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eaiaiaiaoi/venv/lib/python2.7/site-packages/scipy/interpolate/tests/test_interpolate.py

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from __future__ import division, print_function, absolute_import
import itertools
from numpy.testing import (assert_, assert_equal, assert_almost_equal,
assert_array_almost_equal, assert_array_equal,
assert_allclose)
from pytest import raises as assert_raises
import pytest
from numpy import mgrid, pi, sin, ogrid, poly1d, linspace
import numpy as np
from scipy._lib.six import xrange
from scipy._lib._numpy_compat import _assert_warns, suppress_warnings
from scipy.interpolate import (interp1d, interp2d, lagrange, PPoly, BPoly,
splrep, splev, splantider, splint, sproot, Akima1DInterpolator,
RegularGridInterpolator, LinearNDInterpolator, NearestNDInterpolator,
RectBivariateSpline, interpn, NdPPoly, BSpline)
from scipy.special import poch, gamma
from scipy.interpolate import _ppoly
from scipy._lib._gcutils import assert_deallocated, IS_PYPY
from scipy.integrate import nquad
from scipy.special import binom
class TestInterp2D(object):
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_method(self):
self.x5 = np.arange(5.)
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.y225 = np.arange(20.).reshape((2, 2, 5))
self.y25 = np.arange(10.).reshape((2, 5))
self.y235 = np.arange(30.).reshape((2, 3, 5))
self.y325 = np.arange(30.).reshape((3, 2, 5))
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.
for kind in ('nearest', 'zero', 'linear', 'slinear', 'quadratic',
'cubic', 'previous', 'next'):
interp1d(self.x10, self.y10, kind=kind)
interp1d(self.x10, self.y10, kind=kind, fill_value="extrapolate")
interp1d(self.x10, self.y10, kind='linear', fill_value=(-1, 1))
interp1d(self.x10, self.y10, kind='linear',
fill_value=np.array([-1]))
interp1d(self.x10, self.y10, kind='linear',
fill_value=(-1,))
interp1d(self.x10, self.y10, kind='linear',
fill_value=-1)
interp1d(self.x10, self.y10, kind='linear',
fill_value=(-1, -1))
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)
interp1d(self.x10, self.y210, kind='linear', axis=-1,
fill_value=(-1, -1))
interp1d(self.x2, self.y210, kind='linear', axis=0,
fill_value=np.ones(10))
interp1d(self.x2, self.y210, kind='linear', axis=0,
fill_value=(np.ones(10), np.ones(10)))
interp1d(self.x2, self.y210, kind='linear', axis=0,
fill_value=(np.ones(10), -1))
# 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)
# Bad fill values
assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
fill_value=(-1, -1, -1)) # doesn't broadcast
assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
fill_value=[-1, -1, -1]) # doesn't broadcast
assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
fill_value=np.array((-1, -1, -1))) # doesn't broadcast
assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
fill_value=[[-1]]) # doesn't broadcast
assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
fill_value=[-1, -1]) # doesn't broadcast
assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
fill_value=np.array([])) # doesn't broadcast
assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
fill_value=()) # doesn't broadcast
assert_raises(ValueError, interp1d, self.x2, self.y210, kind='linear',
axis=0, fill_value=[-1, -1]) # doesn't broadcast
assert_raises(ValueError, interp1d, self.x2, self.y210, kind='linear',
axis=0, fill_value=(0., [-1, -1])) # above doesn't bc
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, fill_value=(1.0, 2.0)).fill_value,
(1.0, 2.0))
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):
for kind in ['linear', 'slinear']:
self._check_linear(kind)
def _check_linear(self, kind):
# Check the actual implementation of linear interpolation.
interp10 = interp1d(self.x10, self.y10, kind=kind)
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]))
# test fill_value="extrapolate"
extrapolator = interp1d(self.x10, self.y10, kind=kind,
fill_value='extrapolate')
assert_allclose(extrapolator([-1., 0, 9, 11]),
[-1, 0, 9, 11], rtol=1e-14)
opts = dict(kind=kind,
fill_value='extrapolate',
bounds_error=True)
assert_raises(ValueError, interp1d, self.x10, self.y10, **opts)
def test_linear_dtypes(self):
# regression test for gh-5898, where 1D linear interpolation has been
# delegated to numpy.interp for all float dtypes, and the latter was
# not handling e.g. np.float128.
for dtyp in np.sctypes["float"]:
x = np.arange(8, dtype=dtyp)
y = x
yp = interp1d(x, y, kind='linear')(x)
assert_equal(yp.dtype, dtyp)
assert_allclose(yp, y, atol=1e-15)
def test_slinear_dtypes(self):
# regression test for gh-7273: 1D slinear interpolation fails with
# float32 inputs
dt_r = [np.float16, np.float32, np.float64]
dt_rc = dt_r + [np.complex64, np.complex128]
spline_kinds = ['slinear', 'zero', 'quadratic', 'cubic']
for dtx in dt_r:
x = np.arange(0, 10, dtype=dtx)
for dty in dt_rc:
y = np.exp(-x/3.0).astype(dty)
for dtn in dt_r:
xnew = x.astype(dtn)
for kind in spline_kinds:
f = interp1d(x, y, kind=kind, bounds_error=False)
assert_allclose(f(xnew), y, atol=1e-7,
err_msg="%s, %s %s" % (dtx, dty, dtn))
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.]),)
# test fill_value="extrapolate"
extrapolator = interp1d(self.x10, self.y10, kind='nearest',
fill_value='extrapolate')
assert_allclose(extrapolator([-1., 0, 9, 11]),
[0, 0, 9, 9], rtol=1e-14)
opts = dict(kind='nearest',
fill_value='extrapolate',
bounds_error=True)
assert_raises(ValueError, interp1d, self.x10, self.y10, **opts)
def test_previous(self):
