1 SUBROUTINE ZTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
2 $ LDC, SCALE, INFO )
3 *
4 * -- LAPACK routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * .. Scalar Arguments ..
10 CHARACTER TRANA, TRANB
11 INTEGER INFO, ISGN, LDA, LDB, LDC, M, N
12 DOUBLE PRECISION SCALE
13 * ..
14 * .. Array Arguments ..
15 COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * ZTRSYL solves the complex Sylvester matrix equation:
22 *
23 * op(A)*X + X*op(B) = scale*C or
24 * op(A)*X - X*op(B) = scale*C,
25 *
26 * where op(A) = A or A**H, and A and B are both upper triangular. A is
27 * M-by-M and B is N-by-N; the right hand side C and the solution X are
28 * M-by-N; and scale is an output scale factor, set <= 1 to avoid
29 * overflow in X.
30 *
31 * Arguments
32 * =========
33 *
34 * TRANA (input) CHARACTER*1
35 * Specifies the option op(A):
36 * = 'N': op(A) = A (No transpose)
37 * = 'C': op(A) = A**H (Conjugate transpose)
38 *
39 * TRANB (input) CHARACTER*1
40 * Specifies the option op(B):
41 * = 'N': op(B) = B (No transpose)
42 * = 'C': op(B) = B**H (Conjugate transpose)
43 *
44 * ISGN (input) INTEGER
45 * Specifies the sign in the equation:
46 * = +1: solve op(A)*X + X*op(B) = scale*C
47 * = -1: solve op(A)*X - X*op(B) = scale*C
48 *
49 * M (input) INTEGER
50 * The order of the matrix A, and the number of rows in the
51 * matrices X and C. M >= 0.
52 *
53 * N (input) INTEGER
54 * The order of the matrix B, and the number of columns in the
55 * matrices X and C. N >= 0.
56 *
57 * A (input) COMPLEX*16 array, dimension (LDA,M)
58 * The upper triangular matrix A.
59 *
60 * LDA (input) INTEGER
61 * The leading dimension of the array A. LDA >= max(1,M).
62 *
63 * B (input) COMPLEX*16 array, dimension (LDB,N)
64 * The upper triangular matrix B.
65 *
66 * LDB (input) INTEGER
67 * The leading dimension of the array B. LDB >= max(1,N).
68 *
69 * C (input/output) COMPLEX*16 array, dimension (LDC,N)
70 * On entry, the M-by-N right hand side matrix C.
71 * On exit, C is overwritten by the solution matrix X.
72 *
73 * LDC (input) INTEGER
74 * The leading dimension of the array C. LDC >= max(1,M)
75 *
76 * SCALE (output) DOUBLE PRECISION
77 * The scale factor, scale, set <= 1 to avoid overflow in X.
78 *
79 * INFO (output) INTEGER
80 * = 0: successful exit
81 * < 0: if INFO = -i, the i-th argument had an illegal value
82 * = 1: A and B have common or very close eigenvalues; perturbed
83 * values were used to solve the equation (but the matrices
84 * A and B are unchanged).
85 *
86 * =====================================================================
87 *
88 * .. Parameters ..
89 DOUBLE PRECISION ONE
90 PARAMETER ( ONE = 1.0D+0 )
91 * ..
92 * .. Local Scalars ..
93 LOGICAL NOTRNA, NOTRNB
94 INTEGER J, K, L
95 DOUBLE PRECISION BIGNUM, DA11, DB, EPS, SCALOC, SGN, SMIN,
96 $ SMLNUM
97 COMPLEX*16 A11, SUML, SUMR, VEC, X11
98 * ..
99 * .. Local Arrays ..
100 DOUBLE PRECISION DUM( 1 )
101 * ..
102 * .. External Functions ..
103 LOGICAL LSAME
104 DOUBLE PRECISION DLAMCH, ZLANGE
105 COMPLEX*16 ZDOTC, ZDOTU, ZLADIV
106 EXTERNAL LSAME, DLAMCH, ZLANGE, ZDOTC, ZDOTU, ZLADIV
107 * ..
108 * .. External Subroutines ..
109 EXTERNAL DLABAD, XERBLA, ZDSCAL
110 * ..
111 * .. Intrinsic Functions ..
112 INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, MAX, MIN
113 * ..
