1 SUBROUTINE DLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL,
2 $ CSR, SNR )
3 *
4 * -- LAPACK auxiliary routine (version 3.2.2) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * June 2010
8 *
9 * .. Scalar Arguments ..
10 INTEGER LDA, LDB
11 DOUBLE PRECISION CSL, CSR, SNL, SNR
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION A( LDA, * ), ALPHAI( 2 ), ALPHAR( 2 ),
15 $ B( LDB, * ), BETA( 2 )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * DLAGV2 computes the Generalized Schur factorization of a real 2-by-2
22 * matrix pencil (A,B) where B is upper triangular. This routine
23 * computes orthogonal (rotation) matrices given by CSL, SNL and CSR,
24 * SNR such that
25 *
26 * 1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0
27 * types), then
28 *
29 * [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]
30 * [ 0 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]
31 *
32 * [ b11 b12 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]
33 * [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ],
34 *
35 * 2) if the pencil (A,B) has a pair of complex conjugate eigenvalues,
36 * then
37 *
38 * [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]
39 * [ a21 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]
40 *
41 * [ b11 0 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]
42 * [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ]
43 *
44 * where b11 >= b22 > 0.
45 *
46 *
47 * Arguments
48 * =========
49 *
50 * A (input/output) DOUBLE PRECISION array, dimension (LDA, 2)
51 * On entry, the 2 x 2 matrix A.
52 * On exit, A is overwritten by the ``A-part'' of the
53 * generalized Schur form.
54 *
55 * LDA (input) INTEGER
56 * THe leading dimension of the array A. LDA >= 2.
57 *
58 * B (input/output) DOUBLE PRECISION array, dimension (LDB, 2)
59 * On entry, the upper triangular 2 x 2 matrix B.
60 * On exit, B is overwritten by the ``B-part'' of the
61 * generalized Schur form.
62 *
63 * LDB (input) INTEGER
64 * THe leading dimension of the array B. LDB >= 2.
65 *
66 * ALPHAR (output) DOUBLE PRECISION array, dimension (2)
67 * ALPHAI (output) DOUBLE PRECISION array, dimension (2)
68 * BETA (output) DOUBLE PRECISION array, dimension (2)
69 * (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the
70 * pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may
71 * be zero.
72 *
73 * CSL (output) DOUBLE PRECISION
74 * The cosine of the left rotation matrix.
75 *
76 * SNL (output) DOUBLE PRECISION
77 * The sine of the left rotation matrix.
78 *
79 * CSR (output) DOUBLE PRECISION
80 * The cosine of the right rotation matrix.
81 *
82 * SNR (output) DOUBLE PRECISION
83 * The sine of the right rotation matrix.
84 *
85 * Further Details
86 * ===============
87 *
88 * Based on contributions by
89 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
90 *
91 * =====================================================================
92 *
93 * .. Parameters ..
94 DOUBLE PRECISION ZERO, ONE
95 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
96 * ..
97 * .. Local Scalars ..
98 DOUBLE PRECISION ANORM, ASCALE, BNORM, BSCALE, H1, H2, H3, QQ,
99 $ R, RR, SAFMIN, SCALE1, SCALE2, T, ULP, WI, WR1,
100 $ WR2
101 * ..
102 * .. External Subroutines ..
103 EXTERNAL DLAG2, DLARTG, DLASV2, DROT
104 * ..
105 * .. External Functions ..
106 DOUBLE PRECISION DLAMCH, DLAPY2
107 EXTERNAL DLAMCH, DLAPY2
108 * ..
109 * .. Intrinsic Functions ..
110 INTRINSIC ABS, MAX
111 * ..
112 * .. Executable Statements ..
