1 /* -- translated by f2c (version 20100827).
2 You must link the resulting object file with libf2c:
3 on Microsoft Windows system, link with libf2c.lib;
4 on Linux or Unix systems, link with .../path/to/libf2c.a -lm
5 or, if you install libf2c.a in a standard place, with -lf2c -lm
6 -- in that order, at the end of the command line, as in
7 cc *.o -lf2c -lm
8 Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
9
10 http://www.netlib.org/f2c/libf2c.zip
11 */
12
13 #include "../config.h"
14 #include "f2c.h"
15
16 #if BLAS_COMPLEX_FUNCTIONS_AS_ROUTINES
cdotu_fun(int * n,complex * x,blasint * incx,complex * y,blasint * incy)17 complex cdotu_fun(int *n, complex *x, blasint *incx, complex *y, blasint *incy) {
18 extern void cdotu_(complex *, blasint *, complex *, blasint *, complex *, blasint *);
19 complex result;
20 cdotu_(&result, n, x, incx, y, incy);
21 return result;
22 }
23 #define cdotu_ cdotu_fun
24
cdotc_fun(int * n,complex * x,blasint * incx,complex * y,blasint * incy)25 complex cdotc_fun(int *n, complex *x, blasint *incx, complex *y, blasint *incy) {
26 extern void cdotc_(complex *, blasint *, complex *, blasint *, complex *, blasint *);
27 complex result;
28 cdotc_(&result, n, x, incx, y, incy);
29 return result;
30 }
31 #define cdotc_ cdotc_fun
32 #endif
33
34 #if LAPACK_BLAS_COMPLEX_FUNCTIONS_AS_ROUTINES
cladiv_fun(complex * a,complex * b)35 complex cladiv_fun(complex *a, complex *b) {
36 extern void cladiv_(complex *, complex *, complex *);
37 complex result;
38 cladiv_(&result, a, b);
39 return result;
40 }
41 #define cladiv_ cladiv_fun
42 #endif
43
44 /* Table of constant values */
45
46 static blasint c__1 = 1;
47
48 /** RELAPACK_CTRSYL_REC2 solves the complex Sylvester matrix equation (unblocked algorithm)
49 *
50 * This routine is an exact copy of LAPACK's ctrsyl.
51 * It serves as an unblocked kernel in the recursive algorithms.
52 * */
RELAPACK_ctrsyl_rec2(char * trana,char * tranb,int * isgn,blasint * m,blasint * n,complex * a,blasint * lda,complex * b,int * ldb,complex * c__,blasint * ldc,float * scale,blasint * info,ftnlen trana_len,ftnlen tranb_len)53 /* Subroutine */ void RELAPACK_ctrsyl_rec2(char *trana, char *tranb, int
54 *isgn, blasint *m, blasint *n, complex *a, blasint *lda, complex *b,
55 int *ldb, complex *c__, blasint *ldc, float *scale, blasint *info,
56 ftnlen trana_len, ftnlen tranb_len)
57 {
58 /* System generated locals */
59 blasint a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
60 i__3, i__4;
61 float r__1, r__2;
62 complex q__1, q__2, q__3, q__4;
63
64 /* Builtin functions */
65 float r_imag(complex *);
66 void r_cnjg(complex *, complex *);
67
68 /* Local variables */
69 static blasint j, k, l;
70 static complex a11;
71 static float db;
72 static complex x11;
73 static float da11;
74 static complex vec;
75 static float dum[1], eps, sgn, smin;
76 static complex suml, sumr;
77 /* Complex */ complex cdotc_(int *, complex *, int
78 *, complex *, blasint *);
79 extern blasint lsame_(char *, char *, ftnlen, ftnlen);
80 /* Complex */ complex cdotu_(int *, complex *, int
81 *, complex *, blasint *);
