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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 blasint logical;
  52. typedef char logical1;
  53. typedef char integer1;
  54. #define TRUE_ (1)
  55. #define FALSE_ (0)
  56. /* Extern is for use with -E */
  57. #ifndef Extern
  58. #define Extern extern
  59. #endif
  60. /* I/O stuff */
  61. typedef int flag;
  62. typedef int ftnlen;
  63. typedef int ftnint;
  64. /*external read, write*/
  65. typedef struct
  66. { flag cierr;
  67. ftnint ciunit;
  68. flag ciend;
  69. char *cifmt;
  70. ftnint cirec;
  71. } cilist;
  72. /*internal read, write*/
  73. typedef struct
  74. { flag icierr;
  75. char *iciunit;
  76. flag iciend;
  77. char *icifmt;
  78. ftnint icirlen;
  79. ftnint icirnum;
  80. } icilist;
  81. /*open*/
  82. typedef struct
  83. { flag oerr;
  84. ftnint ounit;
  85. char *ofnm;
  86. ftnlen ofnmlen;
  87. char *osta;
  88. char *oacc;
  89. char *ofm;
  90. ftnint orl;
  91. char *oblnk;
  92. } olist;
  93. /*close*/
  94. typedef struct
  95. { flag cerr;
  96. ftnint cunit;
  97. char *csta;
  98. } cllist;
  99. /*rewind, backspace, endfile*/
  100. typedef struct
  101. { flag aerr;
  102. ftnint aunit;
  103. } alist;
  104. /* inquire */
  105. typedef struct
  106. { flag inerr;
  107. ftnint inunit;
  108. char *infile;
  109. ftnlen infilen;
  110. ftnint *inex; /*parameters in standard's order*/
  111. ftnint *inopen;
  112. ftnint *innum;
  113. ftnint *innamed;
  114. char *inname;
  115. ftnlen innamlen;
  116. char *inacc;
  117. ftnlen inacclen;
  118. char *inseq;
  119. ftnlen inseqlen;
  120. char *indir;
  121. ftnlen indirlen;
  122. char *infmt;
  123. ftnlen infmtlen;
  124. char *inform;
  125. ftnint informlen;
  126. char *inunf;
  127. ftnlen inunflen;
  128. ftnint *inrecl;
  129. ftnint *innrec;
  130. char *inblank;
  131. ftnlen inblanklen;
  132. } inlist;
  133. #define VOID void
  134. union Multitype { /* for multiple entry points */
  135. integer1 g;
  136. shortint h;
  137. integer i;
  138. /* longint j; */
  139. real r;
  140. doublereal d;
  141. complex c;
  142. doublecomplex z;
  143. };
  144. typedef union Multitype Multitype;
  145. struct Vardesc { /* for Namelist */
  146. char *name;
  147. char *addr;
  148. ftnlen *dims;
  149. int type;
  150. };
  151. typedef struct Vardesc Vardesc;
  152. struct Namelist {
  153. char *name;
  154. Vardesc **vars;
  155. int nvars;
  156. };
  157. typedef struct Namelist Namelist;
  158. #define abs(x) ((x) >= 0 ? (x) : -(x))
  159. #define dabs(x) (fabs(x))
  160. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  161. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  162. #define dmin(a,b) (f2cmin(a,b))
  163. #define dmax(a,b) (f2cmax(a,b))
  164. #define bit_test(a,b) ((a) >> (b) & 1)
  165. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  166. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  167. #define abort_() { sig_die("Fortran abort routine called", 1); }
  168. #define c_abs(z) (cabsf(Cf(z)))
  169. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  170. #ifdef _MSC_VER
  171. #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]);}
  172. #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]);}
  173. #else
  174. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  175. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  176. #endif
  177. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  178. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  179. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  180. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  181. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  182. #define d_abs(x) (fabs(*(x)))
  183. #define d_acos(x) (acos(*(x)))
  184. #define d_asin(x) (asin(*(x)))
  185. #define d_atan(x) (atan(*(x)))
  186. #define d_atn2(x, y) (atan2(*(x),*(y)))
  187. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  188. #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
  189. #define d_cos(x) (cos(*(x)))
  190. #define d_cosh(x) (cosh(*(x)))
  191. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  192. #define d_exp(x) (exp(*(x)))
  193. #define d_imag(z) (cimag(Cd(z)))
  194. #define r_imag(z) (cimagf(Cf(z)))
  195. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  196. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  197. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  198. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  199. #define d_log(x) (log(*(x)))
  200. #define d_mod(x, y) (fmod(*(x), *(y)))
  201. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  202. #define d_nint(x) u_nint(*(x))
  203. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  204. #define d_sign(a,b) u_sign(*(a),*(b))
