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cla_syamv.f
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*> \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
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_syamv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cla_syamv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_syamv.f">
*> [TXT]</a>
*> \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.
*
*> \date June 2017
*
*> \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 (version 3.7.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* June 2017
*
* .. 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