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author | Daniel Baumann <daniel.baumann@progress-linux.org> | 2024-04-16 19:23:18 +0000 |
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committer | Daniel Baumann <daniel.baumann@progress-linux.org> | 2024-04-16 19:23:18 +0000 |
commit | 43a123c1ae6613b3efeed291fa552ecd909d3acf (patch) | |
tree | fd92518b7024bc74031f78a1cf9e454b65e73665 /src/math/big/hilbert_test.go | |
parent | Initial commit. (diff) | |
download | golang-1.20-upstream.tar.xz golang-1.20-upstream.zip |
Adding upstream version 1.20.14.upstream/1.20.14upstream
Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>
Diffstat (limited to 'src/math/big/hilbert_test.go')
-rw-r--r-- | src/math/big/hilbert_test.go | 160 |
1 files changed, 160 insertions, 0 deletions
diff --git a/src/math/big/hilbert_test.go b/src/math/big/hilbert_test.go new file mode 100644 index 0000000..1a84341 --- /dev/null +++ b/src/math/big/hilbert_test.go @@ -0,0 +1,160 @@ +// Copyright 2009 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// A little test program and benchmark for rational arithmetics. +// Computes a Hilbert matrix, its inverse, multiplies them +// and verifies that the product is the identity matrix. + +package big + +import ( + "fmt" + "testing" +) + +type matrix struct { + n, m int + a []*Rat +} + +func (a *matrix) at(i, j int) *Rat { + if !(0 <= i && i < a.n && 0 <= j && j < a.m) { + panic("index out of range") + } + return a.a[i*a.m+j] +} + +func (a *matrix) set(i, j int, x *Rat) { + if !(0 <= i && i < a.n && 0 <= j && j < a.m) { + panic("index out of range") + } + a.a[i*a.m+j] = x +} + +func newMatrix(n, m int) *matrix { + if !(0 <= n && 0 <= m) { + panic("illegal matrix") + } + a := new(matrix) + a.n = n + a.m = m + a.a = make([]*Rat, n*m) + return a +} + +func newUnit(n int) *matrix { + a := newMatrix(n, n) + for i := 0; i < n; i++ { + for j := 0; j < n; j++ { + x := NewRat(0, 1) + if i == j { + x.SetInt64(1) + } + a.set(i, j, x) + } + } + return a +} + +func newHilbert(n int) *matrix { + a := newMatrix(n, n) + for i := 0; i < n; i++ { + for j := 0; j < n; j++ { + a.set(i, j, NewRat(1, int64(i+j+1))) + } + } + return a +} + +func newInverseHilbert(n int) *matrix { + a := newMatrix(n, n) + for i := 0; i < n; i++ { + for j := 0; j < n; j++ { + x1 := new(Rat).SetInt64(int64(i + j + 1)) + x2 := new(Rat).SetInt(new(Int).Binomial(int64(n+i), int64(n-j-1))) + x3 := new(Rat).SetInt(new(Int).Binomial(int64(n+j), int64(n-i-1))) + x4 := new(Rat).SetInt(new(Int).Binomial(int64(i+j), int64(i))) + + x1.Mul(x1, x2) + x1.Mul(x1, x3) + x1.Mul(x1, x4) + x1.Mul(x1, x4) + + if (i+j)&1 != 0 { + x1.Neg(x1) + } + + a.set(i, j, x1) + } + } + return a +} + +func (a *matrix) mul(b *matrix) *matrix { + if a.m != b.n { + panic("illegal matrix multiply") + } + c := newMatrix(a.n, b.m) + for i := 0; i < c.n; i++ { + for j := 0; j < c.m; j++ { + x := NewRat(0, 1) + for k := 0; k < a.m; k++ { + x.Add(x, new(Rat).Mul(a.at(i, k), b.at(k, j))) + } + c.set(i, j, x) + } + } + return c +} + +func (a *matrix) eql(b *matrix) bool { + if a.n != b.n || a.m != b.m { + return false + } + for i := 0; i < a.n; i++ { + for j := 0; j < a.m; j++ { + if a.at(i, j).Cmp(b.at(i, j)) != 0 { + return false + } + } + } + return true +} + +func (a *matrix) String() string { + s := "" + for i := 0; i < a.n; i++ { + for j := 0; j < a.m; j++ { + s += fmt.Sprintf("\t%s", a.at(i, j)) + } + s += "\n" + } + return s +} + +func doHilbert(t *testing.T, n int) { + a := newHilbert(n) + b := newInverseHilbert(n) + I := newUnit(n) + ab := a.mul(b) + if !ab.eql(I) { + if t == nil { + panic("Hilbert failed") + } + t.Errorf("a = %s\n", a) + t.Errorf("b = %s\n", b) + t.Errorf("a*b = %s\n", ab) + t.Errorf("I = %s\n", I) + } +} + +func TestHilbert(t *testing.T) { + doHilbert(t, 10) +} + +func BenchmarkHilbert(b *testing.B) { + for i := 0; i < b.N; i++ { + doHilbert(nil, 10) + } +} |