numeric-linalg

Educational material on the SciPy implementation of numerical linear algebra algorithms

Name	Size	Mode
..
lapack/SRC/zsymv.f	9929B	-rw-r--r--

*> \brief \b ZSYMV computes a matrix-vector product for a complex symmetric matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZSYMV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsymv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsymv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsymv.f">
*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INCX, INCY, LDA, N
*       COMPLEX*16         ALPHA, BETA
*       ..
*       .. Array Arguments ..
*       COMPLEX*16         A( LDA, * ), X( * ), Y( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZSYMV  performs the matrix-vector  operation
*>
*>    y := alpha*A*x + beta*y,
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric matrix.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>           On entry, UPLO specifies whether the upper or lower
*>           triangular part of the array A is to be referenced as
*>           follows:
*>
*>              UPLO = 'U' or 'u'   Only the upper triangular part of A
*>                                  is to be referenced.
*>
*>              UPLO = 'L' or 'l'   Only the lower triangular part of A
*>                                  is to be referenced.
*>
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>           On entry, N specifies the order of the matrix A.
*>           N must be at least zero.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*>          ALPHA is COMPLEX*16
*>           On entry, ALPHA specifies the scalar alpha.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX*16 array, dimension ( LDA, N )
*>           Before entry, with  UPLO = 'U' or 'u', the leading n by n
*>           upper triangular part of the array A must contain the upper
*>           triangular part of the symmetric matrix and the strictly
*>           lower triangular part of A is not referenced.
*>           Before entry, with UPLO = 'L' or 'l', the leading n by n
*>           lower triangular part of the array A must contain the lower
*>           triangular part of the symmetric matrix and the strictly
*>           upper triangular part of A is not referenced.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>           On entry, LDA specifies the first dimension of A as declared
*>           in the calling (sub) program. LDA must be at least
*>           max( 1, N ).
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*>          X is COMPLEX*16 array, dimension at least
*>           ( 1 + ( N - 1 )*abs( INCX ) ).
*>           Before entry, the incremented array X must contain the N-
*>           element vector x.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*>          INCX is INTEGER
*>           On entry, INCX specifies the increment for the elements of
*>           X. INCX must not be zero.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*>          BETA is COMPLEX*16
*>           On entry, BETA specifies the scalar beta. When BETA is
*>           supplied as zero then Y need not be set on input.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*>          Y is COMPLEX*16 array, dimension at least
*>           ( 1 + ( N - 1 )*abs( INCY ) ).
*>           Before entry, the incremented array Y must contain the n
*>           element vector y. On exit, Y is overwritten by the updated
*>           vector y.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*>          INCY is INTEGER
*>           On entry, INCY specifies the increment for the elements of
*>           Y. INCY must not be zero.
*>           Unchanged on exit.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hemv
*
*  =====================================================================
      SUBROUTINE ZSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
     $                  INCY )
*
*  -- LAPACK auxiliary 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            INCX, INCY, LDA, N
      COMPLEX*16         ALPHA, BETA
*     ..
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * ), Y( * )
*     ..
*
* =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
      COMPLEX*16         ZERO
      PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            I, INFO, IX, IY, J, JX, JY, KX, KY
      COMPLEX*16         TEMP1, TEMP2
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF( .NOT.LSAME( UPLO, 'U' ) .AND.
     $    .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = 1
      ELSE IF( N.LT.0 ) THEN
         INFO = 2
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = 5
      ELSE IF( INCX.EQ.0 ) THEN
         INFO = 7
      ELSE IF( INCY.EQ.0 ) THEN
         INFO = 10
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'ZSYMV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     Set up the start points in  X  and  Y.
*
      IF( INCX.GT.0 ) THEN
         KX = 1
      ELSE
         KX = 1 - ( N-1 )*INCX
      END IF
      IF( INCY.GT.0 ) THEN
         KY = 1
      ELSE
         KY = 1 - ( N-1 )*INCY
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through the triangular part
*     of A.
*
*     First form  y := beta*y.
*
      IF( BETA.NE.ONE ) THEN
         IF( INCY.EQ.1 ) THEN
            IF( BETA.EQ.ZERO ) THEN
               DO 10 I = 1, N
                  Y( I ) = ZERO
   10          CONTINUE
            ELSE
               DO 20 I = 1, N
                  Y( I ) = BETA*Y( I )
   20          CONTINUE
            END IF
         ELSE
            IY = KY
            IF( BETA.EQ.ZERO ) THEN
               DO 30 I = 1, N
                  Y( IY ) = ZERO
                  IY = IY + INCY
   30          CONTINUE
            ELSE
               DO 40 I = 1, N
                  Y( IY ) = BETA*Y( IY )
                  IY = IY + INCY
   40          CONTINUE
            END IF
         END IF
      END IF
      IF( ALPHA.EQ.ZERO )
     $   RETURN
      IF( LSAME( UPLO, 'U' ) ) THEN
*
*        Form  y  when A is stored in upper triangle.
*
         IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
            DO 60 J = 1, N
               TEMP1 = ALPHA*X( J )
               TEMP2 = ZERO
               DO 50 I = 1, J - 1
                  Y( I ) = Y( I ) + TEMP1*A( I, J )
                  TEMP2 = TEMP2 + A( I, J )*X( I )
   50          CONTINUE
               Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2
   60       CONTINUE
         ELSE
            JX = KX
            JY = KY
            DO 80 J = 1, N
               TEMP1 = ALPHA*X( JX )
               TEMP2 = ZERO
               IX = KX
               IY = KY
               DO 70 I = 1, J - 1
                  Y( IY ) = Y( IY ) + TEMP1*A( I, J )
                  TEMP2 = TEMP2 + A( I, J )*X( IX )
                  IX = IX + INCX
                  IY = IY + INCY
   70          CONTINUE
               Y( JY ) = Y( JY ) + TEMP1*A( J, J ) + ALPHA*TEMP2
               JX = JX + INCX
               JY = JY + INCY
   80       CONTINUE
         END IF
      ELSE
*
*        Form  y  when A is stored in lower triangle.
*
         IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
            DO 100 J = 1, N
               TEMP1 = ALPHA*X( J )
               TEMP2 = ZERO
               Y( J ) = Y( J ) + TEMP1*A( J, J )
               DO 90 I = J + 1, N
                  Y( I ) = Y( I ) + TEMP1*A( I, J )
                  TEMP2 = TEMP2 + A( I, J )*X( I )
   90          CONTINUE
               Y( J ) = Y( J ) + ALPHA*TEMP2
  100       CONTINUE
         ELSE
            JX = KX
            JY = KY
            DO 120 J = 1, N
               TEMP1 = ALPHA*X( JX )
               TEMP2 = ZERO
               Y( JY ) = Y( JY ) + TEMP1*A( J, J )
               IX = JX
               IY = JY
               DO 110 I = J + 1, N
                  IX = IX + INCX
                  IY = IY + INCY
                  Y( IY ) = Y( IY ) + TEMP1*A( I, J )
                  TEMP2 = TEMP2 + A( I, J )*X( IX )
  110          CONTINUE
               Y( JY ) = Y( JY ) + ALPHA*TEMP2
               JX = JX + INCX
               JY = JY + INCY
  120       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZSYMV
*
      END