Why Gemfury?
Push, build, and install
RubyGems
npm packages
Python packages
Maven artifacts
PHP packages
Go Modules
Debian packages
RPM packages
NuGet packages
Repository URL to install this package:
|
Version:
0.15.1 ▾
|
from __future__ import division, print_function, absolute_import
import itertools
import warnings
from numpy.testing import (assert_, assert_equal, assert_almost_equal,
assert_array_almost_equal, assert_raises, assert_array_equal,
dec, TestCase, run_module_suite, assert_allclose)
from numpy import mgrid, pi, sin, ogrid, poly1d, linspace
import numpy as np
from scipy.lib.six import xrange
from scipy.lib._version import NumpyVersion
from scipy.interpolate import (interp1d, interp2d, lagrange, PPoly, BPoly,
ppform, splrep, splev, splantider, splint, sproot, Akima1DInterpolator,
RegularGridInterpolator, LinearNDInterpolator, NearestNDInterpolator,
RectBivariateSpline, interpn)
from scipy.interpolate import _ppoly
from scipy.lib._gcutils import assert_deallocated
class TestInterp2D(TestCase):
def test_interp2d(self):
y, x = mgrid[0:2:20j, 0:pi:21j]
z = sin(x+0.5*y)
I = interp2d(x, y, z)
assert_almost_equal(I(1.0, 2.0), sin(2.0), decimal=2)
v,u = ogrid[0:2:24j, 0:pi:25j]
assert_almost_equal(I(u.ravel(), v.ravel()), sin(u+0.5*v), decimal=2)
def test_interp2d_meshgrid_input(self):
# Ticket #703
x = linspace(0, 2, 16)
y = linspace(0, pi, 21)
z = sin(x[None,:] + y[:,None]/2.)
I = interp2d(x, y, z)
assert_almost_equal(I(1.0, 2.0), sin(2.0), decimal=2)
def test_interp2d_meshgrid_input_unsorted(self):
np.random.seed(1234)
x = linspace(0, 2, 16)
y = linspace(0, pi, 21)
z = sin(x[None,:] + y[:,None]/2.)
ip1 = interp2d(x.copy(), y.copy(), z, kind='cubic')
np.random.shuffle(x)
z = sin(x[None,:] + y[:,None]/2.)
ip2 = interp2d(x.copy(), y.copy(), z, kind='cubic')
np.random.shuffle(x)
np.random.shuffle(y)
z = sin(x[None,:] + y[:,None]/2.)
ip3 = interp2d(x, y, z, kind='cubic')
x = linspace(0, 2, 31)
y = linspace(0, pi, 30)
assert_equal(ip1(x, y), ip2(x, y))
assert_equal(ip1(x, y), ip3(x, y))
def test_interp2d_eval_unsorted(self):
y, x = mgrid[0:2:20j, 0:pi:21j]
z = sin(x + 0.5*y)
func = interp2d(x, y, z)
xe = np.array([3, 4, 5])
ye = np.array([5.3, 7.1])
assert_allclose(func(xe, ye), func(xe, ye[::-1]))
assert_raises(ValueError, func, xe, ye[::-1], 0, 0, True)
def test_interp2d_linear(self):
# Ticket #898
a = np.zeros([5, 5])
a[2, 2] = 1.0
x = y = np.arange(5)
b = interp2d(x, y, a, 'linear')
assert_almost_equal(b(2.0, 1.5), np.array([0.5]), decimal=2)
assert_almost_equal(b(2.0, 2.5), np.array([0.5]), decimal=2)
def test_interp2d_bounds(self):
x = np.linspace(0, 1, 5)
y = np.linspace(0, 2, 7)
z = x[None, :]**2 + y[:, None]
ix = np.linspace(-1, 3, 31)
iy = np.linspace(-1, 3, 33)
b = interp2d(x, y, z, bounds_error=True)
assert_raises(ValueError, b, ix, iy)
b = interp2d(x, y, z, fill_value=np.nan)
iz = b(ix, iy)
mx = (ix < 0) | (ix > 1)
my = (iy < 0) | (iy > 2)
assert_(np.isnan(iz[my,:]).all())
assert_(np.isnan(iz[:,mx]).all())
assert_(np.isfinite(iz[~my,:][:,~mx]).all())
class TestInterp1D(object):
def setUp(self):
self.x10 = np.arange(10.)
self.y10 = np.arange(10.)
self.x25 = self.x10.reshape((2,5))
self.x2 = np.arange(2.)
self.y2 = np.arange(2.)
self.x1 = np.array([0.])
self.y1 = np.array([0.])
self.y210 = np.arange(20.).reshape((2, 10))
self.y102 = np.arange(20.).reshape((10, 2))
self.fill_value = -100.0
def test_validation(self):
# Make sure that appropriate exceptions are raised when invalid values
# are given to the constructor.
# These should all work.
interp1d(self.x10, self.y10, kind='linear')
interp1d(self.x10, self.y10, kind='cubic')
interp1d(self.x10, self.y10, kind='slinear')
interp1d(self.x10, self.y10, kind='quadratic')
interp1d(self.x10, self.y10, kind='zero')
interp1d(self.x10, self.y10, kind='nearest')
interp1d(self.x10, self.y10, kind=0)
interp1d(self.x10, self.y10, kind=1)
interp1d(self.x10, self.y10, kind=2)
interp1d(self.x10, self.y10, kind=3)
# x array must be 1D.
assert_raises(ValueError, interp1d, self.x25, self.y10)
# y array cannot be a scalar.
assert_raises(ValueError, interp1d, self.x10, np.array(0))
# Check for x and y arrays having the same length.
assert_raises(ValueError, interp1d, self.x10, self.y2)
assert_raises(ValueError, interp1d, self.x2, self.y10)
assert_raises(ValueError, interp1d, self.x10, self.y102)
interp1d(self.x10, self.y210)
interp1d(self.x10, self.y102, axis=0)
# Check for x and y having at least 1 element.
assert_raises(ValueError, interp1d, self.x1, self.y10)
assert_raises(ValueError, interp1d, self.x10, self.y1)
assert_raises(ValueError, interp1d, self.x1, self.y1)
def test_init(self):
# Check that the attributes are initialized appropriately by the
# constructor.
assert_(interp1d(self.x10, self.y10).copy)
assert_(not interp1d(self.x10, self.y10, copy=False).copy)
assert_(interp1d(self.x10, self.y10).bounds_error)
assert_(not interp1d(self.x10, self.y10, bounds_error=False).bounds_error)
assert_(np.isnan(interp1d(self.x10, self.y10).fill_value))
assert_equal(interp1d(self.x10, self.y10, fill_value=3.0).fill_value,
3.0)
assert_equal(interp1d(self.x10, self.y10).axis, 0)
assert_equal(interp1d(self.x10, self.y210).axis, 1)
assert_equal(interp1d(self.x10, self.y102, axis=0).axis, 0)
assert_array_equal(interp1d(self.x10, self.y10).x, self.x10)
assert_array_equal(interp1d(self.x10, self.y10).y, self.y10)
assert_array_equal(interp1d(self.x10, self.y210).y, self.y210)
def test_assume_sorted(self):
# Check for unsorted arrays
interp10 = interp1d(self.x10, self.y10)
interp10_unsorted = interp1d(self.x10[::-1], self.y10[::-1])
assert_array_almost_equal(interp10_unsorted(self.x10), self.y10)
assert_array_almost_equal(interp10_unsorted(1.2), np.array([1.2]))
assert_array_almost_equal(interp10_unsorted([2.4, 5.6, 6.0]),
interp10([2.4, 5.6, 6.0]))
# Check assume_sorted keyword (defaults to False)
interp10_assume_kw = interp1d(self.x10[::-1], self.y10[::-1],
assume_sorted=False)
assert_array_almost_equal(interp10_assume_kw(self.x10), self.y10)
interp10_assume_kw2 = interp1d(self.x10[::-1], self.y10[::-1],
assume_sorted=True)
# Should raise an error for unsorted input if assume_sorted=True
assert_raises(ValueError, interp10_assume_kw2, self.x10)
# Check that if y is a 2-D array, things are still consistent
interp10_y_2d = interp1d(self.x10, self.y210)
interp10_y_2d_unsorted = interp1d(self.x10[::-1], self.y210[:, ::-1])
assert_array_almost_equal(interp10_y_2d(self.x10),
interp10_y_2d_unsorted(self.x10))
def test_linear(self):
