dget04.f

Go to the documentation of this file.

      SUBROUTINE dget04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
*
*  -- LAPACK test routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      INTEGER            ldx, ldxact, n, nrhs
      DOUBLE PRECISION   rcond, resid
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   x( ldx, * ), xact( ldxact, * )
*     ..
*
*  Purpose
*  =======
*
*  DGET04 computes the difference between a computed solution and the
*  true solution to a system of linear equations.
*
*  RESID =  ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
*  where RCOND is the reciprocal of the condition number and EPS is the
*  machine epsilon.
*
*  Arguments
*  =========
*
*  N       (input) INTEGER
*          The number of rows of the matrices X and XACT.  N >= 0.
*
*  NRHS    (input) INTEGER
*          The number of columns of the matrices X and XACT.  NRHS >= 0.
*
*  X       (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
*          The computed solution vectors.  Each vector is stored as a
*          column of the matrix X.
*
*  LDX     (input) INTEGER
*          The leading dimension of the array X.  LDX >= max(1,N).
*
*  XACT    (input) DOUBLE PRECISION array, dimension( LDX, NRHS )
*          The exact solution vectors.  Each vector is stored as a
*          column of the matrix XACT.
*
*  LDXACT  (input) INTEGER
*          The leading dimension of the array XACT.  LDXACT >= max(1,N).
*
*  RCOND   (input) DOUBLE PRECISION
*          The reciprocal of the condition number of the coefficient
*          matrix in the system of equations.
*
*  RESID   (output) DOUBLE PRECISION
*          The maximum over the NRHS solution vectors of
*          ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   zero
      parameter( zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            i, ix, j
      DOUBLE PRECISION   diffnm, eps, xnorm
*     ..
*     .. External Functions ..
      INTEGER            idamax
      DOUBLE PRECISION   dlamch
      EXTERNAL           idamax, dlamch
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0 or NRHS = 0.
*
      IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
         resid = zero
         return
      END IF
*
*     Exit with RESID = 1/EPS if RCOND is invalid.
*
      eps = dlamch( 'Epsilon' )
      IF( rcond.LT.zero ) THEN
         resid = 1.0d0 / eps
         return
      END IF
*
*     Compute the maximum of
*        norm(X - XACT) / ( norm(XACT) * EPS )
*     over all the vectors X and XACT .
*
      resid = zero
      DO 20 j = 1, nrhs
         ix = idamax( n, xact( 1, j ), 1 )
         xnorm = abs( xact( ix, j ) )
         diffnm = zero
         DO 10 i = 1, n
            diffnm = max( diffnm, abs( x( i, j )-xact( i, j ) ) )
   10    continue
         IF( xnorm.LE.zero ) THEN
            IF( diffnm.GT.zero )
     $         resid = 1.0d0 / eps
         ELSE
            resid = max( resid, ( diffnm / xnorm )*rcond )
         END IF
   20 continue
      IF( resid*eps.LT.1.0d0 )
     $   resid = resid / eps
*
      return
*
*     End of DGET04
*
      END