ppcon(3)

NAME
ppcon - ppcon: condition number estimate

SYNOPSIS

  Functions
subroutine cppcon (uplo, n, ap, anorm, rcond, work, rwork, info)
CPPCON
subroutine dppcon (uplo, n, ap, anorm, rcond, work, iwork, info)
DPPCON
subroutine sppcon (uplo, n, ap, anorm, rcond, work, iwork, info)
SPPCON
subroutine zppcon (uplo, n, ap, anorm, rcond, work, rwork, info)
ZPPCON

Detailed Description

Function Documentation

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

CPPCON

Purpose:

     CPPCON estimates the reciprocal of the condition number (in the
     1-norm) of a complex Hermitian positive definite packed matrix using
     the Cholesky factorization A = U**H*U or A = L*L**H computed by
     CPPTRF.
     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
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

    N

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

    AP

              AP is COMPLEX array, dimension (N*(N+1)/2)
              The triangular factor U or L from the Cholesky factorization
              A = U**H*U or A = L*L**H, packed columnwise in a linear
              array.  The j-th column of U or L is stored in the array AP
              as follows:
              if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
              if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

    ANORM

              ANORM is REAL
              The 1-norm (or infinity-norm) of the Hermitian 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)

    RWORK

              RWORK is REAL 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 117 of file cppcon.f.

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

DPPCON

Purpose:

     DPPCON estimates the reciprocal of the condition number (in the
     1-norm) of a real symmetric positive definite packed matrix using
     the Cholesky factorization A = U**T*U or A = L*L**T computed by
     DPPTRF.
     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
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

    N

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

    AP

              AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
              The triangular factor U or L from the Cholesky factorization
              A = U**T*U or A = L*L**T, packed columnwise in a linear
              array.  The j-th column of U or L is stored in the array AP
              as follows:
              if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
              if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

    ANORM

              ANORM is DOUBLE PRECISION
              The 1-norm (or infinity-norm) of the symmetric 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 (3*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 117 of file dppcon.f.

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

SPPCON

Purpose:

     SPPCON estimates the reciprocal of the condition number (in the
     1-norm) of a real symmetric positive definite packed matrix using
     the Cholesky factorization A = U**T*U or A = L*L**T computed by
     SPPTRF.
     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
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

    N

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

    AP

              AP is REAL array, dimension (N*(N+1)/2)
              The triangular factor U or L from the Cholesky factorization
              A = U**T*U or A = L*L**T, packed columnwise in a linear
              array.  The j-th column of U or L is stored in the array AP
              as follows:
              if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
              if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

    ANORM

              ANORM is REAL
              The 1-norm (or infinity-norm) of the symmetric 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 (3*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 117 of file sppcon.f.

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

ZPPCON

Purpose:

     ZPPCON estimates the reciprocal of the condition number (in the
     1-norm) of a complex Hermitian positive definite packed matrix using
     the Cholesky factorization A = U**H*U or A = L*L**H computed by
     ZPPTRF.
     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
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

    N

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

    AP

              AP is COMPLEX*16 array, dimension (N*(N+1)/2)
              The triangular factor U or L from the Cholesky factorization
              A = U**H*U or A = L*L**H, packed columnwise in a linear
              array.  The j-th column of U or L is stored in the array AP
              as follows:
              if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
              if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

    ANORM

              ANORM is DOUBLE PRECISION
              The 1-norm (or infinity-norm) of the Hermitian 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)

    RWORK

              RWORK is DOUBLE PRECISION 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 117 of file zppcon.f.

Author

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