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dtgsja.c 37 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 doublereal c_b1 = 0.;
  487. static doublereal c_b15 = 1.;
  488. static integer c__1 = 1;
  489. static doublereal c_b44 = -1.;
  490. /* > \brief \b DTGSJA */
  491. /* =========== DOCUMENTATION =========== */
  492. /* Online html documentation available at */
  493. /* http://www.netlib.org/lapack/explore-html/ */
  494. /* > \htmlonly */
  495. /* > Download DTGSJA + dependencies */
  496. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtgsja.
  497. f"> */
  498. /* > [TGZ]</a> */
  499. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtgsja.
  500. f"> */
  501. /* > [ZIP]</a> */
  502. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtgsja.
  503. f"> */
  504. /* > [TXT]</a> */
  505. /* > \endhtmlonly */
  506. /* Definition: */
  507. /* =========== */
  508. /* SUBROUTINE DTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B, */
  509. /* LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV, */
  510. /* Q, LDQ, WORK, NCALL MYCYCLE, INFO ) */
  511. /* CHARACTER JOBQ, JOBU, JOBV */
  512. /* INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, */
  513. /* $ NCALL MYCYCLE, P */
  514. /* DOUBLE PRECISION TOLA, TOLB */
  515. /* DOUBLE PRECISION A( LDA, * ), ALPHA( * ), B( LDB, * ), */
  516. /* $ BETA( * ), Q( LDQ, * ), U( LDU, * ), */
  517. /* $ V( LDV, * ), WORK( * ) */
  518. /* > \par Purpose: */
  519. /* ============= */
  520. /* > */
  521. /* > \verbatim */
  522. /* > */
  523. /* > DTGSJA computes the generalized singular value decomposition (GSVD) */
  524. /* > of two real upper triangular (or trapezoidal) matrices A and B. */
  525. /* > */
  526. /* > On entry, it is assumed that matrices A and B have the following */
  527. /* > forms, which may be obtained by the preprocessing subroutine DGGSVP */
  528. /* > from a general M-by-N matrix A and P-by-N matrix B: */
  529. /* > */
  530. /* > N-K-L K L */
  531. /* > A = K ( 0 A12 A13 ) if M-K-L >= 0; */
  532. /* > L ( 0 0 A23 ) */
  533. /* > M-K-L ( 0 0 0 ) */
  534. /* > */
  535. /* > N-K-L K L */
  536. /* > A = K ( 0 A12 A13 ) if M-K-L < 0; */
  537. /* > M-K ( 0 0 A23 ) */
  538. /* > */
  539. /* > N-K-L K L */
  540. /* > B = L ( 0 0 B13 ) */
  541. /* > P-L ( 0 0 0 ) */
  542. /* > */
  543. /* > where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular */
  544. /* > upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, */
  545. /* > otherwise A23 is (M-K)-by-L upper trapezoidal. */
  546. /* > */
  547. /* > On exit, */
  548. /* > */
  549. /* > U**T *A*Q = D1*( 0 R ), V**T *B*Q = D2*( 0 R ), */
  550. /* > */
  551. /* > where U, V and Q are orthogonal matrices. */
  552. /* > R is a nonsingular upper triangular matrix, and D1 and D2 are */
  553. /* > ``diagonal'' matrices, which are of the following structures: */
  554. /* > */
  555. /* > If M-K-L >= 0, */
  556. /* > */
  557. /* > K L */
  558. /* > D1 = K ( I 0 ) */
  559. /* > L ( 0 C ) */
