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94 lines
2.8 KiB
Go
94 lines
2.8 KiB
Go
// Copyright ©2025 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package mathext
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import (
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"math"
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"math/cmplx"
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"testing"
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"gonum.org/v1/gonum/cmplxs/cscalar"
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)
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func TestDiLogValues(t *testing.T) {
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t.Parallel()
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const tol = 1e-12
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for _, test := range []struct {
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in, want complex128
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}{
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// Reference values were generated using Python's scipy.special.spence
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// (where Li2(z) = spence(1 - z)) and verified with a computer algebra system.
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// well known values
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{in: 0, want: 0},
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{in: 1, want: math.Pi * math.Pi / 6},
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{in: -1, want: -math.Pi * math.Pi / 12},
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{in: 0.5, want: math.Pi*math.Pi/12 - math.Ln2*math.Ln2/2},
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{in: 2, want: complex(math.Pi*math.Pi/4, -math.Pi*math.Ln2)},
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// abs(z) < 0.5
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{in: 0.1 + 0.1i, want: 0.099751196798713 + 0.105220383905600i},
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{in: -0.3 + 0.39i, want: -0.306174046754339 + 0.337550668621259i},
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{in: 0.001 - 0.49i, want: -0.055831393285929 - 0.478156430372353i},
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// 0.5 < abs(z) < 1
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{in: -0.9999 + 0.001i, want: -0.8223978143206974 + 0.0006931664732411i},
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{in: 0.5 + 0.7i, want: 0.359364350522653 + 0.856767712327590i},
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{in: complex(math.Pi/4, -math.Pi/7), want: 0.828086461155377 - 0.739345385309341i},
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{in: -0.8 - 0.0001i, want: -0.679781588954542 - 0.000073473333084i},
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// abs(z) > 1
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{in: -1.1 + 0.1i, want: -0.8917388814454027 + 0.0674285967726009i},
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{in: 5 + 0i, want: 1.783719161266631 - 5.056198322111862i},
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{in: -10 + 0i, want: -4.198277886858104 + 0i},
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{in: 1000 + 10000i, want: -42.71073756884990 + 15.39396088869304i},
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{in: -1791.91931 + 0.5i, want: -29.70223568904652 + 0.00209038439188i},
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} {
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got := Li2(test.in)
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diff := cmplx.Abs(got - test.want)
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if cmplx.Abs(test.want) != 0 {
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if !cscalar.EqualWithinRel(got, test.want, tol) {
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t.Errorf("Li2(%g) relative error %g exceeds tol %g", test.in, diff/cmplx.Abs(test.want), tol)
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}
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} else if !cscalar.EqualWithinAbs(got, test.want, tol) {
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t.Errorf("Li2(%g) abs error %g exceeds tol %g", test.in, diff, tol)
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}
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}
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}
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func TestDiLogProperties(t *testing.T) {
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t.Parallel()
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const tol = 1e-12
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// Duplication formula: Li2(z^2) = 2*(Li2(z) + Li2(-z))
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for i, z := range []complex128{
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0.1 + 0.1i,
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-0.3 + 0.4i,
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0.5,
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200,
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} {
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lhs := Li2(z * z)
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rhs := 2 * (Li2(z) + Li2(-z))
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if !cscalar.EqualWithinAbs(lhs, rhs, tol) {
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t.Errorf("duplication formula failed for case %d, z=%v: got %v want %v", i, z, lhs, rhs)
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}
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}
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// Conjugation symmetry: Li2(conj(z)) == conj(Li2(z))
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// Valid for all z not on the branch cut (real z > 1).
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for i, z := range []complex128{
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0.3 + 0.5i,
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-0.8 + 0.1i,
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2 + 0.7i,
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} {
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lhs := Li2(cmplx.Conj(z))
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rhs := cmplx.Conj(Li2(z))
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if !cscalar.EqualWithinAbs(lhs, rhs, tol) {
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t.Errorf("conjugation symmetry failed for case %d, z=%v: got %v want %v", i, z, lhs, rhs)
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}
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}
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}
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