chbmvf.f

SUBROUTINECHBMVF( UPLO, N, K, ALPHA, A, LDA, X, INCX,
$BETA, Y, INCY )
* .. Scalar Arguments ..
COMPLEX ALPHA, BETA
INTEGER INCX, INCY, K, LDA, N
CHARACTER*1 UPLO
* .. Array Arguments ..
COMPLEX A( LDA, * ), X( * ), Y( * )
* ..
*
* Purpose
* =======
*
* CHBMV performs the matrix-vector operation
*
* y := alpha*A*x + beta*y,
*
* where alpha and beta are scalars, x and y are n element vectors and
* A is an n by n hermitian band matrix, with k super-diagonals.
*
* Parameters
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the upper or lower
* triangular part of the band matrix A is being supplied as
* follows:
*
* UPLO = 'U' or 'u' The upper triangular part of A is
* being supplied.
*
* UPLO = 'L' or 'l' The lower triangular part of A is
* being supplied.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* K - INTEGER.
* On entry, K specifies the number of super-diagonals of the
* matrix A. K must satisfy 0 .le. K.
* Unchanged on exit.
*
* ALPHA - COMPLEX .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX array of DIMENSION ( LDA, n ).
* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
* by n part of the array A must contain the upper triangular
* band part of the hermitian matrix, supplied column by
* column, with the leading diagonal of the matrix in row
* ( k + 1 ) of the array, the first super-diagonal starting at
* position 2 in row k, and so on. The top left k by k triangle
* of the array A is not referenced.
* The following program segment will transfer the upper
* triangular part of a hermitian band matrix from conventional
* full matrix storage to band storage:
*
* DO 20, J = 1, N
* M = K + 1 - J
* DO 10, I = MAX( 1, J - K ), J
* A( M + I, J ) = matrix( I, J )
* 10 CONTINUE
* 20 CONTINUE
*
* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
* by n part of the array A must contain the lower triangular
* band part of the hermitian matrix, supplied column by
* column, with the leading diagonal of the matrix in row 1 of
* the array, the first sub-diagonal starting at position 1 in
* row 2, and so on. The bottom right k by k triangle of the
* array A is not referenced.
* The following program segment will transfer the lower
* triangular part of a hermitian band matrix from conventional
* full matrix storage to band storage:
*
* DO 20, J = 1, N
* M = 1 - J
* DO 10, I = J, MIN( N, J + K )
* A( M + I, J ) = matrix( I, J )
* 10 CONTINUE
* 20 CONTINUE
*
* Note that the imaginary parts of the diagonal elements need
* not be set and are assumed to be zero.
* 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
* ( k + 1 ).
* Unchanged on exit.
*
* X - COMPLEX array of DIMENSION at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* 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 .
* On entry, BETA specifies the scalar beta.
* Unchanged on exit.
*
* Y - COMPLEX array of DIMENSION at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* 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 ONE
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
COMPLEX ZERO
PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
* .. Local Scalars ..
COMPLEX TEMP1, TEMP2
INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* .. External Subroutines ..
EXTERNAL XERBLA
* .. Intrinsic Functions ..
INTRINSIC CONJG, MAX, MIN, REAL
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
 INFO =0
IF ( .NOT.LSAME( UPLO, 'U' ).AND.
 $ .NOT.LSAME( UPLO, 'L' ) )THEN
 INFO =1
ELSEIF( N.LT.0 )THEN
 INFO =2
ELSEIF( K.LT.0 )THEN
 INFO =3
ELSEIF( LDA.LT.( K +1 ) )THEN
 INFO =6
ELSEIF( INCX.EQ.0 )THEN
 INFO =8
ELSEIF( INCY.EQ.0 )THEN
 INFO =11
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'CHBMV ', INFO )
RETURN
END IF
*
* Quick return if possible.
*
IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
 $ RETURN
*
* Set up the start points in X and Y.