113 *
114 SAFMIN = DLAMCH( 'S' )
115 ULP = DLAMCH( 'P' )
116 *
117 * Scale A
118 *
119 ANORM = MAX( ABS( A( 1, 1 ) )+ABS( A( 2, 1 ) ),
120 $ ABS( A( 1, 2 ) )+ABS( A( 2, 2 ) ), SAFMIN )
121 ASCALE = ONE / ANORM
122 A( 1, 1 ) = ASCALE*A( 1, 1 )
123 A( 1, 2 ) = ASCALE*A( 1, 2 )
124 A( 2, 1 ) = ASCALE*A( 2, 1 )
125 A( 2, 2 ) = ASCALE*A( 2, 2 )
126 *
127 * Scale B
128 *
129 BNORM = MAX( ABS( B( 1, 1 ) ), ABS( B( 1, 2 ) )+ABS( B( 2, 2 ) ),
130 $ SAFMIN )
131 BSCALE = ONE / BNORM
132 B( 1, 1 ) = BSCALE*B( 1, 1 )
133 B( 1, 2 ) = BSCALE*B( 1, 2 )
134 B( 2, 2 ) = BSCALE*B( 2, 2 )
135 *
136 * Check if A can be deflated
137 *
138 IF( ABS( A( 2, 1 ) ).LE.ULP ) THEN
139 CSL = ONE
140 SNL = ZERO
141 CSR = ONE
142 SNR = ZERO
143 A( 2, 1 ) = ZERO
144 B( 2, 1 ) = ZERO
145 WI = ZERO
146 *
147 * Check if B is singular
148 *
149 ELSE IF( ABS( B( 1, 1 ) ).LE.ULP ) THEN
150 CALL DLARTG( A( 1, 1 ), A( 2, 1 ), CSL, SNL, R )
151 CSR = ONE
152 SNR = ZERO
153 CALL DROT( 2, A( 1, 1 ), LDA, A( 2, 1 ), LDA, CSL, SNL )
154 CALL DROT( 2, B( 1, 1 ), LDB, B( 2, 1 ), LDB, CSL, SNL )
155 A( 2, 1 ) = ZERO
156 B( 1, 1 ) = ZERO
157 B( 2, 1 ) = ZERO
158 WI = ZERO
159 *
160 ELSE IF( ABS( B( 2, 2 ) ).LE.ULP ) THEN
161 CALL DLARTG( A( 2, 2 ), A( 2, 1 ), CSR, SNR, T )
162 SNR = -SNR
163 CALL DROT( 2, A( 1, 1 ), 1, A( 1, 2 ), 1, CSR, SNR )
164 CALL DROT( 2, B( 1, 1 ), 1, B( 1, 2 ), 1, CSR, SNR )
165 CSL = ONE
166 SNL = ZERO
167 A( 2, 1 ) = ZERO
168 B( 2, 1 ) = ZERO
169 B( 2, 2 ) = ZERO
170 WI = ZERO
171 *
172 ELSE
173 *
174 * B is nonsingular, first compute the eigenvalues of (A,B)
175 *
176 CALL DLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2,
177 $ WI )
178 *
179 IF( WI.EQ.ZERO ) THEN
180 *
181 * two real eigenvalues, compute s*A-w*B
182 *
183 H1 = SCALE1*A( 1, 1 ) - WR1*B( 1, 1 )
184 H2 = SCALE1*A( 1, 2 ) - WR1*B( 1, 2 )
185 H3 = SCALE1*A( 2, 2 ) - WR1*B( 2, 2 )
186 *
187 RR = DLAPY2( H1, H2 )
188 QQ = DLAPY2( SCALE1*A( 2, 1 ), H3 )
189 *
190 IF( RR.GT.QQ ) THEN
191 *
192 * find right rotation matrix to zero 1,1 element of
193 * (sA - wB)
194 *
195 CALL DLARTG( H2, H1, CSR, SNR, T )
196 *
197 ELSE
198 *
199 * find right rotation matrix to zero 2,1 element of
200 * (sA - wB)
201 *
202 CALL DLARTG( H3, SCALE1*A( 2, 1 ), CSR, SNR, T )
203 *
204 END IF
205 *
206 SNR = -SNR
207 CALL DROT( 2, A( 1, 1 ), 1, A( 1, 2 ), 1, CSR, SNR )