# Check the actual implementation of previous interpolation.
interp10 = interp1d(self.x10, self.y10, kind='previous')
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., 5., 6.]),)
# test fill_value="extrapolate"
extrapolator = interp1d(self.x10, self.y10, kind='previous',
fill_value='extrapolate')
assert_allclose(extrapolator([-1., 0, 9, 11]),
[0, 0, 9, 9], rtol=1e-14)
opts = dict(kind='previous',
fill_value='extrapolate',
bounds_error=True)
assert_raises(ValueError, interp1d, self.x10, self.y10, **opts)
def test_next(self):
# Check the actual implementation of next interpolation.
interp10 = interp1d(self.x10, self.y10, kind='next')
assert_array_almost_equal(interp10(self.x10), self.y10)
assert_array_almost_equal(interp10(1.2), np.array(2.))
assert_array_almost_equal(interp10([2.4, 5.6, 6.0]),
np.array([3., 6., 6.]),)
# test fill_value="extrapolate"
extrapolator = interp1d(self.x10, self.y10, kind='next',
fill_value='extrapolate')
assert_allclose(extrapolator([-1., 0, 9, 11]),
[0, 0, 9, 9], rtol=1e-14)
opts = dict(kind='next',
fill_value='extrapolate',
bounds_error=True)
assert_raises(ValueError, interp1d, self.x10, self.y10, **opts)
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., 5., 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, False],
[False, 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', 'previous', 'next',
'slinear', 'zero', 'quadratic'):
self._bounds_check(kind)
self._bounds_check_int_nan_fill(kind)
def _check_fill_value(self, kind):
interp = interp1d(self.x10, self.y10, kind=kind,
fill_value=(-100, 100), bounds_error=False)
assert_array_almost_equal(interp(10), 100)
assert_array_almost_equal(interp(-10), -100)
assert_array_almost_equal(interp([-10, 10]), [-100, 100])
# Proper broadcasting:
# interp along axis of length 5
# other dim=(2, 3), (3, 2), (2, 2), or (2,)
# one singleton fill_value (works for all)
for y in (self.y235, self.y325, self.y225, self.y25):
interp = interp1d(self.x5, y, kind=kind, axis=-1,
fill_value=100, bounds_error=False)
assert_array_almost_equal(interp(10), 100)
assert_array_almost_equal(interp(-10), 100)
assert_array_almost_equal(interp([-10, 10]), 100)
# singleton lower, singleton upper
interp = interp1d(self.x5, y, kind=kind, axis=-1,
fill_value=(-100, 100), bounds_error=False)
assert_array_almost_equal(interp(10), 100)
assert_array_almost_equal(interp(-10), -100)
if y.ndim == 3:
result = [[[-100, 100]] * y.shape[1]] * y.shape[0]
else:
result = [[-100, 100]] * y.shape[0]
assert_array_almost_equal(interp([-10, 10]), result)
# one broadcastable (3,) fill_value
fill_value = [100, 200, 300]
for y in (self.y325, self.y225):
assert_raises(ValueError, interp1d, self.x5, y, kind=kind,
axis=-1, fill_value=fill_value, bounds_error=False)
interp = interp1d(self.x5, self.y235, kind=kind, axis=-1,
fill_value=fill_value, bounds_error=False)
assert_array_almost_equal(interp(10), [[100, 200, 300]] * 2)
assert_array_almost_equal(interp(-10), [[100, 200, 300]] * 2)
assert_array_almost_equal(interp([-10, 10]), [[[100, 100],
[200, 200],
[300, 300]]] * 2)
# one broadcastable (2,) fill_value
fill_value = [100, 200]
assert_raises(ValueError, interp1d, self.x5, self.y235, kind=kind,
axis=-1, fill_value=fill_value, bounds_error=False)
for y in (self.y225, self.y325, self.y25):
interp = interp1d(self.x5, y, kind=kind, axis=-1,
fill_value=fill_value, bounds_error=False)
result = [100, 200]
if y.ndim == 3:
result = [result] * y.shape[0]
assert_array_almost_equal(interp(10), result)
assert_array_almost_equal(interp(-10), result)
result = [[100, 100], [200, 200]]
if y.ndim == 3:
result = [result] * y.shape[0]
assert_array_almost_equal(interp([-10, 10]), result)
# broadcastable (3,) lower, singleton upper
fill_value = (np.array([-100, -200, -300]), 100)
for y in (self.y325, self.y225):
assert_raises(ValueError, interp1d, self.x5, y, kind=kind,
axis=-1, fill_value=fill_value, bounds_error=False)
interp = interp1d(self.x5, self.y235, kind=kind, axis=-1,
fill_value=fill_value, bounds_error=False)
assert_array_almost_equal(interp(10), 100)
assert_array_almost_equal(interp(-10), [[-100, -200, -300]] * 2)
assert_array_almost_equal(interp([-10, 10]), [[[-100, 100],
[-200, 100],
[-300, 100]]] * 2)
# broadcastable (2,) lower, singleton upper
fill_value = (np.array([-100, -200]), 100)
assert_raises(ValueError, interp1d, self.x5, self.y235, kind=kind,
axis=-1, fill_value=fill_value, bounds_error=False)
for y in (self.y225, self.y325, self.y25):
interp = interp1d(self.x5, y, kind=kind, axis=-1,
fill_value=fill_value, bounds_error=False)
assert_array_almost_equal(interp(10), 100)
result = [-100, -200]
if y.ndim == 3:
result = [result] * y.shape[0]
assert_array_almost_equal(interp(-10), result)
result = [[-100, 100], [-200, 100]]
if y.ndim == 3:
result = [result] * y.shape[0]
assert_array_almost_equal(interp([-10, 10]), result)
# broadcastable (3,) lower, broadcastable (3,) upper
fill_value = ([-100, -200, -300], [100, 200, 300])
for y in (self.y325, self.y225):
assert_raises(ValueError, interp1d, self.x5, y, kind=kind,
