hecon_rook(3)

NAME
hecon_rook - {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
    !>
    !>

  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
    !>
    !>

  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
    !>
    !>

  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
    !>
    !>

  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
    !>
    !>

  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
    !>
    !>

Author

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