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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"
)
// Dlansy returns the value of the specified norm of an n×n symmetric matrix. If
// norm == lapack.MaxColumnSum or norm == lapack.MaxRowSum, work must have length
// at least n, otherwise work is unused.
func (impl Implementation) Dlansy(norm lapack.MatrixNorm, uplo blas.Uplo, 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 n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
}
// Quick return if possible.
if n == 0 {
return 0
}
switch {
case len(a) < (n-1)*lda+n:
panic(shortA)
case (norm == lapack.MaxColumnSum || norm == lapack.MaxRowSum) && len(work) < n:
panic(shortWork)
}
switch norm {
case lapack.MaxAbs:
if uplo == blas.Upper {
var max float64
for i := 0; i < n; i++ {
for j := i; j < n; j++ {
v := math.Abs(a[i*lda+j])
if math.IsNaN(v) {
return math.NaN()
}
if v > max {
max = v
}
}
}
return max
}
var max float64
for i := 0; i < n; i++ {
for j := 0; j <= i; j++ {
v := math.Abs(a[i*lda+j])
if math.IsNaN(v) {
return math.NaN()
}
if v > max {
max = v
}
}
}
return max
case lapack.MaxRowSum, lapack.MaxColumnSum:
// A symmetric matrix has the same 1-norm and ∞-norm.
for i := 0; i < n; i++ {
work[i] = 0
}
if uplo == blas.Upper {
for i := 0; i < n; i++ {
work[i] += math.Abs(a[i*lda+i])
for j := i + 1; j < n; j++ {
v := math.Abs(a[i*lda+j])
work[i] += v
work[j] += v
}
}
} else {
for i := 0; i < n; i++ {
for j := 0; j < i; j++ {
v := math.Abs(a[i*lda+j])
work[i] += v
work[j] += v
}
work[i] += math.Abs(a[i*lda+i])
}
}
var max float64
for i := 0; i < n; i++ {
v := work[i]
if math.IsNaN(v) {
return math.NaN()
}
if v > max {
max = v
}
}
return max
default:
// lapack.Frobenius:
scale := 0.0
ssq := 1.0
// Sum off-diagonals.
if uplo == blas.Upper {
for i := 0; i < n-1; i++ {
rowscale, rowssq := impl.Dlassq(n-i-1, a[i*lda+i+1:], 1, 0, 1)
scale, ssq = impl.Dcombssq(scale, ssq, rowscale, rowssq)
}
} else {
for i := 1; i < n; i++ {
rowscale, rowssq := impl.Dlassq(i, a[i*lda:], 1, 0, 1)
scale, ssq = impl.Dcombssq(scale, ssq, rowscale, rowssq)
}
}
ssq *= 2
// Sum diagonal.
dscale, dssq := impl.Dlassq(n, a, lda+1, 0, 1)
scale, ssq = impl.Dcombssq(scale, ssq, dscale, dssq)
return scale * math.Sqrt(ssq)
}
}