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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]/df(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 complex c_b1 = {0.f,0.f};
  487. static complex c_b2 = {1.f,0.f};
  488. static integer c__6 = 6;
  489. static integer c__0 = 0;
  490. static integer c__2 = 2;
  491. static integer c_n1 = -1;
  492. static integer c__1 = 1;
  493. /* > \brief <b> CGESVD computes the singular value decomposition (SVD) for GE matrices</b> */
  494. /* =========== DOCUMENTATION =========== */
  495. /* Online html documentation available at */
  496. /* http://www.netlib.org/lapack/explore-html/ */
  497. /* > \htmlonly */
  498. /* > Download CGESVD + dependencies */
  499. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgesvd.
  500. f"> */
  501. /* > [TGZ]</a> */
  502. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgesvd.
  503. f"> */
  504. /* > [ZIP]</a> */
  505. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgesvd.
  506. f"> */
  507. /* > [TXT]</a> */
  508. /* > \endhtmlonly */
  509. /* Definition: */
  510. /* =========== */
  511. /* SUBROUTINE CGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, */
  512. /* WORK, LWORK, RWORK, INFO ) */
  513. /* CHARACTER JOBU, JOBVT */
  514. /* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */
  515. /* REAL RWORK( * ), S( * ) */
  516. /* COMPLEX A( LDA, * ), U( LDU, * ), VT( LDVT, * ), */
  517. /* $ WORK( * ) */
  518. /* > \par Purpose: */
  519. /* ============= */
  520. /* > */
  521. /* > \verbatim */
  522. /* > */
  523. /* > CGESVD computes the singular value decomposition (SVD) of a complex */
  524. /* > M-by-N matrix A, optionally computing the left and/or right singular */
  525. /* > vectors. The SVD is written */
  526. /* > */
  527. /* > A = U * SIGMA * conjugate-transpose(V) */
  528. /* > */
  529. /* > where SIGMA is an M-by-N matrix which is zero except for its */
  530. /* > f2cmin(m,n) diagonal elements, U is an M-by-M unitary matrix, and */
  531. /* > V is an N-by-N unitary matrix. The diagonal elements of SIGMA */
  532. /* > are the singular values of A; they are real and non-negative, and */
  533. /* > are returned in descending order. The first f2cmin(m,n) columns of */
  534. /* > U and V are the left and right singular vectors of A. */
  535. /* > */
  536. /* > Note that the routine returns V**H, not V. */
  537. /* > \endverbatim */
  538. /* Arguments: */
  539. /* ========== */
  540. /* > \param[in] JOBU */
  541. /* > \verbatim */
  542. /* > JOBU is CHARACTER*1 */
  543. /* > Specifies options for computing all or part of the matrix U: */
  544. /* > = 'A': all M columns of U are returned in array U: */
  545. /* > = 'S': the first f2cmin(m,n) columns of U (the left singular */
  546. /* > vectors) are returned in the array U; */
  547. /* > = 'O': the first f2cmin(m,n) columns of U (the left singular */
  548. /* > vectors) are overwritten on the array A; */
  549. /* > = 'N': no columns of U (no left singular vectors) are */
  550. /* > computed. */
  551. /* > \endverbatim */
  552. /* > */
  553. /* > \param[in] JOBVT */
  554. /* > \verbatim */
  555. /* > JOBVT is CHARACTER*1 */
  556. /* > Specifies options for computing all or part of the matrix */
  557. /* > V**H: */
  558. /* > = 'A': all N rows of V**H are returned in the array VT; */
  559. /* > = 'S': the first f2cmin(m,n) rows of V**H (the right singular */
  560. /* > vectors) are returned in the array VT; */
  561. /* > = 'O': the first f2cmin(m,n) rows of V**H (the right singular */
  562. /* > vectors) are overwritten on the array A; */
  563. /* > = 'N': no rows of V**H (no right singular vectors) are */
  564. /* > computed. */
  565. /* > */
  566. /* > JOBVT and JOBU cannot both be 'O'. */
  567. /* > \endverbatim */
  568. /* > */
  569. /* > \param[in] M */
  570. /* > \verbatim */
  571. /* > M is INTEGER */
  572. /* > The number of rows of the input matrix A. M >= 0. */
  573. /* > \endverbatim */
  574. /* > */
  575. /* > \param[in] N */
  576. /* > \verbatim */
  577. /* > N is INTEGER */
  578. /* > The number of columns of the input matrix A. N >= 0. */
  579. /* > \endverbatim */
  580. /* > */
  581. /* > \param[in,out] A */
  582. /* > \verbatim */
  583. /* > A is COMPLEX array, dimension (LDA,N) */
  584. /* > On entry, the M-by-N matrix A. */
  585. /* > On exit, */
  586. /* > if JOBU = 'O', A is overwritten with the first f2cmin(m,n) */
  587. /* > columns of U (the left singular vectors, */
  588. /* > stored columnwise); */
  589. /* > if JOBVT = 'O', A is overwritten with the first f2cmin(m,n) */
  590. /* > rows of V**H (the right singular vectors, */
  591. /* > stored rowwise); */
  592. /* > if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A */
  593. /* > are destroyed. */
  594. /* > \endverbatim */
  595. /* > */
  596. /* > \param[in] LDA */
  597. /* > \verbatim */
  598. /* > LDA is INTEGER */
  599. /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
  600. /* > \endverbatim */
  601. /* > */
  602. /* > \param[out] S */
  603. /* > \verbatim */
  604. /* > S is REAL array, dimension (f2cmin(M,N)) */
  605. /* > The singular values of A, sorted so that S(i) >= S(i+1). */
  606. /* > \endverbatim */
  607. /* > */
  608. /* > \param[out] U */
  609. /* > \verbatim */
  610. /* > U is COMPLEX array, dimension (LDU,UCOL) */
  611. /* > (LDU,M) if JOBU = 'A' or (LDU,f2cmin(M,N)) if JOBU = 'S'. */
  612. /* > If JOBU = 'A', U contains the M-by-M unitary matrix U; */
  613. /* > if JOBU = 'S', U contains the first f2cmin(m,n) columns of U */
  614. /* > (the left singular vectors, stored columnwise); */
  615. /* > if JOBU = 'N' or 'O', U is not referenced. */
  616. /* > \endverbatim */
  617. /* > */
  618. /* > \param[in] LDU */
  619. /* > \verbatim */
  620. /* > LDU is INTEGER */
  621. /* > The leading dimension of the array U. LDU >= 1; if */
  622. /* > JOBU = 'S' or 'A', LDU >= M. */
  623. /* > \endverbatim */
  624. /* > */
  625. /* > \param[out] VT */
  626. /* > \verbatim */
  627. /* > VT is COMPLEX array, dimension (LDVT,N) */
  628. /* > If JOBVT = 'A', VT contains the N-by-N unitary matrix */
  629. /* > V**H; */
  630. /* > if JOBVT = 'S', VT contains the first f2cmin(m,n) rows of */
  631. /* > V**H (the right singular vectors, stored rowwise); */
  632. /* > if JOBVT = 'N' or 'O', VT is not referenced. */
  633. /* > \endverbatim */
  634. /* > */
  635. /* > \param[in] LDVT */
  636. /* > \verbatim */
  637. /* > LDVT is INTEGER */
  638. /* > The leading dimension of the array VT. LDVT >= 1; if */
  639. /* > JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= f2cmin(M,N). */
  640. /* > \endverbatim */
  641. /* > */
  642. /* > \param[out] WORK */
  643. /* > \verbatim */
  644. /* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
  645. /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
  646. /* > \endverbatim */
  647. /* > */
  648. /* > \param[in] LWORK */
  649. /* > \verbatim */
  650. /* > LWORK is INTEGER */
  651. /* > The dimension of the array WORK. */
  652. /* > LWORK >= MAX(1,2*MIN(M,N)+MAX(M,N)). */
  653. /* > For good performance, LWORK should generally be larger. */
  654. /* > */
  655. /* > If LWORK = -1, then a workspace query is assumed; the routine */
  656. /* > only calculates the optimal size of the WORK array, returns */
  657. /* > this value as the first entry of the WORK array, and no error */
  658. /* > message related to LWORK is issued by XERBLA. */
  659. /* > \endverbatim */
  660. /* > */
  661. /* > \param[out] RWORK */
  662. /* > \verbatim */
  663. /* > RWORK is REAL array, dimension (5*f2cmin(M,N)) */
  664. /* > On exit, if INFO > 0, RWORK(1:MIN(M,N)-1) contains the */
  665. /* > unconverged superdiagonal elements of an upper bidiagonal */
  666. /* > matrix B whose diagonal is in S (not necessarily sorted). */
  667. /* > B satisfies A = U * B * VT, so it has the same singular */
  668. /* > values as A, and singular vectors related by U and VT. */
  669. /* > \endverbatim */
  670. /* > */
  671. /* > \param[out] INFO */
  672. /* > \verbatim */
  673. /* > INFO is INTEGER */
  674. /* > = 0: successful exit. */
  675. /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
  676. /* > > 0: if CBDSQR did not converge, INFO specifies how many */
  677. /* > superdiagonals of an intermediate bidiagonal form B */
  678. /* > did not converge to zero. See the description of RWORK */
  679. /* > above for details. */
  680. /* > \endverbatim */
  681. /* Authors: */
  682. /* ======== */
  683. /* > \author Univ. of Tennessee */
  684. /* > \author Univ. of California Berkeley */
  685. /* > \author Univ. of Colorado Denver */
  686. /* > \author NAG Ltd. */
  687. /* > \date April 2012 */
  688. /* > \ingroup complexGEsing */
  689. /* ===================================================================== */
  690. /* Subroutine */ int cgesvd_(char *jobu, char *jobvt, integer *m, integer *n,
  691. complex *a, integer *lda, real *s, complex *u, integer *ldu, complex *
  692. vt, integer *ldvt, complex *work, integer *lwork, real *rwork,
  693. integer *info)
  694. {
  695. /* System generated locals */
  696. address a__1[2];
  697. integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1[2],
  698. i__2, i__3, i__4;
  699. char ch__1[2];
  700. /* Local variables */
  701. complex cdum[1];
  702. integer iscl;
  703. real anrm;
  704. integer ierr, itau, ncvt, nrvt, lwork_cgebrd__, lwork_cgelqf__,
  705. lwork_cgeqrf__, i__;
  706. extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
  707. integer *, complex *, complex *, integer *, complex *, integer *,
  708. complex *, complex *, integer *);
  709. extern logical lsame_(char *, char *);
  710. integer chunk, minmn, wrkbl, itaup, itauq, mnthr, iwork;
  711. logical wntua, wntva, wntun, wntuo, wntvn, wntvo, wntus, wntvs;
  712. integer ie;
  713. extern /* Subroutine */ int cgebrd_(integer *, integer *, complex *,
  714. integer *, real *, real *, complex *, complex *, complex *,
  715. integer *, integer *);
  716. extern real clange_(char *, integer *, integer *, complex *, integer *,
  717. real *);
  718. integer ir, iu;
  719. extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *,
  720. integer *, complex *, complex *, integer *, integer *), clascl_(
  721. char *, integer *, integer *, real *, real *, integer *, integer *
  722. , complex *, integer *, integer *), cgeqrf_(integer *,
  723. integer *, complex *, integer *, complex *, complex *, integer *,
  724. integer *);
  725. extern real slamch_(char *);
  726. extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
  727. *, integer *, complex *, integer *), claset_(char *,
  728. integer *, integer *, complex *, complex *, complex *, integer *), cbdsqr_(char *, integer *, integer *, integer *, integer
  729. *, real *, real *, complex *, integer *, complex *, integer *,
  730. complex *, integer *, real *, integer *), xerbla_(char *,
  731. integer *, ftnlen), cungbr_(char *, integer *, integer *, integer
  732. *, complex *, integer *, complex *, complex *, integer *, integer
  733. *);
  734. real bignum;
  735. extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
  736. real *, integer *, integer *, real *, integer *, integer *);
  737. extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
  738. integer *, integer *, ftnlen, ftnlen);
  739. extern /* Subroutine */ int cunmbr_(char *, char *, char *, integer *,
  740. integer *, integer *, complex *, integer *, complex *, complex *,
  741. integer *, complex *, integer *, integer *), cunglq_(integer *, integer *, integer *, complex *,
  742. integer *, complex *, complex *, integer *, integer *), cungqr_(
  743. integer *, integer *, integer *, complex *, integer *, complex *,
  744. complex *, integer *, integer *);
  745. integer ldwrkr, minwrk, ldwrku, maxwrk;
  746. real smlnum;
  747. integer irwork;
  748. logical lquery, wntuas, wntvas;
  749. integer lwork_cungbr_p__, lwork_cungbr_q__, lwork_cunglq_n__,
  750. lwork_cunglq_m__, lwork_cungqr_m__, lwork_cungqr_n__, blk, ncu;
  751. real dum[1], eps;
  752. integer nru;
  753. /* -- LAPACK driver routine (version 3.7.0) -- */
  754. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  755. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  756. /* April 2012 */
  757. /* ===================================================================== */
  758. /* Test the input arguments */
  759. /* Parameter adjustments */
  760. a_dim1 = *lda;
  761. a_offset = 1 + a_dim1 * 1;
  762. a -= a_offset;
  763. --s;
  764. u_dim1 = *ldu;
  765. u_offset = 1 + u_dim1 * 1;
  766. u -= u_offset;
  767. vt_dim1 = *ldvt;
  768. vt_offset = 1 + vt_dim1 * 1;
  769. vt -= vt_offset;
  770. --work;
  771. --rwork;
  772. /* Function Body */
  773. *info = 0;
  774. minmn = f2cmin(*m,*n);
  775. wntua = lsame_(jobu, "A");
  776. wntus = lsame_(jobu, "S");
  777. wntuas = wntua || wntus;
  778. wntuo = lsame_(jobu, "O");
  779. wntun = lsame_(jobu, "N");
  780. wntva = lsame_(jobvt, "A");
  781. wntvs = lsame_(jobvt, "S");
  782. wntvas = wntva || wntvs;
  783. wntvo = lsame_(jobvt, "O");
  784. wntvn = lsame_(jobvt, "N");
  785. lquery = *lwork == -1;
  786. if (! (wntua || wntus || wntuo || wntun)) {
  787. *info = -1;