  560. /* > M-K-L ( 0 0 ) */
  561. /* > */
  562. /* > K L */
  563. /* > D2 = L ( 0 S ) */
  564. /* > P-L ( 0 0 ) */
  565. /* > */
  566. /* > N-K-L K L */
  567. /* > ( 0 R ) = K ( 0 R11 R12 ) K */
  568. /* > L ( 0 0 R22 ) L */
  569. /* > */
  570. /* > where */
  571. /* > */
  572. /* > C = diag( ALPHA(K+1), ... , ALPHA(K+L) ), */
  573. /* > S = diag( BETA(K+1), ... , BETA(K+L) ), */
  574. /* > C**2 + S**2 = I. */
  575. /* > */
  576. /* > R is stored in A(1:K+L,N-K-L+1:N) on exit. */
  577. /* > */
  578. /* > If M-K-L < 0, */
  579. /* > */
  580. /* > K M-K K+L-M */
  581. /* > D1 = K ( I 0 0 ) */
  582. /* > M-K ( 0 C 0 ) */
  583. /* > */
  584. /* > K M-K K+L-M */
  585. /* > D2 = M-K ( 0 S 0 ) */
  586. /* > K+L-M ( 0 0 I ) */
  587. /* > P-L ( 0 0 0 ) */
  588. /* > */
  589. /* > N-K-L K M-K K+L-M */
  590. /* > ( 0 R ) = K ( 0 R11 R12 R13 ) */
  591. /* > M-K ( 0 0 R22 R23 ) */
  592. /* > K+L-M ( 0 0 0 R33 ) */
  593. /* > */
  594. /* > where */
  595. /* > C = diag( ALPHA(K+1), ... , ALPHA(M) ), */
  596. /* > S = diag( BETA(K+1), ... , BETA(M) ), */
  597. /* > C**2 + S**2 = I. */
  598. /* > */
  599. /* > R = ( R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N) and R33 is stored */
  600. /* > ( 0 R22 R23 ) */
  601. /* > in B(M-K+1:L,N+M-K-L+1:N) on exit. */
  602. /* > */
  603. /* > The computation of the orthogonal transformation matrices U, V or Q */
  604. /* > is optional. These matrices may either be formed explicitly, or they */
  605. /* > may be postmultiplied into input matrices U1, V1, or Q1. */
  606. /* > \endverbatim */
  607. /* Arguments: */
  608. /* ========== */
  609. /* > \param[in] JOBU */
  610. /* > \verbatim */
  611. /* > JOBU is CHARACTER*1 */
  612. /* > = 'U': U must contain an orthogonal matrix U1 on entry, and */
  613. /* > the product U1*U is returned; */
  614. /* > = 'I': U is initialized to the unit matrix, and the */
  615. /* > orthogonal matrix U is returned; */
  616. /* > = 'N': U is not computed. */
  617. /* > \endverbatim */
  618. /* > */
  619. /* > \param[in] JOBV */
  620. /* > \verbatim */
  621. /* > JOBV is CHARACTER*1 */
  622. /* > = 'V': V must contain an orthogonal matrix V1 on entry, and */
  623. /* > the product V1*V is returned; */
  624. /* > = 'I': V is initialized to the unit matrix, and the */
  625. /* > orthogonal matrix V is returned; */
  626. /* > = 'N': V is not computed. */
  627. /* > \endverbatim */
  628. /* > */
  629. /* > \param[in] JOBQ */
  630. /* > \verbatim */
  631. /* > JOBQ is CHARACTER*1 */
  632. /* > = 'Q': Q must contain an orthogonal matrix Q1 on entry, and */
  633. /* > the product Q1*Q is returned; */
  634. /* > = 'I': Q is initialized to the unit matrix, and the */
  635. /* > orthogonal matrix Q is returned; */
  636. /* > = 'N': Q is not computed. */
  637. /* > \endverbatim */
  638. /* > */
  639. /* > \param[in] M */
  640. /* > \verbatim */
  641. /* > M is INTEGER */
  642. /* > The number of rows of the matrix A. M >= 0. */
  643. /* > \endverbatim */
