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// 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)
}
}