451 lines
14 KiB
FortranFixed
451 lines
14 KiB
FortranFixed
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SUBROUTINE ZGBMVF( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX,
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$ BETA, Y, INCY )
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* .. Scalar Arguments ..
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COMPLEX*16 ALPHA, BETA
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INTEGER INCX, INCY, KL, KU, LDA, M, N
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CHARACTER*1 TRANS
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* .. Array Arguments ..
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COMPLEX*16 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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* ZGBMV performs one of the matrix-vector operations
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*
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* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or
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*
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* y := alpha*conjg( A' )*x + beta*y,
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*
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* where alpha and beta are scalars, x and y are vectors and A is an
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* m by n band matrix, with kl sub-diagonals and ku super-diagonals.
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*
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* Parameters
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* ==========
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*
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* TRANS - CHARACTER*1.
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* On entry, TRANS specifies the operation to be performed as
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* follows:
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*
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* TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
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*
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* TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
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*
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* TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y.
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*
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* Unchanged on exit.
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*
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* M - INTEGER.
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* On entry, M specifies the number of rows of the matrix A.
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* M must be at least zero.
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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 number of columns 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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* KL - INTEGER.
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* On entry, KL specifies the number of sub-diagonals of the
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* matrix A. KL must satisfy 0 .le. KL.
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* Unchanged on exit.
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*
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* KU - INTEGER.
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* On entry, KU specifies the number of super-diagonals of the
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* matrix A. KU must satisfy 0 .le. KU.
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* Unchanged on exit.
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*
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* ALPHA - COMPLEX*16 .
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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*16 array of DIMENSION ( LDA, n ).
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* Before entry, the leading ( kl + ku + 1 ) by n part of the
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* array A must contain the matrix of coefficients, supplied
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* column by column, with the leading diagonal of the matrix in
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* row ( ku + 1 ) of the array, the first super-diagonal
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* starting at position 2 in row ku, the first sub-diagonal
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* starting at position 1 in row ( ku + 2 ), and so on.
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* Elements in the array A that do not correspond to elements
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* in the band matrix (such as the top left ku by ku triangle)
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* are not referenced.
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* The following program segment will transfer a band matrix
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* from conventional full matrix storage to band storage:
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*
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* DO 20, J = 1, N
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* K = KU + 1 - J
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* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
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* A( K + 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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* ( kl + ku + 1 ).
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* Unchanged on exit.
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*
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* X - COMPLEX*16 array of DIMENSION at least
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* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
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* and at least
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* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
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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 - COMPLEX*16 .
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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*16 array of DIMENSION at least
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* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
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* and at least
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* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
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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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*
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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*16 ONE
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PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
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COMPLEX*16 ZERO
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PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
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* .. Local Scalars ..
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COMPLEX*16 TEMP
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INTEGER I, INFO, IX, IY, J, JX, JY, K, KUP1, KX, KY,
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$ LENX, LENY
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LOGICAL NOCONJ, NOTRANS, XCONJ
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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 DCONJG, 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( TRANS, 'N' ).AND.
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$ .NOT.LSAME( TRANS, 'T' ).AND.
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$ .NOT.LSAME( TRANS, 'R' ).AND.
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$ .NOT.LSAME( TRANS, 'C' ).AND.
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$ .NOT.LSAME( TRANS, 'O' ).AND.
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$ .NOT.LSAME( TRANS, 'U' ).AND.
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$ .NOT.LSAME( TRANS, 'S' ).AND.
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$ .NOT.LSAME( TRANS, 'D' ) )THEN
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INFO = 1
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ELSE IF( M.LT.0 )THEN
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INFO = 2
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ELSE IF( N.LT.0 )THEN
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INFO = 3
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ELSE IF( KL.LT.0 )THEN
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INFO = 4
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ELSE IF( KU.LT.0 )THEN
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INFO = 5
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ELSE IF( LDA.LT.( KL + KU + 1 ) )THEN
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INFO = 8
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ELSE IF( INCX.EQ.0 )THEN
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INFO = 10
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ELSE IF( INCY.EQ.0 )THEN
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INFO = 13
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END IF
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IF( INFO.NE.0 )THEN
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CALL XERBLA( 'ZGBMV ', 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( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
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$ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
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$ RETURN
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*
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NOCONJ = (LSAME( TRANS, 'N' ) .OR. LSAME( TRANS, 'T' )
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$ .OR. LSAME( TRANS, 'O' ) .OR. LSAME( TRANS, 'U' ))
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NOTRANS = (LSAME( TRANS, 'N' ) .OR. LSAME( TRANS, 'R' )
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$ .OR. LSAME( TRANS, 'O' ) .OR. LSAME( TRANS, 'S' ))
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XCONJ = (LSAME( TRANS, 'N' ) .OR. LSAME( TRANS, 'T' )
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$ .OR. LSAME( TRANS, 'R' ) .OR. LSAME( TRANS, 'C' ))
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*
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* Set LENX and LENY, the lengths of the vectors x and y, and set
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* up the start points in X and Y.