  644. /* > */
  645. /* > \param[in] P */
  646. /* > \verbatim */
  647. /* > P is INTEGER */
  648. /* > The number of rows of the matrix B. P >= 0. */
  649. /* > \endverbatim */
  650. /* > */
  651. /* > \param[in] N */
  652. /* > \verbatim */
  653. /* > N is INTEGER */
  654. /* > The number of columns of the matrices A and B. N >= 0. */
  655. /* > \endverbatim */
  656. /* > */
  657. /* > \param[in] K */
  658. /* > \verbatim */
  659. /* > K is INTEGER */
  660. /* > \endverbatim */
  661. /* > */
  662. /* > \param[in] L */
  663. /* > \verbatim */
  664. /* > L is INTEGER */
  665. /* > */
  666. /* > K and L specify the subblocks in the input matrices A and B: */
  667. /* > A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,N-L+1:N) */
  668. /* > of A and B, whose GSVD is going to be computed by DTGSJA. */
  669. /* > See Further Details. */
  670. /* > \endverbatim */
  671. /* > */
  672. /* > \param[in,out] A */
  673. /* > \verbatim */
  674. /* > A is DOUBLE PRECISION array, dimension (LDA,N) */
  675. /* > On entry, the M-by-N matrix A. */
  676. /* > On exit, A(N-K+1:N,1:MIN(K+L,M) ) contains the triangular */
  677. /* > matrix R or part of R. See Purpose for details. */
  678. /* > \endverbatim */
  679. /* > */
  680. /* > \param[in] LDA */
  681. /* > \verbatim */
  682. /* > LDA is INTEGER */
  683. /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
  684. /* > \endverbatim */
  685. /* > */
  686. /* > \param[in,out] B */
  687. /* > \verbatim */
  688. /* > B is DOUBLE PRECISION array, dimension (LDB,N) */
  689. /* > On entry, the P-by-N matrix B. */
  690. /* > On exit, if necessary, B(M-K+1:L,N+M-K-L+1:N) contains */
  691. /* > a part of R. See Purpose for details. */
  692. /* > \endverbatim */
  693. /* > */
  694. /* > \param[in] LDB */
  695. /* > \verbatim */
  696. /* > LDB is INTEGER */
  697. /* > The leading dimension of the array B. LDB >= f2cmax(1,P). */
  698. /* > \endverbatim */
  699. /* > */
  700. /* > \param[in] TOLA */
  701. /* > \verbatim */
  702. /* > TOLA is DOUBLE PRECISION */
  703. /* > \endverbatim */
  704. /* > */
  705. /* > \param[in] TOLB */
  706. /* > \verbatim */
  707. /* > TOLB is DOUBLE PRECISION */
  708. /* > */
  709. /* > TOLA and TOLB are the convergence criteria for the Jacobi- */
  710. /* > Kogbetliantz iteration procedure. Generally, they are the */
  711. /* > same as used in the preprocessing step, say */
  712. /* > TOLA = f2cmax(M,N)*norm(A)*MAZHEPS, */
  713. /* > TOLB = f2cmax(P,N)*norm(B)*MAZHEPS. */
  714. /* > \endverbatim */
  715. /* > */
  716. /* > \param[out] ALPHA */
  717. /* > \verbatim */
  718. /* > ALPHA is DOUBLE PRECISION array, dimension (N) */
  719. /* > \endverbatim */
  720. /* > */
  721. /* > \param[out] BETA */
  722. /* > \verbatim */
  723. /* > BETA is DOUBLE PRECISION array, dimension (N) */
  724. /* > */
  725. /* > On exit, ALPHA and BETA contain the generalized singular */
  726. /* > value pairs of A and B; */
  727. /* > ALPHA(1:K) = 1, */
  728. /* > BETA(1:K) = 0, */
