*> \brief \b ZLA_GBAMV performs a matrix-vector operation to calculate error bounds. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLA_GBAMV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, * INCX, BETA, Y, INCY ) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA, BETA * INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS * .. * .. Array Arguments .. * COMPLEX*16 AB( LDAB, * ), X( * ) * DOUBLE PRECISION Y( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLA_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. *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANS *> \verbatim *> TRANS is 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. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of the matrix A. *> M must be at least zero. *> Unchanged on exit. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of the matrix A. *> N must be at least zero. *> Unchanged on exit. *> \endverbatim *> *> \param[in] KL *> \verbatim *> KL is INTEGER *> The number of subdiagonals within the band of A. KL >= 0. *> \endverbatim *> *> \param[in] KU *> \verbatim *> KU is INTEGER *> The number of superdiagonals within the band of A. KU >= 0. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION *> On entry, ALPHA specifies the scalar alpha. *> Unchanged on exit. *> \endverbatim *> *> \param[in] AB *> \verbatim *> AB is COMPLEX*16 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. *> \endverbatim *> *> \param[in] LDAB *> \verbatim *> LDAB is INTEGER *> On entry, LDAB specifies the first dimension of AB as declared *> in the calling (sub) program. LDAB must be at least *> max( 1, m ). *> Unchanged on exit. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 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. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> Unchanged on exit. *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is 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. *> \endverbatim *> *> \param[in,out] Y *> \verbatim *> Y is DOUBLE PRECISION 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. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> Unchanged on exit. *> *> Level 2 Blas routine. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date September 2012 * *> \ingroup complex16GBcomputational * * ===================================================================== SUBROUTINE ZLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, $ INCX, BETA, Y, INCY ) * * -- LAPACK computational routine (version 3.4.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * September 2012 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS * .. * .. Array Arguments .. COMPLEX*16 AB( LDAB, * ), X( * ) DOUBLE PRECISION Y( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 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, KD, KE COMPLEX*16 CDUM * .. * .. External Subroutines .. EXTERNAL XERBLA, DLAMCH DOUBLE PRECISION DLAMCH * .. * .. External Functions .. EXTERNAL ILATRANS INTEGER ILATRANS * .. * .. Intrinsic Functions .. INTRINSIC MAX, ABS, REAL, DIMAG, SIGN * .. * .. Statement Functions DOUBLE PRECISION CABS1 * .. * .. Statement Function Definitions .. CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) * .. * .. 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( 'ZLA_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 = 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. * 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. 0.0D+0 ) THEN SYMB_ZERO = .TRUE. Y( IY ) = 0.0D+0 ELSE IF ( Y( IY ) .EQ. 0.0D+0 ) THEN SYMB_ZERO = .TRUE. ELSE SYMB_ZERO = .FALSE. Y( IY ) = BETA * ABS( Y( IY ) ) END IF IF ( ALPHA .NE. 0.0D+0 ) THEN DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX ) TEMP = CABS1( AB( KD+I-J, J ) ) SYMB_ZERO = SYMB_ZERO .AND. $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO ) Y( IY ) = Y( IY ) + ALPHA*CABS1( 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. 0.0D+0 ) THEN SYMB_ZERO = .TRUE. Y( IY ) = 0.0D+0 ELSE IF ( Y( IY ) .EQ. 0.0D+0 ) THEN SYMB_ZERO = .TRUE. ELSE SYMB_ZERO = .FALSE. Y( IY ) = BETA * ABS( Y( IY ) ) END IF IF ( ALPHA .NE. 0.0D+0 ) THEN DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX ) TEMP = CABS1( AB( KE-I+J, I ) ) SYMB_ZERO = SYMB_ZERO .AND. $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO ) Y( IY ) = Y( IY ) + ALPHA*CABS1( 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. 0.0D+0 ) THEN SYMB_ZERO = .TRUE. Y( IY ) = 0.0D+0 ELSE IF ( Y( IY ) .EQ. 0.0D+0 ) THEN SYMB_ZERO = .TRUE. ELSE SYMB_ZERO = .FALSE. Y( IY ) = BETA * ABS( Y( IY ) ) END IF IF ( ALPHA .NE. 0.0D+0 ) THEN JX = KX DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX ) TEMP = CABS1( AB( KD+I-J, J ) ) SYMB_ZERO = SYMB_ZERO .AND. $ ( X( JX ) .EQ. ZERO .OR. TEMP .EQ. ZERO ) Y( IY ) = Y( IY ) + ALPHA*CABS1( 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. 0.0D+0 ) THEN SYMB_ZERO = .TRUE. Y( IY ) = 0.0D+0 ELSE IF ( Y( IY ) .EQ. 0.0D+0 ) THEN SYMB_ZERO = .TRUE. ELSE SYMB_ZERO = .FALSE. Y( IY ) = BETA * ABS( Y( IY ) ) END IF IF ( ALPHA .NE. 0.0D+0 ) THEN JX = KX DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX ) TEMP = CABS1( AB( KE-I+J, I ) ) SYMB_ZERO = SYMB_ZERO .AND. $ ( X( JX ) .EQ. ZERO .OR. TEMP .EQ. ZERO ) Y( IY ) = Y( IY ) + ALPHA*CABS1( 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 ZLA_GBAMV * END