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+ SUBROUTINE DGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX,
+ $ BETA, Y, INCY )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION ALPHA, BETA
+ INTEGER INCX, INCY, KL, KU, LDA, M, N
+ CHARACTER*1 TRANS
+* .. Array Arguments ..
+ DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
+* ..
+*
+* Purpose
+* =======
+*
+* DGBMV performs one of the matrix-vector operations
+*
+* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
+*
+* where alpha and beta are scalars, x and y are vectors and A is an
+* m by n band matrix, with kl sub-diagonals and ku super-diagonals.
+*
+* Parameters
+* ==========
+*
+* TRANS - CHARACTER*1.
+* On entry, TRANS specifies the operation to be performed as
+* follows:
+*
+* TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
+*
+* TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
+*
+* TRANS = 'C' or 'c' y := alpha*A'*x + beta*y.
+*
+* Unchanged on exit.
+*
+* M - INTEGER.
+* On entry, M specifies the number of rows of the matrix A.
+* M must be at least zero.
+* Unchanged on exit.
+*
+* N - INTEGER.
+* On entry, N specifies the number of columns of the matrix A.
+* N must be at least zero.
+* Unchanged on exit.
+*
+* KL - INTEGER.
+* On entry, KL specifies the number of sub-diagonals of the
+* matrix A. KL must satisfy 0 .le. KL.
+* Unchanged on exit.
+*
+* KU - INTEGER.
+* On entry, KU specifies the number of super-diagonals of the
+* matrix A. KU must satisfy 0 .le. KU.
+* Unchanged on exit.
+*
+* ALPHA - DOUBLE PRECISION.
+* On entry, ALPHA specifies the scalar alpha.
+* Unchanged on exit.
+*
+* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
+* Before entry, the leading ( kl + ku + 1 ) by n part of the
+* array A must contain the matrix of coefficients, supplied
+* column by column, with the leading diagonal of the matrix in
+* row ( ku + 1 ) of the array, the first super-diagonal
+* starting at position 2 in row ku, the first sub-diagonal
+* starting at position 1 in row ( ku + 2 ), and so on.
+* Elements in the array A that do not correspond to elements
+* in the band matrix (such as the top left ku by ku triangle)
+* are not referenced.
+* The following program segment will transfer a band matrix
+* from conventional full matrix storage to band storage:
+*
+* DO 20, J = 1, N
+* K = KU + 1 - J
+* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
+* A( K + I, J ) = matrix( I, J )
+* 10 CONTINUE
+* 20 CONTINUE
+*
+* Unchanged on exit.
+*
+* LDA - INTEGER.
+* On entry, LDA specifies the first dimension of A as declared
+* in the calling (sub) program. LDA must be at least
+* ( kl + ku + 1 ).
+* Unchanged on exit.
+*
+* X - DOUBLE PRECISION array of DIMENSION at least
+* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
+* and at least
+* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
+* Before entry, the incremented array X must contain the
+* vector x.
+* Unchanged on exit.
+*
+* INCX - INTEGER.
+* On entry, INCX specifies the increment for the elements of
+* X. INCX must not be zero.
+* Unchanged on exit.
+*
+* BETA - DOUBLE PRECISION.
+* On entry, BETA specifies the scalar beta. When BETA is
+* supplied as zero then Y need not be set on input.
+* Unchanged on exit.
+*
+* Y - DOUBLE PRECISION array of DIMENSION at least
+* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
+* and at least
+* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
+* Before entry, the incremented array Y must contain the
+* vector y. On exit, Y is overwritten by the updated vector y.
+*
+* INCY - INTEGER.
+* On entry, INCY specifies the increment for the elements of
+* Y. INCY must not be zero.
+* Unchanged on exit.
+*
+*
+* Level 2 Blas routine.
+*
+* -- Written on 22-October-1986.
+* Jack Dongarra, Argonne National Lab.
+* Jeremy Du Croz, Nag Central Office.
+* Sven Hammarling, Nag Central Office.
+* Richard Hanson, Sandia National Labs.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ONE , ZERO
+ PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+* .. Local Scalars ..
+ DOUBLE PRECISION TEMP
+ INTEGER I, INFO, IX, IY, J, JX, JY, K, KUP1, KX, KY,
+ $ LENX, LENY
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+ INFO = 0
+ IF ( .NOT.LSAME( TRANS, 'N' ).AND.
+ $ .NOT.LSAME( TRANS, 'T' ).AND.