  729. /* > and if M-K-L >= 0, */
  730. /* > ALPHA(K+1:K+L) = diag(C), */
  731. /* > BETA(K+1:K+L) = diag(S), */
  732. /* > or if M-K-L < 0, */
  733. /* > ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0 */
  734. /* > BETA(K+1:M) = S, BETA(M+1:K+L) = 1. */
  735. /* > Furthermore, if K+L < N, */
  736. /* > ALPHA(K+L+1:N) = 0 and */
  737. /* > BETA(K+L+1:N) = 0. */
  738. /* > \endverbatim */
  739. /* > */
  740. /* > \param[in,out] U */
  741. /* > \verbatim */
  742. /* > U is DOUBLE PRECISION array, dimension (LDU,M) */
  743. /* > On entry, if JOBU = 'U', U must contain a matrix U1 (usually */
  744. /* > the orthogonal matrix returned by DGGSVP). */
  745. /* > On exit, */
  746. /* > if JOBU = 'I', U contains the orthogonal matrix U; */
  747. /* > if JOBU = 'U', U contains the product U1*U. */
  748. /* > If JOBU = 'N', U is not referenced. */
  749. /* > \endverbatim */
  750. /* > */
  751. /* > \param[in] LDU */
  752. /* > \verbatim */
  753. /* > LDU is INTEGER */
  754. /* > The leading dimension of the array U. LDU >= f2cmax(1,M) if */
  755. /* > JOBU = 'U'; LDU >= 1 otherwise. */
  756. /* > \endverbatim */
  757. /* > */
  758. /* > \param[in,out] V */
  759. /* > \verbatim */
  760. /* > V is DOUBLE PRECISION array, dimension (LDV,P) */
  761. /* > On entry, if JOBV = 'V', V must contain a matrix V1 (usually */
  762. /* > the orthogonal matrix returned by DGGSVP). */
  763. /* > On exit, */
  764. /* > if JOBV = 'I', V contains the orthogonal matrix V; */
  765. /* > if JOBV = 'V', V contains the product V1*V. */
  766. /* > If JOBV = 'N', V is not referenced. */
  767. /* > \endverbatim */
  768. /* > */
  769. /* > \param[in] LDV */
  770. /* > \verbatim */
  771. /* > LDV is INTEGER */
  772. /* > The leading dimension of the array V. LDV >= f2cmax(1,P) if */
  773. /* > JOBV = 'V'; LDV >= 1 otherwise. */
  774. /* > \endverbatim */
  775. /* > */
  776. /* > \param[in,out] Q */
  777. /* > \verbatim */
  778. /* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
  779. /* > On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually */
  780. /* > the orthogonal matrix returned by DGGSVP). */
  781. /* > On exit, */
  782. /* > if JOBQ = 'I', Q contains the orthogonal matrix Q; */
  783. /* > if JOBQ = 'Q', Q contains the product Q1*Q. */
  784. /* > If JOBQ = 'N', Q is not referenced. */
  785. /* > \endverbatim */
  786. /* > */
  787. /* > \param[in] LDQ */
  788. /* > \verbatim */
  789. /* > LDQ is INTEGER */
  790. /* > The leading dimension of the array Q. LDQ >= f2cmax(1,N) if */
  791. /* > JOBQ = 'Q'; LDQ >= 1 otherwise. */
  792. /* > \endverbatim */
  793. /* > */
  794. /* > \param[out] WORK */
  795. /* > \verbatim */
  796. /* > WORK is DOUBLE PRECISION array, dimension (2*N) */
  797. /* > \endverbatim */
  798. /* > */
  799. /* > \param[out] NCALL MYCYCLE */
  800. /* > \verbatim */
  801. /* > NCALL MYCYCLE is INTEGER */
  802. /* > The number of cycles required for convergence. */
  803. /* > \endverbatim */
