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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"
)
// Dpocon estimates the reciprocal of the condition number of a positive-definite
// matrix A given the Cholesky decomposition of A. The condition number computed
// is based on the 1-norm and the ∞-norm.
//
// anorm is the 1-norm and the ∞-norm of the original matrix A.
//
// work is a temporary data slice of length at least 3*n and Dpocon will panic otherwise.
//
// iwork is a temporary data slice of length at least n and Dpocon will panic otherwise.
func (impl Implementation) Dpocon(uplo blas.Uplo, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64 {
switch {
case uplo != blas.Upper && uplo != blas.Lower:
panic(badUplo)
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
case anorm < 0:
panic(negANorm)
}
// Quick return if possible.
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)
}
if anorm == 0 {
return 0
}
bi := blas64.Implementation()
var (
smlnum = dlamchS
rcond float64
sl, su float64
normin bool
ainvnm float64
kase int
isave [3]int
)
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
}
if uplo == blas.Upper {
sl = impl.Dlatrs(blas.Upper, blas.Trans, blas.NonUnit, normin, n, a, lda, work, work[2*n:])
normin = true
su = impl.Dlatrs(blas.Upper, blas.NoTrans, blas.NonUnit, normin, n, a, lda, work, work[2*n:])
} else {
sl = impl.Dlatrs(blas.Lower, blas.NoTrans, blas.NonUnit, normin, n, a, lda, work, work[2*n:])
normin = true
su = impl.Dlatrs(blas.Lower, blas.Trans, blas.NonUnit, normin, n, a, lda, work, work[2*n:])
}
scale := sl * su
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)
}
}
}