--- /dev/null
+// 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 (
+ "testing"
+
+ "golang.org/x/exp/rand"
+
+ "gonum.org/v1/gonum/blas"
+ "gonum.org/v1/gonum/blas/blas64"
+ "gonum.org/v1/gonum/floats"
+)
+
+type Dgelser interface {
+ Dgels(trans blas.Transpose, m, n, nrhs int, a []float64, lda int, b []float64, ldb int, work []float64, lwork int) bool
+}
+
+func DgelsTest(t *testing.T, impl Dgelser) {
+ rnd := rand.New(rand.NewSource(1))
+ for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+ for _, test := range []struct {
+ m, n, nrhs, lda, ldb int
+ }{
+ {3, 4, 5, 0, 0},
+ {3, 5, 4, 0, 0},
+ {4, 3, 5, 0, 0},
+ {4, 5, 3, 0, 0},
+ {5, 3, 4, 0, 0},
+ {5, 4, 3, 0, 0},
+ {3, 4, 5, 10, 20},
+ {3, 5, 4, 10, 20},
+ {4, 3, 5, 10, 20},
+ {4, 5, 3, 10, 20},
+ {5, 3, 4, 10, 20},
+ {5, 4, 3, 10, 20},
+ {3, 4, 5, 20, 10},
+ {3, 5, 4, 20, 10},
+ {4, 3, 5, 20, 10},
+ {4, 5, 3, 20, 10},
+ {5, 3, 4, 20, 10},
+ {5, 4, 3, 20, 10},
+ {200, 300, 400, 0, 0},
+ {200, 400, 300, 0, 0},
+ {300, 200, 400, 0, 0},
+ {300, 400, 200, 0, 0},
+ {400, 200, 300, 0, 0},
+ {400, 300, 200, 0, 0},
+ {200, 300, 400, 500, 600},
+ {200, 400, 300, 500, 600},
+ {300, 200, 400, 500, 600},
+ {300, 400, 200, 500, 600},
+ {400, 200, 300, 500, 600},
+ {400, 300, 200, 500, 600},
+ {200, 300, 400, 600, 500},
+ {200, 400, 300, 600, 500},
+ {300, 200, 400, 600, 500},
+ {300, 400, 200, 600, 500},
+ {400, 200, 300, 600, 500},
+ {400, 300, 200, 600, 500},
+ } {
+ m := test.m
+ n := test.n
+ nrhs := test.nrhs
+
+ lda := test.lda
+ if lda == 0 {
+ lda = n
+ }
+ a := make([]float64, m*lda)
+ for i := range a {
+ a[i] = rnd.Float64()
+ }
+ aCopy := make([]float64, len(a))
+ copy(aCopy, a)
+
+ // Size of b is the same trans or no trans, because the number of rows
+ // has to be the max of (m,n).
+ mb := max(m, n)
+ nb := nrhs
+ ldb := test.ldb
+ if ldb == 0 {
+ ldb = nb
+ }
+ b := make([]float64, mb*ldb)
+ for i := range b {
+ b[i] = rnd.Float64()
+ }
+ bCopy := make([]float64, len(b))
+ copy(bCopy, b)
+
+ // Find optimal work length.
+ work := make([]float64, 1)
+ impl.Dgels(trans, m, n, nrhs, a, lda, b, ldb, work, -1)
+
+ // Perform linear solve
+ work = make([]float64, int(work[0]))
+ lwork := len(work)
+ for i := range work {
+ work[i] = rnd.Float64()
+ }
+ impl.Dgels(trans, m, n, nrhs, a, lda, b, ldb, work, lwork)
+
+ // Check that the answer is correct by comparing to the normal equations.
+ aMat := blas64.General{
+ Rows: m,
+ Cols: n,
+ Stride: lda,
+ Data: make([]float64, len(aCopy)),
+ }
+ copy(aMat.Data, aCopy)
+ szAta := n
+ if trans == blas.Trans {
+ szAta = m
+ }
+ aTA := blas64.General{
+ Rows: szAta,
+ Cols: szAta,
+ Stride: szAta,
+ Data: make([]float64, szAta*szAta),
+ }
+
+ // Compute A^T * A if notrans and A * A^T otherwise.
+ if trans == blas.NoTrans {
+ blas64.Gemm(blas.Trans, blas.NoTrans, 1, aMat, aMat, 0, aTA)
+ } else {
+ blas64.Gemm(blas.NoTrans, blas.Trans, 1, aMat, aMat, 0, aTA)
+ }
+
+ // Multiply by X.
+ X := blas64.General{
+ Rows: szAta,
+ Cols: nrhs,
+ Stride: ldb,
+ Data: b,
+ }
+ ans := blas64.General{
+ Rows: aTA.Rows,
+ Cols: X.Cols,
+ Stride: X.Cols,
+ Data: make([]float64, aTA.Rows*X.Cols),
+ }
+ blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aTA, X, 0, ans)
+
+ B := blas64.General{
+ Rows: szAta,
+ Cols: nrhs,
+ Stride: ldb,
+ Data: make([]float64, len(bCopy)),
+ }
+
+ copy(B.Data, bCopy)
+ var ans2 blas64.General
+ if trans == blas.NoTrans {
+ ans2 = blas64.General{
+ Rows: aMat.Cols,
+ Cols: B.Cols,
+ Stride: B.Cols,
+ Data: make([]float64, aMat.Cols*B.Cols),
+ }
+ } else {
+ ans2 = blas64.General{
+ Rows: aMat.Rows,
+ Cols: B.Cols,
+ Stride: B.Cols,
+ Data: make([]float64, aMat.Rows*B.Cols),
+ }
+ }
+
+ // Compute A^T B if Trans or A * B otherwise
+ if trans == blas.NoTrans {
+ blas64.Gemm(blas.Trans, blas.NoTrans, 1, aMat, B, 0, ans2)
+ } else {
+ blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aMat, B, 0, ans2)
+ }
+ if !floats.EqualApprox(ans.Data, ans2.Data, 1e-12) {
+ t.Errorf("Normal equations not satisfied")
+ }
+ }
+ }
+}
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