SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP) * .. Scalar Arguments .. REAL ALPHA INTEGER INCX,N CHARACTER UPLO * .. * .. Array Arguments .. COMPLEX AP(*),X(*) * .. * * Purpose * ======= * * CHPR 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, supplied in packed form. * * Arguments * ========== * * 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 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. * * Further Details * =============== * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * ===================================================================== * * .. Parameters .. COMPLEX ZERO PARAMETER (ZERO= (0.0E+0,0.0E+0)) * .. * .. Local Scalars .. COMPLEX TEMP INTEGER I,INFO,IX,J,JX,K,KK,KX * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG,REAL * .. * * 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('CHPR ',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. * KK = 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*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 * * 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*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 * RETURN * * End of CHPR . * END

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