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SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
*
* -- LAPACK auxiliary routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER INCX, N
DOUBLE PRECISION SCALE, SUMSQ
* ..
* .. Array Arguments ..
DOUBLE PRECISION X( * )
* ..
*
* Purpose
* =======
*
* DLASSQ returns the values scl and smsq such that
*
* ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
*
* where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is
* assumed to be non-negative and scl returns the value
*
* scl = max( scale, abs( x( i ) ) ).
*
* scale and sumsq must be supplied in SCALE and SUMSQ and
* scl and smsq are overwritten on SCALE and SUMSQ respectively.
*
* The routine makes only one pass through the vector x.
*
* Arguments
* =========
*
* N (input) INTEGER
* The number of elements to be used from the vector X.
*
* X (input) DOUBLE PRECISION array, dimension (N)
* The vector for which a scaled sum of squares is computed.
* x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
*
* INCX (input) INTEGER
* The increment between successive values of the vector X.
* INCX > 0.
*
* SCALE (input/output) DOUBLE PRECISION
* On entry, the value scale in the equation above.
* On exit, SCALE is overwritten with scl , the scaling factor
* for the sum of squares.
*
* SUMSQ (input/output) DOUBLE PRECISION
* On entry, the value sumsq in the equation above.
* On exit, SUMSQ is overwritten with smsq , the basic sum of
* squares from which scl has been factored out.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER IX
DOUBLE PRECISION ABSXI
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS
* ..
* .. Executable Statements ..
*
IF( N.GT.0 ) THEN
DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX
IF( X( IX ).NE.ZERO ) THEN
ABSXI = ABS( X( IX ) )
IF( SCALE.LT.ABSXI ) THEN
SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2
SCALE = ABSXI
ELSE
SUMSQ = SUMSQ + ( ABSXI / SCALE )**2
END IF
END IF
10 CONTINUE
END IF
RETURN
*
* End of DLASSQ
*
END
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