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*> \brief \b SGBMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* .. Scalar Arguments ..
* REAL ALPHA,BETA
* INTEGER INCX,INCY,KL,KU,LDA,M,N
* CHARACTER TRANS
* ..
* .. Array Arguments ..
* REAL A(LDA,*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SGBMV performs one of the matrix-vector operations
*>
*> y := alpha*A*x + beta*y, or y := alpha*A**T*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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANS
*> \verbatim
*> TRANS is 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**T*x + beta*y.
*>
*> TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of the matrix A.
*> M must be at least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] KL
*> \verbatim
*> KL is INTEGER
*> On entry, KL specifies the number of sub-diagonals of the
*> matrix A. KL must satisfy 0 .le. KL.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*> KU is INTEGER
*> On entry, KU specifies the number of super-diagonals of the
*> matrix A. KU must satisfy 0 .le. KU.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is REAL
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is REAL 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
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is REAL 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.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is REAL
*> On entry, BETA specifies the scalar beta. When BETA is
*> supplied as zero then Y need not be set on input.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*> Y is REAL 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.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup single_blas_level2
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> The vector and matrix arguments are not referenced when N = 0, or M = 0
*>
*> -- 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE SGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* -- Reference BLAS level2 routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
REAL ALPHA,BETA
INTEGER INCX,INCY,KL,KU,LDA,M,N
CHARACTER TRANS
* ..
* .. Array Arguments ..
REAL A(LDA,*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE,ZERO
PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
* ..
* .. Local Scalars ..
REAL 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
* ..
*
* 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('SGBMV ',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
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
JX = JX + INCX
60 CONTINUE
ELSE
DO 80 J = 1,N
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
JX = JX + INCX
IF (J.GT.KU) KY = KY + INCY
80 CONTINUE
END IF
ELSE
*
* Form y := alpha*A**T*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 SGBMV .
*
END
|
