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// Copyright ©2019 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"
)
// Dlansb returns the given norm of an n×n symmetric band matrix with kd
// super-diagonals.
//
// When norm is lapack.MaxColumnSum or lapack.MaxRowSum, the length of work must
// be at least n.
func (impl Implementation) Dlansb(norm lapack.MatrixNorm, uplo blas.Uplo, n, kd int, ab []float64, ldab int, work []float64) float64 {
switch {
case norm != lapack.MaxAbs && norm != lapack.MaxRowSum && norm != lapack.MaxColumnSum && norm != lapack.Frobenius:
panic(badNorm)
case uplo != blas.Upper && uplo != blas.Lower:
panic(badUplo)
case n < 0:
panic(nLT0)
case kd < 0:
panic(kdLT0)
case ldab < kd+1:
panic(badLdA)
}
// Quick return if possible.
if n == 0 {
return 0
}
switch {
case len(ab) < (n-1)*ldab+kd+1:
panic(shortAB)
case len(work) < n && (norm == lapack.MaxColumnSum || norm == lapack.MaxRowSum):
panic(shortWork)
}
var value float64
switch norm {
case lapack.MaxAbs:
if uplo == blas.Upper {
for i := 0; i < n; i++ {
for j := 0; j < min(n-i, kd+1); j++ {
aij := math.Abs(ab[i*ldab+j])
if aij > value || math.IsNaN(aij) {
value = aij
}
}
}
} else {
for i := 0; i < n; i++ {
for j := max(0, kd-i); j < kd+1; j++ {
aij := math.Abs(ab[i*ldab+j])
if aij > value || math.IsNaN(aij) {
value = aij
}
}
}
}
case lapack.MaxColumnSum, lapack.MaxRowSum:
work = work[:n]
var sum float64
if uplo == blas.Upper {
for i := range work {
work[i] = 0
}
for i := 0; i < n; i++ {
sum := work[i] + math.Abs(ab[i*ldab])
for j := i + 1; j < min(i+kd+1, n); j++ {
aij := math.Abs(ab[i*ldab+j-i])
sum += aij
work[j] += aij
}
if sum > value || math.IsNaN(sum) {
value = sum
}
}
} else {
for i := 0; i < n; i++ {
sum = 0
for j := max(0, i-kd); j < i; j++ {
aij := math.Abs(ab[i*ldab+kd+j-i])
sum += aij
work[j] += aij
}
work[i] = sum + math.Abs(ab[i*ldab+kd])
}
for _, sum := range work {
if sum > value || math.IsNaN(sum) {
value = sum
}
}
}
case lapack.Frobenius:
scale := 0.0
ssq := 1.0
if uplo == blas.Upper {
if kd > 0 {
// Sum off-diagonals.
for i := 0; i < n-1; i++ {
ilen := min(n-i-1, kd)
rowscale, rowssq := impl.Dlassq(ilen, ab[i*ldab+1:], 1, 0, 1)
scale, ssq = impl.Dcombssq(scale, ssq, rowscale, rowssq)
}
ssq *= 2
}
// Sum diagonal.
dscale, dssq := impl.Dlassq(n, ab, ldab, 0, 1)
scale, ssq = impl.Dcombssq(scale, ssq, dscale, dssq)
} else {
if kd > 0 {
// Sum off-diagonals.
for i := 1; i < n; i++ {
ilen := min(i, kd)
rowscale, rowssq := impl.Dlassq(ilen, ab[i*ldab+kd-ilen:], 1, 0, 1)
scale, ssq = impl.Dcombssq(scale, ssq, rowscale, rowssq)
}
ssq *= 2
}
// Sum diagonal.
dscale, dssq := impl.Dlassq(n, ab[kd:], ldab, 0, 1)
scale, ssq = impl.Dcombssq(scale, ssq, dscale, dssq)
}
value = scale * math.Sqrt(ssq)
}
return value
}