cgbmvf.f

SUBROUTINECGBMVF( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX,
$BETA, Y, INCY )
* .. Scalar Arguments ..
COMPLEX ALPHA, BETA
INTEGER INCX, INCY, KL, KU, LDA, M, N
CHARACTER*1 TRANS
* .. Array Arguments ..
COMPLEX 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, NOTRANS, XCONJ
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* .. External Subroutines ..
EXTERNAL XERBLA
* .. Intrinsic Functions ..
INTRINSIC CONJG, MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
 INFO =0
IF ( .NOT.LSAME( TRANS, 'N' ).AND.
 $ .NOT.LSAME( TRANS, 'T' ).AND.
 $ .NOT.LSAME( TRANS, 'R' ).AND.
 $ .NOT.LSAME( TRANS, 'C' ).AND.
 $ .NOT.LSAME( TRANS, 'O' ).AND.
 $ .NOT.LSAME( TRANS, 'U' ).AND.
 $ .NOT.LSAME( TRANS, 'S' ).AND.
 $ .NOT.LSAME( TRANS, 'D' ) )THEN
 INFO =1
ELSEIF( M.LT.0 )THEN
 INFO =2
ELSEIF( N.LT.0 )THEN
 INFO =3
ELSEIF( KL.LT.0 )THEN
 INFO =4
ELSEIF( KU.LT.0 )THEN
 INFO =5
ELSEIF( LDA.LT.( KL + KU +1 ) )THEN
 INFO =8
ELSEIF( INCX.EQ.0 )THEN
 INFO =10
ELSEIF( 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, 'N' ) .OR. LSAME( TRANS, 'T' )
 $ .OR. LSAME( TRANS, 'O' ) .OR. LSAME( TRANS, 'U' ))

 NOTRANS = (LSAME( TRANS, 'N' ) .OR. LSAME( TRANS, 'R' )
 $ .OR. LSAME( TRANS, 'O' ) .OR. LSAME( TRANS, 'S' ))

 XCONJ = (LSAME( TRANS, 'N' ) .OR. LSAME( TRANS, 'T' )
 $ .OR. LSAME( TRANS, 'R' ) .OR. LSAME( TRANS, 'C' ))
*
* Set LENX and LENY, the lengths of the vectors x and y, and set
* up the start points in X and Y.
*
IF(NOTRANS)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
DO10, I =1, LENY
 Y( I ) = ZERO
10CONTINUE
ELSE
DO20, I =1, LENY
 Y( I ) = BETA*Y( I )
20CONTINUE
END IF
ELSE
 IY = KY
IF( BETA.EQ.ZERO )THEN
DO30, I =1, LENY
 Y( IY ) = ZERO
 IY = IY + INCY
30CONTINUE
ELSE
DO40, I =1, LENY
 Y( IY ) = BETA*Y( IY )
 IY = IY + INCY
40CONTINUE
END IF
END IF
END IF
IF( ALPHA.EQ.ZERO )
 $ RETURN

 KUP1 = KU +1

IF(XCONJ)THEN

IF(NOTRANS)THEN
*
* Form y := alpha*A*x + y.
*
 JX = KX
IF( INCY.EQ.1 )THEN
DO60, J =1, N
IF( X( JX ).NE.ZERO )THEN
 TEMP = ALPHA*X( JX )
 K = KUP1 - J
IF( NOCONJ )THEN
DO50, I =MAX( 1, J - KU ), MIN( M, J + KL )
 Y( I ) = Y( I ) + TEMP*A( K + I, J )
50CONTINUE
ELSE
DO55, I =MAX( 1, J - KU ), MIN( M, J + KL )
 Y( I ) = Y( I ) + TEMP*CONJG(A( K + I, J ))
55CONTINUE
END IF

END IF
 JX = JX + INCX
60CONTINUE
ELSE
DO80, J =1, N
IF( X( JX ).NE.ZERO )THEN
 TEMP = ALPHA*X( JX )
 IY = KY
 K = KUP1 - J
IF( NOCONJ )THEN
DO70, I =MAX( 1, J - KU ), MIN( M, J + KL )
 Y( IY ) = Y( IY ) + TEMP*A( K + I, J )
 IY = IY + INCY
70CONTINUE
ELSE
DO75, I =MAX( 1, J - KU ), MIN( M, J + KL )
 Y( IY ) = Y( IY ) + TEMP*CONJG(A( K + I, J ))
 IY = IY + INCY
75CONTINUE
END IF