114 * .. Executable Statements ..
115 *
116 * Decode and Test input parameters
117 *
118 NOTRNA = LSAME( TRANA, 'N' )
119 NOTRNB = LSAME( TRANB, 'N' )
120 *
121 INFO = 0
122 IF( .NOT.NOTRNA .AND. .NOT.LSAME( TRANA, 'C' ) ) THEN
123 INFO = -1
124 ELSE IF( .NOT.NOTRNB .AND. .NOT.LSAME( TRANB, 'C' ) ) THEN
125 INFO = -2
126 ELSE IF( ISGN.NE.1 .AND. ISGN.NE.-1 ) THEN
127 INFO = -3
128 ELSE IF( M.LT.0 ) THEN
129 INFO = -4
130 ELSE IF( N.LT.0 ) THEN
131 INFO = -5
132 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
133 INFO = -7
134 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
135 INFO = -9
136 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
137 INFO = -11
138 END IF
139 IF( INFO.NE.0 ) THEN
140 CALL XERBLA( 'ZTRSYL', -INFO )
141 RETURN
142 END IF
143 *
144 * Quick return if possible
145 *
146 SCALE = ONE
147 IF( M.EQ.0 .OR. N.EQ.0 )
148 $ RETURN
149 *
150 * Set constants to control overflow
151 *
152 EPS = DLAMCH( 'P' )
153 SMLNUM = DLAMCH( 'S' )
154 BIGNUM = ONE / SMLNUM
155 CALL DLABAD( SMLNUM, BIGNUM )
156 SMLNUM = SMLNUM*DBLE( M*N ) / EPS
157 BIGNUM = ONE / SMLNUM
158 SMIN = MAX( SMLNUM, EPS*ZLANGE( 'M', M, M, A, LDA, DUM ),
159 $ EPS*ZLANGE( 'M', N, N, B, LDB, DUM ) )
160 SGN = ISGN
161 *
162 IF( NOTRNA .AND. NOTRNB ) THEN
163 *
164 * Solve A*X + ISGN*X*B = scale*C.
165 *
166 * The (K,L)th block of X is determined starting from
167 * bottom-left corner column by column by
168 *
169 * A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
170 *
171 * Where
172 * M L-1
173 * R(K,L) = SUM [A(K,I)*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)].
174 * I=K+1 J=1
175 *
176 DO 30 L = 1, N
177 DO 20 K = M, 1, -1
178 *
179 SUML = ZDOTU( M-K, A( K, MIN( K+1, M ) ), LDA,
180 $ C( MIN( K+1, M ), L ), 1 )
181 SUMR = ZDOTU( L-1, C( K, 1 ), LDC, B( 1, L ), 1 )
182 VEC = C( K, L ) - ( SUML+SGN*SUMR )
183 *
184 SCALOC = ONE
185 A11 = A( K, K ) + SGN*B( L, L )
186 DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) )
187 IF( DA11.LE.SMIN ) THEN
188 A11 = SMIN
189 DA11 = SMIN
190 INFO = 1
191 END IF
192 DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) )
193 IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
194 IF( DB.GT.BIGNUM*DA11 )
195 $ SCALOC = ONE / DB
196 END IF
197 X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 )
198 *
199 IF( SCALOC.NE.ONE ) THEN
200 DO 10 J = 1, N
201 CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 )
202 10 CONTINUE
203 SCALE = SCALE*SCALOC
204 END IF
205 C( K, L ) = X11
206 *
207 20 CONTINUE
208 30 CONTINUE
209 *
210 ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN
211 *
212 * Solve A**H *X + ISGN*X*B = scale*C.