axis=-1, fill_value=fill_value, bounds_error=False)
for ii in range(2): # check ndarray as well as list here
if ii == 1:
fill_value = tuple(np.array(f) for f in fill_value)
interp = interp1d(self.x5, self.y235, kind=kind, axis=-1,
fill_value=fill_value, bounds_error=False)
assert_array_almost_equal(interp(10), [[100, 200, 300]] * 2)
assert_array_almost_equal(interp(-10), [[-100, -200, -300]] * 2)
assert_array_almost_equal(interp([-10, 10]), [[[-100, 100],
[-200, 200],
[-300, 300]]] * 2)
# broadcastable (2,) lower, broadcastable (2,) upper
fill_value = ([-100, -200], [100, 200])
assert_raises(ValueError, interp1d, self.x5, self.y235, kind=kind,
axis=-1, fill_value=fill_value, bounds_error=False)
for y in (self.y325, self.y225, self.y25):
interp = interp1d(self.x5, y, kind=kind, axis=-1,
fill_value=fill_value, bounds_error=False)
result = [100, 200]
if y.ndim == 3:
result = [result] * y.shape[0]
assert_array_almost_equal(interp(10), result)
result = [-100, -200]
if y.ndim == 3:
result = [result] * y.shape[0]
assert_array_almost_equal(interp(-10), result)
result = [[-100, 100], [-200, 200]]
if y.ndim == 3:
result = [result] * y.shape[0]
assert_array_almost_equal(interp([-10, 10]), result)
# one broadcastable (2, 2) array-like
fill_value = [[100, 200], [1000, 2000]]
for y in (self.y235, self.y325, self.y25):
assert_raises(ValueError, interp1d, self.x5, y, kind=kind,
axis=-1, fill_value=fill_value, bounds_error=False)
for ii in range(2):
if ii == 1:
fill_value = np.array(fill_value)
interp = interp1d(self.x5, self.y225, kind=kind, axis=-1,
fill_value=fill_value, bounds_error=False)
assert_array_almost_equal(interp(10), [[100, 200], [1000, 2000]])
assert_array_almost_equal(interp(-10), [[100, 200], [1000, 2000]])
assert_array_almost_equal(interp([-10, 10]), [[[100, 100],
[200, 200]],
[[1000, 1000],
[2000, 2000]]])
# broadcastable (2, 2) lower, broadcastable (2, 2) upper
fill_value = ([[-100, -200], [-1000, -2000]],
[[100, 200], [1000, 2000]])
for y in (self.y235, self.y325, self.y25):
assert_raises(ValueError, interp1d, self.x5, y, kind=kind,
axis=-1, fill_value=fill_value, bounds_error=False)
for ii in range(2):
if ii == 1:
fill_value = (np.array(fill_value[0]), np.array(fill_value[1]))
interp = interp1d(self.x5, self.y225, kind=kind, axis=-1,
fill_value=fill_value, bounds_error=False)
assert_array_almost_equal(interp(10), [[100, 200], [1000, 2000]])
assert_array_almost_equal(interp(-10), [[-100, -200],
[-1000, -2000]])
assert_array_almost_equal(interp([-10, 10]), [[[-100, 100],
[-200, 200]],
[[-1000, 1000],
[-2000, 2000]]])
def test_fill_value(self):
# test that two-element fill value works
for kind in ('linear', 'nearest', 'cubic', 'slinear', 'quadratic',
'zero', 'previous', 'next'):
self._check_fill_value(kind)
def test_fill_value_writeable(self):
# backwards compat: fill_value is a public writeable attribute
interp = interp1d(self.x10, self.y10, fill_value=123.0)
assert_equal(interp.fill_value, 123.0)
interp.fill_value = 321.0
assert_equal(interp.fill_value, 321.0)
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',
'zero', 'previous', 'next'):
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', 'previous', 'next'):
self._check_complex(np.complex64, kind)
self._check_complex(np.complex128, kind)
@pytest.mark.skipif(IS_PYPY, reason="Test not meaningful on PyPy")
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
def test_overflow_nearest(self):
# Test that the x range doesn't overflow when given integers as input
for kind in ('nearest', 'previous', 'next'):
x = np.array([0, 50, 127], dtype=np.int8)
ii = interp1d(x, x, kind=kind)
assert_array_almost_equal(ii(x), x)
def test_local_nans(self):
# check that for local interpolation kinds (slinear, zero) a single nan
# only affects its local neighborhood
x = np.arange(10).astype(float)
y = x.copy()
y[6] = np.nan
for kind in ('zero', 'slinear'):
ir = interp1d(x, y, kind=kind)
vals = ir([4.9, 7.0])
assert_(np.isfinite(vals).all())
def test_spline_nans(self):
# Backwards compat: a single nan makes the whole spline interpolation
# return nans in an array of the correct shape. And it doesn't raise,
# just quiet nans because of backcompat.
x = np.arange(8).astype(float)
y = x.copy()
yn = y.copy()
yn[3] = np.nan
for kind in ['quadratic', 'cubic']:
ir = interp1d(x, y, kind=kind)
irn = interp1d(x, yn, kind=kind)
for xnew in (6, [1, 6], [[1, 6], [3, 5]]):
xnew = np.asarray(xnew)
out, outn = ir(x), irn(x)
assert_(np.isnan(outn).all())
assert_equal(out.shape, outn.shape)
def test_read_only(self):
x = np.arange(0, 10)
y = np.exp(-x / 3.0)
xnew = np.arange(0, 9, 0.1)
# Check both read-only and not read-only:
for writeable in (True, False):
xnew.flags.writeable = writeable
for kind in ('linear', 'nearest', 'zero', 'slinear', 'quadratic',
'cubic'):
f = interp1d(x, y, kind=kind)
vals = f(xnew)
assert_(np.isfinite(vals).all())
class TestLagrange(object):
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(object):
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_degenerate_case_multidimensional(self):
