2 files changed, 103 insertions(+), 0 deletions(-)

A linalg.go
A linalg_test.go

@@ 0,0 1,67 @@
+package main
+
+import (
+	"math/big"
+)
+
+type Matrix [][]big.Rat
+
+func (M Matrix) RREF() {
+	lead := 0
+	rowCount := len(M)
+	if rowCount == 0 {
+		return
+	}
+	columnCount := len(M[0])
+	zero := big.NewRat(0, 1)
+
+	for r := 0; r < rowCount; r++ {
+		if lead >= columnCount {
+			return
+		}
+		i := r
+		for M[i][lead].Cmp(zero) == 0 {
+			i++
+			if rowCount == i {
+				i = r
+				lead++
+				if columnCount == lead {
+					return
+				}
+			}
+		}
+		M[i], M[r] = M[r], M[i]
+		f := &big.Rat{}
+		f.Inv(&M[r][lead])
+		for j := range M[r] {
+			M[r][j].Mul(&M[r][j], f)
+		}
+		for i = 0; i < rowCount; i++ {
+			if i != r {
+				f.Set(&M[i][lead])
+				for j, e := range M[r] {
+					M[i][j].Sub(&M[i][j], new(big.Rat).Mul(&e, f))
+				}
+			}
+		}
+		lead++
+	}
+}
+
+// assumes `M' and `other' are valid matrices
+func (M Matrix) Equals(other Matrix) bool {
+	if len(M) != len(other) {
+		return false
+	}
+	if len(M) > 0 && len(M[0]) != len(other[0]) {
+		return false
+	}
+	for r := range M {
+		for c := range M[r] {
+			if M[r][c].Cmp(&other[r][c]) != 0 {
+				return false
+			}
+		}
+	}
+	return true
+}

@@ 0,0 1,36 @@
+package main
+
+import (
+	"math/big"
+	"testing"
+)
+
+func TestRREF(t *testing.T) {
+	mat := Matrix{
+		{*big.NewRat( 1, 1), *big.NewRat(2, 1), *big.NewRat(-1, 1), *big.NewRat( -4, 1)},
+		{*big.NewRat( 2, 1), *big.NewRat(3, 1), *big.NewRat(-1, 1), *big.NewRat(-11, 1)},
+		{*big.NewRat(-2, 1), *big.NewRat(0, 1), *big.NewRat(-3, 1), *big.NewRat( 22, 1)},
+	}
+	mat.RREF()
+	result := Matrix{
+		{*big.NewRat(1, 1), *big.NewRat(0, 1), *big.NewRat(0, 1), *big.NewRat(-8, 1)},
+		{*big.NewRat(0, 1), *big.NewRat(1, 1), *big.NewRat(0, 1), *big.NewRat( 1, 1)},
+		{*big.NewRat(0, 1), *big.NewRat(0, 1), *big.NewRat(1, 1), *big.NewRat(-2, 1)},
+	}
+	if !mat.Equals(result) {
+		t.Fail()
+	}
+
+	mat = Matrix{
+		{*big.NewRat(1, 1), *big.NewRat(3, 1), *big.NewRat(-1, 1)},
+		{*big.NewRat(0, 1), *big.NewRat(1, 1),  *big.NewRat(7, 1)},
+	}
+	mat.RREF()
+	result = Matrix{
+		{*big.NewRat(1, 1), *big.NewRat(0, 1), *big.NewRat(-22, 1)},
+		{*big.NewRat(0, 1), *big.NewRat(1, 1), *big.NewRat(  7, 1)},
+	}
+	if !mat.Equals(result) {
+		t.Fail()
+	}
+}