sppsv(3S)

NAME
     SPPSV - compute the solution to a real system of linear equations A * X =
     B,

SYNOPSIS
     SUBROUTINE SPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )

         CHARACTER     UPLO

         INTEGER       INFO, LDB, N, NRHS

         REAL          AP( * ), B( LDB, * )

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
     SPPSV computes the solution to a real system of linear equations A * X =
     B, where A is an N-by-N symmetric positive definite matrix stored in
     packed format and X and B are N-by-NRHS matrices.

     The Cholesky decomposition is used to factor A as
        A = U**T* U,  if UPLO = 'U', or
        A = L * L**T,  if UPLO = 'L',
     where U is an upper triangular matrix and L is a lower triangular matrix.
     The factored form of A is then used to solve the system of equations A *
     X = B.


ARGUMENTS
     UPLO    (input) CHARACTER*1
             = 'U':  Upper triangle of A is stored;
             = 'L':  Lower triangle of A is stored.

     N       (input) INTEGER
             The number of linear equations, i.e., the order of the matrix A.
             N >= 0.

     NRHS    (input) INTEGER
             The number of right hand sides, i.e., the number of columns of
             the matrix B.  NRHS >= 0.
     AP      (input/output) REAL array, dimension (N*(N+1)/2)
             On entry, the upper or lower triangle of the symmetric 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.  See below for further details.

             On exit, if INFO = 0, the factor U or L from the Cholesky
             factorization A = U**T*U or A = L*L**T, in the same storage
             format as A.

     B       (input/output) REAL array, dimension (LDB,NRHS)
             On entry, the N-by-NRHS right hand side matrix B.  On exit, if
             INFO = 0, the N-by-NRHS solution matrix X.

     LDB     (input) INTEGER
             The leading dimension of the array B.  LDB >= max(1,N).

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value
             > 0:  if INFO = i, the leading minor of order i of A is not
             positive definite, so the factorization could not be completed,
             and the solution has not been computed.

FURTHER DETAILS
     The packed storage scheme is illustrated by the following example when N
     = 4, UPLO = 'U':

     Two-dimensional storage of the symmetric matrix A:

        a11 a12 a13 a14
            a22 a23 a24
                a33 a34     (aij = conjg(aji))
                    a44

     Packed storage of the upper triangle of A:

     AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]


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

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