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testlapack: add isIdentity helper

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This commit is contained in:
Vladimir Chalupecky
2019-01-03 23:34:53 +01:00
committed by Vladimír Chalupecký
parent 27d556d1f9
commit 87489715e5
6 changed files with 39 additions and 100 deletions
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20
lapack/testlapack/dgetri.go
View File

@@ -5,7 +5,6 @@
package testlapack
import (
"math"
"testing"
"golang.org/x/exp/rand"
@@ -67,23 +66,8 @@ func DgetriTest(t *testing.T, impl Dgetrier) {
// Check that A(inv) * A = I.
ans := make([]float64, len(a))
bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, aCopy, lda, a, lda, 0, ans, lda)
isEye := true
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if i == j {
// This tolerance is so high because computing matrix inverses
// is very unstable.
if math.Abs(ans[i*lda+j]-1) > 5e-2 {
isEye = false
}
} else {
if math.Abs(ans[i*lda+j]) > 5e-2 {
isEye = false
}
}
}
}
if !isEye {
// The tolerance is so high because computing matrix inverses is very unstable.
if !isIdentity(n, ans, lda, 5e-2) {
t.Errorf("Inv(A) * A != I. n = %v, lda = %v", n, lda)
}
}

16
lapack/testlapack/dlarfg.go
View File

@@ -104,21 +104,7 @@ func DlarfgTest(t *testing.T, impl Dlarfger) {
Data: make([]float64, n*n),
}
blas64.Gemm(blas.Trans, blas.NoTrans, 1, hmat, hmat, 0, eye)
iseye := true
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if i == j {
if math.Abs(eye.Data[i*n+j]-1) > 1e-14 {
iseye = false
}
} else {
if math.Abs(eye.Data[i*n+j]) > 1e-14 {
iseye = false
}
}
}
}
if !iseye {
if !isIdentity(n, eye.Data, n, 1e-14) {
t.Errorf("H^T * H is not I %v", eye)
}

19
lapack/testlapack/dtrti2.go
View File

@@ -5,7 +5,6 @@
package testlapack
import (
"math"
"testing"
"golang.org/x/exp/rand"
@@ -149,23 +148,7 @@ func Dtrti2Test(t *testing.T, impl Dtrti2er) {
ans := make([]float64, len(a))
bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, a, lda, aCopy, lda, 0, ans, lda)
// Check that ans is the identity matrix.
iseye := true
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if i == j {
if math.Abs(ans[i*lda+i]-1) > tol {
iseye = false
break
}
} else {
if math.Abs(ans[i*lda+j]) > tol {
iseye = false
break
}
}
}
}
if !iseye {
if !isIdentity(n, ans, lda, tol) {
t.Errorf("inv(A) * A != I. Upper = %v, unit = %v, ans = %v", uplo == blas.Upper, diag == blas.Unit, ans)
}
}

19
lapack/testlapack/dtrtri.go
View File

@@ -5,7 +5,6 @@
package testlapack
import (
"math"
"testing"
"golang.org/x/exp/rand"
@@ -80,23 +79,7 @@ func DtrtriTest(t *testing.T, impl Dtrtrier) {
ans := make([]float64, len(a))
bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, a, lda, aCopy, lda, 0, ans, lda)
// Check that ans is the identity matrix.
iseye := true
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if i == j {
if math.Abs(ans[i*lda+i]-1) > tol {
iseye = false
break
}
} else {
if math.Abs(ans[i*lda+j]) > tol {
iseye = false
break
}
}
}
}
if !iseye {
if !isIdentity(n, ans, lda, tol) {
t.Errorf("inv(A) * A != I. Upper = %v, unit = %v, n = %v, lda = %v",
uplo == blas.Upper, diag == blas.Unit, n, lda)
}

25
lapack/testlapack/general.go
View File

@@ -1464,3 +1464,28 @@ func constructGSVPresults(n, p, m, k, l int, a, b blas64.General) (zeroA, zeroB
return zeroA, zeroB
}
// isIdentity returns whether an n×n matrix A is approximately equal to the
// identity matrix.
func isIdentity(n int, a []float64, lda int, tol float64) bool {
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
aij := a[i*lda+j]
if math.IsNaN(aij) {
return false
}
if i == j {
if math.Abs(aij-1) > tol {
fmt.Println(i, j, aij)
return false
}
} else {
if math.Abs(aij) > tol {
fmt.Println(i, j, aij)
return false
}
}
}
}
return true
}

40
lapack/testlapack/matgen_test.go
View File

@@ -5,7 +5,6 @@
package testlapack
import (
"math"
"testing"
"golang.org/x/exp/rand"
@@ -21,40 +20,19 @@ func TestDlagsy(t *testing.T) {
if lda == 0 {
lda = max(1, n)
}
// D is the identity matrix I.
d := make([]float64, n)
for i := range d {
d[i] = 1
}
a := blas64.General{
Rows: n,
Cols: n,
Stride: lda,
Data: nanSlice(n * lda),
}
work := make([]float64, a.Rows+a.Cols)
Dlagsy(a.Rows, 0, d, a.Data, a.Stride, rnd, work)
isIdentity := true
identityLoop:
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
aij := a.Data[i*a.Stride+j]
if math.IsNaN(aij) {
isIdentity = false
}
if i == j && math.Abs(aij-1) > tol {
isIdentity = false
}
if i != j && math.Abs(aij) > tol {
isIdentity = false
}
if !isIdentity {
break identityLoop
}
}
}
if !isIdentity {
// Allocate an n×n symmetric matrix A and fill it with NaNs.
a := nanSlice(n * lda)
work := make([]float64, 2*n)
// Compute A = U * D * U^T where U is a random orthogonal matrix.
Dlagsy(n, 0, d, a, lda, rnd, work)
// A should be the identity matrix because
// A = U * D * U^T = U * I * U^T = U * U^T = I.
if !isIdentity(n, a, lda, tol) {
t.Errorf("Case n=%v,lda=%v: unexpected result", n, lda)
}
}