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SUBROUTINE SLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
$ INCX, BETA, Y, INCY ) * * -- LAPACK routine (version 3.3.1) -- * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- * -- Jason Riedy of Univ. of California Berkeley. -- * -- June 2010 -- * * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley and NAG Ltd. -- * IMPLICIT NONE * .. * .. Scalar Arguments .. REAL ALPHA, BETA INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS * .. * .. Array Arguments .. REAL AB( LDAB, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * SLA_GBAMV performs one of the matrix-vector operations * * y := alpha*abs(A)*abs(x) + beta*abs(y), * or y := alpha*abs(A)**T*abs(x) + beta*abs(y), * * where alpha and beta are scalars, x and y are vectors and A is an * m by n matrix. * * This function is primarily used in calculating error bounds. * To protect against underflow during evaluation, components in * the resulting vector are perturbed away from zero by (N+1) * times the underflow threshold. To prevent unnecessarily large * errors for block-structure embedded in general matrices, * "symbolically" zero components are not perturbed. A zero * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * * Arguments * ========== * * TRANS (input) INTEGER * On entry, TRANS specifies the operation to be performed as * follows: * * BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) * BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) * BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) * * Unchanged on exit. * * M (input) INTEGER * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N (input) INTEGER * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * KL (input) INTEGER * The number of subdiagonals within the band of A. KL >= 0. * * KU (input) INTEGER * The number of superdiagonals within the band of A. KU >= 0. * * ALPHA (input) REAL * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * AB (input) REAL array of DIMENSION ( LDAB, n ) * Before entry, the leading m by n part of the array AB must * contain the matrix of coefficients. * Unchanged on exit. * * LDAB (input) INTEGER * On entry, LDA specifies the first dimension of AB as declared * in the calling (sub) program. LDAB must be at least * max( 1, m ). * Unchanged on exit. * * X (input) REAL array, dimension * ( 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 (input) INTEGER * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA (input) 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 (input/output) REAL array, dimension * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. * Before entry with BETA non-zero, the incremented array Y * must contain the vector y. On exit, Y is overwritten by the * updated vector y. * * INCY (input) INTEGER * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * ===================================================================== * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. LOGICAL SYMB_ZERO REAL TEMP, SAFE1 INTEGER I, INFO, IY, J, JX, KX, KY, LENX, LENY, KD, KE * .. * .. External Subroutines .. EXTERNAL XERBLA, SLAMCH REAL SLAMCH * .. * .. External Functions .. EXTERNAL ILATRANS INTEGER ILATRANS * .. * .. Intrinsic Functions .. INTRINSIC MAX, ABS, SIGN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.( ( TRANS.EQ.ILATRANS( 'N' ) ) $ .OR. ( TRANS.EQ.ILATRANS( 'T' ) ) $ .OR. ( TRANS.EQ.ILATRANS( '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 .OR. KL.GT.M-1 ) THEN INFO = 4 ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN INFO = 5 ELSE IF( LDAB.LT.KL+KU+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( 'SLA_GBAMV ', 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( TRANS.EQ.ILATRANS( '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 * * Set SAFE1 essentially to be the underflow threshold times the * number of additions in each row. * SAFE1 = SLAMCH( 'Safe minimum' ) SAFE1 = (N+1)*SAFE1 * * Form y := alpha*abs(A)*abs(x) + beta*abs(y). * * The O(M*N) SYMB_ZERO tests could be replaced by O(N) queries to * the inexact flag. Still doesn't help change the iteration order * to per-column. * KD = KU + 1 KE = KL + 1 IY = KY IF ( INCX.EQ.1 ) THEN IF( TRANS.EQ.ILATRANS( 'N' ) )THEN DO I = 1, LENY IF ( BETA .EQ. ZERO ) THEN SYMB_ZERO = .TRUE. Y( IY ) = 0.0 ELSE IF ( Y( IY ) .EQ. ZERO ) THEN SYMB_ZERO = .TRUE. ELSE SYMB_ZERO = .FALSE. Y( IY ) = BETA * ABS( Y( IY ) ) END IF IF ( ALPHA .NE. ZERO ) THEN DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX ) TEMP = ABS( AB( KD+I-J, J ) ) SYMB_ZERO = SYMB_ZERO .AND. $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO ) Y( IY ) = Y( IY ) + ALPHA*ABS( X( J ) )*TEMP END DO END IF IF ( .NOT.SYMB_ZERO ) $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) ) IY = IY + INCY END DO ELSE DO I = 1, LENY IF ( BETA .EQ. ZERO ) THEN SYMB_ZERO = .TRUE. Y( IY ) = 0.0 ELSE IF ( Y( IY ) .EQ. ZERO ) THEN SYMB_ZERO = .TRUE. ELSE SYMB_ZERO = .FALSE. Y( IY ) = BETA * ABS( Y( IY ) ) END IF IF ( ALPHA .NE. ZERO ) THEN DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX ) TEMP = ABS( AB( KE-I+J, I ) ) SYMB_ZERO = SYMB_ZERO .AND. $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO ) Y( IY ) = Y( IY ) + ALPHA*ABS( X( J ) )*TEMP END DO END IF IF ( .NOT.SYMB_ZERO ) $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) ) IY = IY + INCY END DO END IF ELSE IF( TRANS.EQ.ILATRANS( 'N' ) )THEN DO I = 1, LENY IF ( BETA .EQ. ZERO ) THEN SYMB_ZERO = .TRUE. Y( IY ) = 0.0 ELSE IF ( Y( IY ) .EQ. ZERO ) THEN SYMB_ZERO = .TRUE. ELSE SYMB_ZERO = .FALSE. Y( IY ) = BETA * ABS( Y( IY ) ) END IF IF ( ALPHA .NE. ZERO ) THEN JX = KX DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX ) TEMP = ABS( AB( KD+I-J, J ) ) SYMB_ZERO = SYMB_ZERO .AND. $ ( X( JX ) .EQ. ZERO .OR. TEMP .EQ. ZERO ) Y( IY ) = Y( IY ) + ALPHA*ABS( X( JX ) )*TEMP JX = JX + INCX END DO END IF IF ( .NOT.SYMB_ZERO ) $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) ) IY = IY + INCY END DO ELSE DO I = 1, LENY IF ( BETA .EQ. ZERO ) THEN SYMB_ZERO = .TRUE. Y( IY ) = 0.0 ELSE IF ( Y( IY ) .EQ. ZERO ) THEN SYMB_ZERO = .TRUE. ELSE SYMB_ZERO = .FALSE. Y( IY ) = BETA * ABS( Y( IY ) ) END IF IF ( ALPHA .NE. ZERO ) THEN JX = KX DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX ) TEMP = ABS( AB( KE-I+J, I ) ) SYMB_ZERO = SYMB_ZERO .AND. $ ( X( JX ) .EQ. ZERO .OR. TEMP .EQ. ZERO ) Y( IY ) = Y( IY ) + ALPHA*ABS( X( JX ) )*TEMP JX = JX + INCX END DO END IF IF ( .NOT.SYMB_ZERO ) $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) ) IY = IY + INCY END DO END IF END IF * RETURN * * End of SLA_GBAMV * END |