manyi/venv/Lib/site-packages/scipy/interpolate/tests/test_interpolate.py

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))