# This test is for issue #5683.
x = np.array([0, 1, 2])
y = np.vstack((x, x**2)).T
ak = Akima1DInterpolator(x, y)
x_eval = np.array([0.5, 1.5])
y_eval = ak(x_eval)
assert_allclose(y_eval, np.vstack((x_eval, x_eval**2)).T)
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)
match = "Extending a 1D Akima interpolator is not yet implemented"
with pytest.raises(NotImplementedError, match=match):
ak.extend(None, None)
class TestPPolyCommon(object):
# 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_ctor_c(self):
# wrong shape: `c` must be at least 2-dimensional
with assert_raises(ValueError):
PPoly([1, 2], [0, 1])
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])
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_extend_descending(self):
np.random.seed(0)
order = 3
x = np.sort(np.random.uniform(0, 10, 20))
c = np.random.rand(order + 1, x.shape[0] - 1, 2, 3)
for cls in (PPoly, BPoly):
p = cls(c, x)
p1 = cls(c[:, :9], x[:10])
p1.extend(c[:, 9:], x[10:])
p2 = cls(c[:, 10:], x[10:])
p2.extend(c[:, :10], x[:10])
assert_array_equal(p1.c, p.c)
assert_array_equal(p1.x, p.x)
assert_array_equal(p2.c, p.c)
assert_array_equal(p2.x, p.x)
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))), ())
# 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))
def test_axis(self):
np.random.seed(12345)
c = np.random.rand(3, 4, 5, 6, 7, 8)
c_s = c.shape
xp = np.random.random((1, 2))
for axis in (0, 1, 2, 3):
k, m = c.shape[axis], c.shape[axis+1]
x = np.sort(np.random.rand(m+1))
for cls in (PPoly, BPoly):
p = cls(c, x, axis=axis)
assert_equal(p.c.shape,
c_s[axis:axis+2] + c_s[:axis] + c_s[axis+2:])
res = p(xp)
targ_shape = c_s[:axis] + xp.shape + c_s[2+axis:]
assert_equal(res.shape, targ_shape)
# deriv/antideriv does not drop the axis
for p1 in [cls(c, x, axis=axis).derivative(),
cls(c, x, axis=axis).derivative(2),
cls(c, x, axis=axis).antiderivative(),
cls(c, x, axis=axis).antiderivative(2)]:
assert_equal(p1.axis, p.axis)
# c array needs two axes for the coefficients and intervals, so
# 0 <= axis < c.ndim-1; raise otherwise
for axis in (-1, 4, 5, 6):
for cls in (BPoly, PPoly):
assert_raises(ValueError, cls, **dict(c=c, x=x, axis=axis))
class TestPolySubclassing(object):
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(object):
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_periodic(self):
c = np.array([[1, 4], [2, 5], [3, 6]])
x = np.array([0, 0.5, 1])
p = PPoly(c, x, extrapolate='periodic')
assert_allclose(p(1.3), 1 * 0.3 ** 2 + 2 * 0.3 + 3)
assert_allclose(p(-0.3), 4 * (0.7 - 0.5) ** 2 + 5 * (0.7 - 0.5) + 6)
assert_allclose(p(1.3, 1), 2 * 0.3 + 2)
assert_allclose(p(-0.3, 1), 8 * (0.7 - 0.5) + 5)
def test_descending(self):
def binom_matrix(power):
n = np.arange(power + 1).reshape(-1, 1)
k = np.arange(power + 1)
B = binom(n, k)
return B[::-1, ::-1]
np.random.seed(0)
power = 3
for m in [10, 20, 30]:
x = np.sort(np.random.uniform(0, 10, m + 1))
ca = np.random.uniform(-2, 2, size=(power + 1, m))
h = np.diff(x)
h_powers = h[None, :] ** np.arange(power + 1)[::-1, None]
B = binom_matrix(power)
cap = ca * h_powers
cdp = np.dot(B.T, cap)
cd = cdp / h_powers
pa = PPoly(ca, x, extrapolate=True)
pd = PPoly(cd[:, ::-1], x[::-1], extrapolate=True)
x_test = np.random.uniform(-10, 20, 100)
assert_allclose(pa(x_test), pd(x_test), rtol=1e-13)
assert_allclose(pa(x_test, 1), pd(x_test, 1), rtol=1e-13)
pa_d = pa.derivative()
pd_d = pd.derivative()
assert_allclose(pa_d(x_test), pd_d(x_test), rtol=1e-13)
