zpttrf(3S)

NAME
     ZPTTRF - compute the L*D*L' factorization of a complex Hermitian positive
     definite tridiagonal matrix A

SYNOPSIS
     SUBROUTINE ZPTTRF( N, D, E, INFO )

         INTEGER        INFO, N

         DOUBLE         PRECISION D( * )

         COMPLEX*16     E( * )

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
     ZPTTRF computes the L*D*L' factorization of a complex Hermitian positive
     definite tridiagonal matrix A. The factorization may also be regarded as
     having the form A = U'*D*U.


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

     D       (input/output) DOUBLE PRECISION array, dimension (N)
             On entry, the n diagonal elements of the tridiagonal matrix A.
             On exit, the n diagonal elements of the diagonal matrix D from
             the L*D*L' factorization of A.

     E       (input/output) COMPLEX*16 array, dimension (N-1)
             On entry, the (n-1) subdiagonal elements of the tridiagonal
             matrix A.  On exit, the (n-1) subdiagonal elements of the unit
             bidiagonal factor L from the L*D*L' factorization of A.  E can
             also be regarded as the superdiagonal of the unit bidiagonal
             factor U from the U'*D*U factorization of A.

     INFO    (output) INTEGER
             = 0: successful exit
             < 0: if INFO = -k, the k-th argument had an illegal value
             > 0: if INFO = k, the leading minor of order k is not positive
             definite; if k < N, the factorization could not be completed,
             while if k = N, the factorization was completed, but D(N) = 0.

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

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