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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 gonum
import (
"math"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/lapack"
)
// Dlantr computes the specified norm of an m×n trapezoidal matrix A. If
// norm == lapack.MaxColumnSum work must have length at least n, otherwise work
// is unused.
func (impl Implementation) Dlantr(norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, m, n int, a []float64, lda int, work []float64) float64 {
switch {
case norm != lapack.MaxRowSum && norm != lapack.MaxColumnSum && norm != lapack.Frobenius && norm != lapack.MaxAbs:
panic(badNorm)
case uplo != blas.Upper && uplo != blas.Lower:
panic(badUplo)
case diag != blas.Unit && diag != blas.NonUnit:
panic(badDiag)
case m < 0:
panic(mLT0)
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
}
// Quick return if possible.
minmn := min(m, n)
if minmn == 0 {
return 0
}
switch {
case len(a) < (m-1)*lda+n:
panic(shortA)
case norm == lapack.MaxColumnSum && len(work) < n:
panic(shortWork)
}
switch norm {
case lapack.MaxAbs:
if diag == blas.Unit {
value := 1.0
if uplo == blas.Upper {
for i := 0; i < m; i++ {
for j := i + 1; j < n; j++ {
tmp := math.Abs(a[i*lda+j])
if math.IsNaN(tmp) {
return tmp
}
if tmp > value {
value = tmp
}
}
}
return value
}
for i := 1; i < m; i++ {
for j := 0; j < min(i, n); j++ {
tmp := math.Abs(a[i*lda+j])
if math.IsNaN(tmp) {
return tmp
}
if tmp > value {
value = tmp
}
}
}
return value
}
var value float64
if uplo == blas.Upper {
for i := 0; i < m; i++ {
for j := i; j < n; j++ {
tmp := math.Abs(a[i*lda+j])
if math.IsNaN(tmp) {
return tmp
}
if tmp > value {
value = tmp
}
}
}
return value
}
for i := 0; i < m; i++ {
for j := 0; j <= min(i, n-1); j++ {
tmp := math.Abs(a[i*lda+j])
if math.IsNaN(tmp) {
return tmp
}
if tmp > value {
value = tmp
}
}
}
return value
case lapack.MaxColumnSum:
if diag == blas.Unit {
for i := 0; i < minmn; i++ {
work[i] = 1
}
for i := minmn; i < n; i++ {
work[i] = 0
}
if uplo == blas.Upper {
for i := 0; i < m; i++ {
for j := i + 1; j < n; j++ {
work[j] += math.Abs(a[i*lda+j])
}
}
} else {
for i := 1; i < m; i++ {
for j := 0; j < min(i, n); j++ {
work[j] += math.Abs(a[i*lda+j])
}
}
}
} else {
for i := 0; i < n; i++ {
work[i] = 0
}
if uplo == blas.Upper {
for i := 0; i < m; i++ {
for j := i; j < n; j++ {
work[j] += math.Abs(a[i*lda+j])
}
}
} else {
for i := 0; i < m; i++ {
for j := 0; j <= min(i, n-1); j++ {
work[j] += math.Abs(a[i*lda+j])
}
}
}
}
var max float64
for _, v := range work[:n] {
if math.IsNaN(v) {
return math.NaN()
}
if v > max {
max = v
}
}
return max
case lapack.MaxRowSum:
var maxsum float64
if diag == blas.Unit {
if uplo == blas.Upper {
for i := 0; i < m; i++ {
var sum float64
if i < minmn {
sum = 1
}
for j := i + 1; j < n; j++ {
sum += math.Abs(a[i*lda+j])
}
if math.IsNaN(sum) {
return math.NaN()
}
if sum > maxsum {
maxsum = sum
}
}
return maxsum
} else {
for i := 0; i < m; i++ {
var sum float64
if i < minmn {
sum = 1
}
for j := 0; j < min(i, n); j++ {
sum += math.Abs(a[i*lda+j])
}
if math.IsNaN(sum) {
return math.NaN()
}
if sum > maxsum {
maxsum = sum
}
}
return maxsum
}
} else {
if uplo == blas.Upper {
for i := 0; i < m; i++ {
var sum float64
for j := i; j < n; j++ {
sum += math.Abs(a[i*lda+j])
}
if math.IsNaN(sum) {
return sum
}
if sum > maxsum {
maxsum = sum
}
}
return maxsum
} else {
for i := 0; i < m; i++ {
var sum float64
for j := 0; j <= min(i, n-1); j++ {
sum += math.Abs(a[i*lda+j])
}
if math.IsNaN(sum) {
return sum
}
if sum > maxsum {
maxsum = sum
}
}
return maxsum
}
}
default:
// lapack.Frobenius:
var scale, sum float64
if diag == blas.Unit {
scale = 1
sum = float64(min(m, n))
if uplo == blas.Upper {
for i := 0; i < min(m, n); i++ {
scale, sum = impl.Dlassq(n-i-1, a[i*lda+i+1:], 1, scale, sum)
}
} else {
for i := 1; i < m; i++ {
scale, sum = impl.Dlassq(min(i, n), a[i*lda:], 1, scale, sum)
}
}
} else {
scale = 0
sum = 1
if uplo == blas.Upper {
for i := 0; i < min(m, n); i++ {
scale, sum = impl.Dlassq(n-i, a[i*lda+i:], 1, scale, sum)
}
} else {
for i := 0; i < m; i++ {
scale, sum = impl.Dlassq(min(i+1, n), a[i*lda:], 1, scale, sum)
}
}
}
return scale * math.Sqrt(sum)
}
}
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