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SUBROUTINE CHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) |
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* .. Scalar Arguments .. |
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COMPLEX ALPHA |
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INTEGER INCX,INCY,LDA,N |
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CHARACTER UPLO |
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* .. |
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* .. Array Arguments .. |
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COMPLEX A(LDA,*),X(*),Y(*) |
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* .. |
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* |
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* Purpose |
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* ======= |
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* |
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* CHER2 performs the hermitian rank 2 operation |
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* |
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* A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, |
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* |
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* where alpha is a scalar, x and y are n element vectors and A is an n |
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* by n hermitian matrix. |
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* |
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* Arguments |
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* ========== |
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* |
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* UPLO - CHARACTER*1. |
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* On entry, UPLO specifies whether the upper or lower |
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* triangular part of the array A is to be referenced as |
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* follows: |
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* |
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* UPLO = 'U' or 'u' Only the upper triangular part of A |
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* is to be referenced. |
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* |
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* UPLO = 'L' or 'l' Only the lower triangular part of A |
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* is to be referenced. |
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* |
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* Unchanged on exit. |
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* |
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* N - INTEGER. |
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* On entry, N specifies the order of the matrix A. |
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* N must be at least zero. |
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* Unchanged on exit. |
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* |
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* ALPHA - COMPLEX . |
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* On entry, ALPHA specifies the scalar alpha. |
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* Unchanged on exit. |
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* |
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* X - COMPLEX array of dimension at least |
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* ( 1 + ( n - 1 )*abs( INCX ) ). |
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* Before entry, the incremented array X must contain the n |
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* element vector x. |
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* Unchanged on exit. |
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* |
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* INCX - INTEGER. |
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* On entry, INCX specifies the increment for the elements of |
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* X. INCX must not be zero. |
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* Unchanged on exit. |
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* |
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* Y - COMPLEX array of dimension at least |
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* ( 1 + ( n - 1 )*abs( INCY ) ). |
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* Before entry, the incremented array Y must contain the n |
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* element vector y. |
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* Unchanged on exit. |
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* |
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* INCY - INTEGER. |
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* On entry, INCY specifies the increment for the elements of |
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* Y. INCY must not be zero. |
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* Unchanged on exit. |
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* |
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* A - COMPLEX array of DIMENSION ( LDA, n ). |
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* Before entry with UPLO = 'U' or 'u', the leading n by n |
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* upper triangular part of the array A must contain the upper |
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* triangular part of the hermitian matrix and the strictly |
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* lower triangular part of A is not referenced. On exit, the |
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* upper triangular part of the array A is overwritten by the |
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* upper triangular part of the updated matrix. |
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* Before entry with UPLO = 'L' or 'l', the leading n by n |
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* lower triangular part of the array A must contain the lower |
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* triangular part of the hermitian matrix and the strictly |
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* upper triangular part of A is not referenced. On exit, the |
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* lower triangular part of the array A is overwritten by the |
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* lower triangular part of the updated matrix. |
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* Note that the imaginary parts of the diagonal elements need |
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* not be set, they are assumed to be zero, and on exit they |
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* are set to zero. |
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* |
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* LDA - INTEGER. |
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* On entry, LDA specifies the first dimension of A as declared |
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* in the calling (sub) program. LDA must be at least |
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* max( 1, n ). |
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* Unchanged on exit. |
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* |
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* |
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* Level 2 Blas routine. |
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* |
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* -- Written on 22-October-1986. |
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* Jack Dongarra, Argonne National Lab. |
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* Jeremy Du Croz, Nag Central Office. |
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* Sven Hammarling, Nag Central Office. |
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* Richard Hanson, Sandia National Labs. |
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* |
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* |
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* .. Parameters .. |
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COMPLEX ZERO |
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PARAMETER (ZERO= (0.0E+0,0.0E+0)) |
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* .. |
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* .. Local Scalars .. |
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COMPLEX TEMP1,TEMP2 |
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INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY |
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* .. |
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* .. External Functions .. |
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LOGICAL LSAME |
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EXTERNAL LSAME |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL XERBLA |
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* .. |
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* .. Intrinsic Functions .. |
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INTRINSIC CONJG,MAX,REAL |
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* .. |
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* |