82 extern /* Subroutine */ blasint slabad_(float *, float *);
83 extern float clange_(char *, blasint *, blasint *, complex *,
84 blasint *, float *, ftnlen);
85 /* Complex */ complex cladiv_(complex *, complex *);
86 static float scaloc;
87 extern float slamch_(char *, ftnlen);
88 extern /* Subroutine */ blasint csscal_(int *, float *, complex *, int
89 *), xerbla_(char *, blasint *, ftnlen);
90 static float bignum;
91 static blasint notrna, notrnb;
92 static float smlnum;
93
94 /* Parameter adjustments */
95 a_dim1 = *lda;
96 a_offset = 1 + a_dim1;
97 a -= a_offset;
98 b_dim1 = *ldb;
99 b_offset = 1 + b_dim1;
100 b -= b_offset;
101 c_dim1 = *ldc;
102 c_offset = 1 + c_dim1;
103 c__ -= c_offset;
104
105 /* Function Body */
106 notrna = lsame_(trana, "N", (ftnlen)1, (ftnlen)1);
107 notrnb = lsame_(tranb, "N", (ftnlen)1, (ftnlen)1);
108 *info = 0;
109 if (! notrna && ! lsame_(trana, "C", (ftnlen)1, (ftnlen)1)) {
110 *info = -1;
111 } else if (! notrnb && ! lsame_(tranb, "C", (ftnlen)1, (ftnlen)1)) {
112 *info = -2;
113 } else if (*isgn != 1 && *isgn != -1) {
114 *info = -3;
115 } else if (*m < 0) {
116 *info = -4;
117 } else if (*n < 0) {
118 *info = -5;
119 } else if (*lda < max(1,*m)) {
120 *info = -7;
121 } else if (*ldb < max(1,*n)) {
122 *info = -9;
123 } else if (*ldc < max(1,*m)) {
124 *info = -11;
125 }
126 if (*info != 0) {
127 i__1 = -(*info);
128 xerbla_("CTRSY2", &i__1, (ftnlen)6);
129 return;
130 }
131 *scale = 1.f;
132 if (*m == 0 || *n == 0) {
133 return;
134 }
135 eps = slamch_("P", (ftnlen)1);
136 smlnum = slamch_("S", (ftnlen)1);
137 bignum = 1.f / smlnum;
138 slabad_(&smlnum, &bignum);
139 smlnum = smlnum * (float) (*m * *n) / eps;
140 bignum = 1.f / smlnum;
141 /* Computing MAX */
142 r__1 = smlnum, r__2 = eps * clange_("M", m, m, &a[a_offset], lda, dum, (
143 ftnlen)1), r__1 = max(r__1,r__2), r__2 = eps * clange_("M", n, n,
144 &b[b_offset], ldb, dum, (ftnlen)1);
145 smin = dmax(r__1,r__2);
146 sgn = (float) (*isgn);
147 if (notrna && notrnb) {
148 i__1 = *n;
149 for (l = 1; l <= i__1; ++l) {
150 for (k = *m; k >= 1; --k) {
151 i__2 = *m - k;
152 /* Computing MIN */
153 i__3 = k + 1;
154 /* Computing MIN */
155 i__4 = k + 1;
156 q__1 = cdotu_(&i__2, &a[k + min(i__3,*m) * a_dim1], lda, &c__[
157 min(i__4,*m) + l * c_dim1], &c__1);
158 suml.r = q__1.r, suml.i = q__1.i;
159 i__2 = l - 1;
160 q__1 = cdotu_(&i__2, &c__[k + c_dim1], ldc, &b[l * b_dim1 + 1]
161 , &c__1);
162 sumr.r = q__1.r, sumr.i = q__1.i;
163 i__2 = k + l * c_dim1;
164 q__3.r = sgn * sumr.r, q__3.i = sgn * sumr.i;
165 q__2.r = suml.r + q__3.r, q__2.i = suml.i + q__3.i;
166 q__1.r = c__[i__2].r - q__2.r, q__1.i = c__[i__2].i - q__2.i;
167 vec.r = q__1.r, vec.i = q__1.i;
168 scaloc = 1.f;
169 i__2 = k + k * a_dim1;
170 i__3 = l + l * b_dim1;
171 q__2.r = sgn * b[i__3].r, q__2.i = sgn * b[i__3].i;
172 q__1.r = a[i__2].r + q__2.r, q__1.i = a[i__2].i + q__2.i;
173 a11.r = q__1.r, a11.i = q__1.i;
174 da11 = (r__1 = a11.r, dabs(r__1)) + (r__2 = r_imag(&a11),
175 dabs(r__2));
176 if (da11 <= smin) {
177 a11.r = smin, a11.i = 0.f;
178 da11 = smin;
179 *info = 1;
180 }
