```01:       SUBROUTINE SLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
02: *
03: *  -- LAPACK auxiliary routine (version 3.2) --
04: *     Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
05: *     November 2006
06: *
07: *     .. Scalar Arguments ..
08:       REAL               SI1, SI2, SR1, SR2
09:       INTEGER            LDH, N
10: *     ..
11: *     .. Array Arguments ..
12:       REAL               H( LDH, * ), V( * )
13: *     ..
14: *
15: *       Given a 2-by-2 or 3-by-3 matrix H, SLAQR1 sets v to a
16: *       scalar multiple of the first column of the product
17: *
18: *       (*)  K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)
19: *
20: *       scaling to avoid overflows and most underflows. It
21: *       is assumed that either
22: *
23: *               1) sr1 = sr2 and si1 = -si2
24: *           or
25: *               2) si1 = si2 = 0.
26: *
27: *       This is useful for starting double implicit shift bulges
28: *       in the QR algorithm.
29: *
30: *
31: *       N      (input) integer
32: *              Order of the matrix H. N must be either 2 or 3.
33: *
34: *       H      (input) REAL array of dimension (LDH,N)
35: *              The 2-by-2 or 3-by-3 matrix H in (*).
36: *
37: *       LDH    (input) integer
38: *              The leading dimension of H as declared in
39: *              the calling procedure.  LDH.GE.N
40: *
41: *       SR1    (input) REAL
42: *       SI1    The shifts in (*).
43: *       SR2
44: *       SI2
45: *
46: *       V      (output) REAL array of dimension N
47: *              A scalar multiple of the first column of the
48: *              matrix K in (*).
49: *
50: *     ================================================================
51: *     Based on contributions by
52: *        Karen Braman and Ralph Byers, Department of Mathematics,
53: *        University of Kansas, USA
54: *
55: *     ================================================================
56: *
57: *     .. Parameters ..
58:       REAL               ZERO
59:       PARAMETER          ( ZERO = 0.0e0 )
60: *     ..
61: *     .. Local Scalars ..
62:       REAL               H21S, H31S, S
63: *     ..
64: *     .. Intrinsic Functions ..
65:       INTRINSIC          ABS
66: *     ..
67: *     .. Executable Statements ..
68:       IF( N.EQ.2 ) THEN
69:          S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) )
70:          IF( S.EQ.ZERO ) THEN
71:             V( 1 ) = ZERO
72:             V( 2 ) = ZERO
73:          ELSE
74:             H21S = H( 2, 1 ) / S
75:             V( 1 ) = H21S*H( 1, 2 ) + ( H( 1, 1 )-SR1 )*
76:      \$               ( ( H( 1, 1 )-SR2 ) / S ) - SI1*( SI2 / S )
77:             V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 )
78:          END IF
79:       ELSE
80:          S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) ) +
81:      \$       ABS( H( 3, 1 ) )
82:          IF( S.EQ.ZERO ) THEN
83:             V( 1 ) = ZERO
84:             V( 2 ) = ZERO
85:             V( 3 ) = ZERO
86:          ELSE
87:             H21S = H( 2, 1 ) / S
88:             H31S = H( 3, 1 ) / S
89:             V( 1 ) = ( H( 1, 1 )-SR1 )*( ( H( 1, 1 )-SR2 ) / S ) -
90:      \$               SI1*( SI2 / S ) + H( 1, 2 )*H21S + H( 1, 3 )*H31S
91:             V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 ) +
92:      \$               H( 2, 3 )*H31S
93:             V( 3 ) = H31S*( H( 1, 1 )+H( 3, 3 )-SR1-SR2 ) +
94:      \$               H21S*H( 3, 2 )
95:          END IF
96:       END IF
97:       END
98: ```