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- SUBROUTINE ZGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX,
- $ BETA, Y, INCY )
-* .. Scalar Arguments ..
- COMPLEX*16 ALPHA, BETA
- INTEGER INCX, INCY, KL, KU, LDA, M, N
- CHARACTER*1 TRANS
-* .. Array Arguments ..
- COMPLEX*16 A( LDA, * ), X( * ), Y( * )
-* ..
-*
-* Purpose
-* =======
-*
-* ZGBMV performs one of the matrix-vector operations
-*
-* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or
-*
-* y := alpha*conjg( 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*conjg( 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 - COMPLEX*16 .
-* On entry, ALPHA specifies the scalar alpha.
-* Unchanged on exit.
-*
-* A - COMPLEX*16 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 - COMPLEX*16 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 - COMPLEX*16 .
-* 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 - COMPLEX*16 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 ..
- COMPLEX*16 ONE
- PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
- COMPLEX*16 ZERO
- PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
-* .. Local Scalars ..
- COMPLEX*16 TEMP
- INTEGER I, INFO, IX, IY, J, JX, JY, K, KUP1, KX, KY,
- $ LENX, LENY
- LOGICAL NOCONJ
-* .. External Functions ..
- LOGICAL LSAME
- EXTERNAL LSAME
-* .. External Subroutines ..
- EXTERNAL XERBLA
-* .. Intrinsic Functions ..
- INTRINSIC DCONJG, 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( 'ZGBMV ', 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
-*
- NOCONJ = LSAME( TRANS, 'T' )
-*
-* 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 or y := alpha*conjg( A' )*x + y.
-*
- JY = KY
- IF( INCX.EQ.1 )THEN
- DO 110, J = 1, N
- TEMP = ZERO
- K = KUP1 - J
- IF( NOCONJ )THEN
- DO 90, I = MAX( 1, J - KU ), MIN( M, J + KL )
- TEMP = TEMP + A( K + I, J )*X( I )
- 90 CONTINUE
- ELSE
- DO 100, I = MAX( 1, J - KU ), MIN( M, J + KL )
- TEMP = TEMP + DCONJG( A( K + I, J ) )*X( I )
- 100 CONTINUE
- END IF
- Y( JY ) = Y( JY ) + ALPHA*TEMP
- JY = JY + INCY
- 110 CONTINUE
- ELSE
- DO 140, J = 1, N
- TEMP = ZERO
- IX = KX
- K = KUP1 - J
- IF( NOCONJ )THEN
- DO 120, I = MAX( 1, J - KU ), MIN( M, J + KL )
- TEMP = TEMP + A( K + I, J )*X( IX )
- IX = IX + INCX
- 120 CONTINUE
- ELSE
- DO 130, I = MAX( 1, J - KU ), MIN( M, J + KL )
- TEMP = TEMP + DCONJG( A( K + I, J ) )*X( IX )
- IX = IX + INCX
- 130 CONTINUE
- END IF
- Y( JY ) = Y( JY ) + ALPHA*TEMP
- JY = JY + INCY
- IF( J.GT.KU )
- $ KX = KX + INCX
- 140 CONTINUE
- END IF
- END IF
-*
- RETURN
-*
-* End of ZGBMV .
-*
- END
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