hecon(3)

Library Functions Manual

hecon(3)

NAME

hecon - {he,sy}con: condition number estimate

SYNOPSIS

Functions

subroutine checon (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
CHECON subroutine csycon (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
CSYCON subroutine dsycon (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info)
DSYCON subroutine ssycon (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info)
SSYCON subroutine zhecon (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
ZHECON subroutine zsycon (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
ZSYCON

Detailed Description

Function Documentation

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

CHECON

Purpose:

 CHECON estimates the reciprocal of the condition number of a complex
 Hermitian matrix A using the factorization A = U*D*U**H or
 A = L*D*L**H computed by CHETRF.
 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
          Specifies whether the details of the factorization are stored
          as an upper or lower triangular matrix.
          = 'U':  Upper triangular, form is A = U*D*U**H;
          = 'L':  Lower triangular, form is A = L*D*L**H.

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

          A is COMPLEX array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by CHETRF.

LDA

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

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by CHETRF.

ANORM

          ANORM is REAL
          The 1-norm of the original 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)

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.

Definition at line 123 of file checon.f.

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

CSYCON

Purpose:

 CSYCON estimates the reciprocal of the condition number (in the
 1-norm) of a complex symmetric matrix A using the factorization
 A = U*D*U**T or A = L*D*L**T computed by CSYTRF.
 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
          Specifies whether the details of the factorization are stored
          as an upper or lower triangular matrix.
          = 'U':  Upper triangular, form is A = U*D*U**T;
          = 'L':  Lower triangular, form is A = L*D*L**T.

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

          A is COMPLEX array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by CSYTRF.

LDA

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

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by CSYTRF.

ANORM

          ANORM is REAL
          The 1-norm of the original 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)

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.

Definition at line 123 of file csycon.f.

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

DSYCON

Purpose:

 DSYCON estimates the reciprocal of the condition number (in the
 1-norm) of a real symmetric matrix A using the factorization
 A = U*D*U**T or A = L*D*L**T computed by DSYTRF.
 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
          Specifies whether the details of the factorization are stored
          as an upper or lower triangular matrix.
          = 'U':  Upper triangular, form is A = U*D*U**T;
          = 'L':  Lower triangular, form is A = L*D*L**T.

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

          A is DOUBLE PRECISION array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by DSYTRF.

LDA

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

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by DSYTRF.

ANORM

          ANORM is DOUBLE PRECISION
          The 1-norm of the original 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 (2*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.

Definition at line 128 of file dsycon.f.

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

SSYCON

Purpose:

 SSYCON estimates the reciprocal of the condition number (in the
 1-norm) of a real symmetric matrix A using the factorization
 A = U*D*U**T or A = L*D*L**T computed by SSYTRF.
 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
          Specifies whether the details of the factorization are stored
          as an upper or lower triangular matrix.
          = 'U':  Upper triangular, form is A = U*D*U**T;
          = 'L':  Lower triangular, form is A = L*D*L**T.

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

          A is REAL array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by SSYTRF.

LDA

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

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by SSYTRF.

ANORM

          ANORM is REAL
          The 1-norm of the original 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 (2*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.

Definition at line 128 of file ssycon.f.

subroutine zhecon (character uplo, integer n, complex16, dimension( lda, ) a, integer lda, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex16, dimension( ) work, integer info)

ZHECON

Purpose:

 ZHECON estimates the reciprocal of the condition number of a complex
 Hermitian matrix A using the factorization A = U*D*U**H or
 A = L*D*L**H computed by ZHETRF.
 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
          Specifies whether the details of the factorization are stored
          as an upper or lower triangular matrix.
          = 'U':  Upper triangular, form is A = U*D*U**H;
          = 'L':  Lower triangular, form is A = L*D*L**H.

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

          A is COMPLEX*16 array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by ZHETRF.

LDA

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

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by ZHETRF.

ANORM

          ANORM is DOUBLE PRECISION
          The 1-norm of the original 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)

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.

Definition at line 123 of file zhecon.f.

subroutine zsycon (character uplo, integer n, complex16, dimension( lda, ) a, integer lda, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex16, dimension( ) work, integer info)

ZSYCON

Purpose:

 ZSYCON estimates the reciprocal of the condition number (in the
 1-norm) of a complex symmetric matrix A using the factorization
 A = U*D*U**T or A = L*D*L**T computed by ZSYTRF.
 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
          Specifies whether the details of the factorization are stored
          as an upper or lower triangular matrix.
          = 'U':  Upper triangular, form is A = U*D*U**T;
          = 'L':  Lower triangular, form is A = L*D*L**T.

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

          A is COMPLEX*16 array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by ZSYTRF.

LDA

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

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by ZSYTRF.

ANORM

          ANORM is DOUBLE PRECISION
          The 1-norm of the original 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)

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.

Definition at line 123 of file zsycon.f.

Author

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