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interpolate
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test_pade.py
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from numpy.testing import (assert_array_equal, assert_array_almost_equal) from scipy.interpolate import pade def test_pade_trivial(): nump, denomp = pade([1.0], 0) assert_array_equal(nump.c, [1.0]) assert_array_equal(denomp.c, [1.0]) nump, denomp = pade([1.0], 0, 0) assert_array_equal(nump.c, [1.0]) assert_array_equal(denomp.c, [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. assert_array_equal(nump_int.c, nump_flt.c) assert_array_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])