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zposv

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

 SYNOPSIS
      SUBROUTINE ZPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )

          CHARACTER     UPLO

          INTEGER       INFO, LDA, LDB, N, NRHS

          COMPLEX*16    A( LDA, * ), B( LDB, * )

 PURPOSE
      ZPOSV 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 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) 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.

      A       (input/output) COMPLEX*16 array, dimension (LDA,N)
              On entry, the Hermitian matrix A.  If UPLO = 'U',
              the leading N-by-N upper triangular part of A con-
              tains the upper triangular part of the matrix A, and
              the strictly lower triangular part of A is not
              referenced.  If UPLO = 'L', the leading N-by-N lower
              triangular part of A contains the lower triangular
              part of the matrix A, and the strictly upper tri-
              angular part of A is not referenced.

              On exit, if INFO = 0, the factor U or L from the
              Cholesky factorization A = U**H*U or A = L*L**H.

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

      B       (input/output) COMPLEX*16 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 com-
              puted.