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SUBROUTINE ZGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
$ RWORK, RESID )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER TRANS
INTEGER LDB, LDX, N, NRHS
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION RWORK( * )
COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
$ X( LDX, * )
* ..
*
* Purpose
* =======
*
* ZGTT02 computes the residual for the solution to a tridiagonal
* system of equations:
* RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
* where EPS is the machine epsilon.
*
* Arguments
* =========
*
* TRANS (input) CHARACTER
* Specifies the form of the residual.
* = 'N': B - A * X (No transpose)
* = 'T': B - A**T * X (Transpose)
* = 'C': B - A**H * X (Conjugate transpose)
*
* N (input) INTEGTER
* 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 B and X. NRHS >= 0.
*
* DL (input) COMPLEX*16 array, dimension (N-1)
* The (n-1) sub-diagonal elements of A.
*
* D (input) COMPLEX*16 array, dimension (N)
* The diagonal elements of A.
*
* DU (input) COMPLEX*16 array, dimension (N-1)
* The (n-1) super-diagonal elements of A.
*
* X (input) COMPLEX*16 array, dimension (LDX,NRHS)
* The computed solution vectors X.
*
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= max(1,N).
*
* B (input/output) COMPLEX*16 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 - op(A)*X.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (N)
*
* RESID (output) DOUBLE PRECISION
* norm(B - op(A)*X) / (norm(A) * norm(X) * EPS)
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER J
DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, DZASUM, ZLANGT
EXTERNAL LSAME, DLAMCH, DZASUM, ZLANGT
* ..
* .. External Subroutines ..
EXTERNAL ZLAGTM
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0 or NRHS = 0
*
RESID = ZERO
IF( N.LE.0 .OR. NRHS.EQ.0 )
$ RETURN
*
* Compute the maximum over the number of right hand sides of
* norm(B - op(A)*X) / ( norm(A) * norm(X) * EPS ).
*
IF( LSAME( TRANS, 'N' ) ) THEN
ANORM = ZLANGT( '1', N, DL, D, DU )
ELSE
ANORM = ZLANGT( 'I', N, DL, D, DU )
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 B - op(A)*X.
*
CALL ZLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B,
$ LDB )
*
DO 10 J = 1, NRHS
BNORM = DZASUM( N, B( 1, J ), 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 ZGTT02
*
END
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