# Check the actual implementation of linear interpolation.
interp10 = interp1d(self.x10, self.y10)
assert_array_almost_equal(interp10(self.x10), self.y10)
assert_array_almost_equal(interp10(1.2), np.array([1.2]))
assert_array_almost_equal(interp10([2.4, 5.6, 6.0]),
np.array([2.4, 5.6, 6.0]))
def test_cubic(self):
# Check the actual implementation of spline interpolation.
interp10 = interp1d(self.x10, self.y10, kind='cubic')
assert_array_almost_equal(interp10(self.x10), self.y10)
assert_array_almost_equal(interp10(1.2), np.array([1.2]))
assert_array_almost_equal(interp10([2.4, 5.6, 6.0]),
np.array([2.4, 5.6, 6.0]),)
def test_nearest(self):
# Check the actual implementation of nearest-neighbour interpolation.
interp10 = interp1d(self.x10, self.y10, kind='nearest')
assert_array_almost_equal(interp10(self.x10), self.y10)
assert_array_almost_equal(interp10(1.2), np.array(1.))
assert_array_almost_equal(interp10([2.4, 5.6, 6.0]),
np.array([2., 6., 6.]),)
@dec.knownfailureif(True, "zero-order splines fail for the last point")
def test_zero(self):
# Check the actual implementation of zero-order spline interpolation.
interp10 = interp1d(self.x10, self.y10, kind='zero')
assert_array_almost_equal(interp10(self.x10), self.y10)
assert_array_almost_equal(interp10(1.2), np.array(1.))
assert_array_almost_equal(interp10([2.4, 5.6, 6.0]),
np.array([2., 6., 6.]))
def _bounds_check(self, kind='linear'):
# Test that our handling of out-of-bounds input is correct.
extrap10 = interp1d(self.x10, self.y10, fill_value=self.fill_value,
bounds_error=False, kind=kind)
assert_array_equal(extrap10(11.2), np.array(self.fill_value))
assert_array_equal(extrap10(-3.4), np.array(self.fill_value))
assert_array_equal(extrap10([[[11.2], [-3.4], [12.6], [19.3]]]),
np.array(self.fill_value),)
assert_array_equal(extrap10._check_bounds(
np.array([-1.0, 0.0, 5.0, 9.0, 11.0])),
np.array([True, False, False, False, True]))
raises_bounds_error = interp1d(self.x10, self.y10, bounds_error=True,
kind=kind)
assert_raises(ValueError, raises_bounds_error, -1.0)
assert_raises(ValueError, raises_bounds_error, 11.0)
raises_bounds_error([0.0, 5.0, 9.0])
def _bounds_check_int_nan_fill(self, kind='linear'):
x = np.arange(10).astype(np.int_)
y = np.arange(10).astype(np.int_)
c = interp1d(x, y, kind=kind, fill_value=np.nan, bounds_error=False)
yi = c(x - 1)
assert_(np.isnan(yi[0]))
assert_array_almost_equal(yi, np.r_[np.nan, y[:-1]])
def test_bounds(self):
for kind in ('linear', 'cubic', 'nearest',
'slinear', 'zero', 'quadratic'):
self._bounds_check(kind)
self._bounds_check_int_nan_fill(kind)
def _nd_check_interp(self, kind='linear'):
# Check the behavior when the inputs and outputs are multidimensional.
# Multidimensional input.
interp10 = interp1d(self.x10, self.y10, kind=kind)
assert_array_almost_equal(interp10(np.array([[3., 5.], [2., 7.]])),
np.array([[3., 5.], [2., 7.]]))
# Scalar input -> 0-dim scalar array output
assert_(isinstance(interp10(1.2), np.ndarray))
assert_equal(interp10(1.2).shape, ())
# Multidimensional outputs.
interp210 = interp1d(self.x10, self.y210, kind=kind)
assert_array_almost_equal(interp210(1.), np.array([1., 11.]))
assert_array_almost_equal(interp210(np.array([1., 2.])),
np.array([[1., 2.], [11., 12.]]))
interp102 = interp1d(self.x10, self.y102, axis=0, kind=kind)
assert_array_almost_equal(interp102(1.), np.array([2.0, 3.0]))
assert_array_almost_equal(interp102(np.array([1., 3.])),
np.array([[2., 3.], [6., 7.]]))
# Both at the same time!
x_new = np.array([[3., 5.], [2., 7.]])
assert_array_almost_equal(interp210(x_new),
np.array([[[3., 5.], [2., 7.]],
[[13., 15.], [12., 17.]]]))
assert_array_almost_equal(interp102(x_new),
np.array([[[6., 7.], [10., 11.]],
[[4., 5.], [14., 15.]]]))
def _nd_check_shape(self, kind='linear'):
# Check large ndim output shape
a = [4, 5, 6, 7]
y = np.arange(np.prod(a)).reshape(*a)
for n, s in enumerate(a):
x = np.arange(s)
z = interp1d(x, y, axis=n, kind=kind)
assert_array_almost_equal(z(x), y, err_msg=kind)
x2 = np.arange(2*3*1).reshape((2,3,1)) / 12.
b = list(a)
b[n:n+1] = [2,3,1]
assert_array_almost_equal(z(x2).shape, b, err_msg=kind)
def test_nd(self):
for kind in ('linear', 'cubic', 'slinear', 'quadratic', 'nearest'):
self._nd_check_interp(kind)
self._nd_check_shape(kind)
def _check_complex(self, dtype=np.complex_, kind='linear'):
x = np.array([1, 2.5, 3, 3.1, 4, 6.4, 7.9, 8.0, 9.5, 10])
y = x * x ** (1 + 2j)
y = y.astype(dtype)
# simple test
c = interp1d(x, y, kind=kind)
assert_array_almost_equal(y[:-1], c(x)[:-1])
# check against interpolating real+imag separately
xi = np.linspace(1, 10, 31)
cr = interp1d(x, y.real, kind=kind)
ci = interp1d(x, y.imag, kind=kind)
assert_array_almost_equal(c(xi).real, cr(xi))
assert_array_almost_equal(c(xi).imag, ci(xi))
def test_complex(self):
for kind in ('linear', 'nearest', 'cubic', 'slinear', 'quadratic',
'zero'):
self._check_complex(np.complex64, kind)
self._check_complex(np.complex128, kind)
@dec.knownfailureif(True, "zero-order splines fail for the last point")
def test_nd_zero_spline(self):
# zero-order splines don't get the last point right,
# see test_zero above
#yield self._nd_check_interp, 'zero'
#yield self._nd_check_interp, 'zero'
pass
def test_circular_refs(self):
# Test interp1d can be automatically garbage collected
x = np.linspace(0, 1)
y = np.linspace(0, 1)
# Confirm interp can be released from memory after use
with assert_deallocated(interp1d, x, y) as interp:
new_y = interp([0.1, 0.2])
del interp
class TestLagrange(TestCase):
def test_lagrange(self):
p = poly1d([5,2,1,4,3])
xs = np.arange(len(p.coeffs))
ys = p(xs)
pl = lagrange(xs,ys)
assert_array_almost_equal(p.coeffs,pl.coeffs)
class TestAkima1DInterpolator(TestCase):
def test_eval(self):
x = np.arange(0., 11.)
y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.])
ak = Akima1DInterpolator(x, y)
xi = np.array([0., 0.5, 1., 1.5, 2.5, 3.5, 4.5, 5.1, 6.5, 7.2,
8.6, 9.9, 10.])
yi = np.array([0., 1.375, 2., 1.5, 1.953125, 2.484375,
4.1363636363636366866103344, 5.9803623910336236590978842,
5.5067291516462386624652936, 5.2031367459745245795943447,
4.1796554159017080820603951, 3.4110386597938129327189927,
3.])
assert_allclose(ak(xi), yi)
def test_eval_2d(self):
x = np.arange(0., 11.)
y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.])
