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// Copyright ©2015 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 (
"fmt"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/lapack"
)
type Dgeqp3er interface {
Dlapmter
Dgeqp3(m, n int, a []float64, lda int, jpvt []int, tau, work []float64, lwork int)
}
func Dgeqp3Test(t *testing.T, impl Dgeqp3er) {
rnd := rand.New(rand.NewSource(1))
for _, m := range []int{0, 1, 2, 3, 4, 5, 12, 23, 129} {
for _, n := range []int{0, 1, 2, 3, 4, 5, 12, 23, 129} {
for _, lda := range []int{max(1, n), n + 3} {
dgeqp3Test(t, impl, rnd, m, n, lda)
}
}
}
}
func dgeqp3Test(t *testing.T, impl Dgeqp3er, rnd *rand.Rand, m, n, lda int) {
const (
tol = 1e-14
all = iota
some
none
)
for _, free := range []int{all, some, none} {
name := fmt.Sprintf("m=%d,n=%d,lda=%d,", m, n, lda)
// Allocate m×n matrix A and fill it with random numbers.
a := randomGeneral(m, n, lda, rnd)
// Store a copy of A for later comparison.
aCopy := cloneGeneral(a)
// Allocate a slice of column pivots.
jpvt := make([]int, n)
for j := range jpvt {
switch free {
case all:
// All columns are free.
jpvt[j] = -1
name += "free=all"
case some:
// Some columns are free, some are leading columns.
jpvt[j] = rnd.Intn(2) - 1 // -1 or 0
name += "free=some"
case none:
// All columns are leading.
jpvt[j] = 0
name += "free=none"
default:
panic("bad freedom")
}
}
// Allocate a slice for scalar factors of elementary
// reflectors and fill it with random numbers. Dgeqp3
// will overwrite them with valid data.
k := min(m, n)
tau := make([]float64, k)
for i := range tau {
tau[i] = rnd.Float64()
}
// Get optimal workspace size for Dgeqp3.
work := make([]float64, 1)
impl.Dgeqp3(m, n, a.Data, a.Stride, jpvt, tau, work, -1)
lwork := int(work[0])
work = make([]float64, lwork)
for i := range work {
work[i] = rnd.Float64()
}
// Compute a QR factorization of A with column pivoting.
impl.Dgeqp3(m, n, a.Data, a.Stride, jpvt, tau, work, lwork)
// Compute Q based on the elementary reflectors stored in A.
q := constructQ("QR", m, n, a.Data, a.Stride, tau)
// Check that Q is orthogonal.
if resid := residualOrthogonal(q, false); resid > tol*float64(max(m, n)) {
t.Errorf("Case %v: Q not orthogonal; resid=%v, want<=%v", name, resid, tol*float64(max(m, n)))
}
// Copy the upper triangle of A into R.
r := zeros(m, n, lda)
for i := 0; i < m; i++ {
for j := i; j < n; j++ {
r.Data[i*r.Stride+j] = a.Data[i*a.Stride+j]
}
}
// Compute Q*R - A*P:
// 1. Rearrange the columns of A based on the permutation in jpvt.
qrap := cloneGeneral(aCopy)
impl.Dlapmt(true, qrap.Rows, qrap.Cols, qrap.Data, qrap.Stride, jpvt)
// Compute Q*R - A*P.
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, r, -1, qrap)
// Check that |Q*R - A*P| is small.
resid := dlange(lapack.MaxColumnSum, qrap.Rows, qrap.Cols, qrap.Data, qrap.Stride)
if resid > tol*float64(max(m, n)) {
t.Errorf("Case %v: |Q*R - A*P|=%v, want<=%v", name, resid, tol*float64(max(m, n)))
}
}
}
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