1 SUBROUTINE DLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1,
2 $ WR2, WI )
3 *
4 * -- LAPACK auxiliary routine (version 3.2) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * November 2006
8 *
9 * .. Scalar Arguments ..
10 INTEGER LDA, LDB
11 DOUBLE PRECISION SAFMIN, SCALE1, SCALE2, WI, WR1, WR2
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION A( LDA, * ), B( LDB, * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DLAG2 computes the eigenvalues of a 2 x 2 generalized eigenvalue
21 * problem A - w B, with scaling as necessary to avoid over-/underflow.
22 *
23 * The scaling factor "s" results in a modified eigenvalue equation
24 *
25 * s A - w B
26 *
27 * where s is a non-negative scaling factor chosen so that w, w B,
28 * and s A do not overflow and, if possible, do not underflow, either.
29 *
30 * Arguments
31 * =========
32 *
33 * A (input) DOUBLE PRECISION array, dimension (LDA, 2)
34 * On entry, the 2 x 2 matrix A. It is assumed that its 1-norm
35 * is less than 1/SAFMIN. Entries less than
36 * sqrt(SAFMIN)*norm(A) are subject to being treated as zero.
37 *
38 * LDA (input) INTEGER
39 * The leading dimension of the array A. LDA >= 2.
40 *
41 * B (input) DOUBLE PRECISION array, dimension (LDB, 2)
42 * On entry, the 2 x 2 upper triangular matrix B. It is
43 * assumed that the one-norm of B is less than 1/SAFMIN. The
44 * diagonals should be at least sqrt(SAFMIN) times the largest
45 * element of B (in absolute value); if a diagonal is smaller
46 * than that, then +/- sqrt(SAFMIN) will be used instead of
47 * that diagonal.
48 *
49 * LDB (input) INTEGER
50 * The leading dimension of the array B. LDB >= 2.
51 *
52 * SAFMIN (input) DOUBLE PRECISION
53 * The smallest positive number s.t. 1/SAFMIN does not
54 * overflow. (This should always be DLAMCH('S') -- it is an
55 * argument in order to avoid having to call DLAMCH frequently.)
56 *
57 * SCALE1 (output) DOUBLE PRECISION
58 * A scaling factor used to avoid over-/underflow in the
59 * eigenvalue equation which defines the first eigenvalue. If
60 * the eigenvalues are complex, then the eigenvalues are
61 * ( WR1 +/- WI i ) / SCALE1 (which may lie outside the
62 * exponent range of the machine), SCALE1=SCALE2, and SCALE1
63 * will always be positive. If the eigenvalues are real, then
64 * the first (real) eigenvalue is WR1 / SCALE1 , but this may
65 * overflow or underflow, and in fact, SCALE1 may be zero or
66 * less than the underflow threshhold if the exact eigenvalue
67 * is sufficiently large.
68 *
69 * SCALE2 (output) DOUBLE PRECISION
70 * A scaling factor used to avoid over-/underflow in the
71 * eigenvalue equation which defines the second eigenvalue. If
72 * the eigenvalues are complex, then SCALE2=SCALE1. If the
73 * eigenvalues are real, then the second (real) eigenvalue is
74 * WR2 / SCALE2 , but this may overflow or underflow, and in
75 * fact, SCALE2 may be zero or less than the underflow
76 * threshhold if the exact eigenvalue is sufficiently large.
77 *
78 * WR1 (output) DOUBLE PRECISION
79 * If the eigenvalue is real, then WR1 is SCALE1 times the
80 * eigenvalue closest to the (2,2) element of A B**(-1). If the
81 * eigenvalue is complex, then WR1=WR2 is SCALE1 times the real
82 * part of the eigenvalues.
83 *
84 * WR2 (output) DOUBLE PRECISION
85 * If the eigenvalue is real, then WR2 is SCALE2 times the
86 * other eigenvalue. If the eigenvalue is complex, then
87 * WR1=WR2 is SCALE1 times the real part of the eigenvalues.