  205. #define r_sign(a,b) u_sign(*(a),*(b))
  206. #define d_sin(x) (sin(*(x)))
  207. #define d_sinh(x) (sinh(*(x)))
  208. #define d_sqrt(x) (sqrt(*(x)))
  209. #define d_tan(x) (tan(*(x)))
  210. #define d_tanh(x) (tanh(*(x)))
  211. #define i_abs(x) abs(*(x))
  212. #define i_dnnt(x) ((integer)u_nint(*(x)))
  213. #define i_len(s, n) (n)
  214. #define i_nint(x) ((integer)u_nint(*(x)))
  215. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  216. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  217. #define pow_si(B,E) spow_ui(*(B),*(E))
  218. #define pow_ri(B,E) spow_ui(*(B),*(E))
  219. #define pow_di(B,E) dpow_ui(*(B),*(E))
  220. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  221. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  222. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  223. #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++ = ' '; }
  224. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  225. #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]; }
  226. #define sig_die(s, kill) { exit(1); }
  227. #define s_stop(s, n) {exit(0);}
  228. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  229. #define z_abs(z) (cabs(Cd(z)))
  230. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  231. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  232. #define myexit_() break;
  233. #define mycycle_() continue;
  234. #define myceiling_(w) {ceil(w)}
  235. #define myhuge_(w) {HUGE_VAL}
  236. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  237. #define mymaxloc_(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  238. /* procedure parameter types for -A and -C++ */
  239. #ifdef __cplusplus
  240. typedef logical (*L_fp)(...);
  241. #else
  242. typedef logical (*L_fp)();
  243. #endif
  244. static float spow_ui(float x, integer n) {
  245. float pow=1.0; unsigned long int u;
  246. if(n != 0) {
  247. if(n < 0) n = -n, x = 1/x;
  248. for(u = n; ; ) {
  249. if(u & 01) pow *= x;
  250. if(u >>= 1) x *= x;
  251. else break;
  252. }
  253. }
  254. return pow;
  255. }
  256. static double dpow_ui(double x, integer n) {
  257. double pow=1.0; unsigned long int u;
  258. if(n != 0) {
  259. if(n < 0) n = -n, x = 1/x;
  260. for(u = n; ; ) {
  261. if(u & 01) pow *= x;
  262. if(u >>= 1) x *= x;
  263. else break;
  264. }
  265. }
  266. return pow;
  267. }
  268. #ifdef _MSC_VER
  269. static _Fcomplex cpow_ui(complex x, integer n) {
  270. complex pow={1.0,0.0}; unsigned long int u;
  271. if(n != 0) {
  272. if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
  273. for(u = n; ; ) {
  274. if(u & 01) pow.r *= x.r, pow.i *= x.i;
  275. if(u >>= 1) x.r *= x.r, x.i *= x.i;
  276. else break;
  277. }
  278. }
  279. _Fcomplex p={pow.r, pow.i};
  280. return p;
  281. }
  282. #else
  283. static _Complex float cpow_ui(_Complex float x, integer n) {
  284. _Complex float pow=1.0; unsigned long int u;
  285. if(n != 0) {
  286. if(n < 0) n = -n, x = 1/x;
  287. for(u = n; ; ) {
  288. if(u & 01) pow *= x;
  289. if(u >>= 1) x *= x;
  290. else break;
  291. }
  292. }
  293. return pow;
  294. }
  295. #endif
  296. #ifdef _MSC_VER
  297. static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
  298. _Dcomplex pow={1.0,0.0}; unsigned long int u;
  299. if(n != 0) {
  300. if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
  301. for(u = n; ; ) {
  302. if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
  303. if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
  304. else break;
  305. }
  306. }
  307. _Dcomplex p = {pow._Val[0], pow._Val[1]};
  308. return p;
  309. }
  310. #else
  311. static _Complex double zpow_ui(_Complex double x, integer n) {
  312. _Complex double pow=1.0; unsigned long int u;
  313. if(n != 0) {
  314. if(n < 0) n = -n, x = 1/x;
  315. for(u = n; ; ) {
  316. if(u & 01) pow *= x;
  317. if(u >>= 1) x *= x;
  318. else break;
  319. }
  320. }
  321. return pow;
  322. }
  323. #endif
  324. static integer pow_ii(integer x, integer n) {
  325. integer pow; unsigned long int u;
  326. if (n <= 0) {
  327. if (n == 0 || x == 1) pow = 1;
  328. else if (x != -1) pow = x == 0 ? 1/x : 0;
  329. else n = -n;
  330. }
  331. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  332. u = n;
  333. for(pow = 1; ; ) {
  334. if(u & 01) pow *= x;
  335. if(u >>= 1) x *= x;
  336. else break;
  337. }
  338. }
  339. return pow;
  340. }
  341. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  342. {
  343. double m; integer i, mi;
  344. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  345. if (w[i-1]>m) mi=i ,m=w[i-1];
  346. return mi-s+1;
  347. }
  348. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  349. {
  350. float m; integer i, mi;
