*> \brief \b ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZSPMV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INCX, INCY, N * COMPLEX*16 ALPHA, BETA * .. * .. Array Arguments .. * COMPLEX*16 AP( * ), X( * ), Y( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZSPMV 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, supplied in packed form. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the matrix A is supplied in the packed *> array AP as follows: *> *> UPLO = 'U' or 'u' The upper triangular part of A is *> supplied in AP. *> *> UPLO = 'L' or 'l' The lower triangular part of A is *> supplied in AP. *> *> 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] AP *> \verbatim *> AP is COMPLEX*16 array, dimension at least *> ( ( N*( N + 1 ) )/2 ). *> Before entry, with UPLO = 'U' or 'u', the array AP must *> contain the upper triangular part of the symmetric matrix *> packed sequentially, column by column, so that AP( 1 ) *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) *> and a( 2, 2 ) respectively, and so on. *> Before entry, with UPLO = 'L' or 'l', the array AP must *> contain the lower triangular part of the symmetric matrix *> packed sequentially, column by column, so that AP( 1 ) *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) *> and a( 3, 1 ) respectively, and so on. *> 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 complex16OTHERauxiliary * * ===================================================================== SUBROUTINE ZSPMV( UPLO, N, ALPHA, AP, 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, N COMPLEX*16 ALPHA, BETA * .. * .. Array Arguments .. COMPLEX*16 AP( * ), 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, K, KK, KX, KY COMPLEX*16 TEMP1, TEMP2 * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. 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( INCX.EQ.0 ) THEN INFO = 6 ELSE IF( INCY.EQ.0 ) THEN INFO = 9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZSPMV ', 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 the array AP * are accessed sequentially with one pass through AP. * * 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 KK = 1 IF( LSAME( UPLO, 'U' ) ) THEN * * Form y when AP contains the upper triangle. * IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN DO 60 J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO K = KK DO 50 I = 1, J - 1 Y( I ) = Y( I ) + TEMP1*AP( K ) TEMP2 = TEMP2 + AP( K )*X( I ) K = K + 1 50 CONTINUE Y( J ) = Y( J ) + TEMP1*AP( KK+J-1 ) + ALPHA*TEMP2 KK = KK + J 60 CONTINUE ELSE JX = KX JY = KY DO 80 J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY DO 70 K = KK, KK + J - 2 Y( IY ) = Y( IY ) + TEMP1*AP( K ) TEMP2 = TEMP2 + AP( K )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*AP( KK+J-1 ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + J 80 CONTINUE END IF ELSE * * Form y when AP contains the 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*AP( KK ) K = KK + 1 DO 90 I = J + 1, N Y( I ) = Y( I ) + TEMP1*AP( K ) TEMP2 = TEMP2 + AP( K )*X( I ) K = K + 1 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 KK = KK + ( N-J+1 ) 100 CONTINUE ELSE JX = KX JY = KY DO 120 J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*AP( KK ) IX = JX IY = JY DO 110 K = KK + 1, KK + N - J IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*AP( K ) TEMP2 = TEMP2 + AP( K )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + ( N-J+1 ) 120 CONTINUE END IF END IF * RETURN * * End of ZSPMV * END