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SUBROUTINE SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)* .. Scalar Arguments .. REAL ALPHA,BETA INTEGER INCX,INCY,K,LDA,N CHARACTER UPLO* ..* .. Array Arguments .. REAL A(LDA,*),X(*),Y(*)* ..** Purpose* =======** SSBMV 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.** Arguments* ==========** 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 - REAL .* On entry, ALPHA specifies the scalar alpha.* Unchanged on exit.** A - REAL 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 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 - REAL 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 - REAL .* On entry, BETA specifies the scalar beta.* Unchanged on exit.** Y - REAL 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.** Further Details* ===============** 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 .. REAL ONE,ZERO PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)* ..* .. Local Scalars .. REAL 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 MAX,MIN* ..** 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('SSBMV ',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 SSBMV .* END
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