  788. } else if (! (wntva || wntvs || wntvo || wntvn) || wntvo && wntuo) {
  789. *info = -2;
  790. } else if (*m < 0) {
  791. *info = -3;
  792. } else if (*n < 0) {
  793. *info = -4;
  794. } else if (*lda < f2cmax(1,*m)) {
  795. *info = -6;
  796. } else if (*ldu < 1 || wntuas && *ldu < *m) {
  797. *info = -9;
  798. } else if (*ldvt < 1 || wntva && *ldvt < *n || wntvs && *ldvt < minmn) {
  799. *info = -11;
  800. }
  801. /* Compute workspace */
  802. /* (Note: Comments in the code beginning "Workspace:" describe the */
  803. /* minimal amount of workspace needed at that point in the code, */
  804. /* as well as the preferred amount for good performance. */
  805. /* CWorkspace refers to complex workspace, and RWorkspace to */
  806. /* real workspace. NB refers to the optimal block size for the */
  807. /* immediately following subroutine, as returned by ILAENV.) */
  808. if (*info == 0) {
  809. minwrk = 1;
  810. maxwrk = 1;
  811. if (*m >= *n && minmn > 0) {
  812. /* Space needed for ZBDSQR is BDSPAC = 5*N */
  813. /* Writing concatenation */
  814. i__1[0] = 1, a__1[0] = jobu;
  815. i__1[1] = 1, a__1[1] = jobvt;
  816. s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
  817. mnthr = ilaenv_(&c__6, "CGESVD", ch__1, m, n, &c__0, &c__0, (
  818. ftnlen)6, (ftnlen)2);
  819. /* Compute space needed for CGEQRF */
  820. cgeqrf_(m, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  821. lwork_cgeqrf__ = (integer) cdum[0].r;
  822. /* Compute space needed for CUNGQR */
  823. cungqr_(m, n, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  824. lwork_cungqr_n__ = (integer) cdum[0].r;
  825. cungqr_(m, m, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  826. lwork_cungqr_m__ = (integer) cdum[0].r;
  827. /* Compute space needed for CGEBRD */
  828. cgebrd_(n, n, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum, &
  829. c_n1, &ierr);
  830. lwork_cgebrd__ = (integer) cdum[0].r;
  831. /* Compute space needed for CUNGBR */
  832. cungbr_("P", n, n, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  833. lwork_cungbr_p__ = (integer) cdum[0].r;
  834. cungbr_("Q", n, n, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  835. lwork_cungbr_q__ = (integer) cdum[0].r;
  836. /* Writing concatenation */
  837. i__1[0] = 1, a__1[0] = jobu;
  838. i__1[1] = 1, a__1[1] = jobvt;
  839. s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
  840. mnthr = ilaenv_(&c__6, "CGESVD", ch__1, m, n, &c__0, &c__0, (
  841. ftnlen)6, (ftnlen)2);
  842. if (*m >= mnthr) {
  843. if (wntun) {
  844. /* Path 1 (M much larger than N, JOBU='N') */
  845. maxwrk = *n + lwork_cgeqrf__;
  846. /* Computing MAX */
  847. i__2 = maxwrk, i__3 = (*n << 1) + lwork_cgebrd__;
  848. maxwrk = f2cmax(i__2,i__3);
  849. if (wntvo || wntvas) {
  850. /* Computing MAX */
  851. i__2 = maxwrk, i__3 = (*n << 1) + lwork_cungbr_p__;
  852. maxwrk = f2cmax(i__2,i__3);
  853. }
  854. minwrk = *n * 3;
  855. } else if (wntuo && wntvn) {
  856. /* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
  857. wrkbl = *n + lwork_cgeqrf__;
  858. /* Computing MAX */
  859. i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
  860. wrkbl = f2cmax(i__2,i__3);
  861. /* Computing MAX */
  862. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
  863. wrkbl = f2cmax(i__2,i__3);
  864. /* Computing MAX */
  865. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
  866. wrkbl = f2cmax(i__2,i__3);
  867. /* Computing MAX */
  868. i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n;
  869. maxwrk = f2cmax(i__2,i__3);
  870. minwrk = (*n << 1) + *m;
  871. } else if (wntuo && wntvas) {
  872. /* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or */
  873. /* 'A') */
  874. wrkbl = *n + lwork_cgeqrf__;
  875. /* Computing MAX */
  876. i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
  877. wrkbl = f2cmax(i__2,i__3);
  878. /* Computing MAX */
  879. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
  880. wrkbl = f2cmax(i__2,i__3);
  881. /* Computing MAX */
  882. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
  883. wrkbl = f2cmax(i__2,i__3);
  884. /* Computing MAX */
  885. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
  886. wrkbl = f2cmax(i__2,i__3);
  887. /* Computing MAX */
  888. i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n;
  889. maxwrk = f2cmax(i__2,i__3);
  890. minwrk = (*n << 1) + *m;
  891. } else if (wntus && wntvn) {
  892. /* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
  893. wrkbl = *n + lwork_cgeqrf__;
  894. /* Computing MAX */
  895. i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
  896. wrkbl = f2cmax(i__2,i__3);
  897. /* Computing MAX */
  898. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
  899. wrkbl = f2cmax(i__2,i__3);
  900. /* Computing MAX */
  901. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
  902. wrkbl = f2cmax(i__2,i__3);
  903. maxwrk = *n * *n + wrkbl;
  904. minwrk = (*n << 1) + *m;
  905. } else if (wntus && wntvo) {
  906. /* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
  907. wrkbl = *n + lwork_cgeqrf__;
  908. /* Computing MAX */
  909. i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
  910. wrkbl = f2cmax(i__2,i__3);
  911. /* Computing MAX */
  912. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
  913. wrkbl = f2cmax(i__2,i__3);
  914. /* Computing MAX */
  915. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
  916. wrkbl = f2cmax(i__2,i__3);
  917. /* Computing MAX */
  918. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
  919. wrkbl = f2cmax(i__2,i__3);
  920. maxwrk = (*n << 1) * *n + wrkbl;
  921. minwrk = (*n << 1) + *m;
  922. } else if (wntus && wntvas) {
  923. /* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or */
  924. /* 'A') */
  925. wrkbl = *n + lwork_cgeqrf__;
  926. /* Computing MAX */
  927. i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
  928. wrkbl = f2cmax(i__2,i__3);
  929. /* Computing MAX */
  930. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
  931. wrkbl = f2cmax(i__2,i__3);
  932. /* Computing MAX */
  933. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
  934. wrkbl = f2cmax(i__2,i__3);
  935. /* Computing MAX */
  936. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
  937. wrkbl = f2cmax(i__2,i__3);
  938. maxwrk = *n * *n + wrkbl;
  939. minwrk = (*n << 1) + *m;
  940. } else if (wntua && wntvn) {
  941. /* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
  942. wrkbl = *n + lwork_cgeqrf__;
  943. /* Computing MAX */
  944. i__2 = wrkbl, i__3 = *n + lwork_cungqr_m__;
  945. wrkbl = f2cmax(i__2,i__3);
  946. /* Computing MAX */
  947. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
  948. wrkbl = f2cmax(i__2,i__3);
  949. /* Computing MAX */
  950. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
  951. wrkbl = f2cmax(i__2,i__3);
  952. maxwrk = *n * *n + wrkbl;
  953. minwrk = (*n << 1) + *m;
  954. } else if (wntua && wntvo) {
  955. /* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
  956. wrkbl = *n + lwork_cgeqrf__;
  957. /* Computing MAX */
  958. i__2 = wrkbl, i__3 = *n + lwork_cungqr_m__;
  959. wrkbl = f2cmax(i__2,i__3);
  960. /* Computing MAX */
  961. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
  962. wrkbl = f2cmax(i__2,i__3);
  963. /* Computing MAX */
  964. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
  965. wrkbl = f2cmax(i__2,i__3);
  966. /* Computing MAX */
  967. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
  968. wrkbl = f2cmax(i__2,i__3);
  969. maxwrk = (*n << 1) * *n + wrkbl;
  970. minwrk = (*n << 1) + *m;
  971. } else if (wntua && wntvas) {
  972. /* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or */
  973. /* 'A') */
  974. wrkbl = *n + lwork_cgeqrf__;
  975. /* Computing MAX */
  976. i__2 = wrkbl, i__3 = *n + lwork_cungqr_m__;
  977. wrkbl = f2cmax(i__2,i__3);
  978. /* Computing MAX */
  979. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
  980. wrkbl = f2cmax(i__2,i__3);
  981. /* Computing MAX */
  982. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
  983. wrkbl = f2cmax(i__2,i__3);
  984. /* Computing MAX */
  985. i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
  986. wrkbl = f2cmax(i__2,i__3);
  987. maxwrk = *n * *n + wrkbl;
  988. minwrk = (*n << 1) + *m;
  989. }
  990. } else {
  991. /* Path 10 (M at least N, but not much larger) */
  992. cgebrd_(m, n, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum,
  993. &c_n1, &ierr);
  994. lwork_cgebrd__ = (integer) cdum[0].r;
  995. maxwrk = (*n << 1) + lwork_cgebrd__;
  996. if (wntus || wntuo) {
  997. cungbr_("Q", m, n, n, &a[a_offset], lda, cdum, cdum, &
  998. c_n1, &ierr);
  999. lwork_cungbr_q__ = (integer) cdum[0].r;
  1000. /* Computing MAX */
  1001. i__2 = maxwrk, i__3 = (*n << 1) + lwork_cungbr_q__;
  1002. maxwrk = f2cmax(i__2,i__3);
  1003. }
  1004. if (wntua) {
  1005. cungbr_("Q", m, m, n, &a[a_offset], lda, cdum, cdum, &
  1006. c_n1, &ierr);
  1007. lwork_cungbr_q__ = (integer) cdum[0].r;
  1008. /* Computing MAX */
  1009. i__2 = maxwrk, i__3 = (*n << 1) + lwork_cungbr_q__;
  1010. maxwrk = f2cmax(i__2,i__3);
  1011. }
  1012. if (! wntvn) {
  1013. /* Computing MAX */
  1014. i__2 = maxwrk, i__3 = (*n << 1) + lwork_cungbr_p__;
  1015. maxwrk = f2cmax(i__2,i__3);
  1016. }
  1017. minwrk = (*n << 1) + *m;
  1018. }
  1019. } else if (minmn > 0) {
  1020. /* Space needed for CBDSQR is BDSPAC = 5*M */
  1021. /* Writing concatenation */
  1022. i__1[0] = 1, a__1[0] = jobu;
  1023. i__1[1] = 1, a__1[1] = jobvt;
  1024. s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
  1025. mnthr = ilaenv_(&c__6, "CGESVD", ch__1, m, n, &c__0, &c__0, (
  1026. ftnlen)6, (ftnlen)2);
  1027. /* Compute space needed for CGELQF */
  1028. cgelqf_(m, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  1029. lwork_cgelqf__ = (integer) cdum[0].r;
  1030. /* Compute space needed for CUNGLQ */
  1031. cunglq_(n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
  1032. lwork_cunglq_n__ = (integer) cdum[0].r;
  1033. cunglq_(m, n, m, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  1034. lwork_cunglq_m__ = (integer) cdum[0].r;
  1035. /* Compute space needed for CGEBRD */
  1036. cgebrd_(m, m, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum, &
  1037. c_n1, &ierr);
  1038. lwork_cgebrd__ = (integer) cdum[0].r;
  1039. /* Compute space needed for CUNGBR P */
  1040. cungbr_("P", m, m, m, &a[a_offset], n, cdum, cdum, &c_n1, &ierr);
  1041. lwork_cungbr_p__ = (integer) cdum[0].r;
  1042. /* Compute space needed for CUNGBR Q */
  1043. cungbr_("Q", m, m, m, &a[a_offset], n, cdum, cdum, &c_n1, &ierr);
  1044. lwork_cungbr_q__ = (integer) cdum[0].r;
  1045. if (*n >= mnthr) {
  1046. if (wntvn) {
  1047. /* Path 1t(N much larger than M, JOBVT='N') */
  1048. maxwrk = *m + lwork_cgelqf__;
  1049. /* Computing MAX */
  1050. i__2 = maxwrk, i__3 = (*m << 1) + lwork_cgebrd__;
  1051. maxwrk = f2cmax(i__2,i__3);
  1052. if (wntuo || wntuas) {
  1053. /* Computing MAX */
  1054. i__2 = maxwrk, i__3 = (*m << 1) + lwork_cungbr_q__;
  1055. maxwrk = f2cmax(i__2,i__3);
  1056. }
  1057. minwrk = *m * 3;
  1058. } else if (wntvo && wntun) {
  1059. /* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
  1060. wrkbl = *m + lwork_cgelqf__;
  1061. /* Computing MAX */
  1062. i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
  1063. wrkbl = f2cmax(i__2,i__3);
  1064. /* Computing MAX */
  1065. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
  1066. wrkbl = f2cmax(i__2,i__3);
  1067. /* Computing MAX */
  1068. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
  1069. wrkbl = f2cmax(i__2,i__3);
  1070. /* Computing MAX */
  1071. i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n;
  1072. maxwrk = f2cmax(i__2,i__3);
  1073. minwrk = (*m << 1) + *n;
  1074. } else if (wntvo && wntuas) {
  1075. /* Path 3t(N much larger than M, JOBU='S' or 'A', */
  1076. /* JOBVT='O') */
  1077. wrkbl = *m + lwork_cgelqf__;
  1078. /* Computing MAX */
  1079. i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
  1080. wrkbl = f2cmax(i__2,i__3);
  1081. /* Computing MAX */
  1082. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
  1083. wrkbl = f2cmax(i__2,i__3);
  1084. /* Computing MAX */
  1085. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
  1086. wrkbl = f2cmax(i__2,i__3);
  1087. /* Computing MAX */
  1088. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
  1089. wrkbl = f2cmax(i__2,i__3);
  1090. /* Computing MAX */
  1091. i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n;
  1092. maxwrk = f2cmax(i__2,i__3);
  1093. minwrk = (*m << 1) + *n;
  1094. } else if (wntvs && wntun) {
  1095. /* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
  1096. wrkbl = *m + lwork_cgelqf__;
  1097. /* Computing MAX */
  1098. i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
  1099. wrkbl = f2cmax(i__2,i__3);
  1100. /* Computing MAX */
  1101. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
  1102. wrkbl = f2cmax(i__2,i__3);
  1103. /* Computing MAX */
  1104. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
  1105. wrkbl = f2cmax(i__2,i__3);
  1106. maxwrk = *m * *m + wrkbl;
  1107. minwrk = (*m << 1) + *n;
  1108. } else if (wntvs && wntuo) {
  1109. /* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
