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RedHat 9 (Linux i386) - man page for cppsv (redhat section l)

CPPSV(l)					)					 CPPSV(l)

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

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

	   CHARACTER	 UPLO

	   INTEGER	 INFO, LDB, N, NRHS

	   COMPLEX	 AP( * ), B( LDB, * )

PURPOSE
       CPPSV  computes the solution to a complex system of linear equations A * X = B, where A is
       an N-by-N Hermitian 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**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 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) COMPLEX array, dimension (N*(N+1)/2)
	       On entry, the upper or lower triangle of the Hermitian 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**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) 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 Hermitian 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 ]

LAPACK version 3.0			   15 June 2000 				 CPPSV(l)


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