88 *
89 * WI (output) DOUBLE PRECISION
90 * If the eigenvalue is real, then WI is zero. If the
91 * eigenvalue is complex, then WI is SCALE1 times the imaginary
92 * part of the eigenvalues. WI will always be non-negative.
93 *
94 * =====================================================================
95 *
96 * .. Parameters ..
97 DOUBLE PRECISION ZERO, ONE, TWO
98 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
99 DOUBLE PRECISION HALF
100 PARAMETER ( HALF = ONE / TWO )
101 DOUBLE PRECISION FUZZY1
102 PARAMETER ( FUZZY1 = ONE+1.0D-5 )
103 * ..
104 * .. Local Scalars ..
105 DOUBLE PRECISION A11, A12, A21, A22, ABI22, ANORM, AS11, AS12,
106 $ AS22, ASCALE, B11, B12, B22, BINV11, BINV22,
107 $ BMIN, BNORM, BSCALE, BSIZE, C1, C2, C3, C4, C5,
108 $ DIFF, DISCR, PP, QQ, R, RTMAX, RTMIN, S1, S2,
109 $ SAFMAX, SHIFT, SS, SUM, WABS, WBIG, WDET,
110 $ WSCALE, WSIZE, WSMALL
111 * ..
112 * .. Intrinsic Functions ..
113 INTRINSIC ABS, MAX, MIN, SIGN, SQRT
114 * ..
115 * .. Executable Statements ..
116 *
117 RTMIN = SQRT( SAFMIN )
118 RTMAX = ONE / RTMIN
119 SAFMAX = ONE / SAFMIN
120 *
121 * Scale A
122 *
123 ANORM = MAX( ABS( A( 1, 1 ) )+ABS( A( 2, 1 ) ),
124 $ ABS( A( 1, 2 ) )+ABS( A( 2, 2 ) ), SAFMIN )
125 ASCALE = ONE / ANORM
126 A11 = ASCALE*A( 1, 1 )
127 A21 = ASCALE*A( 2, 1 )
128 A12 = ASCALE*A( 1, 2 )
129 A22 = ASCALE*A( 2, 2 )
130 *
131 * Perturb B if necessary to insure non-singularity
132 *
133 B11 = B( 1, 1 )
134 B12 = B( 1, 2 )
135 B22 = B( 2, 2 )
136 BMIN = RTMIN*MAX( ABS( B11 ), ABS( B12 ), ABS( B22 ), RTMIN )
137 IF( ABS( B11 ).LT.BMIN )
138 $ B11 = SIGN( BMIN, B11 )
139 IF( ABS( B22 ).LT.BMIN )
140 $ B22 = SIGN( BMIN, B22 )
141 *
142 * Scale B
143 *
144 BNORM = MAX( ABS( B11 ), ABS( B12 )+ABS( B22 ), SAFMIN )
145 BSIZE = MAX( ABS( B11 ), ABS( B22 ) )
146 BSCALE = ONE / BSIZE
147 B11 = B11*BSCALE
148 B12 = B12*BSCALE
149 B22 = B22*BSCALE
150 *
151 * Compute larger eigenvalue by method described by C. van Loan
152 *
153 * ( AS is A shifted by -SHIFT*B )
154 *
155 BINV11 = ONE / B11
156 BINV22 = ONE / B22
157 S1 = A11*BINV11
158 S2 = A22*BINV22
159 IF( ABS( S1 ).LE.ABS( S2 ) ) THEN
160 AS12 = A12 - S1*B12
161 AS22 = A22 - S1*B22
162 SS = A21*( BINV11*BINV22 )