y = np.column_stack((y, 2. * y))
ak = Akima1DInterpolator(x, y)
xi = np.array([0., 0.5, 1., 1.5, 2.5, 3.5, 4.5, 5.1, 6.5, 7.2,
8.6, 9.9, 10.])
yi = np.array([0., 1.375, 2., 1.5, 1.953125, 2.484375,
4.1363636363636366866103344,
5.9803623910336236590978842,
5.5067291516462386624652936,
5.2031367459745245795943447,
4.1796554159017080820603951,
3.4110386597938129327189927, 3.])
yi = np.column_stack((yi, 2. * yi))
assert_allclose(ak(xi), yi)
def test_eval_3d(self):
x = np.arange(0., 11.)
y_ = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.])
y = np.empty((11, 2, 2))
y[:, 0, 0] = y_
y[:, 1, 0] = 2. * y_
y[:, 0, 1] = 3. * y_
y[:, 1, 1] = 4. * y_
ak = Akima1DInterpolator(x, y)
xi = np.array([0., 0.5, 1., 1.5, 2.5, 3.5, 4.5, 5.1, 6.5, 7.2,
8.6, 9.9, 10.])
yi = np.empty((13, 2, 2))
yi_ = np.array([0., 1.375, 2., 1.5, 1.953125, 2.484375,
4.1363636363636366866103344,
5.9803623910336236590978842,
5.5067291516462386624652936,
5.2031367459745245795943447,
4.1796554159017080820603951,
3.4110386597938129327189927, 3.])
yi[:, 0, 0] = yi_
yi[:, 1, 0] = 2. * yi_
yi[:, 0, 1] = 3. * yi_
yi[:, 1, 1] = 4. * yi_
assert_allclose(ak(xi), yi)
def test_extend(self):
x = np.arange(0., 11.)
y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.])
ak = Akima1DInterpolator(x, y)
try:
ak.extend()
except NotImplementedError as e:
if str(e) != ("Extending a 1D Akima interpolator is not "
"yet implemented"):
raise
except:
raise
class TestPPolyCommon(TestCase):
# test basic functionality for PPoly and BPoly
def test_sort_check(self):
c = np.array([[1, 4], [2, 5], [3, 6]])
x = np.array([0, 1, 0.5])
assert_raises(ValueError, PPoly, c, x)
assert_raises(ValueError, BPoly, c, x)
def test_extend(self):
# Test adding new points to the piecewise polynomial
np.random.seed(1234)
order = 3
x = np.unique(np.r_[0, 10 * np.random.rand(30), 10])
c = 2*np.random.rand(order+1, len(x)-1, 2, 3) - 1
for cls in (PPoly, BPoly):
pp = cls(c[:,:9], x[:10])
pp.extend(c[:,9:], x[10:])
pp2 = cls(c[:,10:], x[10:])
pp2.extend(c[:,:10], x[:10], right=False)
pp3 = cls(c, x)
assert_array_equal(pp.c, pp3.c)
assert_array_equal(pp.x, pp3.x)
assert_array_equal(pp2.c, pp3.c)
assert_array_equal(pp2.x, pp3.x)
def test_extend_diff_orders(self):
# Test extending polynomial with different order one
np.random.seed(1234)
x = np.linspace(0, 1, 6)
c = np.random.rand(2, 5)
x2 = np.linspace(1, 2, 6)
c2 = np.random.rand(4, 5)
for cls in (PPoly, BPoly):
pp1 = cls(c, x)
pp2 = cls(c2, x2)
pp_comb = cls(c, x)
pp_comb.extend(c2, x2[1:])
# NB. doesn't match to pp1 at the endpoint, because pp1 is not
# continuous with pp2 as we took random coefs.
xi1 = np.linspace(0, 1, 300, endpoint=False)
xi2 = np.linspace(1, 2, 300)
assert_allclose(pp1(xi1), pp_comb(xi1))
assert_allclose(pp2(xi2), pp_comb(xi2))
def test_shape(self):
np.random.seed(1234)
c = np.random.rand(8, 12, 5, 6, 7)
x = np.sort(np.random.rand(13))
xp = np.random.rand(3, 4)
for cls in (PPoly, BPoly):
p = cls(c, x)
assert_equal(p(xp).shape, (3, 4, 5, 6, 7))
# 'scalars'
for cls in (PPoly, BPoly):
p = cls(c[..., 0, 0, 0], x)
assert_equal(np.shape(p(0.5)), ())
assert_equal(np.shape(p(np.array(0.5))), ())
if NumpyVersion(np.__version__) >= '1.7.0':
# can't use dtype=object (with any numpy; what fails is
# constructing the object array here for old numpy)
assert_raises(ValueError, p, np.array([[0.1, 0.2], [0.4]]))
def test_complex_coef(self):
np.random.seed(12345)
x = np.sort(np.random.random(13))
c = np.random.random((8, 12)) * (1. + 0.3j)
c_re, c_im = c.real, c.imag
xp = np.random.random(5)
for cls in (PPoly, BPoly):
p, p_re, p_im = cls(c, x), cls(c_re, x), cls(c_im, x)
for nu in [0, 1, 2]:
assert_allclose(p(xp, nu).real, p_re(xp, nu))
assert_allclose(p(xp, nu).imag, p_im(xp, nu))
class TestPolySubclassing(TestCase):
class P(PPoly):
pass
class B(BPoly):
pass
def _make_polynomials(self):
np.random.seed(1234)
x = np.sort(np.random.random(3))
c = np.random.random((4, 2))
return self.P(c, x), self.B(c, x)
def test_derivative(self):
pp, bp = self._make_polynomials()
for p in (pp, bp):
pd = p.derivative()
assert_equal(p.__class__, pd.__class__)
ppa = pp.antiderivative()
assert_equal(pp.__class__, ppa.__class__)
def test_from_spline(self):
np.random.seed(1234)
x = np.sort(np.r_[0, np.random.rand(11), 1])
y = np.random.rand(len(x))
spl = splrep(x, y, s=0)
pp = self.P.from_spline(spl)
assert_equal(pp.__class__, self.P)
def test_conversions(self):
pp, bp = self._make_polynomials()
pp1 = self.P.from_bernstein_basis(bp)
assert_equal(pp1.__class__, self.P)
bp1 = self.B.from_power_basis(pp)
assert_equal(bp1.__class__, self.B)
def test_from_derivatives(self):
x = [0, 1, 2]
y = [[1], [2], [3]]
bp = self.B.from_derivatives(x, y)
assert_equal(bp.__class__, self.B)
class TestPPoly(TestCase):
def test_simple(self):
c = np.array([[1, 4], [2, 5], [3, 6]])
x = np.array([0, 0.5, 1])
p = PPoly(c, x)
assert_allclose(p(0.3), 1*0.3**2 + 2*0.3 + 3)
assert_allclose(p(0.7), 4*(0.7-0.5)**2 + 5*(0.7-0.5) + 6)
def test_multi_shape(self):
c = np.random.rand(6, 2, 1, 2, 3)
x = np.array([0, 0.5, 1])
p = PPoly(c, x)
assert_equal(p.x.shape, x.shape)
assert_equal(p.c.shape, c.shape)
assert_equal(p(0.3).shape, c.shape[2:])
assert_equal(p(np.random.rand(5,6)).shape,
(5,6) + c.shape[2:])
dp = p.derivative()
assert_equal(dp.c.shape, (5, 2, 1, 2, 3))
ip = p.antiderivative()
assert_equal(ip.c.shape, (7, 2, 1, 2, 3))
def test_construct_fast(self):
np.random.seed(1234)
c = np.array([[1, 4], [2, 5], [3, 6]], dtype=float)
x = np.array([0, 0.5, 1])
p = PPoly.construct_fast(c, x)
assert_allclose(p(0.3), 1*0.3**2 + 2*0.3 + 3)
assert_allclose(p(0.7), 4*(0.7-0.5)**2 + 5*(0.7-0.5) + 6)
def test_vs_alternative_implementations(self):
np.random.seed(1234)
c = np.random.rand(3, 12, 22)
x = np.sort(np.r_[0, np.random.rand(11), 1])
p = PPoly(c, x)
xp = np.r_[0.3, 0.5, 0.33, 0.6]
expected = _ppoly_eval_1(c, x, xp)
assert_allclose(p(xp), expected)
expected = _ppoly_eval_2(c[:,:,0], x, xp)
assert_allclose(p(xp)[:,0], expected)
def test_from_spline(self):
np.random.seed(1234)
x = np.sort(np.r_[0, np.random.rand(11), 1])
y = np.random.rand(len(x))
spl = splrep(x, y, s=0)
pp = PPoly.from_spline(spl)
xi = np.linspace(0, 1, 200)
assert_allclose(pp(xi), splev(xi, spl))
def test_derivative_simple(self):
np.random.seed(1234)
c = np.array([[4, 3, 2, 1]]).T
