Contents


NAME

     cppsv - compute the solution to a complex system  of  linear
     equations  A * X = B,

SYNOPSIS

     SUBROUTINE CPPSV(UPLO, N, NRHS, A, B, LDB, INFO)

     CHARACTER * 1 UPLO
     COMPLEX A(*), B(LDB,*)
     INTEGER N, NRHS, LDB, INFO

     SUBROUTINE CPPSV_64(UPLO, N, NRHS, A, B, LDB, INFO)

     CHARACTER * 1 UPLO
     COMPLEX A(*), B(LDB,*)
     INTEGER*8 N, NRHS, LDB, INFO

  F95 INTERFACE
     SUBROUTINE PPSV(UPLO, [N], [NRHS], A, B, [LDB], [INFO])

     CHARACTER(LEN=1) :: UPLO
     COMPLEX, DIMENSION(:) :: A
     COMPLEX, DIMENSION(:,:) :: B
     INTEGER :: N, NRHS, LDB, INFO

     SUBROUTINE PPSV_64(UPLO, [N], [NRHS], A, B, [LDB], [INFO])

     CHARACTER(LEN=1) :: UPLO
     COMPLEX, DIMENSION(:) :: A
     COMPLEX, DIMENSION(:,:) :: B
     INTEGER(8) :: N, NRHS, LDB, INFO

  C INTERFACE
     #include <sunperf.h>

     void cppsv(char uplo, int n, int nrhs, complex  *a,  complex
               *b, int ldb, int *info);

     void cppsv_64(char uplo, long n, long nrhs, complex *a, com-
               plex *b, long ldb, long *info);

PURPOSE

     cppsv computes the solution to a complex  system  of  linear
     equations
        A * X = B, where A is an N-by-N Hermitian positive defin-
     ite 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**H* U,  if UPLO = 'U', or
        A = L * L**H,  if UPLO = 'L',
     where U is an upper triangular matrix and L is a lower  tri-
     angular  matrix.   The  factored  form  of A is then used to
     solve the system of equations A * X = B.

ARGUMENTS

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

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

     NRHS (input)
               The number of right hand sides, i.e.,  the  number
               of columns of the matrix B.  NRHS >= 0.

     A (input/output) COMPLEX array, dimension (N*(N+1)/2)
               On entry, the upper or lower triangle of the  Her-
               mitian  matrix  A,  packed  columnwise in a linear
               array.  The j-th column of  A  is  stored  in  the
               array  A  as  follows:   if  UPLO = 'U', A(i + (j-
               1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', A(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**H*U or A = L*L**H,
               in the same storage format as A.

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

     INFO (output)
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal 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 Hermitian matrix A:

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

     Packed storage of the upper triangle of A:

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