208 CALL DROT( 2, B( 1, 1 ), 1, B( 1, 2 ), 1, CSR, SNR )
209 *
210 * compute inf norms of A and B
211 *
212 H1 = MAX( ABS( A( 1, 1 ) )+ABS( A( 1, 2 ) ),
213 $ ABS( A( 2, 1 ) )+ABS( A( 2, 2 ) ) )
214 H2 = MAX( ABS( B( 1, 1 ) )+ABS( B( 1, 2 ) ),
215 $ ABS( B( 2, 1 ) )+ABS( B( 2, 2 ) ) )
216 *
217 IF( ( SCALE1*H1 ).GE.ABS( WR1 )*H2 ) THEN
218 *
219 * find left rotation matrix Q to zero out B(2,1)
220 *
221 CALL DLARTG( B( 1, 1 ), B( 2, 1 ), CSL, SNL, R )
222 *
223 ELSE
224 *
225 * find left rotation matrix Q to zero out A(2,1)
226 *
227 CALL DLARTG( A( 1, 1 ), A( 2, 1 ), CSL, SNL, R )
228 *
229 END IF
230 *
231 CALL DROT( 2, A( 1, 1 ), LDA, A( 2, 1 ), LDA, CSL, SNL )
232 CALL DROT( 2, B( 1, 1 ), LDB, B( 2, 1 ), LDB, CSL, SNL )
233 *
234 A( 2, 1 ) = ZERO
235 B( 2, 1 ) = ZERO
236 *
237 ELSE
238 *
239 * a pair of complex conjugate eigenvalues
240 * first compute the SVD of the matrix B
241 *
242 CALL DLASV2( B( 1, 1 ), B( 1, 2 ), B( 2, 2 ), R, T, SNR,
243 $ CSR, SNL, CSL )
244 *
245 * Form (A,B) := Q(A,B)Z**T where Q is left rotation matrix and
246 * Z is right rotation matrix computed from DLASV2
247 *
248 CALL DROT( 2, A( 1, 1 ), LDA, A( 2, 1 ), LDA, CSL, SNL )
249 CALL DROT( 2, B( 1, 1 ), LDB, B( 2, 1 ), LDB, CSL, SNL )
250 CALL DROT( 2, A( 1, 1 ), 1, A( 1, 2 ), 1, CSR, SNR )
251 CALL DROT( 2, B( 1, 1 ), 1, B( 1, 2 ), 1, CSR, SNR )
252 *
253 B( 2, 1 ) = ZERO
254 B( 1, 2 ) = ZERO
255 *
256 END IF
257 *
258 END IF
259 *
260 * Unscaling
261 *
262 A( 1, 1 ) = ANORM*A( 1, 1 )
263 A( 2, 1 ) = ANORM*A( 2, 1 )
264 A( 1, 2 ) = ANORM*A( 1, 2 )
265 A( 2, 2 ) = ANORM*A( 2, 2 )
266 B( 1, 1 ) = BNORM*B( 1, 1 )
267 B( 2, 1 ) = BNORM*B( 2, 1 )
268 B( 1, 2 ) = BNORM*B( 1, 2 )
269 B( 2, 2 ) = BNORM*B( 2, 2 )
270 *
271 IF( WI.EQ.ZERO ) THEN
272 ALPHAR( 1 ) = A( 1, 1 )
273 ALPHAR( 2 ) = A( 2, 2 )
274 ALPHAI( 1 ) = ZERO
275 ALPHAI( 2 ) = ZERO
276 BETA( 1 ) = B( 1, 1 )
277 BETA( 2 ) = B( 2, 2 )
278 ELSE
279 ALPHAR( 1 ) = ANORM*WR1 / SCALE1 / BNORM
280 ALPHAI( 1 ) = ANORM*WI / SCALE1 / BNORM
281 ALPHAR( 2 ) = ALPHAR( 1 )
282 ALPHAI( 2 ) = -ALPHAI( 1 )
283 BETA( 1 ) = ONE
284 BETA( 2 ) = ONE
285 END IF
286 *
287 RETURN
288 *
289 * End of DLAGV2
290 *
291 END
2 $ CSR, SNR )
3 *
4 * -- LAPACK auxiliary routine (version 3.2.2) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * June 2010
8 *
9 * .. Scalar Arguments ..
