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import numpy as np
from scipy.interpolate import pade
from scipy._lib._array_api import (
xp_assert_equal, assert_array_almost_equal
)
def test_pade_trivial():
nump, denomp = pade([1.0], 0)
xp_assert_equal(nump.c, np.asarray([1.0]))
xp_assert_equal(denomp.c, np.asarray([1.0]))
nump, denomp = pade([1.0], 0, 0)
xp_assert_equal(nump.c, np.asarray([1.0]))
xp_assert_equal(denomp.c, np.asarray([1.0]))
def test_pade_4term_exp():
# First four Taylor coefficients of exp(x).
# Unlike poly1d, the first array element is the zero-order term.
an = [1.0, 1.0, 0.5, 1.0/6]
nump, denomp = pade(an, 0)
assert_array_almost_equal(nump.c, [1.0/6, 0.5, 1.0, 1.0])
assert_array_almost_equal(denomp.c, [1.0])
nump, denomp = pade(an, 1)
assert_array_almost_equal(nump.c, [1.0/6, 2.0/3, 1.0])
assert_array_almost_equal(denomp.c, [-1.0/3, 1.0])
nump, denomp = pade(an, 2)
assert_array_almost_equal(nump.c, [1.0/3, 1.0])
assert_array_almost_equal(denomp.c, [1.0/6, -2.0/3, 1.0])
nump, denomp = pade(an, 3)
assert_array_almost_equal(nump.c, [1.0])
assert_array_almost_equal(denomp.c, [-1.0/6, 0.5, -1.0, 1.0])
# Testing inclusion of optional parameter
nump, denomp = pade(an, 0, 3)
assert_array_almost_equal(nump.c, [1.0/6, 0.5, 1.0, 1.0])
assert_array_almost_equal(denomp.c, [1.0])
nump, denomp = pade(an, 1, 2)
assert_array_almost_equal(nump.c, [1.0/6, 2.0/3, 1.0])
assert_array_almost_equal(denomp.c, [-1.0/3, 1.0])
nump, denomp = pade(an, 2, 1)
assert_array_almost_equal(nump.c, [1.0/3, 1.0])
assert_array_almost_equal(denomp.c, [1.0/6, -2.0/3, 1.0])
nump, denomp = pade(an, 3, 0)
assert_array_almost_equal(nump.c, [1.0])
assert_array_almost_equal(denomp.c, [-1.0/6, 0.5, -1.0, 1.0])
# Testing reducing array.
nump, denomp = pade(an, 0, 2)
assert_array_almost_equal(nump.c, [0.5, 1.0, 1.0])
assert_array_almost_equal(denomp.c, [1.0])
nump, denomp = pade(an, 1, 1)
assert_array_almost_equal(nump.c, [1.0/2, 1.0])
assert_array_almost_equal(denomp.c, [-1.0/2, 1.0])
nump, denomp = pade(an, 2, 0)
assert_array_almost_equal(nump.c, [1.0])
assert_array_almost_equal(denomp.c, [1.0/2, -1.0, 1.0])
def test_pade_ints():
# Simple test sequences (one of ints, one of floats).
an_int = [1, 2, 3, 4]
an_flt = [1.0, 2.0, 3.0, 4.0]
# Make sure integer arrays give the same result as float arrays with same values.
for i in range(0, len(an_int)):
for j in range(0, len(an_int) - i):
# Create float and int pade approximation for given order.
nump_int, denomp_int = pade(an_int, i, j)
nump_flt, denomp_flt = pade(an_flt, i, j)
# Check that they are the same.
xp_assert_equal(nump_int.c, nump_flt.c)
xp_assert_equal(denomp_int.c, denomp_flt.c)
def test_pade_complex():
# Test sequence with known solutions - see page 6 of 10.1109/PESGM.2012.6344759.
# Variable x is parameter - these tests will work with any complex number.
x = 0.2 + 0.6j
an = [1.0, x, -x*x.conjugate(), x.conjugate()*(x**2) + x*(x.conjugate()**2),
-(x**3)*x.conjugate() - 3*(x*x.conjugate())**2 - x*(x.conjugate()**3)]
nump, denomp = pade(an, 1, 1)
assert_array_almost_equal(nump.c, [x + x.conjugate(), 1.0])
assert_array_almost_equal(denomp.c, [x.conjugate(), 1.0])
nump, denomp = pade(an, 1, 2)
assert_array_almost_equal(nump.c, [x**2, 2*x + x.conjugate(), 1.0])
assert_array_almost_equal(denomp.c, [x + x.conjugate(), 1.0])
nump, denomp = pade(an, 2, 2)
assert_array_almost_equal(
nump.c,
[x**2 + x*x.conjugate() + x.conjugate()**2, 2*(x + x.conjugate()), 1.0]
)
assert_array_almost_equal(denomp.c, [x.conjugate()**2, x + 2*x.conjugate(), 1.0])
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