github.com/gonum/lapack@v0.0.0-20181123203213-e4cdc5a0bff9/native/dpocon.go (about)

     1  // Copyright ©2015 The gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package native
     6  
     7  import (
     8  	"math"
     9  
    10  	"github.com/gonum/blas"
    11  	"github.com/gonum/blas/blas64"
    12  )
    13  
    14  // Dpocon estimates the reciprocal of the condition number of a positive-definite
    15  // matrix A given the Cholesky decomposition of A. The condition number computed
    16  // is based on the 1-norm and the ∞-norm.
    17  //
    18  // anorm is the 1-norm and the ∞-norm of the original matrix A.
    19  //
    20  // work is a temporary data slice of length at least 3*n and Dpocon will panic otherwise.
    21  //
    22  // iwork is a temporary data slice of length at least n and Dpocon will panic otherwise.
    23  func (impl Implementation) Dpocon(uplo blas.Uplo, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64 {
    24  	checkMatrix(n, n, a, lda)
    25  	if uplo != blas.Upper && uplo != blas.Lower {
    26  		panic(badUplo)
    27  	}
    28  	if len(work) < 3*n {
    29  		panic(badWork)
    30  	}
    31  	if len(iwork) < n {
    32  		panic(badWork)
    33  	}
    34  	var rcond float64
    35  	if n == 0 {
    36  		return 1
    37  	}
    38  	if anorm == 0 {
    39  		return rcond
    40  	}
    41  
    42  	bi := blas64.Implementation()
    43  	var ainvnm float64
    44  	smlnum := dlamchS
    45  	upper := uplo == blas.Upper
    46  	var kase int
    47  	var normin bool
    48  	isave := new([3]int)
    49  	var sl, su float64
    50  	for {
    51  		ainvnm, kase = impl.Dlacn2(n, work[n:], work, iwork, ainvnm, kase, isave)
    52  		if kase == 0 {
    53  			if ainvnm != 0 {
    54  				rcond = (1 / ainvnm) / anorm
    55  			}
    56  			return rcond
    57  		}
    58  		if upper {
    59  			sl = impl.Dlatrs(blas.Upper, blas.Trans, blas.NonUnit, normin, n, a, lda, work, work[2*n:])
    60  			normin = true
    61  			su = impl.Dlatrs(blas.Upper, blas.NoTrans, blas.NonUnit, normin, n, a, lda, work, work[2*n:])
    62  		} else {
    63  			sl = impl.Dlatrs(blas.Lower, blas.NoTrans, blas.NonUnit, normin, n, a, lda, work, work[2*n:])
    64  			normin = true
    65  			su = impl.Dlatrs(blas.Lower, blas.Trans, blas.NonUnit, normin, n, a, lda, work, work[2*n:])
    66  		}
    67  		scale := sl * su
    68  		if scale != 1 {
    69  			ix := bi.Idamax(n, work, 1)
    70  			if scale == 0 || scale < math.Abs(work[ix])*smlnum {
    71  				return rcond
    72  			}
    73  			impl.Drscl(n, scale, work, 1)
    74  		}
    75  	}
    76  }