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