numeric-linalg

Educational material on the SciPy implementation of numerical linear algebra algorithms

Name	Size	Mode
..
lapack/TESTING/LIN/ztbt02.f	6919B	-rw-r--r--

*> \brief \b ZTBT02
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
*                          LDX, B, LDB, WORK, RWORK, RESID )
*
*       .. Scalar Arguments ..
*       CHARACTER          DIAG, TRANS, UPLO
*       INTEGER            KD, LDAB, LDB, LDX, N, NRHS
*       DOUBLE PRECISION   RESID
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   RWORK( * )
*       COMPLEX*16         AB( LDAB, * ), B( LDB, * ), WORK( * ),
*      $                   X( LDX, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZTBT02 computes the residual for the computed solution to a
*> triangular system of linear equations op(A)*X = B, when A is a
*> triangular band matrix. The test ratio is the maximum over
*>    norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
*> where op(A) = A, A**T, or A**H, b is the column of B, x is the
*> solution vector, and EPS is the machine epsilon.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the matrix A is upper or lower triangular.
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          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)
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*>          DIAG is CHARACTER*1
*>          Specifies whether or not the matrix A is unit triangular.
*>          = 'N':  Non-unit triangular
*>          = 'U':  Unit triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] KD
*> \verbatim
*>          KD is INTEGER
*>          The number of superdiagonals or subdiagonals of the
*>          triangular band matrix A.  KD >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of right hand sides, i.e., the number of columns
*>          of the matrices X and B.  NRHS >= 0.
*> \endverbatim
*>
*> \param[in] AB
*> \verbatim
*>          AB is COMPLEX*16 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).
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*>          LDAB is INTEGER
*>          The leading dimension of the array AB.  LDAB >= max(1,KD+1).
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*>          X is COMPLEX*16 array, dimension (LDX,NRHS)
*>          The computed solution vectors for the system of linear
*>          equations.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*>          LDX is INTEGER
*>          The leading dimension of the array X.  LDX >= max(1,N).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*>          B is COMPLEX*16 array, dimension (LDB,NRHS)
*>          The right hand side vectors for the system of linear
*>          equations.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 array, dimension (N)
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is DOUBLE PRECISION
*>          The maximum over the number of right hand sides of
*>          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16_lin
*
*  =====================================================================
      SUBROUTINE ZTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
     $                   LDX, B, LDB, WORK, RWORK, RESID )
*
*  -- 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          DIAG, TRANS, UPLO
      INTEGER            KD, LDAB, LDB, LDX, N, NRHS
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         AB( LDAB, * ), B( LDB, * ), WORK( * ),
     $                   X( LDX, * )
*     ..
*
*  =====================================================================
*
*     .. 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, ZLANTB
      EXTERNAL           LSAME, DLAMCH, DZASUM, ZLANTB
*     ..
*     .. External Subroutines ..
      EXTERNAL           ZAXPY, ZCOPY, ZTBMV
*     ..
*     .. 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 op(A).
*
      IF( LSAME( TRANS, 'N' ) ) THEN
         ANORM = ZLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB, RWORK )
      ELSE
         ANORM = ZLANTB( 'I', UPLO, DIAG, N, KD, AB, LDAB, 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 ZTBMV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, 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 ZTBT02
*
      END