346 lines
10 KiB
Fortran
346 lines
10 KiB
Fortran
*> \brief \b CSBMV
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CSBMV( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y,
|
|
* INCY )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER UPLO
|
|
* INTEGER INCX, INCY, K, LDA, N
|
|
* COMPLEX ALPHA, BETA
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* COMPLEX A( LDA, * ), X( * ), Y( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CSBMV 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 symmetric band matrix, with k super-diagonals.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \verbatim
|
|
*> 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, 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 symmetric 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 symmetric 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 symmetric 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 symmetric 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
|
|
*>
|
|
*> 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, 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, 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.
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \ingroup complex_eig
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE CSBMV( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y,
|
|
$ INCY )
|
|
*
|
|
* -- LAPACK test routine --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER UPLO
|
|
INTEGER INCX, INCY, K, LDA, N
|
|
COMPLEX ALPHA, BETA
|
|
* ..
|
|
* .. Array Arguments ..
|
|
COMPLEX A( LDA, * ), X( * ), Y( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
COMPLEX ONE
|
|
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
|
|
COMPLEX ZERO
|
|
PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L
|
|
COMPLEX TEMP1, TEMP2
|
|
* ..
|
|
* .. 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( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
|
|
INFO = 1
|
|
ELSE IF( N.LT.0 ) THEN
|
|
INFO = 2
|
|
ELSE IF( K.LT.0 ) THEN
|
|
INFO = 3
|
|
ELSE IF( LDA.LT.( K+1 ) ) THEN
|
|
INFO = 6
|
|
ELSE IF( INCX.EQ.0 ) THEN
|
|
INFO = 8
|
|
ELSE IF( INCY.EQ.0 ) THEN
|
|
INFO = 11
|
|
END IF
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'CSBMV ', 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
|
|
DO 10 I = 1, N
|
|
Y( I ) = ZERO
|
|
10 CONTINUE
|
|
ELSE
|
|
DO 20 I = 1, N
|
|
Y( I ) = BETA*Y( I )
|
|
20 CONTINUE
|
|
END IF
|
|
ELSE
|
|
IY = KY
|
|
IF( BETA.EQ.ZERO ) THEN
|
|
DO 30 I = 1, N
|
|
Y( IY ) = ZERO
|
|
IY = IY + INCY
|
|
30 CONTINUE
|
|
ELSE
|
|
DO 40 I = 1, N
|
|
Y( IY ) = BETA*Y( IY )
|
|
IY = IY + INCY
|
|
40 CONTINUE
|
|
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
|
|
DO 60 J = 1, N
|
|
TEMP1 = ALPHA*X( J )
|
|
TEMP2 = ZERO
|
|
L = KPLUS1 - J
|
|
DO 50 I = MAX( 1, J-K ), J - 1
|
|
Y( I ) = Y( I ) + TEMP1*A( L+I, J )
|
|
TEMP2 = TEMP2 + A( L+I, J )*X( I )
|
|
50 CONTINUE
|
|
Y( J ) = Y( J ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2
|
|
60 CONTINUE
|
|
ELSE
|
|
JX = KX
|
|
JY = KY
|
|
DO 80 J = 1, N
|
|
TEMP1 = ALPHA*X( JX )
|
|
TEMP2 = ZERO
|
|
IX = KX
|
|
IY = KY
|
|
L = KPLUS1 - J
|
|
DO 70 I = MAX( 1, J-K ), J - 1
|
|
Y( IY ) = Y( IY ) + TEMP1*A( L+I, J )
|
|
TEMP2 = TEMP2 + A( L+I, J )*X( IX )
|
|
IX = IX + INCX
|
|
IY = IY + INCY
|
|
70 CONTINUE
|
|
Y( JY ) = Y( JY ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2
|
|
JX = JX + INCX
|
|
JY = JY + INCY
|
|
IF( J.GT.K ) THEN
|
|
KX = KX + INCX
|
|
KY = KY + INCY
|
|
END IF
|
|
80 CONTINUE
|
|
END IF
|
|
ELSE
|
|
*
|
|
* Form y when lower triangle of A is stored.
|
|
*
|
|
IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
|
|
DO 100 J = 1, N
|
|
TEMP1 = ALPHA*X( J )
|
|
TEMP2 = ZERO
|
|
Y( J ) = Y( J ) + TEMP1*A( 1, J )
|
|
L = 1 - J
|
|
DO 90 I = J + 1, MIN( N, J+K )
|
|
Y( I ) = Y( I ) + TEMP1*A( L+I, J )
|
|
TEMP2 = TEMP2 + A( L+I, J )*X( I )
|
|
90 CONTINUE
|
|
Y( J ) = Y( J ) + ALPHA*TEMP2
|
|
100 CONTINUE
|
|
ELSE
|
|
JX = KX
|
|
JY = KY
|
|
DO 120 J = 1, N
|
|
TEMP1 = ALPHA*X( JX )
|
|
TEMP2 = ZERO
|
|
Y( JY ) = Y( JY ) + TEMP1*A( 1, J )
|
|
L = 1 - J
|
|
IX = JX
|
|
IY = JY
|
|
DO 110 I = J + 1, MIN( N, J+K )
|
|
IX = IX + INCX
|
|
IY = IY + INCY
|
|
Y( IY ) = Y( IY ) + TEMP1*A( L+I, J )
|
|
TEMP2 = TEMP2 + A( L+I, J )*X( IX )
|
|
110 CONTINUE
|
|
Y( JY ) = Y( JY ) + ALPHA*TEMP2
|
|
JX = JX + INCX
|
|
JY = JY + INCY
|
|
120 CONTINUE
|
|
END IF
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CSBMV
|
|
*
|
|
END
|