10 INTEGER LDA, LDB
11 DOUBLE PRECISION CSL, CSR, SNL, SNR
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION A( LDA, * ), ALPHAI( 2 ), ALPHAR( 2 ),
15 $ B( LDB, * ), BETA( 2 )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * DLAGV2 computes the Generalized Schur factorization of a real 2-by-2
22 * matrix pencil (A,B) where B is upper triangular. This routine
23 * computes orthogonal (rotation) matrices given by CSL, SNL and CSR,
24 * SNR such that
25 *
26 * 1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0
27 * types), then
28 *
29 * [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]
30 * [ 0 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]
31 *
32 * [ b11 b12 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]
33 * [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ],
34 *
35 * 2) if the pencil (A,B) has a pair of complex conjugate eigenvalues,
36 * then
37 *
38 * [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]
39 * [ a21 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]
40 *
41 * [ b11 0 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]
42 * [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ]
43 *
44 * where b11 >= b22 > 0.
45 *
46 *
47 * Arguments
48 * =========
49 *
50 * A (input/output) DOUBLE PRECISION array, dimension (LDA, 2)
51 * On entry, the 2 x 2 matrix A.
52 * On exit, A is overwritten by the ``A-part'' of the
53 * generalized Schur form.
54 *
55 * LDA (input) INTEGER
56 * THe leading dimension of the array A. LDA >= 2.
57 *
58 * B (input/output) DOUBLE PRECISION array, dimension (LDB, 2)
59 * On entry, the upper triangular 2 x 2 matrix B.
60 * On exit, B is overwritten by the ``B-part'' of the
61 * generalized Schur form.
62 *
63 * LDB (input) INTEGER
64 * THe leading dimension of the array B. LDB >= 2.
65 *
66 * ALPHAR (output) DOUBLE PRECISION array, dimension (2)
67 * ALPHAI (output) DOUBLE PRECISION array, dimension (2)
68 * BETA (output) DOUBLE PRECISION array, dimension (2)
69 * (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the
70 * pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may
71 * be zero.
72 *
73 * CSL (output) DOUBLE PRECISION
74 * The cosine of the left rotation matrix.
75 *
76 * SNL (output) DOUBLE PRECISION
77 * The sine of the left rotation matrix.
78 *
79 * CSR (output) DOUBLE PRECISION
80 * The cosine of the right rotation matrix.
81 *
82 * SNR (output) DOUBLE PRECISION
83 * The sine of the right rotation matrix.
84 *
85 * Further Details
86 * ===============
87 *
88 * Based on contributions by
89 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
90 *
91 * =====================================================================
92 *
93 * .. Parameters ..
94 DOUBLE PRECISION ZERO, ONE
95 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
96 * ..
97 * .. Local Scalars ..
98 DOUBLE PRECISION ANORM, ASCALE, BNORM, BSCALE, H1, H2, H3, QQ,
99 $ R, RR, SAFMIN, SCALE1, SCALE2, T, ULP, WI, WR1,
100 $ WR2
101 * ..
102 * .. External Subroutines ..
103 EXTERNAL DLAG2, DLARTG, DLASV2, DROT
104 * ..
105 * .. External Functions ..
106 DOUBLE PRECISION DLAMCH, DLAPY2
107 EXTERNAL DLAMCH, DLAPY2
108 * ..
109 * .. Intrinsic Functions ..
110 INTRINSIC ABS, MAX
111 * ..
112 * .. Executable Statements ..
