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from numpy.testing import *
from scipy.interpolate import KroghInterpolator, krogh_interpolate, \
BarycentricInterpolator, barycentric_interpolate, \
PiecewisePolynomial, piecewise_polynomial_interpolate, \
approximate_taylor_polynomial
import scipy
import numpy as np
from scipy.interpolate import splrep, splev
class CheckKrogh(TestCase):
def setUp(self):
self.true_poly = scipy.poly1d([-2,3,1,5,-4])
self.test_xs = np.linspace(-1,1,100)
self.xs = np.linspace(-1,1,5)
self.ys = self.true_poly(self.xs)
def test_lagrange(self):
P = KroghInterpolator(self.xs,self.ys)
assert_almost_equal(self.true_poly(self.test_xs),P(self.test_xs))
def test_scalar(self):
P = KroghInterpolator(self.xs,self.ys)
assert_almost_equal(self.true_poly(7),P(7))
def test_derivatives(self):
P = KroghInterpolator(self.xs,self.ys)
D = P.derivatives(self.test_xs)
for i in xrange(D.shape[0]):
assert_almost_equal(self.true_poly.deriv(i)(self.test_xs),
D[i])
def test_low_derivatives(self):
P = KroghInterpolator(self.xs,self.ys)
D = P.derivatives(self.test_xs,len(self.xs)+2)
for i in xrange(D.shape[0]):
assert_almost_equal(self.true_poly.deriv(i)(self.test_xs),
D[i])
def test_derivative(self):
P = KroghInterpolator(self.xs,self.ys)
m = 10
r = P.derivatives(self.test_xs,m)
for i in xrange(m):
assert_almost_equal(P.derivative(self.test_xs,i),r[i])
def test_high_derivative(self):
P = KroghInterpolator(self.xs,self.ys)
for i in xrange(len(self.xs),2*len(self.xs)):
assert_almost_equal(P.derivative(self.test_xs,i),
np.zeros(len(self.test_xs)))
def test_hermite(self):
xs = [0,0,0,1,1,1,2]
ys = [self.true_poly(0),
self.true_poly.deriv(1)(0),
self.true_poly.deriv(2)(0),
self.true_poly(1),
self.true_poly.deriv(1)(1),
self.true_poly.deriv(2)(1),
self.true_poly(2)]
P = KroghInterpolator(self.xs,self.ys)
assert_almost_equal(self.true_poly(self.test_xs),P(self.test_xs))
def test_vector(self):
xs = [0, 1, 2]
ys = np.array([[0,1],[1,0],[2,1]])
P = KroghInterpolator(xs,ys)
Pi = [KroghInterpolator(xs,ys[:,i]) for i in xrange(ys.shape[1])]
test_xs = np.linspace(-1,3,100)
assert_almost_equal(P(test_xs),
np.rollaxis(np.asarray([p(test_xs) for p in Pi]),-1))
assert_almost_equal(P.derivatives(test_xs),
np.transpose(np.asarray([p.derivatives(test_xs) for p in Pi]),
(1,2,0)))
def test_empty(self):
P = KroghInterpolator(self.xs,self.ys)
assert_array_equal(P([]), [])
def test_shapes_scalarvalue(self):
P = KroghInterpolator(self.xs,self.ys)
assert_array_equal(np.shape(P(0)), ())
assert_array_equal(np.shape(P([0])), (1,))
assert_array_equal(np.shape(P([0,1])), (2,))
def test_shapes_scalarvalue_derivative(self):
P = KroghInterpolator(self.xs,self.ys)
n = P.n
assert_array_equal(np.shape(P.derivatives(0)), (n,))
assert_array_equal(np.shape(P.derivatives([0])), (n,1))
assert_array_equal(np.shape(P.derivatives([0,1])), (n,2))
def test_shapes_vectorvalue(self):
P = KroghInterpolator(self.xs,np.outer(self.ys,np.arange(3)))
assert_array_equal(np.shape(P(0)), (3,))
assert_array_equal(np.shape(P([0])), (1,3))
assert_array_equal(np.shape(P([0,1])), (2,3))
def test_shapes_1d_vectorvalue(self):
P = KroghInterpolator(self.xs,np.outer(self.ys,[1]))
