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from numpy.testing import *
from numpy import mgrid, pi, sin, ogrid, poly1d, linspace
import numpy as np
from scipy.interpolate import interp1d, interp2d, lagrange
class TestInterp2D(TestCase):
def test_interp2d(self):
y, x = mgrid[0:2:20j, 0:pi:21j]
z = sin(x+0.5*y)
I = interp2d(x, y, z)
assert_almost_equal(I(1.0, 2.0), sin(2.0), decimal=2)
v,u = ogrid[0:2:24j, 0:pi:25j]
assert_almost_equal(I(u.ravel(), v.ravel()), sin(u+0.5*v), decimal=2)
def test_interp2d_meshgrid_input(self):
# Ticket #703
x = linspace(0, 2, 16)
y = linspace(0, pi, 21)
z = sin(x[None,:] + y[:,None]/2.)
I = interp2d(x, y, z)
assert_almost_equal(I(1.0, 2.0), sin(2.0), decimal=2)
class TestInterp1D(object):
def setUp(self):
self.x10 = np.arange(10.)
self.y10 = np.arange(10.)
self.x25 = self.x10.reshape((2,5))
self.x2 = np.arange(2.)
self.y2 = np.arange(2.)
self.x1 = np.array([0.])
self.y1 = np.array([0.])
self.y210 = np.arange(20.).reshape((2, 10))
self.y102 = np.arange(20.).reshape((10, 2))
self.fill_value = -100.0
def test_validation(self):
""" Make sure that appropriate exceptions are raised when invalid values
are given to the constructor.
"""
# These should all work.
interp1d(self.x10, self.y10, kind='linear')
interp1d(self.x10, self.y10, kind='cubic')
interp1d(self.x10, self.y10, kind='slinear')
interp1d(self.x10, self.y10, kind='quadratic')
interp1d(self.x10, self.y10, kind='zero')
interp1d(self.x10, self.y10, kind='nearest')
interp1d(self.x10, self.y10, kind=0)
interp1d(self.x10, self.y10, kind=1)
interp1d(self.x10, self.y10, kind=2)
interp1d(self.x10, self.y10, kind=3)
# x array must be 1D.
assert_raises(ValueError, interp1d, self.x25, self.y10)
# y array cannot be a scalar.
assert_raises(ValueError, interp1d, self.x10, np.array(0))
# Check for x and y arrays having the same length.
assert_raises(ValueError, interp1d, self.x10, self.y2)
assert_raises(ValueError, interp1d, self.x2, self.y10)
assert_raises(ValueError, interp1d, self.x10, self.y102)
interp1d(self.x10, self.y210)
interp1d(self.x10, self.y102, axis=0)
# Check for x and y having at least 1 element.
assert_raises(ValueError, interp1d, self.x1, self.y10)
assert_raises(ValueError, interp1d, self.x10, self.y1)
assert_raises(ValueError, interp1d, self.x1, self.y1)
def test_init(self):
""" Check that the attributes are initialized appropriately by the
constructor.
"""
assert interp1d(self.x10, self.y10).copy
assert not interp1d(self.x10, self.y10, copy=False).copy
assert interp1d(self.x10, self.y10).bounds_error
assert not interp1d(self.x10, self.y10, bounds_error=False).bounds_error
assert np.isnan(interp1d(self.x10, self.y10).fill_value)
assert_equal(
interp1d(self.x10, self.y10, fill_value=3.0).fill_value,
3.0,
)
assert_equal(
interp1d(self.x10, self.y10).axis,
0,
)
assert_equal(
interp1d(self.x10, self.y210).axis,
1,
)
assert_equal(
interp1d(self.x10, self.y102, axis=0).axis,
0,
)
assert_array_equal(
interp1d(self.x10, self.y10).x,
self.x10,
)
assert_array_equal(
interp1d(self.x10, self.y10).y,
self.y10,
)
assert_array_equal(
interp1d(self.x10, self.y210).y,
self.y210,
)
def test_linear(self):
""" Check the actual implementation of linear interpolation.
"""
interp10 = interp1d(self.x10, self.y10)
assert_array_almost_equal(
interp10(self.x10),
self.y10,
)
assert_array_almost_equal(
interp10(1.2),
np.array([1.2]),
)
assert_array_almost_equal(
interp10([2.4, 5.6, 6.0]),
np.array([2.4, 5.6, 6.0]),
)
def test_cubic(self):
""" Check the actual implementation of spline interpolation.
"""
interp10 = interp1d(self.x10, self.y10, kind='cubic')
assert_array_almost_equal(
interp10(self.x10),
self.y10,
)
assert_array_almost_equal(
interp10(1.2),
np.array([1.2]),
)
assert_array_almost_equal(
interp10([2.4, 5.6, 6.0]),
np.array([2.4, 5.6, 6.0]),
)
def test_nearest(self):
"""Check the actual implementation of nearest-neighbour interpolation.
"""
interp10 = interp1d(self.x10, self.y10, kind='nearest')
assert_array_almost_equal(
interp10(self.x10),
self.y10,
)
assert_array_almost_equal(
interp10(1.2),
np.array(1.),
)
assert_array_almost_equal(
interp10([2.4, 5.6, 6.0]),
np.array([2., 6., 6.]),
)
@dec.knownfailureif(True, "zero-order splines fail for the last point")
def test_zero(self):
"""Check the actual implementation of zero-order spline interpolation.