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*
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IF(NOTRANS)THEN
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LENX = N
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LENY = M
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ELSE
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LENX = M
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LENY = N
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END IF
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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 - ( LENX - 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 - ( LENY - 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 band part 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, LENY
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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, LENY
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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, LENY
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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, LENY
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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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KUP1 = KU + 1
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IF(XCONJ)THEN
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IF(NOTRANS)THEN
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*
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* Form y := alpha*A*x + y.
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*
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JX = KX
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IF( INCY.EQ.1 )THEN
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DO 60, J = 1, N
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IF( X( JX ).NE.ZERO )THEN
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TEMP = ALPHA*X( JX )
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K = KUP1 - J
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IF( NOCONJ )THEN
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DO 50, I = MAX( 1, J - KU ), MIN( M, J + KL )
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Y( I ) = Y( I ) + TEMP*A( K + I, J )
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50 CONTINUE
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ELSE
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DO 55, I = MAX( 1, J - KU ), MIN( M, J + KL )
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Y( I ) = Y( I ) + TEMP*DCONJG(A( K + I, J ))
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55 CONTINUE
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END IF
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END IF
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JX = JX + INCX
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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 )THEN
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TEMP = ALPHA*X( JX )
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IY = KY
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K = KUP1 - J
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IF( NOCONJ )THEN
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DO 70, I = MAX( 1, J - KU ), MIN( M, J + KL )
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Y( IY ) = Y( IY ) + TEMP*A( K + I, J )
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IY = IY + INCY
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70 CONTINUE
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ELSE
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DO 75, I = MAX( 1, J - KU ), MIN( M, J + KL )
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Y( IY ) = Y( IY ) + TEMP*DCONJG(A( K + I, J ))
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IY = IY + INCY
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75 CONTINUE
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END IF
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END IF
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JX = JX + INCX
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IF( J.GT.KU )
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$ KY = KY + INCY
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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 := alpha*A'*x + y or y := alpha*conjg( A' )*x + y.
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*
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JY = KY
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IF( INCX.EQ.1 )THEN
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DO 110, J = 1, N
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TEMP = ZERO
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K = KUP1 - J
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IF( NOCONJ )THEN
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DO 90, I = MAX( 1, J - KU ), MIN( M, J + KL )
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TEMP = TEMP + A( K + I, J )*X( I )
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90 CONTINUE
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ELSE
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DO 100, I = MAX( 1, J - KU ), MIN( M, J + KL )
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TEMP = TEMP + DCONJG( A( K + I, J ) )*X( I )
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100 CONTINUE
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END IF
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Y( JY ) = Y( JY ) + ALPHA*TEMP
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JY = JY + INCY
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110 CONTINUE
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ELSE
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DO 140, J = 1, N
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TEMP = ZERO
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IX = KX
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K = KUP1 - J
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IF( NOCONJ )THEN
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DO 120, I = MAX( 1, J - KU ), MIN( M, J + KL )
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TEMP = TEMP + A( K + I, J )*X( IX )
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IX = IX + INCX
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120 CONTINUE
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ELSE
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DO 130, I = MAX( 1, J - KU ), MIN( M, J + KL )
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TEMP = TEMP + DCONJG( A( K + I, J ) )*X( IX )
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IX = IX + INCX
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130 CONTINUE
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END IF
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Y( JY ) = Y( JY ) + ALPHA*TEMP
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JY = JY + INCY
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IF( J.GT.KU )
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$ KX = KX + INCX
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140 CONTINUE
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END IF
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END IF
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ELSE
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IF(NOTRANS)THEN
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*
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* Form y := alpha*A*x + y.