163 ABI22 = AS22*BINV22 - SS*B12
164 PP = HALF*ABI22
165 SHIFT = S1
166 ELSE
167 AS12 = A12 - S2*B12
168 AS11 = A11 - S2*B11
169 SS = A21*( BINV11*BINV22 )
170 ABI22 = -SS*B12
171 PP = HALF*( AS11*BINV11+ABI22 )
172 SHIFT = S2
173 END IF
174 QQ = SS*AS12
175 IF( ABS( PP*RTMIN ).GE.ONE ) THEN
176 DISCR = ( RTMIN*PP )**2 + QQ*SAFMIN
177 R = SQRT( ABS( DISCR ) )*RTMAX
178 ELSE
179 IF( PP**2+ABS( QQ ).LE.SAFMIN ) THEN
180 DISCR = ( RTMAX*PP )**2 + QQ*SAFMAX
181 R = SQRT( ABS( DISCR ) )*RTMIN
182 ELSE
183 DISCR = PP**2 + QQ
184 R = SQRT( ABS( DISCR ) )
185 END IF
186 END IF
187 *
188 * Note: the test of R in the following IF is to cover the case when
189 * DISCR is small and negative and is flushed to zero during
190 * the calculation of R. On machines which have a consistent
191 * flush-to-zero threshhold and handle numbers above that
192 * threshhold correctly, it would not be necessary.
193 *
194 IF( DISCR.GE.ZERO .OR. R.EQ.ZERO ) THEN
195 SUM = PP + SIGN( R, PP )
196 DIFF = PP - SIGN( R, PP )
197 WBIG = SHIFT + SUM
198 *
199 * Compute smaller eigenvalue
200 *
201 WSMALL = SHIFT + DIFF
202 IF( HALF*ABS( WBIG ).GT.MAX( ABS( WSMALL ), SAFMIN ) ) THEN
203 WDET = ( A11*A22-A12*A21 )*( BINV11*BINV22 )
204 WSMALL = WDET / WBIG
205 END IF
206 *
207 * Choose (real) eigenvalue closest to 2,2 element of A*B**(-1)
208 * for WR1.
209 *
210 IF( PP.GT.ABI22 ) THEN
211 WR1 = MIN( WBIG, WSMALL )
212 WR2 = MAX( WBIG, WSMALL )
213 ELSE
214 WR1 = MAX( WBIG, WSMALL )
215 WR2 = MIN( WBIG, WSMALL )
216 END IF
217 WI = ZERO
218 ELSE
219 *
220 * Complex eigenvalues
221 *
222 WR1 = SHIFT + PP
223 WR2 = WR1
224 WI = R
225 END IF
226 *
227 * Further scaling to avoid underflow and overflow in computing
228 * SCALE1 and overflow in computing w*B.
229 *
230 * This scale factor (WSCALE) is bounded from above using C1 and C2,
231 * and from below using C3 and C4.
232 * C1 implements the condition s A must never overflow.
233 * C2 implements the condition w B must never overflow.
234 * C3, with C2,
235 * implement the condition that s A - w B must never overflow.
236 * C4 implements the condition s should not underflow.
237 * C5 implements the condition max(s,|w|) should be at least 2.
