349 lines
11 KiB
Fortran
349 lines
11 KiB
Fortran
SUBROUTINE CHEMVF ( UPLO, N, ALPHA, A, LDA, X, INCX,
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$ BETA, Y, INCY )
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* .. Scalar Arguments ..
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COMPLEX ALPHA, BETA
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INTEGER INCX, INCY, LDA, N
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CHARACTER*1 UPLO
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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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* CHEMV performs the matrix-vector operation
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*
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* y := alpha*A*x + beta*y,
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*
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* where alpha and beta are scalars, x and y are n element vectors and
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* A is an n by n hermitian matrix.
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*
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* Parameters
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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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* 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.
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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.
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* Note that the imaginary parts of the diagonal elements need
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* not be set and are assumed to be zero.
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* Unchanged on exit.
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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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* 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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* BETA - COMPLEX .
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* On entry, BETA specifies the scalar beta. When BETA is
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* supplied as zero then Y need not be set on input.
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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. On exit, Y is overwritten by the updated
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* vector y.
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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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*
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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 ONE
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PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
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COMPLEX ZERO
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PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
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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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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* .. Intrinsic Functions ..
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INTRINSIC CONJG, MAX, REAL
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* ..
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* .. Executable Statements ..
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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.
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$ .NOT.LSAME( UPLO, 'L' ).AND.
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$ .NOT.LSAME( UPLO, 'V' ).AND.
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$ .NOT.LSAME( UPLO, 'M' ))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( LDA.LT.MAX( 1, N ) )THEN
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INFO = 5
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ELSE IF( INCX.EQ.0 )THEN
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INFO = 7
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ELSE IF( INCY.EQ.0 )THEN
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INFO = 10
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END IF
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IF( INFO.NE.0 )THEN
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CALL XERBLA( 'CHEMV ', 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 ).AND.( BETA.EQ.ONE ) ) )
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$ RETURN
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*
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* Set up the start points in X and Y.
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*
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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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*
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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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* First form y := beta*y.
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*
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IF( BETA.NE.ONE )THEN
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IF( INCY.EQ.1 )THEN
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IF( BETA.EQ.ZERO )THEN
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DO 10, I = 1, N
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Y( I ) = ZERO
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10 CONTINUE
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ELSE
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DO 20, I = 1, N
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Y( I ) = BETA*Y( I )
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20 CONTINUE
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END IF
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ELSE
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IY = KY
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IF( BETA.EQ.ZERO )THEN
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DO 30, I = 1, N
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Y( IY ) = ZERO
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IY = IY + INCY
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30 CONTINUE
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ELSE
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DO 40, I = 1, N
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Y( IY ) = BETA*Y( IY )
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IY = IY + INCY
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40 CONTINUE
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END IF
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END IF
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END IF
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IF( ALPHA.EQ.ZERO )
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$ RETURN
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IF( LSAME( UPLO, 'U' ) )THEN
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*
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* Form y when A is stored in upper 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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TEMP1 = ALPHA*X( J )
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TEMP2 = ZERO
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DO 50, I = 1, J - 1
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Y( I ) = Y( I ) + TEMP1*A( I, J )
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TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( I )
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50 CONTINUE
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Y( J ) = Y( J ) + TEMP1*REAL( A( J, J ) ) + ALPHA*TEMP2
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60 CONTINUE
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ELSE
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JX = KX
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JY = KY
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DO 80, J = 1, N
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TEMP1 = ALPHA*X( JX )
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TEMP2 = ZERO
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IX = KX
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IY = KY
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DO 70, I = 1, J - 1
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Y( IY ) = Y( IY ) + TEMP1*A( I, J )
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TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( IX )
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IX = IX + INCX
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IY = IY + INCY
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70 CONTINUE
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Y( JY ) = Y( JY ) + TEMP1*REAL( A( J, J ) ) + ALPHA*TEMP2
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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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RETURN
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ENDIF
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IF( LSAME( UPLO, 'L' ) )THEN
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*
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* Form y when A is stored in lower triangle.