dc = np.array([[3*4, 2*3, 2]]).T
ddc = np.array([[2*3*4, 1*2*3]]).T
x = np.array([0, 1])
pp = PPoly(c, x)
dpp = PPoly(dc, x)
ddpp = PPoly(ddc, x)
assert_allclose(pp.derivative().c, dpp.c)
assert_allclose(pp.derivative(2).c, ddpp.c)
def test_derivative_eval(self):
np.random.seed(1234)
x = np.sort(np.r_[0, np.random.rand(11), 1])
y = np.random.rand(len(x))
spl = splrep(x, y, s=0)
pp = PPoly.from_spline(spl)
xi = np.linspace(0, 1, 200)
for dx in range(0, 3):
assert_allclose(pp(xi, dx), splev(xi, spl, dx))
def test_derivative(self):
np.random.seed(1234)
x = np.sort(np.r_[0, np.random.rand(11), 1])
y = np.random.rand(len(x))
spl = splrep(x, y, s=0, k=5)
pp = PPoly.from_spline(spl)
xi = np.linspace(0, 1, 200)
for dx in range(0, 10):
assert_allclose(pp(xi, dx), pp.derivative(dx)(xi),
err_msg="dx=%d" % (dx,))
def test_antiderivative_of_constant(self):
# https://github.com/scipy/scipy/issues/4216
np.random.seed(1234)
p = PPoly([[1.]], [0, 1])
assert_equal(p.antiderivative().c, PPoly([[1], [0]], [0, 1]).c)
assert_equal(p.antiderivative().x, PPoly([[1], [0]], [0, 1]).x)
def test_antiderivative_simple(self):
np.random.seed(1234)
# [ p1(x) = 3*x**2 + 2*x + 1,
# p2(x) = 1.6875]
c = np.array([[3, 2, 1], [0, 0, 1.6875]]).T
# [ pp1(x) = x**3 + x**2 + x,
# pp2(x) = 1.6875*(x - 0.25) + pp1(0.25)]
ic = np.array([[1, 1, 1, 0], [0, 0, 1.6875, 0.328125]]).T
# [ ppp1(x) = (1/4)*x**4 + (1/3)*x**3 + (1/2)*x**2,
# ppp2(x) = (1.6875/2)*(x - 0.25)**2 + pp1(0.25)*x + ppp1(0.25)]
iic = np.array([[1/4, 1/3, 1/2, 0, 0],
[0, 0, 1.6875/2, 0.328125, 0.037434895833333336]]).T
x = np.array([0, 0.25, 1])
pp = PPoly(c, x)
ipp = pp.antiderivative()
iipp = pp.antiderivative(2)
iipp2 = ipp.antiderivative()
assert_allclose(ipp.x, x)
assert_allclose(ipp.c.T, ic.T)
assert_allclose(iipp.c.T, iic.T)
assert_allclose(iipp2.c.T, iic.T)
def test_antiderivative_vs_derivative(self):
np.random.seed(1234)
x = np.linspace(0, 1, 30)**2
y = np.random.rand(len(x))
spl = splrep(x, y, s=0, k=5)
pp = PPoly.from_spline(spl)
for dx in range(0, 10):
ipp = pp.antiderivative(dx)
# check that derivative is inverse op
pp2 = ipp.derivative(dx)
assert_allclose(pp.c, pp2.c)
# check continuity
for k in range(dx):
pp2 = ipp.derivative(k)
r = 1e-13
endpoint = r*pp2.x[:-1] + (1 - r)*pp2.x[1:]
assert_allclose(pp2(pp2.x[1:]), pp2(endpoint),
rtol=1e-7, err_msg="dx=%d k=%d" % (dx, k))
def test_antiderivative_vs_spline(self):
np.random.seed(1234)
x = np.sort(np.r_[0, np.random.rand(11), 1])
y = np.random.rand(len(x))
spl = splrep(x, y, s=0, k=5)
pp = PPoly.from_spline(spl)
for dx in range(0, 10):
pp2 = pp.antiderivative(dx)
spl2 = splantider(spl, dx)
xi = np.linspace(0, 1, 200)
assert_allclose(pp2(xi), splev(xi, spl2),
rtol=1e-7)
def test_integrate(self):
np.random.seed(1234)
x = np.sort(np.r_[0, np.random.rand(11), 1])
y = np.random.rand(len(x))
spl = splrep(x, y, s=0, k=5)
pp = PPoly.from_spline(spl)
a, b = 0.3, 0.9
ig = pp.integrate(a, b)
ipp = pp.antiderivative()
assert_allclose(ig, ipp(b) - ipp(a))
assert_allclose(ig, splint(a, b, spl))
a, b = -0.3, 0.9
ig = pp.integrate(a, b, extrapolate=True)
assert_allclose(ig, ipp(b) - ipp(a))
assert_(np.isnan(pp.integrate(a, b, extrapolate=False)).all())
def test_roots(self):
x = np.linspace(0, 1, 31)**2
y = np.sin(30*x)
spl = splrep(x, y, s=0, k=3)
pp = PPoly.from_spline(spl)
r = pp.roots()
r = r[(r >= 0 - 1e-15) & (r <= 1 + 1e-15)]
assert_allclose(r, sproot(spl), atol=1e-15)
def test_roots_idzero(self):
# Roots for piecewise polynomials with identically zero
# sections.
c = np.array([[-1, 0.25], [0, 0], [-1, 0.25]]).T
x = np.array([0, 0.4, 0.6, 1.0])
pp = PPoly(c, x)
assert_array_equal(pp.roots(),
[0.25, 0.4, np.nan, 0.6 + 0.25])
def test_roots_repeated(self):
# Check roots repeated in multiple sections are reported only
# once.
# [(x + 1)**2 - 1, -x**2] ; x == 0 is a repeated root
c = np.array([[1, 0, -1], [-1, 0, 0]]).T
x = np.array([-1, 0, 1])
pp = PPoly(c, x)
assert_array_equal(pp.roots(), [-2, 0])
assert_array_equal(pp.roots(extrapolate=False), [0])
def test_roots_discont(self):
# Check that a discontinuity across zero is reported as root
c = np.array([[1], [-1]]).T
x = np.array([0, 0.5, 1])
pp = PPoly(c, x)
assert_array_equal(pp.roots(), [0.5])
assert_array_equal(pp.roots(discontinuity=False), [])
def test_roots_random(self):
# Check high-order polynomials with random coefficients
np.random.seed(1234)
num = 0
for extrapolate in (True, False):
for order in range(0, 20):
x = np.unique(np.r_[0, 10 * np.random.rand(30), 10])
c = 2*np.random.rand(order+1, len(x)-1, 2, 3) - 1
pp = PPoly(c, x)
r = pp.roots(discontinuity=False, extrapolate=extrapolate)
for i in range(2):
for j in range(3):
rr = r[i,j]
if rr.size > 0:
# Check that the reported roots indeed are roots
num += rr.size
val = pp(rr, extrapolate=extrapolate)[:,i,j]
cmpval = pp(rr, nu=1, extrapolate=extrapolate)[:,i,j]
assert_allclose(val/cmpval, 0, atol=1e-7,
err_msg="(%r) r = %s" % (extrapolate,
repr(rr),))
# Check that we checked a number of roots
assert_(num > 100, repr(num))
def test_roots_croots(self):
# Test the complex root finding algorithm
np.random.seed(1234)
for k in range(1, 15):
c = np.random.rand(k, 1, 130)
if k == 3:
# add a case with zero discriminant
c[:,0,0] = 1, 2, 1
w = np.empty(c.shape, dtype=complex)
_ppoly._croots_poly1(c, w)
if k == 1:
assert_(np.isnan(w).all())
continue
res = 0
cres = 0
for i in range(k):
res += c[i,None] * w**(k-1-i)
cres += abs(c[i,None] * w**(k-1-i))
with np.errstate(invalid='ignore'):
res /= cres
res = res.ravel()
res = res[~np.isnan(res)]
assert_allclose(res, 0, atol=1e-10)
def test_extrapolate_attr(self):
# [ 1 - x**2 ]
c = np.array([[-1, 0, 1]]).T
x = np.array([0, 1])
for extrapolate in [True, False, None]:
pp = PPoly(c, x, extrapolate=extrapolate)
pp_d = pp.derivative()
pp_i = pp.antiderivative()
if extrapolate is False:
assert_(np.isnan(pp([-0.1, 1.1])).all())
assert_(np.isnan(pp_i([-0.1, 1.1])).all())
assert_(np.isnan(pp_d([-0.1, 1.1])).all())
assert_equal(pp.roots(), [1])
else:
assert_allclose(pp([-0.1, 1.1]), [1-0.1**2, 1-1.1**2])
assert_(not np.isnan(pp_i([-0.1, 1.1])).any())
assert_(not np.isnan(pp_d([-0.1, 1.1])).any())
assert_allclose(pp.roots(), [1, -1])
class TestBPoly(TestCase):
def test_simple(self):
x = [0, 1]
c = [[3]]
bp = BPoly(c, x)
assert_allclose(bp(0.1), 3.)
