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ztgsyl.c 38 kB

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  1. #include <math.h>
  2. #include <stdlib.h>
  3. #include <string.h>
  4. #include <stdio.h>
  5. #include <complex.h>
  6. #ifdef complex
  7. #undef complex
  8. #endif
  9. #ifdef I
  10. #undef I
  11. #endif
  12. #if defined(_WIN64)
  13. typedef long long BLASLONG;
  14. typedef unsigned long long BLASULONG;
  15. #else
  16. typedef long BLASLONG;
  17. typedef unsigned long BLASULONG;
  18. #endif
  19. #ifdef LAPACK_ILP64
  20. typedef BLASLONG blasint;
  21. #if defined(_WIN64)
  22. #define blasabs(x) llabs(x)
  23. #else
  24. #define blasabs(x) labs(x)
  25. #endif
  26. #else
  27. typedef int blasint;
  28. #define blasabs(x) abs(x)
  29. #endif
  30. typedef blasint integer;
  31. typedef unsigned int uinteger;
  32. typedef char *address;
  33. typedef short int shortint;
  34. typedef float real;
  35. typedef double doublereal;
  36. typedef struct { real r, i; } complex;
  37. typedef struct { doublereal r, i; } doublecomplex;
  38. #ifdef _MSC_VER
  39. static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
  40. static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
  41. static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
  42. static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
  43. #else
  44. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  45. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  46. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  47. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  48. #endif
  49. #define pCf(z) (*_pCf(z))
  50. #define pCd(z) (*_pCd(z))
  51. typedef int logical;
  52. typedef short int shortlogical;
  53. typedef char logical1;
  54. typedef char integer1;
  55. #define TRUE_ (1)
  56. #define FALSE_ (0)
  57. /* Extern is for use with -E */
  58. #ifndef Extern
  59. #define Extern extern
  60. #endif
  61. /* I/O stuff */
  62. typedef int flag;
  63. typedef int ftnlen;
  64. typedef int ftnint;
  65. /*external read, write*/
  66. typedef struct
  67. { flag cierr;
  68. ftnint ciunit;
  69. flag ciend;
  70. char *cifmt;
  71. ftnint cirec;
  72. } cilist;
  73. /*internal read, write*/
  74. typedef struct
  75. { flag icierr;
  76. char *iciunit;
  77. flag iciend;
  78. char *icifmt;
  79. ftnint icirlen;
  80. ftnint icirnum;
  81. } icilist;
  82. /*open*/
  83. typedef struct
  84. { flag oerr;
  85. ftnint ounit;
  86. char *ofnm;
  87. ftnlen ofnmlen;
  88. char *osta;
  89. char *oacc;
  90. char *ofm;
  91. ftnint orl;
  92. char *oblnk;
  93. } olist;
  94. /*close*/
  95. typedef struct
  96. { flag cerr;
  97. ftnint cunit;
  98. char *csta;
  99. } cllist;
  100. /*rewind, backspace, endfile*/
  101. typedef struct
  102. { flag aerr;
  103. ftnint aunit;
  104. } alist;
  105. /* inquire */
  106. typedef struct
  107. { flag inerr;
  108. ftnint inunit;
  109. char *infile;
  110. ftnlen infilen;
  111. ftnint *inex; /*parameters in standard's order*/
  112. ftnint *inopen;
  113. ftnint *innum;
  114. ftnint *innamed;
  115. char *inname;
  116. ftnlen innamlen;
  117. char *inacc;
  118. ftnlen inacclen;
  119. char *inseq;
  120. ftnlen inseqlen;
  121. char *indir;
  122. ftnlen indirlen;
  123. char *infmt;
  124. ftnlen infmtlen;
  125. char *inform;
  126. ftnint informlen;
  127. char *inunf;
  128. ftnlen inunflen;
  129. ftnint *inrecl;
  130. ftnint *innrec;
  131. char *inblank;
  132. ftnlen inblanklen;
  133. } inlist;
  134. #define VOID void
  135. union Multitype { /* for multiple entry points */
  136. integer1 g;
  137. shortint h;
  138. integer i;
  139. /* longint j; */
  140. real r;
  141. doublereal d;
  142. complex c;
  143. doublecomplex z;
  144. };
  145. typedef union Multitype Multitype;
  146. struct Vardesc { /* for Namelist */
  147. char *name;
  148. char *addr;
  149. ftnlen *dims;
  150. int type;
  151. };
  152. typedef struct Vardesc Vardesc;
  153. struct Namelist {
  154. char *name;
  155. Vardesc **vars;
  156. int nvars;
  157. };
  158. typedef struct Namelist Namelist;
  159. #define abs(x) ((x) >= 0 ? (x) : -(x))
  160. #define dabs(x) (fabs(x))
  161. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  162. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  163. #define dmin(a,b) (f2cmin(a,b))
  164. #define dmax(a,b) (f2cmax(a,b))
  165. #define bit_test(a,b) ((a) >> (b) & 1)
  166. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  167. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  168. #define abort_() { sig_die("Fortran abort routine called", 1); }
  169. #define c_abs(z) (cabsf(Cf(z)))
  170. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  171. #ifdef _MSC_VER
  172. #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
  173. #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/Cd(b)._Val[1]);}
  174. #else
  175. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  176. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  177. #endif
  178. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  179. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  180. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  181. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  182. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  183. #define d_abs(x) (fabs(*(x)))
