def testMatch(self):
N = 11
x0 = random.random(N); x0.sort()
y0 = random.random(N)
for interp_type in ('linear', 'cubic'):
y = interp(x0, y0, interp_type)
x = x0.copy()
self.assertAlmostEqual(abs(value(y(x) - y0)).max(), 0)
def testMatchDeriv(self):
N = 11
x0 = random.random(N); x0.sort()
y0 = random.random(N)
y = interp(x0, y0, 'cubic')
x = x0.copy()
yp0 = value(y.y0[:,1])
yp1 = value(y.derivative(x))
yp2 = np.diag(y(x).diff(x).todense())
self.assertAlmostEqual(abs(yp1 - yp0).max(), 0)
self.assertAlmostEqual(abs(yp2 - yp0).max(), 0)
def testDiagonalPerturbation(self):
import pylab
N = 2
A_additional_diag = array(1)
A = random.random([N, N]) + A_additional_diag * eye(N)
b = eye(N)
Ainv = solve(A, b)
Ainv_diff_A_diag = Ainv.diff(A_additional_diag)
Ainv_diff_A_diag = np.array(Ainv_diff_A_diag.todense()).reshape([N, N])
Ainv_diff_A_diag_analytical = -np.dot(value(Ainv), value(Ainv))
difference = Ainv_diff_A_diag - Ainv_diff_A_diag_analytical
self.assertAlmostEqual(abs(difference).max(), 0)