238 *
239 C1 = BSIZE*( SAFMIN*MAX( ONE, ASCALE ) )
240 C2 = SAFMIN*MAX( ONE, BNORM )
241 C3 = BSIZE*SAFMIN
242 IF( ASCALE.LE.ONE .AND. BSIZE.LE.ONE ) THEN
243 C4 = MIN( ONE, ( ASCALE / SAFMIN )*BSIZE )
244 ELSE
245 C4 = ONE
246 END IF
247 IF( ASCALE.LE.ONE .OR. BSIZE.LE.ONE ) THEN
248 C5 = MIN( ONE, ASCALE*BSIZE )
249 ELSE
250 C5 = ONE
251 END IF
252 *
253 * Scale first eigenvalue
254 *
255 WABS = ABS( WR1 ) + ABS( WI )
256 WSIZE = MAX( SAFMIN, C1, FUZZY1*( WABS*C2+C3 ),
257 $ MIN( C4, HALF*MAX( WABS, C5 ) ) )
258 IF( WSIZE.NE.ONE ) THEN
259 WSCALE = ONE / WSIZE
260 IF( WSIZE.GT.ONE ) THEN
261 SCALE1 = ( MAX( ASCALE, BSIZE )*WSCALE )*
262 $ MIN( ASCALE, BSIZE )
263 ELSE
264 SCALE1 = ( MIN( ASCALE, BSIZE )*WSCALE )*
265 $ MAX( ASCALE, BSIZE )
266 END IF
267 WR1 = WR1*WSCALE
268 IF( WI.NE.ZERO ) THEN
269 WI = WI*WSCALE
270 WR2 = WR1
271 SCALE2 = SCALE1
272 END IF
273 ELSE
274 SCALE1 = ASCALE*BSIZE
275 SCALE2 = SCALE1
276 END IF
277 *
278 * Scale second eigenvalue (if real)
279 *
280 IF( WI.EQ.ZERO ) THEN
281 WSIZE = MAX( SAFMIN, C1, FUZZY1*( ABS( WR2 )*C2+C3 ),
282 $ MIN( C4, HALF*MAX( ABS( WR2 ), C5 ) ) )
283 IF( WSIZE.NE.ONE ) THEN
284 WSCALE = ONE / WSIZE
285 IF( WSIZE.GT.ONE ) THEN
286 SCALE2 = ( MAX( ASCALE, BSIZE )*WSCALE )*
287 $ MIN( ASCALE, BSIZE )
288 ELSE
289 SCALE2 = ( MIN( ASCALE, BSIZE )*WSCALE )*
290 $ MAX( ASCALE, BSIZE )
291 END IF
292 WR2 = WR2*WSCALE
293 ELSE
294 SCALE2 = ASCALE*BSIZE
295 END IF
296 END IF
297 *
298 * End of DLAG2
299 *
300 RETURN
301 END
2 $ WR2, WI )
3 *
4 * -- LAPACK auxiliary routine (version 3.2) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * November 2006
8 *
9 * .. Scalar Arguments ..
10 INTEGER LDA, LDB
11 DOUBLE PRECISION SAFMIN, SCALE1, SCALE2, WI, WR1, WR2
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION A( LDA, * ), B( LDB, * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DLAG2 computes the eigenvalues of a 2 x 2 generalized eigenvalue
21 * problem A - w B, with scaling as necessary to avoid over-/underflow.
22 *
23 * The scaling factor "s" results in a modified eigenvalue equation
24 *
25 * s A - w B
26 *
27 * where s is a non-negative scaling factor chosen so that w, w B,
28 * and s A do not overflow and, if possible, do not underflow, either.
29 *
30 * Arguments
31 * =========
32 *
33 * A (input) DOUBLE PRECISION array, dimension (LDA, 2)
34 * On entry, the 2 x 2 matrix A. It is assumed that its 1-norm
35 * is less than 1/SAFMIN. Entries less than
36 * sqrt(SAFMIN)*norm(A) are subject to being treated as zero.
37 *
38 * LDA (input) INTEGER
39 * The leading dimension of the array A. LDA >= 2.
40 *
41 * B (input) DOUBLE PRECISION array, dimension (LDB, 2)
42 * On entry, the 2 x 2 upper triangular matrix B. It is
43 * assumed that the one-norm of B is less than 1/SAFMIN. The
44 * diagonals should be at least sqrt(SAFMIN) times the largest
45 * element of B (in absolute value); if a diagonal is smaller
46 * than that, then +/- sqrt(SAFMIN) will be used instead of
47 * that diagonal.
48 *
49 * LDB (input) INTEGER
50 * The leading dimension of the array B. LDB >= 2.