  1110. wrkbl = *m + lwork_cgelqf__;
  1111. /* Computing MAX */
  1112. i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
  1113. wrkbl = f2cmax(i__2,i__3);
  1114. /* Computing MAX */
  1115. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
  1116. wrkbl = f2cmax(i__2,i__3);
  1117. /* Computing MAX */
  1118. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
  1119. wrkbl = f2cmax(i__2,i__3);
  1120. /* Computing MAX */
  1121. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
  1122. wrkbl = f2cmax(i__2,i__3);
  1123. maxwrk = (*m << 1) * *m + wrkbl;
  1124. minwrk = (*m << 1) + *n;
  1125. } else if (wntvs && wntuas) {
  1126. /* Path 6t(N much larger than M, JOBU='S' or 'A', */
  1127. /* JOBVT='S') */
  1128. wrkbl = *m + lwork_cgelqf__;
  1129. /* Computing MAX */
  1130. i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
  1131. wrkbl = f2cmax(i__2,i__3);
  1132. /* Computing MAX */
  1133. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
  1134. wrkbl = f2cmax(i__2,i__3);
  1135. /* Computing MAX */
  1136. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
  1137. wrkbl = f2cmax(i__2,i__3);
  1138. /* Computing MAX */
  1139. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
  1140. wrkbl = f2cmax(i__2,i__3);
  1141. maxwrk = *m * *m + wrkbl;
  1142. minwrk = (*m << 1) + *n;
  1143. } else if (wntva && wntun) {
  1144. /* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
  1145. wrkbl = *m + lwork_cgelqf__;
  1146. /* Computing MAX */
  1147. i__2 = wrkbl, i__3 = *m + lwork_cunglq_n__;
  1148. wrkbl = f2cmax(i__2,i__3);
  1149. /* Computing MAX */
  1150. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
  1151. wrkbl = f2cmax(i__2,i__3);
  1152. /* Computing MAX */
  1153. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
  1154. wrkbl = f2cmax(i__2,i__3);
  1155. maxwrk = *m * *m + wrkbl;
  1156. minwrk = (*m << 1) + *n;
  1157. } else if (wntva && wntuo) {
  1158. /* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
  1159. wrkbl = *m + lwork_cgelqf__;
  1160. /* Computing MAX */
  1161. i__2 = wrkbl, i__3 = *m + lwork_cunglq_n__;
  1162. wrkbl = f2cmax(i__2,i__3);
  1163. /* Computing MAX */
  1164. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
  1165. wrkbl = f2cmax(i__2,i__3);
  1166. /* Computing MAX */
  1167. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
  1168. wrkbl = f2cmax(i__2,i__3);
  1169. /* Computing MAX */
  1170. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
  1171. wrkbl = f2cmax(i__2,i__3);
  1172. maxwrk = (*m << 1) * *m + wrkbl;
  1173. minwrk = (*m << 1) + *n;
  1174. } else if (wntva && wntuas) {
  1175. /* Path 9t(N much larger than M, JOBU='S' or 'A', */
  1176. /* JOBVT='A') */
  1177. wrkbl = *m + lwork_cgelqf__;
  1178. /* Computing MAX */
  1179. i__2 = wrkbl, i__3 = *m + lwork_cunglq_n__;
  1180. wrkbl = f2cmax(i__2,i__3);
  1181. /* Computing MAX */
  1182. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
  1183. wrkbl = f2cmax(i__2,i__3);
  1184. /* Computing MAX */
  1185. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
  1186. wrkbl = f2cmax(i__2,i__3);
  1187. /* Computing MAX */
  1188. i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
  1189. wrkbl = f2cmax(i__2,i__3);
  1190. maxwrk = *m * *m + wrkbl;
  1191. minwrk = (*m << 1) + *n;
  1192. }
  1193. } else {
  1194. /* Path 10t(N greater than M, but not much larger) */
  1195. cgebrd_(m, n, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum,
  1196. &c_n1, &ierr);
  1197. lwork_cgebrd__ = (integer) cdum[0].r;
  1198. maxwrk = (*m << 1) + lwork_cgebrd__;
  1199. if (wntvs || wntvo) {
  1200. /* Compute space needed for CUNGBR P */
  1201. cungbr_("P", m, n, m, &a[a_offset], n, cdum, cdum, &c_n1,
  1202. &ierr);
  1203. lwork_cungbr_p__ = (integer) cdum[0].r;
  1204. /* Computing MAX */
  1205. i__2 = maxwrk, i__3 = (*m << 1) + lwork_cungbr_p__;
  1206. maxwrk = f2cmax(i__2,i__3);
  1207. }
  1208. if (wntva) {
  1209. cungbr_("P", n, n, m, &a[a_offset], n, cdum, cdum, &c_n1,
  1210. &ierr);
  1211. lwork_cungbr_p__ = (integer) cdum[0].r;
  1212. /* Computing MAX */
  1213. i__2 = maxwrk, i__3 = (*m << 1) + lwork_cungbr_p__;
  1214. maxwrk = f2cmax(i__2,i__3);
  1215. }
  1216. if (! wntun) {
  1217. /* Computing MAX */
  1218. i__2 = maxwrk, i__3 = (*m << 1) + lwork_cungbr_q__;
  1219. maxwrk = f2cmax(i__2,i__3);
  1220. }
  1221. minwrk = (*m << 1) + *n;
  1222. }
  1223. }
  1224. maxwrk = f2cmax(minwrk,maxwrk);
  1225. work[1].r = (real) maxwrk, work[1].i = 0.f;
  1226. if (*lwork < minwrk && ! lquery) {
  1227. *info = -13;
  1228. }
  1229. }
  1230. if (*info != 0) {
  1231. i__2 = -(*info);
  1232. xerbla_("CGESVD", &i__2, (ftnlen)6);
  1233. return 0;
  1234. } else if (lquery) {
  1235. return 0;
  1236. }
  1237. /* Quick return if possible */
  1238. if (*m == 0 || *n == 0) {
  1239. return 0;
  1240. }
  1241. /* Get machine constants */
  1242. eps = slamch_("P");
  1243. smlnum = sqrt(slamch_("S")) / eps;
  1244. bignum = 1.f / smlnum;
  1245. /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
  1246. anrm = clange_("M", m, n, &a[a_offset], lda, dum);
  1247. iscl = 0;
  1248. if (anrm > 0.f && anrm < smlnum) {
  1249. iscl = 1;
  1250. clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
  1251. ierr);
  1252. } else if (anrm > bignum) {
  1253. iscl = 1;
  1254. clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &
  1255. ierr);
  1256. }
  1257. if (*m >= *n) {
  1258. /* A has at least as many rows as columns. If A has sufficiently */
  1259. /* more rows than columns, first reduce using the QR */
  1260. /* decomposition (if sufficient workspace available) */
  1261. if (*m >= mnthr) {
  1262. if (wntun) {
  1263. /* Path 1 (M much larger than N, JOBU='N') */
  1264. /* No left singular vectors to be computed */
  1265. itau = 1;
  1266. iwork = itau + *n;
  1267. /* Compute A=Q*R */
  1268. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1269. /* (RWorkspace: need 0) */
  1270. i__2 = *lwork - iwork + 1;
  1271. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
  1272. i__2, &ierr);
  1273. /* Zero out below R */
  1274. if (*n > 1) {
  1275. i__2 = *n - 1;
  1276. i__3 = *n - 1;
  1277. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[a_dim1 + 2],
  1278. lda);
  1279. }
  1280. ie = 1;
  1281. itauq = 1;
  1282. itaup = itauq + *n;
  1283. iwork = itaup + *n;
  1284. /* Bidiagonalize R in A */
  1285. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  1286. /* (RWorkspace: need N) */
  1287. i__2 = *lwork - iwork + 1;
  1288. cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1289. itauq], &work[itaup], &work[iwork], &i__2, &ierr);
  1290. ncvt = 0;
  1291. if (wntvo || wntvas) {
  1292. /* If right singular vectors desired, generate P'. */
  1293. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  1294. /* (RWorkspace: 0) */
  1295. i__2 = *lwork - iwork + 1;
  1296. cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &
  1297. work[iwork], &i__2, &ierr);
  1298. ncvt = *n;
  1299. }
  1300. irwork = ie + *n;
  1301. /* Perform bidiagonal QR iteration, computing right */
  1302. /* singular vectors of A in A if desired */
  1303. /* (CWorkspace: 0) */
  1304. /* (RWorkspace: need BDSPAC) */
  1305. cbdsqr_("U", n, &ncvt, &c__0, &c__0, &s[1], &rwork[ie], &a[
  1306. a_offset], lda, cdum, &c__1, cdum, &c__1, &rwork[
  1307. irwork], info);
  1308. /* If right singular vectors desired in VT, copy them there */
  1309. if (wntvas) {
  1310. clacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset],
  1311. ldvt);
  1312. }
  1313. } else if (wntuo && wntvn) {
  1314. /* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
  1315. /* N left singular vectors to be overwritten on A and */
  1316. /* no right singular vectors to be computed */
  1317. if (*lwork >= *n * *n + *n * 3) {
  1318. /* Sufficient workspace for a fast algorithm */
  1319. ir = 1;
  1320. /* Computing MAX */
  1321. i__2 = wrkbl, i__3 = *lda * *n;
  1322. if (*lwork >= f2cmax(i__2,i__3) + *lda * *n) {
  1323. /* WORK(IU) is LDA by N, WORK(IR) is LDA by N */
  1324. ldwrku = *lda;
  1325. ldwrkr = *lda;
  1326. } else /* if(complicated condition) */ {
  1327. /* Computing MAX */
  1328. i__2 = wrkbl, i__3 = *lda * *n;
  1329. if (*lwork >= f2cmax(i__2,i__3) + *n * *n) {
  1330. /* WORK(IU) is LDA by N, WORK(IR) is N by N */
  1331. ldwrku = *lda;
  1332. ldwrkr = *n;
  1333. } else {
  1334. /* WORK(IU) is LDWRKU by N, WORK(IR) is N by N */
  1335. ldwrku = (*lwork - *n * *n) / *n;
  1336. ldwrkr = *n;
  1337. }
  1338. }
  1339. itau = ir + ldwrkr * *n;
  1340. iwork = itau + *n;
  1341. /* Compute A=Q*R */
  1342. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1343. /* (RWorkspace: 0) */
  1344. i__2 = *lwork - iwork + 1;
  1345. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
  1346. , &i__2, &ierr);
  1347. /* Copy R to WORK(IR) and zero out below it */
  1348. clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
  1349. i__2 = *n - 1;
  1350. i__3 = *n - 1;
  1351. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[ir + 1], &
  1352. ldwrkr);
  1353. /* Generate Q in A */
  1354. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1355. /* (RWorkspace: 0) */
  1356. i__2 = *lwork - iwork + 1;
  1357. cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
  1358. iwork], &i__2, &ierr);
  1359. ie = 1;
  1360. itauq = itau;
  1361. itaup = itauq + *n;
  1362. iwork = itaup + *n;
  1363. /* Bidiagonalize R in WORK(IR) */
  1364. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
  1365. /* (RWorkspace: need N) */
  1366. i__2 = *lwork - iwork + 1;
  1367. cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
  1368. work[itauq], &work[itaup], &work[iwork], &i__2, &
  1369. ierr);
  1370. /* Generate left vectors bidiagonalizing R */
  1371. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
  1372. /* (RWorkspace: need 0) */
  1373. i__2 = *lwork - iwork + 1;
  1374. cungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
  1375. work[iwork], &i__2, &ierr);
  1376. irwork = ie + *n;
  1377. /* Perform bidiagonal QR iteration, computing left */
  1378. /* singular vectors of R in WORK(IR) */
  1379. /* (CWorkspace: need N*N) */
  1380. /* (RWorkspace: need BDSPAC) */
  1381. cbdsqr_("U", n, &c__0, n, &c__0, &s[1], &rwork[ie], cdum,
  1382. &c__1, &work[ir], &ldwrkr, cdum, &c__1, &rwork[
  1383. irwork], info);
  1384. iu = itauq;
  1385. /* Multiply Q in A by left singular vectors of R in */
  1386. /* WORK(IR), storing result in WORK(IU) and copying to A */
  1387. /* (CWorkspace: need N*N+N, prefer N*N+M*N) */
  1388. /* (RWorkspace: 0) */
  1389. i__2 = *m;
  1390. i__3 = ldwrku;
  1391. for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
  1392. i__3) {
  1393. /* Computing MIN */
  1394. i__4 = *m - i__ + 1;
  1395. chunk = f2cmin(i__4,ldwrku);
  1396. cgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1]
  1397. , lda, &work[ir], &ldwrkr, &c_b1, &work[iu], &
  1398. ldwrku);
  1399. clacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
  1400. a_dim1], lda);
  1401. /* L10: */
  1402. }
  1403. } else {
  1404. /* Insufficient workspace for a fast algorithm */
  1405. ie = 1;
  1406. itauq = 1;
  1407. itaup = itauq + *n;
  1408. iwork = itaup + *n;
  1409. /* Bidiagonalize A */
  1410. /* (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) */
  1411. /* (RWorkspace: N) */
  1412. i__3 = *lwork - iwork + 1;
  1413. cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1414. itauq], &work[itaup], &work[iwork], &i__3, &ierr);
  1415. /* Generate left vectors bidiagonalizing A */
  1416. /* (CWorkspace: need 3*N, prefer 2*N+N*NB) */
  1417. /* (RWorkspace: 0) */
  1418. i__3 = *lwork - iwork + 1;
  1419. cungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
  1420. work[iwork], &i__3, &ierr);
  1421. irwork = ie + *n;
  1422. /* Perform bidiagonal QR iteration, computing left */
  1423. /* singular vectors of A in A */
  1424. /* (CWorkspace: need 0) */
  1425. /* (RWorkspace: need BDSPAC) */
  1426. cbdsqr_("U", n, &c__0, m, &c__0, &s[1], &rwork[ie], cdum,
  1427. &c__1, &a[a_offset], lda, cdum, &c__1, &rwork[
  1428. irwork], info);
  1429. }
  1430. } else if (wntuo && wntvas) {
  1431. /* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A') */
  1432. /* N left singular vectors to be overwritten on A and */
  1433. /* N right singular vectors to be computed in VT */
  1434. if (*lwork >= *n * *n + *n * 3) {
  1435. /* Sufficient workspace for a fast algorithm */
  1436. ir = 1;
  1437. /* Computing MAX */
  1438. i__3 = wrkbl, i__2 = *lda * *n;
  1439. if (*lwork >= f2cmax(i__3,i__2) + *lda * *n) {
  1440. /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
  1441. ldwrku = *lda;
  1442. ldwrkr = *lda;
  1443. } else /* if(complicated condition) */ {
  1444. /* Computing MAX */
  1445. i__3 = wrkbl, i__2 = *lda * *n;
  1446. if (*lwork >= f2cmax(i__3,i__2) + *n * *n) {
  1447. /* WORK(IU) is LDA by N and WORK(IR) is N by N */
  1448. ldwrku = *lda;
  1449. ldwrkr = *n;
  1450. } else {
  1451. /* WORK(IU) is LDWRKU by N and WORK(IR) is N by N */
  1452. ldwrku = (*lwork - *n * *n) / *n;
  1453. ldwrkr = *n;
  1454. }
  1455. }
  1456. itau = ir + ldwrkr * *n;
  1457. iwork = itau + *n;
  1458. /* Compute A=Q*R */