assert_array_equal(np.shape(P(0)), (1,))
assert_array_equal(np.shape(P([0])), (1,1))
assert_array_equal(np.shape(P([0,1])), (2,1))
def test_shapes_vectorvalue_derivative(self):
P = KroghInterpolator(self.xs,np.outer(self.ys,np.arange(3)))
n = P.n
assert_array_equal(np.shape(P.derivatives(0)), (n,3))
assert_array_equal(np.shape(P.derivatives([0])), (n,1,3))
assert_array_equal(np.shape(P.derivatives([0,1])), (n,2,3))
def test_wrapper(self):
P = KroghInterpolator(self.xs,self.ys)
assert_almost_equal(P(self.test_xs),krogh_interpolate(self.xs,self.ys,self.test_xs))
assert_almost_equal(P.derivative(self.test_xs,2),krogh_interpolate(self.xs,self.ys,self.test_xs,der=2))
assert_almost_equal(P.derivatives(self.test_xs,2),krogh_interpolate(self.xs,self.ys,self.test_xs,der=[0,1]))
class CheckTaylor(TestCase):
def test_exponential(self):
degree = 5
p = approximate_taylor_polynomial(np.exp, 0, degree, 1, 15)
for i in xrange(degree+1):
assert_almost_equal(p(0),1)
p = p.deriv()
assert_almost_equal(p(0),0)
class CheckBarycentric(TestCase):
def setUp(self):
self.true_poly = scipy.poly1d([-2,3,1,5,-4])
self.test_xs = np.linspace(-1,1,100)
self.xs = np.linspace(-1,1,5)
self.ys = self.true_poly(self.xs)
def test_lagrange(self):
P = BarycentricInterpolator(self.xs,self.ys)
assert_almost_equal(self.true_poly(self.test_xs),P(self.test_xs))
def test_scalar(self):
P = BarycentricInterpolator(self.xs,self.ys)
assert_almost_equal(self.true_poly(7),P(7))
def test_delayed(self):
P = BarycentricInterpolator(self.xs)
P.set_yi(self.ys)
assert_almost_equal(self.true_poly(self.test_xs),P(self.test_xs))
def test_append(self):
P = BarycentricInterpolator(self.xs[:3],self.ys[:3])
P.add_xi(self.xs[3:],self.ys[3:])
assert_almost_equal(self.true_poly(self.test_xs),P(self.test_xs))
def test_vector(self):
xs = [0, 1, 2]
ys = np.array([[0,1],[1,0],[2,1]])
P = BarycentricInterpolator(xs,ys)
Pi = [BarycentricInterpolator(xs,ys[:,i]) for i in xrange(ys.shape[1])]
test_xs = np.linspace(-1,3,100)
assert_almost_equal(P(test_xs),
np.rollaxis(np.asarray([p(test_xs) for p in Pi]),-1))
def test_shapes_scalarvalue(self):
P = BarycentricInterpolator(self.xs,self.ys)
assert_array_equal(np.shape(P(0)), ())
assert_array_equal(np.shape(P([0])), (1,))
assert_array_equal(np.shape(P([0,1])), (2,))
def test_shapes_vectorvalue(self):
P = BarycentricInterpolator(self.xs,np.outer(self.ys,np.arange(3)))
assert_array_equal(np.shape(P(0)), (3,))
assert_array_equal(np.shape(P([0])), (1,3))
assert_array_equal(np.shape(P([0,1])), (2,3))
def test_shapes_1d_vectorvalue(self):
P = BarycentricInterpolator(self.xs,np.outer(self.ys,[1]))
assert_array_equal(np.shape(P(0)), (1,))
assert_array_equal(np.shape(P([0])), (1,1))
assert_array_equal(np.shape(P([0,1])), (2,1))
def test_wrapper(self):
P = BarycentricInterpolator(self.xs,self.ys)
assert_almost_equal(P(self.test_xs),barycentric_interpolate(self.xs,self.ys,self.test_xs))
class CheckPiecewise(TestCase):
def setUp(self):
self.tck = splrep([0,1,2,3,4,5],[0,10,-1,3,7,2],s=0)
self.test_xs = np.linspace(-1,6,100)
self.spline_ys = splev(self.test_xs, self.tck)
self.spline_yps = splev(self.test_xs, self.tck, der=1)
self.xi = np.unique(self.tck[0])
