dsposv.f(3)							      LAPACK							       dsposv.f(3)

NAME

       dsposv.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dsposv (UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK, ITER, INFO)
	    DSPOSV computes the solution to system of linear equations A * X = B for PO matrices

Function/Subroutine Documentation
   subroutine dsposv (characterUPLO, integerN, integerNRHS, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb,
       * )B, integerLDB, double precision, dimension( ldx, * )X, integerLDX, double precision, dimension( n, * )WORK, real, dimension( * )SWORK,
       integerITER, integerINFO)
	DSPOSV computes the solution to system of linear equations A * X = B for PO matrices

       Purpose:

	    DSPOSV 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.

	    DSPOSV first attempts to factorize the matrix in SINGLE PRECISION
	    and use this factorization within an iterative refinement procedure
	    to produce a solution with DOUBLE PRECISION normwise backward error
	    quality (see below). If the approach fails the method switches to a
	    DOUBLE PRECISION factorization and solve.

	    The iterative refinement is not going to be a winning strategy if
	    the ratio SINGLE PRECISION performance over DOUBLE PRECISION
	    performance is too small. A reasonable strategy should take the
	    number of right-hand sides and the size of the matrix into account.
	    This might be done with a call to ILAENV in the future. Up to now, we
	    always try iterative refinement.

	    The iterative refinement process is stopped if
		ITER > ITERMAX
	    or for all the RHS we have:
		RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
	    where
		o ITER is the number of the current iteration in the iterative
		  refinement process
		o RNRM is the infinity-norm of the residual
		o XNRM is the infinity-norm of the solution
		o ANRM is the infinity-operator-norm of the matrix A
		o EPS is the machine epsilon returned by DLAMCH('Epsilon')
	    The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
	    respectively.

       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.

	   A

		     A is 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 iterative refinement has been successfully used
		     (INFO.EQ.0 and ITER.GE.0, see description below), then A is
		     unchanged, if double precision factorization has been used
		     (INFO.EQ.0 and ITER.LT.0, see description below), then the
		     array A contains the factor U or L from the Cholesky
		     factorization A = U**T*U or A = L*L**T.

	   LDA

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

	   B

		     B is DOUBLE PRECISION array, dimension (LDB,NRHS)
		     The N-by-NRHS right hand side matrix B.

	   LDB

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

	   X

		     X is DOUBLE PRECISION array, dimension (LDX,NRHS)
		     If INFO = 0, the N-by-NRHS solution matrix X.

	   LDX

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

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (N,NRHS)
		     This array is used to hold the residual vectors.

	   SWORK

		     SWORK is REAL array, dimension (N*(N+NRHS))
		     This array is used to use the single precision matrix and the
		     right-hand sides or solutions in single precision.

	   ITER

		     ITER is INTEGER
		     < 0: iterative refinement has failed, double precision
			  factorization has been performed
			  -1 : the routine fell back to full precision for
			       implementation- or machine-specific reasons
			  -2 : narrowing the precision induced an overflow,
			       the routine fell back to full precision
			  -3 : failure of SPOTRF
			  -31: stop the iterative refinement after the 30th
			       iterations
		     > 0: iterative refinement has been sucessfully used.
			  Returns the number of iterations

	   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 (DOUBLE
			   PRECISION) 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

       Definition at line 199 of file dsposv.f.

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

Version 3.4.1							  Sun May 26 2013						       dsposv.f(3)