  184. #define d_acos(x) (acos(*(x)))
  185. #define d_asin(x) (asin(*(x)))
  186. #define d_atan(x) (atan(*(x)))
  187. #define d_atn2(x, y) (atan2(*(x),*(y)))
  188. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  189. #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
  190. #define d_cos(x) (cos(*(x)))
  191. #define d_cosh(x) (cosh(*(x)))
  192. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  193. #define d_exp(x) (exp(*(x)))
  194. #define d_imag(z) (cimag(Cd(z)))
  195. #define r_imag(z) (cimagf(Cf(z)))
  196. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  197. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  198. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  199. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  200. #define d_log(x) (log(*(x)))
  201. #define d_mod(x, y) (fmod(*(x), *(y)))
  202. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  203. #define d_nint(x) u_nint(*(x))
  204. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  205. #define d_sign(a,b) u_sign(*(a),*(b))
  206. #define r_sign(a,b) u_sign(*(a),*(b))
  207. #define d_sin(x) (sin(*(x)))
  208. #define d_sinh(x) (sinh(*(x)))
  209. #define d_sqrt(x) (sqrt(*(x)))
  210. #define d_tan(x) (tan(*(x)))
  211. #define d_tanh(x) (tanh(*(x)))
  212. #define i_abs(x) abs(*(x))
  213. #define i_dnnt(x) ((integer)u_nint(*(x)))
  214. #define i_len(s, n) (n)
  215. #define i_nint(x) ((integer)u_nint(*(x)))
  216. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  217. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  218. #define pow_si(B,E) spow_ui(*(B),*(E))
  219. #define pow_ri(B,E) spow_ui(*(B),*(E))
  220. #define pow_di(B,E) dpow_ui(*(B),*(E))
  221. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  222. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  223. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  224. #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
  225. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  226. #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
  227. #define sig_die(s, kill) { exit(1); }
  228. #define s_stop(s, n) {exit(0);}
  229. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  230. #define z_abs(z) (cabs(Cd(z)))
  231. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  232. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  233. #define myexit_() break;
  234. #define mycycle_() continue;
  235. #define myceiling_(w) {ceil(w)}
  236. #define myhuge_(w) {HUGE_VAL}
  237. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  238. #define mymaxloc_(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  239. /* procedure parameter types for -A and -C++ */
  240. #define F2C_proc_par_types 1
  241. #ifdef __cplusplus
  242. typedef logical (*L_fp)(...);
  243. #else
  244. typedef logical (*L_fp)();
  245. #endif
  246. static float spow_ui(float x, integer n) {
  247. float pow=1.0; unsigned long int u;
  248. if(n != 0) {
  249. if(n < 0) n = -n, x = 1/x;
  250. for(u = n; ; ) {
  251. if(u & 01) pow *= x;
  252. if(u >>= 1) x *= x;
  253. else break;
  254. }
  255. }
  256. return pow;
  257. }
  258. static double dpow_ui(double x, integer n) {
  259. double pow=1.0; unsigned long int u;
  260. if(n != 0) {
  261. if(n < 0) n = -n, x = 1/x;
  262. for(u = n; ; ) {
  263. if(u & 01) pow *= x;
  264. if(u >>= 1) x *= x;
  265. else break;
  266. }
  267. }
  268. return pow;
  269. }
  270. #ifdef _MSC_VER
  271. static _Fcomplex cpow_ui(complex x, integer n) {
  272. complex pow={1.0,0.0}; unsigned long int u;
  273. if(n != 0) {
  274. if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
  275. for(u = n; ; ) {
  276. if(u & 01) pow.r *= x.r, pow.i *= x.i;
  277. if(u >>= 1) x.r *= x.r, x.i *= x.i;
  278. else break;
  279. }
  280. }
  281. _Fcomplex p={pow.r, pow.i};
  282. return p;
  283. }
  284. #else
  285. static _Complex float cpow_ui(_Complex float x, integer n) {
  286. _Complex float pow=1.0; unsigned long int u;
  287. if(n != 0) {
  288. if(n < 0) n = -n, x = 1/x;
  289. for(u = n; ; ) {
  290. if(u & 01) pow *= x;
  291. if(u >>= 1) x *= x;
  292. else break;
  293. }
  294. }
  295. return pow;
  296. }
  297. #endif
  298. #ifdef _MSC_VER
  299. static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
  300. _Dcomplex pow={1.0,0.0}; unsigned long int u;
  301. if(n != 0) {
  302. if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
  303. for(u = n; ; ) {
  304. if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
  305. if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
  306. else break;
  307. }
  308. }
  309. _Dcomplex p = {pow._Val[0], pow._Val[1]};
  310. return p;
  311. }
  312. #else
  313. static _Complex double zpow_ui(_Complex double x, integer n) {
  314. _Complex double pow=1.0; unsigned long int u;
  315. if(n != 0) {
  316. if(n < 0) n = -n, x = 1/x;
  317. for(u = n; ; ) {
  318. if(u & 01) pow *= x;
  319. if(u >>= 1) x *= x;
  320. else break;
  321. }
  322. }
  323. return pow;
  324. }
  325. #endif
  326. static integer pow_ii(integer x, integer n) {
  327. integer pow; unsigned long int u;
  328. if (n <= 0) {
