* ************************************************************************ * SUBROUTINE ECHPR ( UPLO, N, ALPHA, X, INCX, AP ) * .. Scalar Arguments .. REAL ALPHA INTEGER INCX, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 X( * ) COMPLEX AP( * ) * .. * * Purpose * ======= * * ECHPR 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 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. * * 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. * * AP - COMPLEX array of 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 hermitian 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 hermitian 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. At least double precision arithmetic is * used in the computation of A. * * * 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, K, KK, KX * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, DBLE, 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 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ECHPR ', 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 the array AP * are accessed sequentially with one pass through AP. * K = 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*DCONJG( X( J ) ) DO 10, I = 1, J - 1 AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 10 CONTINUE AP( K ) = REAL( AP( K ) ) + DBLE( X( J )*TEMP ) ELSE K = K + J - 1 AP( K ) = REAL( AP( K ) ) END IF K = K + 1 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( X( JX ) ) IX = KX KK = K DO 30, K = KK, KK + J - 2 AP( K ) = AP( K ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE AP( K ) = REAL( AP( K ) ) + DBLE( X( JX )*TEMP ) ELSE K = K + J - 1 AP( K ) = REAL( AP( K ) ) END IF K = K + 1 JX = JX + INCX 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*DCONJG( X( J ) ) AP( K ) = REAL( AP( K ) ) + DBLE( TEMP*X( J ) ) K = K + 1 DO 50, I = J + 1, N AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 50 CONTINUE ELSE AP( K ) = REAL( AP( K ) ) K = K + N - J + 1 END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( X( JX ) ) AP( K ) = REAL( AP( K ) ) + DBLE( TEMP*X( JX ) ) IX = JX KK = K + 1 DO 70, K = KK, KK + N - J - 1 IX = IX + INCX AP( K ) = AP( K ) + X( IX )*TEMP 70 CONTINUE ELSE AP( K ) = REAL( AP( K ) ) K = K + N - J + 1 END IF JX = JX + INCX 80 CONTINUE END IF END IF * RETURN * * End of ECHPR . * END