ztrt02.f

Go to the documentation of this file.

      SUBROUTINE ZTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
     $                   LDB, WORK, RWORK, RESID )
*
*  -- LAPACK test routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, TRANS, UPLO
      INTEGER            LDA, LDB, LDX, N, NRHS
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * ),
     $                   X( LDX, * )
*     ..
*
*  Purpose
*  =======
*
*  ZTRT02 computes the residual for the computed solution to a
*  triangular system of linear equations  A*x = b,  A**T *x = b,
*  or A**H *x = b.  Here A is a triangular matrix, A**T is the transpose
*  of A, A**H is the conjugate transpose of A, and x and b are N by NRHS
*  matrices.  The test ratio is the maximum over the number of right
*  hand sides of
*     norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*  where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the matrix A is upper or lower triangular.
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  TRANS   (input) CHARACTER*1
*          Specifies the operation applied to A.
*          = 'N':  A *x = b     (No transpose)
*          = 'T':  A**T *x = b  (Transpose)
*          = 'C':  A**H *x = b  (Conjugate transpose)
*
*  DIAG    (input) CHARACTER*1
*          Specifies whether or not the matrix A is unit triangular.
*          = 'N':  Non-unit triangular
*          = 'U':  Unit triangular
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  NRHS    (input) INTEGER
*          The number of right hand sides, i.e., the number of columns
*          of the matrices X and B.  NRHS >= 0.
*
*  A       (input) COMPLEX*16 array, dimension (LDA,N)
*          The triangular matrix A.  If UPLO = 'U', the leading n by n
*          upper triangular part of the array A contains the upper
*          triangular matrix, and the strictly lower triangular part of
*          A is not referenced.  If UPLO = 'L', the leading n by n lower
*          triangular part of the array A contains the lower triangular
*          matrix, and the strictly upper triangular part of A is not
*          referenced.  If DIAG = 'U', the diagonal elements of A are
*          also not referenced and are assumed to be 1.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  X       (input) COMPLEX*16 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) COMPLEX*16 array, dimension (LDB,NRHS)
*          The right hand side vectors for the system of linear
*          equations.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B.  LDB >= max(1,N).
*
*  WORK    (workspace) COMPLEX*16 array, dimension (N)
*
*  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
*
*  RESID   (output) DOUBLE PRECISION
*          The maximum over the number of right hand sides of
*          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J
      DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLAMCH, DZASUM, ZLANTR
      EXTERNAL           LSAME, DLAMCH, DZASUM, ZLANTR
*     ..
*     .. External Subroutines ..
      EXTERNAL           ZAXPY, ZCOPY, ZTRMV
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          DCMPLX, 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
*
*     Compute the 1-norm of A or A**H.
*
      IF( LSAME( TRANS, 'N' ) ) THEN
         ANORM = ZLANTR( '1', UPLO, DIAG, N, N, A, LDA, RWORK )
      ELSE
         ANORM = ZLANTR( 'I', UPLO, DIAG, N, N, A, LDA, RWORK )
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0.
*
      EPS = DLAMCH( 'Epsilon' )
      IF( ANORM.LE.ZERO ) THEN
         RESID = ONE / EPS
         RETURN
      END IF
*
*     Compute the maximum over the number of right hand sides of
*        norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS )
*
      RESID = ZERO
      DO 10 J = 1, NRHS
         CALL ZCOPY( N, X( 1, J ), 1, WORK, 1 )
         CALL ZTRMV( UPLO, TRANS, DIAG, N, A, LDA, WORK, 1 )
         CALL ZAXPY( N, DCMPLX( -ONE ), B( 1, J ), 1, WORK, 1 )
         BNORM = DZASUM( N, WORK, 1 )
         XNORM = DZASUM( N, X( 1, J ), 1 )
         IF( XNORM.LE.ZERO ) THEN
            RESID = ONE / EPS
         ELSE
            RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
         END IF
   10 CONTINUE
*
      RETURN
*
*     End of ZTRT02
*
      END