  329. if (n == 0 || x == 1) pow = 1;
  330. else if (x != -1) pow = x == 0 ? 1/x : 0;
  331. else n = -n;
  332. }
  333. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  334. u = n;
  335. for(pow = 1; ; ) {
  336. if(u & 01) pow *= x;
  337. if(u >>= 1) x *= x;
  338. else break;
  339. }
  340. }
  341. return pow;
  342. }
  343. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  344. {
  345. double m; integer i, mi;
  346. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  347. if (w[i-1]>m) mi=i ,m=w[i-1];
  348. return mi-s+1;
  349. }
  350. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  351. {
  352. float m; integer i, mi;
  353. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  354. if (w[i-1]>m) mi=i ,m=w[i-1];
  355. return mi-s+1;
  356. }
  357. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  358. integer n = *n_, incx = *incx_, incy = *incy_, i;
  359. #ifdef _MSC_VER
  360. _Fcomplex zdotc = {0.0, 0.0};
  361. if (incx == 1 && incy == 1) {
  362. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  363. zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
  364. zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
  365. }
  366. } else {
  367. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  368. zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
  369. zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
  370. }
  371. }
  372. pCf(z) = zdotc;
  373. }
  374. #else
  375. _Complex float zdotc = 0.0;
  376. if (incx == 1 && incy == 1) {
  377. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  378. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  379. }
  380. } else {
  381. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  382. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  383. }
  384. }
  385. pCf(z) = zdotc;
  386. }
  387. #endif
  388. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  389. integer n = *n_, incx = *incx_, incy = *incy_, i;
  390. #ifdef _MSC_VER
  391. _Dcomplex zdotc = {0.0, 0.0};
  392. if (incx == 1 && incy == 1) {
  393. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  394. zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
  395. zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
  396. }
  397. } else {
  398. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  399. zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
  400. zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
  401. }
  402. }
  403. pCd(z) = zdotc;
  404. }
  405. #else
  406. _Complex double zdotc = 0.0;
  407. if (incx == 1 && incy == 1) {
  408. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  409. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  410. }
  411. } else {
  412. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  413. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  414. }
  415. }
  416. pCd(z) = zdotc;
  417. }
  418. #endif
  419. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  420. integer n = *n_, incx = *incx_, incy = *incy_, i;
  421. #ifdef _MSC_VER
  422. _Fcomplex zdotc = {0.0, 0.0};
  423. if (incx == 1 && incy == 1) {
  424. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  425. zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
  426. zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
  427. }
  428. } else {
  429. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  430. zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
  431. zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
  432. }
  433. }
  434. pCf(z) = zdotc;
  435. }
  436. #else
  437. _Complex float zdotc = 0.0;
  438. if (incx == 1 && incy == 1) {
  439. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  440. zdotc += Cf(&x[i]) * Cf(&y[i]);
  441. }
  442. } else {
  443. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  444. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  445. }
  446. }
  447. pCf(z) = zdotc;
  448. }
  449. #endif
  450. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  451. integer n = *n_, incx = *incx_, incy = *incy_, i;
  452. #ifdef _MSC_VER
  453. _Dcomplex zdotc = {0.0, 0.0};
  454. if (incx == 1 && incy == 1) {
  455. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  456. zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
  457. zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
  458. }
  459. } else {
  460. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  461. zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
  462. zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
  463. }
  464. }
  465. pCd(z) = zdotc;
  466. }
  467. #else
  468. _Complex double zdotc = 0.0;
  469. if (incx == 1 && incy == 1) {
  470. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  471. zdotc += Cd(&x[i]) * Cd(&y[i]);
  472. }
  473. } else {
  474. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  475. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  476. }
  477. }
  478. pCd(z) = zdotc;
  479. }
  480. #endif
  481. /* -- translated by f2c (version 20000121).
  482. You must link the resulting object file with the libraries:
  483. -lf2c -lm (in that order)
  484. */
  485. /* Table of constant values */
  486. static doublecomplex c_b1 = {0.,0.};
  487. static integer c__2 = 2;
