304 lines
9.6 KiB
Fortran
304 lines
9.6 KiB
Fortran
SUBROUTINE DSBMVF( UPLO, N, K, ALPHA, A, LDA, X, INCX,
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$ BETA, Y, INCY )
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* .. Scalar Arguments ..
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DOUBLE PRECISION ALPHA, BETA
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INTEGER INCX, INCY, K, LDA, N
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CHARACTER*1 UPLO
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* .. Array Arguments ..
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DOUBLE PRECISION 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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* DSBMV 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 symmetric band matrix, with k super-diagonals.
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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 band matrix A is being supplied as
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* follows:
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*
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* UPLO = 'U' or 'u' The upper triangular part of A is
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* being supplied.
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*
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* UPLO = 'L' or 'l' The lower triangular part of A is
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* being supplied.
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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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* K - INTEGER.
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* On entry, K specifies the number of super-diagonals of the
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* matrix A. K must satisfy 0 .le. K.
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* Unchanged on exit.
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*
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* ALPHA - DOUBLE PRECISION.
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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 - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
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* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
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* by n part of the array A must contain the upper triangular
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* band part of the symmetric matrix, supplied column by
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* column, with the leading diagonal of the matrix in row
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* ( k + 1 ) of the array, the first super-diagonal starting at
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* position 2 in row k, and so on. The top left k by k triangle
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* of the array A is not referenced.
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* The following program segment will transfer the upper
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* triangular part of a symmetric band matrix from conventional
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* full matrix storage to band storage:
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*
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* DO 20, J = 1, N
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* M = K + 1 - J
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* DO 10, I = MAX( 1, J - K ), J
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* A( M + I, J ) = matrix( I, J )
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* 10 CONTINUE
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* 20 CONTINUE
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*
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* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
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* by n part of the array A must contain the lower triangular
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* band part of the symmetric matrix, supplied column by
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* column, with the leading diagonal of the matrix in row 1 of
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* the array, the first sub-diagonal starting at position 1 in
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* row 2, and so on. The bottom right k by k triangle of the
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* array A is not referenced.
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* The following program segment will transfer the lower
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* triangular part of a symmetric band matrix from conventional
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* full matrix storage to band storage:
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*
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* DO 20, J = 1, N
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* M = 1 - J
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* DO 10, I = J, MIN( N, J + K )
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* A( M + I, J ) = matrix( I, J )
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* 10 CONTINUE
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* 20 CONTINUE
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*
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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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* ( k + 1 ).
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* Unchanged on exit.
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*
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* X - DOUBLE PRECISION 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
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* 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 - DOUBLE PRECISION.
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* On entry, BETA specifies the scalar beta.
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* Unchanged on exit.
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*
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* Y - DOUBLE PRECISION 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
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* vector y. On exit, Y is overwritten by the updated 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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DOUBLE PRECISION ONE , ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* .. Local Scalars ..
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DOUBLE PRECISION TEMP1, TEMP2
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INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L
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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 MAX, MIN
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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' ) )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( K.LT.0 )THEN
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INFO = 3
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ELSE IF( LDA.LT.( K + 1 ) )THEN
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INFO = 6
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ELSE IF( INCX.EQ.0 )THEN
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INFO = 8
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ELSE IF( INCY.EQ.0 )THEN
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INFO = 11
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END IF
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IF( INFO.NE.0 )THEN
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CALL XERBLA( 'DSBMV ', 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 the array A
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* are accessed sequentially with one pass through 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 upper triangle of A is stored.
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*
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KPLUS1 = K + 1
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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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L = KPLUS1 - J
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DO 50, I = MAX( 1, J - K ), J - 1
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Y( I ) = Y( I ) + TEMP1*A( L + I, J )
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TEMP2 = TEMP2 + A( L + I, J )*X( I )
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50 CONTINUE
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Y( J ) = Y( J ) + TEMP1*A( KPLUS1, 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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L = KPLUS1 - J
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DO 70, I = MAX( 1, J - K ), J - 1
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Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
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TEMP2 = TEMP2 + A( L + 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*A( KPLUS1, J ) + ALPHA*TEMP2
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JX = JX + INCX
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JY = JY + INCY
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IF( J.GT.K )THEN
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KX = KX + INCX
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KY = KY + INCY
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END IF
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80 CONTINUE
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END IF
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ELSE
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*
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* Form y when lower triangle of A is stored.
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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*A( 1, J )
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L = 1 - J
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DO 90, I = J + 1, MIN( N, J + K )
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Y( I ) = Y( I ) + TEMP1*A( L + I, J )
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TEMP2 = TEMP2 + A( L + 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*A( 1, J )
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L = 1 - J
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IX = JX
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IY = JY
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DO 110, I = J + 1, MIN( N, J + K )
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IX = IX + INCX
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IY = IY + INCY
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Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
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TEMP2 = TEMP2 + A( L + 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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END IF
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*
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RETURN
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*
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* End of DSBMV .
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*
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END
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