vendor/gonum.org/v1/gonum/lapack/testlapack/dgerqf.go

   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         "math"
   9         "testing"
  10
  11         "golang.org/x/exp/rand"
  12
  13         "gonum.org/v1/gonum/blas"
  14         "gonum.org/v1/gonum/blas/blas64"
  15 )
  16
  17 type Dgerqfer interface {
  18         Dgerqf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
  19 }
  20
  21 func DgerqfTest(t *testing.T, impl Dgerqfer) {
  22         const tol = 1e-13
  23
  24         rnd := rand.New(rand.NewSource(1))
  25         for c, test := range []struct {
  26                 m, n, lda int
  27         }{
  28                 {1, 1, 0},
  29                 {2, 2, 0},
  30                 {3, 2, 0},
  31                 {2, 3, 0},
  32                 {1, 12, 0},
  33                 {2, 6, 0},
  34                 {3, 4, 0},
  35                 {4, 3, 0},
  36                 {6, 2, 0},
  37                 {12, 1, 0},
  38                 {200, 180, 0},
  39                 {180, 200, 0},
  40                 {200, 200, 0},
  41                 {1, 1, 20},
  42                 {2, 2, 20},
  43                 {3, 2, 20},
  44                 {2, 3, 20},
  45                 {1, 12, 20},
  46                 {2, 6, 20},
  47                 {3, 4, 20},
  48                 {4, 3, 20},
  49                 {6, 2, 20},
  50                 {12, 1, 20},
  51                 {200, 180, 220},
  52                 {180, 200, 220},
  53                 {200, 200, 220},
  54         } {
  55                 n := test.n
  56                 m := test.m
  57                 lda := test.lda
  58                 if lda == 0 {
  59                         lda = test.n
  60                 }
  61                 a := make([]float64, m*lda)
  62                 for i := range a {
  63                         a[i] = rnd.Float64()
  64                 }
  65                 aCopy := make([]float64, len(a))
  66                 copy(aCopy, a)
  67                 k := min(m, n)
  68                 tau := make([]float64, k)
  69                 for i := range tau {
  70                         tau[i] = rnd.Float64()
  71                 }
  72                 work := []float64{0}
  73                 impl.Dgerqf(m, n, a, lda, tau, work, -1)
  74                 lwkopt := int(work[0])
  75                 for _, wk := range []struct {
  76                         name   string
  77                         length int
  78                 }{
  79                         {name: "short", length: m},
  80                         {name: "medium", length: lwkopt - 1},
  81                         {name: "long", length: lwkopt},
  82                 } {
  83                         if wk.length < max(1, m) {
  84                                 continue
  85                         }
  86                         lwork := wk.length
  87                         work = make([]float64, lwork)
  88                         for i := range work {
  89                                 work[i] = rnd.Float64()
  90                         }
  91                         copy(a, aCopy)
  92                         impl.Dgerqf(m, n, a, lda, tau, work, lwork)
  93
  94                         // Test that the RQ factorization has completed successfully. Compute
  95                         // Q based on the vectors.
  96                         q := constructQ("RQ", m, n, a, lda, tau)
  97
  98                         // Check that q is orthonormal
  99                         for i := 0; i < q.Rows; i++ {
 100                                 nrm := blas64.Nrm2(q.Cols, blas64.Vector{Inc: 1, Data: q.Data[i*q.Stride:]})
 101                                 if math.IsNaN(nrm) || math.Abs(nrm-1) > 1e-14 {
 102                                         t.Errorf("Case %v, q not normal", c)
 103                                 }
 104                                 for j := 0; j < i; j++ {
 105                                         dot := blas64.Dot(q.Cols, blas64.Vector{Inc: 1, Data: q.Data[i*q.Stride:]}, blas64.Vector{Inc: 1, Data: q.Data[j*q.Stride:]})
 106                                         if math.IsNaN(dot) || math.Abs(dot) > 1e-14 {
 107                                                 t.Errorf("Case %v, q not orthogonal", c)
 108                                         }
 109                                 }
 110                         }
 111                         // Check that A = R * Q
 112                         r := blas64.General{
 113                                 Rows:   m,
 114                                 Cols:   n,
 115                                 Stride: n,
 116                                 Data:   make([]float64, m*n),
 117                         }
 118                         for i := 0; i < m; i++ {
 119                                 off := m - n
 120                                 for j := max(0, i-off); j < n; j++ {
 121                                         r.Data[i*r.Stride+j] = a[i*lda+j]
 122                                 }
 123                         }
 124
 125                         got := blas64.General{
 126                                 Rows:   m,
 127                                 Cols:   n,
 128                                 Stride: lda,
 129                                 Data:   make([]float64, m*lda),
 130                         }
 131                         blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, r, q, 0, got)
 132                         want := blas64.General{
 133                                 Rows:   m,
 134                                 Cols:   n,
 135                                 Stride: lda,
 136                                 Data:   aCopy,
 137                         }
 138                         if !equalApproxGeneral(got, want, tol) {
 139                                 t.Errorf("Case %d, R*Q != a %s\ngot: %+v\nwant:%+v", c, wk.name, got, want)
 140                         }
 141                 }
 142         }
 143 }