  488. static integer c_n1 = -1;
  489. static integer c__5 = 5;
  490. static integer c__1 = 1;
  491. static doublecomplex c_b44 = {-1.,0.};
  492. static doublecomplex c_b45 = {1.,0.};
  493. /* > \brief \b ZTGSYL */
  494. /* =========== DOCUMENTATION =========== */
  495. /* Online html documentation available at */
  496. /* http://www.netlib.org/lapack/explore-html/ */
  497. /* > \htmlonly */
  498. /* > Download ZTGSYL + dependencies */
  499. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgsyl.
  500. f"> */
  501. /* > [TGZ]</a> */
  502. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztgsyl.
  503. f"> */
  504. /* > [ZIP]</a> */
  505. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgsyl.
  506. f"> */
  507. /* > [TXT]</a> */
  508. /* > \endhtmlonly */
  509. /* Definition: */
  510. /* =========== */
  511. /* SUBROUTINE ZTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, */
  512. /* LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK, */
  513. /* IWORK, INFO ) */
  514. /* CHARACTER TRANS */
  515. /* INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF, */
  516. /* $ LWORK, M, N */
  517. /* DOUBLE PRECISION DIF, SCALE */
  518. /* INTEGER IWORK( * ) */
  519. /* COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * ), */
  520. /* $ D( LDD, * ), E( LDE, * ), F( LDF, * ), */
  521. /* $ WORK( * ) */
  522. /* > \par Purpose: */
  523. /* ============= */
  524. /* > */
  525. /* > \verbatim */
  526. /* > */
  527. /* > ZTGSYL solves the generalized Sylvester equation: */
  528. /* > */
  529. /* > A * R - L * B = scale * C (1) */
  530. /* > D * R - L * E = scale * F */
  531. /* > */
  532. /* > where R and L are unknown m-by-n matrices, (A, D), (B, E) and */
  533. /* > (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n, */
  534. /* > respectively, with complex entries. A, B, D and E are upper */
  535. /* > triangular (i.e., (A,D) and (B,E) in generalized Schur form). */
  536. /* > */
  537. /* > The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 */
  538. /* > is an output scaling factor chosen to avoid overflow. */
  539. /* > */
  540. /* > In matrix notation (1) is equivalent to solve Zx = scale*b, where Z */
  541. /* > is defined as */
  542. /* > */
  543. /* > Z = [ kron(In, A) -kron(B**H, Im) ] (2) */
  544. /* > [ kron(In, D) -kron(E**H, Im) ], */
  545. /* > */
  546. /* > Here Ix is the identity matrix of size x and X**H is the conjugate */
  547. /* > transpose of X. Kron(X, Y) is the Kronecker product between the */
  548. /* > matrices X and Y. */
  549. /* > */
  550. /* > If TRANS = 'C', y in the conjugate transposed system Z**H *y = scale*b */
  551. /* > is solved for, which is equivalent to solve for R and L in */
  552. /* > */
  553. /* > A**H * R + D**H * L = scale * C (3) */
  554. /* > R * B**H + L * E**H = scale * -F */
  555. /* > */
  556. /* > This case (TRANS = 'C') is used to compute an one-norm-based estimate */
  557. /* > of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D) */
  558. /* > and (B,E), using ZLACON. */
  559. /* > */
  560. /* > If IJOB >= 1, ZTGSYL computes a Frobenius norm-based estimate of */
  561. /* > Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the */
  562. /* > reciprocal of the smallest singular value of Z. */
  563. /* > */
  564. /* > This is a level-3 BLAS algorithm. */
  565. /* > \endverbatim */
  566. /* Arguments: */
  567. /* ========== */
  568. /* > \param[in] TRANS */
  569. /* > \verbatim */
  570. /* > TRANS is CHARACTER*1 */
  571. /* > = 'N': solve the generalized sylvester equation (1). */
  572. /* > = 'C': solve the "conjugate transposed" system (3). */
  573. /* > \endverbatim */
  574. /* > */
  575. /* > \param[in] IJOB */
  576. /* > \verbatim */
  577. /* > IJOB is INTEGER */
  578. /* > Specifies what kind of functionality to be performed. */
  579. /* > =0: solve (1) only. */
  580. /* > =1: The functionality of 0 and 3. */
  581. /* > =2: The functionality of 0 and 4. */
  582. /* > =3: Only an estimate of Dif[(A,D), (B,E)] is computed. */
  583. /* > (look ahead strategy is used). */
  584. /* > =4: Only an estimate of Dif[(A,D), (B,E)] is computed. */
  585. /* > (ZGECON on sub-systems is used). */
  586. /* > Not referenced if TRANS = 'C'. */
  587. /* > \endverbatim */
  588. /* > */
  589. /* > \param[in] M */
  590. /* > \verbatim */
  591. /* > M is INTEGER */
  592. /* > The order of the matrices A and D, and the row dimension of */
  593. /* > the matrices C, F, R and L. */
  594. /* > \endverbatim */
  595. /* > */
  596. /* > \param[in] N */
  597. /* > \verbatim */
  598. /* > N is INTEGER */
  599. /* > The order of the matrices B and E, and the column dimension */
  600. /* > of the matrices C, F, R and L. */
  601. /* > \endverbatim */
  602. /* > */
  603. /* > \param[in] A */
  604. /* > \verbatim */
  605. /* > A is COMPLEX*16 array, dimension (LDA, M) */
  606. /* > The upper triangular matrix A. */
  607. /* > \endverbatim */
  608. /* > */
  609. /* > \param[in] LDA */
  610. /* > \verbatim */
  611. /* > LDA is INTEGER */
  612. /* > The leading dimension of the array A. LDA >= f2cmax(1, M). */
  613. /* > \endverbatim */
  614. /* > */
  615. /* > \param[in] B */
  616. /* > \verbatim */