# Antiderivatives won't be equal because fixing continuity is
# done in the reverse order, but surely the differences should be
# equal.
pa_i = pa.antiderivative()
pd_i = pd.antiderivative()
for a, b in np.random.uniform(-10, 20, (5, 2)):
int_a = pa.integrate(a, b)
int_d = pd.integrate(a, b)
assert_allclose(int_a, int_d, rtol=1e-13)
assert_allclose(pa_i(b) - pa_i(a), pd_i(b) - pd_i(a),
rtol=1e-13)
roots_d = pd.roots()
roots_a = pa.roots()
assert_allclose(roots_a, np.sort(roots_d), rtol=1e-12)
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))
# make sure .from_spline accepts BSpline objects
b = BSpline(*spl)
ppp = PPoly.from_spline(b)
assert_allclose(ppp(xi), b(xi))
# BSpline's extrapolate attribute propagates unless overridden
t, c, k = spl
for extrap in (None, True, False):
b = BSpline(t, c, k, extrapolate=extrap)
p = PPoly.from_spline(b)
assert_equal(p.extrapolate, b.extrapolate)
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
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_regression_4355(self):
# https://github.com/scipy/scipy/issues/4355
p = PPoly([[1., 0.5]], [0, 1, 2])
q = p.antiderivative()
assert_equal(q.c, [[1, 0.5], [0, 1]])
assert_equal(q.x, [0, 1, 2])
assert_allclose(p.integrate(0, 2), 1.5)
assert_allclose(q(2) - q(0), 1.5)
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_antiderivative_continuity(self):
c = np.array([[2, 1, 2, 2], [2, 1, 3, 3]]).T
x = np.array([0, 0.5, 1])
p = PPoly(c, x)
ip = p.antiderivative()
# check continuity
assert_allclose(ip(0.5 - 1e-9), ip(0.5 + 1e-9), rtol=1e-8)
# check that only lowest order coefficients were changed
p2 = ip.derivative()
assert_allclose(p2.c, p.c)
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_integrate_periodic(self):
x = np.array([1, 2, 4])
c = np.array([[0., 0.], [-1., -1.], [2., -0.], [1., 2.]])
P = PPoly(c, x, extrapolate='periodic')
I = P.antiderivative()
period_int = I(4) - I(1)
assert_allclose(P.integrate(1, 4), period_int)
assert_allclose(P.integrate(-10, -7), period_int)
assert_allclose(P.integrate(-10, -4), 2 * period_int)
assert_allclose(P.integrate(1.5, 2.5), I(2.5) - I(1.5))
assert_allclose(P.integrate(3.5, 5), I(2) - I(1) + I(4) - I(3.5))
assert_allclose(P.integrate(3.5 + 12, 5 + 12),
I(2) - I(1) + I(4) - I(3.5))
assert_allclose(P.integrate(3.5, 5 + 12),
I(2) - I(1) + I(4) - I(3.5) + 4 * period_int)
assert_allclose(P.integrate(0, -1), I(2) - I(3))
assert_allclose(P.integrate(-9, -10), I(2) - I(3))
assert_allclose(P.integrate(0, -10), I(2) - I(3) - 3 * period_int)
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])
# ditto for p.solve(const) with sections identically equal const
const = 2.
c1 = c.copy()
c1[1, :] += const
pp1 = PPoly(c1, x)
assert_array_equal(pp1.solve(const),
[0.25, 0.4, np.nan, 0.6 + 0.25])
def test_roots_all_zero(self):
# test the code path for the polynomial being identically zero everywhere
c = [[0], [0]]
x = [0, 1]
p = PPoly(c, x)
assert_array_equal(p.roots(), [0, np.nan])
assert_array_equal(p.solve(0), [0, np.nan])
assert_array_equal(p.solve(1), [])
c = [[0, 0], [0, 0]]
x = [0, 1, 2]
p = PPoly(c, x)
assert_array_equal(p.roots(), [0, np.nan, 1, np.nan])
assert_array_equal(p.solve(0), [0, np.nan, 1, np.nan])
assert_array_equal(p.solve(1), [])
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), [])
# ditto for a discontinuity across y:
assert_array_equal(pp.solve(0.5), [0.5])
assert_array_equal(pp.solve(0.5, discontinuity=False), [])
assert_array_equal(pp.solve(1.5), [])
assert_array_equal(pp.solve(1.5, 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)
for y in [0, np.random.random()]:
r = pp.solve(y, 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]
msg = "(%r) r = %s" % (extrapolate, repr(rr),)
assert_allclose((val-y) / cmpval, 0, atol=1e-7,
err_msg=msg)
# 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
for y in [0, np.random.random()]:
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(object):
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_periodic(self):
x = [0, 1, 3]
c = [[3, 0], [0, 0], [0, 2]]
# [3*(1-x)**2, 2*((x-1)/2)**2]
bp = BPoly(c, x, extrapolate='periodic')
assert_allclose(bp(3.4), 3 * 0.6**2)
assert_allclose(bp(-1.3), 2 * (0.7/2)**2)
assert_allclose(bp(3.4, 1), -6 * 0.6)
assert_allclose(bp(-1.3, 1), 2 * (0.7/2))
def test_descending(self):
np.random.seed(0)
power = 3
for m in [10, 20, 30]:
x = np.sort(np.random.uniform(0, 10, m + 1))
ca = np.random.uniform(-0.1, 0.1, size=(power + 1, m))
# We need only to flip coefficients to get it right!
cd = ca[::-1].copy()
pa = BPoly(ca, x, extrapolate=True)
pd = BPoly(cd[:, ::-1], x[::-1], extrapolate=True)
x_test = np.random.uniform(-10, 20, 100)
assert_allclose(pa(x_test), pd(x_test), rtol=1e-13)
assert_allclose(pa(x_test, 1), pd(x_test, 1), rtol=1e-13)
pa_d = pa.derivative()
pd_d = pd.derivative()
assert_allclose(pa_d(x_test), pd_d(x_test), rtol=1e-13)
# Antiderivatives won't be equal because fixing continuity is
# done in the reverse order, but surely the differences should be
# equal.
pa_i = pa.antiderivative()
pd_i = pd.antiderivative()
for a, b in np.random.uniform(-10, 20, (5, 2)):
int_a = pa.integrate(a, b)
int_d = pd.integrate(a, b)
assert_allclose(int_a, int_d, rtol=1e-12)
assert_allclose(pa_i(b) - pa_i(a), pd_i(b) - pd_i(a),
rtol=1e-12)
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(object):
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))
# test both real and complex coefficients
for cc in [c.copy(), c*(1. + 2.j)]:
bp = BPoly(cc, x)
xp = np.linspace(x[0], x[-1], 21)
for i in range(k):
assert_allclose(bp(xp, i), bp.derivative(i)(xp))
def test_antiderivative_simple(self):