213 *
214 * The (K,L)th block of X is determined starting from
215 * upper-left corner column by column by
216 *
217 * A**H(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
218 *
219 * Where
220 * K-1 L-1
221 * R(K,L) = SUM [A**H(I,K)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]
222 * I=1 J=1
223 *
224 DO 60 L = 1, N
225 DO 50 K = 1, M
226 *
227 SUML = ZDOTC( K-1, A( 1, K ), 1, C( 1, L ), 1 )
228 SUMR = ZDOTU( L-1, C( K, 1 ), LDC, B( 1, L ), 1 )
229 VEC = C( K, L ) - ( SUML+SGN*SUMR )
230 *
231 SCALOC = ONE
232 A11 = DCONJG( A( K, K ) ) + SGN*B( L, L )
233 DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) )
234 IF( DA11.LE.SMIN ) THEN
235 A11 = SMIN
236 DA11 = SMIN
237 INFO = 1
238 END IF
239 DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) )
240 IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
241 IF( DB.GT.BIGNUM*DA11 )
242 $ SCALOC = ONE / DB
243 END IF
244 *
245 X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 )
246 *
247 IF( SCALOC.NE.ONE ) THEN
248 DO 40 J = 1, N
249 CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 )
250 40 CONTINUE
251 SCALE = SCALE*SCALOC
252 END IF
253 C( K, L ) = X11
254 *
255 50 CONTINUE
256 60 CONTINUE
257 *
258 ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN
259 *
260 * Solve A**H*X + ISGN*X*B**H = C.
261 *
262 * The (K,L)th block of X is determined starting from
263 * upper-right corner column by column by
264 *
265 * A**H(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L)
266 *
267 * Where
268 * K-1
269 * R(K,L) = SUM [A**H(I,K)*X(I,L)] +
270 * I=1
271 * N
272 * ISGN*SUM [X(K,J)*B**H(L,J)].
273 * J=L+1
274 *
275 DO 90 L = N, 1, -1
276 DO 80 K = 1, M
277 *
278 SUML = ZDOTC( K-1, A( 1, K ), 1, C( 1, L ), 1 )
279 SUMR = ZDOTC( N-L, C( K, MIN( L+1, N ) ), LDC,
280 $ B( L, MIN( L+1, N ) ), LDB )
281 VEC = C( K, L ) - ( SUML+SGN*DCONJG( SUMR ) )
282 *
283 SCALOC = ONE
284 A11 = DCONJG( A( K, K )+SGN*B( L, L ) )
285 DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) )
286 IF( DA11.LE.SMIN ) THEN
287 A11 = SMIN
288 DA11 = SMIN
289 INFO = 1
290 END IF
291 DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) )
292 IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
293 IF( DB.GT.BIGNUM*DA11 )
294 $ SCALOC = ONE / DB
295 END IF
296 *
297 X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 )
298 *
299 IF( SCALOC.NE.ONE ) THEN
300 DO 70 J = 1, N
301 CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 )
302 70 CONTINUE
303 SCALE = SCALE*SCALOC
304 END IF
305 C( K, L ) = X11
306 *
307 80 CONTINUE
308 90 CONTINUE
309 *
310 ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN
311 *
312 * Solve A*X + ISGN*X*B**H = C.
313 *
314 * The (K,L)th block of X is determined starting from
315 * bottom-left corner column by column by
316 *
317 * A(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L)
318 *
319 * Where
320 * M N
321 * R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B**H(L,J)]
322 * I=K+1 J=L+1
323 *
324 DO 120 L = N, 1, -1
325 DO 110 K = M, 1, -1
326 *
327 SUML = ZDOTU( M-K, A( K, MIN( K+1, M ) ), LDA,
328 $ C( MIN( K+1, M ), L ), 1 )
329 SUMR = ZDOTC( N-L, C( K, MIN( L+1, N ) ), LDC,
330 $ B( L, MIN( L+1, N ) ), LDB )
331 VEC = C( K, L ) - ( SUML+SGN*DCONJG( SUMR ) )
332 *
333 SCALOC = ONE
334 A11 = A( K, K ) + SGN*DCONJG( B( L, L ) )
335 DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) )
336 IF( DA11.LE.SMIN ) THEN
337 A11 = SMIN
338 DA11 = SMIN
339 INFO = 1
340 END IF
341 DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) )
342 IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
343 IF( DB.GT.BIGNUM*DA11 )
344 $ SCALOC = ONE / DB
345 END IF
346 *
347 X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 )
348 *
349 IF( SCALOC.NE.ONE ) THEN
350 DO 100 J = 1, N
351 CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 )
352 100 CONTINUE
353 SCALE = SCALE*SCALOC
354 END IF
355 C( K, L ) = X11
356 *
357 110 CONTINUE
358 120 CONTINUE
359 *
360 END IF
361 *
362 RETURN
363 *
364 * End of ZTRSYL
365 *
366 END
2 $ LDC, SCALE, INFO )
3 *
4 * -- LAPACK routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * .. Scalar Arguments ..