51 *
52 * SAFMIN (input) DOUBLE PRECISION
53 * The smallest positive number s.t. 1/SAFMIN does not
54 * overflow. (This should always be DLAMCH('S') -- it is an
55 * argument in order to avoid having to call DLAMCH frequently.)
56 *
57 * SCALE1 (output) DOUBLE PRECISION
58 * A scaling factor used to avoid over-/underflow in the
59 * eigenvalue equation which defines the first eigenvalue. If
60 * the eigenvalues are complex, then the eigenvalues are
61 * ( WR1 +/- WI i ) / SCALE1 (which may lie outside the
62 * exponent range of the machine), SCALE1=SCALE2, and SCALE1
63 * will always be positive. If the eigenvalues are real, then
64 * the first (real) eigenvalue is WR1 / SCALE1 , but this may
65 * overflow or underflow, and in fact, SCALE1 may be zero or
66 * less than the underflow threshhold if the exact eigenvalue
67 * is sufficiently large.
68 *
69 * SCALE2 (output) DOUBLE PRECISION
70 * A scaling factor used to avoid over-/underflow in the
71 * eigenvalue equation which defines the second eigenvalue. If
72 * the eigenvalues are complex, then SCALE2=SCALE1. If the
73 * eigenvalues are real, then the second (real) eigenvalue is
74 * WR2 / SCALE2 , but this may overflow or underflow, and in
75 * fact, SCALE2 may be zero or less than the underflow
76 * threshhold if the exact eigenvalue is sufficiently large.
77 *
78 * WR1 (output) DOUBLE PRECISION
79 * If the eigenvalue is real, then WR1 is SCALE1 times the
80 * eigenvalue closest to the (2,2) element of A B**(-1). If the
81 * eigenvalue is complex, then WR1=WR2 is SCALE1 times the real
82 * part of the eigenvalues.
83 *
84 * WR2 (output) DOUBLE PRECISION
85 * If the eigenvalue is real, then WR2 is SCALE2 times the
86 * other eigenvalue. If the eigenvalue is complex, then
87 * WR1=WR2 is SCALE1 times the real part of the eigenvalues.
88 *
89 * WI (output) DOUBLE PRECISION
90 * If the eigenvalue is real, then WI is zero. If the
91 * eigenvalue is complex, then WI is SCALE1 times the imaginary
92 * part of the eigenvalues. WI will always be non-negative.
93 *
94 * =====================================================================
95 *
96 * .. Parameters ..
97 DOUBLE PRECISION ZERO, ONE, TWO
98 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
99 DOUBLE PRECISION HALF
100 PARAMETER ( HALF = ONE / TWO )
101 DOUBLE PRECISION FUZZY1
102 PARAMETER ( FUZZY1 = ONE+1.0D-5 )
103 * ..
104 * .. Local Scalars ..
105 DOUBLE PRECISION A11, A12, A21, A22, ABI22, ANORM, AS11, AS12,
106 $ AS22, ASCALE, B11, B12, B22, BINV11, BINV22,
107 $ BMIN, BNORM, BSCALE, BSIZE, C1, C2, C3, C4, C5,
108 $ DIFF, DISCR, PP, QQ, R, RTMAX, RTMIN, S1, S2,
109 $ SAFMAX, SHIFT, SS, SUM, WABS, WBIG, WDET,
110 $ WSCALE, WSIZE, WSMALL
111 * ..
112 * .. Intrinsic Functions ..
113 INTRINSIC ABS, MAX, MIN, SIGN, SQRT
114 * ..
115 * .. Executable Statements ..