  804. /* > */
  805. /* > \param[out] INFO */
  806. /* > \verbatim */
  807. /* > INFO is INTEGER */
  808. /* > = 0: successful exit */
  809. /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
  810. /* > = 1: the procedure does not converge after MAXIT cycles. */
  811. /* > \endverbatim */
  812. /* > */
  813. /* > \verbatim */
  814. /* > Internal Parameters */
  815. /* > =================== */
  816. /* > */
  817. /* > MAXIT INTEGER */
  818. /* > MAXIT specifies the total loops that the iterative procedure */
  819. /* > may take. If after MAXIT cycles, the routine fails to */
  820. /* > converge, we return INFO = 1. */
  821. /* > \endverbatim */
  822. /* Authors: */
  823. /* ======== */
  824. /* > \author Univ. of Tennessee */
  825. /* > \author Univ. of California Berkeley */
  826. /* > \author Univ. of Colorado Denver */
  827. /* > \author NAG Ltd. */
  828. /* > \date December 2016 */
  829. /* > \ingroup doubleOTHERcomputational */
  830. /* > \par Further Details: */
  831. /* ===================== */
  832. /* > */
  833. /* > \verbatim */
  834. /* > */
  835. /* > DTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce */
  836. /* > f2cmin(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L */
  837. /* > matrix B13 to the form: */
  838. /* > */
  839. /* > U1**T *A13*Q1 = C1*R1; V1**T *B13*Q1 = S1*R1, */
  840. /* > */
  841. /* > where U1, V1 and Q1 are orthogonal matrix, and Z**T is the transpose */
  842. /* > of Z. C1 and S1 are diagonal matrices satisfying */
  843. /* > */
  844. /* > C1**2 + S1**2 = I, */
  845. /* > */
  846. /* > and R1 is an L-by-L nonsingular upper triangular matrix. */
  847. /* > \endverbatim */
  848. /* > */
  849. /* ===================================================================== */
  850. /* Subroutine */ int dtgsja_(char *jobu, char *jobv, char *jobq, integer *m,
  851. integer *p, integer *n, integer *k, integer *l, doublereal *a,
  852. integer *lda, doublereal *b, integer *ldb, doublereal *tola,
  853. doublereal *tolb, doublereal *alpha, doublereal *beta, doublereal *u,
  854. integer *ldu, doublereal *v, integer *ldv, doublereal *q, integer *
  855. ldq, doublereal *work, integer *ncallmycycle, integer *info)
  856. {
  857. /* System generated locals */
  858. integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1,
  859. u_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4;
  860. doublereal d__1;
  861. /* Local variables */
  862. extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
  863. doublereal *, integer *, doublereal *, doublereal *);
  864. integer kcallmycycle, i__, j;
  865. doublereal gamma;
  866. extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
  867. integer *);
  868. extern logical lsame_(char *, char *);
  869. extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
  870. doublereal *, integer *);
  871. doublereal a1;
  872. logical initq;
  873. doublereal a2, a3, b1;
  874. logical initu, initv, wantq, upper;
  875. doublereal b2, b3;
  876. logical wantu, wantv;