  1459. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1460. /* (RWorkspace: 0) */
  1461. i__3 = *lwork - iwork + 1;
  1462. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
  1463. , &i__3, &ierr);
  1464. /* Copy R to VT, zeroing out below it */
  1465. clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
  1466. ldvt);
  1467. if (*n > 1) {
  1468. i__3 = *n - 1;
  1469. i__2 = *n - 1;
  1470. claset_("L", &i__3, &i__2, &c_b1, &c_b1, &vt[vt_dim1
  1471. + 2], ldvt);
  1472. }
  1473. /* Generate Q in A */
  1474. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1475. /* (RWorkspace: 0) */
  1476. i__3 = *lwork - iwork + 1;
  1477. cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
  1478. iwork], &i__3, &ierr);
  1479. ie = 1;
  1480. itauq = itau;
  1481. itaup = itauq + *n;
  1482. iwork = itaup + *n;
  1483. /* Bidiagonalize R in VT, copying result to WORK(IR) */
  1484. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
  1485. /* (RWorkspace: need N) */
  1486. i__3 = *lwork - iwork + 1;
  1487. cgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie], &
  1488. work[itauq], &work[itaup], &work[iwork], &i__3, &
  1489. ierr);
  1490. clacpy_("L", n, n, &vt[vt_offset], ldvt, &work[ir], &
  1491. ldwrkr);
  1492. /* Generate left vectors bidiagonalizing R in WORK(IR) */
  1493. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
  1494. /* (RWorkspace: 0) */
  1495. i__3 = *lwork - iwork + 1;
  1496. cungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
  1497. work[iwork], &i__3, &ierr);
  1498. /* Generate right vectors bidiagonalizing R in VT */
  1499. /* (CWorkspace: need N*N+3*N-1, prefer N*N+2*N+(N-1)*NB) */
  1500. /* (RWorkspace: 0) */
  1501. i__3 = *lwork - iwork + 1;
  1502. cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
  1503. &work[iwork], &i__3, &ierr);
  1504. irwork = ie + *n;
  1505. /* Perform bidiagonal QR iteration, computing left */
  1506. /* singular vectors of R in WORK(IR) and computing right */
  1507. /* singular vectors of R in VT */
  1508. /* (CWorkspace: need N*N) */
  1509. /* (RWorkspace: need BDSPAC) */
  1510. cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &vt[
  1511. vt_offset], ldvt, &work[ir], &ldwrkr, cdum, &c__1,
  1512. &rwork[irwork], info);
  1513. iu = itauq;
  1514. /* Multiply Q in A by left singular vectors of R in */
  1515. /* WORK(IR), storing result in WORK(IU) and copying to A */
  1516. /* (CWorkspace: need N*N+N, prefer N*N+M*N) */
  1517. /* (RWorkspace: 0) */
  1518. i__3 = *m;
  1519. i__2 = ldwrku;
  1520. for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
  1521. i__2) {
  1522. /* Computing MIN */
  1523. i__4 = *m - i__ + 1;
  1524. chunk = f2cmin(i__4,ldwrku);
  1525. cgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1]
  1526. , lda, &work[ir], &ldwrkr, &c_b1, &work[iu], &
  1527. ldwrku);
  1528. clacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
  1529. a_dim1], lda);
  1530. /* L20: */
  1531. }
  1532. } else {
  1533. /* Insufficient workspace for a fast algorithm */
  1534. itau = 1;
  1535. iwork = itau + *n;
  1536. /* Compute A=Q*R */
  1537. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1538. /* (RWorkspace: 0) */
  1539. i__2 = *lwork - iwork + 1;
  1540. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
  1541. , &i__2, &ierr);
  1542. /* Copy R to VT, zeroing out below it */
  1543. clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
  1544. ldvt);
  1545. if (*n > 1) {
  1546. i__2 = *n - 1;
  1547. i__3 = *n - 1;
  1548. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &vt[vt_dim1
  1549. + 2], ldvt);
  1550. }
  1551. /* Generate Q in A */
  1552. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1553. /* (RWorkspace: 0) */
  1554. i__2 = *lwork - iwork + 1;
  1555. cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
  1556. iwork], &i__2, &ierr);
  1557. ie = 1;
  1558. itauq = itau;
  1559. itaup = itauq + *n;
  1560. iwork = itaup + *n;
  1561. /* Bidiagonalize R in VT */
  1562. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  1563. /* (RWorkspace: N) */
  1564. i__2 = *lwork - iwork + 1;
  1565. cgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie], &
  1566. work[itauq], &work[itaup], &work[iwork], &i__2, &
  1567. ierr);
  1568. /* Multiply Q in A by left vectors bidiagonalizing R */
  1569. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  1570. /* (RWorkspace: 0) */
  1571. i__2 = *lwork - iwork + 1;
  1572. cunmbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt, &
  1573. work[itauq], &a[a_offset], lda, &work[iwork], &
  1574. i__2, &ierr);
  1575. /* Generate right vectors bidiagonalizing R in VT */
  1576. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  1577. /* (RWorkspace: 0) */
  1578. i__2 = *lwork - iwork + 1;
  1579. cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
  1580. &work[iwork], &i__2, &ierr);
  1581. irwork = ie + *n;
  1582. /* Perform bidiagonal QR iteration, computing left */
  1583. /* singular vectors of A in A and computing right */
  1584. /* singular vectors of A in VT */
  1585. /* (CWorkspace: 0) */
  1586. /* (RWorkspace: need BDSPAC) */
  1587. cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &vt[
  1588. vt_offset], ldvt, &a[a_offset], lda, cdum, &c__1,
  1589. &rwork[irwork], info);
  1590. }
  1591. } else if (wntus) {
  1592. if (wntvn) {
  1593. /* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
  1594. /* N left singular vectors to be computed in U and */
  1595. /* no right singular vectors to be computed */
  1596. if (*lwork >= *n * *n + *n * 3) {
  1597. /* Sufficient workspace for a fast algorithm */
  1598. ir = 1;
  1599. if (*lwork >= wrkbl + *lda * *n) {
  1600. /* WORK(IR) is LDA by N */
  1601. ldwrkr = *lda;
  1602. } else {
  1603. /* WORK(IR) is N by N */
  1604. ldwrkr = *n;
  1605. }
  1606. itau = ir + ldwrkr * *n;
  1607. iwork = itau + *n;
  1608. /* Compute A=Q*R */
  1609. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1610. /* (RWorkspace: 0) */
  1611. i__2 = *lwork - iwork + 1;
  1612. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  1613. iwork], &i__2, &ierr);
  1614. /* Copy R to WORK(IR), zeroing out below it */
  1615. clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &
  1616. ldwrkr);
  1617. i__2 = *n - 1;
  1618. i__3 = *n - 1;
  1619. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[ir + 1]
  1620. , &ldwrkr);
  1621. /* Generate Q in A */
  1622. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1623. /* (RWorkspace: 0) */
  1624. i__2 = *lwork - iwork + 1;
  1625. cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &
  1626. work[iwork], &i__2, &ierr);
  1627. ie = 1;
  1628. itauq = itau;
  1629. itaup = itauq + *n;
  1630. iwork = itaup + *n;
  1631. /* Bidiagonalize R in WORK(IR) */
  1632. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
  1633. /* (RWorkspace: need N) */
  1634. i__2 = *lwork - iwork + 1;
  1635. cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
  1636. work[itauq], &work[itaup], &work[iwork], &
  1637. i__2, &ierr);
  1638. /* Generate left vectors bidiagonalizing R in WORK(IR) */
  1639. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
  1640. /* (RWorkspace: 0) */
  1641. i__2 = *lwork - iwork + 1;
  1642. cungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
  1643. , &work[iwork], &i__2, &ierr);
  1644. irwork = ie + *n;
  1645. /* Perform bidiagonal QR iteration, computing left */
  1646. /* singular vectors of R in WORK(IR) */
  1647. /* (CWorkspace: need N*N) */
  1648. /* (RWorkspace: need BDSPAC) */
  1649. cbdsqr_("U", n, &c__0, n, &c__0, &s[1], &rwork[ie],
  1650. cdum, &c__1, &work[ir], &ldwrkr, cdum, &c__1,
  1651. &rwork[irwork], info);
  1652. /* Multiply Q in A by left singular vectors of R in */
  1653. /* WORK(IR), storing result in U */
  1654. /* (CWorkspace: need N*N) */
  1655. /* (RWorkspace: 0) */
  1656. cgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &
  1657. work[ir], &ldwrkr, &c_b1, &u[u_offset], ldu);
  1658. } else {
  1659. /* Insufficient workspace for a fast algorithm */
  1660. itau = 1;
  1661. iwork = itau + *n;
  1662. /* Compute A=Q*R, copying result to U */
  1663. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1664. /* (RWorkspace: 0) */
  1665. i__2 = *lwork - iwork + 1;
  1666. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  1667. iwork], &i__2, &ierr);
  1668. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  1669. ldu);
  1670. /* Generate Q in U */
  1671. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1672. /* (RWorkspace: 0) */
  1673. i__2 = *lwork - iwork + 1;
  1674. cungqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
  1675. work[iwork], &i__2, &ierr);
  1676. ie = 1;
  1677. itauq = itau;
  1678. itaup = itauq + *n;
  1679. iwork = itaup + *n;
  1680. /* Zero out below R in A */
  1681. if (*n > 1) {
  1682. i__2 = *n - 1;
  1683. i__3 = *n - 1;
  1684. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
  1685. a_dim1 + 2], lda);
  1686. }
  1687. /* Bidiagonalize R in A */
  1688. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  1689. /* (RWorkspace: need N) */
  1690. i__2 = *lwork - iwork + 1;
  1691. cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
  1692. work[itauq], &work[itaup], &work[iwork], &
  1693. i__2, &ierr);
  1694. /* Multiply Q in U by left vectors bidiagonalizing R */
  1695. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  1696. /* (RWorkspace: 0) */
  1697. i__2 = *lwork - iwork + 1;
  1698. cunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
  1699. work[itauq], &u[u_offset], ldu, &work[iwork],
  1700. &i__2, &ierr)
  1701. ;
  1702. irwork = ie + *n;
  1703. /* Perform bidiagonal QR iteration, computing left */
  1704. /* singular vectors of A in U */
  1705. /* (CWorkspace: 0) */
  1706. /* (RWorkspace: need BDSPAC) */
  1707. cbdsqr_("U", n, &c__0, m, &c__0, &s[1], &rwork[ie],
  1708. cdum, &c__1, &u[u_offset], ldu, cdum, &c__1, &
  1709. rwork[irwork], info);
  1710. }
  1711. } else if (wntvo) {
  1712. /* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
  1713. /* N left singular vectors to be computed in U and */
  1714. /* N right singular vectors to be overwritten on A */
  1715. if (*lwork >= (*n << 1) * *n + *n * 3) {
  1716. /* Sufficient workspace for a fast algorithm */
  1717. iu = 1;
  1718. if (*lwork >= wrkbl + (*lda << 1) * *n) {
  1719. /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
  1720. ldwrku = *lda;
  1721. ir = iu + ldwrku * *n;
  1722. ldwrkr = *lda;
  1723. } else if (*lwork >= wrkbl + (*lda + *n) * *n) {
  1724. /* WORK(IU) is LDA by N and WORK(IR) is N by N */
  1725. ldwrku = *lda;
  1726. ir = iu + ldwrku * *n;
  1727. ldwrkr = *n;
  1728. } else {
  1729. /* WORK(IU) is N by N and WORK(IR) is N by N */
  1730. ldwrku = *n;
  1731. ir = iu + ldwrku * *n;
  1732. ldwrkr = *n;
  1733. }
  1734. itau = ir + ldwrkr * *n;
  1735. iwork = itau + *n;
  1736. /* Compute A=Q*R */
  1737. /* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
  1738. /* (RWorkspace: 0) */
  1739. i__2 = *lwork - iwork + 1;
  1740. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  1741. iwork], &i__2, &ierr);
  1742. /* Copy R to WORK(IU), zeroing out below it */
  1743. clacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
  1744. ldwrku);
  1745. i__2 = *n - 1;
  1746. i__3 = *n - 1;
  1747. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
  1748. , &ldwrku);
  1749. /* Generate Q in A */
  1750. /* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
  1751. /* (RWorkspace: 0) */
  1752. i__2 = *lwork - iwork + 1;
  1753. cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &
  1754. work[iwork], &i__2, &ierr);
  1755. ie = 1;
  1756. itauq = itau;
  1757. itaup = itauq + *n;
  1758. iwork = itaup + *n;
  1759. /* Bidiagonalize R in WORK(IU), copying result to */
  1760. /* WORK(IR) */
  1761. /* (CWorkspace: need 2*N*N+3*N, */
  1762. /* prefer 2*N*N+2*N+2*N*NB) */
  1763. /* (RWorkspace: need N) */
  1764. i__2 = *lwork - iwork + 1;
  1765. cgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  1766. work[itauq], &work[itaup], &work[iwork], &
  1767. i__2, &ierr);
  1768. clacpy_("U", n, n, &work[iu], &ldwrku, &work[ir], &
  1769. ldwrkr);
  1770. /* Generate left bidiagonalizing vectors in WORK(IU) */
  1771. /* (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) */
  1772. /* (RWorkspace: 0) */
  1773. i__2 = *lwork - iwork + 1;
  1774. cungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
  1775. , &work[iwork], &i__2, &ierr);
  1776. /* Generate right bidiagonalizing vectors in WORK(IR) */
  1777. /* (CWorkspace: need 2*N*N+3*N-1, */
  1778. /* prefer 2*N*N+2*N+(N-1)*NB) */
  1779. /* (RWorkspace: 0) */
  1780. i__2 = *lwork - iwork + 1;
  1781. cungbr_("P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
  1782. , &work[iwork], &i__2, &ierr);
  1783. irwork = ie + *n;
  1784. /* Perform bidiagonal QR iteration, computing left */
  1785. /* singular vectors of R in WORK(IU) and computing */
  1786. /* right singular vectors of R in WORK(IR) */
  1787. /* (CWorkspace: need 2*N*N) */
  1788. /* (RWorkspace: need BDSPAC) */
  1789. cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &work[
  1790. ir], &ldwrkr, &work[iu], &ldwrku, cdum, &c__1,
  1791. &rwork[irwork], info);
