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// 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) {
t.Parallel()
const tol = 1e-14
rnd := rand.New(rand.NewSource(1))
for cas, 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, rnd.NormFloat64())
}
}
var want Dense
want.CloneFrom(a)
var lq LQ
lq.Factorize(a)
if !EqualApprox(a, &lq, tol) {
t.Errorf("case %d: A and LQ are not equal", cas)
}
var l, q Dense
lq.QTo(&q)
if !isOrthonormal(&q, tol) {
t.Errorf("Q is not orthonormal: m = %v, n = %v", m, n)
}
lq.LTo(&l)
var got Dense
got.Mul(&l, &q)
if !EqualApprox(&got, &want, tol) {
t.Errorf("LQ does not equal original matrix. \nWant: %v\nGot: %v", want, got)
}
}
}
func TestLQSolveTo(t *testing.T) {
t.Parallel()
rnd := rand.New(rand.NewSource(1))
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, rnd.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, rnd.Float64())
}
}
var x Dense
lq := &LQ{}
lq.Factorize(a)
err := lq.SolveTo(&x, trans, b)
if err != nil {
t.Errorf("unexpected error from LQ solve: %v", err)
}
// Test that the normal equations hold.
// Aᵀ * A * x = Aᵀ * b if !trans
// A * Aᵀ * 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 TestLQSolveToVec(t *testing.T) {
t.Parallel()
rnd := rand.New(rand.NewSource(1))
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, rnd.Float64())
}
}
br := m
if trans {
br = n
}
b := NewVecDense(br, nil)
for i := 0; i < br; i++ {
b.SetVec(i, rnd.Float64())
}
var x VecDense
lq := &LQ{}
lq.Factorize(a)
err := lq.SolveVecTo(&x, trans, b)
if err != nil {
t.Errorf("unexpected error from LQ solve: %v", err)
}
// Test that the normal equations hold.
// Aᵀ * A * x = Aᵀ * b if !trans
// A * Aᵀ * 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 TestLQSolveToCond(t *testing.T) {
t.Parallel()
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.SolveTo(&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.SolveVecTo(&xvec, false, bvec); err == nil {
t.Error("No error for near-singular matrix in matrix solve.")
}
}
}
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