github.com/jingcheng-WU/gonum@v0.9.1-0.20210323123734-f1a2a11a8f7b/lapack/testlapack/dgeqp3.go (about)

     1  // Copyright ©2015 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package testlapack
     6  
     7  import (
     8  	"fmt"
     9  	"testing"
    10  
    11  	"golang.org/x/exp/rand"
    12  
    13  	"github.com/jingcheng-WU/gonum/blas"
    14  	"github.com/jingcheng-WU/gonum/blas/blas64"
    15  	"github.com/jingcheng-WU/gonum/lapack"
    16  )
    17  
    18  type Dgeqp3er interface {
    19  	Dlapmter
    20  	Dgeqp3(m, n int, a []float64, lda int, jpvt []int, tau, work []float64, lwork int)
    21  }
    22  
    23  func Dgeqp3Test(t *testing.T, impl Dgeqp3er) {
    24  	rnd := rand.New(rand.NewSource(1))
    25  	for _, m := range []int{0, 1, 2, 3, 4, 5, 12, 23, 129} {
    26  		for _, n := range []int{0, 1, 2, 3, 4, 5, 12, 23, 129} {
    27  			for _, lda := range []int{max(1, n), n + 3} {
    28  				dgeqp3Test(t, impl, rnd, m, n, lda)
    29  			}
    30  		}
    31  	}
    32  }
    33  
    34  func dgeqp3Test(t *testing.T, impl Dgeqp3er, rnd *rand.Rand, m, n, lda int) {
    35  	const (
    36  		tol = 1e-14
    37  
    38  		all = iota
    39  		some
    40  		none
    41  	)
    42  	for _, free := range []int{all, some, none} {
    43  		name := fmt.Sprintf("m=%d,n=%d,lda=%d,", m, n, lda)
    44  
    45  		// Allocate m×n matrix A and fill it with random numbers.
    46  		a := randomGeneral(m, n, lda, rnd)
    47  		// Store a copy of A for later comparison.
    48  		aCopy := cloneGeneral(a)
    49  		// Allocate a slice of column pivots.
    50  		jpvt := make([]int, n)
    51  		for j := range jpvt {
    52  			switch free {
    53  			case all:
    54  				// All columns are free.
    55  				jpvt[j] = -1
    56  				name += "free=all"
    57  			case some:
    58  				// Some columns are free, some are leading columns.
    59  				jpvt[j] = rnd.Intn(2) - 1 // -1 or 0
    60  				name += "free=some"
    61  			case none:
    62  				// All columns are leading.
    63  				jpvt[j] = 0
    64  				name += "free=none"
    65  			default:
    66  				panic("bad freedom")
    67  			}
    68  		}
    69  		// Allocate a slice for scalar factors of elementary
    70  		// reflectors and fill it with random numbers. Dgeqp3
    71  		// will overwrite them with valid data.
    72  		k := min(m, n)
    73  		tau := make([]float64, k)
    74  		for i := range tau {
    75  			tau[i] = rnd.Float64()
    76  		}
    77  		// Get optimal workspace size for Dgeqp3.
    78  		work := make([]float64, 1)
    79  		impl.Dgeqp3(m, n, a.Data, a.Stride, jpvt, tau, work, -1)
    80  		lwork := int(work[0])
    81  		work = make([]float64, lwork)
    82  		for i := range work {
    83  			work[i] = rnd.Float64()
    84  		}
    85  
    86  		// Compute a QR factorization of A with column pivoting.
    87  		impl.Dgeqp3(m, n, a.Data, a.Stride, jpvt, tau, work, lwork)
    88  
    89  		// Compute Q based on the elementary reflectors stored in A.
    90  		q := constructQ("QR", m, n, a.Data, a.Stride, tau)
    91  		// Check that Q is orthogonal.
    92  		if resid := residualOrthogonal(q, false); resid > tol*float64(max(m, n)) {
    93  			t.Errorf("Case %v: Q not orthogonal; resid=%v, want<=%v", name, resid, tol*float64(max(m, n)))
    94  		}
    95  
    96  		// Copy the upper triangle of A into R.
    97  		r := zeros(m, n, lda)
    98  		for i := 0; i < m; i++ {
    99  			for j := i; j < n; j++ {
   100  				r.Data[i*r.Stride+j] = a.Data[i*a.Stride+j]
   101  			}
   102  		}
   103  		// Compute Q*R - A*P:
   104  		// 1. Rearrange the columns of A based on the permutation in jpvt.
   105  		qrap := cloneGeneral(aCopy)
   106  		impl.Dlapmt(true, qrap.Rows, qrap.Cols, qrap.Data, qrap.Stride, jpvt)
   107  		// Compute Q*R - A*P.
   108  		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, r, -1, qrap)
   109  		// Check that |Q*R - A*P| is small.
   110  		resid := dlange(lapack.MaxColumnSum, qrap.Rows, qrap.Cols, qrap.Data, qrap.Stride)
   111  		if resid > tol*float64(max(m, n)) {
   112  			t.Errorf("Case %v: |Q*R - A*P|=%v, want<=%v", name, resid, tol*float64(max(m, n)))
   113  
   114  		}
   115  	}
   116  }