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(*) * .. * * Purpose * ======= * * 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. * * Arguments * ========== * * TRANS - 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. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * KL - INTEGER. * On entry, KL specifies the number of sub-diagonals of the * matrix A. KL must satisfy 0 .le. KL. * Unchanged on exit. * * KU - INTEGER. * On entry, KU specifies the number of super-diagonals of the * matrix A. KU must satisfy 0 .le. KU. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - 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 * * 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 * ( kl + ku + 1 ). * Unchanged on exit. * * X - 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. * 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. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - 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. * * 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. * 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. * * ===================================================================== * * .. 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 IF (X(JX).NE.ZERO) THEN 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 END IF JX = JX + INCX 60 CONTINUE ELSE DO 80 J = 1,N IF (X(JX).NE.ZERO) THEN 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 END IF 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