  351. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  352. if (w[i-1]>m) mi=i ,m=w[i-1];
  353. return mi-s+1;
  354. }
  355. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  356. integer n = *n_, incx = *incx_, incy = *incy_, i;
  357. #ifdef _MSC_VER
  358. _Fcomplex zdotc = {0.0, 0.0};
  359. if (incx == 1 && incy == 1) {
  360. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  361. zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
  362. zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
  363. }
  364. } else {
  365. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  366. zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
  367. zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
  368. }
  369. }
  370. pCf(z) = zdotc;
  371. }
  372. #else
  373. _Complex float zdotc = 0.0;
  374. if (incx == 1 && incy == 1) {
  375. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  376. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  377. }
  378. } else {
  379. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  380. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  381. }
  382. }
  383. pCf(z) = zdotc;
  384. }
  385. #endif
  386. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  387. integer n = *n_, incx = *incx_, incy = *incy_, i;
  388. #ifdef _MSC_VER
  389. _Dcomplex zdotc = {0.0, 0.0};
  390. if (incx == 1 && incy == 1) {
  391. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  392. zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
  393. zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
  394. }
  395. } else {
  396. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  397. zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
  398. zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
  399. }
  400. }
  401. pCd(z) = zdotc;
  402. }
  403. #else
  404. _Complex double zdotc = 0.0;
  405. if (incx == 1 && incy == 1) {
  406. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  407. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  408. }
  409. } else {
  410. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  411. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  412. }
  413. }
  414. pCd(z) = zdotc;
  415. }
  416. #endif
  417. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  418. integer n = *n_, incx = *incx_, incy = *incy_, i;
  419. #ifdef _MSC_VER
  420. _Fcomplex zdotc = {0.0, 0.0};
  421. if (incx == 1 && incy == 1) {
  422. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  423. zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
  424. zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
  425. }
  426. } else {
  427. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  428. zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
  429. zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
  430. }
  431. }
  432. pCf(z) = zdotc;
  433. }
  434. #else
  435. _Complex float zdotc = 0.0;
  436. if (incx == 1 && incy == 1) {
  437. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  438. zdotc += Cf(&x[i]) * Cf(&y[i]);
  439. }
  440. } else {
  441. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  442. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  443. }
  444. }
  445. pCf(z) = zdotc;
  446. }
  447. #endif
  448. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  449. integer n = *n_, incx = *incx_, incy = *incy_, i;
  450. #ifdef _MSC_VER
  451. _Dcomplex zdotc = {0.0, 0.0};
  452. if (incx == 1 && incy == 1) {
  453. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  454. zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
  455. zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
  456. }
  457. } else {
  458. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  459. zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
  460. zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
  461. }
  462. }
  463. pCd(z) = zdotc;
  464. }
  465. #else
  466. _Complex double zdotc = 0.0;
  467. if (incx == 1 && incy == 1) {
  468. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  469. zdotc += Cd(&x[i]) * Cd(&y[i]);
  470. }
  471. } else {
  472. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  473. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  474. }
  475. }
  476. pCd(z) = zdotc;
  477. }
  478. #endif
  479. /* -- translated by f2c (version 20000121).
  480. You must link the resulting object file with the libraries:
  481. -lf2c -lm (in that order)
  482. */
  483. /* Table of constant values */
  484. static doublereal c_b1 = 0.;
  485. static doublereal c_b15 = 1.;
  486. static integer c__1 = 1;
  487. static doublereal c_b44 = -1.;
  488. /* > \brief \b DTGSJA */
  489. /* =========== DOCUMENTATION =========== */
  490. /* Online html documentation available at */