116 *
117 RTMIN = SQRT( SAFMIN )
118 RTMAX = ONE / RTMIN
119 SAFMAX = ONE / SAFMIN
120 *
121 * Scale A
122 *
123 ANORM = MAX( ABS( A( 1, 1 ) )+ABS( A( 2, 1 ) ),
124 $ ABS( A( 1, 2 ) )+ABS( A( 2, 2 ) ), SAFMIN )
125 ASCALE = ONE / ANORM
126 A11 = ASCALE*A( 1, 1 )
127 A21 = ASCALE*A( 2, 1 )
128 A12 = ASCALE*A( 1, 2 )
129 A22 = ASCALE*A( 2, 2 )
130 *
131 * Perturb B if necessary to insure non-singularity
132 *
133 B11 = B( 1, 1 )
134 B12 = B( 1, 2 )
135 B22 = B( 2, 2 )
136 BMIN = RTMIN*MAX( ABS( B11 ), ABS( B12 ), ABS( B22 ), RTMIN )
137 IF( ABS( B11 ).LT.BMIN )
138 $ B11 = SIGN( BMIN, B11 )
139 IF( ABS( B22 ).LT.BMIN )
140 $ B22 = SIGN( BMIN, B22 )
141 *
142 * Scale B
143 *
144 BNORM = MAX( ABS( B11 ), ABS( B12 )+ABS( B22 ), SAFMIN )
145 BSIZE = MAX( ABS( B11 ), ABS( B22 ) )
146 BSCALE = ONE / BSIZE
147 B11 = B11*BSCALE
148 B12 = B12*BSCALE
149 B22 = B22*BSCALE
150 *
151 * Compute larger eigenvalue by method described by C. van Loan
152 *
153 * ( AS is A shifted by -SHIFT*B )
154 *
155 BINV11 = ONE / B11
156 BINV22 = ONE / B22
157 S1 = A11*BINV11
158 S2 = A22*BINV22
159 IF( ABS( S1 ).LE.ABS( S2 ) ) THEN
160 AS12 = A12 - S1*B12
161 AS22 = A22 - S1*B22
162 SS = A21*( BINV11*BINV22 )
163 ABI22 = AS22*BINV22 - SS*B12
164 PP = HALF*ABI22
165 SHIFT = S1
166 ELSE
167 AS12 = A12 - S2*B12
168 AS11 = A11 - S2*B11
169 SS = A21*( BINV11*BINV22 )
170 ABI22 = -SS*B12
171 PP = HALF*( AS11*BINV11+ABI22 )
172 SHIFT = S2
173 END IF
174 QQ = SS*AS12
175 IF( ABS( PP*RTMIN ).GE.ONE ) THEN
176 DISCR = ( RTMIN*PP )**2 + QQ*SAFMIN
177 R = SQRT( ABS( DISCR ) )*RTMAX
178 ELSE
179 IF( PP**2+ABS( QQ ).LE.SAFMIN ) THEN
180 DISCR = ( RTMAX*PP )**2 + QQ*SAFMAX
181 R = SQRT( ABS( DISCR ) )*RTMIN
182 ELSE
183 DISCR = PP**2 + QQ
184 R = SQRT( ABS( DISCR ) )
185 END IF
186 END IF
187 *
188 * Note: the test of R in the following IF is to cover the case when
189 * DISCR is small and negative and is flushed to zero during
190 * the calculation of R. On machines which have a consistent
191 * flush-to-zero threshhold and handle numbers above that
192 * threshhold correctly, it would not be necessary.
193 *
194 IF( DISCR.GE.ZERO .OR. R.EQ.ZERO ) THEN
195 SUM = PP + SIGN( R, PP )
196 DIFF = PP - SIGN( R, PP )
197 WBIG = SHIFT + SUM
198 *
199 * Compute smaller eigenvalue
200 *
201 WSMALL = SHIFT + DIFF
202 IF( HALF*ABS( WBIG ).GT.MAX( ABS( WSMALL ), SAFMIN ) ) THEN
203 WDET = ( A11*A22-A12*A21 )*( BINV11*BINV22 )
204 WSMALL = WDET / WBIG
205 END IF
206 *
207 * Choose (real) eigenvalue closest to 2,2 element of A*B**(-1)
208 * for WR1.