  617. /* > B is COMPLEX*16 array, dimension (LDB, N) */
  618. /* > The upper triangular matrix B. */
  619. /* > \endverbatim */
  620. /* > */
  621. /* > \param[in] LDB */
  622. /* > \verbatim */
  623. /* > LDB is INTEGER */
  624. /* > The leading dimension of the array B. LDB >= f2cmax(1, N). */
  625. /* > \endverbatim */
  626. /* > */
  627. /* > \param[in,out] C */
  628. /* > \verbatim */
  629. /* > C is COMPLEX*16 array, dimension (LDC, N) */
  630. /* > On entry, C contains the right-hand-side of the first matrix */
  631. /* > equation in (1) or (3). */
  632. /* > On exit, if IJOB = 0, 1 or 2, C has been overwritten by */
  633. /* > the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R, */
  634. /* > the solution achieved during the computation of the */
  635. /* > Dif-estimate. */
  636. /* > \endverbatim */
  637. /* > */
  638. /* > \param[in] LDC */
  639. /* > \verbatim */
  640. /* > LDC is INTEGER */
  641. /* > The leading dimension of the array C. LDC >= f2cmax(1, M). */
  642. /* > \endverbatim */
  643. /* > */
  644. /* > \param[in] D */
  645. /* > \verbatim */
  646. /* > D is COMPLEX*16 array, dimension (LDD, M) */
  647. /* > The upper triangular matrix D. */
  648. /* > \endverbatim */
  649. /* > */
  650. /* > \param[in] LDD */
  651. /* > \verbatim */
  652. /* > LDD is INTEGER */
  653. /* > The leading dimension of the array D. LDD >= f2cmax(1, M). */
  654. /* > \endverbatim */
  655. /* > */
  656. /* > \param[in] E */
  657. /* > \verbatim */
  658. /* > E is COMPLEX*16 array, dimension (LDE, N) */
  659. /* > The upper triangular matrix E. */
  660. /* > \endverbatim */
  661. /* > */
  662. /* > \param[in] LDE */
  663. /* > \verbatim */
  664. /* > LDE is INTEGER */
  665. /* > The leading dimension of the array E. LDE >= f2cmax(1, N). */
  666. /* > \endverbatim */
  667. /* > */
  668. /* > \param[in,out] F */
  669. /* > \verbatim */
  670. /* > F is COMPLEX*16 array, dimension (LDF, N) */
  671. /* > On entry, F contains the right-hand-side of the second matrix */
  672. /* > equation in (1) or (3). */
  673. /* > On exit, if IJOB = 0, 1 or 2, F has been overwritten by */
  674. /* > the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L, */
  675. /* > the solution achieved during the computation of the */
  676. /* > Dif-estimate. */
  677. /* > \endverbatim */
  678. /* > */
  679. /* > \param[in] LDF */
  680. /* > \verbatim */
  681. /* > LDF is INTEGER */
  682. /* > The leading dimension of the array F. LDF >= f2cmax(1, M). */
  683. /* > \endverbatim */
  684. /* > */
  685. /* > \param[out] DIF */
  686. /* > \verbatim */
  687. /* > DIF is DOUBLE PRECISION */
  688. /* > On exit DIF is the reciprocal of a lower bound of the */
  689. /* > reciprocal of the Dif-function, i.e. DIF is an upper bound of */
  690. /* > Dif[(A,D), (B,E)] = sigma-f2cmin(Z), where Z as in (2). */
  691. /* > IF IJOB = 0 or TRANS = 'C', DIF is not referenced. */
  692. /* > \endverbatim */
  693. /* > */
  694. /* > \param[out] SCALE */
  695. /* > \verbatim */
  696. /* > SCALE is DOUBLE PRECISION */
  697. /* > On exit SCALE is the scaling factor in (1) or (3). */
  698. /* > If 0 < SCALE < 1, C and F hold the solutions R and L, resp., */
  699. /* > to a slightly perturbed system but the input matrices A, B, */
  700. /* > D and E have not been changed. If SCALE = 0, R and L will */
  701. /* > hold the solutions to the homogenious system with C = F = 0. */
  702. /* > \endverbatim */
  703. /* > */
  704. /* > \param[out] WORK */
  705. /* > \verbatim */
  706. /* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */
  707. /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
  708. /* > \endverbatim */
  709. /* > */
  710. /* > \param[in] LWORK */
  711. /* > \verbatim */
  712. /* > LWORK is INTEGER */
  713. /* > The dimension of the array WORK. LWORK > = 1. */
  714. /* > If IJOB = 1 or 2 and TRANS = 'N', LWORK >= f2cmax(1,2*M*N). */
  715. /* > */
  716. /* > If LWORK = -1, then a workspace query is assumed; the routine */
  717. /* > only calculates the optimal size of the WORK array, returns */
  718. /* > this value as the first entry of the WORK array, and no error */
  719. /* > message related to LWORK is issued by XERBLA. */
  720. /* > \endverbatim */
  721. /* > */
  722. /* > \param[out] IWORK */
  723. /* > \verbatim */
  724. /* > IWORK is INTEGER array, dimension (M+N+2) */
  725. /* > \endverbatim */
  726. /* > */
  727. /* > \param[out] INFO */
  728. /* > \verbatim */
  729. /* > INFO is INTEGER */
  730. /* > =0: successful exit */
  731. /* > <0: If INFO = -i, the i-th argument had an illegal value. */
  732. /* > >0: (A, D) and (B, E) have common or very close */
  733. /* > eigenvalues. */
  734. /* > \endverbatim */
  735. /* Authors: */
  736. /* ======== */
  737. /* > \author Univ. of Tennessee */
  738. /* > \author Univ. of California Berkeley */
  739. /* > \author Univ. of Colorado Denver */
  740. /* > \author NAG Ltd. */
  741. /* > \date December 2016 */
  742. /* > \ingroup complex16SYcomputational */
  743. /* > \par Contributors: */
  744. /* ================== */
  745. /* > */
  746. /* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
  747. /* > Umea University, S-901 87 Umea, Sweden. */