def test_simple2(self):
x = [0, 1]
c = [[3], [1]]
bp = BPoly(c, x) # 3*(1-x) + 1*x
assert_allclose(bp(0.1), 3*0.9 + 1.*0.1)
def test_simple3(self):
x = [0, 1]
c = [[3], [1], [4]]
bp = BPoly(c, x) # 3 * (1-x)**2 + 2 * x (1-x) + 4 * x**2
assert_allclose(bp(0.2),
3 * 0.8*0.8 + 1 * 2*0.2*0.8 + 4 * 0.2*0.2)
def test_simple4(self):
x = [0, 1]
c = [[1], [1], [1], [2]]
bp = BPoly(c, x)
assert_allclose(bp(0.3), 0.7**3 +
3 * 0.7**2 * 0.3 +
3 * 0.7 * 0.3**2 +
2 * 0.3**3)
def test_simple5(self):
x = [0, 1]
c = [[1], [1], [8], [2], [1]]
bp = BPoly(c, x)
assert_allclose(bp(0.3), 0.7**4 +
4 * 0.7**3 * 0.3 +
8 * 6 * 0.7**2 * 0.3**2 +
2 * 4 * 0.7 * 0.3**3 +
0.3**4)
def test_multi_shape(self):
c = np.random.rand(6, 2, 1, 2, 3)
x = np.array([0, 0.5, 1])
p = BPoly(c, x)
assert_equal(p.x.shape, x.shape)
assert_equal(p.c.shape, c.shape)
assert_equal(p(0.3).shape, c.shape[2:])
assert_equal(p(np.random.rand(5,6)).shape,
(5,6)+c.shape[2:])
dp = p.derivative()
assert_equal(dp.c.shape, (5, 2, 1, 2, 3))
def test_interval_length(self):
x = [0, 2]
c = [[3], [1], [4]]
bp = BPoly(c, x)
xval = 0.1
s = xval / 2 # s = (x - xa) / (xb - xa)
assert_allclose(bp(xval), 3 * (1-s)*(1-s) + 1 * 2*s*(1-s) + 4 * s*s)
def test_two_intervals(self):
x = [0, 1, 3]
c = [[3, 0], [0, 0], [0, 2]]
bp = BPoly(c, x) # [3*(1-x)**2, 2*((x-1)/2)**2]
assert_allclose(bp(0.4), 3 * 0.6*0.6)
assert_allclose(bp(1.7), 2 * (0.7/2)**2)
def test_extrapolate_attr(self):
x = [0, 2]
c = [[3], [1], [4]]
bp = BPoly(c, x)
for extrapolate in (True, False, None):
bp = BPoly(c, x, extrapolate=extrapolate)
bp_d = bp.derivative()
if extrapolate is False:
assert_(np.isnan(bp([-0.1, 2.1])).all())
assert_(np.isnan(bp_d([-0.1, 2.1])).all())
else:
assert_(not np.isnan(bp([-0.1, 2.1])).any())
assert_(not np.isnan(bp_d([-0.1, 2.1])).any())
class TestBPolyCalculus(TestCase):
def test_derivative(self):
x = [0, 1, 3]
c = [[3, 0], [0, 0], [0, 2]]
bp = BPoly(c, x) # [3*(1-x)**2, 2*((x-1)/2)**2]
bp_der = bp.derivative()
assert_allclose(bp_der(0.4), -6*(0.6))
assert_allclose(bp_der(1.7), 0.7)
# derivatives in-place
assert_allclose([bp(0.4, nu=1), bp(0.4, nu=2), bp(0.4, nu=3)],
[-6*(1-0.4), 6., 0.])
assert_allclose([bp(1.7, nu=1), bp(1.7, nu=2), bp(1.7, nu=3)],
[0.7, 1., 0])
def test_derivative_ppoly(self):
# make sure it's consistent w/ power basis
np.random.seed(1234)
m, k = 5, 8 # number of intervals, order
x = np.sort(np.random.random(m))
c = np.random.random((k, m-1))
bp = BPoly(c, x)
pp = PPoly.from_bernstein_basis(bp)
for d in range(k):
bp = bp.derivative()
pp = pp.derivative()
xp = np.linspace(x[0], x[-1], 21)
assert_allclose(bp(xp), pp(xp))
def test_deriv_inplace(self):
np.random.seed(1234)
m, k = 5, 8 # number of intervals, order
x = np.sort(np.random.random(m))
c = np.random.random((k, m-1))
bp = BPoly(c, x)
xp = np.linspace(x[0], x[-1], 21)
for i in range(k):
assert_allclose(bp(xp, i), bp.derivative(i)(xp))
class TestPolyConversions(TestCase):
def test_bp_from_pp(self):
x = [0, 1, 3]
c = [[3, 2], [1, 8], [4, 3]]
pp = PPoly(c, x)
bp = BPoly.from_power_basis(pp)
pp1 = PPoly.from_bernstein_basis(bp)
xp = [0.1, 1.4]
assert_allclose(pp(xp), bp(xp))
assert_allclose(pp(xp), pp1(xp))
def test_bp_from_pp_random(self):
np.random.seed(1234)
m, k = 5, 8 # number of intervals, order
x = np.sort(np.random.random(m))
c = np.random.random((k, m-1))
pp = PPoly(c, x)
bp = BPoly.from_power_basis(pp)
pp1 = PPoly.from_bernstein_basis(bp)
xp = np.linspace(x[0], x[-1], 21)
assert_allclose(pp(xp), bp(xp))
assert_allclose(pp(xp), pp1(xp))
def test_pp_from_bp(self):
x = [0, 1, 3]
c = [[3, 3], [1, 1], [4, 2]]
bp = BPoly(c, x)
pp = PPoly.from_bernstein_basis(bp)
bp1 = BPoly.from_power_basis(pp)
xp = [0.1, 1.4]
assert_allclose(bp(xp), pp(xp))
assert_allclose(bp(xp), bp1(xp))
class TestBPolyFromDerivatives(TestCase):
def test_make_poly_1(self):
c1 = BPoly._construct_from_derivatives(0, 1, [2], [3])
assert_allclose(c1, [2., 3.])
def test_make_poly_2(self):
c1 = BPoly._construct_from_derivatives(0, 1, [1, 0], [1])
assert_allclose(c1, [1., 1., 1.])
# f'(0) = 3
c2 = BPoly._construct_from_derivatives(0, 1, [2, 3], [1])
assert_allclose(c2, [2., 7./2, 1.])
# f'(1) = 3
c3 = BPoly._construct_from_derivatives(0, 1, [2], [1, 3])
assert_allclose(c3, [2., -0.5, 1.])
def test_make_poly_3(self):
# f'(0)=2, f''(0)=3
c1 = BPoly._construct_from_derivatives(0, 1, [1, 2, 3], [4])
assert_allclose(c1, [1., 5./3, 17./6, 4.])
