claptm.f

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*> \brief \b CLAPTM
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE CLAPTM( UPLO, N, NRHS, ALPHA, D, E, X, LDX, BETA, B,
*                          LDB )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            LDB, LDX, N, NRHS
*       REAL               ALPHA, BETA
*       ..
*       .. Array Arguments ..
*       REAL               D( * )
*       COMPLEX            B( LDB, * ), E( * ), X( LDX, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CLAPTM multiplies an N by NRHS matrix X by a Hermitian tridiagonal
*> matrix A and stores the result in a matrix B.  The operation has the
*> form
*>
*>    B := alpha * A * X + beta * B
*>
*> where alpha may be either 1. or -1. and beta may be 0., 1., or -1.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER
*>          Specifies whether the superdiagonal or the subdiagonal of the
*>          tridiagonal matrix A is stored.
*>          = 'U':  Upper, E is the superdiagonal of A.
*>          = 'L':  Lower, E is the subdiagonal of A.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 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.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*>          ALPHA is REAL
*>          The scalar alpha.  ALPHA must be 1. or -1.; otherwise,
*>          it is assumed to be 0.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*>          D is REAL array, dimension (N)
*>          The n diagonal elements of the tridiagonal matrix A.
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*>          E is COMPLEX array, dimension (N-1)
*>          The (n-1) subdiagonal or superdiagonal elements of A.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*>          X is COMPLEX array, dimension (LDX,NRHS)
*>          The N by NRHS matrix X.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*>          LDX is INTEGER
*>          The leading dimension of the array X.  LDX >= max(N,1).
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*>          BETA is REAL
*>          The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
*>          it is assumed to be 1.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is COMPLEX array, dimension (LDB,NRHS)
*>          On entry, the N by NRHS matrix B.
*>          On exit, B is overwritten by the matrix expression
*>          B := alpha * A * X + beta * B.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  LDB >= max(N,1).
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex_lin
*
*  =====================================================================
      SUBROUTINE claptm( UPLO, N, NRHS, ALPHA, D, E, X, LDX, BETA, B,
     $                   LDB )
*
*  -- 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          UPLO
      INTEGER            LDB, LDX, N, NRHS
      REAL               ALPHA, BETA
*     ..
*     .. Array Arguments ..
      REAL               D( * )
      COMPLEX            B( LDB, * ), E( * ), X( LDX, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      parameter( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          conjg
*     ..
*     .. Executable Statements ..
*
      IF( n.EQ.0 )
     $   RETURN
*
      IF( beta.EQ.zero ) THEN
         DO 20 j = 1, nrhs
            DO 10 i = 1, n
               b( i, j ) = zero
   10       CONTINUE
   20    CONTINUE
      ELSE IF( beta.EQ.-one ) THEN
         DO 40 j = 1, nrhs
            DO 30 i = 1, n
               b( i, j ) = -b( i, j )
   30       CONTINUE
   40    CONTINUE
      END IF
*
      IF( alpha.EQ.one ) THEN
         IF( lsame( uplo, 'U' ) ) THEN
*
*           Compute B := B + A*X, where E is the superdiagonal of A.
*
            DO 60 j = 1, nrhs
               IF( n.EQ.1 ) THEN
                  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j )
               ELSE
                  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j ) +
     $                        e( 1 )*x( 2, j )
                  b( n, j ) = b( n, j ) + conjg( e( n-1 ) )*
     $                        x( n-1, j ) + d( n )*x( n, j )
                  DO 50 i = 2, n - 1
                     b( i, j ) = b( i, j ) + conjg( e( i-1 ) )*
     $                           x( i-1, j ) + d( i )*x( i, j ) +
     $                           e( i )*x( i+1, j )
   50             CONTINUE
               END IF
   60       CONTINUE
         ELSE
*
*           Compute B := B + A*X, where E is the subdiagonal of A.
*
            DO 80 j = 1, nrhs
               IF( n.EQ.1 ) THEN
                  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j )
               ELSE
                  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j ) +
     $                        conjg( e( 1 ) )*x( 2, j )
                  b( n, j ) = b( n, j ) + e( n-1 )*x( n-1, j ) +
     $                        d( n )*x( n, j )
                  DO 70 i = 2, n - 1
                     b( i, j ) = b( i, j ) + e( i-1 )*x( i-1, j ) +
     $                           d( i )*x( i, j ) +
     $                           conjg( e( i ) )*x( i+1, j )
   70             CONTINUE
               END IF
   80       CONTINUE
         END IF
      ELSE IF( alpha.EQ.-one ) THEN
         IF( lsame( uplo, 'U' ) ) THEN
*
*           Compute B := B - A*X, where E is the superdiagonal of A.
*
            DO 100 j = 1, nrhs
               IF( n.EQ.1 ) THEN
                  b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j )
               ELSE
                  b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j ) -
     $                        e( 1 )*x( 2, j )
                  b( n, j ) = b( n, j ) - conjg( e( n-1 ) )*
     $                        x( n-1, j ) - d( n )*x( n, j )
                  DO 90 i = 2, n - 1
                     b( i, j ) = b( i, j ) - conjg( e( i-1 ) )*
     $                           x( i-1, j ) - d( i )*x( i, j ) -
     $                           e( i )*x( i+1, j )
   90             CONTINUE
               END IF
  100       CONTINUE
         ELSE
*
*           Compute B := B - A*X, where E is the subdiagonal of A.
*
            DO 120 j = 1, nrhs
               IF( n.EQ.1 ) THEN
                  b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j )
               ELSE
                  b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j ) -
     $                        conjg( e( 1 ) )*x( 2, j )
                  b( n, j ) = b( n, j ) - e( n-1 )*x( n-1, j ) -
     $                        d( n )*x( n, j )
                  DO 110 i = 2, n - 1
                     b( i, j ) = b( i, j ) - e( i-1 )*x( i-1, j ) -
     $                           d( i )*x( i, j ) -
     $                           conjg( e( i ) )*x( i+1, j )
  110             CONTINUE
               END IF
  120       CONTINUE
         END IF
      END IF
      RETURN
*
*     End of CLAPTM
*
      END