order-1)
for a in numpy.arange(aspl.getMinTime(),aspl.getMaxTime()-1e-15,0.4*dt):
for i in numpy.arange(aspl.getMinTime(), aspl.getMaxTime()-1e-15, 0.4*dt):
#print "Eval at %f\n" % (i)
f = fp.splint(a,float(i),fspl)
b = aspl.evalI(a,i)
self.assertAlmostEqual(b, f, msg="order %d spline integral evaluated on [%f,%f] (%f != %f) was not right" % (order, a,i,float(b),f))