# f'(1)=2, f''(1)=3
c2 = BPoly._construct_from_derivatives(0, 1, [1], [4, 2, 3])
assert_allclose(c2, [1., 19./6, 10./3, 4.])
# f'(0)=2, f'(1)=3
c3 = BPoly._construct_from_derivatives(0, 1, [1, 2], [4, 3])
assert_allclose(c3, [1., 5./3, 3., 4.])
def test_make_poly_12(self):
np.random.seed(12345)
ya = np.r_[0, np.random.random(5)]
yb = np.r_[0, np.random.random(5)]
c = BPoly._construct_from_derivatives(0, 1, ya, yb)
pp = BPoly(c[:, None], [0, 1])
for j in range(6):
assert_allclose([pp(0.), pp(1.)], [ya[j], yb[j]])
pp = pp.derivative()
def test_raise_degree(self):
np.random.seed(12345)
x = [0, 1]
k, d = 8, 5
c = np.random.random((k, 1, 2, 3, 4))
bp = BPoly(c, x)
c1 = BPoly._raise_degree(c, d)
bp1 = BPoly(c1, x)
xp = np.linspace(0, 1, 11)
assert_allclose(bp(xp), bp1(xp))
def test_xi_yi(self):
assert_raises(ValueError, BPoly.from_derivatives, [0, 1], [0])
def test_coords_order(self):
xi = [0, 0, 1]
yi = [[0], [0], [0]]
assert_raises(ValueError, BPoly.from_derivatives, xi, yi)
def test_zeros(self):
xi = [0, 1, 2, 3]
yi = [[0, 0], [0], [0, 0], [0, 0]] # NB: will have to raise the degree
pp = BPoly.from_derivatives(xi, yi)
assert_(pp.c.shape == (4, 3))
ppd = pp.derivative()
for xp in [0., 0.1, 1., 1.1, 1.9, 2., 2.5]:
assert_allclose([pp(xp), ppd(xp)], [0., 0.])
def _make_random_mk(self, m, k):
# k derivatives at each breakpoint
np.random.seed(1234)
xi = np.asarray([1. * j**2 for j in range(m+1)])
yi = [np.random.random(k) for j in range(m+1)]
return xi, yi
def test_random_12(self):
m, k = 5, 12
xi, yi = self._make_random_mk(m, k)
pp = BPoly.from_derivatives(xi, yi)
for order in range(k//2):
assert_allclose(pp(xi), [yy[order] for yy in yi])
pp = pp.derivative()
def test_order_zero(self):
m, k = 5, 12
xi, yi = self._make_random_mk(m, k)
assert_raises(ValueError, BPoly.from_derivatives,
**dict(xi=xi, yi=yi, orders=0))
def test_orders_too_high(self):
m, k = 5, 12
xi, yi = self._make_random_mk(m, k)
pp = BPoly.from_derivatives(xi, yi, orders=2*k-1) # this is still ok
assert_raises(ValueError, BPoly.from_derivatives, # but this is not
**dict(xi=xi, yi=yi, orders=2*k))
def test_orders_global(self):
m, k = 5, 12
xi, yi = self._make_random_mk(m, k)
# ok, this is confusing. Local polynomials will be of the order 5
# which means that up to the 2nd derivatives will be used at each point
order = 5
pp = BPoly.from_derivatives(xi, yi, orders=order)
for j in range(order//2+1):
assert_allclose(pp(xi[1:-1] - 1e-12), pp(xi[1:-1] + 1e-12))
pp = pp.derivative()
assert_(not np.allclose(pp(xi[1:-1] - 1e-12), pp(xi[1:-1] + 1e-12)))
# now repeat with `order` being even: on each interval, it uses
# order//2 'derivatives' @ the right-hand endpoint and
# order//2+1 @ 'derivatives' the left-hand endpoint
order = 6
pp = BPoly.from_derivatives(xi, yi, orders=order)
for j in range(order//2):
assert_allclose(pp(xi[1:-1] - 1e-12), pp(xi[1:-1] + 1e-12))
pp = pp.derivative()
assert_(not np.allclose(pp(xi[1:-1] - 1e-12), pp(xi[1:-1] + 1e-12)))
def test_orders_local(self):
m, k = 7, 12
xi, yi = self._make_random_mk(m, k)
orders = [o + 1 for o in range(m)]
for i, x in enumerate(xi[1:-1]):
pp = BPoly.from_derivatives(xi, yi, orders=orders)
for j in range(orders[i] // 2 + 1):
assert_allclose(pp(x - 1e-12), pp(x + 1e-12))
pp = pp.derivative()
assert_(not np.allclose(pp(x - 1e-12), pp(x + 1e-12)))
def test_yi_trailing_dims(self):
m, k = 7, 5
xi = np.sort(np.random.random(m+1))
yi = np.random.random((m+1, k, 6, 7, 8))
pp = BPoly.from_derivatives(xi, yi)
assert_equal(pp.c.shape, (2*k, m, 6, 7, 8))
class TestPpform(TestCase):
def test_shape(self):
with warnings.catch_warnings():
warnings.simplefilter("ignore", DeprecationWarning)
np.random.seed(1234)
c = np.random.rand(3, 12, 5, 6, 7)
x = np.sort(np.random.rand(13))
p = ppform(c, x)
xp = np.random.rand(3, 4)
assert_equal(p(xp).shape, (3, 4, 5, 6, 7))
def _ppoly_eval_1(c, x, xps):
"""Evaluate piecewise polynomial manually"""
out = np.zeros((len(xps), c.shape[2]))
for i, xp in enumerate(xps):
if xp < 0 or xp > 1:
out[i,:] = np.nan
continue
j = np.searchsorted(x, xp) - 1
d = xp - x[j]
assert_(x[j] <= xp < x[j+1])
r = sum(c[k,j] * d**(c.shape[0]-k-1)
for k in range(c.shape[0]))
out[i,:] = r
return out
def _ppoly_eval_2(coeffs, breaks, xnew, fill=np.nan):
"""Evaluate piecewise polynomial manually (another way)"""
a = breaks[0]
b = breaks[-1]
K = coeffs.shape[0]
saveshape = np.shape(xnew)
xnew = np.ravel(xnew)
res = np.empty_like(xnew)
mask = (xnew >= a) & (xnew <= b)
res[~mask] = fill
xx = xnew.compress(mask)
indxs = np.searchsorted(breaks, xx)-1
indxs = indxs.clip(0, len(breaks))
pp = coeffs
diff = xx - breaks.take(indxs)
V = np.vander(diff, N=K)
values = np.array([np.dot(V[k, :], pp[:, indxs[k]]) for k in xrange(len(xx))])
res[mask] = values
res.shape = saveshape
return res
class TestRegularGridInterpolator(TestCase):
def _get_sample_4d(self):
# create a 4d grid of 3 points in each dimension
points = [(0., .5, 1.)] * 4
values = np.asarray([0., .5, 1.])
values0 = values[:, np.newaxis, np.newaxis, np.newaxis]
values1 = values[np.newaxis, :, np.newaxis, np.newaxis]
values2 = values[np.newaxis, np.newaxis, :, np.newaxis]
values3 = values[np.newaxis, np.newaxis, np.newaxis, :]
values = (values0 + values1 * 10 + values2 * 100 + values3 * 1000)
return points, values
def _get_sample_4d_2(self):
# create another 4d grid of 3 points in each dimension
points = [(0., .5, 1.)] * 2 + [(0., 5., 10.)] * 2
values = np.asarray([0., .5, 1.])
