*> \brief \b CSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CSPR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CSPR( UPLO, N, ALPHA, X, INCX, AP ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INCX, N * COMPLEX ALPHA * .. * .. Array Arguments .. * COMPLEX AP( * ), X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CSPR performs the symmetric rank 1 operation *> *> A := alpha*x*x**H + A, *> *> where alpha is a complex scalar, x is an n element vector 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 *> On entry, ALPHA specifies the scalar alpha. *> Unchanged on exit. *> \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. *> 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,out] 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 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. On exit, the array *> AP is overwritten by the upper triangular part of the *> updated matrix. *> 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. On exit, the array *> AP is overwritten by the lower triangular part of the *> updated matrix. *> Note that the imaginary parts of the diagonal elements need *> not be set, they are assumed to be zero, and on exit they *> are set to zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complexOTHERauxiliary * * ===================================================================== SUBROUTINE CSPR( UPLO, N, ALPHA, X, INCX, AP ) * * -- 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, N COMPLEX ALPHA * .. * .. Array Arguments .. COMPLEX AP( * ), X( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER I, INFO, IX, J, JX, K, KK, KX COMPLEX TEMP * .. * .. 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 = 5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CSPR ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.ZERO ) ) \$ RETURN * * Set the start point in X if the increment is not unity. * IF( INCX.LE.0 ) THEN KX = 1 - ( N-1 )*INCX ELSE IF( INCX.NE.1 ) THEN KX = 1 END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * KK = 1 IF( LSAME( UPLO, 'U' ) ) THEN * * Form A when upper triangle is stored in AP. * IF( INCX.EQ.1 ) THEN DO 20 J = 1, N IF( X( J ).NE.ZERO ) THEN TEMP = ALPHA*X( J ) K = KK DO 10 I = 1, J - 1 AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 10 CONTINUE AP( KK+J-1 ) = AP( KK+J-1 ) + X( J )*TEMP ELSE AP( KK+J-1 ) = AP( KK+J-1 ) END IF KK = KK + J 20 CONTINUE ELSE JX = KX DO 40 J = 1, N IF( X( JX ).NE.ZERO ) THEN TEMP = ALPHA*X( JX ) IX = KX DO 30 K = KK, KK + J - 2 AP( K ) = AP( K ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE AP( KK+J-1 ) = AP( KK+J-1 ) + X( JX )*TEMP ELSE AP( KK+J-1 ) = AP( KK+J-1 ) END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF( INCX.EQ.1 ) THEN DO 60 J = 1, N IF( X( J ).NE.ZERO ) THEN TEMP = ALPHA*X( J ) AP( KK ) = AP( KK ) + TEMP*X( J ) K = KK + 1 DO 50 I = J + 1, N AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 50 CONTINUE ELSE AP( KK ) = AP( KK ) END IF KK = KK + N - J + 1 60 CONTINUE ELSE JX = KX DO 80 J = 1, N IF( X( JX ).NE.ZERO ) THEN TEMP = ALPHA*X( JX ) AP( KK ) = AP( KK ) + TEMP*X( JX ) IX = JX DO 70 K = KK + 1, KK + N - J IX = IX + INCX AP( K ) = AP( K ) + X( IX )*TEMP 70 CONTINUE ELSE AP( KK ) = AP( KK ) END IF JX = JX + INCX KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of CSPR * END