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*
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JX = KX
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IF( INCY.EQ.1 )THEN
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DO 160, J = 1, N
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IF( X( JX ).NE.ZERO )THEN
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TEMP = ALPHA*DCONJG(X( JX ))
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K = KUP1 - J
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|
IF( NOCONJ )THEN
|
||
|
|
DO 150, I = MAX( 1, J - KU ), MIN( M, J + KL )
|
||
|
|
Y( I ) = Y( I ) + TEMP*A( K + I, J )
|
||
|
|
150 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 155, I = MAX( 1, J - KU ), MIN( M, J + KL )
|
||
|
|
Y( I ) = Y( I ) + TEMP*DCONJG(A( K + I, J ))
|
||
|
|
155 CONTINUE
|
||
|
|
END IF
|
||
|
|
|
||
|
|
END IF
|
||
|
|
JX = JX + INCX
|
||
|
|
160 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 180, J = 1, N
|
||
|
|
IF( X( JX ).NE.ZERO )THEN
|
||
|
|
TEMP = ALPHA*DCONJG(X( JX ))
|
||
|
|
IY = KY
|
||
|
|
K = KUP1 - J
|
||
|
|
IF( NOCONJ )THEN
|
||
|
|
DO 170, I = MAX( 1, J - KU ), MIN( M, J + KL )
|
||
|
|
Y( IY ) = Y( IY ) + TEMP*A( K + I, J )
|
||
|
|
IY = IY + INCY
|
||
|
|
170 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 175, I = MAX( 1, J - KU ), MIN( M, J + KL )
|
||
|
|
Y( IY ) = Y( IY ) + TEMP*DCONJG(A( K + I, J ))
|
||
|
|
IY = IY + INCY
|
||
|
|
175 CONTINUE
|
||
|
|
END IF
|
||
|
|
|
||
|
|
END IF
|
||
|
|
JX = JX + INCX
|
||
|
|
IF( J.GT.KU )
|
||
|
|
$ KY = KY + INCY
|
||
|
|
180 CONTINUE
|
||
|
|
END IF
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y.
|
||
|
|
*
|
||
|
|
JY = KY
|
||
|
|
IF( INCX.EQ.1 )THEN
|
||
|
|
DO 210, J = 1, N
|
||
|
|
TEMP = ZERO
|
||
|
|
K = KUP1 - J
|
||
|
|
IF( NOCONJ )THEN
|
||
|
|
DO 190, I = MAX( 1, J - KU ), MIN( M, J + KL )
|
||
|
|
TEMP = TEMP + A( K + I, J )*DCONJG(X( I ))
|
||
|
|
190 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 200, I = MAX( 1, J - KU ), MIN( M, J + KL )
|
||
|
|
TEMP = TEMP + DCONJG( A( K + I, J ) )*DCONJG(X( I ))
|
||
|
|
200 CONTINUE
|
||
|
|
END IF
|
||
|
|
Y( JY ) = Y( JY ) + ALPHA*TEMP
|
||
|
|
JY = JY + INCY
|
||
|
|
210 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 240, J = 1, N
|
||
|
|
TEMP = ZERO
|
||
|
|
IX = KX
|
||
|
|
K = KUP1 - J
|
||
|
|
IF( NOCONJ )THEN
|
||
|
|
DO 220, I = MAX( 1, J - KU ), MIN( M, J + KL )
|
||
|
|
TEMP = TEMP + A( K + I, J )*DCONJG(X( IX ))
|
||
|
|
IX = IX + INCX
|
||
|
|
220 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 230, I = MAX( 1, J - KU ), MIN( M, J + KL )
|
||
|
|
TEMP = TEMP + DCONJG( A( K + I, J ) )*DCONJG(X(IX ))
|
||
|
|
IX = IX + INCX
|
||
|
|
230 CONTINUE
|
||
|
|
END IF
|
||
|
|
Y( JY ) = Y( JY ) + ALPHA*TEMP
|
||
|
|
JY = JY + INCY
|
||
|
|
IF( J.GT.KU )
|
||
|
|
$ KX = KX + INCX
|
||
|
|
240 CONTINUE
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
|
||
|
|
END IF
|
||
|
|
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of ZGBMV .
|
||
|
|
*
|
||
|
|
END
|