self.yi = [[splev(x,self.tck,der=j) for j in xrange(3)] for x in self.xi]
def test_construction(self):
P = PiecewisePolynomial(self.xi,self.yi,3)
assert_almost_equal(P(self.test_xs),self.spline_ys)
def test_scalar(self):
P = PiecewisePolynomial(self.xi,self.yi,3)
assert_almost_equal(P(self.test_xs[0]),self.spline_ys[0])
assert_almost_equal(P.derivative(self.test_xs[0],1),self.spline_yps[0])
def test_derivative(self):
P = PiecewisePolynomial(self.xi,self.yi,3)
assert_almost_equal(P.derivative(self.test_xs,1),self.spline_yps)
def test_derivatives(self):
P = PiecewisePolynomial(self.xi,self.yi,3)
m = 4
r = P.derivatives(self.test_xs,m)
#print r.shape, r
for i in xrange(m):
assert_almost_equal(P.derivative(self.test_xs,i),r[i])
def test_vector(self):
xs = [0, 1, 2]
ys = [[[0,1]],[[1,0],[-1,-1]],[[2,1]]]
P = PiecewisePolynomial(xs,ys)
Pi = [PiecewisePolynomial(xs,[[yd[i] for yd in y] for y in ys])
for i in xrange(len(ys[0][0]))]
test_xs = np.linspace(-1,3,100)
assert_almost_equal(P(test_xs),
np.rollaxis(np.asarray([p(test_xs) for p in Pi]),-1))
assert_almost_equal(P.derivative(test_xs,1),
np.transpose(np.asarray([p.derivative(test_xs,1) for p in Pi]),
(1,0)))
def test_incremental(self):
P = PiecewisePolynomial([self.xi[0]], [self.yi[0]], 3)
for i in xrange(1,len(self.xi)):
P.append(self.xi[i],self.yi[i],3)
assert_almost_equal(P(self.test_xs),self.spline_ys)
def test_shapes_scalarvalue(self):
P = PiecewisePolynomial(self.xi,self.yi,4)
assert_array_equal(np.shape(P(0)), ())
assert_array_equal(np.shape(P([0])), (1,))
assert_array_equal(np.shape(P([0,1])), (2,))
def test_shapes_scalarvalue_derivative(self):
P = PiecewisePolynomial(self.xi,self.yi,4)
n = 4
assert_array_equal(np.shape(P.derivative(0,1)), ())
assert_array_equal(np.shape(P.derivative([0],1)), (1,))
assert_array_equal(np.shape(P.derivative([0,1],1)), (2,))
def test_shapes_vectorvalue(self):
yi = np.multiply.outer(np.asarray(self.yi),np.arange(3))
P = PiecewisePolynomial(self.xi,yi,4)
assert_array_equal(np.shape(P(0)), (3,))
assert_array_equal(np.shape(P([0])), (1,3))
assert_array_equal(np.shape(P([0,1])), (2,3))
def test_shapes_vectorvalue_1d(self):
yi = np.multiply.outer(np.asarray(self.yi),np.arange(1))
P = PiecewisePolynomial(self.xi,yi,4)
assert_array_equal(np.shape(P(0)), (1,))
assert_array_equal(np.shape(P([0])), (1,1))
assert_array_equal(np.shape(P([0,1])), (2,1))
def test_shapes_vectorvalue_derivative(self):
P = PiecewisePolynomial(self.xi,np.multiply.outer(self.yi,np.arange(3)),4)
n = 4
assert_array_equal(np.shape(P.derivative(0,1)), (3,))
assert_array_equal(np.shape(P.derivative([0],1)), (1,3))
assert_array_equal(np.shape(P.derivative([0,1],1)), (2,3))
def test_wrapper(self):
P = PiecewisePolynomial(self.xi,self.yi)
assert_almost_equal(P(self.test_xs),piecewise_polynomial_interpolate(self.xi,self.yi,self.test_xs))
assert_almost_equal(P.derivative(self.test_xs,2),piecewise_polynomial_interpolate(self.xi,self.yi,self.test_xs,der=2))
assert_almost_equal(P.derivatives(self.test_xs,2),piecewise_polynomial_interpolate(self.xi,self.yi,self.test_xs,der=[0,1]))
if __name__=='__main__':
run_module_suite()
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