181 db = (r__1 = vec.r, dabs(r__1)) + (r__2 = r_imag(&vec), dabs(
182 r__2));
183 if (da11 < 1.f && db > 1.f) {
184 if (db > bignum * da11) {
185 scaloc = 1.f / db;
186 }
187 }
188 q__3.r = scaloc, q__3.i = 0.f;
189 q__2.r = vec.r * q__3.r - vec.i * q__3.i, q__2.i = vec.r *
190 q__3.i + vec.i * q__3.r;
191 q__1 = cladiv_(&q__2, &a11);
192 x11.r = q__1.r, x11.i = q__1.i;
193 if (scaloc != 1.f) {
194 i__2 = *n;
195 for (j = 1; j <= i__2; ++j) {
196 csscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
197 /* L10: */
198 }
199 *scale *= scaloc;
200 }
201 i__2 = k + l * c_dim1;
202 c__[i__2].r = x11.r, c__[i__2].i = x11.i;
203 /* L20: */
204 }
205 /* L30: */
206 }
207 } else if (! notrna && notrnb) {
208 i__1 = *n;
209 for (l = 1; l <= i__1; ++l) {
210 i__2 = *m;
211 for (k = 1; k <= i__2; ++k) {
212 i__3 = k - 1;
213 q__1 = cdotc_(&i__3, &a[k * a_dim1 + 1], &c__1, &c__[l *
214 c_dim1 + 1], &c__1);
215 suml.r = q__1.r, suml.i = q__1.i;
216 i__3 = l - 1;
217 q__1 = cdotu_(&i__3, &c__[k + c_dim1], ldc, &b[l * b_dim1 + 1]
218 , &c__1);
219 sumr.r = q__1.r, sumr.i = q__1.i;
220 i__3 = k + l * c_dim1;
221 q__3.r = sgn * sumr.r, q__3.i = sgn * sumr.i;
222 q__2.r = suml.r + q__3.r, q__2.i = suml.i + q__3.i;
223 q__1.r = c__[i__3].r - q__2.r, q__1.i = c__[i__3].i - q__2.i;
224 vec.r = q__1.r, vec.i = q__1.i;
225 scaloc = 1.f;
226 r_cnjg(&q__2, &a[k + k * a_dim1]);
227 i__3 = l + l * b_dim1;
228 q__3.r = sgn * b[i__3].r, q__3.i = sgn * b[i__3].i;
229 q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
230 a11.r = q__1.r, a11.i = q__1.i;
231 da11 = (r__1 = a11.r, dabs(r__1)) + (r__2 = r_imag(&a11),
232 dabs(r__2));
233 if (da11 <= smin) {
234 a11.r = smin, a11.i = 0.f;
235 da11 = smin;
236 *info = 1;
237 }
238 db = (r__1 = vec.r, dabs(r__1)) + (r__2 = r_imag(&vec), dabs(
239 r__2));
240 if (da11 < 1.f && db > 1.f) {
241 if (db > bignum * da11) {
242 scaloc = 1.f / db;
243 }
244 }
245 q__3.r = scaloc, q__3.i = 0.f;
246 q__2.r = vec.r * q__3.r - vec.i * q__3.i, q__2.i = vec.r *
247 q__3.i + vec.i * q__3.r;
248 q__1 = cladiv_(&q__2, &a11);
249 x11.r = q__1.r, x11.i = q__1.i;
250 if (scaloc != 1.f) {
251 i__3 = *n;
252 for (j = 1; j <= i__3; ++j) {
253 csscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
254 /* L40: */
255 }
256 *scale *= scaloc;
257 }
258 i__3 = k + l * c_dim1;
259 c__[i__3].r = x11.r, c__[i__3].i = x11.i;
260 /* L50: */
261 }
262 /* L60: */
263 }
264 } else if (! notrna && ! notrnb) {
265 for (l = *n; l >= 1; --l) {
266 i__1 = *m;
267 for (k = 1; k <= i__1; ++k) {
268 i__2 = k - 1;
269 q__1 = cdotc_(&i__2, &a[k * a_dim1 + 1], &c__1, &c__[l *
270 c_dim1 + 1], &c__1);
271 suml.r = q__1.r, suml.i = q__1.i;
272 i__2 = *n - l;
273 /* Computing MIN */
274 i__3 = l + 1;
275 /* Computing MIN */
276 i__4 = l + 1;
277 q__1 = cdotc_(&i__2, &c__[k + min(i__3,*n) * c_dim1], ldc, &b[
278 l + min(i__4,*n) * b_dim1], ldb);
279 sumr.r = q__1.r, sumr.i = q__1.i;
280 i__2 = k + l * c_dim1;
281 r_cnjg(&q__4, &sumr);
282 q__3.r = sgn * q__4.r, q__3.i = sgn * q__4.i;
283 q__2.r = suml.r + q__3.r, q__2.i = suml.i + q__3.i;
284 q__1.r = c__[i__2].r - q__2.r, q__1.i = c__[i__2].i - q__2.i;