  1792. /* Multiply Q in A by left singular vectors of R in */
  1793. /* WORK(IU), storing result in U */
  1794. /* (CWorkspace: need N*N) */
  1795. /* (RWorkspace: 0) */
  1796. cgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &
  1797. work[iu], &ldwrku, &c_b1, &u[u_offset], ldu);
  1798. /* Copy right singular vectors of R to A */
  1799. /* (CWorkspace: need N*N) */
  1800. /* (RWorkspace: 0) */
  1801. clacpy_("F", n, n, &work[ir], &ldwrkr, &a[a_offset],
  1802. lda);
  1803. } else {
  1804. /* Insufficient workspace for a fast algorithm */
  1805. itau = 1;
  1806. iwork = itau + *n;
  1807. /* Compute A=Q*R, copying result to U */
  1808. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1809. /* (RWorkspace: 0) */
  1810. i__2 = *lwork - iwork + 1;
  1811. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  1812. iwork], &i__2, &ierr);
  1813. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  1814. ldu);
  1815. /* Generate Q in U */
  1816. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1817. /* (RWorkspace: 0) */
  1818. i__2 = *lwork - iwork + 1;
  1819. cungqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
  1820. work[iwork], &i__2, &ierr);
  1821. ie = 1;
  1822. itauq = itau;
  1823. itaup = itauq + *n;
  1824. iwork = itaup + *n;
  1825. /* Zero out below R in A */
  1826. if (*n > 1) {
  1827. i__2 = *n - 1;
  1828. i__3 = *n - 1;
  1829. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
  1830. a_dim1 + 2], lda);
  1831. }
  1832. /* Bidiagonalize R in A */
  1833. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  1834. /* (RWorkspace: need N) */
  1835. i__2 = *lwork - iwork + 1;
  1836. cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
  1837. work[itauq], &work[itaup], &work[iwork], &
  1838. i__2, &ierr);
  1839. /* Multiply Q in U by left vectors bidiagonalizing R */
  1840. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  1841. /* (RWorkspace: 0) */
  1842. i__2 = *lwork - iwork + 1;
  1843. cunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
  1844. work[itauq], &u[u_offset], ldu, &work[iwork],
  1845. &i__2, &ierr)
  1846. ;
  1847. /* Generate right vectors bidiagonalizing R in A */
  1848. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  1849. /* (RWorkspace: 0) */
  1850. i__2 = *lwork - iwork + 1;
  1851. cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup],
  1852. &work[iwork], &i__2, &ierr);
  1853. irwork = ie + *n;
  1854. /* Perform bidiagonal QR iteration, computing left */
  1855. /* singular vectors of A in U and computing right */
  1856. /* singular vectors of A in A */
  1857. /* (CWorkspace: 0) */
  1858. /* (RWorkspace: need BDSPAC) */
  1859. cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &a[
  1860. a_offset], lda, &u[u_offset], ldu, cdum, &
  1861. c__1, &rwork[irwork], info);
  1862. }
  1863. } else if (wntvas) {
  1864. /* Path 6 (M much larger than N, JOBU='S', JOBVT='S' */
  1865. /* or 'A') */
  1866. /* N left singular vectors to be computed in U and */
  1867. /* N right singular vectors to be computed in VT */
  1868. if (*lwork >= *n * *n + *n * 3) {
  1869. /* Sufficient workspace for a fast algorithm */
  1870. iu = 1;
  1871. if (*lwork >= wrkbl + *lda * *n) {
  1872. /* WORK(IU) is LDA by N */
  1873. ldwrku = *lda;
  1874. } else {
  1875. /* WORK(IU) is N by N */
  1876. ldwrku = *n;
  1877. }
  1878. itau = iu + ldwrku * *n;
  1879. iwork = itau + *n;
  1880. /* Compute A=Q*R */
  1881. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1882. /* (RWorkspace: 0) */
  1883. i__2 = *lwork - iwork + 1;
  1884. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  1885. iwork], &i__2, &ierr);
  1886. /* Copy R to WORK(IU), zeroing out below it */
  1887. clacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
  1888. ldwrku);
  1889. i__2 = *n - 1;
  1890. i__3 = *n - 1;
  1891. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
  1892. , &ldwrku);
  1893. /* Generate Q in A */
  1894. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1895. /* (RWorkspace: 0) */
  1896. i__2 = *lwork - iwork + 1;
  1897. cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &
  1898. work[iwork], &i__2, &ierr);
  1899. ie = 1;
  1900. itauq = itau;
  1901. itaup = itauq + *n;
  1902. iwork = itaup + *n;
  1903. /* Bidiagonalize R in WORK(IU), copying result to VT */
  1904. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
  1905. /* (RWorkspace: need N) */
  1906. i__2 = *lwork - iwork + 1;
  1907. cgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  1908. work[itauq], &work[itaup], &work[iwork], &
  1909. i__2, &ierr);
  1910. clacpy_("U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
  1911. ldvt);
  1912. /* Generate left bidiagonalizing vectors in WORK(IU) */
  1913. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
  1914. /* (RWorkspace: 0) */
  1915. i__2 = *lwork - iwork + 1;
  1916. cungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
  1917. , &work[iwork], &i__2, &ierr);
  1918. /* Generate right bidiagonalizing vectors in VT */
  1919. /* (CWorkspace: need N*N+3*N-1, */
  1920. /* prefer N*N+2*N+(N-1)*NB) */
  1921. /* (RWorkspace: 0) */
  1922. i__2 = *lwork - iwork + 1;
  1923. cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
  1924. itaup], &work[iwork], &i__2, &ierr)
  1925. ;
  1926. irwork = ie + *n;
  1927. /* Perform bidiagonal QR iteration, computing left */
  1928. /* singular vectors of R in WORK(IU) and computing */
  1929. /* right singular vectors of R in VT */
  1930. /* (CWorkspace: need N*N) */
  1931. /* (RWorkspace: need BDSPAC) */
  1932. cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &vt[
  1933. vt_offset], ldvt, &work[iu], &ldwrku, cdum, &
  1934. c__1, &rwork[irwork], info);
  1935. /* Multiply Q in A by left singular vectors of R in */
  1936. /* WORK(IU), storing result in U */
  1937. /* (CWorkspace: need N*N) */
  1938. /* (RWorkspace: 0) */
  1939. cgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &
  1940. work[iu], &ldwrku, &c_b1, &u[u_offset], ldu);
  1941. } else {
  1942. /* Insufficient workspace for a fast algorithm */
  1943. itau = 1;
  1944. iwork = itau + *n;
  1945. /* Compute A=Q*R, copying result to U */
  1946. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1947. /* (RWorkspace: 0) */
  1948. i__2 = *lwork - iwork + 1;
  1949. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  1950. iwork], &i__2, &ierr);
  1951. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  1952. ldu);
  1953. /* Generate Q in U */
  1954. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1955. /* (RWorkspace: 0) */
  1956. i__2 = *lwork - iwork + 1;
  1957. cungqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
  1958. work[iwork], &i__2, &ierr);
  1959. /* Copy R to VT, zeroing out below it */
  1960. clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
  1961. ldvt);
  1962. if (*n > 1) {
  1963. i__2 = *n - 1;
  1964. i__3 = *n - 1;
  1965. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &vt[
  1966. vt_dim1 + 2], ldvt);
  1967. }
  1968. ie = 1;
  1969. itauq = itau;
  1970. itaup = itauq + *n;
  1971. iwork = itaup + *n;
  1972. /* Bidiagonalize R in VT */
  1973. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  1974. /* (RWorkspace: need N) */
  1975. i__2 = *lwork - iwork + 1;
  1976. cgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie],
  1977. &work[itauq], &work[itaup], &work[iwork], &
  1978. i__2, &ierr);
  1979. /* Multiply Q in U by left bidiagonalizing vectors */
  1980. /* in VT */
  1981. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  1982. /* (RWorkspace: 0) */
  1983. i__2 = *lwork - iwork + 1;
  1984. cunmbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt,
  1985. &work[itauq], &u[u_offset], ldu, &work[iwork],
  1986. &i__2, &ierr);
  1987. /* Generate right bidiagonalizing vectors in VT */
  1988. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  1989. /* (RWorkspace: 0) */
  1990. i__2 = *lwork - iwork + 1;
  1991. cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
  1992. itaup], &work[iwork], &i__2, &ierr)
  1993. ;
  1994. irwork = ie + *n;
  1995. /* Perform bidiagonal QR iteration, computing left */
  1996. /* singular vectors of A in U and computing right */
  1997. /* singular vectors of A in VT */
  1998. /* (CWorkspace: 0) */
  1999. /* (RWorkspace: need BDSPAC) */
  2000. cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &vt[
  2001. vt_offset], ldvt, &u[u_offset], ldu, cdum, &
  2002. c__1, &rwork[irwork], info);
  2003. }
  2004. }
  2005. } else if (wntua) {
  2006. if (wntvn) {
  2007. /* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
  2008. /* M left singular vectors to be computed in U and */
  2009. /* no right singular vectors to be computed */
  2010. /* Computing MAX */
  2011. i__2 = *n + *m, i__3 = *n * 3;
  2012. if (*lwork >= *n * *n + f2cmax(i__2,i__3)) {
  2013. /* Sufficient workspace for a fast algorithm */
  2014. ir = 1;
  2015. if (*lwork >= wrkbl + *lda * *n) {
  2016. /* WORK(IR) is LDA by N */
  2017. ldwrkr = *lda;
  2018. } else {
  2019. /* WORK(IR) is N by N */
  2020. ldwrkr = *n;
  2021. }
  2022. itau = ir + ldwrkr * *n;
  2023. iwork = itau + *n;
  2024. /* Compute A=Q*R, copying result to U */
  2025. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  2026. /* (RWorkspace: 0) */
  2027. i__2 = *lwork - iwork + 1;
  2028. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2029. iwork], &i__2, &ierr);
  2030. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  2031. ldu);
  2032. /* Copy R to WORK(IR), zeroing out below it */
  2033. clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &
  2034. ldwrkr);
  2035. i__2 = *n - 1;
  2036. i__3 = *n - 1;
  2037. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[ir + 1]
  2038. , &ldwrkr);
  2039. /* Generate Q in U */
  2040. /* (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB) */
  2041. /* (RWorkspace: 0) */
  2042. i__2 = *lwork - iwork + 1;
  2043. cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
  2044. work[iwork], &i__2, &ierr);
  2045. ie = 1;
  2046. itauq = itau;
  2047. itaup = itauq + *n;
  2048. iwork = itaup + *n;
  2049. /* Bidiagonalize R in WORK(IR) */
  2050. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
  2051. /* (RWorkspace: need N) */
  2052. i__2 = *lwork - iwork + 1;
  2053. cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
  2054. work[itauq], &work[itaup], &work[iwork], &
  2055. i__2, &ierr);
  2056. /* Generate left bidiagonalizing vectors in WORK(IR) */
  2057. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
  2058. /* (RWorkspace: 0) */
  2059. i__2 = *lwork - iwork + 1;
  2060. cungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
  2061. , &work[iwork], &i__2, &ierr);
  2062. irwork = ie + *n;
  2063. /* Perform bidiagonal QR iteration, computing left */
  2064. /* singular vectors of R in WORK(IR) */
  2065. /* (CWorkspace: need N*N) */
  2066. /* (RWorkspace: need BDSPAC) */
  2067. cbdsqr_("U", n, &c__0, n, &c__0, &s[1], &rwork[ie],
  2068. cdum, &c__1, &work[ir], &ldwrkr, cdum, &c__1,
  2069. &rwork[irwork], info);
  2070. /* Multiply Q in U by left singular vectors of R in */
  2071. /* WORK(IR), storing result in A */
  2072. /* (CWorkspace: need N*N) */
  2073. /* (RWorkspace: 0) */
  2074. cgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &
  2075. work[ir], &ldwrkr, &c_b1, &a[a_offset], lda);
  2076. /* Copy left singular vectors of A from A to U */
  2077. clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
  2078. ldu);
  2079. } else {
  2080. /* Insufficient workspace for a fast algorithm */
  2081. itau = 1;
  2082. iwork = itau + *n;
  2083. /* Compute A=Q*R, copying result to U */
  2084. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  2085. /* (RWorkspace: 0) */
  2086. i__2 = *lwork - iwork + 1;
  2087. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2088. iwork], &i__2, &ierr);
  2089. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  2090. ldu);
  2091. /* Generate Q in U */
  2092. /* (CWorkspace: need N+M, prefer N+M*NB) */
  2093. /* (RWorkspace: 0) */
  2094. i__2 = *lwork - iwork + 1;
  2095. cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
  2096. work[iwork], &i__2, &ierr);
  2097. ie = 1;
  2098. itauq = itau;
  2099. itaup = itauq + *n;
  2100. iwork = itaup + *n;
  2101. /* Zero out below R in A */
  2102. if (*n > 1) {
  2103. i__2 = *n - 1;
  2104. i__3 = *n - 1;
  2105. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
  2106. a_dim1 + 2], lda);
  2107. }
  2108. /* Bidiagonalize R in A */
  2109. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  2110. /* (RWorkspace: need N) */
  2111. i__2 = *lwork - iwork + 1;
  2112. cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
  2113. work[itauq], &work[itaup], &work[iwork], &
  2114. i__2, &ierr);
  2115. /* Multiply Q in U by left bidiagonalizing vectors */
  2116. /* in A */
  2117. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  2118. /* (RWorkspace: 0) */
  2119. i__2 = *lwork - iwork + 1;
  2120. cunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
  2121. work[itauq], &u[u_offset], ldu, &work[iwork],
  2122. &i__2, &ierr)
  2123. ;
  2124. irwork = ie + *n;
  2125. /* Perform bidiagonal QR iteration, computing left */