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*
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IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
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DO 100, J = 1, N
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TEMP1 = ALPHA*X( J )
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TEMP2 = ZERO
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Y( J ) = Y( J ) + TEMP1*REAL( A( J, J ) )
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DO 90, I = J + 1, N
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Y( I ) = Y( I ) + TEMP1*A( I, J )
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TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( I )
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90 CONTINUE
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Y( J ) = Y( J ) + ALPHA*TEMP2
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100 CONTINUE
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ELSE
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JX = KX
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JY = KY
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DO 120, J = 1, N
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TEMP1 = ALPHA*X( JX )
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TEMP2 = ZERO
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Y( JY ) = Y( JY ) + TEMP1*REAL( A( J, J ) )
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IX = JX
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IY = JY
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DO 110, I = J + 1, N
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IX = IX + INCX
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IY = IY + INCY
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Y( IY ) = Y( IY ) + TEMP1*A( I, J )
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TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( IX )
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110 CONTINUE
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Y( JY ) = Y( JY ) + ALPHA*TEMP2
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JX = JX + INCX
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JY = JY + INCY
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120 CONTINUE
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END IF
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RETURN
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END IF
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IF( LSAME( UPLO, 'V' ) )THEN
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*
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* Form y when A is stored in upper triangle.
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*
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IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
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DO 160, J = 1, N
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TEMP1 = ALPHA*X( J )
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TEMP2 = ZERO
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DO 150, I = 1, J - 1
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Y( I ) = Y( I ) + TEMP1* CONJG(A( I, J ))
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TEMP2 = TEMP2 + A( I, J )*X( I )
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150 CONTINUE
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Y( J ) = Y( J ) + TEMP1*REAL( A( J, J ) ) + ALPHA*TEMP2
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160 CONTINUE
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ELSE
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JX = KX
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JY = KY
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DO 180, J = 1, N
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TEMP1 = ALPHA*X( JX )
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TEMP2 = ZERO
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IX = KX
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IY = KY
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DO 170, I = 1, J - 1
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Y( IY ) = Y( IY ) + TEMP1* CONJG(A( I, J ))
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TEMP2 = TEMP2 + A( I, J )*X( IX )
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IX = IX + INCX
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IY = IY + INCY
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170 CONTINUE
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Y( JY ) = Y( JY ) + TEMP1*REAL( A( J, J ) ) + ALPHA*TEMP2
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JX = JX + INCX
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JY = JY + INCY
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180 CONTINUE
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END IF
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RETURN
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ENDIF
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IF( LSAME( UPLO, 'M' ) )THEN
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*
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* Form y when A is stored in lower triangle.
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*
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IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
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DO 200, J = 1, N
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TEMP1 = ALPHA*X( J )
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TEMP2 = ZERO
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Y( J ) = Y( J ) + TEMP1*REAL( A( J, J ) )
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DO 190, I = J + 1, N
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Y( I ) = Y( I ) + TEMP1*CONJG(A( I, J ))
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TEMP2 = TEMP2 + A( I, J )*X( I )
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190 CONTINUE
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Y( J ) = Y( J ) + ALPHA*TEMP2
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200 CONTINUE
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ELSE
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JX = KX
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JY = KY
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DO 220, J = 1, N
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TEMP1 = ALPHA*X( JX )
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TEMP2 = ZERO
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Y( JY ) = Y( JY ) + TEMP1*REAL( A( J, J ) )
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IX = JX
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IY = JY
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DO 210, I = J + 1, N
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IX = IX + INCX
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IY = IY + INCY
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Y( IY ) = Y( IY ) + TEMP1*CONJG(A( I, J ))
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TEMP2 = TEMP2 + A( I, J )*X( IX )
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210 CONTINUE
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Y( JY ) = Y( JY ) + ALPHA*TEMP2
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JX = JX + INCX
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JY = JY + INCY
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220 CONTINUE
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END IF
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RETURN
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END IF
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*
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*
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* End of CHEMV .
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*
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END
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