dormqr.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 (
	"fmt"
	"testing"

	"golang.org/x/exp/rand"

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

type Dormqrer interface {
	Dorm2rer
	Dormqr(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)
}

func DormqrTest(t *testing.T, impl Dormqrer) {
	rnd := rand.New(rand.NewSource(1))
	for _, side := range []blas.Side{blas.Left, blas.Right} {
		for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
			for _, test := range []struct {
				common, adim, cdim, lda, ldc int
			}{
				{6, 7, 8, 0, 0},
				{6, 8, 7, 0, 0},
				{7, 6, 8, 0, 0},
				{7, 8, 6, 0, 0},
				{8, 6, 7, 0, 0},
				{8, 7, 6, 0, 0},
				{100, 200, 300, 0, 0},
				{100, 300, 200, 0, 0},
				{200, 100, 300, 0, 0},
				{200, 300, 100, 0, 0},
				{300, 100, 200, 0, 0},
				{300, 200, 100, 0, 0},
				{100, 200, 300, 400, 500},
				{100, 300, 200, 400, 500},
				{200, 100, 300, 400, 500},
				{200, 300, 100, 400, 500},
				{300, 100, 200, 400, 500},
				{300, 200, 100, 400, 500},
				{100, 200, 300, 500, 400},
				{100, 300, 200, 500, 400},
				{200, 100, 300, 500, 400},
				{200, 300, 100, 500, 400},
				{300, 100, 200, 500, 400},
				{300, 200, 100, 500, 400},
			} {
				var ma, na, mc, nc int
				if side == blas.Left {
					ma = test.common
					na = test.adim
					mc = test.common
					nc = test.cdim
				} else {
					ma = test.common
					na = test.adim
					mc = test.cdim
					nc = test.common
				}
				// Generate a random matrix
				lda := test.lda
				if lda == 0 {
					lda = na
				}
				a := make([]float64, ma*lda)
				for i := range a {
					a[i] = rnd.Float64()
				}
				// Compute random C matrix
				ldc := test.ldc
				if ldc == 0 {
					ldc = nc
				}
				c := make([]float64, mc*ldc)
				for i := range c {
					c[i] = rnd.Float64()
				}

				// Compute QR
				k := min(ma, na)
				tau := make([]float64, k)
				work := make([]float64, 1)
				impl.Dgeqrf(ma, na, a, lda, tau, work, -1)
				work = make([]float64, int(work[0]))
				impl.Dgeqrf(ma, na, a, lda, tau, work, len(work))

				cCopy := make([]float64, len(c))
				copy(cCopy, c)
				ans := make([]float64, len(c))
				copy(ans, cCopy)

				if side == blas.Left {
					work = make([]float64, nc)
				} else {
					work = make([]float64, mc)
				}
				impl.Dorm2r(side, trans, mc, nc, k, a, lda, tau, ans, ldc, work)

				// Make sure Dorm2r and Dormqr match with small work
				for i := range work {
					work[i] = rnd.Float64()
				}
				copy(c, cCopy)
				impl.Dormqr(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, len(work))
				if !floats.EqualApprox(c, ans, 1e-12) {
					t.Errorf("Dormqr and Dorm2r mismatch for small work")
				}

				// Try with the optimum amount of work
				copy(c, cCopy)
				impl.Dormqr(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, -1)
				work = make([]float64, int(work[0]))
				for i := range work {
					work[i] = rnd.Float64()
				}
				impl.Dormqr(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, len(work))
				if !floats.EqualApprox(c, ans, 1e-12) {
					t.Errorf("Dormqr and Dorm2r mismatch for full work")
					fmt.Println("ccopy")
					for i := 0; i < mc; i++ {
						fmt.Println(cCopy[i*ldc : (i+1)*ldc])
					}
					fmt.Println("ans =")
					for i := 0; i < mc; i++ {
						fmt.Println(ans[i*ldc : (i+1)*ldc])
					}
					fmt.Println("c =")
					for i := 0; i < mc; i++ {
						fmt.Println(c[i*ldc : (i+1)*ldc])
					}
				}

				// Try with amount of work that is less than
				// optimal but still long enough to use the
				// blocked code.
				copy(c, cCopy)
				if side == blas.Left {
					work = make([]float64, 3*nc)
				} else {
					work = make([]float64, 3*mc)
				}
				impl.Dormqr(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, len(work))
				if !floats.EqualApprox(c, ans, 1e-12) {
					t.Errorf("Dormqr and Dorm2r mismatch for medium work")
				}
			}
		}
	}
}