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120 lines
3.5 KiB
Go
120 lines
3.5 KiB
Go
// Copyright ©2017 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package testlapack
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import (
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"math"
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"testing"
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"golang.org/x/exp/rand"
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/blas/blas64"
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"gonum.org/v1/gonum/floats/scalar"
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)
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type Dlags2er interface {
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Dlags2(upper bool, a1, a2, a3, b1, b2, b3 float64) (csu, snu, csv, snv, csq, snq float64)
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}
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func Dlags2Test(t *testing.T, impl Dlags2er) {
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rnd := rand.New(rand.NewSource(1))
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for _, upper := range []bool{true, false} {
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for i := 0; i < 100; i++ {
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// Generate randomly the elements of a 2×2 matrix A
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// [ a1 a2 ] or [ a1 0 ]
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// [ 0 a3 ] [ a2 a3 ]
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a1 := rnd.Float64()
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a2 := rnd.Float64()
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a3 := rnd.Float64()
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// Generate randomly the elements of a 2×2 matrix B.
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// [ b1 b2 ] or [ b1 0 ]
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// [ 0 b3 ] [ b2 b3 ]
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b1 := rnd.Float64()
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b2 := rnd.Float64()
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b3 := rnd.Float64()
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// Compute orthogal matrices U, V, Q
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// U = [ csu snu ], V = [ csv snv ], Q = [ csq snq ]
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// [ -snu csu ] [ -snv csv ] [ -snq csq ]
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// that transform A and B.
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csu, snu, csv, snv, csq, snq := impl.Dlags2(upper, a1, a2, a3, b1, b2, b3)
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// Check that U, V, Q are orthogonal matrices (their
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// determinant is equal to 1).
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detU := det2x2(csu, snu, -snu, csu)
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if !scalar.EqualWithinAbsOrRel(math.Abs(detU), 1, 1e-14, 1e-14) {
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t.Errorf("U not orthogonal: det(U)=%v", detU)
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}
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detV := det2x2(csv, snv, -snv, csv)
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if !scalar.EqualWithinAbsOrRel(math.Abs(detV), 1, 1e-14, 1e-14) {
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t.Errorf("V not orthogonal: det(V)=%v", detV)
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}
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detQ := det2x2(csq, snq, -snq, csq)
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if !scalar.EqualWithinAbsOrRel(math.Abs(detQ), 1, 1e-14, 1e-14) {
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t.Errorf("Q not orthogonal: det(Q)=%v", detQ)
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}
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// Create U, V, Q explicitly as dense matrices.
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u := blas64.General{
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Rows: 2,
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Cols: 2,
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Stride: 2,
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Data: []float64{csu, snu, -snu, csu},
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}
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v := blas64.General{
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Rows: 2,
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Cols: 2,
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Stride: 2,
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Data: []float64{csv, snv, -snv, csv},
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}
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q := blas64.General{
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Rows: 2,
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Cols: 2,
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Stride: 2,
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Data: []float64{csq, snq, -snq, csq},
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}
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// Create A and B explicitly as dense matrices.
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a := blas64.General{Rows: 2, Cols: 2, Stride: 2}
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b := blas64.General{Rows: 2, Cols: 2, Stride: 2}
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if upper {
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a.Data = []float64{a1, a2, 0, a3}
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b.Data = []float64{b1, b2, 0, b3}
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} else {
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a.Data = []float64{a1, 0, a2, a3}
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b.Data = []float64{b1, 0, b2, b3}
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}
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tmp := blas64.General{Rows: 2, Cols: 2, Stride: 2, Data: make([]float64, 4)}
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// Transform A as Uᵀ*A*Q.
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blas64.Gemm(blas.Trans, blas.NoTrans, 1, u, a, 0, tmp)
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blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, q, 0, a)
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// Transform B as Vᵀ*A*Q.
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blas64.Gemm(blas.Trans, blas.NoTrans, 1, v, b, 0, tmp)
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blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, q, 0, b)
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// Extract elements of transformed A and B that should be equal to zero.
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var gotA, gotB float64
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if upper {
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gotA = a.Data[1]
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gotB = b.Data[1]
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} else {
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gotA = a.Data[2]
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gotB = b.Data[2]
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}
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// Check that they are indeed zero.
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if !scalar.EqualWithinAbsOrRel(gotA, 0, 1e-14, 1e-14) {
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t.Errorf("unexpected non-zero value for zero triangle of Uᵀ*A*Q: %v", gotA)
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}
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if !scalar.EqualWithinAbsOrRel(gotB, 0, 1e-14, 1e-14) {
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t.Errorf("unexpected non-zero value for zero triangle of Vᵀ*B*Q: %v", gotB)
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}
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}
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}
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}
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func det2x2(a, b, c, d float64) float64 { return a*d - b*c }
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