forked from gonum/gonum
/
dlaln2.go
152 lines (134 loc) · 3.91 KB
/
dlaln2.go
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
// Copyright ©2016 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"
"math"
"math/cmplx"
"testing"
"golang.org/x/exp/rand"
)
type Dlaln2er interface {
Dlaln2(trans bool, na, nw int, smin, ca float64, a []float64, lda int, d1, d2 float64, b []float64, ldb int, wr, wi float64, x []float64, ldx int) (scale, xnorm float64, ok bool)
}
func Dlaln2Test(t *testing.T, impl Dlaln2er) {
rnd := rand.New(rand.NewSource(1))
for _, trans := range []bool{true, false} {
for _, na := range []int{1, 2} {
for _, nw := range []int{1, 2} {
for _, extra := range []int{0, 1, 2, 13} {
for cas := 0; cas < 1000; cas++ {
testDlaln2(t, impl, trans, na, nw, extra, rnd)
}
}
}
}
}
}
func testDlaln2(t *testing.T, impl Dlaln2er, trans bool, na, nw, extra int, rnd *rand.Rand) {
const tol = 1e-11
// Generate random input scalars.
ca := rnd.NormFloat64()
d1 := rnd.NormFloat64()
d2 := rnd.NormFloat64()
var w complex128
if nw == 1 {
w = complex(rand.NormFloat64(), 0)
} else {
w = complex(rand.NormFloat64(), rand.NormFloat64())
}
smin := dlamchP * (math.Abs(real(w)) + math.Abs(imag(w)))
// Generate random input matrices.
a := randomGeneral(na, na, na+extra, rnd)
b := randomGeneral(na, nw, nw+extra, rnd)
x := randomGeneral(na, nw, nw+extra, rnd)
scale, xnormGot, ok := impl.Dlaln2(trans, na, nw, smin, ca, a.Data, a.Stride, d1, d2, b.Data, b.Stride, real(w), imag(w), x.Data, x.Stride)
prefix := fmt.Sprintf("Case trans=%t, na=%v, nw=%v, extra=%v", trans, na, nw, extra)
if !generalOutsideAllNaN(a) {
t.Errorf("%v: out-of-range write to A\n%v", prefix, a.Data)
}
if !generalOutsideAllNaN(b) {
t.Errorf("%v: out-of-range write to B\n%v", prefix, b.Data)
}
if !generalOutsideAllNaN(x) {
t.Errorf("%v: out-of-range write to X\n%v", prefix, x.Data)
}
// Scale is documented to be <= 1.
if scale <= 0 || 1 < scale {
t.Errorf("%v: invalid value of scale=%v", prefix, scale)
}
// Calculate the infinity norm of X explicitly.
var xnormWant float64
for i := 0; i < na; i++ {
var rowsum float64
for j := 0; j < nw; j++ {
rowsum += math.Abs(x.Data[i*x.Stride+j])
}
if rowsum > xnormWant {
xnormWant = rowsum
}
}
if xnormWant != xnormGot {
t.Errorf("Case %v: unexpected xnorm with scale=%v. Want %v, got %v", prefix, scale, xnormWant, xnormGot)
}
if !ok {
// If ok is false, the matrix has been perturbed but we don't
// know how. Return without comparing both sides of the
// equation.
return
}
// Compute a complex matrix
// M := ca * A - w * D
// or
// M := ca * Aᵀ - w * D.
m := make([]complex128, na*na)
if trans {
// M = ca * Aᵀ
for i := 0; i < na; i++ {
for j := 0; j < na; j++ {
m[i*na+j] = complex(ca*a.Data[j*a.Stride+i], 0)
}
}
} else {
// M = ca * Aᵀ
for i := 0; i < na; i++ {
for j := 0; j < na; j++ {
m[i*na+j] = complex(ca*a.Data[i*a.Stride+j], 0)
}
}
}
// Subtract the diagonal matrix w * D.
m[0] -= w * complex(d1, 0)
if na == 2 {
m[3] -= w * complex(d2, 0)
}
// Convert real na×2 matrices X and scale*B into complex na-vectors.
cx := make([]complex128, na)
cb := make([]complex128, na)
switch nw {
case 1:
for i := 0; i < na; i++ {
cx[i] = complex(x.Data[i*x.Stride], 0)
cb[i] = complex(scale*b.Data[i*x.Stride], 0)
}
case 2:
for i := 0; i < na; i++ {
cx[i] = complex(x.Data[i*x.Stride], x.Data[i*x.Stride+1])
cb[i] = complex(scale*b.Data[i*b.Stride], scale*b.Data[i*b.Stride+1])
}
}
// Compute M * X.
mx := make([]complex128, na)
for i := 0; i < na; i++ {
for j := 0; j < na; j++ {
mx[i] += m[i*na+j] * cx[j]
}
}
// Check whether |M * X - scale * B|_max <= tol.
for i := 0; i < na; i++ {
if cmplx.Abs(mx[i]-cb[i]) > tol {
t.Errorf("Case %v: unexpected value of left-hand side at row %v with scale=%v. Want %v, got %v", prefix, i, scale, cb[i], mx[i])
}
}
}