*DECK CHPR SUBROUTINE CHPR (UPLO, N, ALPHA, X, INCX, AP) C***BEGIN PROLOGUE CHPR C***PURPOSE Perform the hermitian rank 1 operation. C***LIBRARY SLATEC (BLAS) C***CATEGORY D1B4 C***TYPE COMPLEX (CHPR-C) C***KEYWORDS LEVEL 2 BLAS, LINEAR ALGEBRA C***AUTHOR Dongarra, J. J., (ANL) C Du Croz, J., (NAG) C Hammarling, S., (NAG) C Hanson, R. J., (SNLA) C***DESCRIPTION C C CHPR performs the hermitian rank 1 operation C C A := alpha*x*conjg( x') + A, C C where alpha is a real scalar, x is an n element vector and A is an C n by n hermitian matrix, supplied in packed form. C C Parameters C ========== C C UPLO - CHARACTER*1. C On entry, UPLO specifies whether the upper or lower C triangular part of the matrix A is supplied in the packed C array AP as follows: C C UPLO = 'U' or 'u' The upper triangular part of A is C supplied in AP. C C UPLO = 'L' or 'l' The lower triangular part of A is C supplied in AP. C C Unchanged on exit. C C N - INTEGER. C On entry, N specifies the order of the matrix A. C N must be at least zero. C Unchanged on exit. C C ALPHA - REAL . C On entry, ALPHA specifies the scalar alpha. C Unchanged on exit. C C X - COMPLEX array of dimension at least C ( 1 + ( n - 1 )*abs( INCX ) ). C Before entry, the incremented array X must contain the n C element vector x. C Unchanged on exit. C C INCX - INTEGER. C On entry, INCX specifies the increment for the elements of C X. INCX must not be zero. C Unchanged on exit. C C AP - COMPLEX array of DIMENSION at least C ( ( n*( n + 1 ) )/2 ). C Before entry with UPLO = 'U' or 'u', the array AP must C contain the upper triangular part of the hermitian matrix C packed sequentially, column by column, so that AP( 1 ) C contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) C and a( 2, 2 ) respectively, and so on. On exit, the array C AP is overwritten by the upper triangular part of the C updated matrix. C Before entry with UPLO = 'L' or 'l', the array AP must C contain the lower triangular part of the hermitian matrix C packed sequentially, column by column, so that AP( 1 ) C contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) C and a( 3, 1 ) respectively, and so on. On exit, the array C AP is overwritten by the lower triangular part of the C updated matrix. C Note that the imaginary parts of the diagonal elements need C not be set, they are assumed to be zero, and on exit they C are set to zero. C C***REFERENCES Dongarra, J. J., Du Croz, J., Hammarling, S., and C Hanson, R. J. An extended set of Fortran basic linear C algebra subprograms. ACM TOMS, Vol. 14, No. 1, C pp. 1-17, March 1988. C***ROUTINES CALLED LSAME, XERBLA C***REVISION HISTORY (YYMMDD) C 861022 DATE WRITTEN C 910605 Modified to meet SLATEC prologue standards. Only comment C lines were modified. (BKS) C***END PROLOGUE CHPR C .. Scalar Arguments .. REAL ALPHA INTEGER INCX, N CHARACTER*1 UPLO C .. Array Arguments .. COMPLEX AP( * ), X( * ) C .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) C .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX C .. External Functions .. LOGICAL LSAME EXTERNAL LSAME C .. External Subroutines .. EXTERNAL XERBLA C .. Intrinsic Functions .. INTRINSIC CONJG, REAL C***FIRST EXECUTABLE STATEMENT CHPR C C Test the input parameters. C 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( 'CHPR ', INFO ) RETURN END IF C C Quick return if possible. C IF( ( N.EQ.0 ).OR.( ALPHA.EQ.REAL( ZERO ) ) ) $ RETURN C C Set the start point in X if the increment is not unity. C IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF C C Start the operations. In this version the elements of the array AP C are accessed sequentially with one pass through AP. C KK = 1 IF( LSAME( UPLO, 'U' ) )THEN C C Form A when upper triangle is stored in AP. C IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*CONJG( 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 ) = REAL( AP( KK + J - 1 ) ) $ + REAL( X( J )*TEMP ) ELSE AP( KK + J - 1 ) = REAL( 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*CONJG( 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 ) = REAL( AP( KK + J - 1 ) ) $ + REAL( X( JX )*TEMP ) ELSE AP( KK + J - 1 ) = REAL( AP( KK + J - 1 ) ) END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE C C Form A when lower triangle is stored in AP. C IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*CONJG( X( J ) ) AP( KK ) = REAL( AP( KK ) ) + REAL( 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 ) = REAL( 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*CONJG( X( JX ) ) AP( KK ) = REAL( AP( KK ) ) + REAL( 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 ) = REAL( AP( KK ) ) END IF JX = JX + INCX KK = KK + N - J + 1 80 CONTINUE END IF END IF C RETURN C C End of CHPR . C END