```01:       SUBROUTINE SLASSQ( N, X, INCX, SCALE, SUMSQ )
02: *
03: *  -- LAPACK auxiliary routine (version 3.2) --
04: *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
05: *     November 2006
06: *
07: *     .. Scalar Arguments ..
08:       INTEGER            INCX, N
09:       REAL               SCALE, SUMSQ
10: *     ..
11: *     .. Array Arguments ..
12:       REAL               X( * )
13: *     ..
14: *
15: *  Purpose
16: *  =======
17: *
18: *  SLASSQ  returns the values  scl  and  smsq  such that
19: *
20: *     ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
21: *
22: *  where  x( i ) = X( 1 + ( i - 1 )*INCX ). The value of  sumsq  is
23: *  assumed to be non-negative and  scl  returns the value
24: *
25: *     scl = max( scale, abs( x( i ) ) ).
26: *
27: *  scale and sumsq must be supplied in SCALE and SUMSQ and
28: *  scl and smsq are overwritten on SCALE and SUMSQ respectively.
29: *
30: *  The routine makes only one pass through the vector x.
31: *
32: *  Arguments
33: *  =========
34: *
35: *  N       (input) INTEGER
36: *          The number of elements to be used from the vector X.
37: *
38: *  X       (input) REAL array, dimension (N)
39: *          The vector for which a scaled sum of squares is computed.
40: *             x( i )  = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
41: *
42: *  INCX    (input) INTEGER
43: *          The increment between successive values of the vector X.
44: *          INCX > 0.
45: *
46: *  SCALE   (input/output) REAL
47: *          On entry, the value  scale  in the equation above.
48: *          On exit, SCALE is overwritten with  scl , the scaling factor
49: *          for the sum of squares.
50: *
51: *  SUMSQ   (input/output) REAL
52: *          On entry, the value  sumsq  in the equation above.
53: *          On exit, SUMSQ is overwritten with  smsq , the basic sum of
54: *          squares from which  scl  has been factored out.
55: *
56: * =====================================================================
57: *
58: *     .. Parameters ..
59:       REAL               ZERO
60:       PARAMETER          ( ZERO = 0.0E+0 )
61: *     ..
62: *     .. Local Scalars ..
63:       INTEGER            IX
64:       REAL               ABSXI
65: *     ..
66: *     .. Intrinsic Functions ..
67:       INTRINSIC          ABS
68: *     ..
69: *     .. Executable Statements ..
70: *
71:       IF( N.GT.0 ) THEN
72:          DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX
73:             IF( X( IX ).NE.ZERO ) THEN
74:                ABSXI = ABS( X( IX ) )
75:                IF( SCALE.LT.ABSXI ) THEN
76:                   SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2
77:                   SCALE = ABSXI
78:                ELSE
79:                   SUMSQ = SUMSQ + ( ABSXI / SCALE )**2
80:                END IF
81:             END IF
82:    10    CONTINUE
83:       END IF
84:       RETURN
85: *
86: *     End of SLASSQ
87: *
88:       END
89: ```