END IF
 JX = JX + INCX
IF( J.GT.KU )
 $ KY = KY + INCY
80CONTINUE
END IF
ELSE
*
* Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y.
*
 JY = KY
IF( INCX.EQ.1 )THEN
DO110, J =1, N
 TEMP = ZERO
 K = KUP1 - J
IF( NOCONJ )THEN
DO90, I =MAX( 1, J - KU ), MIN( M, J + KL )
 TEMP = TEMP + A( K + I, J )*X( I )
90CONTINUE
ELSE
DO100, I =MAX( 1, J - KU ), MIN( M, J + KL )
 TEMP = TEMP +CONJG( A( K + I, J ) )*X( I )
100CONTINUE
END IF
 Y( JY ) = Y( JY ) + ALPHA*TEMP
 JY = JY + INCY
110CONTINUE
ELSE
DO140, J =1, N
 TEMP = ZERO
 IX = KX
 K = KUP1 - J
IF( NOCONJ )THEN
DO120, I =MAX( 1, J - KU ), MIN( M, J + KL )
 TEMP = TEMP + A( K + I, J )*X( IX )
 IX = IX + INCX
120CONTINUE
ELSE
DO130, I =MAX( 1, J - KU ), MIN( M, J + KL )
 TEMP = TEMP +CONJG( A( K + I, J ) )*X( IX )
 IX = IX + INCX
130CONTINUE
END IF
 Y( JY ) = Y( JY ) + ALPHA*TEMP
 JY = JY + INCY
IF( J.GT.KU )
 $ KX = KX + INCX
140CONTINUE
END IF
END IF

ELSE

IF(NOTRANS)THEN
*
* Form y := alpha*A*x + y.
*
 JX = KX
IF( INCY.EQ.1 )THEN
DO160, J =1, N
IF( X( JX ).NE.ZERO )THEN
 TEMP = ALPHA*CONJG(X( JX ))
 K = KUP1 - J
IF( NOCONJ )THEN
DO150, I =MAX( 1, J - KU ), MIN( M, J + KL )
 Y( I ) = Y( I ) + TEMP*A( K + I, J )
150CONTINUE
ELSE
DO155, I =MAX( 1, J - KU ), MIN( M, J + KL )
 Y( I ) = Y( I ) + TEMP*CONJG(A( K + I, J ))
155CONTINUE
END IF

END IF
 JX = JX + INCX
160CONTINUE
ELSE
DO180, J =1, N
IF( X( JX ).NE.ZERO )THEN
 TEMP = ALPHA*CONJG(X( JX ))
 IY = KY
 K = KUP1 - J
IF( NOCONJ )THEN
DO170, I =MAX( 1, J - KU ), MIN( M, J + KL )
 Y( IY ) = Y( IY ) + TEMP*A( K + I, J )
 IY = IY + INCY
170CONTINUE
ELSE
DO175, I =MAX( 1, J - KU ), MIN( M, J + KL )
 Y( IY ) = Y( IY ) + TEMP*CONJG(A( K + I, J ))
 IY = IY + INCY
175CONTINUE
END IF

END IF
 JX = JX + INCX
IF( J.GT.KU )
 $ KY = KY + INCY
180CONTINUE
END IF
ELSE
*
* Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y.
*
 JY = KY
IF( INCX.EQ.1 )THEN
DO210, J =1, N
 TEMP = ZERO
 K = KUP1 - J
IF( NOCONJ )THEN
DO190, I =MAX( 1, J - KU ), MIN( M, J + KL )
 TEMP = TEMP + A( K + I, J )*CONJG(X( I ))
190CONTINUE
ELSE
DO200, I =MAX( 1, J - KU ), MIN( M, J + KL )
 TEMP = TEMP +CONJG( A( K + I, J ) )*CONJG(X( I ))
200CONTINUE
END IF
 Y( JY ) = Y( JY ) + ALPHA*TEMP
 JY = JY + INCY
210CONTINUE
ELSE
DO240, J =1, N
 TEMP = ZERO
 IX = KX
 K = KUP1 - J
IF( NOCONJ )THEN
DO220, I =MAX( 1, J - KU ), MIN( M, J + KL )
 TEMP = TEMP + A( K + I, J )*CONJG(X( IX ))
 IX = IX + INCX
220CONTINUE
ELSE
DO230, I =MAX( 1, J - KU ), MIN( M, J + KL )
 TEMP = TEMP +CONJG( A( K + I, J ) )*CONJG(X(IX ))
 IX = IX + INCX
230CONTINUE
END IF
 Y( JY ) = Y( JY ) + ALPHA*TEMP
 JY = JY + INCY
IF( J.GT.KU )
 $ KX = KX + INCX
240CONTINUE
END IF
END IF

END IF

*
RETURN
*
* End of ZGBMV .
*
END