+ $ .NOT.LSAME( TRANS, 'C' ) )THEN
+ INFO = 1
+ ELSE IF( M.LT.0 )THEN
+ INFO = 2
+ ELSE IF( N.LT.0 )THEN
+ INFO = 3
+ ELSE IF( KL.LT.0 )THEN
+ INFO = 4
+ ELSE IF( KU.LT.0 )THEN
+ INFO = 5
+ ELSE IF( LDA.LT.( KL + KU + 1 ) )THEN
+ INFO = 8
+ ELSE IF( INCX.EQ.0 )THEN
+ INFO = 10
+ ELSE IF( INCY.EQ.0 )THEN
+ INFO = 13
+ END IF
+ IF( INFO.NE.0 )THEN
+ CALL XERBLA( 'DGBMV ', INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible.
+*
+ IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
+ $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
+ $ RETURN
+*
+* Set LENX and LENY, the lengths of the vectors x and y, and set
+* up the start points in X and Y.
+*
+ IF( LSAME( TRANS, 'N' ) )THEN
+ LENX = N
+ LENY = M
+ ELSE
+ LENX = M
+ LENY = N
+ END IF
+ IF( INCX.GT.0 )THEN
+ KX = 1
+ ELSE
+ KX = 1 - ( LENX - 1 )*INCX
+ END IF
+ IF( INCY.GT.0 )THEN
+ KY = 1
+ ELSE
+ KY = 1 - ( LENY - 1 )*INCY
+ END IF
+*
+* Start the operations. In this version the elements of A are
+* accessed sequentially with one pass through the band part of A.
+*
+* First form y := beta*y.
+*
+ IF( BETA.NE.ONE )THEN
+ IF( INCY.EQ.1 )THEN
+ IF( BETA.EQ.ZERO )THEN
+ DO 10, I = 1, LENY
+ Y( I ) = ZERO
+ 10 CONTINUE
+ ELSE
+ DO 20, I = 1, LENY
+ Y( I ) = BETA*Y( I )
+ 20 CONTINUE
+ END IF
+ ELSE
+ IY = KY
+ IF( BETA.EQ.ZERO )THEN
+ DO 30, I = 1, LENY
+ Y( IY ) = ZERO
+ IY = IY + INCY
+ 30 CONTINUE
+ ELSE
+ DO 40, I = 1, LENY
+ Y( IY ) = BETA*Y( IY )
+ IY = IY + INCY
+ 40 CONTINUE
+ END IF
+ END IF
+ END IF
+ IF( ALPHA.EQ.ZERO )
+ $ RETURN
+ KUP1 = KU + 1
+ IF( LSAME( TRANS, 'N' ) )THEN
+*
+* Form y := alpha*A*x + y.
+*
+ JX = KX
+ IF( INCY.EQ.1 )THEN
+ DO 60, J = 1, N
+ IF( X( JX ).NE.ZERO )THEN
+ TEMP = ALPHA*X( JX )
+ K = KUP1 - J
+ DO 50, I = MAX( 1, J - KU ), MIN( M, J + KL )
+ Y( I ) = Y( I ) + TEMP*A( K + I, J )
+ 50 CONTINUE
+ END IF
+ JX = JX + INCX
+ 60 CONTINUE
+ ELSE
+ DO 80, J = 1, N
+ IF( X( JX ).NE.ZERO )THEN
+ TEMP = ALPHA*X( JX )
+ IY = KY
+ K = KUP1 - J
+ DO 70, I = MAX( 1, J - KU ), MIN( M, J + KL )
+ Y( IY ) = Y( IY ) + TEMP*A( K + I, J )
+ IY = IY + INCY
+ 70 CONTINUE
+ END IF
+ JX = JX + INCX
+ IF( J.GT.KU )
+ $ KY = KY + INCY
+ 80 CONTINUE
+ END IF
+ ELSE
+*
+* Form y := alpha*A'*x + y.
+*
+ JY = KY
+ IF( INCX.EQ.1 )THEN
+ DO 100, J = 1, N
+ TEMP = ZERO
+ K = KUP1 - J
+ DO 90, I = MAX( 1, J - KU ), MIN( M, J + KL )
+ TEMP = TEMP + A( K + I, J )*X( I )
+ 90 CONTINUE
+ Y( JY ) = Y( JY ) + ALPHA*TEMP
+ JY = JY + INCY
+ 100 CONTINUE
+ ELSE
+ DO 120, J = 1, N
+ TEMP = ZERO
+ IX = KX
+ K = KUP1 - J
+ DO 110, I = MAX( 1, J - KU ), MIN( M, J + KL )
+ TEMP = TEMP + A( K + I, J )*X( IX )
+ IX = IX + INCX
+ 110 CONTINUE
+ Y( JY ) = Y( JY ) + ALPHA*TEMP
+ JY = JY + INCY
+ IF( J.GT.KU )
+ $ KX = KX + INCX
+ 120 CONTINUE
+ END IF
+ END IF
+*
+ RETURN
+*
+* End of DGBMV .
+*
+ END