*> \brief \b CLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CLA_SYAMV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CLA_SYAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, * INCY ) * * .. Scalar Arguments .. * REAL ALPHA, BETA * INTEGER INCX, INCY, LDA, N * INTEGER UPLO * .. * .. Array Arguments .. * COMPLEX A( LDA, * ), X( * ) * REAL Y( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CLA_SYAMV performs the matrix-vector operation *> *> y := alpha*abs(A)*abs(x) + beta*abs(y), *> *> where alpha and beta are scalars, x and y are vectors and A is an *> n by n symmetric 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] UPLO *> \verbatim *> UPLO is INTEGER *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: *> *> UPLO = BLAS_UPPER Only the upper triangular part of A *> is to be referenced. *> *> UPLO = BLAS_LOWER Only the lower triangular part of A *> is to be referenced. *> *> 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] ALPHA *> \verbatim *> ALPHA is REAL . *> On entry, ALPHA specifies the scalar alpha. *> Unchanged on exit. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX array, dimension ( LDA, n ). *> Before entry, the leading m by n part of the array A must *> contain the matrix of coefficients. *> Unchanged on exit. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, n ). *> Unchanged on exit. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX array, dimension *> ( 1 + ( n - 1 )*abs( INCX ) ) *> 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 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. *> \endverbatim *> *> \param[in,out] Y *> \verbatim *> Y is REAL array, dimension *> ( 1 + ( n - 1 )*abs( INCY ) ) *> 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. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complexSYcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> *> -- 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. *> -- Modified for the absolute-value product, April 2006 *> Jason Riedy, UC Berkeley *> \endverbatim *> * ===================================================================== SUBROUTINE CLA_SYAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, \$ INCY ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. REAL ALPHA, BETA INTEGER INCX, INCY, LDA, N INTEGER UPLO * .. * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ) REAL Y( * ) * .. * * ===================================================================== * * .. 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 COMPLEX ZDUM * .. * .. External Subroutines .. EXTERNAL XERBLA, SLAMCH REAL SLAMCH * .. * .. External Functions .. EXTERNAL ILAUPLO INTEGER ILAUPLO * .. * .. Intrinsic Functions .. INTRINSIC MAX, ABS, SIGN, REAL, AIMAG * .. * .. Statement Functions .. REAL CABS1 * .. * .. Statement Function Definitions .. CABS1( ZDUM ) = ABS( REAL ( ZDUM ) ) + ABS( AIMAG ( ZDUM ) ) * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( UPLO.NE.ILAUPLO( 'U' ) .AND. \$ UPLO.NE.ILAUPLO( 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 5 ELSE IF( INCX.EQ.0 )THEN INFO = 7 ELSE IF( INCY.EQ.0 )THEN INFO = 10 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CLA_SYAMV', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) \$ RETURN * * Set up the start points in X and Y. * IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 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(N^2) 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 ( UPLO .EQ. ILAUPLO( 'U' ) ) THEN DO I = 1, N 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 = 1, I TEMP = CABS1( A( 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 DO J = I+1, N TEMP = CABS1( A( I, 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, N 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 = 1, I TEMP = CABS1( A( I, 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 DO J = I+1, N TEMP = CABS1( A( 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 ( UPLO .EQ. ILAUPLO( 'U' ) ) THEN DO I = 1, N 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 JX = KX IF ( ALPHA .NE. ZERO ) THEN DO J = 1, I TEMP = CABS1( A( J, I ) ) SYMB_ZERO = SYMB_ZERO .AND. \$ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO ) Y( IY ) = Y( IY ) + ALPHA*CABS1( X( JX ) )*TEMP JX = JX + INCX END DO DO J = I+1, N TEMP = CABS1( A( I, J ) ) SYMB_ZERO = SYMB_ZERO .AND. \$ ( X( J ) .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, N 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 JX = KX IF ( ALPHA .NE. ZERO ) THEN DO J = 1, I TEMP = CABS1( A( I, J ) ) SYMB_ZERO = SYMB_ZERO .AND. \$ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO ) Y( IY ) = Y( IY ) + ALPHA*CABS1( X( JX ) )*TEMP JX = JX + INCX END DO DO J = I+1, N TEMP = CABS1( A( J, I ) ) SYMB_ZERO = SYMB_ZERO .AND. \$ ( X( J ) .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 CLA_SYAMV * END