SUBROUTINE CHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) * .. Scalar Arguments .. COMPLEX ALPHA INTEGER INCX,INCY,LDA,N CHARACTER UPLO * .. * .. Array Arguments .. COMPLEX A(LDA,*),X(*),Y(*) * .. * * Purpose * ======= * * CHER2 performs the hermitian rank 2 operation * * A := alpha*x*y**H + conjg( alpha )*y*x**H + A, * * where alpha is a scalar, x and y are n element vectors and A is an n * by n hermitian matrix. * * Arguments * ========== * * 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 - COMPLEX . * 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. * * Y - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY 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. * * 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. * * 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 TEMP1,TEMP2 INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG,MAX,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 ELSE IF (INCY.EQ.0) THEN INFO = 7 ELSE IF (LDA.LT.MAX(1,N)) THEN INFO = 9 END IF IF (INFO.NE.0) THEN CALL XERBLA('CHER2 ',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (N-1)*INCX END IF IF (INCY.GT.0) THEN KY = 1 ELSE KY = 1 - (N-1)*INCY END IF JX = KX JY = KY 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 the upper triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 20 J = 1,N IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN TEMP1 = ALPHA*CONJG(Y(J)) TEMP2 = CONJG(ALPHA*X(J)) DO 10 I = 1,J - 1 A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 10 CONTINUE A(J,J) = REAL(A(J,J)) + + REAL(X(J)*TEMP1+Y(J)*TEMP2) ELSE A(J,J) = REAL(A(J,J)) END IF 20 CONTINUE ELSE DO 40 J = 1,N IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN TEMP1 = ALPHA*CONJG(Y(JY)) TEMP2 = CONJG(ALPHA*X(JX)) IX = KX IY = KY DO 30 I = 1,J - 1 A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE A(J,J) = REAL(A(J,J)) + + REAL(X(JX)*TEMP1+Y(JY)*TEMP2) ELSE A(J,J) = REAL(A(J,J)) END IF JX = JX + INCX JY = JY + INCY 40 CONTINUE END IF ELSE * * Form A when A is stored in the lower triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 60 J = 1,N IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN TEMP1 = ALPHA*CONJG(Y(J)) TEMP2 = CONJG(ALPHA*X(J)) A(J,J) = REAL(A(J,J)) + + REAL(X(J)*TEMP1+Y(J)*TEMP2) DO 50 I = J + 1,N A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 50 CONTINUE ELSE A(J,J) = REAL(A(J,J)) END IF 60 CONTINUE ELSE DO 80 J = 1,N IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN TEMP1 = ALPHA*CONJG(Y(JY)) TEMP2 = CONJG(ALPHA*X(JX)) A(J,J) = REAL(A(J,J)) + + REAL(X(JX)*TEMP1+Y(JY)*TEMP2) IX = JX IY = JY DO 70 I = J + 1,N IX = IX + INCX IY = IY + INCY A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 70 CONTINUE ELSE A(J,J) = REAL(A(J,J)) END IF JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF END IF * RETURN * * End of CHER2 . * END