  748. /* > \par References: */
  749. /* ================ */
  750. /* > */
  751. /* > [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */
  752. /* > for Solving the Generalized Sylvester Equation and Estimating the */
  753. /* > Separation between Regular Matrix Pairs, Report UMINF - 93.23, */
  754. /* > Department of Computing Science, Umea University, S-901 87 Umea, */
  755. /* > Sweden, December 1993, Revised April 1994, Also as LAPACK Working */
  756. /* > Note 75. To appear in ACM Trans. on Math. Software, Vol 22, */
  757. /* > No 1, 1996. */
  758. /* > \n */
  759. /* > [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester */
  760. /* > Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal. */
  761. /* > Appl., 15(4):1045-1060, 1994. */
  762. /* > \n */
  763. /* > [3] B. Kagstrom and L. Westin, Generalized Schur Methods with */
  764. /* > Condition Estimators for Solving the Generalized Sylvester */
  765. /* > Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, */
  766. /* > July 1989, pp 745-751. */
  767. /* > */
  768. /* ===================================================================== */
  769. /* Subroutine */ int ztgsyl_(char *trans, integer *ijob, integer *m, integer *
  770. n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb,
  771. doublecomplex *c__, integer *ldc, doublecomplex *d__, integer *ldd,
  772. doublecomplex *e, integer *lde, doublecomplex *f, integer *ldf,
  773. doublereal *scale, doublereal *dif, doublecomplex *work, integer *
  774. lwork, integer *iwork, integer *info)
  775. {
  776. /* System generated locals */
  777. integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, d_dim1,
  778. d_offset, e_dim1, e_offset, f_dim1, f_offset, i__1, i__2, i__3,
  779. i__4;
  780. doublecomplex z__1;
  781. /* Local variables */
  782. doublereal dsum;
  783. integer i__, j, k, p, q;
  784. extern logical lsame_(char *, char *);
  785. integer ifunc, linfo;
  786. extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
  787. doublecomplex *, integer *), zgemm_(char *, char *, integer *,
  788. integer *, integer *, doublecomplex *, doublecomplex *, integer *,
  789. doublecomplex *, integer *, doublecomplex *, doublecomplex *,
  790. integer *);
  791. integer lwmin;
  792. doublereal scale2;
  793. integer ie, je, mb, nb;
  794. doublereal dscale;
  795. integer is, js, pq;
  796. extern /* Subroutine */ int ztgsy2_(char *, integer *, integer *, integer
  797. *, doublecomplex *, integer *, doublecomplex *, integer *,
  798. doublecomplex *, integer *, doublecomplex *, integer *,
  799. doublecomplex *, integer *, doublecomplex *, integer *,
  800. doublereal *, doublereal *, doublereal *, integer *);
  801. doublereal scaloc;
  802. extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
  803. extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
  804. integer *, integer *, ftnlen, ftnlen);
  805. integer iround;
  806. logical notran;
  807. integer isolve;
  808. extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
  809. doublecomplex *, integer *, doublecomplex *, integer *),
  810. zlaset_(char *, integer *, integer *, doublecomplex *,
  811. doublecomplex *, doublecomplex *, integer *);
  812. logical lquery;
  813. /* -- LAPACK computational routine (version 3.7.0) -- */
  814. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  815. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  816. /* December 2016 */
  817. /* ===================================================================== */
  818. /* Replaced various illegal calls to CCOPY by calls to CLASET. */
  819. /* Sven Hammarling, 1/5/02. */
  820. /* Decode and test input parameters */
  821. /* Parameter adjustments */
  822. a_dim1 = *lda;
  823. a_offset = 1 + a_dim1 * 1;
  824. a -= a_offset;
  825. b_dim1 = *ldb;
  826. b_offset = 1 + b_dim1 * 1;
  827. b -= b_offset;
  828. c_dim1 = *ldc;
  829. c_offset = 1 + c_dim1 * 1;
  830. c__ -= c_offset;
  831. d_dim1 = *ldd;
  832. d_offset = 1 + d_dim1 * 1;
  833. d__ -= d_offset;
  834. e_dim1 = *lde;
  835. e_offset = 1 + e_dim1 * 1;
  836. e -= e_offset;
  837. f_dim1 = *ldf;
  838. f_offset = 1 + f_dim1 * 1;
  839. f -= f_offset;
  840. --work;
  841. --iwork;
  842. /* Function Body */
  843. *info = 0;
  844. notran = lsame_(trans, "N");
  845. lquery = *lwork == -1;
  846. if (! notran && ! lsame_(trans, "C")) {
  847. *info = -1;
  848. } else if (notran) {
  849. if (*ijob < 0 || *ijob > 4) {
  850. *info = -2;
  851. }
  852. }
  853. if (*info == 0) {
  854. if (*m <= 0) {
  855. *info = -3;
  856. } else if (*n <= 0) {
  857. *info = -4;
  858. } else if (*lda < f2cmax(1,*m)) {
  859. *info = -6;
  860. } else if (*ldb < f2cmax(1,*n)) {
  861. *info = -8;
  862. } else if (*ldc < f2cmax(1,*m)) {
  863. *info = -10;
  864. } else if (*ldd < f2cmax(1,*m)) {
  865. *info = -12;
  866. } else if (*lde < f2cmax(1,*n)) {
  867. *info = -14;
  868. } else if (*ldf < f2cmax(1,*m)) {
  869. *info = -16;
  870. }
  871. }
  872. if (*info == 0) {
  873. if (notran) {
  874. if (*ijob == 1 || *ijob == 2) {
  875. /* Computing MAX */
  876. i__1 = 1, i__2 = (*m << 1) * *n;
  877. lwmin = f2cmax(i__1,i__2);
  878. } else {
  879. lwmin = 1;
  880. }
  881. } else {