  491. /* http://www.netlib.org/lapack/explore-html/ */
  492. /* > \htmlonly */
  493. /* > Download DTGSJA + dependencies */
  494. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtgsja.
  495. f"> */
  496. /* > [TGZ]</a> */
  497. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtgsja.
  498. f"> */
  499. /* > [ZIP]</a> */
  500. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtgsja.
  501. f"> */
  502. /* > [TXT]</a> */
  503. /* > \endhtmlonly */
  504. /* Definition: */
  505. /* =========== */
  506. /* SUBROUTINE DTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B, */
  507. /* LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV, */
  508. /* Q, LDQ, WORK, NCALL MYCYCLE, INFO ) */
  509. /* CHARACTER JOBQ, JOBU, JOBV */
  510. /* INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, */
  511. /* $ NCALL MYCYCLE, P */
  512. /* DOUBLE PRECISION TOLA, TOLB */
  513. /* DOUBLE PRECISION A( LDA, * ), ALPHA( * ), B( LDB, * ), */
  514. /* $ BETA( * ), Q( LDQ, * ), U( LDU, * ), */
  515. /* $ V( LDV, * ), WORK( * ) */
  516. /* > \par Purpose: */
  517. /* ============= */
  518. /* > */
  519. /* > \verbatim */
  520. /* > */
  521. /* > DTGSJA computes the generalized singular value decomposition (GSVD) */
  522. /* > of two real upper triangular (or trapezoidal) matrices A and B. */
  523. /* > */
  524. /* > On entry, it is assumed that matrices A and B have the following */
  525. /* > forms, which may be obtained by the preprocessing subroutine DGGSVP */
  526. /* > from a general M-by-N matrix A and P-by-N matrix B: */
  527. /* > */
  528. /* > N-K-L K L */
  529. /* > A = K ( 0 A12 A13 ) if M-K-L >= 0; */
  530. /* > L ( 0 0 A23 ) */
  531. /* > M-K-L ( 0 0 0 ) */
  532. /* > */
  533. /* > N-K-L K L */
  534. /* > A = K ( 0 A12 A13 ) if M-K-L < 0; */
  535. /* > M-K ( 0 0 A23 ) */
  536. /* > */
  537. /* > N-K-L K L */
  538. /* > B = L ( 0 0 B13 ) */
  539. /* > P-L ( 0 0 0 ) */
  540. /* > */
  541. /* > where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular */
  542. /* > upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, */
  543. /* > otherwise A23 is (M-K)-by-L upper trapezoidal. */
  544. /* > */
  545. /* > On exit, */
  546. /* > */
  547. /* > U**T *A*Q = D1*( 0 R ), V**T *B*Q = D2*( 0 R ), */
  548. /* > */
  549. /* > where U, V and Q are orthogonal matrices. */
  550. /* > R is a nonsingular upper triangular matrix, and D1 and D2 are */
  551. /* > ``diagonal'' matrices, which are of the following structures: */
  552. /* > */
  553. /* > If M-K-L >= 0, */
  554. /* > */
  555. /* > K L */
  556. /* > D1 = K ( I 0 ) */
  557. /* > L ( 0 C ) */
  558. /* > M-K-L ( 0 0 ) */
  559. /* > */
  560. /* > K L */
  561. /* > D2 = L ( 0 S ) */
  562. /* > P-L ( 0 0 ) */
  563. /* > */
  564. /* > N-K-L K L */
  565. /* > ( 0 R ) = K ( 0 R11 R12 ) K */
  566. /* > L ( 0 0 R22 ) L */
  567. /* > */
  568. /* > where */
  569. /* > */
  570. /* > C = diag( ALPHA(K+1), ... , ALPHA(K+L) ), */
  571. /* > S = diag( BETA(K+1), ... , BETA(K+L) ), */
  572. /* > C**2 + S**2 = I. */
  573. /* > */
  574. /* > R is stored in A(1:K+L,N-K-L+1:N) on exit. */
  575. /* > */
  576. /* > If M-K-L < 0, */
  577. /* > */
  578. /* > K M-K K+L-M */
  579. /* > D1 = K ( I 0 0 ) */
  580. /* > M-K ( 0 C 0 ) */
  581. /* > */
  582. /* > K M-K K+L-M */
  583. /* > D2 = M-K ( 0 S 0 ) */
  584. /* > K+L-M ( 0 0 I ) */
  585. /* > P-L ( 0 0 0 ) */
  586. /* > */
  587. /* > N-K-L K M-K K+L-M */
  588. /* > ( 0 R ) = K ( 0 R11 R12 R13 ) */
  589. /* > M-K ( 0 0 R22 R23 ) */
  590. /* > K+L-M ( 0 0 0 R33 ) */
  591. /* > */
  592. /* > where */
  593. /* > C = diag( ALPHA(K+1), ... , ALPHA(M) ), */
  594. /* > S = diag( BETA(K+1), ... , BETA(M) ), */
  595. /* > C**2 + S**2 = I. */
  596. /* > */
  597. /* > R = ( R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N) and R33 is stored */
  598. /* > ( 0 R22 R23 ) */
  599. /* > in B(M-K+1:L,N+M-K-L+1:N) on exit. */
  600. /* > */
  601. /* > The computation of the orthogonal transformation matrices U, V or Q */
  602. /* > is optional. These matrices may either be formed explicitly, or they */
  603. /* > may be postmultiplied into input matrices U1, V1, or Q1. */
  604. /* > \endverbatim */
  605. /* Arguments: */
  606. /* ========== */
  607. /* > \param[in] JOBU */
  608. /* > \verbatim */
  609. /* > JOBU is CHARACTER*1 */
  610. /* > = 'U': U must contain an orthogonal matrix U1 on entry, and */
  611. /* > the product U1*U is returned; */
  612. /* > = 'I': U is initialized to the unit matrix, and the */
  613. /* > orthogonal matrix U is returned; */
  614. /* > = 'N': U is not computed. */
  615. /* > \endverbatim */
  616. /* > */
  617. /* > \param[in] JOBV */
  618. /* > \verbatim */
  619. /* > JOBV is CHARACTER*1 */