  877. doublereal error, ssmin;
  878. extern /* Subroutine */ int dlags2_(logical *, doublereal *, doublereal *,
  879. doublereal *, doublereal *, doublereal *, doublereal *,
  880. doublereal *, doublereal *, doublereal *, doublereal *,
  881. doublereal *, doublereal *), dlapll_(integer *, doublereal *,
  882. integer *, doublereal *, integer *, doublereal *), dlartg_(
  883. doublereal *, doublereal *, doublereal *, doublereal *,
  884. doublereal *), dlaset_(char *, integer *, integer *, doublereal *,
  885. doublereal *, doublereal *, integer *), xerbla_(char *,
  886. integer *, ftnlen);
  887. // extern integer myhuge_(doublereal *);
  888. doublereal csq, csu, csv, snq, rwk, snu, snv;
  889. /* -- LAPACK computational routine (version 3.7.0) -- */
  890. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  891. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  892. /* December 2016 */
  893. /* ===================================================================== */
  894. /* Decode and test the input parameters */
  895. /* Parameter adjustments */
  896. a_dim1 = *lda;
  897. a_offset = 1 + a_dim1 * 1;
  898. a -= a_offset;
  899. b_dim1 = *ldb;
  900. b_offset = 1 + b_dim1 * 1;
  901. b -= b_offset;
  902. --alpha;
  903. --beta;
  904. u_dim1 = *ldu;
  905. u_offset = 1 + u_dim1 * 1;
  906. u -= u_offset;
  907. v_dim1 = *ldv;
  908. v_offset = 1 + v_dim1 * 1;
  909. v -= v_offset;
  910. q_dim1 = *ldq;
  911. q_offset = 1 + q_dim1 * 1;
  912. q -= q_offset;
  913. --work;
  914. /* Function Body */
  915. initu = lsame_(jobu, "I");
  916. wantu = initu || lsame_(jobu, "U");
  917. initv = lsame_(jobv, "I");
  918. wantv = initv || lsame_(jobv, "V");
  919. initq = lsame_(jobq, "I");
  920. wantq = initq || lsame_(jobq, "Q");
  921. *info = 0;
  922. if (! (initu || wantu || lsame_(jobu, "N"))) {
  923. *info = -1;
  924. } else if (! (initv || wantv || lsame_(jobv, "N")))
  925. {
  926. *info = -2;
  927. } else if (! (initq || wantq || lsame_(jobq, "N")))
  928. {
  929. *info = -3;
  930. } else if (*m < 0) {
  931. *info = -4;
  932. } else if (*p < 0) {
  933. *info = -5;
  934. } else if (*n < 0) {
  935. *info = -6;
  936. } else if (*lda < f2cmax(1,*m)) {
  937. *info = -10;
  938. } else if (*ldb < f2cmax(1,*p)) {
  939. *info = -12;
  940. } else if (*ldu < 1 || wantu && *ldu < *m) {
  941. *info = -18;
  942. } else if (*ldv < 1 || wantv && *ldv < *p) {
  943. *info = -20;
  944. } else if (*ldq < 1 || wantq && *ldq < *n) {
  945. *info = -22;
  946. }
  947. if (*info != 0) {
  948. i__1 = -(*info);
  949. xerbla_("DTGSJA", &i__1, (ftnlen)6);
  950. return 0;
  951. }
  952. /* Initialize U, V and Q, if necessary */
  953. if (initu) {
  954. dlaset_("Full", m, m, &c_b1, &c_b15, &u[u_offset], ldu);
  955. }
  956. if (initv) {
  957. dlaset_("Full", p, p, &c_b1, &c_b15, &v[v_offset], ldv);
  958. }
  959. if (initq) {
  960. dlaset_("Full", n, n, &c_b1, &c_b15, &q[q_offset], ldq);
  961. }
  962. /* Loop until convergence */
  963. upper = FALSE_;