285 vec.r = q__1.r, vec.i = q__1.i;
286 scaloc = 1.f;
287 i__2 = k + k * a_dim1;
288 i__3 = l + l * b_dim1;
289 q__3.r = sgn * b[i__3].r, q__3.i = sgn * b[i__3].i;
290 q__2.r = a[i__2].r + q__3.r, q__2.i = a[i__2].i + q__3.i;
291 r_cnjg(&q__1, &q__2);
292 a11.r = q__1.r, a11.i = q__1.i;
293 da11 = (r__1 = a11.r, dabs(r__1)) + (r__2 = r_imag(&a11),
294 dabs(r__2));
295 if (da11 <= smin) {
296 a11.r = smin, a11.i = 0.f;
297 da11 = smin;
298 *info = 1;
299 }
300 db = (r__1 = vec.r, dabs(r__1)) + (r__2 = r_imag(&vec), dabs(
301 r__2));
302 if (da11 < 1.f && db > 1.f) {
303 if (db > bignum * da11) {
304 scaloc = 1.f / db;
305 }
306 }
307 q__3.r = scaloc, q__3.i = 0.f;
308 q__2.r = vec.r * q__3.r - vec.i * q__3.i, q__2.i = vec.r *
309 q__3.i + vec.i * q__3.r;
310 q__1 = cladiv_(&q__2, &a11);
311 x11.r = q__1.r, x11.i = q__1.i;
312 if (scaloc != 1.f) {
313 i__2 = *n;
314 for (j = 1; j <= i__2; ++j) {
315 csscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
316 /* L70: */
317 }
318 *scale *= scaloc;
319 }
320 i__2 = k + l * c_dim1;
321 c__[i__2].r = x11.r, c__[i__2].i = x11.i;
322 /* L80: */
323 }
324 /* L90: */
325 }
326 } else if (notrna && ! notrnb) {
327 for (l = *n; l >= 1; --l) {
328 for (k = *m; k >= 1; --k) {
329 i__1 = *m - k;
330 /* Computing MIN */
331 i__2 = k + 1;
332 /* Computing MIN */
333 i__3 = k + 1;
334 q__1 = cdotu_(&i__1, &a[k + min(i__2,*m) * a_dim1], lda, &c__[
335 min(i__3,*m) + l * c_dim1], &c__1);
336 suml.r = q__1.r, suml.i = q__1.i;
337 i__1 = *n - l;
338 /* Computing MIN */
339 i__2 = l + 1;
340 /* Computing MIN */
341 i__3 = l + 1;
342 q__1 = cdotc_(&i__1, &c__[k + min(i__2,*n) * c_dim1], ldc, &b[
343 l + min(i__3,*n) * b_dim1], ldb);
344 sumr.r = q__1.r, sumr.i = q__1.i;
345 i__1 = k + l * c_dim1;
346 r_cnjg(&q__4, &sumr);
347 q__3.r = sgn * q__4.r, q__3.i = sgn * q__4.i;
348 q__2.r = suml.r + q__3.r, q__2.i = suml.i + q__3.i;
349 q__1.r = c__[i__1].r - q__2.r, q__1.i = c__[i__1].i - q__2.i;
350 vec.r = q__1.r, vec.i = q__1.i;
351 scaloc = 1.f;
352 i__1 = k + k * a_dim1;
353 r_cnjg(&q__3, &b[l + l * b_dim1]);
354 q__2.r = sgn * q__3.r, q__2.i = sgn * q__3.i;
355 q__1.r = a[i__1].r + q__2.r, q__1.i = a[i__1].i + q__2.i;
356 a11.r = q__1.r, a11.i = q__1.i;
357 da11 = (r__1 = a11.r, dabs(r__1)) + (r__2 = r_imag(&a11),
358 dabs(r__2));
359 if (da11 <= smin) {
360 a11.r = smin, a11.i = 0.f;
361 da11 = smin;
362 *info = 1;
363 }
364 db = (r__1 = vec.r, dabs(r__1)) + (r__2 = r_imag(&vec), dabs(
365 r__2));
366 if (da11 < 1.f && db > 1.f) {
367 if (db > bignum * da11) {
368 scaloc = 1.f / db;
369 }
370 }
371 q__3.r = scaloc, q__3.i = 0.f;
372 q__2.r = vec.r * q__3.r - vec.i * q__3.i, q__2.i = vec.r *
373 q__3.i + vec.i * q__3.r;
374 q__1 = cladiv_(&q__2, &a11);
375 x11.r = q__1.r, x11.i = q__1.i;
376 if (scaloc != 1.f) {
377 i__1 = *n;
378 for (j = 1; j <= i__1; ++j) {
379 csscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
380 /* L100: */
381 }
382 *scale *= scaloc;
383 }
384 i__1 = k + l * c_dim1;
385 c__[i__1].r = x11.r, c__[i__1].i = x11.i;
386 /* L110: */
387 }
388 /* L120: */
389 }
390 }
391 return;
392 }
393