hecon_rook - Man Page

{he,sy}con_rook: condition number estimate

Synopsis

Functions

subroutine checon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
CHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)
subroutine csycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
CSYCON_ROOK
subroutine dsycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info)
DSYCON_ROOK
subroutine ssycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info)
SSYCON_ROOK
subroutine zhecon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
ZHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)
subroutine zsycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
ZSYCON_ROOK

Detailed Description

Function Documentation

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

CHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)  

Purpose:

 CHECON_ROOK 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_ROOK.

 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

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

A

          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_ROOK.

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_ROOK.

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.

Contributors:

  December 2016,  Igor Kozachenko,
                  Computer Science Division,
                  University of California, Berkeley

  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                  School of Mathematics,
                  University of Manchester

Definition at line 137 of file checon_rook.f.

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

CSYCON_ROOK  

Purpose:

 CSYCON_ROOK 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_ROOK.

 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

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

A

          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_ROOK.

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_ROOK.

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.

Contributors:

   April 2012, Igor Kozachenko,
                  Computer Science Division,
                  University of California, Berkeley

  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                  School of Mathematics,
                  University of Manchester

Definition at line 137 of file csycon_rook.f.

subroutine dsycon_rook (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_ROOK  

Purpose:

 DSYCON_ROOK 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_ROOK.

 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

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

A

          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_ROOK.

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_ROOK.

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.

Contributors:

   April 2012, Igor Kozachenko,
                  Computer Science Division,
                  University of California, Berkeley

  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                  School of Mathematics,
                  University of Manchester

Definition at line 142 of file dsycon_rook.f.

subroutine ssycon_rook (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_ROOK  

Purpose:

 SSYCON_ROOK 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_ROOK.

 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

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

A

          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_ROOK.

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_ROOK.

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.

Contributors:

   December 2016, Igor Kozachenko,
                  Computer Science Division,
                  University of California, Berkeley

  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                  School of Mathematics,
                  University of Manchester

Definition at line 142 of file ssycon_rook.f.

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

ZHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)  

Purpose:

 ZHECON_ROOK 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_ROOK.

 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

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

A

          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 CHETRF_ROOK.

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_ROOK.

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.

Contributors:

  June 2017,  Igor Kozachenko,
                  Computer Science Division,
                  University of California, Berkeley

  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                  School of Mathematics,
                  University of Manchester

Definition at line 137 of file zhecon_rook.f.

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

ZSYCON_ROOK  

Purpose:

 ZSYCON_ROOK 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_ROOK.

 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

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

A

          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_ROOK.

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_ROOK.

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.

Contributors:

   December 2016, Igor Kozachenko,
                  Computer Science Division,
                  University of California, Berkeley

  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                  School of Mathematics,
                  University of Manchester

Definition at line 137 of file zsycon_rook.f.

Author

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