ctptri(3S)

NAME
     CTPTRI - compute the inverse of a complex upper or lower triangular
     matrix A stored in packed format

SYNOPSIS
     SUBROUTINE CTPTRI( UPLO, DIAG, N, AP, INFO )

         CHARACTER      DIAG, UPLO

         INTEGER        INFO, N

         COMPLEX        AP( * )

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
     CTPTRI computes the inverse of a complex upper or lower triangular matrix
     A stored in packed format.

ARGUMENTS
     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/output) COMPLEX array, dimension (N*(N+1)/2)
             On entry, the upper or lower triangular matrix A, stored
             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)*((2*n-j)/2) =
             A(i,j) for j<=i<=n.  See below for further details.  On exit, the
             (triangular) inverse of the original matrix, in the same packed
             storage format.
     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value
             > 0:  if INFO = i, A(i,i) is exactly zero.  The triangular matrix
             is singular and its inverse can not be computed.

FURTHER DETAILS
     A triangular matrix A can be transferred to packed storage using one of
     the following program segments:

     UPLO = 'U':                      UPLO = 'L':

           JC = 1                           JC = 1
           DO 2 J = 1, N                    DO 2 J = 1, N
              DO 1 I = 1, J                    DO 1 I = J, N
                 AP(JC+I-1) = A(I,J)              AP(JC+I-J) = A(I,J)
         1    CONTINUE                    1    CONTINUE
              JC = JC + J                      JC = JC + N - J + 1
         2 CONTINUE                       2 CONTINUE


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

     This man page is available only online.