10 CHARACTER TRANA, TRANB
11 INTEGER INFO, ISGN, LDA, LDB, LDC, M, N
12 DOUBLE PRECISION SCALE
13 * ..
14 * .. Array Arguments ..
15 COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * ZTRSYL solves the complex Sylvester matrix equation:
22 *
23 * op(A)*X + X*op(B) = scale*C or
24 * op(A)*X - X*op(B) = scale*C,
25 *
26 * where op(A) = A or A**H, and A and B are both upper triangular. A is
27 * M-by-M and B is N-by-N; the right hand side C and the solution X are
28 * M-by-N; and scale is an output scale factor, set <= 1 to avoid
29 * overflow in X.
30 *
31 * Arguments
32 * =========
33 *
34 * TRANA (input) CHARACTER*1
35 * Specifies the option op(A):
36 * = 'N': op(A) = A (No transpose)
37 * = 'C': op(A) = A**H (Conjugate transpose)
38 *
39 * TRANB (input) CHARACTER*1
40 * Specifies the option op(B):
41 * = 'N': op(B) = B (No transpose)
42 * = 'C': op(B) = B**H (Conjugate transpose)
43 *
44 * ISGN (input) INTEGER
45 * Specifies the sign in the equation:
46 * = +1: solve op(A)*X + X*op(B) = scale*C
47 * = -1: solve op(A)*X - X*op(B) = scale*C
48 *
49 * M (input) INTEGER
50 * The order of the matrix A, and the number of rows in the
51 * matrices X and C. M >= 0.
52 *
53 * N (input) INTEGER
54 * The order of the matrix B, and the number of columns in the
55 * matrices X and C. N >= 0.
56 *
57 * A (input) COMPLEX*16 array, dimension (LDA,M)
58 * The upper triangular matrix A.
59 *
60 * LDA (input) INTEGER
61 * The leading dimension of the array A. LDA >= max(1,M).
62 *
63 * B (input) COMPLEX*16 array, dimension (LDB,N)
64 * The upper triangular matrix B.
65 *
66 * LDB (input) INTEGER
67 * The leading dimension of the array B. LDB >= max(1,N).
68 *
69 * C (input/output) COMPLEX*16 array, dimension (LDC,N)
70 * On entry, the M-by-N right hand side matrix C.
71 * On exit, C is overwritten by the solution matrix X.
72 *
73 * LDC (input) INTEGER
74 * The leading dimension of the array C. LDC >= max(1,M)
75 *
76 * SCALE (output) DOUBLE PRECISION
77 * The scale factor, scale, set <= 1 to avoid overflow in X.
78 *
79 * INFO (output) INTEGER
80 * = 0: successful exit
81 * < 0: if INFO = -i, the i-th argument had an illegal value
82 * = 1: A and B have common or very close eigenvalues; perturbed
83 * values were used to solve the equation (but the matrices
84 * A and B are unchanged).
85 *
86 * =====================================================================
87 *
88 * .. Parameters ..
89 DOUBLE PRECISION ONE
90 PARAMETER ( ONE = 1.0D+0 )
91 * ..
92 * .. Local Scalars ..
93 LOGICAL NOTRNA, NOTRNB
94 INTEGER J, K, L
95 DOUBLE PRECISION BIGNUM, DA11, DB, EPS, SCALOC, SGN, SMIN,
96 $ SMLNUM
97 COMPLEX*16 A11, SUML, SUMR, VEC, X11
98 * ..
99 * .. Local Arrays ..
100 DOUBLE PRECISION DUM( 1 )
101 * ..
102 * .. External Functions ..
103 LOGICAL LSAME
104 DOUBLE PRECISION DLAMCH, ZLANGE
105 COMPLEX*16 ZDOTC, ZDOTU, ZLADIV
106 EXTERNAL LSAME, DLAMCH, ZLANGE, ZDOTC, ZDOTU, ZLADIV
107 * ..
108 * .. External Subroutines ..
109 EXTERNAL DLABAD, XERBLA, ZDSCAL
110 * ..
111 * .. Intrinsic Functions ..
112 INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, MAX, MIN
113 * ..
