*DECK SSBMV SUBROUTINE SSBMV (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, \$ INCY) C***BEGIN PROLOGUE SSBMV C***PURPOSE Multiply a real vector by a real symmetric band matrix. C***LIBRARY SLATEC (BLAS) C***CATEGORY D1B4 C***TYPE SINGLE PRECISION (SSBMV-S, DSBMV-D, CSBMV-C) C***KEYWORDS LEVEL 2 BLAS, LINEAR ALGEBRA C***AUTHOR Dongarra, J. J., (ANL) C Du Croz, J., (NAG) C Hammarling, S., (NAG) C Hanson, R. J., (SNLA) C***DESCRIPTION C C SSBMV performs the matrix-vector operation C C y := alpha*A*x + beta*y, C C where alpha and beta are scalars, x and y are n element vectors and C A is an n by n symmetric band matrix, with k super-diagonals. C C Parameters C ========== C C UPLO - CHARACTER*1. C On entry, UPLO specifies whether the upper or lower C triangular part of the band matrix A is being supplied as C follows: C C UPLO = 'U' or 'u' The upper triangular part of A is C being supplied. C C UPLO = 'L' or 'l' The lower triangular part of A is C being supplied. C C Unchanged on exit. C C N - INTEGER. C On entry, N specifies the order of the matrix A. C N must be at least zero. C Unchanged on exit. C C K - INTEGER. C On entry, K specifies the number of super-diagonals of the C matrix A. K must satisfy 0 .le. K. C Unchanged on exit. C C ALPHA - REAL . C On entry, ALPHA specifies the scalar alpha. C Unchanged on exit. C C A - REAL array of DIMENSION ( LDA, n ). C Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) C by n part of the array A must contain the upper triangular C band part of the symmetric matrix, supplied column by C column, with the leading diagonal of the matrix in row C ( k + 1 ) of the array, the first super-diagonal starting at C position 2 in row k, and so on. The top left k by k triangle C of the array A is not referenced. C The following program segment will transfer the upper C triangular part of a symmetric band matrix from conventional C full matrix storage to band storage: C C DO 20, J = 1, N C M = K + 1 - J C DO 10, I = MAX( 1, J - K ), J C A( M + I, J ) = matrix( I, J ) C 10 CONTINUE C 20 CONTINUE C C Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) C by n part of the array A must contain the lower triangular C band part of the symmetric matrix, supplied column by C column, with the leading diagonal of the matrix in row 1 of C the array, the first sub-diagonal starting at position 1 in C row 2, and so on. The bottom right k by k triangle of the C array A is not referenced. C The following program segment will transfer the lower C triangular part of a symmetric band matrix from conventional C full matrix storage to band storage: C C DO 20, J = 1, N C M = 1 - J C DO 10, I = J, MIN( N, J + K ) C A( M + I, J ) = matrix( I, J ) C 10 CONTINUE C 20 CONTINUE C C Unchanged on exit. C C LDA - INTEGER. C On entry, LDA specifies the first dimension of A as declared C in the calling (sub) program. LDA must be at least C ( k + 1 ). C Unchanged on exit. C C X - REAL array of DIMENSION at least C ( 1 + ( n - 1 )*abs( INCX ) ). C Before entry, the incremented array X must contain the C vector x. C Unchanged on exit. C C INCX - INTEGER. C On entry, INCX specifies the increment for the elements of C X. INCX must not be zero. C Unchanged on exit. C C BETA - REAL . C On entry, BETA specifies the scalar beta. C Unchanged on exit. C C Y - REAL array of DIMENSION at least C ( 1 + ( n - 1 )*abs( INCY ) ). C Before entry, the incremented array Y must contain the C vector y. On exit, Y is overwritten by the updated vector y. C C INCY - INTEGER. C On entry, INCY specifies the increment for the elements of C Y. INCY must not be zero. C Unchanged on exit. C C***REFERENCES Dongarra, J. J., Du Croz, J., Hammarling, S., and C Hanson, R. J. An extended set of Fortran basic linear C algebra subprograms. ACM TOMS, Vol. 14, No. 1, C pp. 1-17, March 1988. C***ROUTINES CALLED LSAME, XERBLA C***REVISION HISTORY (YYMMDD) C 861022 DATE WRITTEN C 910605 Modified to meet SLATEC prologue standards. Only comment C lines were modified. (BKS) C***END PROLOGUE SSBMV C .. Scalar Arguments .. REAL ALPHA, BETA INTEGER INCX, INCY, K, LDA, N CHARACTER*1 UPLO C .. Array Arguments .. REAL A( LDA, * ), X( * ), Y( * ) C .. Parameters .. REAL ONE , ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) C .. Local Scalars .. REAL TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L C .. External Functions .. LOGICAL LSAME EXTERNAL LSAME C .. External Subroutines .. EXTERNAL XERBLA C .. Intrinsic Functions .. INTRINSIC MAX, MIN C***FIRST EXECUTABLE STATEMENT SSBMV C C Test the input parameters. C 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 C C Quick return if possible. C IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) \$ RETURN C C Set up the start points in X and Y. C 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 C C Start the operations. In this version the elements of the array A C are accessed sequentially with one pass through A. C C First form y := beta*y. C 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 C C Form y when upper triangle of A is stored. C 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 C C Form y when lower triangle of A is stored. C 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 C RETURN C C End of SSBMV . C END