*> \brief \b CLASSQ updates a sum of squares represented in scaled form. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CLASSQ + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CLASSQ( N, X, INCX, SCALE, SUMSQ ) * * .. Scalar Arguments .. * INTEGER INCX, N * REAL SCALE, SUMSQ * .. * .. Array Arguments .. * COMPLEX X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CLASSQ returns the values scl and ssq such that *> *> ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, *> *> where x( i ) = abs( X( 1 + ( i - 1 )*INCX ) ). The value of sumsq is *> assumed to be at least unity and the value of ssq will then satisfy *> *> 1.0 .le. ssq .le. ( sumsq + 2*n ). *> *> scale is assumed to be non-negative and scl returns the value *> *> scl = max( scale, abs( real( x( i ) ) ), abs( aimag( x( i ) ) ) ), *> i *> *> scale and sumsq must be supplied in SCALE and SUMSQ respectively. *> SCALE and SUMSQ are overwritten by scl and ssq respectively. *> *> The routine makes only one pass through the vector X. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of elements to be used from the vector X. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX array, dimension (N) *> The vector x as described above. *> x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> The increment between successive values of the vector X. *> INCX > 0. *> \endverbatim *> *> \param[in,out] SCALE *> \verbatim *> SCALE is REAL *> On entry, the value scale in the equation above. *> On exit, SCALE is overwritten with the value scl . *> \endverbatim *> *> \param[in,out] SUMSQ *> \verbatim *> SUMSQ is REAL *> On entry, the value sumsq in the equation above. *> On exit, SUMSQ is overwritten with the value ssq . *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complexOTHERauxiliary * * ===================================================================== SUBROUTINE CLASSQ( N, X, INCX, SCALE, SUMSQ ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INCX, N REAL SCALE, SUMSQ * .. * .. Array Arguments .. COMPLEX X( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER IX REAL TEMP1 * .. * .. External Functions .. LOGICAL SISNAN EXTERNAL SISNAN * .. * .. Intrinsic Functions .. INTRINSIC ABS, AIMAG, REAL * .. * .. Executable Statements .. * IF( N.GT.0 ) THEN DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX TEMP1 = ABS( REAL( X( IX ) ) ) IF( TEMP1.GT.ZERO.OR.SISNAN( TEMP1 ) ) THEN IF( SCALE.LT.TEMP1 ) THEN SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2 SCALE = TEMP1 ELSE SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2 END IF END IF TEMP1 = ABS( AIMAG( X( IX ) ) ) IF( TEMP1.GT.ZERO.OR.SISNAN( TEMP1 ) ) THEN IF( SCALE.LT.TEMP1 .OR. SISNAN( TEMP1 ) ) THEN SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2 SCALE = TEMP1 ELSE SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2 END IF END IF 10 CONTINUE END IF * RETURN * * End of CLASSQ * END