zgbt02()

subroutine zgbt02	(	character	trans,
		integer	m,
		integer	n,
		integer	kl,
		integer	ku,
		integer	nrhs,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( ldx, * )	x,
		integer	ldx,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		double precision, dimension( * )	rwork,
		double precision	resid
	)

ZGBT02

Purpose:

 ZGBT02 computes the residual for a solution of a banded system of
 equations op(A)*X = B:
    RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
 where op(A) = A, A**T, or A**H, depending on TRANS, and EPS is the
 machine epsilon.

Parameters

[in]	TRANS	TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose)
[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in]	KL	KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.
[in]	KU	KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of B. NRHS >= 0.
[in]	A	A is COMPLEX*16 array, dimension (LDA,N) The original matrix A in band storage, stored in rows 1 to KL+KU+1.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,KL+KU+1).
[in]	X	X is COMPLEX*16 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. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
[in,out]	B	B is 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 - A*X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)), where LRWORK >= M when TRANS = 'T' or 'C'; otherwise, RWORK is not referenced.
[out]	RESID	RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 146 of file zgbt02.f.

*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          TRANS
      INTEGER            KL, KU, LDA, LDB, LDX, M, N, NRHS
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         A( LDA, * ), B( LDB, * ), X( LDX, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
      COMPLEX*16         CONE
      parameter( cone = ( 1.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            I1, I2, J, KD, N1
      DOUBLE PRECISION   ANORM, BNORM, EPS, TEMP, XNORM
      COMPLEX*16         ZDUM
*     ..
*     .. External Functions ..
      LOGICAL            DISNAN, LSAME
      DOUBLE PRECISION   DLAMCH, DZASUM
      EXTERNAL           disnan, dlamch, dzasum, lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           zgbmv
*     ..
*     .. Statement Functions ..
      DOUBLE PRECISION   CABS1
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, dble, dimag, max, min
*     ..
*     .. Statement Function definitions ..
      cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
*     ..
*     .. Executable Statements ..
*
*     Quick return if N = 0 pr NRHS = 0
*
      IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.LE.0 ) THEN
         resid = zero
         RETURN
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0.
*
      eps = dlamch( 'Epsilon' )
      anorm = zero
      IF( lsame( trans, 'N' ) ) THEN
*
*        Find norm1(A).
*
         kd = ku + 1
         DO 10 j = 1, n
            i1 = max( kd+1-j, 1 )
            i2 = min( kd+m-j, kl+kd )
            IF( i2.GE.i1 ) THEN
               temp = dzasum( i2-i1+1, a( i1, j ), 1 )
               IF( anorm.LT.temp .OR. disnan( temp ) ) anorm = temp
            END IF
   10    CONTINUE
      ELSE
*
*        Find normI(A).
*
         DO 12 i1 = 1, m
            rwork( i1 ) = zero
   12    CONTINUE
         DO 16 j = 1, n
            kd = ku + 1 - j
            DO 14 i1 = max( 1, j-ku ), min( m, j+kl )
               rwork( i1 ) = rwork( i1 ) + cabs1( a( kd+i1, j ) )
   14       CONTINUE
   16    CONTINUE
         DO 18 i1 = 1, m
            temp = rwork( i1 )
            IF( anorm.LT.temp .OR. disnan( temp ) ) anorm = temp
   18    CONTINUE
      END IF
      IF( anorm.LE.zero ) THEN
         resid = one / eps
         RETURN
      END IF
*
      IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
         n1 = n
      ELSE
         n1 = m
      END IF
*
*     Compute B - op(A)*X
*
      DO 20 j = 1, nrhs
         CALL zgbmv( trans, m, n, kl, ku, -cone, a, lda, x( 1, j ), 1,
     $               cone, b( 1, j ), 1 )
   20 CONTINUE
*
*     Compute the maximum over the number of right hand sides of
*        norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
*
      resid = zero
      DO 30 j = 1, nrhs
         bnorm = dzasum( n1, b( 1, j ), 1 )
         xnorm = dzasum( n1, x( 1, j ), 1 )
         IF( xnorm.LE.zero ) THEN
            resid = one / eps
         ELSE
            resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
         END IF
   30 CONTINUE
*
      RETURN
*
*     End of ZGBT02
*

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