  620. /* > = 'V': V must contain an orthogonal matrix V1 on entry, and */
  621. /* > the product V1*V is returned; */
  622. /* > = 'I': V is initialized to the unit matrix, and the */
  623. /* > orthogonal matrix V is returned; */
  624. /* > = 'N': V is not computed. */
  625. /* > \endverbatim */
  626. /* > */
  627. /* > \param[in] JOBQ */
  628. /* > \verbatim */
  629. /* > JOBQ is CHARACTER*1 */
  630. /* > = 'Q': Q must contain an orthogonal matrix Q1 on entry, and */
  631. /* > the product Q1*Q is returned; */
  632. /* > = 'I': Q is initialized to the unit matrix, and the */
  633. /* > orthogonal matrix Q is returned; */
  634. /* > = 'N': Q is not computed. */
  635. /* > \endverbatim */
  636. /* > */
  637. /* > \param[in] M */
  638. /* > \verbatim */
  639. /* > M is INTEGER */
  640. /* > The number of rows of the matrix A. M >= 0. */
  641. /* > \endverbatim */
  642. /* > */
  643. /* > \param[in] P */
  644. /* > \verbatim */
  645. /* > P is INTEGER */
  646. /* > The number of rows of the matrix B. P >= 0. */
  647. /* > \endverbatim */
  648. /* > */
  649. /* > \param[in] N */
  650. /* > \verbatim */
  651. /* > N is INTEGER */
  652. /* > The number of columns of the matrices A and B. N >= 0. */
  653. /* > \endverbatim */
  654. /* > */
  655. /* > \param[in] K */
  656. /* > \verbatim */
  657. /* > K is INTEGER */
  658. /* > \endverbatim */
  659. /* > */
  660. /* > \param[in] L */
  661. /* > \verbatim */
  662. /* > L is INTEGER */
  663. /* > */
  664. /* > K and L specify the subblocks in the input matrices A and B: */
  665. /* > A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,N-L+1:N) */
  666. /* > of A and B, whose GSVD is going to be computed by DTGSJA. */
  667. /* > See Further Details. */
  668. /* > \endverbatim */
  669. /* > */
  670. /* > \param[in,out] A */
  671. /* > \verbatim */
  672. /* > A is DOUBLE PRECISION array, dimension (LDA,N) */
  673. /* > On entry, the M-by-N matrix A. */
  674. /* > On exit, A(N-K+1:N,1:MIN(K+L,M) ) contains the triangular */
  675. /* > matrix R or part of R. See Purpose for details. */
  676. /* > \endverbatim */
  677. /* > */
  678. /* > \param[in] LDA */
  679. /* > \verbatim */
  680. /* > LDA is INTEGER */
  681. /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
  682. /* > \endverbatim */
  683. /* > */
  684. /* > \param[in,out] B */
  685. /* > \verbatim */
  686. /* > B is DOUBLE PRECISION array, dimension (LDB,N) */
  687. /* > On entry, the P-by-N matrix B. */
  688. /* > On exit, if necessary, B(M-K+1:L,N+M-K-L+1:N) contains */
  689. /* > a part of R. See Purpose for details. */
  690. /* > \endverbatim */
  691. /* > */
  692. /* > \param[in] LDB */
  693. /* > \verbatim */
  694. /* > LDB is INTEGER */
  695. /* > The leading dimension of the array B. LDB >= f2cmax(1,P). */
  696. /* > \endverbatim */
  697. /* > */
  698. /* > \param[in] TOLA */
  699. /* > \verbatim */
  700. /* > TOLA is DOUBLE PRECISION */
  701. /* > \endverbatim */
  702. /* > */
  703. /* > \param[in] TOLB */
  704. /* > \verbatim */
  705. /* > TOLB is DOUBLE PRECISION */
  706. /* > */
  707. /* > TOLA and TOLB are the convergence criteria for the Jacobi- */
  708. /* > Kogbetliantz iteration procedure. Generally, they are the */
  709. /* > same as used in the preprocessing step, say */
  710. /* > TOLA = f2cmax(M,N)*norm(A)*MAZHEPS, */
  711. /* > TOLB = f2cmax(P,N)*norm(B)*MAZHEPS. */
  712. /* > \endverbatim */
  713. /* > */
  714. /* > \param[out] ALPHA */
  715. /* > \verbatim */
  716. /* > ALPHA is DOUBLE PRECISION array, dimension (N) */
  717. /* > \endverbatim */
  718. /* > */
  719. /* > \param[out] BETA */
  720. /* > \verbatim */
  721. /* > BETA is DOUBLE PRECISION array, dimension (N) */
  722. /* > */
  723. /* > On exit, ALPHA and BETA contain the generalized singular */
  724. /* > value pairs of A and B; */
  725. /* > ALPHA(1:K) = 1, */
  726. /* > BETA(1:K) = 0, */
  727. /* > and if M-K-L >= 0, */
  728. /* > ALPHA(K+1:K+L) = diag(C), */
  729. /* > BETA(K+1:K+L) = diag(S), */
  730. /* > or if M-K-L < 0, */
  731. /* > ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0 */
  732. /* > BETA(K+1:M) = S, BETA(M+1:K+L) = 1. */
  733. /* > Furthermore, if K+L < N, */
  734. /* > ALPHA(K+L+1:N) = 0 and */
  735. /* > BETA(K+L+1:N) = 0. */
  736. /* > \endverbatim */
  737. /* > */
  738. /* > \param[in,out] U */
  739. /* > \verbatim */
  740. /* > U is DOUBLE PRECISION array, dimension (LDU,M) */
  741. /* > On entry, if JOBU = 'U', U must contain a matrix U1 (usually */
  742. /* > the orthogonal matrix returned by DGGSVP). */
  743. /* > On exit, */
  744. /* > if JOBU = 'I', U contains the orthogonal matrix U; */
  745. /* > if JOBU = 'U', U contains the product U1*U. */