# f(x) = x for x \in [0, 1),
# (x-1)/2 for x \in [1, 3]
#
# antiderivative is then
# F(x) = x**2 / 2 for x \in [0, 1),
# 0.5*x*(x/2 - 1) + A for x \in [1, 3]
# where A = 3/4 for continuity at x = 1.
x = [0, 1, 3]
c = [[0, 0], [1, 1]]
bp = BPoly(c, x)
bi = bp.antiderivative()
xx = np.linspace(0, 3, 11)
assert_allclose(bi(xx),
np.where(xx < 1, xx**2 / 2.,
0.5 * xx * (xx/2. - 1) + 3./4),
atol=1e-12, rtol=1e-12)
def test_der_antider(self):
np.random.seed(1234)
x = np.sort(np.random.random(11))
c = np.random.random((4, 10, 2, 3))
bp = BPoly(c, x)
xx = np.linspace(x[0], x[-1], 100)
assert_allclose(bp.antiderivative().derivative()(xx),
bp(xx), atol=1e-12, rtol=1e-12)
def test_antider_ppoly(self):
np.random.seed(1234)
x = np.sort(np.random.random(11))
c = np.random.random((4, 10, 2, 3))
bp = BPoly(c, x)
pp = PPoly.from_bernstein_basis(bp)
xx = np.linspace(x[0], x[-1], 10)
assert_allclose(bp.antiderivative(2)(xx),
pp.antiderivative(2)(xx), atol=1e-12, rtol=1e-12)
def test_antider_continuous(self):
np.random.seed(1234)
x = np.sort(np.random.random(11))
c = np.random.random((4, 10))
bp = BPoly(c, x).antiderivative()
xx = bp.x[1:-1]
assert_allclose(bp(xx - 1e-14),
bp(xx + 1e-14), atol=1e-12, rtol=1e-12)
def test_integrate(self):
np.random.seed(1234)
x = np.sort(np.random.random(11))
c = np.random.random((4, 10))
bp = BPoly(c, x)
pp = PPoly.from_bernstein_basis(bp)
assert_allclose(bp.integrate(0, 1),
pp.integrate(0, 1), atol=1e-12, rtol=1e-12)
def test_integrate_extrap(self):
c = [[1]]
x = [0, 1]
b = BPoly(c, x)
# default is extrapolate=True
assert_allclose(b.integrate(0, 2), 2., atol=1e-14)
# .integrate argument overrides self.extrapolate
b1 = BPoly(c, x, extrapolate=False)
assert_(np.isnan(b1.integrate(0, 2)))
assert_allclose(b1.integrate(0, 2, extrapolate=True), 2., atol=1e-14)
def test_integrate_periodic(self):
x = np.array([1, 2, 4])
c = np.array([[0., 0.], [-1., -1.], [2., -0.], [1., 2.]])
P = BPoly.from_power_basis(PPoly(c, x), extrapolate='periodic')
I = P.antiderivative()
period_int = I(4) - I(1)
assert_allclose(P.integrate(1, 4), period_int)
assert_allclose(P.integrate(-10, -7), period_int)
assert_allclose(P.integrate(-10, -4), 2 * period_int)
assert_allclose(P.integrate(1.5, 2.5), I(2.5) - I(1.5))
assert_allclose(P.integrate(3.5, 5), I(2) - I(1) + I(4) - I(3.5))
assert_allclose(P.integrate(3.5 + 12, 5 + 12),
I(2) - I(1) + I(4) - I(3.5))
assert_allclose(P.integrate(3.5, 5 + 12),
I(2) - I(1) + I(4) - I(3.5) + 4 * period_int)
assert_allclose(P.integrate(0, -1), I(2) - I(3))
assert_allclose(P.integrate(-9, -10), I(2) - I(3))
assert_allclose(P.integrate(0, -10), I(2) - I(3) - 3 * period_int)
def test_antider_neg(self):
# .derivative(-nu) ==> .andiderivative(nu) and vice versa
c = [[1]]
x = [0, 1]
b = BPoly(c, x)
xx = np.linspace(0, 1, 21)
assert_allclose(b.derivative(-1)(xx), b.antiderivative()(xx),
atol=1e-12, rtol=1e-12)
assert_allclose(b.derivative(1)(xx), b.antiderivative(-1)(xx),
atol=1e-12, rtol=1e-12)
class TestPolyConversions(object):
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(object):
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))
def test_gh_5430(self):
