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from __future__ import division, print_function, absolute_import
import warnings
from numpy.testing import (assert_almost_equal, assert_array_equal,
TestCase, run_module_suite, assert_allclose, assert_equal, assert_)
from scipy.interpolate import (KroghInterpolator, krogh_interpolate,
BarycentricInterpolator, barycentric_interpolate,
PiecewisePolynomial, piecewise_polynomial_interpolate,
approximate_taylor_polynomial, pchip, PchipInterpolator)
from scipy.lib.six import xrange
import scipy
import numpy as np
from scipy.interpolate import splrep, splev
def check_shape(interpolator_cls, x_shape, y_shape, deriv_shape=None, axis=0):
np.random.seed(1234)
x = [-1, 0, 1]
s = list(range(1, len(y_shape)+1))
s.insert(axis % (len(y_shape)+1), 0)
y = np.random.rand(*((3,) + y_shape)).transpose(s)
# Cython code chokes on y.shape = (0, 3) etc, skip them
if y.size == 0:
return
xi = np.zeros(x_shape)
yi = interpolator_cls(x, y, axis=axis)(xi)
target_shape = ((deriv_shape or ()) + y.shape[:axis]
+ x_shape + y.shape[axis:][1:])
assert_equal(yi.shape, target_shape)
# check it works also with lists
if x_shape and y.size > 0:
interpolator_cls(list(x), list(y), axis=axis)(list(xi))
# check also values
if xi.size > 0 and deriv_shape is None:
bs_shape = (y.shape[:axis] + ((1,)*len(x_shape)) + y.shape[axis:][1:])
yv = y[((slice(None,None,None),)*(axis % y.ndim))+(1,)].reshape(bs_shape)
yi, y = np.broadcast_arrays(yi, yv)
assert_allclose(yi, y)
SHAPES = [(), (0,), (1,), (3,2,5)]
def test_shapes():
for ip in [KroghInterpolator, BarycentricInterpolator, pchip]:
for s1 in SHAPES:
for s2 in SHAPES:
for axis in range(-len(s2), len(s2)):
yield check_shape, ip, s1, s2, None, axis
def test_derivs_shapes():
def krogh_derivs(x, y, axis=0):
return KroghInterpolator(x, y, axis).derivatives
for s1 in SHAPES:
for s2 in SHAPES:
for axis in range(-len(s2), len(s2)):
yield check_shape, krogh_derivs, s1, s2, (3,), axis
def test_deriv_shapes():
def krogh_deriv(x, y, axis=0):
return KroghInterpolator(x, y, axis).derivative
def pchip_deriv(x, y, axis=0):
return pchip(x, y, axis).derivative()
def pchip_deriv2(x, y, axis=0):
return pchip(x, y, axis).derivative(2)
def pchip_deriv_inplace(x, y, axis=0):
class P(PchipInterpolator):
def __call__(self, x):
return PchipInterpolator.__call__(self, x, 1)
pass
return P(x, y, axis)
for ip in [krogh_deriv, pchip_deriv, pchip_deriv2, pchip_deriv_inplace]:
for s1 in SHAPES:
for s2 in SHAPES:
for axis in range(-len(s2), len(s2)):
yield check_shape, ip, s1, s2, (), axis
def _check_complex(ip):
x = [1, 2, 3, 4]
y = [1, 2, 1j, 3]
p = ip(x, y)
assert_allclose(y, p(x))
def test_complex():
for ip in [KroghInterpolator, BarycentricInterpolator, pchip]:
yield _check_complex, ip
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))
assert_almost_equal(self.true_poly(np.array(7)), P(np.array(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(np.array(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(np.array(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))
assert_almost_equal(self.true_poly(np.array(7)),P(np.array(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(np.array(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):
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
P = PiecewisePolynomial(self.xi, self.yi, 3)
assert_almost_equal(P(self.test_xs), self.spline_ys)
def test_scalar(self):
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
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])
assert_almost_equal(P(np.array(self.test_xs[0])),self.spline_ys[0])
assert_almost_equal(P.derivative(np.array(self.test_xs[0]),1),
self.spline_yps[0])
def test_derivative(self):
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
P = PiecewisePolynomial(self.xi,self.yi,3)
assert_almost_equal(P.derivative(self.test_xs,1),self.spline_yps)
def test_derivatives(self):
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
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]]]
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
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):
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
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):
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
P = PiecewisePolynomial(self.xi,self.yi,4)
assert_array_equal(np.shape(P(0)), ())
assert_array_equal(np.shape(P(np.array(0))), ())
assert_array_equal(np.shape(P([0])), (1,))
assert_array_equal(np.shape(P([0,1])), (2,))
def test_shapes_scalarvalue_derivative(self):
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
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(np.array(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))
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
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))
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
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):
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
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):
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
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]))
class TestPCHIP(TestCase):
def _make_random(self, npts=20):
np.random.seed(1234)
xi = np.sort(np.random.random(npts))
yi = np.random.random(npts)
return pchip(xi, yi), xi, yi
def test_overshoot(self):
# PCHIP should not overshoot
p, xi, yi = self._make_random()
for i in range(len(xi)-1):
x1, x2 = xi[i], xi[i+1]
y1, y2 = yi[i], yi[i+1]
if y1 > y2:
y1, y2 = y2, y1
xp = np.linspace(x1, x2, 10)
yp = p(xp)
assert_(((y1 <= yp) & (yp <= y2)).all())
def test_monotone(self):
# PCHIP should preserve monotonicty
p, xi, yi = self._make_random()
for i in range(len(xi)-1):
x1, x2 = xi[i], xi[i+1]
y1, y2 = yi[i], yi[i+1]
xp = np.linspace(x1, x2, 10)
yp = p(xp)
assert_(((y2-y1) * (yp[1:] - yp[:1]) > 0).all())
if __name__ == '__main__':
run_module_suite()
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