  746. /* > If JOBU = 'N', U is not referenced. */
  747. /* > \endverbatim */
  748. /* > */
  749. /* > \param[in] LDU */
  750. /* > \verbatim */
  751. /* > LDU is INTEGER */
  752. /* > The leading dimension of the array U. LDU >= f2cmax(1,M) if */
  753. /* > JOBU = 'U'; LDU >= 1 otherwise. */
  754. /* > \endverbatim */
  755. /* > */
  756. /* > \param[in,out] V */
  757. /* > \verbatim */
  758. /* > V is DOUBLE PRECISION array, dimension (LDV,P) */
  759. /* > On entry, if JOBV = 'V', V must contain a matrix V1 (usually */
  760. /* > the orthogonal matrix returned by DGGSVP). */
  761. /* > On exit, */
  762. /* > if JOBV = 'I', V contains the orthogonal matrix V; */
  763. /* > if JOBV = 'V', V contains the product V1*V. */
  764. /* > If JOBV = 'N', V is not referenced. */
  765. /* > \endverbatim */
  766. /* > */
  767. /* > \param[in] LDV */
  768. /* > \verbatim */
  769. /* > LDV is INTEGER */
  770. /* > The leading dimension of the array V. LDV >= f2cmax(1,P) if */
  771. /* > JOBV = 'V'; LDV >= 1 otherwise. */
  772. /* > \endverbatim */
  773. /* > */
  774. /* > \param[in,out] Q */
  775. /* > \verbatim */
  776. /* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
  777. /* > On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually */
  778. /* > the orthogonal matrix returned by DGGSVP). */
  779. /* > On exit, */
  780. /* > if JOBQ = 'I', Q contains the orthogonal matrix Q; */
  781. /* > if JOBQ = 'Q', Q contains the product Q1*Q. */
  782. /* > If JOBQ = 'N', Q is not referenced. */
  783. /* > \endverbatim */
  784. /* > */
  785. /* > \param[in] LDQ */
  786. /* > \verbatim */
  787. /* > LDQ is INTEGER */
  788. /* > The leading dimension of the array Q. LDQ >= f2cmax(1,N) if */
  789. /* > JOBQ = 'Q'; LDQ >= 1 otherwise. */
  790. /* > \endverbatim */
  791. /* > */
  792. /* > \param[out] WORK */
  793. /* > \verbatim */
  794. /* > WORK is DOUBLE PRECISION array, dimension (2*N) */
  795. /* > \endverbatim */
  796. /* > */
  797. /* > \param[out] NCALL MYCYCLE */
  798. /* > \verbatim */
  799. /* > NCALL MYCYCLE is INTEGER */
  800. /* > The number of cycles required for convergence. */
  801. /* > \endverbatim */
  802. /* > */
  803. /* > \param[out] INFO */
  804. /* > \verbatim */
  805. /* > INFO is INTEGER */
  806. /* > = 0: successful exit */
  807. /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
  808. /* > = 1: the procedure does not converge after MAXIT cycles. */
  809. /* > \endverbatim */
  810. /* > */
  811. /* > \verbatim */
  812. /* > Internal Parameters */
  813. /* > =================== */
  814. /* > */
  815. /* > MAXIT INTEGER */
  816. /* > MAXIT specifies the total loops that the iterative procedure */
  817. /* > may take. If after MAXIT cycles, the routine fails to */
  818. /* > converge, we return INFO = 1. */
  819. /* > \endverbatim */
  820. /* Authors: */
  821. /* ======== */
  822. /* > \author Univ. of Tennessee */
  823. /* > \author Univ. of California Berkeley */
  824. /* > \author Univ. of Colorado Denver */
  825. /* > \author NAG Ltd. */
  826. /* > \date December 2016 */
  827. /* > \ingroup doubleOTHERcomputational */
  828. /* > \par Further Details: */
  829. /* ===================== */
  830. /* > */
  831. /* > \verbatim */
  832. /* > */
  833. /* > DTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce */
  834. /* > f2cmin(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L */
  835. /* > matrix B13 to the form: */
  836. /* > */
  837. /* > U1**T *A13*Q1 = C1*R1; V1**T *B13*Q1 = S1*R1, */
  838. /* > */
  839. /* > where U1, V1 and Q1 are orthogonal matrix, and Z**T is the transpose */
  840. /* > of Z. C1 and S1 are diagonal matrices satisfying */
  841. /* > */
  842. /* > C1**2 + S1**2 = I, */
  843. /* > */
  844. /* > and R1 is an L-by-L nonsingular upper triangular matrix. */
  845. /* > \endverbatim */
  846. /* > */
  847. /* ===================================================================== */
  848. /* Subroutine */ void dtgsja_(char *jobu, char *jobv, char *jobq, integer *m,
  849. integer *p, integer *n, integer *k, integer *l, doublereal *a,
  850. integer *lda, doublereal *b, integer *ldb, doublereal *tola,
  851. doublereal *tolb, doublereal *alpha, doublereal *beta, doublereal *u,
  852. integer *ldu, doublereal *v, integer *ldv, doublereal *q, integer *
  853. ldq, doublereal *work, integer *ncallmycycle, integer *info)
  854. {
  855. /* System generated locals */
  856. integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1,
  857. u_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4;
  858. doublereal d__1;
  859. /* Local variables */
  860. extern /* Subroutine */ void drot_(integer *, doublereal *, integer *,
  861. doublereal *, integer *, doublereal *, doublereal *);
