mirror of
https://github.com/gonum/gonum.git
synced 2025-10-04 23:02:42 +08:00
119 lines
3.5 KiB
Go
119 lines
3.5 KiB
Go
// Copyright ©2017 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 (
|
||
"math"
|
||
"math/rand/v2"
|
||
"testing"
|
||
|
||
"gonum.org/v1/gonum/blas"
|
||
"gonum.org/v1/gonum/blas/blas64"
|
||
"gonum.org/v1/gonum/floats/scalar"
|
||
)
|
||
|
||
type Dlags2er interface {
|
||
Dlags2(upper bool, a1, a2, a3, b1, b2, b3 float64) (csu, snu, csv, snv, csq, snq float64)
|
||
}
|
||
|
||
func Dlags2Test(t *testing.T, impl Dlags2er) {
|
||
rnd := rand.New(rand.NewPCG(1, 1))
|
||
for _, upper := range []bool{true, false} {
|
||
for i := 0; i < 100; i++ {
|
||
// Generate randomly the elements of a 2×2 matrix A
|
||
// [ a1 a2 ] or [ a1 0 ]
|
||
// [ 0 a3 ] [ a2 a3 ]
|
||
a1 := rnd.Float64()
|
||
a2 := rnd.Float64()
|
||
a3 := rnd.Float64()
|
||
// Generate randomly the elements of a 2×2 matrix B.
|
||
// [ b1 b2 ] or [ b1 0 ]
|
||
// [ 0 b3 ] [ b2 b3 ]
|
||
b1 := rnd.Float64()
|
||
b2 := rnd.Float64()
|
||
b3 := rnd.Float64()
|
||
|
||
// Compute orthogonal matrices U, V, Q
|
||
// U = [ csu snu ], V = [ csv snv ], Q = [ csq snq ]
|
||
// [ -snu csu ] [ -snv csv ] [ -snq csq ]
|
||
// that transform A and B.
|
||
csu, snu, csv, snv, csq, snq := impl.Dlags2(upper, a1, a2, a3, b1, b2, b3)
|
||
|
||
// Check that U, V, Q are orthogonal matrices (their
|
||
// determinant is equal to 1).
|
||
detU := det2x2(csu, snu, -snu, csu)
|
||
if !scalar.EqualWithinAbsOrRel(math.Abs(detU), 1, 1e-14, 1e-14) {
|
||
t.Errorf("U not orthogonal: det(U)=%v", detU)
|
||
}
|
||
detV := det2x2(csv, snv, -snv, csv)
|
||
if !scalar.EqualWithinAbsOrRel(math.Abs(detV), 1, 1e-14, 1e-14) {
|
||
t.Errorf("V not orthogonal: det(V)=%v", detV)
|
||
}
|
||
detQ := det2x2(csq, snq, -snq, csq)
|
||
if !scalar.EqualWithinAbsOrRel(math.Abs(detQ), 1, 1e-14, 1e-14) {
|
||
t.Errorf("Q not orthogonal: det(Q)=%v", detQ)
|
||
}
|
||
|
||
// Create U, V, Q explicitly as dense matrices.
|
||
u := blas64.General{
|
||
Rows: 2,
|
||
Cols: 2,
|
||
Stride: 2,
|
||
Data: []float64{csu, snu, -snu, csu},
|
||
}
|
||
v := blas64.General{
|
||
Rows: 2,
|
||
Cols: 2,
|
||
Stride: 2,
|
||
Data: []float64{csv, snv, -snv, csv},
|
||
}
|
||
q := blas64.General{
|
||
Rows: 2,
|
||
Cols: 2,
|
||
Stride: 2,
|
||
Data: []float64{csq, snq, -snq, csq},
|
||
}
|
||
|
||
// Create A and B explicitly as dense matrices.
|
||
a := blas64.General{Rows: 2, Cols: 2, Stride: 2}
|
||
b := blas64.General{Rows: 2, Cols: 2, Stride: 2}
|
||
if upper {
|
||
a.Data = []float64{a1, a2, 0, a3}
|
||
b.Data = []float64{b1, b2, 0, b3}
|
||
} else {
|
||
a.Data = []float64{a1, 0, a2, a3}
|
||
b.Data = []float64{b1, 0, b2, b3}
|
||
}
|
||
|
||
tmp := blas64.General{Rows: 2, Cols: 2, Stride: 2, Data: make([]float64, 4)}
|
||
// Transform A as Uᵀ*A*Q.
|
||
blas64.Gemm(blas.Trans, blas.NoTrans, 1, u, a, 0, tmp)
|
||
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, q, 0, a)
|
||
// Transform B as Vᵀ*A*Q.
|
||
blas64.Gemm(blas.Trans, blas.NoTrans, 1, v, b, 0, tmp)
|
||
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, q, 0, b)
|
||
|
||
// Extract elements of transformed A and B that should be equal to zero.
|
||
var gotA, gotB float64
|
||
if upper {
|
||
gotA = a.Data[1]
|
||
gotB = b.Data[1]
|
||
} else {
|
||
gotA = a.Data[2]
|
||
gotB = b.Data[2]
|
||
}
|
||
// Check that they are indeed zero.
|
||
if !scalar.EqualWithinAbsOrRel(gotA, 0, 1e-14, 1e-14) {
|
||
t.Errorf("unexpected non-zero value for zero triangle of Uᵀ*A*Q: %v", gotA)
|
||
}
|
||
if !scalar.EqualWithinAbsOrRel(gotB, 0, 1e-14, 1e-14) {
|
||
t.Errorf("unexpected non-zero value for zero triangle of Vᵀ*B*Q: %v", gotB)
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
func det2x2(a, b, c, d float64) float64 { return a*d - b*c }
|