  964. for (kcallmycycle = 1; kcallmycycle <= 40; ++kcallmycycle) {
  965. upper = ! upper;
  966. i__1 = *l - 1;
  967. for (i__ = 1; i__ <= i__1; ++i__) {
  968. i__2 = *l;
  969. for (j = i__ + 1; j <= i__2; ++j) {
  970. a1 = 0.;
  971. a2 = 0.;
  972. a3 = 0.;
  973. if (*k + i__ <= *m) {
  974. a1 = a[*k + i__ + (*n - *l + i__) * a_dim1];
  975. }
  976. if (*k + j <= *m) {
  977. a3 = a[*k + j + (*n - *l + j) * a_dim1];
  978. }
  979. b1 = b[i__ + (*n - *l + i__) * b_dim1];
  980. b3 = b[j + (*n - *l + j) * b_dim1];
  981. if (upper) {
  982. if (*k + i__ <= *m) {
  983. a2 = a[*k + i__ + (*n - *l + j) * a_dim1];
  984. }
  985. b2 = b[i__ + (*n - *l + j) * b_dim1];
  986. } else {
  987. if (*k + j <= *m) {
  988. a2 = a[*k + j + (*n - *l + i__) * a_dim1];
  989. }
  990. b2 = b[j + (*n - *l + i__) * b_dim1];
  991. }
  992. dlags2_(&upper, &a1, &a2, &a3, &b1, &b2, &b3, &csu, &snu, &
  993. csv, &snv, &csq, &snq);
  994. /* Update (K+I)-th and (K+J)-th rows of matrix A: U**T *A */
  995. if (*k + j <= *m) {
  996. drot_(l, &a[*k + j + (*n - *l + 1) * a_dim1], lda, &a[*k
  997. + i__ + (*n - *l + 1) * a_dim1], lda, &csu, &snu);
  998. }
  999. /* Update I-th and J-th rows of matrix B: V**T *B */
  1000. drot_(l, &b[j + (*n - *l + 1) * b_dim1], ldb, &b[i__ + (*n - *
  1001. l + 1) * b_dim1], ldb, &csv, &snv);
  1002. /* Update (N-L+I)-th and (N-L+J)-th columns of matrices */
  1003. /* A and B: A*Q and B*Q */
  1004. /* Computing MIN */
  1005. i__4 = *k + *l;
  1006. i__3 = f2cmin(i__4,*m);
  1007. drot_(&i__3, &a[(*n - *l + j) * a_dim1 + 1], &c__1, &a[(*n - *
  1008. l + i__) * a_dim1 + 1], &c__1, &csq, &snq);
  1009. drot_(l, &b[(*n - *l + j) * b_dim1 + 1], &c__1, &b[(*n - *l +
  1010. i__) * b_dim1 + 1], &c__1, &csq, &snq);
  1011. if (upper) {
  1012. if (*k + i__ <= *m) {
  1013. a[*k + i__ + (*n - *l + j) * a_dim1] = 0.;
  1014. }
  1015. b[i__ + (*n - *l + j) * b_dim1] = 0.;
  1016. } else {
  1017. if (*k + j <= *m) {
  1018. a[*k + j + (*n - *l + i__) * a_dim1] = 0.;
  1019. }
  1020. b[j + (*n - *l + i__) * b_dim1] = 0.;
  1021. }
  1022. /* Update orthogonal matrices U, V, Q, if desired. */
  1023. if (wantu && *k + j <= *m) {
  1024. drot_(m, &u[(*k + j) * u_dim1 + 1], &c__1, &u[(*k + i__) *
  1025. u_dim1 + 1], &c__1, &csu, &snu);
  1026. }
  1027. if (wantv) {
  1028. drot_(p, &v[j * v_dim1 + 1], &c__1, &v[i__ * v_dim1 + 1],
  1029. &c__1, &csv, &snv);
  1030. }
  1031. if (wantq) {
  1032. drot_(n, &q[(*n - *l + j) * q_dim1 + 1], &c__1, &q[(*n - *
  1033. l + i__) * q_dim1 + 1], &c__1, &csq, &snq);
  1034. }
  1035. /* L10: */
  1036. }
  1037. /* L20: */
  1038. }
  1039. if (! upper) {
  1040. /* The matrices A13 and B13 were lower triangular at the start */
  1041. /* of the cycle, and are now upper triangular. */
  1042. /* Convergence test: test the parallelism of the corresponding */
  1043. /* rows of A and B. */
  1044. error = 0.;
  1045. /* Computing MIN */
  1046. i__2 = *l, i__3 = *m - *k;
  1047. i__1 = f2cmin(i__2,i__3);
  1048. for (i__ = 1; i__ <= i__1; ++i__) {
