* ************************************************************************ * SUBROUTINE ECHER ( UPLO, N, ALPHA, X, INCX, A, LDA ) * .. Scalar Arguments .. REAL ALPHA INTEGER INCX, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 X( * ) COMPLEX A( LDA, * ) * .. * * Purpose * ======= * * ECHER performs the hermitian rank 1 operation * * A := alpha*x*conjg( x' ) + A, * * where alpha is a real scalar, x is an n element vector and A is an * n by n hermitian matrix. Additional precision arithmetic is used in * the computation. * * Parameters * ========== * * UPLO - 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 - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX*16 array of 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 - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * A - COMPLEX array of 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 hermitian 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 hermitian 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. * 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. At least double precision arithmetic is * used in the computation of A. * * LDA - 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. * * * Level 2 Blas routine. * * -- Written on 20-July-1986. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JX, KX * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, DBLE, MAX, REAL * .. * .. 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( 'ECHER ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.REAL( 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*DCONJG( X( J ) ) DO 10, I = 1, J - 1 A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE A( J, J ) = REAL( A( J, J ) ) + DBLE( X( J )*TEMP ) ELSE A( J, J ) = REAL( A( J, J ) ) END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( X( JX ) ) IX = KX DO 30, I = 1, J - 1 A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE A( J, J ) = REAL( A( J, J ) ) + DBLE( X( JX )*TEMP ) ELSE A( J, J ) = REAL( A( J, J ) ) 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*DCONJG( X( J ) ) A( J, J ) = REAL( A( J, J ) ) + DBLE( TEMP*X( J ) ) DO 50, I = J + 1, N A( I, J ) = A( I, J ) + X( I )*TEMP 50 CONTINUE ELSE A( J, J ) = REAL( A( J, J ) ) END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( X( JX ) ) A( J, J ) = REAL( A( J, J ) ) + DBLE( TEMP*X( JX ) ) IX = JX DO 70, I = J + 1, N IX = IX + INCX A( I, J ) = A( I, J ) + X( IX )*TEMP 70 CONTINUE ELSE A( J, J ) = REAL( A( J, J ) ) END IF JX = JX + INCX 80 CONTINUE END IF END IF * RETURN * * End of ECHER . * END