# At least one of these raises an error unless gh-5430 is
# fixed. In py2k an int is implemented using a C long, so
# which one fails depends on your system. In py3k there is only
# one arbitrary precision integer type, so both should fail.
orders = np.int32(1)
p = BPoly.from_derivatives([0, 1], [[0], [0]], orders=orders)
assert_almost_equal(p(0), 0)
orders = np.int64(1)
p = BPoly.from_derivatives([0, 1], [[0], [0]], orders=orders)
assert_almost_equal(p(0), 0)
orders = 1
# This worked before; make sure it still works
p = BPoly.from_derivatives([0, 1], [[0], [0]], orders=orders)
assert_almost_equal(p(0), 0)
orders = 1
class TestNdPPoly(object):
def test_simple_1d(self):
np.random.seed(1234)
c = np.random.rand(4, 5)
x = np.linspace(0, 1, 5+1)
xi = np.random.rand(200)
p = NdPPoly(c, (x,))
v1 = p((xi,))
v2 = _ppoly_eval_1(c[:,:,None], x, xi).ravel()
assert_allclose(v1, v2)
def test_simple_2d(self):
np.random.seed(1234)
c = np.random.rand(4, 5, 6, 7)
x = np.linspace(0, 1, 6+1)
y = np.linspace(0, 1, 7+1)**2
xi = np.random.rand(200)
yi = np.random.rand(200)
v1 = np.empty([len(xi), 1], dtype=c.dtype)
v1.fill(np.nan)
_ppoly.evaluate_nd(c.reshape(4*5, 6*7, 1),
(x, y),
np.array([4, 5], dtype=np.intc),
np.c_[xi, yi],
np.array([0, 0], dtype=np.intc),
1,
v1)
v1 = v1.ravel()
v2 = _ppoly2d_eval(c, (x, y), xi, yi)
assert_allclose(v1, v2)
p = NdPPoly(c, (x, y))
for nu in (None, (0, 0), (0, 1), (1, 0), (2, 3), (9, 2)):
v1 = p(np.c_[xi, yi], nu=nu)
v2 = _ppoly2d_eval(c, (x, y), xi, yi, nu=nu)
assert_allclose(v1, v2, err_msg=repr(nu))
def test_simple_3d(self):
np.random.seed(1234)
c = np.random.rand(4, 5, 6, 7, 8, 9)
x = np.linspace(0, 1, 7+1)
y = np.linspace(0, 1, 8+1)**2
z = np.linspace(0, 1, 9+1)**3
xi = np.random.rand(40)
yi = np.random.rand(40)
zi = np.random.rand(40)
p = NdPPoly(c, (x, y, z))
for nu in (None, (0, 0, 0), (0, 1, 0), (1, 0, 0), (2, 3, 0),
(6, 0, 2)):
v1 = p((xi, yi, zi), nu=nu)
v2 = _ppoly3d_eval(c, (x, y, z), xi, yi, zi, nu=nu)
assert_allclose(v1, v2, err_msg=repr(nu))
def test_simple_4d(self):
np.random.seed(1234)
c = np.random.rand(4, 5, 6, 7, 8, 9, 10, 11)
x = np.linspace(0, 1, 8+1)
y = np.linspace(0, 1, 9+1)**2
z = np.linspace(0, 1, 10+1)**3
u = np.linspace(0, 1, 11+1)**4
xi = np.random.rand(20)
yi = np.random.rand(20)
zi = np.random.rand(20)
ui = np.random.rand(20)
p = NdPPoly(c, (x, y, z, u))
v1 = p((xi, yi, zi, ui))
v2 = _ppoly4d_eval(c, (x, y, z, u), xi, yi, zi, ui)
assert_allclose(v1, v2)
def test_deriv_1d(self):
np.random.seed(1234)
c = np.random.rand(4, 5)
x = np.linspace(0, 1, 5+1)
p = NdPPoly(c, (x,))
# derivative
dp = p.derivative(nu=[1])
p1 = PPoly(c, x)
dp1 = p1.derivative()
assert_allclose(dp.c, dp1.c)
# antiderivative
dp = p.antiderivative(nu=[2])
p1 = PPoly(c, x)
dp1 = p1.antiderivative(2)
assert_allclose(dp.c, dp1.c)
def test_deriv_3d(self):
np.random.seed(1234)
c = np.random.rand(4, 5, 6, 7, 8, 9)
x = np.linspace(0, 1, 7+1)
y = np.linspace(0, 1, 8+1)**2
z = np.linspace(0, 1, 9+1)**3
p = NdPPoly(c, (x, y, z))
# differentiate vs x
p1 = PPoly(c.transpose(0, 3, 1, 2, 4, 5), x)
dp = p.derivative(nu=[2])
dp1 = p1.derivative(2)
assert_allclose(dp.c,
dp1.c.transpose(0, 2, 3, 1, 4, 5))
# antidifferentiate vs y
p1 = PPoly(c.transpose(1, 4, 0, 2, 3, 5), y)
dp = p.antiderivative(nu=[0, 1, 0])
dp1 = p1.antiderivative(1)
assert_allclose(dp.c,
dp1.c.transpose(2, 0, 3, 4, 1, 5))
# differentiate vs z
p1 = PPoly(c.transpose(2, 5, 0, 1, 3, 4), z)
dp = p.derivative(nu=[0, 0, 3])
dp1 = p1.derivative(3)
assert_allclose(dp.c,
dp1.c.transpose(2, 3, 0, 4, 5, 1))
def test_deriv_3d_simple(self):
