def testNaturalSplineDerivative1(self):
"""Test fitting a natural spline to a smooth function and finding its derivative"""
sp = afwMath.TautSpline(self.x, self.ySin)
y2 = afwMath.vectorD()
sp.derivative(self.x2, y2)
for x, y in zip(self.x2, y2):
self.assertTrue(abs(y - self.smooth(x, True)) < 1.5e-3)
def testNaturalSplineDerivative1(self):
"""Test fitting a natural spline to a smooth function and finding its derivative"""
sp = afwMath.TautSpline(self.x, self.ySin)
y2 = []
sp.derivative(self.x2, y2)
for x, y in zip(self.x2, y2):
self.assertAlmostEqual(y, self.smooth(x, True), delta=1.5e-3)
def testNaturalSpline1(self):
"""Test fitting a natural spline to a smooth function"""
gamma = 0
sp = afwMath.TautSpline(self.x, self.ySin, gamma)
y2 = afwMath.vectorD()
sp.interpolate(self.x2, y2)
for x, y in zip(self.x2, y2):
self.assertAlmostEqual(y, self.smooth(x), 1) # fails at 2 places!
def testTautSpline2(self):
"""Test fitting a taut spline to a non-differentiable function"""
gamma = 2.5
sp = afwMath.TautSpline(self.x, self.yND, gamma)
y2 = afwMath.vectorD()
sp.interpolate(self.x2, y2)
for x, y in zip(self.x2, y2):
self.assertAlmostEqual(y, self.noDerivative(x))
def testTautSpline1(self):
"""Test fitting a taut spline to a smooth function"""
gamma = 2.5
sp = afwMath.TautSpline(self.x, self.ySin, gamma)
y2 = afwMath.vectorD()
sp.interpolate(self.x2, y2)
for x, y in zip(self.x2, y2):
self.assertAlmostEqual(y, self.smooth(x), 4)
def testNaturalSpline2(self):
"""Test fitting a natural spline to a non-differentiable function (we basically fail)"""
gamma = 0
sp = afwMath.TautSpline(self.x, self.yND, gamma)
y2 = afwMath.vectorD()
sp.interpolate(self.x2, y2)
for x, y in zip(self.x2, y2):
self.assertAlmostEqual(y, self.noDerivative(x), 1) # fails at 2 places!
def testRootFinding(self):
"""Test finding roots of Spline = value"""
gamma = 2.5
sp = afwMath.TautSpline(self.x, self.yND, gamma)
for value in (0.1, 0.5):
self.assertEqual(sp.roots(value, self.x[0], self.x[-1])[0], 1 - value)
if False:
y = afwMath.vectorD()
sp.interpolate(self.x, y)
for x, y in zip(self.x, y):
print(x, y)
#
# Solve sin(x) = 0.5
#
sp = afwMath.TautSpline(self.x, self.ySin)
roots = [math.degrees(x) for x in sp.roots(0.5, self.x[0], self.x[-1])]
self.assertAlmostEqual(roots[0], 30, 5)
self.assertAlmostEqual(roots[1], 150, 5)
