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

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