  862. integer kcallmycycle, i__, j;
  863. doublereal gamma;
  864. extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
  865. integer *);
  866. extern logical lsame_(char *, char *);
  867. extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *,
  868. doublereal *, integer *);
  869. doublereal a1;
  870. logical initq;
  871. doublereal a2, a3, b1;
  872. logical initu, initv, wantq, upper;
  873. doublereal b2, b3;
  874. logical wantu, wantv;
  875. doublereal error, ssmin;
  876. extern /* Subroutine */ void dlags2_(logical *, doublereal *, doublereal *,
  877. doublereal *, doublereal *, doublereal *, doublereal *,
  878. doublereal *, doublereal *, doublereal *, doublereal *,
  879. doublereal *, doublereal *), dlapll_(integer *, doublereal *,
  880. integer *, doublereal *, integer *, doublereal *), dlartg_(
  881. doublereal *, doublereal *, doublereal *, doublereal *,
  882. doublereal *), dlaset_(char *, integer *, integer *, doublereal *,
  883. doublereal *, doublereal *, integer *);
  884. extern int xerbla_(char *, integer *, ftnlen);
  885. // extern integer myhuge_(doublereal *);
  886. doublereal csq, csu, csv, snq, rwk, snu, snv;
  887. /* -- LAPACK computational routine (version 3.7.0) -- */
  888. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  889. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  890. /* December 2016 */
  891. /* ===================================================================== */
  892. /* Decode and test the input parameters */
  893. /* Parameter adjustments */
  894. a_dim1 = *lda;
  895. a_offset = 1 + a_dim1 * 1;
  896. a -= a_offset;
  897. b_dim1 = *ldb;
  898. b_offset = 1 + b_dim1 * 1;
  899. b -= b_offset;
  900. --alpha;
  901. --beta;
  902. u_dim1 = *ldu;
  903. u_offset = 1 + u_dim1 * 1;
  904. u -= u_offset;
  905. v_dim1 = *ldv;
  906. v_offset = 1 + v_dim1 * 1;
  907. v -= v_offset;
  908. q_dim1 = *ldq;
  909. q_offset = 1 + q_dim1 * 1;
  910. q -= q_offset;
  911. --work;
  912. /* Function Body */
  913. initu = lsame_(jobu, "I");
  914. wantu = initu || lsame_(jobu, "U");
  915. initv = lsame_(jobv, "I");
  916. wantv = initv || lsame_(jobv, "V");
  917. initq = lsame_(jobq, "I");
  918. wantq = initq || lsame_(jobq, "Q");
  919. *info = 0;
  920. if (! (initu || wantu || lsame_(jobu, "N"))) {
  921. *info = -1;
  922. } else if (! (initv || wantv || lsame_(jobv, "N")))
  923. {
  924. *info = -2;
  925. } else if (! (initq || wantq || lsame_(jobq, "N")))
  926. {
  927. *info = -3;
  928. } else if (*m < 0) {
  929. *info = -4;
  930. } else if (*p < 0) {
  931. *info = -5;
  932. } else if (*n < 0) {
  933. *info = -6;
  934. } else if (*lda < f2cmax(1,*m)) {
  935. *info = -10;
  936. } else if (*ldb < f2cmax(1,*p)) {
  937. *info = -12;
  938. } else if (*ldu < 1 || wantu && *ldu < *m) {
  939. *info = -18;
  940. } else if (*ldv < 1 || wantv && *ldv < *p) {
  941. *info = -20;
  942. } else if (*ldq < 1 || wantq && *ldq < *n) {
  943. *info = -22;
  944. }
  945. if (*info != 0) {
  946. i__1 = -(*info);
  947. xerbla_("DTGSJA", &i__1, (ftnlen)6);
  948. return;
  949. }
  950. /* Initialize U, V and Q, if necessary */
  951. if (initu) {
  952. dlaset_("Full", m, m, &c_b1, &c_b15, &u[u_offset], ldu);
  953. }
  954. if (initv) {
  955. dlaset_("Full", p, p, &c_b1, &c_b15, &v[v_offset], ldv);
  956. }
  957. if (initq) {
  958. dlaset_("Full", n, n, &c_b1, &c_b15, &q[q_offset], ldq);
  959. }
  960. /* Loop until convergence */
  961. upper = FALSE_;
  962. for (kcallmycycle = 1; kcallmycycle <= 40; ++kcallmycycle) {
  963. upper = ! upper;
  964. i__1 = *l - 1;
  965. for (i__ = 1; i__ <= i__1; ++i__) {
  966. i__2 = *l;
  967. for (j = i__ + 1; j <= i__2; ++j) {
  968. a1 = 0.;
  969. a2 = 0.;
  970. a3 = 0.;
  971. if (*k + i__ <= *m) {
  972. a1 = a[*k + i__ + (*n - *l + i__) * a_dim1];
  973. }
  974. if (*k + j <= *m) {
  975. a3 = a[*k + j + (*n - *l + j) * a_dim1];
  976. }
  977. b1 = b[i__ + (*n - *l + i__) * b_dim1];
  978. b3 = b[j + (*n - *l + j) * b_dim1];
  979. if (upper) {
  980. if (*k + i__ <= *m) {
  981. a2 = a[*k + i__ + (*n - *l + j) * a_dim1];
  982. }
  983. b2 = b[i__ + (*n - *l + j) * b_dim1];
  984. } else {
  985. if (*k + j <= *m) {
  986. a2 = a[*k + j + (*n - *l + i__) * a_dim1];
  987. }
  988. b2 = b[j + (*n - *l + i__) * b_dim1];
  989. }
  990. dlags2_(&upper, &a1, &a2, &a3, &b1, &b2, &b3, &csu, &snu, &
  991. csv, &snv, &csq, &snq);
  992. /* Update (K+I)-th and (K+J)-th rows of matrix A: U**T *A */
  993. if (*k + j <= *m) {
  994. drot_(l, &a[*k + j + (*n - *l + 1) * a_dim1], lda, &a[*k
  995. + i__ + (*n - *l + 1) * a_dim1], lda, &csu, &snu);
  996. }
  997. /* Update I-th and J-th rows of matrix B: V**T *B */
  998. drot_(l, &b[j + (*n - *l + 1) * b_dim1], ldb, &b[i__ + (*n - *