"""
interp10 = interp1d(self.x10, self.y10, kind='zero')
assert_array_almost_equal(interp10(self.x10), self.y10)
assert_array_almost_equal(interp10(1.2), np.array(1.))
assert_array_almost_equal(interp10([2.4, 5.6, 6.0]),
np.array([2., 6., 6.]))
def _bounds_check(self, kind='linear'):
""" Test that our handling of out-of-bounds input is correct.
"""
extrap10 = interp1d(self.x10, self.y10, fill_value=self.fill_value,
bounds_error=False, kind=kind)
assert_array_equal(
extrap10(11.2),
np.array(self.fill_value),
)
assert_array_equal(
extrap10(-3.4),
np.array(self.fill_value),
)
assert_array_equal(
extrap10([[[11.2], [-3.4], [12.6], [19.3]]]),
np.array(self.fill_value),
)
assert_array_equal(
extrap10._check_bounds(np.array([-1.0, 0.0, 5.0, 9.0, 11.0])),
np.array([True, False, False, False, True]),
)
raises_bounds_error = interp1d(self.x10, self.y10, bounds_error=True,
kind=kind)
assert_raises(ValueError, raises_bounds_error, -1.0)
assert_raises(ValueError, raises_bounds_error, 11.0)
raises_bounds_error([0.0, 5.0, 9.0])
def _bounds_check_int_nan_fill(self, kind='linear'):
x = np.arange(10).astype(np.int_)
y = np.arange(10).astype(np.int_)
c = interp1d(x, y, kind=kind, fill_value=np.nan, bounds_error=False)
yi = c(x - 1)
assert np.isnan(yi[0])
assert_array_almost_equal(yi, np.r_[np.nan, y[:-1]])
def test_bounds(self):
for kind in ('linear', 'cubic', 'nearest',
'slinear', 'zero', 'quadratic'):
yield self._bounds_check, kind
yield self._bounds_check_int_nan_fill, kind
def _nd_check_interp(self, kind='linear'):
"""Check the behavior when the inputs and outputs are multidimensional.
"""
# Multidimensional input.
interp10 = interp1d(self.x10, self.y10, kind=kind)
assert_array_almost_equal(
interp10(np.array([[3., 5.], [2., 7.]])),
np.array([[3., 5.], [2., 7.]]),
)
# Scalar input -> 0-dim scalar array output
assert isinstance(interp10(1.2), np.ndarray)
assert_equal(interp10(1.2).shape, ())
# Multidimensional outputs.
interp210 = interp1d(self.x10, self.y210, kind=kind)
assert_array_almost_equal(
interp210(1.),
np.array([1., 11.]),
)
assert_array_almost_equal(
interp210(np.array([1., 2.])),
np.array([[1., 2.],
[11., 12.]]),
)
interp102 = interp1d(self.x10, self.y102, axis=0, kind=kind)
assert_array_almost_equal(
interp102(1.),
np.array([2.0, 3.0]),
)
assert_array_almost_equal(
interp102(np.array([1., 3.])),
np.array([[2., 3.],
[6., 7.]]),
)
# Both at the same time!
x_new = np.array([[3., 5.], [2., 7.]])
assert_array_almost_equal(
interp210(x_new),
np.array([[[3., 5.], [2., 7.]],
[[13., 15.], [12., 17.]]]),
)
assert_array_almost_equal(
interp102(x_new),
np.array([[[6., 7.], [10., 11.]],
[[4., 5.], [14., 15.]]]),
)
def _nd_check_shape(self, kind='linear'):
# Check large ndim output shape
a = [4, 5, 6, 7]
y = np.arange(np.prod(a)).reshape(*a)
for n, s in enumerate(a):
x = np.arange(s)
z = interp1d(x, y, axis=n, kind=kind)
assert_array_almost_equal(z(x), y, err_msg=kind)
x2 = np.arange(2*3*1).reshape((2,3,1)) / 12.
b = list(a)
b[n:n+1] = [2,3,1]
assert_array_almost_equal(z(x2).shape, b, err_msg=kind)
def test_nd(self):
for kind in ('linear', 'cubic', 'slinear', 'quadratic', 'nearest'):
yield self._nd_check_interp, kind
yield 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'):
yield self._check_complex, np.complex64, kind
yield self._check_complex, np.complex128, kind
@dec.knownfailureif(True, "zero-order splines fail for the last point")
def test_nd_zero_spline(self):
# zero-order splines don't get the last point right,
# see test_zero above
#yield self._nd_check_interp, 'zero'
#yield self._nd_check_interp, 'zero'
pass
class TestLagrange(TestCase):
def test_lagrange(self):
p = poly1d([5,2,1,4,3])
xs = np.arange(len(p.coeffs))
ys = p(xs)
pl = lagrange(xs,ys)
assert_array_almost_equal(p.coeffs,pl.coeffs)
if __name__ == "__main__":
run_module_suite()
|