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* Test the input parameters. |
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* |
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INFO = 0 |
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IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN |
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INFO = 1 |
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ELSE IF (N.LT.0) THEN |
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INFO = 2 |
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ELSE IF (INCX.EQ.0) THEN |
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INFO = 5 |
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ELSE IF (INCY.EQ.0) THEN |
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INFO = 7 |
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ELSE IF (LDA.LT.MAX(1,N)) THEN |
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INFO = 9 |
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END IF |
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IF (INFO.NE.0) THEN |
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CALL XERBLA('CHER2 ',INFO)
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RETURN |
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END IF |
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* |
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* Quick return if possible. |
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* |
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IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN |
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* |
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* Set up the start points in X and Y if the increments are not both |
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* unity. |
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* |
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IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN |
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IF (INCX.GT.0) THEN |
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KX = 1 |
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ELSE |
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KX = 1 - (N-1)*INCX |
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END IF |
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IF (INCY.GT.0) THEN |
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KY = 1 |
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ELSE |
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KY = 1 - (N-1)*INCY |
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END IF |
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JX = KX |
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JY = KY |
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END IF |
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* |
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* Start the operations. In this version the elements of A are |
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* accessed sequentially with one pass through the triangular part |
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* of A. |
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* |
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IF (LSAME(UPLO,'U')) THEN |
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* |
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* Form A when A is stored in the upper triangle. |
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* |
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IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN |
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DO 20 J = 1,N |
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IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN |
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TEMP1 = ALPHA*CONJG(Y(J)) |
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TEMP2 = CONJG(ALPHA*X(J)) |
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DO 10 I = 1,J - 1 |
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A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 |
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10 CONTINUE |
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A(J,J) = REAL(A(J,J)) + |
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+ REAL(X(J)*TEMP1+Y(J)*TEMP2) |
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ELSE |
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A(J,J) = REAL(A(J,J)) |
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END IF |
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20 CONTINUE |
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ELSE |
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DO 40 J = 1,N |
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IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN |
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TEMP1 = ALPHA*CONJG(Y(JY)) |
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TEMP2 = CONJG(ALPHA*X(JX)) |
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IX = KX |
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IY = KY |
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DO 30 I = 1,J - 1 |
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A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 |
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IX = IX + INCX |
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IY = IY + INCY |
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30 CONTINUE |
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A(J,J) = REAL(A(J,J)) + |
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+ REAL(X(JX)*TEMP1+Y(JY)*TEMP2) |
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ELSE |
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A(J,J) = REAL(A(J,J)) |
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END IF |
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JX = JX + INCX |
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JY = JY + INCY |
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40 CONTINUE |
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END IF |
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ELSE |
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* |
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* Form A when A is stored in the lower triangle. |
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* |
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IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN |
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DO 60 J = 1,N |
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IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN |
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TEMP1 = ALPHA*CONJG(Y(J)) |
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TEMP2 = CONJG(ALPHA*X(J)) |
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A(J,J) = REAL(A(J,J)) + |
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+ REAL(X(J)*TEMP1+Y(J)*TEMP2) |
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DO 50 I = J + 1,N |
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A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 |
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50 CONTINUE |
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ELSE |
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A(J,J) = REAL(A(J,J)) |
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END IF |
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60 CONTINUE |
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ELSE |
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DO 80 J = 1,N |
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IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN |
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TEMP1 = ALPHA*CONJG(Y(JY)) |
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TEMP2 = CONJG(ALPHA*X(JX)) |
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A(J,J) = REAL(A(J,J)) + |
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+ REAL(X(JX)*TEMP1+Y(JY)*TEMP2) |
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IX = JX |
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IY = JY |
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DO 70 I = J + 1,N |
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IX = IX + INCX |
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IY = IY + INCY |
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A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 |
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70 CONTINUE |
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ELSE |
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A(J,J) = REAL(A(J,J)) |
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END IF |
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JX = JX + INCX |
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JY = JY + INCY |
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80 CONTINUE |
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END IF |
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END IF |
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* |
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RETURN |
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* |
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* End of CHER2 . |
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* |
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END |