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lapack/testlapack: extend test for Dlasy2 to cover rescaling
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@vladimir-ch
vladimir-ch committed Jun 15, 2021
1 parent e102cf2 commit 7fe5bb7
Showing 1 changed file with 59 additions and 40 deletions.
99 changes: 59 additions & 40 deletions lapack/testlapack/dlasy2.go
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Original file line number Diff line number Diff line change
Expand Up @@ -6,13 +6,13 @@ package testlapack

import (
"fmt"
"math"
"testing"

"golang.org/x/exp/rand"

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

type Dlasy2er interface {
Expand All @@ -26,9 +26,13 @@ func Dlasy2Test(t *testing.T, impl Dlasy2er) {
for _, isgn := range []int{1, -1} {
for _, n1 := range []int{0, 1, 2} {
for _, n2 := range []int{0, 1, 2} {
for _, extra := range []int{0, 1, 2, 13} {
for cas := 0; cas < 1000; cas++ {
testDlasy2(t, impl, tranl, tranr, isgn, n1, n2, extra, rnd)
for _, extra := range []int{0, 3} {
for cas := 0; cas < 100; cas++ {
var big bool
if cas%2 == 0 {
big = true
}
testDlasy2(t, impl, tranl, tranr, isgn, n1, n2, extra, big, rnd)
}
}
}
Expand All @@ -38,68 +42,83 @@ func Dlasy2Test(t *testing.T, impl Dlasy2er) {
}
}

func testDlasy2(t *testing.T, impl Dlasy2er, tranl, tranr bool, isgn, n1, n2, extra int, rnd *rand.Rand) {
const tol = 1e-10
func testDlasy2(t *testing.T, impl Dlasy2er, tranl, tranr bool, isgn, n1, n2, extra int, big bool, rnd *rand.Rand) {
const tol = 1e-14

name := fmt.Sprintf("Case n1=%v, n2=%v, isgn=%v, big=%v", n1, n2, isgn, big)

tl := randomGeneral(n1, n1, n1+extra, rnd)
tr := randomGeneral(n2, n2, n2+extra, rnd)
b := randomGeneral(n1, n2, n2+extra, rnd)
x := randomGeneral(n1, n2, n2+extra, rnd)
b := randomGeneral(n1, n2, n2+extra, rnd)
if big {
for i := 0; i < n1; i++ {
for j := 0; j < n2; j++ {
b.Data[i*b.Stride+j] *= bignum
}
}
}

tlCopy := cloneGeneral(tl)
trCopy := cloneGeneral(tr)
bCopy := cloneGeneral(b)

scale, xnorm, ok := impl.Dlasy2(tranl, tranr, isgn, n1, n2, tl.Data, tl.Stride, tr.Data, tr.Stride, b.Data, b.Stride, x.Data, x.Stride)
if scale > 1 {
t.Errorf("invalid value of scale, want <= 1, got %v", scale)

// Check any invalid modifications in read-only input.
if !equalGeneral(tl, tlCopy) {
t.Errorf("%v: unexpected modification in TL", name)
}
if n1 == 0 || n2 == 0 {
return
if !equalGeneral(tr, trCopy) {
t.Errorf("%v: unexpected modification in TR", name)
}
if !equalGeneral(b, bCopy) {
t.Errorf("%v: unexpected modification in B", name)
}

prefix := fmt.Sprintf("Case n1=%v, n2=%v, isgn=%v", n1, n2, isgn)

// Check any invalid modifications of x.
if !generalOutsideAllNaN(x) {
t.Errorf("%v: out-of-range write to x\n%v", prefix, x.Data)
t.Errorf("%v: out-of-range write to x\n%v", name, x.Data)
}

var xnormWant float64
for i := 0; i < n1; i++ {
var rowsum float64
for j := 0; j < n2; j++ {
rowsum += math.Abs(x.Data[i*x.Stride+j])
}
if rowsum > xnormWant {
xnormWant = rowsum
}
if n1 == 0 || n2 == 0 {
return
}

if scale <= 0 || 1 < scale {
t.Errorf("%v: invalid value of scale, want in (0,1], got %v", name, scale)
}

xnormWant := dlange(lapack.MaxRowSum, x.Rows, x.Cols, x.Data, x.Stride)
if xnormWant != xnorm {
t.Errorf("%v: unexpected xnorm: want %v, got %v", prefix, xnormWant, xnorm)
t.Errorf("%v: unexpected xnorm: want %v, got %v", name, xnormWant, xnorm)
}

// Multiply b by scale to get the wanted right-hand side.
for i := 0; i < n1; i++ {
for j := 0; j < n2; j++ {
b.Data[i*b.Stride+j] *= scale
}
if !ok {
t.Logf("%v: Dlasy2 returned ok=false", name)
return
}
// Compute the wanted left-hand side.
lhsWant := randomGeneral(n1, n2, n2, rnd)

// Compute diff := op(TL)*X + sgn*X*op(TR) - scale*B.
diff := zeros(n1, n2, n2)
if tranl {
blas64.Gemm(blas.Trans, blas.NoTrans, 1, tl, x, 0, lhsWant)
blas64.Gemm(blas.Trans, blas.NoTrans, 1, tl, x, 0, diff)
} else {
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tl, x, 0, lhsWant)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tl, x, 0, diff)
}
if tranr {
blas64.Gemm(blas.NoTrans, blas.Trans, float64(isgn), x, tr, 1, lhsWant)
blas64.Gemm(blas.NoTrans, blas.Trans, float64(isgn), x, tr, 1, diff)
} else {
blas64.Gemm(blas.NoTrans, blas.NoTrans, float64(isgn), x, tr, 1, lhsWant)
blas64.Gemm(blas.NoTrans, blas.NoTrans, float64(isgn), x, tr, 1, diff)
}
// Compare them.
for i := 0; i < n1; i++ {
for j := 0; j < n2; j++ {
diff := lhsWant.Data[i*lhsWant.Stride+j] - b.Data[i*b.Stride+j]
if math.Abs(diff) > tol && ok {
t.Errorf("%v: unexpected result, diff[%v,%v]=%v", prefix, i, j, diff)
}
diff.Data[i*diff.Stride+j] -= scale * b.Data[i*b.Stride+j]
}
}
// Check that residual |op(TL)*X + sgn*X*op(TR) - scale*B| / |X| is small.
resid := dlange(lapack.MaxColumnSum, n1, n2, diff.Data, diff.Stride) / xnorm
if resid > tol {
t.Errorf("%v: unexpected result, resid=%v, want<=%v", name, resid, tol)
}
}

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