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lapack/testlapack: clean up isOrthonormal

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This commit is contained in:
Vladimir Chalupecky
2018-07-23 11:40:44 +02:00
committed by Vladimír Chalupecký
parent 6cb44aa022
commit 6c36e0d6b7
1 changed files with 19 additions and 12 deletions
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29
lapack/testlapack/general.go
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@@ -818,27 +818,34 @@ func printRowise(a []float64, m, n, lda int, beyond bool) {
} }
} }
// isOrthonormal checks that a general matrix is orthonormal. // isOrthonormal returns whether a square matrix Q is orthogonal.
func isOrthonormal(q blas64.General) bool { func isOrthonormal(q blas64.General) bool {
n := q.Rows n := q.Rows
if n != q.Cols {
panic("matrix not square")
}
// A real square matrix is orthogonal if and only if its rows form
// an orthonormal basis of the Euclidean space R^n.
const tol = 1e-13
for i := 0; i < n; i++ { for i := 0; i < n; i++ {
for j := i; j < n; j++ { nrm := blas64.Nrm2(n, blas64.Vector{Data: q.Data[i*q.Stride:], Inc: 1})
if math.IsNaN(nrm) {
return false
}
if math.Abs(nrm-1) > tol {
return false
}
for j := i + 1; j < n; j++ {
dot := blas64.Dot(n, dot := blas64.Dot(n,
blas64.Vector{Inc: 1, Data: q.Data[i*q.Stride:]}, blas64.Vector{Data: q.Data[i*q.Stride:], Inc: 1},
blas64.Vector{Inc: 1, Data: q.Data[j*q.Stride:]}, blas64.Vector{Data: q.Data[j*q.Stride:], Inc: 1},
) )
if math.IsNaN(dot) { if math.IsNaN(dot) {
return false return false
} }
if i == j { if math.Abs(dot) > tol {
if math.Abs(dot-1) > 1e-10 {
return false return false
} }
} else {
if math.Abs(dot) > 1e-10 {
return false
}
}
} }
} }
return true return true