sppsv(l) [redhat man page]

SPPSV(l)								 )								  SPPSV(l)

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, * )

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 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.

       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 ]

LAPACK version 3.0						   15 June 2000 							  SPPSV(l)

sppsv.f(3)							      LAPACK								sppsv.f(3)

NAME

       sppsv.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sppsv (UPLO, N, NRHS, AP, B, LDB, INFO)
	    SPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Function/Subroutine Documentation
   subroutine sppsv (characterUPLO, integerN, integerNRHS, real, dimension( * )AP, real, dimension( ldb, * )B, integerLDB, integerINFO)
	SPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

       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.

       Parameters:
	   UPLO

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

	   N

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

	   NRHS

		     NRHS is INTEGER
		     The number of right hand sides, i.e., the number of columns
		     of the matrix B.  NRHS >= 0.

	   AP

		     AP is 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

		     B is 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

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

	   INFO

		     INFO is 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       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 ]

       Definition at line 145 of file sppsv.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012							sppsv.f(3)