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SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
* * -- LAPACK auxiliary routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INCX, LDA, N COMPLEX*16 ALPHA * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ) * .. * * Purpose * ======= * * 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. * * Arguments * ========== * * UPLO (input) 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. * * N (input) INTEGER * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA (input) COMPLEX*16 * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X (input) 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. * * INCX (input) INTEGER * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * A (input/output) 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. * * LDA (input) 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. * * ===================================================================== * * .. 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 |