  2126. /* singular vectors of A in U */
  2127. /* (CWorkspace: 0) */
  2128. /* (RWorkspace: need BDSPAC) */
  2129. cbdsqr_("U", n, &c__0, m, &c__0, &s[1], &rwork[ie],
  2130. cdum, &c__1, &u[u_offset], ldu, cdum, &c__1, &
  2131. rwork[irwork], info);
  2132. }
  2133. } else if (wntvo) {
  2134. /* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
  2135. /* M left singular vectors to be computed in U and */
  2136. /* N right singular vectors to be overwritten on A */
  2137. /* Computing MAX */
  2138. i__2 = *n + *m, i__3 = *n * 3;
  2139. if (*lwork >= (*n << 1) * *n + f2cmax(i__2,i__3)) {
  2140. /* Sufficient workspace for a fast algorithm */
  2141. iu = 1;
  2142. if (*lwork >= wrkbl + (*lda << 1) * *n) {
  2143. /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
  2144. ldwrku = *lda;
  2145. ir = iu + ldwrku * *n;
  2146. ldwrkr = *lda;
  2147. } else if (*lwork >= wrkbl + (*lda + *n) * *n) {
  2148. /* WORK(IU) is LDA by N and WORK(IR) is N by N */
  2149. ldwrku = *lda;
  2150. ir = iu + ldwrku * *n;
  2151. ldwrkr = *n;
  2152. } else {
  2153. /* WORK(IU) is N by N and WORK(IR) is N by N */
  2154. ldwrku = *n;
  2155. ir = iu + ldwrku * *n;
  2156. ldwrkr = *n;
  2157. }
  2158. itau = ir + ldwrkr * *n;
  2159. iwork = itau + *n;
  2160. /* Compute A=Q*R, copying result to U */
  2161. /* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
  2162. /* (RWorkspace: 0) */
  2163. i__2 = *lwork - iwork + 1;
  2164. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2165. iwork], &i__2, &ierr);
  2166. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  2167. ldu);
  2168. /* Generate Q in U */
  2169. /* (CWorkspace: need 2*N*N+N+M, prefer 2*N*N+N+M*NB) */
  2170. /* (RWorkspace: 0) */
  2171. i__2 = *lwork - iwork + 1;
  2172. cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
  2173. work[iwork], &i__2, &ierr);
  2174. /* Copy R to WORK(IU), zeroing out below it */
  2175. clacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
  2176. ldwrku);
  2177. i__2 = *n - 1;
  2178. i__3 = *n - 1;
  2179. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
  2180. , &ldwrku);
  2181. ie = 1;
  2182. itauq = itau;
  2183. itaup = itauq + *n;
  2184. iwork = itaup + *n;
  2185. /* Bidiagonalize R in WORK(IU), copying result to */
  2186. /* WORK(IR) */
  2187. /* (CWorkspace: need 2*N*N+3*N, */
  2188. /* prefer 2*N*N+2*N+2*N*NB) */
  2189. /* (RWorkspace: need N) */
  2190. i__2 = *lwork - iwork + 1;
  2191. cgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  2192. work[itauq], &work[itaup], &work[iwork], &
  2193. i__2, &ierr);
  2194. clacpy_("U", n, n, &work[iu], &ldwrku, &work[ir], &
  2195. ldwrkr);
  2196. /* Generate left bidiagonalizing vectors in WORK(IU) */
  2197. /* (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) */
  2198. /* (RWorkspace: 0) */
  2199. i__2 = *lwork - iwork + 1;
  2200. cungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
  2201. , &work[iwork], &i__2, &ierr);
  2202. /* Generate right bidiagonalizing vectors in WORK(IR) */
  2203. /* (CWorkspace: need 2*N*N+3*N-1, */
  2204. /* prefer 2*N*N+2*N+(N-1)*NB) */
  2205. /* (RWorkspace: 0) */
  2206. i__2 = *lwork - iwork + 1;
  2207. cungbr_("P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
  2208. , &work[iwork], &i__2, &ierr);
  2209. irwork = ie + *n;
  2210. /* Perform bidiagonal QR iteration, computing left */
  2211. /* singular vectors of R in WORK(IU) and computing */
  2212. /* right singular vectors of R in WORK(IR) */
  2213. /* (CWorkspace: need 2*N*N) */
  2214. /* (RWorkspace: need BDSPAC) */
  2215. cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &work[
  2216. ir], &ldwrkr, &work[iu], &ldwrku, cdum, &c__1,
  2217. &rwork[irwork], info);
  2218. /* Multiply Q in U by left singular vectors of R in */
  2219. /* WORK(IU), storing result in A */
  2220. /* (CWorkspace: need N*N) */
  2221. /* (RWorkspace: 0) */
  2222. cgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &
  2223. work[iu], &ldwrku, &c_b1, &a[a_offset], lda);
  2224. /* Copy left singular vectors of A from A to U */
  2225. clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
  2226. ldu);
  2227. /* Copy right singular vectors of R from WORK(IR) to A */
  2228. clacpy_("F", n, n, &work[ir], &ldwrkr, &a[a_offset],
  2229. lda);
  2230. } else {
  2231. /* Insufficient workspace for a fast algorithm */
  2232. itau = 1;
  2233. iwork = itau + *n;
  2234. /* Compute A=Q*R, copying result to U */
  2235. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  2236. /* (RWorkspace: 0) */
  2237. i__2 = *lwork - iwork + 1;
  2238. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2239. iwork], &i__2, &ierr);
  2240. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  2241. ldu);
  2242. /* Generate Q in U */
  2243. /* (CWorkspace: need N+M, prefer N+M*NB) */
  2244. /* (RWorkspace: 0) */
  2245. i__2 = *lwork - iwork + 1;
  2246. cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
  2247. work[iwork], &i__2, &ierr);
  2248. ie = 1;
  2249. itauq = itau;
  2250. itaup = itauq + *n;
  2251. iwork = itaup + *n;
  2252. /* Zero out below R in A */
  2253. if (*n > 1) {
  2254. i__2 = *n - 1;
  2255. i__3 = *n - 1;
  2256. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
  2257. a_dim1 + 2], lda);
  2258. }
  2259. /* Bidiagonalize R in A */
  2260. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  2261. /* (RWorkspace: need N) */
  2262. i__2 = *lwork - iwork + 1;
  2263. cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
  2264. work[itauq], &work[itaup], &work[iwork], &
  2265. i__2, &ierr);
  2266. /* Multiply Q in U by left bidiagonalizing vectors */
  2267. /* in A */
  2268. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  2269. /* (RWorkspace: 0) */
  2270. i__2 = *lwork - iwork + 1;
  2271. cunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
  2272. work[itauq], &u[u_offset], ldu, &work[iwork],
  2273. &i__2, &ierr)
  2274. ;
  2275. /* Generate right bidiagonalizing vectors in A */
  2276. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  2277. /* (RWorkspace: 0) */
  2278. i__2 = *lwork - iwork + 1;
  2279. cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup],
  2280. &work[iwork], &i__2, &ierr);
  2281. irwork = ie + *n;
  2282. /* Perform bidiagonal QR iteration, computing left */
  2283. /* singular vectors of A in U and computing right */
  2284. /* singular vectors of A in A */
  2285. /* (CWorkspace: 0) */
  2286. /* (RWorkspace: need BDSPAC) */
  2287. cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &a[
  2288. a_offset], lda, &u[u_offset], ldu, cdum, &
  2289. c__1, &rwork[irwork], info);
  2290. }
  2291. } else if (wntvas) {
  2292. /* Path 9 (M much larger than N, JOBU='A', JOBVT='S' */
  2293. /* or 'A') */
  2294. /* M left singular vectors to be computed in U and */
  2295. /* N right singular vectors to be computed in VT */
  2296. /* Computing MAX */
  2297. i__2 = *n + *m, i__3 = *n * 3;
  2298. if (*lwork >= *n * *n + f2cmax(i__2,i__3)) {
  2299. /* Sufficient workspace for a fast algorithm */
  2300. iu = 1;
  2301. if (*lwork >= wrkbl + *lda * *n) {
  2302. /* WORK(IU) is LDA by N */
  2303. ldwrku = *lda;
  2304. } else {
  2305. /* WORK(IU) is N by N */
  2306. ldwrku = *n;
  2307. }
  2308. itau = iu + ldwrku * *n;
  2309. iwork = itau + *n;
  2310. /* Compute A=Q*R, copying result to U */
  2311. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  2312. /* (RWorkspace: 0) */
  2313. i__2 = *lwork - iwork + 1;
  2314. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2315. iwork], &i__2, &ierr);
  2316. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  2317. ldu);
  2318. /* Generate Q in U */
  2319. /* (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB) */
  2320. /* (RWorkspace: 0) */
  2321. i__2 = *lwork - iwork + 1;
  2322. cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
  2323. work[iwork], &i__2, &ierr);
  2324. /* Copy R to WORK(IU), zeroing out below it */
  2325. clacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
  2326. ldwrku);
  2327. i__2 = *n - 1;
  2328. i__3 = *n - 1;
  2329. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
  2330. , &ldwrku);
  2331. ie = 1;
  2332. itauq = itau;
  2333. itaup = itauq + *n;
  2334. iwork = itaup + *n;
  2335. /* Bidiagonalize R in WORK(IU), copying result to VT */
  2336. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
  2337. /* (RWorkspace: need N) */
  2338. i__2 = *lwork - iwork + 1;
  2339. cgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  2340. work[itauq], &work[itaup], &work[iwork], &
  2341. i__2, &ierr);
  2342. clacpy_("U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
  2343. ldvt);
  2344. /* Generate left bidiagonalizing vectors in WORK(IU) */
  2345. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
  2346. /* (RWorkspace: 0) */
  2347. i__2 = *lwork - iwork + 1;
  2348. cungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
  2349. , &work[iwork], &i__2, &ierr);
  2350. /* Generate right bidiagonalizing vectors in VT */
  2351. /* (CWorkspace: need N*N+3*N-1, */
  2352. /* prefer N*N+2*N+(N-1)*NB) */
  2353. /* (RWorkspace: need 0) */
  2354. i__2 = *lwork - iwork + 1;
  2355. cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
  2356. itaup], &work[iwork], &i__2, &ierr)
  2357. ;
  2358. irwork = ie + *n;
  2359. /* Perform bidiagonal QR iteration, computing left */
  2360. /* singular vectors of R in WORK(IU) and computing */
  2361. /* right singular vectors of R in VT */
  2362. /* (CWorkspace: need N*N) */
  2363. /* (RWorkspace: need BDSPAC) */
  2364. cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &vt[
  2365. vt_offset], ldvt, &work[iu], &ldwrku, cdum, &
  2366. c__1, &rwork[irwork], info);
  2367. /* Multiply Q in U by left singular vectors of R in */
  2368. /* WORK(IU), storing result in A */
  2369. /* (CWorkspace: need N*N) */
  2370. /* (RWorkspace: 0) */
  2371. cgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &
  2372. work[iu], &ldwrku, &c_b1, &a[a_offset], lda);
  2373. /* Copy left singular vectors of A from A to U */
  2374. clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
  2375. ldu);
  2376. } else {
  2377. /* Insufficient workspace for a fast algorithm */
  2378. itau = 1;
  2379. iwork = itau + *n;
  2380. /* Compute A=Q*R, copying result to U */
  2381. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  2382. /* (RWorkspace: 0) */
  2383. i__2 = *lwork - iwork + 1;
  2384. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2385. iwork], &i__2, &ierr);
  2386. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  2387. ldu);
  2388. /* Generate Q in U */
  2389. /* (CWorkspace: need N+M, prefer N+M*NB) */
  2390. /* (RWorkspace: 0) */
  2391. i__2 = *lwork - iwork + 1;
  2392. cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
  2393. work[iwork], &i__2, &ierr);
  2394. /* Copy R from A to VT, zeroing out below it */
  2395. clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
  2396. ldvt);
  2397. if (*n > 1) {
  2398. i__2 = *n - 1;
  2399. i__3 = *n - 1;
  2400. claset_("L", &i__2, &i__3, &c_b1, &c_b1, &vt[
  2401. vt_dim1 + 2], ldvt);
  2402. }
  2403. ie = 1;
  2404. itauq = itau;
  2405. itaup = itauq + *n;
  2406. iwork = itaup + *n;
  2407. /* Bidiagonalize R in VT */
  2408. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  2409. /* (RWorkspace: need N) */
  2410. i__2 = *lwork - iwork + 1;
  2411. cgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie],
  2412. &work[itauq], &work[itaup], &work[iwork], &
  2413. i__2, &ierr);
  2414. /* Multiply Q in U by left bidiagonalizing vectors */
  2415. /* in VT */
  2416. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  2417. /* (RWorkspace: 0) */
  2418. i__2 = *lwork - iwork + 1;
  2419. cunmbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt,
  2420. &work[itauq], &u[u_offset], ldu, &work[iwork],
  2421. &i__2, &ierr);
  2422. /* Generate right bidiagonalizing vectors in VT */
  2423. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  2424. /* (RWorkspace: 0) */
  2425. i__2 = *lwork - iwork + 1;
  2426. cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
  2427. itaup], &work[iwork], &i__2, &ierr)
  2428. ;
  2429. irwork = ie + *n;
  2430. /* Perform bidiagonal QR iteration, computing left */
  2431. /* singular vectors of A in U and computing right */
  2432. /* singular vectors of A in VT */
  2433. /* (CWorkspace: 0) */
  2434. /* (RWorkspace: need BDSPAC) */
  2435. cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &vt[
  2436. vt_offset], ldvt, &u[u_offset], ldu, cdum, &
  2437. c__1, &rwork[irwork], info);
  2438. }
  2439. }
  2440. }
  2441. } else {
  2442. /* M .LT. MNTHR */
  2443. /* Path 10 (M at least N, but not much larger) */
  2444. /* Reduce to bidiagonal form without QR decomposition */
  2445. ie = 1;
  2446. itauq = 1;
  2447. itaup = itauq + *n;
  2448. iwork = itaup + *n;
  2449. /* Bidiagonalize A */
  2450. /* (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) */
  2451. /* (RWorkspace: need N) */
  2452. i__2 = *lwork - iwork + 1;
  2453. cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  2454. &work[itaup], &work[iwork], &i__2, &ierr);
  2455. if (wntuas) {
  2456. /* If left singular vectors desired in U, copy result to U */
