lapack/testlapack/dgerqf.go

// Copyright ©2015 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 testlapack

import (
	"math"
	"math/rand"
	"testing"

	"gonum.org/v1/gonum/blas"
	"gonum.org/v1/gonum/blas/blas64"
)

type Dgerqfer interface {
	Dgerqf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
}

func DgerqfTest(t *testing.T, impl Dgerqfer) {
	const tol = 1e-13

	rnd := rand.New(rand.NewSource(1))
	for c, test := range []struct {
		m, n, lda int
	}{
		{1, 1, 0},
		{2, 2, 0},
		{3, 2, 0},
		{2, 3, 0},
		{1, 12, 0},
		{2, 6, 0},
		{3, 4, 0},
		{4, 3, 0},
		{6, 2, 0},
		{12, 1, 0},
		{200, 180, 0},
		{180, 200, 0},
		{200, 200, 0},
		{1, 1, 20},
		{2, 2, 20},
		{3, 2, 20},
		{2, 3, 20},
		{1, 12, 20},
		{2, 6, 20},
		{3, 4, 20},
		{4, 3, 20},
		{6, 2, 20},
		{12, 1, 20},
		{200, 180, 220},
		{180, 200, 220},
		{200, 200, 220},
	} {
		n := test.n
		m := test.m
		lda := test.lda
		if lda == 0 {
			lda = test.n
		}
		a := make([]float64, m*lda)
		for i := range a {
			a[i] = rnd.Float64()
		}
		aCopy := make([]float64, len(a))
		copy(aCopy, a)
		k := min(m, n)
		tau := make([]float64, k)
		for i := range tau {
			tau[i] = rnd.Float64()
		}
		work := []float64{0}
		impl.Dgerqf(m, n, a, lda, tau, work, -1)
		lwkopt := int(work[0])
		for _, wk := range []struct {
			name   string
			length int
		}{
			{name: "short", length: m},
			{name: "medium", length: lwkopt - 1},
			{name: "long", length: lwkopt},
		} {
			if wk.length < max(1, m) {
				continue
			}
			lwork := wk.length
			work = make([]float64, lwork)
			for i := range work {
				work[i] = rnd.Float64()
			}
			copy(a, aCopy)
			impl.Dgerqf(m, n, a, lda, tau, work, lwork)

			// Test that the RQ factorization has completed successfully. Compute
			// Q based on the vectors.
			q := constructQ("RQ", m, n, a, lda, tau)

			// Check that q is orthonormal
			for i := 0; i < q.Rows; i++ {
				nrm := blas64.Nrm2(q.Cols, blas64.Vector{Inc: 1, Data: q.Data[i*q.Stride:]})
				if math.IsNaN(nrm) || math.Abs(nrm-1) > 1e-14 {
					t.Errorf("Case %v, q not normal", c)
				}
				for j := 0; j < i; j++ {
					dot := blas64.Dot(q.Cols, blas64.Vector{Inc: 1, Data: q.Data[i*q.Stride:]}, blas64.Vector{Inc: 1, Data: q.Data[j*q.Stride:]})
					if math.IsNaN(dot) || math.Abs(dot) > 1e-14 {
						t.Errorf("Case %v, q not orthogonal", c)
					}
				}
			}
			// Check that A = R * Q
			r := blas64.General{
				Rows:   m,
				Cols:   n,
				Stride: n,
				Data:   make([]float64, m*n),
			}
			for i := 0; i < m; i++ {
				off := m - n
				for j := max(0, i-off); j < n; j++ {
					r.Data[i*r.Stride+j] = a[i*lda+j]
				}
			}

			got := blas64.General{
				Rows:   m,
				Cols:   n,
				Stride: lda,
				Data:   make([]float64, m*lda),
			}
			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, r, q, 0, got)
			want := blas64.General{
				Rows:   m,
				Cols:   n,
				Stride: lda,
				Data:   aCopy,
			}
			if !equalApproxGeneral(got, want, tol) {
				t.Errorf("Case %d, R*Q != a %s\ngot: %+v\nwant:%+v", c, wk.name, got, want)
			}
		}
	}
}