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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 (
"math"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/floats"
"gonum.org/v1/gonum/lapack"
)
type Dlasrer interface {
Dlasr(side blas.Side, pivot lapack.Pivot, direct lapack.Direct, m, n int, c, s, a []float64, lda int)
}
func DlasrTest(t *testing.T, impl Dlasrer) {
rnd := rand.New(rand.NewSource(1))
for _, side := range []blas.Side{blas.Left, blas.Right} {
for _, pivot := range []lapack.Pivot{lapack.Variable, lapack.Top, lapack.Bottom} {
for _, direct := range []lapack.Direct{lapack.Forward, lapack.Backward} {
for _, test := range []struct {
m, n, lda int
}{
{5, 5, 0},
{5, 10, 0},
{10, 5, 0},
{5, 5, 20},
{5, 10, 20},
{10, 5, 20},
} {
m := test.m
n := test.n
lda := test.lda
if lda == 0 {
lda = n
}
// Allocate n×n matrix A and fill it with random numbers.
a := make([]float64, m*lda)
for i := range a {
a[i] = rnd.Float64()
}
// Allocate slices for implicitly
// represented rotation matrices.
var s, c []float64
if side == blas.Left {
s = make([]float64, m-1)
c = make([]float64, m-1)
} else {
s = make([]float64, n-1)
c = make([]float64, n-1)
}
for k := range s {
// Generate a random number in [0,2*pi).
theta := rnd.Float64() * 2 * math.Pi
s[k] = math.Sin(theta)
c[k] = math.Cos(theta)
}
aCopy := make([]float64, len(a))
copy(a, aCopy)
// Apply plane a sequence of plane
// rotation in s and c to the matrix A.
impl.Dlasr(side, pivot, direct, m, n, c, s, a, lda)
// Compute a reference solution by multiplying A
// by explicitly formed rotation matrix P.
pSize := m
if side == blas.Right {
pSize = n
}
// Allocate matrix P.
p := blas64.General{
Rows: pSize,
Cols: pSize,
Stride: pSize,
Data: make([]float64, pSize*pSize),
}
// Allocate matrix P_k.
pk := blas64.General{
Rows: pSize,
Cols: pSize,
Stride: pSize,
Data: make([]float64, pSize*pSize),
}
ptmp := blas64.General{
Rows: pSize,
Cols: pSize,
Stride: pSize,
Data: make([]float64, pSize*pSize),
}
// Initialize P to the identity matrix.
for i := 0; i < pSize; i++ {
p.Data[i*p.Stride+i] = 1
ptmp.Data[i*p.Stride+i] = 1
}
// Iterate over the sequence of plane rotations.
for k := range s {
// Set P_k to the identity matrix.
for i := range p.Data {
pk.Data[i] = 0
}
for i := 0; i < pSize; i++ {
pk.Data[i*p.Stride+i] = 1
}
// Set the corresponding elements of P_k.
switch pivot {
case lapack.Variable:
pk.Data[k*p.Stride+k] = c[k]
pk.Data[k*p.Stride+k+1] = s[k]
pk.Data[(k+1)*p.Stride+k] = -s[k]
pk.Data[(k+1)*p.Stride+k+1] = c[k]
case lapack.Top:
pk.Data[0] = c[k]
pk.Data[k+1] = s[k]
pk.Data[(k+1)*p.Stride] = -s[k]
pk.Data[(k+1)*p.Stride+k+1] = c[k]
case lapack.Bottom:
pk.Data[(pSize-1-k)*p.Stride+pSize-k-1] = c[k]
pk.Data[(pSize-1-k)*p.Stride+pSize-1] = s[k]
pk.Data[(pSize-1)*p.Stride+pSize-1-k] = -s[k]
pk.Data[(pSize-1)*p.Stride+pSize-1] = c[k]
}
// Compute P <- P_k * P or P <- P * P_k.
if direct == lapack.Forward {
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, pk, ptmp, 0, p)
} else {
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, ptmp, pk, 0, p)
}
copy(ptmp.Data, p.Data)
}
aMat := blas64.General{
Rows: m,
Cols: n,
Stride: lda,
Data: make([]float64, m*lda),
}
copy(a, aCopy)
newA := blas64.General{
Rows: m,
Cols: n,
Stride: lda,
Data: make([]float64, m*lda),
}
// Compute P * A or A * P.
if side == blas.Left {
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, p, aMat, 0, newA)
} else {
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aMat, p, 0, newA)
}
// Compare the result from Dlasr with the reference solution.
if !floats.EqualApprox(newA.Data, a, 1e-12) {
t.Errorf("A update mismatch")
}
}
}
}
}
}
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