114 * .. Executable Statements ..
115 *
116 * Decode and Test input parameters
117 *
118 NOTRNA = LSAME( TRANA, 'N' )
119 NOTRNB = LSAME( TRANB, 'N' )
120 *
121 INFO = 0
122 IF( .NOT.NOTRNA .AND. .NOT.LSAME( TRANA, 'C' ) ) THEN
123 INFO = -1
124 ELSE IF( .NOT.NOTRNB .AND. .NOT.LSAME( TRANB, 'C' ) ) THEN
125 INFO = -2
126 ELSE IF( ISGN.NE.1 .AND. ISGN.NE.-1 ) THEN
127 INFO = -3
128 ELSE IF( M.LT.0 ) THEN
129 INFO = -4
130 ELSE IF( N.LT.0 ) THEN
131 INFO = -5
132 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
133 INFO = -7
134 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
135 INFO = -9
136 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
137 INFO = -11
138 END IF
139 IF( INFO.NE.0 ) THEN
140 CALL XERBLA( 'ZTRSYL', -INFO )
141 RETURN
142 END IF
143 *
144 * Quick return if possible
145 *
146 SCALE = ONE
147 IF( M.EQ.0 .OR. N.EQ.0 )
148 $ RETURN
149 *
150 * Set constants to control overflow
151 *
152 EPS = DLAMCH( 'P' )
153 SMLNUM = DLAMCH( 'S' )
154 BIGNUM = ONE / SMLNUM
155 CALL DLABAD( SMLNUM, BIGNUM )
156 SMLNUM = SMLNUM*DBLE( M*N ) / EPS
157 BIGNUM = ONE / SMLNUM
158 SMIN = MAX( SMLNUM, EPS*ZLANGE( 'M', M, M, A, LDA, DUM ),
159 $ EPS*ZLANGE( 'M', N, N, B, LDB, DUM ) )
160 SGN = ISGN
161 *
162 IF( NOTRNA .AND. NOTRNB ) THEN
163 *
164 * Solve A*X + ISGN*X*B = scale*C.
165 *
166 * The (K,L)th block of X is determined starting from
167 * bottom-left corner column by column by
168 *
169 * A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
170 *
171 * Where
172 * M L-1
173 * R(K,L) = SUM [A(K,I)*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)].
174 * I=K+1 J=1
175 *
176 DO 30 L = 1, N
177 DO 20 K = M, 1, -1
178 *
179 SUML = ZDOTU( M-K, A( K, MIN( K+1, M ) ), LDA,
180 $ C( MIN( K+1, M ), L ), 1 )
181 SUMR = ZDOTU( L-1, C( K, 1 ), LDC, B( 1, L ), 1 )
182 VEC = C( K, L ) - ( SUML+SGN*SUMR )
183 *
184 SCALOC = ONE
185 A11 = A( K, K ) + SGN*B( L, L )
186 DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) )
187 IF( DA11.LE.SMIN ) THEN
188 A11 = SMIN
189 DA11 = SMIN
190 INFO = 1
191 END IF
192 DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) )
193 IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
194 IF( DB.GT.BIGNUM*DA11 )
195 $ SCALOC = ONE / DB
196 END IF
197 X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 )
198 *
199 IF( SCALOC.NE.ONE ) THEN
200 DO 10 J = 1, N
201 CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 )
202 10 CONTINUE
203 SCALE = SCALE*SCALOC
204 END IF
205 C( K, L ) = X11
206 *
207 20 CONTINUE
208 30 CONTINUE
209 *
210 ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN
211 *
212 * Solve A**H *X + ISGN*X*B = scale*C.
