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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/blas/blas64"
"gonum.org/v1/gonum/lapack"
)
// Dtrcon estimates the reciprocal of the condition number of a triangular matrix A.
// The condition number computed may be based on the 1-norm or the ∞-norm.
//
// work is a temporary data slice of length at least 3*n and Dtrcon will panic otherwise.
//
// iwork is a temporary data slice of length at least n and Dtrcon will panic otherwise.
func (impl Implementation) Dtrcon(norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int, work []float64, iwork []int) float64 {
switch {
case norm != lapack.MaxColumnSum && norm != lapack.MaxRowSum:
panic(badNorm)
case uplo != blas.Upper && uplo != blas.Lower:
panic(badUplo)
case diag != blas.NonUnit && diag != blas.Unit:
panic(badDiag)
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
}
if n == 0 {
return 1
}
switch {
case len(a) < (n-1)*lda+n:
panic(shortA)
case len(work) < 3*n:
panic(shortWork)
case len(iwork) < n:
panic(shortIWork)
}
bi := blas64.Implementation()
var rcond float64
smlnum := dlamchS * float64(n)
anorm := impl.Dlantr(norm, uplo, diag, n, n, a, lda, work)
if anorm <= 0 {
return rcond
}
var ainvnm float64
var normin bool
kase1 := 2
if norm == lapack.MaxColumnSum {
kase1 = 1
}
var kase int
isave := new([3]int)
var scale float64
for {
ainvnm, kase = impl.Dlacn2(n, work[n:], work, iwork, ainvnm, kase, isave)
if kase == 0 {
if ainvnm != 0 {
rcond = (1 / anorm) / ainvnm
}
return rcond
}
if kase == kase1 {
scale = impl.Dlatrs(uplo, blas.NoTrans, diag, normin, n, a, lda, work, work[2*n:])
} else {
scale = impl.Dlatrs(uplo, blas.Trans, diag, normin, n, a, lda, work, work[2*n:])
}
normin = true
if scale != 1 {
ix := bi.Idamax(n, work, 1)
xnorm := math.Abs(work[ix])
if scale == 0 || scale < xnorm*smlnum {
return rcond
}
impl.Drscl(n, scale, work, 1)
}
}
}
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