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go/test/hilbert.go

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// $G $D/$F.go && $L $F.$A && ./$A.out
// 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 for rational arithmetics.
// Computes a Hilbert matrix, its inverse, multiplies them
// and verifies that the product is the identity matrix.
package main
import Big "bignum"
import Fmt "fmt"
func assert(p bool) {
if !p {
panic("assert failed");
}
}
var (
Zero = Big.Rat(0, 1);
One = Big.Rat(1, 1);
)
type Matrix struct {
n, m int;
a *[]*Big.Rational;
}
func (a *Matrix) at(i, j int) *Big.Rational {
assert(0 <= i && i < a.n && 0 <= j && j < a.m);
return a.a[i*a.m + j];
}
func (a *Matrix) set(i, j int, x *Big.Rational) {
assert(0 <= i && i < a.n && 0 <= j && j < a.m);
a.a[i*a.m + j] = x;
}
func NewMatrix(n, m int) *Matrix {
assert(0 <= n && 0 <= m);
a := new(Matrix);
a.n = n;
a.m = m;
a.a = new([]*Big.Rational, 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 := Zero;
if i == j {
x = One;
}
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++ {
x := Big.Rat(1, i + j + 1);
a.set(i, j, x);
}
}
return a;
}
func MakeRat(x *Big.Natural) *Big.Rational {
return Big.MakeRat(Big.MakeInt(false, x), Big.Nat(1));
}
func NewInverseHilbert(n int) *Matrix {
a := NewMatrix(n, n);
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
x0 := One;
if (i+j)&1 != 0 {
x0 = x0.Neg();
}
x1 := Big.Rat(i + j + 1, 1);
x2 := MakeRat(Big.Binomial(uint(n+i), uint(n-j-1)));
x3 := MakeRat(Big.Binomial(uint(n+j), uint(n-i-1)));
x4 := MakeRat(Big.Binomial(uint(i+j), uint(i)));
x4 = x4.Mul(x4);
a.set(i, j, x0.Mul(x1).Mul(x2).Mul(x3).Mul(x4));
}
}
return a;
}
func (a *Matrix) Mul(b *Matrix) *Matrix {
assert(a.m == b.n);
c := NewMatrix(a.n, b.m);
for i := 0; i < c.n; i++ {
for j := 0; j < c.m; j++ {
x := Zero;
for k := 0; k < a.m; k++ {
x = x.Add(a.at(i, k).Mul(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++ {
x := a.at(i, j); // BUG 6g bug
s += Fmt.sprintf("\t%s", x);
}
s += "\n";
}
return s;
}
func main() {
n := 10;
a := NewHilbert(n);
b := NewInverseHilbert(n);
I := NewUnit(n);
ab := a.Mul(b);
if !ab.Eql(I) {
Fmt.println("a =", a);
Fmt.println("b =", b);
Fmt.println("a*b =", ab);
Fmt.println("I =", I);
panic("FAILED");
}
}