* ************************************************************************ * SUBROUTINE ESGBMV( 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*1 TRANS * .. Array Arguments .. DOUBLE PRECISION Y( * ) REAL A( LDA, * ), X( * ) * .. * * Purpose * ======= * * ESGBMV performs one of the matrix-vector operations * * y := alpha*A*x + beta*y, or y := alpha*A'*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. * Additional precision arithmetic is used in the computation. * * Parameters * ========== * * 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'*x + beta*y. * * TRANS = 'C' or 'c' y := alpha*A'*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 - DOUBLE PRECISION 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. * At least REAL arithmetic is used in the * computation of y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 20-July-1986. * 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 .. DOUBLE PRECISION 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, DBLE * .. * .. Executable Statements .. * * 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( 'ESGBMV', 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. * IF( LSAME( TRANS, 'N' ) )THEN LENX = N LENY = M ELSE LENX = M LENY = N 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 and set up the start points in X and Y * if the increments are not both unity. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN IF( BETA.NE.ONE )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 END IF ELSE 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 IF( BETA.NE.ONE )THEN 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. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = DBLE( ALPHA )*X( J ) 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 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = DBLE( 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'*x + y. * IF( ( INCX.EQ.1 ).AND.( INCY.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 )*DBLE( X( I ) ) 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP 100 CONTINUE ELSE JY = KY 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 )*DBLE( 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 ESGBMV. * END