dpotrs(l) [redhat man page]

DPOTRS(l)								 )								 DPOTRS(l)

NAME

       DPOTRS - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U
       or A = L*L**T computed by DPOTRF

SYNOPSIS

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

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDA, LDB, N, NRHS

	   DOUBLE	  PRECISION A( LDA, * ), B( LDB, * )

PURPOSE

       DPOTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A =  U**T*U
       or A = L*L**T computed by DPOTRF.

ARGUMENTS

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

       N       (input) INTEGER
	       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) DOUBLE PRECISION array, dimension (LDA,N)
	       The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by DPOTRF.

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

       B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
	       On entry, the right hand side matrix B.	On exit, the 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

LAPACK version 3.0						   15 June 2000 							 DPOTRS(l)

DPOSV(l)								 )								  DPOSV(l)

NAME

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

SYNOPSIS

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

	   CHARACTER	 UPLO

	   INTEGER	 INFO, LDA, LDB, N, NRHS

	   DOUBLE	 PRECISION A( LDA, * ), B( LDB, * )

PURPOSE

       DPOSV  computes	the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix 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 equa-
       tions 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) DOUBLE PRECISION array, dimension (LDA,N)
	       On  entry, the symmetric matrix A.  If UPLO = 'U', the leading N-by-N upper triangular part of A contains 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 triangular part of A is not referenced.

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

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

       B       (input/output) DOUBLE PRECISION 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.

LAPACK version 3.0						   15 June 2000 							  DPOSV(l)