209 *
210 IF( PP.GT.ABI22 ) THEN
211 WR1 = MIN( WBIG, WSMALL )
212 WR2 = MAX( WBIG, WSMALL )
213 ELSE
214 WR1 = MAX( WBIG, WSMALL )
215 WR2 = MIN( WBIG, WSMALL )
216 END IF
217 WI = ZERO
218 ELSE
219 *
220 * Complex eigenvalues
221 *
222 WR1 = SHIFT + PP
223 WR2 = WR1
224 WI = R
225 END IF
226 *
227 * Further scaling to avoid underflow and overflow in computing
228 * SCALE1 and overflow in computing w*B.
229 *
230 * This scale factor (WSCALE) is bounded from above using C1 and C2,
231 * and from below using C3 and C4.
232 * C1 implements the condition s A must never overflow.
233 * C2 implements the condition w B must never overflow.
234 * C3, with C2,
235 * implement the condition that s A - w B must never overflow.
236 * C4 implements the condition s should not underflow.
237 * C5 implements the condition max(s,|w|) should be at least 2.
238 *
239 C1 = BSIZE*( SAFMIN*MAX( ONE, ASCALE ) )
240 C2 = SAFMIN*MAX( ONE, BNORM )
241 C3 = BSIZE*SAFMIN
242 IF( ASCALE.LE.ONE .AND. BSIZE.LE.ONE ) THEN
243 C4 = MIN( ONE, ( ASCALE / SAFMIN )*BSIZE )
244 ELSE
245 C4 = ONE
246 END IF
247 IF( ASCALE.LE.ONE .OR. BSIZE.LE.ONE ) THEN
248 C5 = MIN( ONE, ASCALE*BSIZE )
249 ELSE
250 C5 = ONE
251 END IF
252 *
253 * Scale first eigenvalue
254 *
255 WABS = ABS( WR1 ) + ABS( WI )
256 WSIZE = MAX( SAFMIN, C1, FUZZY1*( WABS*C2+C3 ),
257 $ MIN( C4, HALF*MAX( WABS, C5 ) ) )
258 IF( WSIZE.NE.ONE ) THEN
259 WSCALE = ONE / WSIZE
260 IF( WSIZE.GT.ONE ) THEN
261 SCALE1 = ( MAX( ASCALE, BSIZE )*WSCALE )*
262 $ MIN( ASCALE, BSIZE )
263 ELSE
264 SCALE1 = ( MIN( ASCALE, BSIZE )*WSCALE )*
265 $ MAX( ASCALE, BSIZE )
266 END IF
267 WR1 = WR1*WSCALE
268 IF( WI.NE.ZERO ) THEN
269 WI = WI*WSCALE
270 WR2 = WR1
271 SCALE2 = SCALE1
272 END IF
273 ELSE
274 SCALE1 = ASCALE*BSIZE
275 SCALE2 = SCALE1
276 END IF
277 *
278 * Scale second eigenvalue (if real)
279 *
280 IF( WI.EQ.ZERO ) THEN
281 WSIZE = MAX( SAFMIN, C1, FUZZY1*( ABS( WR2 )*C2+C3 ),
282 $ MIN( C4, HALF*MAX( ABS( WR2 ), C5 ) ) )
283 IF( WSIZE.NE.ONE ) THEN
284 WSCALE = ONE / WSIZE
285 IF( WSIZE.GT.ONE ) THEN
286 SCALE2 = ( MAX( ASCALE, BSIZE )*WSCALE )*
287 $ MIN( ASCALE, BSIZE )
288 ELSE
289 SCALE2 = ( MIN( ASCALE, BSIZE )*WSCALE )*
290 $ MAX( ASCALE, BSIZE )
291 END IF
292 WR2 = WR2*WSCALE
293 ELSE
294 SCALE2 = ASCALE*BSIZE
295 END IF
296 END IF
297 *
298 * End of DLAG2
299 *
300 RETURN
301 END