  2457. /* and generate left bidiagonalizing vectors in U */
  2458. /* (CWorkspace: need 2*N+NCU, prefer 2*N+NCU*NB) */
  2459. /* (RWorkspace: 0) */
  2460. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  2461. if (wntus) {
  2462. ncu = *n;
  2463. }
  2464. if (wntua) {
  2465. ncu = *m;
  2466. }
  2467. i__2 = *lwork - iwork + 1;
  2468. cungbr_("Q", m, &ncu, n, &u[u_offset], ldu, &work[itauq], &
  2469. work[iwork], &i__2, &ierr);
  2470. }
  2471. if (wntvas) {
  2472. /* If right singular vectors desired in VT, copy result to */
  2473. /* VT and generate right bidiagonalizing vectors in VT */
  2474. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  2475. /* (RWorkspace: 0) */
  2476. clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2477. i__2 = *lwork - iwork + 1;
  2478. cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
  2479. work[iwork], &i__2, &ierr);
  2480. }
  2481. if (wntuo) {
  2482. /* If left singular vectors desired in A, generate left */
  2483. /* bidiagonalizing vectors in A */
  2484. /* (CWorkspace: need 3*N, prefer 2*N+N*NB) */
  2485. /* (RWorkspace: 0) */
  2486. i__2 = *lwork - iwork + 1;
  2487. cungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[
  2488. iwork], &i__2, &ierr);
  2489. }
  2490. if (wntvo) {
  2491. /* If right singular vectors desired in A, generate right */
  2492. /* bidiagonalizing vectors in A */
  2493. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  2494. /* (RWorkspace: 0) */
  2495. i__2 = *lwork - iwork + 1;
  2496. cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[
  2497. iwork], &i__2, &ierr);
  2498. }
  2499. irwork = ie + *n;
  2500. if (wntuas || wntuo) {
  2501. nru = *m;
  2502. }
  2503. if (wntun) {
  2504. nru = 0;
  2505. }
  2506. if (wntvas || wntvo) {
  2507. ncvt = *n;
  2508. }
  2509. if (wntvn) {
  2510. ncvt = 0;
  2511. }
  2512. if (! wntuo && ! wntvo) {
  2513. /* Perform bidiagonal QR iteration, if desired, computing */
  2514. /* left singular vectors in U and computing right singular */
  2515. /* vectors in VT */
  2516. /* (CWorkspace: 0) */
  2517. /* (RWorkspace: need BDSPAC) */
  2518. cbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
  2519. vt_offset], ldvt, &u[u_offset], ldu, cdum, &c__1, &
  2520. rwork[irwork], info);
  2521. } else if (! wntuo && wntvo) {
  2522. /* Perform bidiagonal QR iteration, if desired, computing */
  2523. /* left singular vectors in U and computing right singular */
  2524. /* vectors in A */
  2525. /* (CWorkspace: 0) */
  2526. /* (RWorkspace: need BDSPAC) */
  2527. cbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &a[
  2528. a_offset], lda, &u[u_offset], ldu, cdum, &c__1, &
  2529. rwork[irwork], info);
  2530. } else {
  2531. /* Perform bidiagonal QR iteration, if desired, computing */
  2532. /* left singular vectors in A and computing right singular */
  2533. /* vectors in VT */
  2534. /* (CWorkspace: 0) */
  2535. /* (RWorkspace: need BDSPAC) */
  2536. cbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
  2537. vt_offset], ldvt, &a[a_offset], lda, cdum, &c__1, &
  2538. rwork[irwork], info);
  2539. }
  2540. }
  2541. } else {
  2542. /* A has more columns than rows. If A has sufficiently more */
  2543. /* columns than rows, first reduce using the LQ decomposition (if */
  2544. /* sufficient workspace available) */
  2545. if (*n >= mnthr) {
  2546. if (wntvn) {
  2547. /* Path 1t(N much larger than M, JOBVT='N') */
  2548. /* No right singular vectors to be computed */
  2549. itau = 1;
  2550. iwork = itau + *m;
  2551. /* Compute A=L*Q */
  2552. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  2553. /* (RWorkspace: 0) */
  2554. i__2 = *lwork - iwork + 1;
  2555. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
  2556. i__2, &ierr);
  2557. /* Zero out above L */
  2558. i__2 = *m - 1;
  2559. i__3 = *m - 1;
  2560. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
  2561. , lda);
  2562. ie = 1;
  2563. itauq = 1;
  2564. itaup = itauq + *m;
  2565. iwork = itaup + *m;
  2566. /* Bidiagonalize L in A */
  2567. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  2568. /* (RWorkspace: need M) */
  2569. i__2 = *lwork - iwork + 1;
  2570. cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  2571. itauq], &work[itaup], &work[iwork], &i__2, &ierr);
  2572. if (wntuo || wntuas) {
  2573. /* If left singular vectors desired, generate Q */
  2574. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  2575. /* (RWorkspace: 0) */
  2576. i__2 = *lwork - iwork + 1;
  2577. cungbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq], &
  2578. work[iwork], &i__2, &ierr);
  2579. }
  2580. irwork = ie + *m;
  2581. nru = 0;
  2582. if (wntuo || wntuas) {
  2583. nru = *m;
  2584. }
  2585. /* Perform bidiagonal QR iteration, computing left singular */
  2586. /* vectors of A in A if desired */
  2587. /* (CWorkspace: 0) */
  2588. /* (RWorkspace: need BDSPAC) */
  2589. cbdsqr_("U", m, &c__0, &nru, &c__0, &s[1], &rwork[ie], cdum, &
  2590. c__1, &a[a_offset], lda, cdum, &c__1, &rwork[irwork],
  2591. info);
  2592. /* If left singular vectors desired in U, copy them there */
  2593. if (wntuas) {
  2594. clacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2595. }
  2596. } else if (wntvo && wntun) {
  2597. /* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
  2598. /* M right singular vectors to be overwritten on A and */
  2599. /* no left singular vectors to be computed */
  2600. if (*lwork >= *m * *m + *m * 3) {
  2601. /* Sufficient workspace for a fast algorithm */
  2602. ir = 1;
  2603. /* Computing MAX */
  2604. i__2 = wrkbl, i__3 = *lda * *n;
  2605. if (*lwork >= f2cmax(i__2,i__3) + *lda * *m) {
  2606. /* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
  2607. ldwrku = *lda;
  2608. chunk = *n;
  2609. ldwrkr = *lda;
  2610. } else /* if(complicated condition) */ {
  2611. /* Computing MAX */
  2612. i__2 = wrkbl, i__3 = *lda * *n;
  2613. if (*lwork >= f2cmax(i__2,i__3) + *m * *m) {
  2614. /* WORK(IU) is LDA by N and WORK(IR) is M by M */
  2615. ldwrku = *lda;
  2616. chunk = *n;
  2617. ldwrkr = *m;
  2618. } else {
  2619. /* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
  2620. ldwrku = *m;
  2621. chunk = (*lwork - *m * *m) / *m;
  2622. ldwrkr = *m;
  2623. }
  2624. }
  2625. itau = ir + ldwrkr * *m;
  2626. iwork = itau + *m;
  2627. /* Compute A=L*Q */
  2628. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  2629. /* (RWorkspace: 0) */
  2630. i__2 = *lwork - iwork + 1;
  2631. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
  2632. , &i__2, &ierr);
  2633. /* Copy L to WORK(IR) and zero out above it */
  2634. clacpy_("L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr);
  2635. i__2 = *m - 1;
  2636. i__3 = *m - 1;
  2637. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[ir +
  2638. ldwrkr], &ldwrkr);
  2639. /* Generate Q in A */
  2640. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  2641. /* (RWorkspace: 0) */
  2642. i__2 = *lwork - iwork + 1;
  2643. cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
  2644. iwork], &i__2, &ierr);
  2645. ie = 1;
  2646. itauq = itau;
  2647. itaup = itauq + *m;
  2648. iwork = itaup + *m;
  2649. /* Bidiagonalize L in WORK(IR) */
  2650. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
  2651. /* (RWorkspace: need M) */
  2652. i__2 = *lwork - iwork + 1;
  2653. cgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
  2654. work[itauq], &work[itaup], &work[iwork], &i__2, &
  2655. ierr);
  2656. /* Generate right vectors bidiagonalizing L */
  2657. /* (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB) */
  2658. /* (RWorkspace: 0) */
  2659. i__2 = *lwork - iwork + 1;
  2660. cungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
  2661. work[iwork], &i__2, &ierr);
  2662. irwork = ie + *m;
  2663. /* Perform bidiagonal QR iteration, computing right */
  2664. /* singular vectors of L in WORK(IR) */
  2665. /* (CWorkspace: need M*M) */
  2666. /* (RWorkspace: need BDSPAC) */
  2667. cbdsqr_("U", m, m, &c__0, &c__0, &s[1], &rwork[ie], &work[
  2668. ir], &ldwrkr, cdum, &c__1, cdum, &c__1, &rwork[
  2669. irwork], info);
  2670. iu = itauq;
  2671. /* Multiply right singular vectors of L in WORK(IR) by Q */
  2672. /* in A, storing result in WORK(IU) and copying to A */
  2673. /* (CWorkspace: need M*M+M, prefer M*M+M*N) */
  2674. /* (RWorkspace: 0) */
  2675. i__2 = *n;
  2676. i__3 = chunk;
  2677. for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
  2678. i__3) {
  2679. /* Computing MIN */
  2680. i__4 = *n - i__ + 1;
  2681. blk = f2cmin(i__4,chunk);
  2682. cgemm_("N", "N", m, &blk, m, &c_b2, &work[ir], &
  2683. ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b1, &
  2684. work[iu], &ldwrku);
  2685. clacpy_("F", m, &blk, &work[iu], &ldwrku, &a[i__ *
  2686. a_dim1 + 1], lda);
  2687. /* L30: */
  2688. }
  2689. } else {
  2690. /* Insufficient workspace for a fast algorithm */
  2691. ie = 1;
  2692. itauq = 1;
  2693. itaup = itauq + *m;
  2694. iwork = itaup + *m;
  2695. /* Bidiagonalize A */
  2696. /* (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) */
  2697. /* (RWorkspace: need M) */
  2698. i__3 = *lwork - iwork + 1;
  2699. cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  2700. itauq], &work[itaup], &work[iwork], &i__3, &ierr);
  2701. /* Generate right vectors bidiagonalizing A */
  2702. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  2703. /* (RWorkspace: 0) */
  2704. i__3 = *lwork - iwork + 1;
  2705. cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
  2706. work[iwork], &i__3, &ierr);
  2707. irwork = ie + *m;
  2708. /* Perform bidiagonal QR iteration, computing right */
  2709. /* singular vectors of A in A */
  2710. /* (CWorkspace: 0) */
  2711. /* (RWorkspace: need BDSPAC) */
  2712. cbdsqr_("L", m, n, &c__0, &c__0, &s[1], &rwork[ie], &a[
  2713. a_offset], lda, cdum, &c__1, cdum, &c__1, &rwork[
  2714. irwork], info);
  2715. }
  2716. } else if (wntvo && wntuas) {
  2717. /* Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O') */
  2718. /* M right singular vectors to be overwritten on A and */
  2719. /* M left singular vectors to be computed in U */
  2720. if (*lwork >= *m * *m + *m * 3) {
  2721. /* Sufficient workspace for a fast algorithm */
  2722. ir = 1;
  2723. /* Computing MAX */
  2724. i__3 = wrkbl, i__2 = *lda * *n;
  2725. if (*lwork >= f2cmax(i__3,i__2) + *lda * *m) {
  2726. /* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
  2727. ldwrku = *lda;
  2728. chunk = *n;
  2729. ldwrkr = *lda;
  2730. } else /* if(complicated condition) */ {
  2731. /* Computing MAX */
  2732. i__3 = wrkbl, i__2 = *lda * *n;
  2733. if (*lwork >= f2cmax(i__3,i__2) + *m * *m) {
  2734. /* WORK(IU) is LDA by N and WORK(IR) is M by M */
  2735. ldwrku = *lda;
  2736. chunk = *n;
  2737. ldwrkr = *m;
  2738. } else {
  2739. /* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
  2740. ldwrku = *m;
  2741. chunk = (*lwork - *m * *m) / *m;
  2742. ldwrkr = *m;
  2743. }
  2744. }
  2745. itau = ir + ldwrkr * *m;
  2746. iwork = itau + *m;
  2747. /* Compute A=L*Q */
  2748. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  2749. /* (RWorkspace: 0) */
  2750. i__3 = *lwork - iwork + 1;
  2751. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
  2752. , &i__3, &ierr);
  2753. /* Copy L to U, zeroing about above it */
  2754. clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2755. i__3 = *m - 1;
  2756. i__2 = *m - 1;
  2757. claset_("U", &i__3, &i__2, &c_b1, &c_b1, &u[(u_dim1 << 1)
  2758. + 1], ldu);
  2759. /* Generate Q in A */
  2760. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  2761. /* (RWorkspace: 0) */
  2762. i__3 = *lwork - iwork + 1;
  2763. cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
  2764. iwork], &i__3, &ierr);
  2765. ie = 1;
  2766. itauq = itau;
  2767. itaup = itauq + *m;
  2768. iwork = itaup + *m;
  2769. /* Bidiagonalize L in U, copying result to WORK(IR) */
  2770. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
  2771. /* (RWorkspace: need M) */
  2772. i__3 = *lwork - iwork + 1;
  2773. cgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &work[
  2774. itauq], &work[itaup], &work[iwork], &i__3, &ierr);
  2775. clacpy_("U", m, m, &u[u_offset], ldu, &work[ir], &ldwrkr);
  2776. /* Generate right vectors bidiagonalizing L in WORK(IR) */
  2777. /* (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB) */
  2778. /* (RWorkspace: 0) */
  2779. i__3 = *lwork - iwork + 1;
  2780. cungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
  2781. work[iwork], &i__3, &ierr);
  2782. /* Generate left vectors bidiagonalizing L in U */
  2783. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
  2784. /* (RWorkspace: 0) */
  2785. i__3 = *lwork - iwork + 1;
  2786. cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
  2787. work[iwork], &i__3, &ierr);
  2788. irwork = ie + *m;
  2789. /* Perform bidiagonal QR iteration, computing left */
  2790. /* singular vectors of L in U, and computing right */
  2791. /* singular vectors of L in WORK(IR) */
  2792. /* (CWorkspace: need M*M) */
  2793. /* (RWorkspace: need BDSPAC) */
  2794. cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[ir],
  2795. &ldwrkr, &u[u_offset], ldu, cdum, &c__1, &rwork[
