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## dsposv()

subroutine dsposv | ( | character | uplo,
|  | integer | n,
|  | integer | nrhs,
|  | double precision, dimension( lda, * ) | a,
|  | integer | lda,
|  | double precision, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | double precision, dimension( ldx, * ) | x,
|  | integer | ldx,
|  | double precision, dimension( n, * ) | work,
|  | real, dimension( * ) | swork,
|  | integer | iter,
|  | integer | info )

DSPOSV computes the solution to system of linear equations A * X = B for PO matrices

Download DSPOSV + dependencies [TGZ] [ZIP] [TXT]

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

  [in]

  UPLO

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

  [in]

  N

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

  [in]

  NRHS

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

  [in,out]

  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 = 0 and ITER >= 0, see description below), then A is
      !>          unchanged, if double precision factorization has been used
      !>          (INFO = 0 and ITER < 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.
      !>

  [in]

  LDA

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

  [in]

  B

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

  [in]

  LDB

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

  [out]

  X

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

  [in]

  LDX

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

  [out]

  WORK

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

  [out]

  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.
      !>

  [out]

  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 successfully used.
      !>               Returns the number of iterations
      !>

  [out]

  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 principal minor of order i
      !>                of (DOUBLE PRECISION) A is not positive, 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.