  882. lwmin = 1;
  883. }
  884. work[1].r = (doublereal) lwmin, work[1].i = 0.;
  885. if (*lwork < lwmin && ! lquery) {
  886. *info = -20;
  887. }
  888. }
  889. if (*info != 0) {
  890. i__1 = -(*info);
  891. xerbla_("ZTGSYL", &i__1, (ftnlen)6);
  892. return 0;
  893. } else if (lquery) {
  894. return 0;
  895. }
  896. /* Quick return if possible */
  897. if (*m == 0 || *n == 0) {
  898. *scale = 1.;
  899. if (notran) {
  900. if (*ijob != 0) {
  901. *dif = 0.;
  902. }
  903. }
  904. return 0;
  905. }
  906. /* Determine optimal block sizes MB and NB */
  907. mb = ilaenv_(&c__2, "ZTGSYL", trans, m, n, &c_n1, &c_n1, (ftnlen)6, (
  908. ftnlen)1);
  909. nb = ilaenv_(&c__5, "ZTGSYL", trans, m, n, &c_n1, &c_n1, (ftnlen)6, (
  910. ftnlen)1);
  911. isolve = 1;
  912. ifunc = 0;
  913. if (notran) {
  914. if (*ijob >= 3) {
  915. ifunc = *ijob - 2;
  916. zlaset_("F", m, n, &c_b1, &c_b1, &c__[c_offset], ldc);
  917. zlaset_("F", m, n, &c_b1, &c_b1, &f[f_offset], ldf);
  918. } else if (*ijob >= 1 && notran) {
  919. isolve = 2;
  920. }
  921. }
  922. if (mb <= 1 && nb <= 1 || mb >= *m && nb >= *n) {
  923. /* Use unblocked Level 2 solver */
  924. i__1 = isolve;
  925. for (iround = 1; iround <= i__1; ++iround) {
  926. *scale = 1.;
  927. dscale = 0.;
  928. dsum = 1.;
  929. pq = *m * *n;
  930. ztgsy2_(trans, &ifunc, m, n, &a[a_offset], lda, &b[b_offset], ldb,
  931. &c__[c_offset], ldc, &d__[d_offset], ldd, &e[e_offset],
  932. lde, &f[f_offset], ldf, scale, &dsum, &dscale, info);
  933. if (dscale != 0.) {
  934. if (*ijob == 1 || *ijob == 3) {
  935. *dif = sqrt((doublereal) ((*m << 1) * *n)) / (dscale *
  936. sqrt(dsum));
  937. } else {
  938. *dif = sqrt((doublereal) pq) / (dscale * sqrt(dsum));
  939. }
  940. }
  941. if (isolve == 2 && iround == 1) {
  942. if (notran) {
  943. ifunc = *ijob;
  944. }
  945. scale2 = *scale;
  946. zlacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m);
  947. zlacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m);
  948. zlaset_("F", m, n, &c_b1, &c_b1, &c__[c_offset], ldc);
  949. zlaset_("F", m, n, &c_b1, &c_b1, &f[f_offset], ldf)
  950. ;
  951. } else if (isolve == 2 && iround == 2) {
  952. zlacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc);
  953. zlacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf);
  954. *scale = scale2;
  955. }
  956. /* L30: */
  957. }
  958. return 0;
  959. }
  960. /* Determine block structure of A */
  961. p = 0;
  962. i__ = 1;
  963. L40:
  964. if (i__ > *m) {
  965. goto L50;
  966. }
  967. ++p;
  968. iwork[p] = i__;
  969. i__ += mb;
  970. if (i__ >= *m) {
  971. goto L50;
  972. }
  973. goto L40;
  974. L50:
  975. iwork[p + 1] = *m + 1;
  976. if (iwork[p] == iwork[p + 1]) {
  977. --p;
  978. }
  979. /* Determine block structure of B */
  980. q = p + 1;
  981. j = 1;
  982. L60:
  983. if (j > *n) {
  984. goto L70;
  985. }
  986. ++q;
  987. iwork[q] = j;
  988. j += nb;
  989. if (j >= *n) {
  990. goto L70;
  991. }
  992. goto L60;
  993. L70:
  994. iwork[q + 1] = *n + 1;
  995. if (iwork[q] == iwork[q + 1]) {
  996. --q;
  997. }
  998. if (notran) {
  999. i__1 = isolve;
  1000. for (iround = 1; iround <= i__1; ++iround) {
  1001. /* Solve (I, J) - subsystem */
  1002. /* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J) */
  1003. /* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J) */
  1004. /* for I = P, P - 1, ..., 1; J = 1, 2, ..., Q */
  1005. pq = 0;
  1006. *scale = 1.;
  1007. dscale = 0.;
  1008. dsum = 1.;
  1009. i__2 = q;
  1010. for (j = p + 2; j <= i__2; ++j) {
  1011. js = iwork[j];
  1012. je = iwork[j + 1] - 1;
  1013. nb = je - js + 1;
  1014. for (i__ = p; i__ >= 1; --i__) {
  1015. is = iwork[i__];
  1016. ie = iwork[i__ + 1] - 1;
  1017. mb = ie - is + 1;
  1018. ztgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1],
  1019. lda, &b[js + js * b_dim1], ldb, &c__[is + js *
  1020. c_dim1], ldc, &d__[is + is * d_dim1], ldd, &e[js
  1021. + js * e_dim1], lde, &f[is + js * f_dim1], ldf, &
  1022. scaloc, &dsum, &dscale, &linfo);
  1023. if (linfo > 0) {
  1024. *info = linfo;
  1025. }
  1026. pq += mb * nb;
  1027. if (scaloc != 1.) {
  1028. i__3 = js - 1;
  1029. for (k = 1; k <= i__3; ++k) {
  1030. z__1.r = scaloc, z__1.i = 0.;
  1031. zscal_(m, &z__1, &c__[k * c_dim1 + 1], &c__1);
  1032. z__1.r = scaloc, z__1.i = 0.;
  1033. zscal_(m, &z__1, &f[k * f_dim1 + 1], &c__1);
  1034. /* L80: */
  1035. }
  1036. i__3 = je;
  1037. for (k = js; k <= i__3; ++k) {
  1038. i__4 = is - 1;
  1039. z__1.r = scaloc, z__1.i = 0.;
  1040. zscal_(&i__4, &z__1, &c__[k * c_dim1 + 1], &c__1);
  1041. i__4 = is - 1;
  1042. z__1.r = scaloc, z__1.i = 0.;
  1043. zscal_(&i__4, &z__1, &f[k * f_dim1 + 1], &c__1);
  1044. /* L90: */
  1045. }
  1046. i__3 = je;
  1047. for (k = js; k <= i__3; ++k) {
  1048. i__4 = *m - ie;
  1049. z__1.r = scaloc, z__1.i = 0.;
  1050. zscal_(&i__4, &z__1, &c__[ie + 1 + k * c_dim1], &
  1051. c__1);
  1052. i__4 = *m - ie;
  1053. z__1.r = scaloc, z__1.i = 0.;
  1054. zscal_(&i__4, &z__1, &f[ie + 1 + k * f_dim1], &
  1055. c__1);
  1056. /* L100: */
  1057. }
  1058. i__3 = *n;
  1059. for (k = je + 1; k <= i__3; ++k) {
  1060. z__1.r = scaloc, z__1.i = 0.;
  1061. zscal_(m, &z__1, &c__[k * c_dim1 + 1], &c__1);