113 *
114 SAFMIN = DLAMCH( 'S' )
115 ULP = DLAMCH( 'P' )
116 *
117 * Scale A
118 *
119 ANORM = MAX( ABS( A( 1, 1 ) )+ABS( A( 2, 1 ) ),
120 $ ABS( A( 1, 2 ) )+ABS( A( 2, 2 ) ), SAFMIN )
121 ASCALE = ONE / ANORM
122 A( 1, 1 ) = ASCALE*A( 1, 1 )
123 A( 1, 2 ) = ASCALE*A( 1, 2 )
124 A( 2, 1 ) = ASCALE*A( 2, 1 )
125 A( 2, 2 ) = ASCALE*A( 2, 2 )
126 *
127 * Scale B
128 *
129 BNORM = MAX( ABS( B( 1, 1 ) ), ABS( B( 1, 2 ) )+ABS( B( 2, 2 ) ),
130 $ SAFMIN )
131 BSCALE = ONE / BNORM
132 B( 1, 1 ) = BSCALE*B( 1, 1 )
133 B( 1, 2 ) = BSCALE*B( 1, 2 )
134 B( 2, 2 ) = BSCALE*B( 2, 2 )
135 *
136 * Check if A can be deflated
137 *
138 IF( ABS( A( 2, 1 ) ).LE.ULP ) THEN
139 CSL = ONE
140 SNL = ZERO
141 CSR = ONE
142 SNR = ZERO
143 A( 2, 1 ) = ZERO
144 B( 2, 1 ) = ZERO
145 WI = ZERO
146 *
147 * Check if B is singular
148 *
149 ELSE IF( ABS( B( 1, 1 ) ).LE.ULP ) THEN
150 CALL DLARTG( A( 1, 1 ), A( 2, 1 ), CSL, SNL, R )
151 CSR = ONE
152 SNR = ZERO
153 CALL DROT( 2, A( 1, 1 ), LDA, A( 2, 1 ), LDA, CSL, SNL )
154 CALL DROT( 2, B( 1, 1 ), LDB, B( 2, 1 ), LDB, CSL, SNL )
155 A( 2, 1 ) = ZERO
156 B( 1, 1 ) = ZERO
157 B( 2, 1 ) = ZERO
158 WI = ZERO
159 *
160 ELSE IF( ABS( B( 2, 2 ) ).LE.ULP ) THEN
161 CALL DLARTG( A( 2, 2 ), A( 2, 1 ), CSR, SNR, T )
162 SNR = -SNR
163 CALL DROT( 2, A( 1, 1 ), 1, A( 1, 2 ), 1, CSR, SNR )
164 CALL DROT( 2, B( 1, 1 ), 1, B( 1, 2 ), 1, CSR, SNR )
165 CSL = ONE
166 SNL = ZERO
167 A( 2, 1 ) = ZERO
168 B( 2, 1 ) = ZERO
169 B( 2, 2 ) = ZERO
170 WI = ZERO
171 *
172 ELSE
173 *
174 * B is nonsingular, first compute the eigenvalues of (A,B)
175 *
176 CALL DLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2,
177 $ WI )
178 *
179 IF( WI.EQ.ZERO ) THEN
180 *
181 * two real eigenvalues, compute s*A-w*B
182 *
183 H1 = SCALE1*A( 1, 1 ) - WR1*B( 1, 1 )
184 H2 = SCALE1*A( 1, 2 ) - WR1*B( 1, 2 )
185 H3 = SCALE1*A( 2, 2 ) - WR1*B( 2, 2 )
186 *
187 RR = DLAPY2( H1, H2 )
188 QQ = DLAPY2( SCALE1*A( 2, 1 ), H3 )
189 *
190 IF( RR.GT.QQ ) THEN
191 *
192 * find right rotation matrix to zero 1,1 element of
193 * (sA - wB)
194 *
195 CALL DLARTG( H2, H1, CSR, SNR, T )
196 *
197 ELSE
198 *
199 * find right rotation matrix to zero 2,1 element of
200 * (sA - wB)
201 *
202 CALL DLARTG( H3, SCALE1*A( 2, 1 ), CSR, SNR, T )
203 *
204 END IF
