spot02.f

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      SUBROUTINE spot02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
     $                   resid )
*
*  -- LAPACK test routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          uplo
      INTEGER            lda, ldb, ldx, n, nrhs
      REAL               resid
*     ..
*     .. Array Arguments ..
      REAL               a( lda, * ), b( ldb, * ), rwork( * ),
     $                   x( ldx, * )
*     ..
*
*  Purpose
*  =======
*
*  SPOT02 computes the residual for the solution of a symmetric system
*  of linear equations  A*x = b:
*
*   RESID = norm( B - A*X ) / ( norm(A) * norm(X) + norm(RHS))* N * EPS )
*
*  where EPS is the machine epsilon.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the upper or lower triangular part of the
*          symmetric matrix A is stored:
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  N       (input) INTEGER
*          The number of rows and columns of the matrix A.  N >= 0.
*
*  NRHS    (input) INTEGER
*          The number of columns of B, the matrix of right hand sides.
*          NRHS >= 0.
*
*  A       (input) REAL array, dimension (LDA,N)
*          The original symmetric matrix A.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N)
*
*  X       (input) REAL array, dimension (LDX,NRHS)
*          The computed solution vectors for the system of linear
*          equations.
*
*  LDX     (input) INTEGER
*          The leading dimension of the array X.   LDX >= max(1,N).
*
*  B       (input/output) REAL array, dimension (LDB,NRHS)
*          On entry, the right hand side vectors for the system of
*          linear equations.
*          On exit, B is overwritten with the difference B - A*X.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B.  LDB >= max(1,N).
*
*  RWORK   (workspace) REAL array, dimension (N)
*
*  RESID   (output) REAL
*          The maximum over the number of right hand sides of
*   norm( B - A*X ) / ( norm(A) * norm(X) + norm(RHS))* N * EPS )
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               zero, one
      parameter( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            j
      REAL               anorm, bnorm, eps, rhsnorm, xnorm
*     ..
*     .. External Functions ..
      REAL               sasum, slamch, slansy, slange
      EXTERNAL           sasum, slamch, slansy, slange
*     ..
*     .. External Subroutines ..
      EXTERNAL           ssymm
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          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 ANORM = 0.
*
      eps = slamch( 'Epsilon' )
      anorm = slansy( '1', uplo, n, a, lda, rwork )
      rhsnorm = slange( '1', n, nrhs, b, ldb, rwork )
      IF( anorm.LE.zero ) THEN
         resid = one / eps
         return
      END IF
*
*     Compute  B - A*X
*
      CALL ssymm( 'Left', uplo, n, nrhs, -one, a, lda, x, ldx, one, b,
     $            ldb )
*
*     Compute the maximum over the number of right hand sides of
*        norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
*
      resid = zero
      DO 10 j = 1, nrhs
         bnorm = sasum( n, b( 1, j ), 1 )
         xnorm = sasum( n, x( 1, j ), 1 )
         IF( xnorm.LE.zero ) THEN
            resid = one / eps
         ELSE
            resid = max( resid, ( bnorm ) / (( anorm * xnorm + rhsnorm)*
     $                 n* eps ))
         END IF
   10 continue
*
      return
*
*     End of SPOT02
*
      END