TESTING/LIN/sppt05.f(3)

NAME
TESTING/LIN/sppt05.f

SYNOPSIS

  Functions/Subroutines
subroutine sppt05 (uplo, n, nrhs, ap, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
SPPT05

Function/Subroutine Documentation

  subroutine sppt05 (character uplo, integer n, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldxact, * ) xact, integer ldxact, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) reslts)

SPPT05

Purpose:

     SPPT05 tests the error bounds from iterative refinement for the
     computed solution to a system of equations A*X = B, where A is a
     symmetric matrix in packed storage format.
     RESLTS(1) = test of the error bound
               = norm(X - XACT) / ( norm(X) * FERR )
     A large value is returned if this ratio is not less than one.
     RESLTS(2) = residual from the iterative refinement routine
               = the maximum of BERR / ( (n+1)*EPS + (*) ), where
                 (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

Parameters
    UPLO

              UPLO is CHARACTER*1
              Specifies whether the upper or lower triangular part of the
              symmetric matrix A is stored.
              = 'U':  Upper triangular
              = 'L':  Lower triangular

    N

              N is INTEGER
              The number of rows of the matrices X, B, and XACT, and the
              order of the matrix A.  N >= 0.

    NRHS

              NRHS is INTEGER
              The number of columns of the matrices X, B, and XACT.
              NRHS >= 0.

    AP

              AP is REAL array, dimension (N*(N+1)/2)
              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.

    B

              B is REAL array, dimension (LDB,NRHS)
              The right hand side vectors for the system of linear
              equations.

    LDB

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

    X

              X is REAL array, dimension (LDX,NRHS)
              The computed solution vectors.  Each vector is stored as a
              column of the matrix X.

    LDX

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

    XACT

              XACT is REAL array, dimension (LDX,NRHS)
              The exact solution vectors.  Each vector is stored as a
              column of the matrix XACT.

    LDXACT

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

    FERR

              FERR is REAL array, dimension (NRHS)
              The estimated forward error bounds for each solution vector
              X.  If XTRUE is the true solution, FERR bounds the magnitude
              of the largest entry in (X - XTRUE) divided by the magnitude
              of the largest entry in X.

    BERR

              BERR is REAL array, dimension (NRHS)
              The componentwise relative backward error of each solution
              vector (i.e., the smallest relative change in any entry of A
              or B that makes X an exact solution).

    RESLTS

              RESLTS is REAL array, dimension (2)
              The maximum over the NRHS solution vectors of the ratios:
              RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
              RESLTS(2) = BERR / ( (n+1)*EPS + (*) )

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 154 of file sppt05.f.

Author

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