156 lines
4.2 KiB
Fortran
156 lines
4.2 KiB
Fortran
*> \brief \b SLASSQ updates a sum of squares represented in scaled form.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SLASSQ + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slassq.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slassq.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slassq.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SLASSQ( N, X, INCX, SCALE, SUMSQ )
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*
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* .. Scalar Arguments ..
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* INTEGER INCX, N
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* REAL SCALE, SUMSQ
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* ..
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* .. Array Arguments ..
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* REAL X( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SLASSQ returns the values scl and smsq such that
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*>
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*> ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
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*>
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*> where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is
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*> assumed to be non-negative and scl returns the value
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*>
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*> scl = max( scale, abs( x( i ) ) ).
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*>
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*> scale and sumsq must be supplied in SCALE and SUMSQ and
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*> scl and smsq are overwritten on SCALE and SUMSQ respectively.
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*>
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*> The routine makes only one pass through the vector x.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of elements to be used from the vector X.
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*> \endverbatim
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*>
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*> \param[in] X
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*> \verbatim
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*> X is REAL array, dimension (1+(N-1)*INCX)
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*> The vector for which a scaled sum of squares is computed.
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*> x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
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*> \endverbatim
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*>
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*> \param[in] INCX
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*> \verbatim
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*> INCX is INTEGER
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*> The increment between successive values of the vector X.
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*> INCX > 0.
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*> \endverbatim
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*>
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*> \param[in,out] SCALE
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*> \verbatim
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*> SCALE is REAL
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*> On entry, the value scale in the equation above.
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*> On exit, SCALE is overwritten with scl , the scaling factor
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*> for the sum of squares.
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*> \endverbatim
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*>
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*> \param[in,out] SUMSQ
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*> \verbatim
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*> SUMSQ is REAL
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*> On entry, the value sumsq in the equation above.
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*> On exit, SUMSQ is overwritten with smsq , the basic sum of
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*> squares from which scl has been factored out.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date December 2016
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*
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*> \ingroup OTHERauxiliary
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*
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* =====================================================================
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SUBROUTINE SLASSQ( N, X, INCX, SCALE, SUMSQ )
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*
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* -- LAPACK auxiliary routine (version 3.7.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
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* .. Scalar Arguments ..
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INTEGER INCX, N
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REAL SCALE, SUMSQ
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* ..
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* .. Array Arguments ..
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REAL X( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO
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PARAMETER ( ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER IX
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REAL ABSXI
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* ..
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* .. External Functions ..
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LOGICAL SISNAN
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EXTERNAL SISNAN
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS
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* ..
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* .. Executable Statements ..
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*
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IF( N.GT.0 ) THEN
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DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX
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ABSXI = ABS( X( IX ) )
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IF( ABSXI.GT.ZERO.OR.SISNAN( ABSXI ) ) THEN
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IF( SCALE.LT.ABSXI ) THEN
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SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2
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SCALE = ABSXI
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ELSE
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SUMSQ = SUMSQ + ( ABSXI / SCALE )**2
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END IF
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END IF
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10 CONTINUE
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END IF
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RETURN
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*
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* End of SLASSQ
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*
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END
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