ztpcon(3S)

NAME
     ZTPCON - estimate the reciprocal of the condition number of a packed
     triangular matrix A, in either the 1-norm or the infinity-norm

SYNOPSIS
     SUBROUTINE ZTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK, INFO )

         CHARACTER      DIAG, NORM, UPLO

         INTEGER        INFO, N

         DOUBLE         PRECISION RCOND

         DOUBLE         PRECISION RWORK( * )

         COMPLEX*16     AP( * ), WORK( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     ZTPCON estimates the reciprocal of the condition number of a packed
     triangular matrix A, in either the 1-norm or the infinity-norm. The norm
     of A is computed and an estimate is obtained for norm(inv(A)), then the
     reciprocal of the condition number is computed as
        RCOND = 1 / ( norm(A) * norm(inv(A)) ).


ARGUMENTS
     NORM    (input) CHARACTER*1
             Specifies whether the 1-norm condition number or the infinity-
             norm condition number is required:
             = '1' or 'O':  1-norm;
             = 'I':         Infinity-norm.

     UPLO    (input) CHARACTER*1
             = 'U':  A is upper triangular;
             = 'L':  A is lower triangular.

     DIAG    (input) CHARACTER*1
             = 'N':  A is non-unit triangular;
             = 'U':  A is unit triangular.
     N       (input) INTEGER
             The order of the matrix A.  N >= 0.

     AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2)
             The upper or lower triangular matrix A, packed columnwise in a
             linear array.  The j-th column of A is stored in the array AP as
             follows:  if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
             if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.  If
             DIAG = 'U', the diagonal elements of A are not referenced and are
             assumed to be 1.

     RCOND   (output) DOUBLE PRECISION
             The reciprocal of the condition number of the matrix A, computed
             as RCOND = 1/(norm(A) * norm(inv(A))).

     WORK    (workspace) COMPLEX*16 array, dimension (2*N)

     RWORK   (workspace) DOUBLE PRECISION array, dimension (N)

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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