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Exponentially scaled modified Bessel functions of order zero and one.

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The functions are conventionally called i0e and i1e. The exponentially scaled version is more numerically stable. The standard Bessel functions can be obtained as i0(x) = exp(|x|) i0e(x)

The code is ported from Cephes and tested against SciPy.
This commit is contained in:
Michael Figurnov
2018-05-31 15:34:53 +01:00
parent 6af1433cb5
commit f216854453
12 changed files with 731 additions and 0 deletions
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40
unsupported/test/special_functions.cpp
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@@ -335,6 +335,46 @@ template<typename ArrayType> void array_special_functions()
ArrayType test = betainc(a, b + one, x) + eps;
verify_component_wise(test, expected););
}
// Test Bessel function i0e. Reference results obtained with SciPy.
{
ArrayType x(21);
ArrayType expected(21);
ArrayType res(21);
x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
expected << 0.0897803118848, 0.0947062952128, 0.100544127361,
0.107615251671, 0.116426221213, 0.127833337163, 0.143431781857,
0.16665743264, 0.207001921224, 0.308508322554, 1.0, 0.308508322554,
0.207001921224, 0.16665743264, 0.143431781857, 0.127833337163,
0.116426221213, 0.107615251671, 0.100544127361, 0.0947062952128,
0.0897803118848;
CALL_SUBTEST(res = i0e(x);
verify_component_wise(res, expected););
}
// Test Bessel function i1e. Reference results obtained with SciPy.
{
ArrayType x(21);
ArrayType expected(21);
ArrayType res(21);
x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
expected << -0.0875062221833, -0.092036796872, -0.0973496147565,
-0.103697667463, -0.11146429929, -0.121262681384, -0.134142493293,
-0.152051459309, -0.178750839502, -0.215269289249, 0.0, 0.215269289249,
0.178750839502, 0.152051459309, 0.134142493293, 0.121262681384,
0.11146429929, 0.103697667463, 0.0973496147565, 0.092036796872,
0.0875062221833;
CALL_SUBTEST(res = i1e(x);
verify_component_wise(res, expected););
}
#endif
}