vendor/gonum.org/v1/gonum/lapack/testlapack/dgels.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         "testing"
   9
  10         "golang.org/x/exp/rand"
  11
  12         "gonum.org/v1/gonum/blas"
  13         "gonum.org/v1/gonum/blas/blas64"
  14         "gonum.org/v1/gonum/floats"
  15 )
  16
  17 type Dgelser interface {
  18         Dgels(trans blas.Transpose, m, n, nrhs int, a []float64, lda int, b []float64, ldb int, work []float64, lwork int) bool
  19 }
  20
  21 func DgelsTest(t *testing.T, impl Dgelser) {
  22         rnd := rand.New(rand.NewSource(1))
  23         for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
  24                 for _, test := range []struct {
  25                         m, n, nrhs, lda, ldb int
  26                 }{
  27                         {3, 4, 5, 0, 0},
  28                         {3, 5, 4, 0, 0},
  29                         {4, 3, 5, 0, 0},
  30                         {4, 5, 3, 0, 0},
  31                         {5, 3, 4, 0, 0},
  32                         {5, 4, 3, 0, 0},
  33                         {3, 4, 5, 10, 20},
  34                         {3, 5, 4, 10, 20},
  35                         {4, 3, 5, 10, 20},
  36                         {4, 5, 3, 10, 20},
  37                         {5, 3, 4, 10, 20},
  38                         {5, 4, 3, 10, 20},
  39                         {3, 4, 5, 20, 10},
  40                         {3, 5, 4, 20, 10},
  41                         {4, 3, 5, 20, 10},
  42                         {4, 5, 3, 20, 10},
  43                         {5, 3, 4, 20, 10},
  44                         {5, 4, 3, 20, 10},
  45                         {200, 300, 400, 0, 0},
  46                         {200, 400, 300, 0, 0},
  47                         {300, 200, 400, 0, 0},
  48                         {300, 400, 200, 0, 0},
  49                         {400, 200, 300, 0, 0},
  50                         {400, 300, 200, 0, 0},
  51                         {200, 300, 400, 500, 600},
  52                         {200, 400, 300, 500, 600},
  53                         {300, 200, 400, 500, 600},
  54                         {300, 400, 200, 500, 600},
  55                         {400, 200, 300, 500, 600},
  56                         {400, 300, 200, 500, 600},
  57                         {200, 300, 400, 600, 500},
  58                         {200, 400, 300, 600, 500},
  59                         {300, 200, 400, 600, 500},
  60                         {300, 400, 200, 600, 500},
  61                         {400, 200, 300, 600, 500},
  62                         {400, 300, 200, 600, 500},
  63                 } {
  64                         m := test.m
  65                         n := test.n
  66                         nrhs := test.nrhs
  67
  68                         lda := test.lda
  69                         if lda == 0 {
  70                                 lda = n
  71                         }
  72                         a := make([]float64, m*lda)
  73                         for i := range a {
  74                                 a[i] = rnd.Float64()
  75                         }
  76                         aCopy := make([]float64, len(a))
  77                         copy(aCopy, a)
  78
  79                         // Size of b is the same trans or no trans, because the number of rows
  80                         // has to be the max of (m,n).
  81                         mb := max(m, n)
  82                         nb := nrhs
  83                         ldb := test.ldb
  84                         if ldb == 0 {
  85                                 ldb = nb
  86                         }
  87                         b := make([]float64, mb*ldb)
  88                         for i := range b {
  89                                 b[i] = rnd.Float64()
  90                         }
  91                         bCopy := make([]float64, len(b))
  92                         copy(bCopy, b)
  93
  94                         // Find optimal work length.
  95                         work := make([]float64, 1)
  96                         impl.Dgels(trans, m, n, nrhs, a, lda, b, ldb, work, -1)
  97
  98                         // Perform linear solve
  99                         work = make([]float64, int(work[0]))
 100                         lwork := len(work)
 101                         for i := range work {
 102                                 work[i] = rnd.Float64()
 103                         }
 104                         impl.Dgels(trans, m, n, nrhs, a, lda, b, ldb, work, lwork)
 105
 106                         // Check that the answer is correct by comparing to the normal equations.
 107                         aMat := blas64.General{
 108                                 Rows:   m,
 109                                 Cols:   n,
 110                                 Stride: lda,
 111                                 Data:   make([]float64, len(aCopy)),
 112                         }
 113                         copy(aMat.Data, aCopy)
 114                         szAta := n
 115                         if trans == blas.Trans {
 116                                 szAta = m
 117                         }
 118                         aTA := blas64.General{
 119                                 Rows:   szAta,
 120                                 Cols:   szAta,
 121                                 Stride: szAta,
 122                                 Data:   make([]float64, szAta*szAta),
 123                         }
 124
 125                         // Compute A^T * A if notrans and A * A^T otherwise.
 126                         if trans == blas.NoTrans {
 127                                 blas64.Gemm(blas.Trans, blas.NoTrans, 1, aMat, aMat, 0, aTA)
 128                         } else {
 129                                 blas64.Gemm(blas.NoTrans, blas.Trans, 1, aMat, aMat, 0, aTA)
 130                         }
 131
 132                         // Multiply by X.
 133                         X := blas64.General{
 134                                 Rows:   szAta,
 135                                 Cols:   nrhs,
 136                                 Stride: ldb,
 137                                 Data:   b,
 138                         }
 139                         ans := blas64.General{
 140                                 Rows:   aTA.Rows,
 141                                 Cols:   X.Cols,
 142                                 Stride: X.Cols,
 143                                 Data:   make([]float64, aTA.Rows*X.Cols),
 144                         }
 145                         blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aTA, X, 0, ans)
 146
 147                         B := blas64.General{
 148                                 Rows:   szAta,
 149                                 Cols:   nrhs,
 150                                 Stride: ldb,
 151                                 Data:   make([]float64, len(bCopy)),
 152                         }
 153
 154                         copy(B.Data, bCopy)
 155                         var ans2 blas64.General
 156                         if trans == blas.NoTrans {
 157                                 ans2 = blas64.General{
 158                                         Rows:   aMat.Cols,
 159                                         Cols:   B.Cols,
 160                                         Stride: B.Cols,
 161                                         Data:   make([]float64, aMat.Cols*B.Cols),
 162                                 }
 163                         } else {
 164                                 ans2 = blas64.General{
 165                                         Rows:   aMat.Rows,
 166                                         Cols:   B.Cols,
 167                                         Stride: B.Cols,
 168                                         Data:   make([]float64, aMat.Rows*B.Cols),
 169                                 }
 170                         }
 171
 172                         // Compute A^T B if Trans or A * B otherwise
 173                         if trans == blas.NoTrans {
 174                                 blas64.Gemm(blas.Trans, blas.NoTrans, 1, aMat, B, 0, ans2)
 175                         } else {
 176                                 blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aMat, B, 0, ans2)
 177                         }
 178                         if !floats.EqualApprox(ans.Data, ans2.Data, 1e-12) {
 179                                 t.Errorf("Normal equations not satisfied")
 180                         }
 181                 }
 182         }
 183 }