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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"
)
// Dgecon estimates the reciprocal of the condition number of the n×n matrix A
// given the LU decomposition of the matrix. The condition number computed may
// be based on the 1-norm or the ∞-norm.
//
// The slice a contains the result of the LU decomposition of A as computed by Dgetrf.
//
// anorm is the corresponding 1-norm or ∞-norm of the original matrix A.
//
// work is a temporary data slice of length at least 4*n and Dgecon will panic otherwise.
//
// iwork is a temporary data slice of length at least n and Dgecon will panic otherwise.
func (impl Implementation) Dgecon(norm lapack.MatrixNorm, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64 {
switch {
case norm != lapack.MaxColumnSum && norm != lapack.MaxRowSum:
panic(badNorm)
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
}
// Quick return if possible.
if n == 0 {
return 1
}
switch {
case len(a) < (n-1)*lda+n:
panic(shortA)
case len(work) < 4*n:
panic(shortWork)
case len(iwork) < n:
panic(shortIWork)
}
// Quick return if possible.
if anorm == 0 {
return 0
}
bi := blas64.Implementation()
var rcond, ainvnm float64
var kase int
var normin bool
isave := new([3]int)
onenrm := norm == lapack.MaxColumnSum
smlnum := dlamchS
kase1 := 2
if onenrm {
kase1 = 1
}
for {
ainvnm, kase = impl.Dlacn2(n, work[n:], work, iwork, ainvnm, kase, isave)
if kase == 0 {
if ainvnm != 0 {
rcond = (1 / ainvnm) / anorm
}
return rcond
}
var sl, su float64
if kase == kase1 {
sl = impl.Dlatrs(blas.Lower, blas.NoTrans, blas.Unit, normin, n, a, lda, work, work[2*n:])
su = impl.Dlatrs(blas.Upper, blas.NoTrans, blas.NonUnit, normin, n, a, lda, work, work[3*n:])
} else {
su = impl.Dlatrs(blas.Upper, blas.Trans, blas.NonUnit, normin, n, a, lda, work, work[3*n:])
sl = impl.Dlatrs(blas.Lower, blas.Trans, blas.Unit, normin, n, a, lda, work, work[2*n:])
}
scale := sl * su
normin = true
if scale != 1 {
ix := bi.Idamax(n, work, 1)
if scale == 0 || scale < math.Abs(work[ix])*smlnum {
return rcond
}
impl.Drscl(n, scale, work, 1)
}
}
}