  1049. i__2 = *l - i__ + 1;
  1050. dcopy_(&i__2, &a[*k + i__ + (*n - *l + i__) * a_dim1], lda, &
  1051. work[1], &c__1);
  1052. i__2 = *l - i__ + 1;
  1053. dcopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &work[*
  1054. l + 1], &c__1);
  1055. i__2 = *l - i__ + 1;
  1056. dlapll_(&i__2, &work[1], &c__1, &work[*l + 1], &c__1, &ssmin);
  1057. error = f2cmax(error,ssmin);
  1058. /* L30: */
  1059. }
  1060. if (abs(error) <= f2cmin(*tola,*tolb)) {
  1061. goto L50;
  1062. }
  1063. }
  1064. /* End of cycle loop */
  1065. /* L40: */
  1066. }
  1067. /* The algorithm has not converged after MAXIT cycles. */
  1068. *info = 1;
  1069. goto L100;
  1070. L50:
  1071. /* If ERROR <= MIN(TOLA,TOLB), then the algorithm has converged. */
  1072. /* Compute the generalized singular value pairs (ALPHA, BETA), and */
  1073. /* set the triangular matrix R to array A. */
  1074. i__1 = *k;
  1075. for (i__ = 1; i__ <= i__1; ++i__) {
  1076. alpha[i__] = 1.;
  1077. beta[i__] = 0.;
  1078. /* L60: */
  1079. }
  1080. /* Computing MIN */
  1081. i__2 = *l, i__3 = *m - *k;
  1082. i__1 = f2cmin(i__2,i__3);
  1083. for (i__ = 1; i__ <= i__1; ++i__) {
  1084. a1 = a[*k + i__ + (*n - *l + i__) * a_dim1];
  1085. b1 = b[i__ + (*n - *l + i__) * b_dim1];
  1086. gamma = b1 / a1;
  1087. if (gamma <= (doublereal) myhuge_(&c_b1) && gamma >= -((doublereal)
  1088. myhuge_(&c_b1))) {
  1089. /* change sign if necessary */
  1090. if (gamma < 0.) {
  1091. i__2 = *l - i__ + 1;
  1092. dscal_(&i__2, &c_b44, &b[i__ + (*n - *l + i__) * b_dim1], ldb)
  1093. ;
  1094. if (wantv) {
  1095. dscal_(p, &c_b44, &v[i__ * v_dim1 + 1], &c__1);
  1096. }
  1097. }
  1098. d__1 = abs(gamma);
  1099. dlartg_(&d__1, &c_b15, &beta[*k + i__], &alpha[*k + i__], &rwk);
  1100. if (alpha[*k + i__] >= beta[*k + i__]) {
  1101. i__2 = *l - i__ + 1;
  1102. d__1 = 1. / alpha[*k + i__];
  1103. dscal_(&i__2, &d__1, &a[*k + i__ + (*n - *l + i__) * a_dim1],
  1104. lda);
  1105. } else {
  1106. i__2 = *l - i__ + 1;
  1107. d__1 = 1. / beta[*k + i__];
  1108. dscal_(&i__2, &d__1, &b[i__ + (*n - *l + i__) * b_dim1], ldb);
  1109. i__2 = *l - i__ + 1;
  1110. dcopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k
  1111. + i__ + (*n - *l + i__) * a_dim1], lda);
  1112. }
  1113. } else {
  1114. alpha[*k + i__] = 0.;
  1115. beta[*k + i__] = 1.;
  1116. i__2 = *l - i__ + 1;
  1117. dcopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k +
  1118. i__ + (*n - *l + i__) * a_dim1], lda);
  1119. }
  1120. /* L70: */
  1121. }
  1122. /* Post-assignment */
  1123. i__1 = *k + *l;
  1124. for (i__ = *m + 1; i__ <= i__1; ++i__) {
  1125. alpha[i__] = 0.;
  1126. beta[i__] = 1.;
  1127. /* L80: */
  1128. }
  1129. if (*k + *l < *n) {
  1130. i__1 = *n;
  1131. for (i__ = *k + *l + 1; i__ <= i__1; ++i__) {
  1132. alpha[i__] = 0.;
  1133. beta[i__] = 0.;
  1134. /* L90: */
  1135. }
  1136. }
  1137. L100:
  1138. *ncallmycycle = kcallmycycle;
  1139. return 0;
  1140. /* End of DTGSJA */
  1141. } /* dtgsja_ */