  999. l + 1) * b_dim1], ldb, &csv, &snv);
  1000. /* Update (N-L+I)-th and (N-L+J)-th columns of matrices */
  1001. /* A and B: A*Q and B*Q */
  1002. /* Computing MIN */
  1003. i__4 = *k + *l;
  1004. i__3 = f2cmin(i__4,*m);
  1005. drot_(&i__3, &a[(*n - *l + j) * a_dim1 + 1], &c__1, &a[(*n - *
  1006. l + i__) * a_dim1 + 1], &c__1, &csq, &snq);
  1007. drot_(l, &b[(*n - *l + j) * b_dim1 + 1], &c__1, &b[(*n - *l +
  1008. i__) * b_dim1 + 1], &c__1, &csq, &snq);
  1009. if (upper) {
  1010. if (*k + i__ <= *m) {
  1011. a[*k + i__ + (*n - *l + j) * a_dim1] = 0.;
  1012. }
  1013. b[i__ + (*n - *l + j) * b_dim1] = 0.;
  1014. } else {
  1015. if (*k + j <= *m) {
  1016. a[*k + j + (*n - *l + i__) * a_dim1] = 0.;
  1017. }
  1018. b[j + (*n - *l + i__) * b_dim1] = 0.;
  1019. }
  1020. /* Update orthogonal matrices U, V, Q, if desired. */
  1021. if (wantu && *k + j <= *m) {
  1022. drot_(m, &u[(*k + j) * u_dim1 + 1], &c__1, &u[(*k + i__) *
  1023. u_dim1 + 1], &c__1, &csu, &snu);
  1024. }
  1025. if (wantv) {
  1026. drot_(p, &v[j * v_dim1 + 1], &c__1, &v[i__ * v_dim1 + 1],
  1027. &c__1, &csv, &snv);
  1028. }
  1029. if (wantq) {
  1030. drot_(n, &q[(*n - *l + j) * q_dim1 + 1], &c__1, &q[(*n - *
  1031. l + i__) * q_dim1 + 1], &c__1, &csq, &snq);
  1032. }
  1033. /* L10: */
  1034. }
  1035. /* L20: */
  1036. }
  1037. if (! upper) {
  1038. /* The matrices A13 and B13 were lower triangular at the start */
  1039. /* of the cycle, and are now upper triangular. */
  1040. /* Convergence test: test the parallelism of the corresponding */
  1041. /* rows of A and B. */
  1042. error = 0.;
  1043. /* Computing MIN */
  1044. i__2 = *l, i__3 = *m - *k;
  1045. i__1 = f2cmin(i__2,i__3);
  1046. for (i__ = 1; i__ <= i__1; ++i__) {
  1047. i__2 = *l - i__ + 1;
  1048. dcopy_(&i__2, &a[*k + i__ + (*n - *l + i__) * a_dim1], lda, &
  1049. work[1], &c__1);
  1050. i__2 = *l - i__ + 1;
  1051. dcopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &work[*
  1052. l + 1], &c__1);
  1053. i__2 = *l - i__ + 1;
  1054. dlapll_(&i__2, &work[1], &c__1, &work[*l + 1], &c__1, &ssmin);
  1055. error = f2cmax(error,ssmin);
  1056. /* L30: */
  1057. }
  1058. if (abs(error) <= f2cmin(*tola,*tolb)) {
  1059. goto L50;
  1060. }
  1061. }
  1062. /* End of cycle loop */
  1063. /* L40: */
  1064. }
  1065. /* The algorithm has not converged after MAXIT cycles. */
  1066. *info = 1;
  1067. goto L100;
  1068. L50:
  1069. /* If ERROR <= MIN(TOLA,TOLB), then the algorithm has converged. */
  1070. /* Compute the generalized singular value pairs (ALPHA, BETA), and */
  1071. /* set the triangular matrix R to array A. */
  1072. i__1 = *k;
  1073. for (i__ = 1; i__ <= i__1; ++i__) {
  1074. alpha[i__] = 1.;
  1075. beta[i__] = 0.;
  1076. /* L60: */
  1077. }
  1078. /* Computing MIN */
  1079. i__2 = *l, i__3 = *m - *k;
  1080. i__1 = f2cmin(i__2,i__3);
  1081. for (i__ = 1; i__ <= i__1; ++i__) {
  1082. a1 = a[*k + i__ + (*n - *l + i__) * a_dim1];
  1083. b1 = b[i__ + (*n - *l + i__) * b_dim1];
  1084. gamma = b1 / a1;
  1085. if (gamma <= (doublereal) myhuge_(&c_b1) && gamma >= -((doublereal)
  1086. myhuge_(&c_b1))) {
  1087. /* change sign if necessary */
  1088. if (gamma < 0.) {
  1089. i__2 = *l - i__ + 1;
  1090. dscal_(&i__2, &c_b44, &b[i__ + (*n - *l + i__) * b_dim1], ldb)
  1091. ;
  1092. if (wantv) {
  1093. dscal_(p, &c_b44, &v[i__ * v_dim1 + 1], &c__1);
  1094. }
  1095. }
  1096. d__1 = abs(gamma);
  1097. dlartg_(&d__1, &c_b15, &beta[*k + i__], &alpha[*k + i__], &rwk);
  1098. if (alpha[*k + i__] >= beta[*k + i__]) {
  1099. i__2 = *l - i__ + 1;
  1100. d__1 = 1. / alpha[*k + i__];
  1101. dscal_(&i__2, &d__1, &a[*k + i__ + (*n - *l + i__) * a_dim1],
  1102. lda);
  1103. } else {
  1104. i__2 = *l - i__ + 1;
  1105. d__1 = 1. / beta[*k + i__];
  1106. dscal_(&i__2, &d__1, &b[i__ + (*n - *l + i__) * b_dim1], ldb);
  1107. i__2 = *l - i__ + 1;
  1108. dcopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k
  1109. + i__ + (*n - *l + i__) * a_dim1], lda);
  1110. }
  1111. } else {
  1112. alpha[*k + i__] = 0.;
  1113. beta[*k + i__] = 1.;
  1114. i__2 = *l - i__ + 1;
  1115. dcopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k +
  1116. i__ + (*n - *l + i__) * a_dim1], lda);
  1117. }
  1118. /* L70: */
  1119. }
  1120. /* Post-assignment */
  1121. i__1 = *k + *l;
  1122. for (i__ = *m + 1; i__ <= i__1; ++i__) {
  1123. alpha[i__] = 0.;
  1124. beta[i__] = 1.;
  1125. /* L80: */
  1126. }
  1127. if (*k + *l < *n) {
  1128. i__1 = *n;
  1129. for (i__ = *k + *l + 1; i__ <= i__1; ++i__) {
  1130. alpha[i__] = 0.;
  1131. beta[i__] = 0.;
  1132. /* L90: */
  1133. }
  1134. }
  1135. L100:
  1136. *ncallmycycle = kcallmycycle;
  1137. return;
  1138. /* End of DTGSJA */
  1139. } /* dtgsja_ */