values0 = values[:, np.newaxis, np.newaxis, np.newaxis]
values1 = values[np.newaxis, :, np.newaxis, np.newaxis]
values2 = values[np.newaxis, np.newaxis, :, np.newaxis]
values3 = values[np.newaxis, np.newaxis, np.newaxis, :]
values = (values0 + values1 * 10 + values2 * 100 + values3 * 1000)
return points, values
def test_list_input(self):
points, values = self._get_sample_4d()
sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8],
[0.5, 0.5, .5, .5]])
for method in ['linear', 'nearest']:
interp = RegularGridInterpolator(points,
values.tolist(),
method=method)
v1 = interp(sample.tolist())
interp = RegularGridInterpolator(points,
values,
method=method)
v2 = interp(sample)
assert_allclose(v1, v2)
def test_complex(self):
points, values = self._get_sample_4d()
values = values - 2j*values
sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8],
[0.5, 0.5, .5, .5]])
for method in ['linear', 'nearest']:
interp = RegularGridInterpolator(points, values,
method=method)
rinterp = RegularGridInterpolator(points, values.real,
method=method)
iinterp = RegularGridInterpolator(points, values.imag,
method=method)
v1 = interp(sample)
v2 = rinterp(sample) + 1j*iinterp(sample)
assert_allclose(v1, v2)
def test_linear_xi1d(self):
points, values = self._get_sample_4d_2()
interp = RegularGridInterpolator(points, values)
sample = np.asarray([0.1, 0.1, 10., 9.])
wanted = 1001.1
assert_array_almost_equal(interp(sample), wanted)
def test_linear_xi3d(self):
points, values = self._get_sample_4d()
interp = RegularGridInterpolator(points, values)
sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8],
[0.5, 0.5, .5, .5]])
wanted = np.asarray([1001.1, 846.2, 555.5])
assert_array_almost_equal(interp(sample), wanted)
def test_nearest(self):
points, values = self._get_sample_4d()
interp = RegularGridInterpolator(points, values, method="nearest")
sample = np.asarray([0.1, 0.1, .9, .9])
wanted = 1100.
assert_array_almost_equal(interp(sample), wanted)
sample = np.asarray([0.1, 0.1, 0.1, 0.1])
wanted = 0.
assert_array_almost_equal(interp(sample), wanted)
sample = np.asarray([0., 0., 0., 0.])
wanted = 0.
assert_array_almost_equal(interp(sample), wanted)
sample = np.asarray([1., 1., 1., 1.])
wanted = 1111.
assert_array_almost_equal(interp(sample), wanted)
sample = np.asarray([0.1, 0.4, 0.6, 0.9])
wanted = 1055.
assert_array_almost_equal(interp(sample), wanted)
def test_linear_edges(self):
points, values = self._get_sample_4d()
interp = RegularGridInterpolator(points, values)
sample = np.asarray([[0., 0., 0., 0.], [1., 1., 1., 1.]])
wanted = np.asarray([0., 1111.])
assert_array_almost_equal(interp(sample), wanted)
def test_valid_create(self):
# create a 2d grid of 3 points in each dimension
points = [(0., .5, 1.), (0., 1., .5)]
values = np.asarray([0., .5, 1.])
values0 = values[:, np.newaxis]
values1 = values[np.newaxis, :]
values = (values0 + values1 * 10)
assert_raises(ValueError, RegularGridInterpolator, points, values)
points = [((0., .5, 1.), ), (0., .5, 1.)]
assert_raises(ValueError, RegularGridInterpolator, points, values)
points = [(0., .5, .75, 1.), (0., .5, 1.)]
assert_raises(ValueError, RegularGridInterpolator, points, values)
points = [(0., .5, 1.), (0., .5, 1.), (0., .5, 1.)]
assert_raises(ValueError, RegularGridInterpolator, points, values)
points = [(0., .5, 1.), (0., .5, 1.)]
assert_raises(ValueError, RegularGridInterpolator, points, values,
method="undefmethod")
def test_valid_call(self):
points, values = self._get_sample_4d()
interp = RegularGridInterpolator(points, values)
sample = np.asarray([[0., 0., 0., 0.], [1., 1., 1., 1.]])
assert_raises(ValueError, interp, sample, "undefmethod")
sample = np.asarray([[0., 0., 0.], [1., 1., 1.]])
assert_raises(ValueError, interp, sample)
sample = np.asarray([[0., 0., 0., 0.], [1., 1., 1., 1.1]])
assert_raises(ValueError, interp, sample)
def test_out_of_bounds_extrap(self):
points, values = self._get_sample_4d()
interp = RegularGridInterpolator(points, values, bounds_error=False,
fill_value=None)
sample = np.asarray([[-.1, -.1, -.1, -.1], [1.1, 1.1, 1.1, 1.1],
[21, 2.1, -1.1, -11], [2.1, 2.1, -1.1, -1.1]])
wanted = np.asarray([0., 1111., 11., 11.])
assert_array_almost_equal(interp(sample, method="nearest"), wanted)
wanted = np.asarray([-111.1, 1222.1, -11068., -1186.9])
assert_array_almost_equal(interp(sample, method="linear"), wanted)
def test_out_of_bounds_extrap2(self):
points, values = self._get_sample_4d_2()
interp = RegularGridInterpolator(points, values, bounds_error=False,
fill_value=None)
sample = np.asarray([[-.1, -.1, -.1, -.1], [1.1, 1.1, 1.1, 1.1],
[21, 2.1, -1.1, -11], [2.1, 2.1, -1.1, -1.1]])
wanted = np.asarray([0., 11., 11., 11.])
assert_array_almost_equal(interp(sample, method="nearest"), wanted)
wanted = np.asarray([-12.1, 133.1, -1069., -97.9])
assert_array_almost_equal(interp(sample, method="linear"), wanted)
def test_out_of_bounds_fill(self):
points, values = self._get_sample_4d()
interp = RegularGridInterpolator(points, values, bounds_error=False,
fill_value=np.nan)
sample = np.asarray([[-.1, -.1, -.1, -.1], [1.1, 1.1, 1.1, 1.1],
[2.1, 2.1, -1.1, -1.1]])
wanted = np.asarray([np.nan, np.nan, np.nan])
assert_array_almost_equal(interp(sample, method="nearest"), wanted)
assert_array_almost_equal(interp(sample, method="linear"), wanted)
sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8],
[0.5, 0.5, .5, .5]])
wanted = np.asarray([1001.1, 846.2, 555.5])
assert_array_almost_equal(interp(sample), wanted)
def test_nearest_compare_qhull(self):
points, values = self._get_sample_4d()
interp = RegularGridInterpolator(points, values, method="nearest")
points_qhull = itertools.product(*points)
points_qhull = [p for p in points_qhull]
points_qhull = np.asarray(points_qhull)
values_qhull = values.reshape(-1)
interp_qhull = NearestNDInterpolator(points_qhull, values_qhull)
sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8],
[0.5, 0.5, .5, .5]])
assert_array_almost_equal(interp(sample), interp_qhull(sample))
def test_linear_compare_qhull(self):
points, values = self._get_sample_4d()
interp = RegularGridInterpolator(points, values)
points_qhull = itertools.product(*points)
points_qhull = [p for p in points_qhull]
points_qhull = np.asarray(points_qhull)
values_qhull = values.reshape(-1)
interp_qhull = LinearNDInterpolator(points_qhull, values_qhull)
sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8],
[0.5, 0.5, .5, .5]])
assert_array_almost_equal(interp(sample), interp_qhull(sample))
def test_duck_typed_values(self):
x = np.linspace(0, 2, 5)
y = np.linspace(0, 1, 7)
values = MyValue((5, 7))
for method in ('nearest', 'linear'):
interp = RegularGridInterpolator((x, y), values,
method=method)
v1 = interp([0.4, 0.7])
interp = RegularGridInterpolator((x, y), values._v,
method=method)
v2 = interp([0.4, 0.7])
assert_allclose(v1, v2)
def test_invalid_fill_value(self):
np.random.seed(1234)
x = np.linspace(0, 2, 5)
y = np.linspace(0, 1, 7)
values = np.random.rand(5, 7)
# integers can be cast to floats
RegularGridInterpolator((x, y), values, fill_value=1)
# complex values cannot
if NumpyVersion(np.__version__) >= '1.6.0':
assert_raises(ValueError, RegularGridInterpolator,
(x, y), values, fill_value=1+2j)
def test_fillvalue_type(self):
# from #3703; test that interpolator object construction succeeds
values = np.ones((10, 20, 30), dtype='>f4')
points = [np.arange(n) for n in values.shape]
xi = [(1, 1, 1)]
interpolator = RegularGridInterpolator(points, values)
interpolator = RegularGridInterpolator(points, values, fill_value=0.)
