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.

  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.

  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.

  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.

  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.

  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.

Author

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