# Integrate to obtain function x y**2 z**4 / (2! 4!)
c = np.ones((1, 1, 1, 3, 4, 5))
x = np.linspace(0, 1, 3+1)**1
y = np.linspace(0, 1, 4+1)**2
z = np.linspace(0, 1, 5+1)**3
p = NdPPoly(c, (x, y, z))
ip = p.antiderivative((1, 0, 4))
ip = ip.antiderivative((0, 2, 0))
xi = np.random.rand(20)
yi = np.random.rand(20)
zi = np.random.rand(20)
assert_allclose(ip((xi, yi, zi)),
xi * yi**2 * zi**4 / (gamma(3)*gamma(5)))
def test_integrate_2d(self):
np.random.seed(1234)
c = np.random.rand(4, 5, 16, 17)
x = np.linspace(0, 1, 16+1)**1
y = np.linspace(0, 1, 17+1)**2
# make continuously differentiable so that nquad() has an
# easier time
c = c.transpose(0, 2, 1, 3)
cx = c.reshape(c.shape[0], c.shape[1], -1).copy()
_ppoly.fix_continuity(cx, x, 2)
c = cx.reshape(c.shape)
c = c.transpose(0, 2, 1, 3)
c = c.transpose(1, 3, 0, 2)
cx = c.reshape(c.shape[0], c.shape[1], -1).copy()
_ppoly.fix_continuity(cx, y, 2)
c = cx.reshape(c.shape)
c = c.transpose(2, 0, 3, 1).copy()
# Check integration
p = NdPPoly(c, (x, y))
for ranges in [[(0, 1), (0, 1)],
[(0, 0.5), (0, 1)],
[(0, 1), (0, 0.5)],
[(0.3, 0.7), (0.6, 0.2)]]:
ig = p.integrate(ranges)
ig2, err2 = nquad(lambda x, y: p((x, y)), ranges,
opts=[dict(epsrel=1e-5, epsabs=1e-5)]*2)
assert_allclose(ig, ig2, rtol=1e-5, atol=1e-5,
err_msg=repr(ranges))
def test_integrate_1d(self):
np.random.seed(1234)
c = np.random.rand(4, 5, 6, 16, 17, 18)
x = np.linspace(0, 1, 16+1)**1
y = np.linspace(0, 1, 17+1)**2
z = np.linspace(0, 1, 18+1)**3
# Check 1D integration
p = NdPPoly(c, (x, y, z))
u = np.random.rand(200)
v = np.random.rand(200)
a, b = 0.2, 0.7
px = p.integrate_1d(a, b, axis=0)
pax = p.antiderivative((1, 0, 0))
assert_allclose(px((u, v)), pax((b, u, v)) - pax((a, u, v)))
py = p.integrate_1d(a, b, axis=1)
pay = p.antiderivative((0, 1, 0))
assert_allclose(py((u, v)), pay((u, b, v)) - pay((u, a, v)))
pz = p.integrate_1d(a, b, axis=2)
paz = p.antiderivative((0, 0, 1))
assert_allclose(pz((u, v)), paz((u, v, b)) - paz((u, v, a)))
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
def _dpow(x, y, n):
"""
d^n (x**y) / dx^n
"""
if n < 0:
raise ValueError("invalid derivative order")
elif n > y:
return 0
else:
return poch(y - n + 1, n) * x**(y - n)
def _ppoly2d_eval(c, xs, xnew, ynew, nu=None):
"""
Straightforward evaluation of 2D piecewise polynomial
"""
if nu is None:
nu = (0, 0)
out = np.empty((len(xnew),), dtype=c.dtype)
nx, ny = c.shape[:2]
for jout, (x, y) in enumerate(zip(xnew, ynew)):
if not ((xs[0][0] <= x <= xs[0][-1]) and
(xs[1][0] <= y <= xs[1][-1])):
out[jout] = np.nan
continue
j1 = np.searchsorted(xs[0], x) - 1
j2 = np.searchsorted(xs[1], y) - 1
s1 = x - xs[0][j1]
s2 = y - xs[1][j2]
val = 0
for k1 in range(c.shape[0]):
for k2 in range(c.shape[1]):
val += (c[nx-k1-1,ny-k2-1,j1,j2]
* _dpow(s1, k1, nu[0])
* _dpow(s2, k2, nu[1]))
out[jout] = val
return out
def _ppoly3d_eval(c, xs, xnew, ynew, znew, nu=None):
"""
Straightforward evaluation of 3D piecewise polynomial
"""
if nu is None:
nu = (0, 0, 0)
out = np.empty((len(xnew),), dtype=c.dtype)
nx, ny, nz = c.shape[:3]
for jout, (x, y, z) in enumerate(zip(xnew, ynew, znew)):
if not ((xs[0][0] <= x <= xs[0][-1]) and
(xs[1][0] <= y <= xs[1][-1]) and
(xs[2][0] <= z <= xs[2][-1])):
out[jout] = np.nan
continue
j1 = np.searchsorted(xs[0], x) - 1
j2 = np.searchsorted(xs[1], y) - 1
j3 = np.searchsorted(xs[2], z) - 1
s1 = x - xs[0][j1]
s2 = y - xs[1][j2]
s3 = z - xs[2][j3]
val = 0
for k1 in range(c.shape[0]):
for k2 in range(c.shape[1]):
for k3 in range(c.shape[2]):
val += (c[nx-k1-1,ny-k2-1,nz-k3-1,j1,j2,j3]
* _dpow(s1, k1, nu[0])
* _dpow(s2, k2, nu[1])
* _dpow(s3, k3, nu[2]))
out[jout] = val
return out
def _ppoly4d_eval(c, xs, xnew, ynew, znew, unew, nu=None):
"""
Straightforward evaluation of 4D piecewise polynomial
"""
if nu is None:
nu = (0, 0, 0, 0)
out = np.empty((len(xnew),), dtype=c.dtype)
mx, my, mz, mu = c.shape[:4]
for jout, (x, y, z, u) in enumerate(zip(xnew, ynew, znew, unew)):
if not ((xs[0][0] <= x <= xs[0][-1]) and
(xs[1][0] <= y <= xs[1][-1]) and
(xs[2][0] <= z <= xs[2][-1]) and
(xs[3][0] <= u <= xs[3][-1])):
out[jout] = np.nan
continue
j1 = np.searchsorted(xs[0], x) - 1
j2 = np.searchsorted(xs[1], y) - 1
j3 = np.searchsorted(xs[2], z) - 1
j4 = np.searchsorted(xs[3], u) - 1
s1 = x - xs[0][j1]
s2 = y - xs[1][j2]
s3 = z - xs[2][j3]
s4 = u - xs[3][j4]
val = 0
for k1 in range(c.shape[0]):
for k2 in range(c.shape[1]):
for k3 in range(c.shape[2]):
for k4 in range(c.shape[3]):
val += (c[mx-k1-1,my-k2-1,mz-k3-1,mu-k4-1,j1,j2,j3,j4]
* _dpow(s1, k1, nu[0])
* _dpow(s2, k2, nu[1])
* _dpow(s3, k3, nu[2])
* _dpow(s4, k4, nu[3]))
out[jout] = val
return out
class TestRegularGridInterpolator(object):
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
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(object):
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
_assert_warns(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))
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