class MyValue(object):
"""
Minimal indexable object
"""
def __init__(self, shape):
self.ndim = 2
self.shape = shape
self._v = np.arange(np.prod(shape)).reshape(shape)
def __getitem__(self, idx):
return self._v[idx]
def __array_interface__(self):
return None
def __array__(self):
raise RuntimeError("No array representation")
class TestInterpN(TestCase):
def _sample_2d_data(self):
x = np.arange(1, 6)
x = np.array([.5, 2., 3., 4., 5.5])
y = np.arange(1, 6)
y = np.array([.5, 2., 3., 4., 5.5])
z = np.array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1],
[1, 2, 2, 2, 1], [1, 2, 1, 2, 1]])
return x, y, z
def test_spline_2d(self):
x, y, z = self._sample_2d_data()
lut = RectBivariateSpline(x, y, z)
xi = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3],
[1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T
assert_array_almost_equal(interpn((x, y), z, xi, method="splinef2d"),
lut.ev(xi[:, 0], xi[:, 1]))
def test_list_input(self):
x, y, z = self._sample_2d_data()
xi = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3],
[1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T
for method in ['nearest', 'linear', 'splinef2d']:
v1 = interpn((x, y), z, xi, method=method)
v2 = interpn((x.tolist(), y.tolist()), z.tolist(),
xi.tolist(), method=method)
assert_allclose(v1, v2, err_msg=method)
def test_spline_2d_outofbounds(self):
x = np.array([.5, 2., 3., 4., 5.5])
y = np.array([.5, 2., 3., 4., 5.5])
z = np.array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1],
[1, 2, 2, 2, 1], [1, 2, 1, 2, 1]])
lut = RectBivariateSpline(x, y, z)
xi = np.array([[1, 2.3, 6.3, 0.5, 3.3, 1.2, 3],
[1, 3.3, 1.2, -4.0, 5.0, 1.0, 3]]).T
actual = interpn((x, y), z, xi, method="splinef2d",
bounds_error=False, fill_value=999.99)
expected = lut.ev(xi[:, 0], xi[:, 1])
expected[2:4] = 999.99
assert_array_almost_equal(actual, expected)
# no extrapolation for splinef2d
assert_raises(ValueError, interpn, (x, y), z, xi, method="splinef2d",
bounds_error=False, fill_value=None)
def _sample_4d_data(self):
points = [(0., .5, 1.)] * 2 + [(0., 5., 10.)] * 2
values = np.asarray([0., .5, 1.])
values0 = values[:, np.newaxis, np.newaxis, np.newaxis]
values1 = values[np.newaxis, :, np.newaxis, np.newaxis]
values2 = values[np.newaxis, np.newaxis, :, np.newaxis]
values3 = values[np.newaxis, np.newaxis, np.newaxis, :]
values = (values0 + values1 * 10 + values2 * 100 + values3 * 1000)
return points, values
def test_linear_4d(self):
# create a 4d grid of 3 points in each dimension
points, values = self._sample_4d_data()
interp_rg = RegularGridInterpolator(points, values)
sample = np.asarray([[0.1, 0.1, 10., 9.]])
wanted = interpn(points, values, sample, method="linear")
assert_array_almost_equal(interp_rg(sample), wanted)
def test_4d_linear_outofbounds(self):
# create a 4d grid of 3 points in each dimension
points, values = self._sample_4d_data()
sample = np.asarray([[0.1, -0.1, 10.1, 9.]])
wanted = 999.99
actual = interpn(points, values, sample, method="linear",
bounds_error=False, fill_value=999.99)
assert_array_almost_equal(actual, wanted)
def test_nearest_4d(self):
# create a 4d grid of 3 points in each dimension
points, values = self._sample_4d_data()
interp_rg = RegularGridInterpolator(points, values, method="nearest")
sample = np.asarray([[0.1, 0.1, 10., 9.]])
wanted = interpn(points, values, sample, method="nearest")
assert_array_almost_equal(interp_rg(sample), wanted)
def test_4d_nearest_outofbounds(self):
# create a 4d grid of 3 points in each dimension
points, values = self._sample_4d_data()
sample = np.asarray([[0.1, -0.1, 10.1, 9.]])
wanted = 999.99
actual = interpn(points, values, sample, method="nearest",
bounds_error=False, fill_value=999.99)
assert_array_almost_equal(actual, wanted)
def test_xi_1d(self):
# verify that 1D xi works as expected
points, values = self._sample_4d_data()
sample = np.asarray([0.1, 0.1, 10., 9.])
v1 = interpn(points, values, sample, bounds_error=False)
v2 = interpn(points, values, sample[None,:], bounds_error=False)
assert_allclose(v1, v2)
def test_xi_nd(self):
# verify that higher-d xi works as expected
points, values = self._sample_4d_data()
np.random.seed(1234)
sample = np.random.rand(2, 3, 4)
v1 = interpn(points, values, sample, method='nearest',
bounds_error=False)
assert_equal(v1.shape, (2, 3))
v2 = interpn(points, values, sample.reshape(-1, 4),
method='nearest', bounds_error=False)
assert_allclose(v1, v2.reshape(v1.shape))
def test_xi_broadcast(self):
# verify that the interpolators broadcast xi
x, y, values = self._sample_2d_data()
points = (x, y)
xi = np.linspace(0, 1, 2)
yi = np.linspace(0, 3, 3)
for method in ['nearest', 'linear', 'splinef2d']:
sample = (xi[:,None], yi[None,:])
v1 = interpn(points, values, sample, method=method,
bounds_error=False)
assert_equal(v1.shape, (2, 3))
xx, yy = np.meshgrid(xi, yi)
sample = np.c_[xx.T.ravel(), yy.T.ravel()]
v2 = interpn(points, values, sample,
method=method, bounds_error=False)
assert_allclose(v1, v2.reshape(v1.shape))
def test_nonscalar_values(self):
# Verify that non-scalar valued values also works
points, values = self._sample_4d_data()
np.random.seed(1234)
values = np.random.rand(3, 3, 3, 3, 6)
sample = np.random.rand(7, 11, 4)
for method in ['nearest', 'linear']:
v = interpn(points, values, sample, method=method,
bounds_error=False)
assert_equal(v.shape, (7, 11, 6), err_msg=method)
vs = [interpn(points, values[...,j], sample, method=method,
bounds_error=False)
for j in range(6)]
v2 = np.array(vs).transpose(1, 2, 0)
assert_allclose(v, v2, err_msg=method)
# Vector-valued splines supported with fitpack
assert_raises(ValueError, interpn, points, values, sample,
method='splinef2d')
def test_complex(self):
x, y, values = self._sample_2d_data()
points = (x, y)
values = values - 2j*values
sample = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3],
[1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T
for method in ['linear', 'nearest']:
v1 = interpn(points, values, sample, method=method)
v2r = interpn(points, values.real, sample, method=method)
v2i = interpn(points, values.imag, sample, method=method)
v2 = v2r + 1j*v2i
assert_allclose(v1, v2)
# Complex-valued data not supported by spline2fd
with warnings.catch_warnings():
warnings.simplefilter("error", category=np.ComplexWarning)
assert_raises(np.ComplexWarning, interpn, points, values,
sample, method='splinef2d')
def test_duck_typed_values(self):
x = np.linspace(0, 2, 5)
y = np.linspace(0, 1, 7)
values = MyValue((5, 7))
for method in ('nearest', 'linear'):
v1 = interpn((x, y), values, [0.4, 0.7], method=method)
v2 = interpn((x, y), values._v, [0.4, 0.7], method=method)
assert_allclose(v1, v2)
def test_matrix_input(self):
x = np.linspace(0, 2, 5)
y = np.linspace(0, 1, 7)
values = np.matrix(np.random.rand(5, 7))
sample = np.random.rand(3, 7, 2)
for method in ('nearest', 'linear', 'splinef2d'):
v1 = interpn((x, y), values, sample, method=method)
v2 = interpn((x, y), np.asarray(values), sample, method=method)
assert_allclose(v1, np.asmatrix(v2))
if __name__ == "__main__":
run_module_suite()