lapack/testlapack/dorgtr.go

// Copyright ©2016 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/blas/blas64"
	"gonum.org/v1/gonum/floats"
)

type Dorgtrer interface {
	Dorgtr(uplo blas.Uplo, n int, a []float64, lda int, tau, work []float64, lwork int)
	Dsytrder
}

func DorgtrTest(t *testing.T, impl Dorgtrer) {
	const tol = 1e-14

	rnd := rand.New(rand.NewSource(1))
	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
		for _, wl := range []worklen{minimumWork, mediumWork, optimumWork} {
			for _, test := range []struct {
				n, lda int
			}{
				{1, 0},
				{2, 0},
				{3, 0},
				{6, 0},
				{33, 0},
				{100, 0},

				{1, 3},
				{2, 5},
				{3, 7},
				{6, 10},
				{33, 50},
				{100, 120},
			} {
				n := test.n
				lda := test.lda
				if lda == 0 {
					lda = n
				}
				// Allocate n×n matrix A and fill it with random numbers.
				a := make([]float64, n*lda)
				for i := range a {
					a[i] = rnd.NormFloat64()
				}
				aCopy := make([]float64, len(a))
				copy(aCopy, a)

				// Allocate slices for the main diagonal and the
				// first off-diagonal of the tri-diagonal matrix.
				d := make([]float64, n)
				e := make([]float64, n-1)
				// Allocate slice for elementary reflector scales.
				tau := make([]float64, n-1)

				// Compute optimum workspace size for Dorgtr call.
				work := make([]float64, 1)
				impl.Dsytrd(uplo, n, a, lda, d, e, tau, work, -1)
				work = make([]float64, int(work[0]))

				// Compute elementary reflectors that reduce the
				// symmetric matrix defined by the uplo triangle
				// of A to a tridiagonal matrix.
				impl.Dsytrd(uplo, n, a, lda, d, e, tau, work, len(work))

				// Compute workspace size for Dorgtr call.
				var lwork int
				switch wl {
				case minimumWork:
					lwork = max(1, n-1)
				case mediumWork:
					work := make([]float64, 1)
					impl.Dorgtr(uplo, n, a, lda, tau, work, -1)
					lwork = (int(work[0]) + n - 1) / 2
					lwork = max(1, lwork)
				case optimumWork:
					work := make([]float64, 1)
					impl.Dorgtr(uplo, n, a, lda, tau, work, -1)
					lwork = int(work[0])
				}
				work = nanSlice(lwork)

				// Generate an orthogonal matrix Q that reduces
				// the uplo triangle of A to a tridiagonal matrix.
				impl.Dorgtr(uplo, n, a, lda, tau, work, len(work))
				q := blas64.General{
					Rows:   n,
					Cols:   n,
					Stride: lda,
					Data:   a,
				}

				name := fmt.Sprintf("uplo=%c,n=%v,lda=%v,work=%v", uplo, n, lda, wl)

				if resid := residualOrthogonal(q, false); resid > tol*float64(n) {
					t.Errorf("Case %v: Q is not orthogonal; resid=%v, want<=%v", name, resid, tol*float64(n))
				}

				// Create the tridiagonal matrix explicitly in
				// dense representation from the diagonals d and e.
				tri := blas64.General{
					Rows:   n,
					Cols:   n,
					Stride: n,
					Data:   make([]float64, n*n),
				}
				for i := 0; i < n; i++ {
					tri.Data[i*tri.Stride+i] = d[i]
					if i != n-1 {
						tri.Data[i*tri.Stride+i+1] = e[i]
						tri.Data[(i+1)*tri.Stride+i] = e[i]
					}
				}

				// Create the symmetric matrix A from the uplo
				// triangle of aCopy, storing it explicitly in dense form.
				aMat := blas64.General{
					Rows:   n,
					Cols:   n,
					Stride: n,
					Data:   make([]float64, n*n),
				}
				if uplo == blas.Upper {
					for i := 0; i < n; i++ {
						for j := i; j < n; j++ {
							v := aCopy[i*lda+j]
							aMat.Data[i*aMat.Stride+j] = v
							aMat.Data[j*aMat.Stride+i] = v
						}
					}
				} else {
					for i := 0; i < n; i++ {
						for j := 0; j <= i; j++ {
							v := aCopy[i*lda+j]
							aMat.Data[i*aMat.Stride+j] = v
							aMat.Data[j*aMat.Stride+i] = v
						}
					}
				}

				// Compute Qᵀ * A * Q and store the result in ans.
				tmp := blas64.General{Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n)}
				blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aMat, q, 0, tmp)
				ans := blas64.General{Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n)}
				blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, tmp, 0, ans)

				// Compare the tridiagonal matrix tri from
				// Dorgtr with the explicit computation ans.
				if !floats.EqualApprox(ans.Data, tri.Data, tol) {
					t.Errorf("Case %v: Recombination mismatch", name)
				}
			}
		}
	}
}