mirror of
https://github.com/gonum/gonum.git
synced 2025-10-31 10:36:30 +08:00
117 lines
3.2 KiB
Go
117 lines
3.2 KiB
Go
// 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)))
|
||
|
||
}
|
||
}
|
||
}
|