  1062. z__1.r = scaloc, z__1.i = 0.;
  1063. zscal_(m, &z__1, &f[k * f_dim1 + 1], &c__1);
  1064. /* L110: */
  1065. }
  1066. *scale *= scaloc;
  1067. }
  1068. /* Substitute R(I,J) and L(I,J) into remaining equation. */
  1069. if (i__ > 1) {
  1070. i__3 = is - 1;
  1071. zgemm_("N", "N", &i__3, &nb, &mb, &c_b44, &a[is *
  1072. a_dim1 + 1], lda, &c__[is + js * c_dim1], ldc,
  1073. &c_b45, &c__[js * c_dim1 + 1], ldc);
  1074. i__3 = is - 1;
  1075. zgemm_("N", "N", &i__3, &nb, &mb, &c_b44, &d__[is *
  1076. d_dim1 + 1], ldd, &c__[is + js * c_dim1], ldc,
  1077. &c_b45, &f[js * f_dim1 + 1], ldf);
  1078. }
  1079. if (j < q) {
  1080. i__3 = *n - je;
  1081. zgemm_("N", "N", &mb, &i__3, &nb, &c_b45, &f[is + js *
  1082. f_dim1], ldf, &b[js + (je + 1) * b_dim1],
  1083. ldb, &c_b45, &c__[is + (je + 1) * c_dim1],
  1084. ldc);
  1085. i__3 = *n - je;
  1086. zgemm_("N", "N", &mb, &i__3, &nb, &c_b45, &f[is + js *
  1087. f_dim1], ldf, &e[js + (je + 1) * e_dim1],
  1088. lde, &c_b45, &f[is + (je + 1) * f_dim1], ldf);
  1089. }
  1090. /* L120: */
  1091. }
  1092. /* L130: */
  1093. }
  1094. if (dscale != 0.) {
  1095. if (*ijob == 1 || *ijob == 3) {
  1096. *dif = sqrt((doublereal) ((*m << 1) * *n)) / (dscale *
  1097. sqrt(dsum));
  1098. } else {
  1099. *dif = sqrt((doublereal) pq) / (dscale * sqrt(dsum));
  1100. }
  1101. }
  1102. if (isolve == 2 && iround == 1) {
  1103. if (notran) {
  1104. ifunc = *ijob;
  1105. }
  1106. scale2 = *scale;
  1107. zlacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m);
  1108. zlacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m);
  1109. zlaset_("F", m, n, &c_b1, &c_b1, &c__[c_offset], ldc);
  1110. zlaset_("F", m, n, &c_b1, &c_b1, &f[f_offset], ldf)
  1111. ;
  1112. } else if (isolve == 2 && iround == 2) {
  1113. zlacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc);
  1114. zlacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf);
  1115. *scale = scale2;
  1116. }
  1117. /* L150: */
  1118. }
  1119. } else {
  1120. /* Solve transposed (I, J)-subsystem */
  1121. /* A(I, I)**H * R(I, J) + D(I, I)**H * L(I, J) = C(I, J) */
  1122. /* R(I, J) * B(J, J) + L(I, J) * E(J, J) = -F(I, J) */
  1123. /* for I = 1,2,..., P; J = Q, Q-1,..., 1 */
  1124. *scale = 1.;
  1125. i__1 = p;
  1126. for (i__ = 1; i__ <= i__1; ++i__) {
  1127. is = iwork[i__];
  1128. ie = iwork[i__ + 1] - 1;
  1129. mb = ie - is + 1;
  1130. i__2 = p + 2;
  1131. for (j = q; j >= i__2; --j) {
  1132. js = iwork[j];
  1133. je = iwork[j + 1] - 1;
  1134. nb = je - js + 1;
  1135. ztgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1], lda, &
  1136. b[js + js * b_dim1], ldb, &c__[is + js * c_dim1], ldc,
  1137. &d__[is + is * d_dim1], ldd, &e[js + js * e_dim1],
  1138. lde, &f[is + js * f_dim1], ldf, &scaloc, &dsum, &
  1139. dscale, &linfo);
  1140. if (linfo > 0) {
  1141. *info = linfo;
  1142. }
  1143. if (scaloc != 1.) {
  1144. i__3 = js - 1;
  1145. for (k = 1; k <= i__3; ++k) {
  1146. z__1.r = scaloc, z__1.i = 0.;
  1147. zscal_(m, &z__1, &c__[k * c_dim1 + 1], &c__1);
  1148. z__1.r = scaloc, z__1.i = 0.;
  1149. zscal_(m, &z__1, &f[k * f_dim1 + 1], &c__1);
  1150. /* L160: */
  1151. }
  1152. i__3 = je;
  1153. for (k = js; k <= i__3; ++k) {
  1154. i__4 = is - 1;
  1155. z__1.r = scaloc, z__1.i = 0.;
  1156. zscal_(&i__4, &z__1, &c__[k * c_dim1 + 1], &c__1);
  1157. i__4 = is - 1;
  1158. z__1.r = scaloc, z__1.i = 0.;
  1159. zscal_(&i__4, &z__1, &f[k * f_dim1 + 1], &c__1);
  1160. /* L170: */
  1161. }
  1162. i__3 = je;
  1163. for (k = js; k <= i__3; ++k) {
  1164. i__4 = *m - ie;
  1165. z__1.r = scaloc, z__1.i = 0.;
  1166. zscal_(&i__4, &z__1, &c__[ie + 1 + k * c_dim1], &c__1)
  1167. ;
  1168. i__4 = *m - ie;
  1169. z__1.r = scaloc, z__1.i = 0.;
  1170. zscal_(&i__4, &z__1, &f[ie + 1 + k * f_dim1], &c__1);
  1171. /* L180: */
  1172. }
  1173. i__3 = *n;
  1174. for (k = je + 1; k <= i__3; ++k) {
  1175. z__1.r = scaloc, z__1.i = 0.;
  1176. zscal_(m, &z__1, &c__[k * c_dim1 + 1], &c__1);
  1177. z__1.r = scaloc, z__1.i = 0.;
  1178. zscal_(m, &z__1, &f[k * f_dim1 + 1], &c__1);
  1179. /* L190: */
  1180. }
  1181. *scale *= scaloc;
  1182. }
  1183. /* Substitute R(I,J) and L(I,J) into remaining equation. */
  1184. if (j > p + 2) {
  1185. i__3 = js - 1;
  1186. zgemm_("N", "C", &mb, &i__3, &nb, &c_b45, &c__[is + js *
  1187. c_dim1], ldc, &b[js * b_dim1 + 1], ldb, &c_b45, &
  1188. f[is + f_dim1], ldf);
  1189. i__3 = js - 1;
  1190. zgemm_("N", "C", &mb, &i__3, &nb, &c_b45, &f[is + js *
  1191. f_dim1], ldf, &e[js * e_dim1 + 1], lde, &c_b45, &
  1192. f[is + f_dim1], ldf);
  1193. }
  1194. if (i__ < p) {
  1195. i__3 = *m - ie;
  1196. zgemm_("C", "N", &i__3, &nb, &mb, &c_b44, &a[is + (ie + 1)
  1197. * a_dim1], lda, &c__[is + js * c_dim1], ldc, &
  1198. c_b45, &c__[ie + 1 + js * c_dim1], ldc);
  1199. i__3 = *m - ie;
  1200. zgemm_("C", "N", &i__3, &nb, &mb, &c_b44, &d__[is + (ie +
  1201. 1) * d_dim1], ldd, &f[is + js * f_dim1], ldf, &
  1202. c_b45, &c__[ie + 1 + js * c_dim1], ldc);
  1203. }
  1204. /* L200: */
  1205. }
  1206. /* L210: */
  1207. }
  1208. }
  1209. work[1].r = (doublereal) lwmin, work[1].i = 0.;
  1210. return 0;
  1211. /* End of ZTGSYL */
  1212. } /* ztgsyl_ */