*> \brief \b CHPMV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) * * .. Scalar Arguments .. * COMPLEX ALPHA,BETA * INTEGER INCX,INCY,N * CHARACTER UPLO * .. * .. Array Arguments .. * COMPLEX AP(*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CHPMV 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 hermitian 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. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] AP *> \verbatim *> AP is COMPLEX 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 hermitian 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 hermitian 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. *> Note that the imaginary parts of the diagonal elements need *> not be set and are assumed to be zero. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is COMPLEX *> On entry, BETA specifies the scalar beta. When BETA is *> supplied as zero then Y need not be set on input. *> \endverbatim *> *> \param[in,out] Y *> \verbatim *> Y is COMPLEX 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. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> The vector and matrix arguments are not referenced when N = 0, or M = 0 *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE CHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) * * -- Reference BLAS level2 routine -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. COMPLEX ALPHA,BETA INTEGER INCX,INCY,N CHARACTER UPLO * .. * .. Array Arguments .. COMPLEX AP(*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX ONE PARAMETER (ONE= (1.0E+0,0.0E+0)) COMPLEX ZERO PARAMETER (ZERO= (0.0E+0,0.0E+0)) * .. * .. Local Scalars .. COMPLEX TEMP1,TEMP2 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG,REAL * .. * * 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('CHPMV ',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 + CONJG(AP(K))*X(I) K = K + 1 50 CONTINUE Y(J) = Y(J) + TEMP1*REAL(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 + CONJG(AP(K))*X(IX) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y(JY) = Y(JY) + TEMP1*REAL(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*REAL(AP(KK)) K = KK + 1 DO 90 I = J + 1,N Y(I) = Y(I) + TEMP1*AP(K) TEMP2 = TEMP2 + CONJG(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*REAL(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 + CONJG(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 CHPMV * END