*> \brief \b ZSYR performs the symmetric rank-1 update of a complex symmetric matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZSYR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INCX, LDA, N * COMPLEX*16 ALPHA * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZSYR 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. *> \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] 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,out] 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. On exit, the *> upper triangular part of the array A is overwritten by the *> upper triangular part of the updated matrix. *> 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. On exit, the *> lower triangular part of the array A is overwritten by the *> lower triangular part of the updated matrix. *> \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 * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16SYauxiliary * * ===================================================================== SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INCX, LDA, N COMPLEX*16 ALPHA * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, INFO, IX, J, JX, KX COMPLEX*16 TEMP * .. * .. 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( INCX.EQ.0 ) THEN INFO = 5 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = 7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZSYR ', 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 A are * accessed sequentially with one pass through the triangular part * of A. * IF( LSAME( UPLO, 'U' ) ) THEN * * Form A when A is stored in upper triangle. * IF( INCX.EQ.1 ) THEN DO 20 J = 1, N IF( X( J ).NE.ZERO ) THEN TEMP = ALPHA*X( J ) DO 10 I = 1, J A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE END IF 20 CONTINUE ELSE JX = KX DO 40 J = 1, N IF( X( JX ).NE.ZERO ) THEN TEMP = ALPHA*X( JX ) IX = KX DO 30 I = 1, J A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JX = JX + INCX 40 CONTINUE END IF ELSE * * Form A when A is stored in lower triangle. * IF( INCX.EQ.1 ) THEN DO 60 J = 1, N IF( X( J ).NE.ZERO ) THEN TEMP = ALPHA*X( J ) DO 50 I = J, N A( I, J ) = A( I, J ) + X( I )*TEMP 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80 J = 1, N IF( X( JX ).NE.ZERO ) THEN TEMP = ALPHA*X( JX ) IX = JX DO 70 I = J, N A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF * RETURN * * End of ZSYR * END