subroutine ctbt02	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	KD,
		integer	NRHS,
		complex, dimension( ldab, * )	AB,
		integer	LDAB,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		real	RESID
	)

CTBT02

Purpose:

 CTBT02 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  when A is a triangular band matrix.  Here A**T denotes
 the transpose of A, A**H denotes 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.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is 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)
[in]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	KD	KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
[in]	AB	AB is COMPLEX array, dimension (LDA,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDAB >= max(1,KD+1).
[in]	X	X is COMPLEX array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	B	B is COMPLEX array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	WORK	WORK is COMPLEX array, dimension (N)
[out]	RWORK	RWORK is REAL array, dimension (N)
[out]	RESID	RESID is REAL The maximum over the number of right hand sides of norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

November 2011

Definition at line 163 of file ctbt02.f.

*
*  -- LAPACK test routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      CHARACTER          diag, trans, uplo
      INTEGER            kd, ldab, ldb, ldx, n, nrhs
      REAL               resid
*     ..
*     .. Array Arguments ..
      REAL               rwork( * )
      COMPLEX            ab( ldab, * ), b( ldb, * ), work( * ),
     $                   x( ldx, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               zero, one
      parameter                ( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            j
      REAL               anorm, bnorm, eps, xnorm
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      REAL               clantb, scasum, slamch
      EXTERNAL           lsame, clantb, scasum, slamch
*     ..
*     .. External Subroutines ..
      EXTERNAL           caxpy, ccopy, ctbmv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          cmplx, 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'.
*
      IF( lsame( trans, 'N' ) ) THEN
         anorm = clantb( '1', uplo, diag, n, kd, ab, ldab, rwork )
      ELSE
         anorm = clantb( 'I', uplo, diag, n, kd, ab, ldab, rwork )
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0.
*
      eps = slamch( '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 ccopy( n, x( 1, j ), 1, work, 1 )
         CALL ctbmv( uplo, trans, diag, n, kd, ab, ldab, work, 1 )
         CALL caxpy( n, cmplx( -one ), b( 1, j ), 1, work, 1 )
         bnorm = scasum( n, work, 1 )
         xnorm = scasum( 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 CTBT02
*

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