chptri(3S)

NAME
     CHPTRI - compute the inverse of a complex Hermitian indefinite matrix A
     in packed storage using the factorization A = U*D*U**H or A = L*D*L**H
     computed by CHPTRF

SYNOPSIS
     SUBROUTINE CHPTRI( UPLO, N, AP, IPIV, WORK, INFO )

         CHARACTER      UPLO

         INTEGER        INFO, N

         INTEGER        IPIV( * )

         COMPLEX        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
     CHPTRI computes the inverse of a complex Hermitian indefinite matrix A in
     packed storage using the factorization A = U*D*U**H or A = L*D*L**H
     computed by CHPTRF.

ARGUMENTS
     UPLO    (input) 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       (input) INTEGER
             The order of the matrix A.  N >= 0.

     AP      (input/output) COMPLEX array, dimension (N*(N+1)/2)
             On entry, 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.

             On exit, if INFO = 0, the (Hermitian) inverse of the original
             matrix, stored as a packed triangular matrix. The j-th column of
             inv(A) is stored in the array AP as follows:  if UPLO = 'U', AP(i
             + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
             (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.

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

     WORK    (workspace) COMPLEX array, dimension (N)

     INFO    (output) INTEGER
             = 0: successful exit
             < 0: if INFO = -i, the i-th argument had an illegal value
             > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
             inverse could not be computed.

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

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