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pocon(3) LAPACK pocon(3)

NAME

pocon - pocon: condition number estimate

SYNOPSIS

Functions


subroutine cpocon (uplo, n, a, lda, anorm, rcond, work, rwork, info)
CPOCON subroutine dpocon (uplo, n, a, lda, anorm, rcond, work, iwork, info)
DPOCON subroutine spocon (uplo, n, a, lda, anorm, rcond, work, iwork, info)
SPOCON subroutine zpocon (uplo, n, a, lda, anorm, rcond, work, rwork, info)
ZPOCON

Detailed Description

Function Documentation

subroutine cpocon (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real anorm, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CPOCON

Purpose:



 CPOCON estimates the reciprocal of the condition number (in the


 1-norm) of a complex Hermitian positive definite matrix using the


 Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF.


 An estimate is obtained for norm(inv(A)), and the reciprocal of the


 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N



          N is INTEGER


          The order of the matrix A.  N >= 0.

A



          A is COMPLEX array, dimension (LDA,N)


          The triangular factor U or L from the Cholesky factorization


          A = U**H*U or A = L*L**H, as computed by CPOTRF.

LDA



          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,N).

ANORM



          ANORM is REAL


          The 1-norm (or infinity-norm) of the Hermitian matrix A.

RCOND



          RCOND is REAL


          The reciprocal of the condition number of the matrix A,


          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an


          estimate of the 1-norm of inv(A) computed in this routine.

WORK



          WORK is COMPLEX array, dimension (2*N)

RWORK



          RWORK is REAL array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dpocon (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DPOCON

Purpose:



 DPOCON estimates the reciprocal of the condition number (in the


 1-norm) of a real symmetric positive definite matrix using the


 Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF.


 An estimate is obtained for norm(inv(A)), and the reciprocal of the


 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N



          N is INTEGER


          The order of the matrix A.  N >= 0.

A



          A is DOUBLE PRECISION array, dimension (LDA,N)


          The triangular factor U or L from the Cholesky factorization


          A = U**T*U or A = L*L**T, as computed by DPOTRF.

LDA



          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,N).

ANORM



          ANORM is DOUBLE PRECISION


          The 1-norm (or infinity-norm) of the symmetric matrix A.

RCOND



          RCOND is DOUBLE PRECISION


          The reciprocal of the condition number of the matrix A,


          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an


          estimate of the 1-norm of inv(A) computed in this routine.

WORK



          WORK is DOUBLE PRECISION array, dimension (3*N)

IWORK



          IWORK is INTEGER array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine spocon (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SPOCON

Purpose:



 SPOCON estimates the reciprocal of the condition number (in the


 1-norm) of a real symmetric positive definite matrix using the


 Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF.


 An estimate is obtained for norm(inv(A)), and the reciprocal of the


 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N



          N is INTEGER


          The order of the matrix A.  N >= 0.

A



          A is REAL array, dimension (LDA,N)


          The triangular factor U or L from the Cholesky factorization


          A = U**T*U or A = L*L**T, as computed by SPOTRF.

LDA



          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,N).

ANORM



          ANORM is REAL


          The 1-norm (or infinity-norm) of the symmetric matrix A.

RCOND



          RCOND is REAL


          The reciprocal of the condition number of the matrix A,


          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an


          estimate of the 1-norm of inv(A) computed in this routine.

WORK



          WORK is REAL array, dimension (3*N)

IWORK



          IWORK is INTEGER array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zpocon (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision anorm, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZPOCON

Purpose:



 ZPOCON estimates the reciprocal of the condition number (in the


 1-norm) of a complex Hermitian positive definite matrix using the


 Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.


 An estimate is obtained for norm(inv(A)), and the reciprocal of the


 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N



          N is INTEGER


          The order of the matrix A.  N >= 0.

A



          A is COMPLEX*16 array, dimension (LDA,N)


          The triangular factor U or L from the Cholesky factorization


          A = U**H*U or A = L*L**H, as computed by ZPOTRF.

LDA



          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,N).

ANORM



          ANORM is DOUBLE PRECISION


          The 1-norm (or infinity-norm) of the Hermitian matrix A.

RCOND



          RCOND is DOUBLE PRECISION


          The reciprocal of the condition number of the matrix A,


          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an


          estimate of the 1-norm of inv(A) computed in this routine.

WORK



          WORK is COMPLEX*16 array, dimension (2*N)

RWORK



          RWORK is DOUBLE PRECISION array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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