205 *
206 SNR = -SNR
207 CALL DROT( 2, A( 1, 1 ), 1, A( 1, 2 ), 1, CSR, SNR )
208 CALL DROT( 2, B( 1, 1 ), 1, B( 1, 2 ), 1, CSR, SNR )
209 *
210 * compute inf norms of A and B
211 *
212 H1 = MAX( ABS( A( 1, 1 ) )+ABS( A( 1, 2 ) ),
213 $ ABS( A( 2, 1 ) )+ABS( A( 2, 2 ) ) )
214 H2 = MAX( ABS( B( 1, 1 ) )+ABS( B( 1, 2 ) ),
215 $ ABS( B( 2, 1 ) )+ABS( B( 2, 2 ) ) )
216 *
217 IF( ( SCALE1*H1 ).GE.ABS( WR1 )*H2 ) THEN
218 *
219 * find left rotation matrix Q to zero out B(2,1)
220 *
221 CALL DLARTG( B( 1, 1 ), B( 2, 1 ), CSL, SNL, R )
222 *
223 ELSE
224 *
225 * find left rotation matrix Q to zero out A(2,1)
226 *
227 CALL DLARTG( A( 1, 1 ), A( 2, 1 ), CSL, SNL, R )
228 *
229 END IF
230 *
231 CALL DROT( 2, A( 1, 1 ), LDA, A( 2, 1 ), LDA, CSL, SNL )
232 CALL DROT( 2, B( 1, 1 ), LDB, B( 2, 1 ), LDB, CSL, SNL )
233 *
234 A( 2, 1 ) = ZERO
235 B( 2, 1 ) = ZERO
236 *
237 ELSE
238 *
239 * a pair of complex conjugate eigenvalues
240 * first compute the SVD of the matrix B
241 *
242 CALL DLASV2( B( 1, 1 ), B( 1, 2 ), B( 2, 2 ), R, T, SNR,
243 $ CSR, SNL, CSL )
244 *
245 * Form (A,B) := Q(A,B)Z**T where Q is left rotation matrix and
246 * Z is right rotation matrix computed from DLASV2
247 *
248 CALL DROT( 2, A( 1, 1 ), LDA, A( 2, 1 ), LDA, CSL, SNL )
249 CALL DROT( 2, B( 1, 1 ), LDB, B( 2, 1 ), LDB, CSL, SNL )
250 CALL DROT( 2, A( 1, 1 ), 1, A( 1, 2 ), 1, CSR, SNR )
251 CALL DROT( 2, B( 1, 1 ), 1, B( 1, 2 ), 1, CSR, SNR )
252 *
253 B( 2, 1 ) = ZERO
254 B( 1, 2 ) = ZERO
255 *
256 END IF
257 *
258 END IF
259 *
260 * Unscaling
261 *
262 A( 1, 1 ) = ANORM*A( 1, 1 )
263 A( 2, 1 ) = ANORM*A( 2, 1 )
264 A( 1, 2 ) = ANORM*A( 1, 2 )
265 A( 2, 2 ) = ANORM*A( 2, 2 )
266 B( 1, 1 ) = BNORM*B( 1, 1 )
267 B( 2, 1 ) = BNORM*B( 2, 1 )
268 B( 1, 2 ) = BNORM*B( 1, 2 )
269 B( 2, 2 ) = BNORM*B( 2, 2 )
270 *
271 IF( WI.EQ.ZERO ) THEN
272 ALPHAR( 1 ) = A( 1, 1 )
273 ALPHAR( 2 ) = A( 2, 2 )
274 ALPHAI( 1 ) = ZERO
275 ALPHAI( 2 ) = ZERO
276 BETA( 1 ) = B( 1, 1 )
277 BETA( 2 ) = B( 2, 2 )
278 ELSE
279 ALPHAR( 1 ) = ANORM*WR1 / SCALE1 / BNORM
280 ALPHAI( 1 ) = ANORM*WI / SCALE1 / BNORM
281 ALPHAR( 2 ) = ALPHAR( 1 )
282 ALPHAI( 2 ) = -ALPHAI( 1 )
283 BETA( 1 ) = ONE
284 BETA( 2 ) = ONE
285 END IF
286 *
287 RETURN
288 *
289 * End of DLAGV2
290 *
291 END