--- /dev/null
+// Copyright ©2013 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat
+
+import (
+ "testing"
+
+ "golang.org/x/exp/rand"
+)
+
+func TestLQ(t *testing.T) {
+ for _, test := range []struct {
+ m, n int
+ }{
+ {5, 5},
+ {5, 10},
+ } {
+ m := test.m
+ n := test.n
+ a := NewDense(m, n, nil)
+ for i := 0; i < m; i++ {
+ for j := 0; j < n; j++ {
+ a.Set(i, j, rand.NormFloat64())
+ }
+ }
+ var want Dense
+ want.Clone(a)
+
+ var lq LQ
+ lq.Factorize(a)
+ q := lq.QTo(nil)
+
+ if !isOrthonormal(q, 1e-10) {
+ t.Errorf("Q is not orthonormal: m = %v, n = %v", m, n)
+ }
+
+ l := lq.LTo(nil)
+
+ var got Dense
+ got.Mul(l, q)
+ if !EqualApprox(&got, &want, 1e-12) {
+ t.Errorf("LQ does not equal original matrix. \nWant: %v\nGot: %v", want, got)
+ }
+ }
+}
+
+func TestSolveLQ(t *testing.T) {
+ for _, trans := range []bool{false, true} {
+ for _, test := range []struct {
+ m, n, bc int
+ }{
+ {5, 5, 1},
+ {5, 10, 1},
+ {5, 5, 3},
+ {5, 10, 3},
+ } {
+ m := test.m
+ n := test.n
+ bc := test.bc
+ a := NewDense(m, n, nil)
+ for i := 0; i < m; i++ {
+ for j := 0; j < n; j++ {
+ a.Set(i, j, rand.Float64())
+ }
+ }
+ br := m
+ if trans {
+ br = n
+ }
+ b := NewDense(br, bc, nil)
+ for i := 0; i < br; i++ {
+ for j := 0; j < bc; j++ {
+ b.Set(i, j, rand.Float64())
+ }
+ }
+ var x Dense
+ lq := &LQ{}
+ lq.Factorize(a)
+ lq.Solve(&x, trans, b)
+
+ // Test that the normal equations hold.
+ // A^T * A * x = A^T * b if !trans
+ // A * A^T * x = A * b if trans
+ var lhs Dense
+ var rhs Dense
+ if trans {
+ var tmp Dense
+ tmp.Mul(a, a.T())
+ lhs.Mul(&tmp, &x)
+ rhs.Mul(a, b)
+ } else {
+ var tmp Dense
+ tmp.Mul(a.T(), a)
+ lhs.Mul(&tmp, &x)
+ rhs.Mul(a.T(), b)
+ }
+ if !EqualApprox(&lhs, &rhs, 1e-10) {
+ t.Errorf("Normal equations do not hold.\nLHS: %v\n, RHS: %v\n", lhs, rhs)
+ }
+ }
+ }
+ // TODO(btracey): Add in testOneInput when it exists.
+}
+
+func TestSolveLQVec(t *testing.T) {
+ for _, trans := range []bool{false, true} {
+ for _, test := range []struct {
+ m, n int
+ }{
+ {5, 5},
+ {5, 10},
+ } {
+ m := test.m
+ n := test.n
+ a := NewDense(m, n, nil)
+ for i := 0; i < m; i++ {
+ for j := 0; j < n; j++ {
+ a.Set(i, j, rand.Float64())
+ }
+ }
+ br := m
+ if trans {
+ br = n
+ }
+ b := NewVecDense(br, nil)
+ for i := 0; i < br; i++ {
+ b.SetVec(i, rand.Float64())
+ }
+ var x VecDense
+ lq := &LQ{}
+ lq.Factorize(a)
+ lq.SolveVec(&x, trans, b)
+
+ // Test that the normal equations hold.
+ // A^T * A * x = A^T * b if !trans
+ // A * A^T * x = A * b if trans
+ var lhs Dense
+ var rhs Dense
+ if trans {
+ var tmp Dense
+ tmp.Mul(a, a.T())
+ lhs.Mul(&tmp, &x)
+ rhs.Mul(a, b)
+ } else {
+ var tmp Dense
+ tmp.Mul(a.T(), a)
+ lhs.Mul(&tmp, &x)
+ rhs.Mul(a.T(), b)
+ }
+ if !EqualApprox(&lhs, &rhs, 1e-10) {
+ t.Errorf("Normal equations do not hold.\nLHS: %v\n, RHS: %v\n", lhs, rhs)
+ }
+ }
+ }
+ // TODO(btracey): Add in testOneInput when it exists.
+}
+
+func TestSolveLQCond(t *testing.T) {
+ for _, test := range []*Dense{
+ NewDense(2, 2, []float64{1, 0, 0, 1e-20}),
+ NewDense(2, 3, []float64{1, 0, 0, 0, 1e-20, 0}),
+ } {
+ m, _ := test.Dims()
+ var lq LQ
+ lq.Factorize(test)
+ b := NewDense(m, 2, nil)
+ var x Dense
+ if err := lq.Solve(&x, false, b); err == nil {
+ t.Error("No error for near-singular matrix in matrix solve.")
+ }
+
+ bvec := NewVecDense(m, nil)
+ var xvec VecDense
+ if err := lq.SolveVec(&xvec, false, bvec); err == nil {
+ t.Error("No error for near-singular matrix in matrix solve.")
+ }
+ }
+}
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