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cf3307fa63
This is not intended to be a completed transition since it leaves the libraries unusable to external client code, but rather as a step towards use of math/rand/v2. This initial step allows repair of sequence change failures without having to worry about API difference.
108 lines
2.6 KiB
Go
108 lines
2.6 KiB
Go
// Copyright ©2021 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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"fmt"
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"math"
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"testing"
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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"
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"gonum.org/v1/gonum/internal/rand"
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"gonum.org/v1/gonum/lapack"
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)
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type Dorgr2er interface {
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Dorgr2(m, n, k int, a []float64, lda int, tau []float64, work []float64)
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Dgerqfer
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}
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func Dorgr2Test(t *testing.T, impl Dorgr2er) {
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rnd := rand.New(rand.NewSource(1))
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for _, k := range []int{0, 1, 2, 5} {
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for _, m := range []int{k, k + 1, k + 2, k + 4} {
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for _, n := range []int{m, m + 1, m + 2, m + 4, m + 7} {
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for _, lda := range []int{max(1, n), n + 5} {
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dorgr2Test(t, impl, rnd, m, n, k, lda)
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}
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}
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}
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}
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}
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func dorgr2Test(t *testing.T, impl Dorgr2er, rnd *rand.Rand, m, n, k, lda int) {
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const tol = 1e-14
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name := fmt.Sprintf("m=%v,n=%v,k=%v,lda=%v", m, n, k, lda)
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// Generate a random m×n matrix A.
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a := randomGeneral(m, n, lda, rnd)
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// Compute the RQ decomposition of A.
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rq := cloneGeneral(a)
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tau := make([]float64, m)
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work := make([]float64, 1)
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impl.Dgerqf(m, n, rq.Data, rq.Stride, tau, work, -1)
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work = make([]float64, int(work[0]))
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impl.Dgerqf(m, n, rq.Data, rq.Stride, tau, work, len(work))
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tauCopy := make([]float64, len(tau))
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copy(tauCopy, tau)
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// Compute the matrix Q using Dorg2r.
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q := cloneGeneral(rq)
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impl.Dorgr2(m, n, k, q.Data, q.Stride, tau[m-k:m], work)
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if m == 0 {
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return
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}
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// Check that tau hasn't been modified.
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if !floats.Equal(tau, tauCopy) {
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t.Errorf("%v: unexpected modification in tau", name)
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}
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// Check that Q has orthonormal rows.
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res := residualOrthogonal(q, true)
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if res > tol || math.IsNaN(res) {
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t.Errorf("%v: residual |I - Q*Qᵀ| too large, got %v, want <= %v", name, res, tol)
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}
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if k == 0 {
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return
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}
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// Extract the k×m upper triangular matrix R from RQ[m-k:m,n-k:n].
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r := zeros(k, m, m)
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for i := 0; i < k; i++ {
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for j := 0; j < k; j++ {
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ii := rq.Rows - k + i
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jj := rq.Cols - k + j
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jr := r.Cols - k + j
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if i <= j {
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r.Data[i*r.Stride+jr] = rq.Data[ii*rq.Stride+jj]
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}
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}
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}
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// Construct a view A[m-k:m,0:n] of the last k rows of A.
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aRec := blas64.General{
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Rows: k,
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Cols: n,
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Data: a.Data[(m-k)*a.Stride:],
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Stride: a.Stride,
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}
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// Compute A - R*Q.
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blas64.Gemm(blas.NoTrans, blas.NoTrans, -1, r, q, 1, aRec)
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// Check that |A - R*Q| is small.
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res = dlange(lapack.MaxColumnSum, aRec.Rows, aRec.Cols, aRec.Data, aRec.Stride)
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if res > tol || math.IsNaN(res) {
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t.Errorf("%v: residual |A - R*Q| too large, got %v, want <= %v", name, res, tol)
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}
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}
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