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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/blas/blas64"
)
// Dpbcon returns an estimate of the reciprocal of the condition number (in the
// 1-norm) of an n×n symmetric positive definite band matrix using the Cholesky
// factorization
//
// A = Uᵀ*U if uplo == blas.Upper
// A = L*Lᵀ if uplo == blas.Lower
//
// computed by Dpbtrf. The estimate is obtained for norm(inv(A)), and the
// reciprocal of the condition number is computed as
//
// rcond = 1 / (anorm * norm(inv(A))).
//
// The length of work must be at least 3*n and the length of iwork must be at
// least n.
func (impl Implementation) Dpbcon(uplo blas.Uplo, n, kd int, ab []float64, ldab int, anorm float64, work []float64, iwork []int) (rcond float64) {
switch {
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)
case anorm < 0:
panic(badNorm)
}
// Quick return if possible.
if n == 0 {
return 1
}
switch {
case len(ab) < (n-1)*ldab+kd+1:
panic(shortAB)
case len(work) < 3*n:
panic(shortWork)
case len(iwork) < n:
panic(shortIWork)
}
// Quick return if possible.
if anorm == 0 {
return 0
}
const smlnum = dlamchS
var (
ainvnm float64
kase int
isave [3]int
normin bool
// Denote work slices.
x = work[:n]
v = work[n : 2*n]
cnorm = work[2*n : 3*n]
)
// Estimate the 1-norm of the inverse.
bi := blas64.Implementation()
for {
ainvnm, kase = impl.Dlacn2(n, v, x, iwork, ainvnm, kase, &isave)
if kase == 0 {
break
}
var op1, op2 blas.Transpose
if uplo == blas.Upper {
// Multiply x by inv(Uᵀ),
op1 = blas.Trans
// then by inv(Uᵀ).
op2 = blas.NoTrans
} else {
// Multiply x by inv(L),
op1 = blas.NoTrans
// then by inv(Lᵀ).
op2 = blas.Trans
}
scaleL := impl.Dlatbs(uplo, op1, blas.NonUnit, normin, n, kd, ab, ldab, x, cnorm)
normin = true
scaleU := impl.Dlatbs(uplo, op2, blas.NonUnit, normin, n, kd, ab, ldab, x, cnorm)
// Multiply x by 1/scale if doing so will not cause overflow.
scale := scaleL * scaleU
if scale != 1 {
ix := bi.Idamax(n, x, 1)
if scale < math.Abs(x[ix])*smlnum || scale == 0 {
return 0
}
impl.Drscl(n, scale, x, 1)
}
}
if ainvnm == 0 {
return 0
}
// Return the estimate of the reciprocal condition number.
return (1 / ainvnm) / anorm
}
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