SUBROUTINE DLA_GEAMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, \$ Y, INCY ) * * -- LAPACK routine (version 3.2.2) -- * -- 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 .. DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, LDA, M, N, TRANS * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DLA_GEAMV performs one of the matrix-vector operations * * y := alpha*abs(A)*abs(x) + beta*abs(y), * or y := alpha*abs(A)'*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')*abs(x) + beta*abs(y) * BLAS_CONJ_TRANS y := alpha*abs(A')*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. * * ALPHA - DOUBLE PRECISION * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ) * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. * Unchanged on exit. * * LDA (input) INTEGER * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * X (input) DOUBLE PRECISION 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 - DOUBLE PRECISION * 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 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 .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL SYMB_ZERO DOUBLE PRECISION TEMP, SAFE1 INTEGER I, INFO, IY, J, JX, KX, KY, LENX, LENY * .. * .. External Subroutines .. EXTERNAL XERBLA, DLAMCH DOUBLE PRECISION DLAMCH * .. * .. 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( LDA.LT.MAX( 1, M ) )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( 'DLA_GEAMV ', 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 = DLAMCH( '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. * 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 ) = 0.0D+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 = 1, LENX TEMP = ABS( A( I, 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 ) = 0.0D+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 = 1, LENX TEMP = ABS( A( 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 ) = 0.0D+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 = 1, LENX TEMP = ABS( A( I, 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 ) = 0.0D+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 = 1, LENX TEMP = ABS( A( 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 DLA_GEAMV * END