You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
338 lines
9.7 KiB
338 lines
9.7 KiB
2 years ago
|
*> \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
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zspmv.f">
|
||
|
|
*> [TGZ]</a>
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zspmv.f">
|
||
|
|
*> [ZIP]</a>
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zspmv.f">
|
||
|
|
*> [TXT]</a>
|
||
|
|
*> \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
|