hpcon(3)

NAME
hpcon - {hp,sp}con: condition number estimate

SYNOPSIS

  Functions
subroutine chpcon (uplo, n, ap, ipiv, anorm, rcond, work, info)
CHPCON
subroutine cspcon (uplo, n, ap, ipiv, anorm, rcond, work, info)
CSPCON
subroutine dspcon (uplo, n, ap, ipiv, anorm, rcond, work, iwork, info)
DSPCON
subroutine sspcon (uplo, n, ap, ipiv, anorm, rcond, work, iwork, info)
SSPCON
subroutine zhpcon (uplo, n, ap, ipiv, anorm, rcond, work, info)
ZHPCON
subroutine zspcon (uplo, n, ap, ipiv, anorm, rcond, work, info)
ZSPCON

Detailed Description

Function Documentation

  subroutine chpcon (character uplo, integer n, complex, dimension( * ) ap, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info)

CHPCON

Purpose:

     CHPCON estimates the reciprocal of the condition number of a complex
     Hermitian packed matrix A using the factorization A = U*D*U**H or
     A = L*D*L**H computed by CHPTRF.
     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.

    AP

              AP is COMPLEX array, dimension (N*(N+1)/2)
              The block diagonal matrix D and the multipliers used to
              obtain the factor U or L as computed by CHPTRF, stored as a
              packed triangular matrix.

    IPIV

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

    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 117 of file chpcon.f.

  subroutine cspcon (character uplo, integer n, complex, dimension( * ) ap, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info)

CSPCON

Purpose:

     CSPCON estimates the reciprocal of the condition number (in the
     1-norm) of a complex symmetric packed matrix A using the
     factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF.
     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.

    AP

              AP is COMPLEX array, dimension (N*(N+1)/2)
              The block diagonal matrix D and the multipliers used to
              obtain the factor U or L as computed by CSPTRF, stored as a
              packed triangular matrix.

    IPIV

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

    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 117 of file cspcon.f.

  subroutine dspcon (character uplo, integer n, double precision, dimension( * ) ap, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DSPCON

Purpose:

     DSPCON estimates the reciprocal of the condition number (in the
     1-norm) of a real symmetric packed matrix A using the factorization
     A = U*D*U**T or A = L*D*L**T computed by DSPTRF.
     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.

    AP

              AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
              The block diagonal matrix D and the multipliers used to
              obtain the factor U or L as computed by DSPTRF, stored as a
              packed triangular matrix.

    IPIV

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

    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 123 of file dspcon.f.

  subroutine sspcon (character uplo, integer n, real, dimension( * ) ap, integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SSPCON

Purpose:

     SSPCON estimates the reciprocal of the condition number (in the
     1-norm) of a real symmetric packed matrix A using the factorization
     A = U*D*U**T or A = L*D*L**T computed by SSPTRF.
     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.

    AP

              AP is REAL array, dimension (N*(N+1)/2)
              The block diagonal matrix D and the multipliers used to
              obtain the factor U or L as computed by SSPTRF, stored as a
              packed triangular matrix.

    IPIV

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

    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 123 of file sspcon.f.

  subroutine zhpcon (character uplo, integer n, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, integer info)

ZHPCON

Purpose:

     ZHPCON estimates the reciprocal of the condition number of a complex
     Hermitian packed matrix A using the factorization A = U*D*U**H or
     A = L*D*L**H computed by ZHPTRF.
     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.

    AP

              AP is COMPLEX*16 array, dimension (N*(N+1)/2)
              The block diagonal matrix D and the multipliers used to
              obtain the factor U or L as computed by ZHPTRF, stored as a
              packed triangular matrix.

    IPIV

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

    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 117 of file zhpcon.f.

  subroutine zspcon (character uplo, integer n, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, integer info)

ZSPCON

Purpose:

     ZSPCON estimates the reciprocal of the condition number (in the
     1-norm) of a complex symmetric packed matrix A using the
     factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF.
     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.

    AP

              AP is COMPLEX*16 array, dimension (N*(N+1)/2)
              The block diagonal matrix D and the multipliers used to
              obtain the factor U or L as computed by ZSPTRF, stored as a
              packed triangular matrix.

    IPIV

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

    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 117 of file zspcon.f.

Author

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