*
IF( INCX.GT.0 )THEN
 KX =1
ELSE
 KX =1- ( N -1 )*INCX
END IF
IF( INCY.GT.0 )THEN
 KY =1
ELSE
 KY =1- ( N -1 )*INCY
END IF
*
* Start the operations. In this version the elements of the array A
* are accessed sequentially with one pass through A.
*
* First form y := beta*y.
*
IF( BETA.NE.ONE )THEN
IF( INCY.EQ.1 )THEN
IF( BETA.EQ.ZERO )THEN
DO10, I =1, N
 Y( I ) = ZERO
10CONTINUE
ELSE
DO20, I =1, N
 Y( I ) = BETA*Y( I )
20CONTINUE
END IF
ELSE
 IY = KY
IF( BETA.EQ.ZERO )THEN
DO30, I =1, N
 Y( IY ) = ZERO
 IY = IY + INCY
30CONTINUE
ELSE
DO40, I =1, N
 Y( IY ) = BETA*Y( IY )
 IY = IY + INCY
40CONTINUE
END IF
END IF
END IF
IF( ALPHA.EQ.ZERO )
 $ RETURN
IF( LSAME( UPLO, 'U' ) )THEN
*
* Form y when upper triangle of A is stored.
*
 KPLUS1 = K +1
IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
DO60, J =1, N
 TEMP1 = ALPHA*X( J )
 TEMP2 = ZERO
 L = KPLUS1 - J
DO50, I =MAX( 1, J - K ), J -1
 Y( I ) = Y( I ) + TEMP1*A( L + I, J )
 TEMP2 = TEMP2 +CONJG( A( L + I, J ) )*X( I )
50CONTINUE
 Y( J ) = Y( J ) + TEMP1*REAL( A( KPLUS1, J ) )
 $ + ALPHA*TEMP2
60CONTINUE
ELSE
 JX = KX
 JY = KY
DO80, J =1, N
 TEMP1 = ALPHA*X( JX )
 TEMP2 = ZERO
 IX = KX
 IY = KY
 L = KPLUS1 - J
DO70, I =MAX( 1, J - K ), J -1
 Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
 TEMP2 = TEMP2 +CONJG( A( L + I, J ) )*X( IX )
 IX = IX + INCX
 IY = IY + INCY
70CONTINUE
 Y( JY ) = Y( JY ) + TEMP1*REAL( A( KPLUS1, J ) )
 $ + ALPHA*TEMP2
 JX = JX + INCX
 JY = JY + INCY
IF( J.GT.K )THEN
 KX = KX + INCX
 KY = KY + INCY
END IF
80CONTINUE
END IF
ELSE
*
* Form y when lower triangle of A is stored.
*
IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
DO100, J =1, N
 TEMP1 = ALPHA*X( J )
 TEMP2 = ZERO
 Y( J ) = Y( J ) + TEMP1*REAL( A( 1, J ) )
 L =1- J
DO90, I = J +1, MIN( N, J + K )
 Y( I ) = Y( I ) + TEMP1*A( L + I, J )
 TEMP2 = TEMP2 +CONJG( A( L + I, J ) )*X( I )
90CONTINUE
 Y( J ) = Y( J ) + ALPHA*TEMP2
100CONTINUE
ELSE
 JX = KX
 JY = KY
DO120, J =1, N
 TEMP1 = ALPHA*X( JX )
 TEMP2 = ZERO
 Y( JY ) = Y( JY ) + TEMP1*REAL( A( 1, J ) )
 L =1- J
 IX = JX
 IY = JY
DO110, I = J +1, MIN( N, J + K )
 IX = IX + INCX
 IY = IY + INCY
 Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
 TEMP2 = TEMP2 +CONJG( A( L + I, J ) )*X( IX )
110CONTINUE
 Y( JY ) = Y( JY ) + ALPHA*TEMP2
 JX = JX + INCX
 JY = JY + INCY
120CONTINUE
END IF
END IF
*
RETURN
*
* End of CHBMV .
*
END