213 *
214 * The (K,L)th block of X is determined starting from
215 * upper-left corner column by column by
216 *
217 * A**H(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
218 *
219 * Where
220 * K-1 L-1
221 * R(K,L) = SUM [A**H(I,K)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]
222 * I=1 J=1
223 *
224 DO 60 L = 1, N
225 DO 50 K = 1, M
226 *
227 SUML = ZDOTC( K-1, A( 1, K ), 1, C( 1, L ), 1 )
228 SUMR = ZDOTU( L-1, C( K, 1 ), LDC, B( 1, L ), 1 )
229 VEC = C( K, L ) - ( SUML+SGN*SUMR )
230 *
231 SCALOC = ONE
232 A11 = DCONJG( A( K, K ) ) + SGN*B( L, L )
233 DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) )
234 IF( DA11.LE.SMIN ) THEN
235 A11 = SMIN
236 DA11 = SMIN
237 INFO = 1
238 END IF
239 DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) )
240 IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
241 IF( DB.GT.BIGNUM*DA11 )
242 $ SCALOC = ONE / DB
243 END IF
244 *
245 X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 )
246 *
247 IF( SCALOC.NE.ONE ) THEN
248 DO 40 J = 1, N
249 CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 )
250 40 CONTINUE
251 SCALE = SCALE*SCALOC
252 END IF
253 C( K, L ) = X11
254 *
255 50 CONTINUE
256 60 CONTINUE
257 *
258 ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN
259 *
260 * Solve A**H*X + ISGN*X*B**H = C.
261 *
262 * The (K,L)th block of X is determined starting from
263 * upper-right corner column by column by
264 *
265 * A**H(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L)
266 *
267 * Where
268 * K-1
269 * R(K,L) = SUM [A**H(I,K)*X(I,L)] +
270 * I=1
271 * N
272 * ISGN*SUM [X(K,J)*B**H(L,J)].
273 * J=L+1
274 *
275 DO 90 L = N, 1, -1
276 DO 80 K = 1, M
277 *
278 SUML = ZDOTC( K-1, A( 1, K ), 1, C( 1, L ), 1 )
279 SUMR = ZDOTC( N-L, C( K, MIN( L+1, N ) ), LDC,
280 $ B( L, MIN( L+1, N ) ), LDB )
281 VEC = C( K, L ) - ( SUML+SGN*DCONJG( SUMR ) )
282 *
283 SCALOC = ONE
284 A11 = DCONJG( A( K, K )+SGN*B( L, L ) )
285 DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) )
286 IF( DA11.LE.SMIN ) THEN
287 A11 = SMIN
288 DA11 = SMIN
289 INFO = 1
290 END IF
291 DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) )
292 IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
293 IF( DB.GT.BIGNUM*DA11 )
294 $ SCALOC = ONE / DB
295 END IF
296 *
297 X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 )
298 *
299 IF( SCALOC.NE.ONE ) THEN
300 DO 70 J = 1, N
301 CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 )
302 70 CONTINUE
303 SCALE = SCALE*SCALOC
304 END IF
305 C( K, L ) = X11
306 *
307 80 CONTINUE
308 90 CONTINUE
309 *
310 ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN
311 *
312 * Solve A*X + ISGN*X*B**H = C.
313 *
314 * The (K,L)th block of X is determined starting from
315 * bottom-left corner column by column by
316 *
317 * A(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L)
318 *
319 * Where
320 * M N
321 * R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B**H(L,J)]
322 * I=K+1 J=L+1
323 *
324 DO 120 L = N, 1, -1
325 DO 110 K = M, 1, -1
326 *
327 SUML = ZDOTU( M-K, A( K, MIN( K+1, M ) ), LDA,
328 $ C( MIN( K+1, M ), L ), 1 )
329 SUMR = ZDOTC( N-L, C( K, MIN( L+1, N ) ), LDC,
330 $ B( L, MIN( L+1, N ) ), LDB )
331 VEC = C( K, L ) - ( SUML+SGN*DCONJG( SUMR ) )
332 *
333 SCALOC = ONE
334 A11 = A( K, K ) + SGN*DCONJG( B( L, L ) )
335 DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) )
336 IF( DA11.LE.SMIN ) THEN
337 A11 = SMIN
338 DA11 = SMIN
339 INFO = 1
340 END IF
341 DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) )
342 IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
343 IF( DB.GT.BIGNUM*DA11 )
344 $ SCALOC = ONE / DB
345 END IF
346 *
347 X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 )
348 *
349 IF( SCALOC.NE.ONE ) THEN
350 DO 100 J = 1, N
351 CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 )
352 100 CONTINUE
353 SCALE = SCALE*SCALOC
354 END IF
355 C( K, L ) = X11
356 *
357 110 CONTINUE
358 120 CONTINUE
359 *
360 END IF
361 *
362 RETURN
363 *
364 * End of ZTRSYL
365 *
366 END