  2796. irwork], info);
  2797. iu = itauq;
  2798. /* Multiply right singular vectors of L in WORK(IR) by Q */
  2799. /* in A, storing result in WORK(IU) and copying to A */
  2800. /* (CWorkspace: need M*M+M, prefer M*M+M*N)) */
  2801. /* (RWorkspace: 0) */
  2802. i__3 = *n;
  2803. i__2 = chunk;
  2804. for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
  2805. i__2) {
  2806. /* Computing MIN */
  2807. i__4 = *n - i__ + 1;
  2808. blk = f2cmin(i__4,chunk);
  2809. cgemm_("N", "N", m, &blk, m, &c_b2, &work[ir], &
  2810. ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b1, &
  2811. work[iu], &ldwrku);
  2812. clacpy_("F", m, &blk, &work[iu], &ldwrku, &a[i__ *
  2813. a_dim1 + 1], lda);
  2814. /* L40: */
  2815. }
  2816. } else {
  2817. /* Insufficient workspace for a fast algorithm */
  2818. itau = 1;
  2819. iwork = itau + *m;
  2820. /* Compute A=L*Q */
  2821. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  2822. /* (RWorkspace: 0) */
  2823. i__2 = *lwork - iwork + 1;
  2824. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
  2825. , &i__2, &ierr);
  2826. /* Copy L to U, zeroing out above it */
  2827. clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2828. i__2 = *m - 1;
  2829. i__3 = *m - 1;
  2830. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &u[(u_dim1 << 1)
  2831. + 1], ldu);
  2832. /* Generate Q in A */
  2833. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  2834. /* (RWorkspace: 0) */
  2835. i__2 = *lwork - iwork + 1;
  2836. cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
  2837. iwork], &i__2, &ierr);
  2838. ie = 1;
  2839. itauq = itau;
  2840. itaup = itauq + *m;
  2841. iwork = itaup + *m;
  2842. /* Bidiagonalize L in U */
  2843. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  2844. /* (RWorkspace: need M) */
  2845. i__2 = *lwork - iwork + 1;
  2846. cgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &work[
  2847. itauq], &work[itaup], &work[iwork], &i__2, &ierr);
  2848. /* Multiply right vectors bidiagonalizing L by Q in A */
  2849. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  2850. /* (RWorkspace: 0) */
  2851. i__2 = *lwork - iwork + 1;
  2852. cunmbr_("P", "L", "C", m, n, m, &u[u_offset], ldu, &work[
  2853. itaup], &a[a_offset], lda, &work[iwork], &i__2, &
  2854. ierr);
  2855. /* Generate left vectors bidiagonalizing L in U */
  2856. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  2857. /* (RWorkspace: 0) */
  2858. i__2 = *lwork - iwork + 1;
  2859. cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
  2860. work[iwork], &i__2, &ierr);
  2861. irwork = ie + *m;
  2862. /* Perform bidiagonal QR iteration, computing left */
  2863. /* singular vectors of A in U and computing right */
  2864. /* singular vectors of A in A */
  2865. /* (CWorkspace: 0) */
  2866. /* (RWorkspace: need BDSPAC) */
  2867. cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &a[
  2868. a_offset], lda, &u[u_offset], ldu, cdum, &c__1, &
  2869. rwork[irwork], info);
  2870. }
  2871. } else if (wntvs) {
  2872. if (wntun) {
  2873. /* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
  2874. /* M right singular vectors to be computed in VT and */
  2875. /* no left singular vectors to be computed */
  2876. if (*lwork >= *m * *m + *m * 3) {
  2877. /* Sufficient workspace for a fast algorithm */
  2878. ir = 1;
  2879. if (*lwork >= wrkbl + *lda * *m) {
  2880. /* WORK(IR) is LDA by M */
  2881. ldwrkr = *lda;
  2882. } else {
  2883. /* WORK(IR) is M by M */
  2884. ldwrkr = *m;
  2885. }
  2886. itau = ir + ldwrkr * *m;
  2887. iwork = itau + *m;
  2888. /* Compute A=L*Q */
  2889. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  2890. /* (RWorkspace: 0) */
  2891. i__2 = *lwork - iwork + 1;
  2892. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2893. iwork], &i__2, &ierr);
  2894. /* Copy L to WORK(IR), zeroing out above it */
  2895. clacpy_("L", m, m, &a[a_offset], lda, &work[ir], &
  2896. ldwrkr);
  2897. i__2 = *m - 1;
  2898. i__3 = *m - 1;
  2899. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[ir +
  2900. ldwrkr], &ldwrkr);
  2901. /* Generate Q in A */
  2902. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  2903. /* (RWorkspace: 0) */
  2904. i__2 = *lwork - iwork + 1;
  2905. cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &
  2906. work[iwork], &i__2, &ierr);
  2907. ie = 1;
  2908. itauq = itau;
  2909. itaup = itauq + *m;
  2910. iwork = itaup + *m;
  2911. /* Bidiagonalize L in WORK(IR) */
  2912. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
  2913. /* (RWorkspace: need M) */
  2914. i__2 = *lwork - iwork + 1;
  2915. cgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
  2916. work[itauq], &work[itaup], &work[iwork], &
  2917. i__2, &ierr);
  2918. /* Generate right vectors bidiagonalizing L in */
  2919. /* WORK(IR) */
  2920. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB) */
  2921. /* (RWorkspace: 0) */
  2922. i__2 = *lwork - iwork + 1;
  2923. cungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
  2924. , &work[iwork], &i__2, &ierr);
  2925. irwork = ie + *m;
  2926. /* Perform bidiagonal QR iteration, computing right */
  2927. /* singular vectors of L in WORK(IR) */
  2928. /* (CWorkspace: need M*M) */
  2929. /* (RWorkspace: need BDSPAC) */
  2930. cbdsqr_("U", m, m, &c__0, &c__0, &s[1], &rwork[ie], &
  2931. work[ir], &ldwrkr, cdum, &c__1, cdum, &c__1, &
  2932. rwork[irwork], info);
  2933. /* Multiply right singular vectors of L in WORK(IR) by */
  2934. /* Q in A, storing result in VT */
  2935. /* (CWorkspace: need M*M) */
  2936. /* (RWorkspace: 0) */
  2937. cgemm_("N", "N", m, n, m, &c_b2, &work[ir], &ldwrkr, &
  2938. a[a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
  2939. } else {
  2940. /* Insufficient workspace for a fast algorithm */
  2941. itau = 1;
  2942. iwork = itau + *m;
  2943. /* Compute A=L*Q */
  2944. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  2945. /* (RWorkspace: 0) */
  2946. i__2 = *lwork - iwork + 1;
  2947. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2948. iwork], &i__2, &ierr);
  2949. /* Copy result to VT */
  2950. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  2951. ldvt);
  2952. /* Generate Q in VT */
  2953. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  2954. /* (RWorkspace: 0) */
  2955. i__2 = *lwork - iwork + 1;
  2956. cunglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
  2957. work[iwork], &i__2, &ierr);
  2958. ie = 1;
  2959. itauq = itau;
  2960. itaup = itauq + *m;
  2961. iwork = itaup + *m;
  2962. /* Zero out above L in A */
  2963. i__2 = *m - 1;
  2964. i__3 = *m - 1;
  2965. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
  2966. 1) + 1], lda);
  2967. /* Bidiagonalize L in A */
  2968. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  2969. /* (RWorkspace: need M) */
  2970. i__2 = *lwork - iwork + 1;
  2971. cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
  2972. work[itauq], &work[itaup], &work[iwork], &
  2973. i__2, &ierr);
  2974. /* Multiply right vectors bidiagonalizing L by Q in VT */
  2975. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  2976. /* (RWorkspace: 0) */
  2977. i__2 = *lwork - iwork + 1;
  2978. cunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
  2979. work[itaup], &vt[vt_offset], ldvt, &work[
  2980. iwork], &i__2, &ierr);
  2981. irwork = ie + *m;
  2982. /* Perform bidiagonal QR iteration, computing right */
  2983. /* singular vectors of A in VT */
  2984. /* (CWorkspace: 0) */
  2985. /* (RWorkspace: need BDSPAC) */
  2986. cbdsqr_("U", m, n, &c__0, &c__0, &s[1], &rwork[ie], &
  2987. vt[vt_offset], ldvt, cdum, &c__1, cdum, &c__1,
  2988. &rwork[irwork], info);
  2989. }
  2990. } else if (wntuo) {
  2991. /* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
  2992. /* M right singular vectors to be computed in VT and */
  2993. /* M left singular vectors to be overwritten on A */
  2994. if (*lwork >= (*m << 1) * *m + *m * 3) {
  2995. /* Sufficient workspace for a fast algorithm */
  2996. iu = 1;
  2997. if (*lwork >= wrkbl + (*lda << 1) * *m) {
  2998. /* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
  2999. ldwrku = *lda;
  3000. ir = iu + ldwrku * *m;
  3001. ldwrkr = *lda;
  3002. } else if (*lwork >= wrkbl + (*lda + *m) * *m) {
  3003. /* WORK(IU) is LDA by M and WORK(IR) is M by M */
  3004. ldwrku = *lda;
  3005. ir = iu + ldwrku * *m;
  3006. ldwrkr = *m;
  3007. } else {
  3008. /* WORK(IU) is M by M and WORK(IR) is M by M */
  3009. ldwrku = *m;
  3010. ir = iu + ldwrku * *m;
  3011. ldwrkr = *m;
  3012. }
  3013. itau = ir + ldwrkr * *m;
  3014. iwork = itau + *m;
  3015. /* Compute A=L*Q */
  3016. /* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
  3017. /* (RWorkspace: 0) */
  3018. i__2 = *lwork - iwork + 1;
  3019. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3020. iwork], &i__2, &ierr);
  3021. /* Copy L to WORK(IU), zeroing out below it */
  3022. clacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
  3023. ldwrku);
  3024. i__2 = *m - 1;
  3025. i__3 = *m - 1;
  3026. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
  3027. ldwrku], &ldwrku);
  3028. /* Generate Q in A */
  3029. /* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
  3030. /* (RWorkspace: 0) */
  3031. i__2 = *lwork - iwork + 1;
  3032. cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &
  3033. work[iwork], &i__2, &ierr);
  3034. ie = 1;
  3035. itauq = itau;
  3036. itaup = itauq + *m;
  3037. iwork = itaup + *m;
  3038. /* Bidiagonalize L in WORK(IU), copying result to */
  3039. /* WORK(IR) */
  3040. /* (CWorkspace: need 2*M*M+3*M, */
  3041. /* prefer 2*M*M+2*M+2*M*NB) */
  3042. /* (RWorkspace: need M) */
  3043. i__2 = *lwork - iwork + 1;
  3044. cgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  3045. work[itauq], &work[itaup], &work[iwork], &
  3046. i__2, &ierr);
  3047. clacpy_("L", m, m, &work[iu], &ldwrku, &work[ir], &
  3048. ldwrkr);
  3049. /* Generate right bidiagonalizing vectors in WORK(IU) */
  3050. /* (CWorkspace: need 2*M*M+3*M-1, */
  3051. /* prefer 2*M*M+2*M+(M-1)*NB) */
  3052. /* (RWorkspace: 0) */
  3053. i__2 = *lwork - iwork + 1;
  3054. cungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
  3055. , &work[iwork], &i__2, &ierr);
  3056. /* Generate left bidiagonalizing vectors in WORK(IR) */
  3057. /* (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) */
  3058. /* (RWorkspace: 0) */
  3059. i__2 = *lwork - iwork + 1;
  3060. cungbr_("Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
  3061. , &work[iwork], &i__2, &ierr);
  3062. irwork = ie + *m;
  3063. /* Perform bidiagonal QR iteration, computing left */
  3064. /* singular vectors of L in WORK(IR) and computing */
  3065. /* right singular vectors of L in WORK(IU) */
  3066. /* (CWorkspace: need 2*M*M) */
  3067. /* (RWorkspace: need BDSPAC) */
  3068. cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
  3069. iu], &ldwrku, &work[ir], &ldwrkr, cdum, &c__1,
  3070. &rwork[irwork], info);
  3071. /* Multiply right singular vectors of L in WORK(IU) by */
  3072. /* Q in A, storing result in VT */
  3073. /* (CWorkspace: need M*M) */
  3074. /* (RWorkspace: 0) */
  3075. cgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
  3076. a[a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
  3077. /* Copy left singular vectors of L to A */
  3078. /* (CWorkspace: need M*M) */
  3079. /* (RWorkspace: 0) */
  3080. clacpy_("F", m, m, &work[ir], &ldwrkr, &a[a_offset],
  3081. lda);
  3082. } else {
  3083. /* Insufficient workspace for a fast algorithm */
  3084. itau = 1;
  3085. iwork = itau + *m;
  3086. /* Compute A=L*Q, copying result to VT */
  3087. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3088. /* (RWorkspace: 0) */
  3089. i__2 = *lwork - iwork + 1;
  3090. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3091. iwork], &i__2, &ierr);
  3092. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3093. ldvt);
  3094. /* Generate Q in VT */
  3095. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3096. /* (RWorkspace: 0) */
  3097. i__2 = *lwork - iwork + 1;
  3098. cunglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3099. work[iwork], &i__2, &ierr);
  3100. ie = 1;
  3101. itauq = itau;
  3102. itaup = itauq + *m;
  3103. iwork = itaup + *m;
  3104. /* Zero out above L in A */
  3105. i__2 = *m - 1;
  3106. i__3 = *m - 1;
  3107. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
  3108. 1) + 1], lda);
  3109. /* Bidiagonalize L in A */
  3110. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  3111. /* (RWorkspace: need M) */
  3112. i__2 = *lwork - iwork + 1;
  3113. cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
  3114. work[itauq], &work[itaup], &work[iwork], &
  3115. i__2, &ierr);
  3116. /* Multiply right vectors bidiagonalizing L by Q in VT */
  3117. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  3118. /* (RWorkspace: 0) */
  3119. i__2 = *lwork - iwork + 1;
  3120. cunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
  3121. work[itaup], &vt[vt_offset], ldvt, &work[
  3122. iwork], &i__2, &ierr);
  3123. /* Generate left bidiagonalizing vectors of L in A */
  3124. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  3125. /* (RWorkspace: 0) */
  3126. i__2 = *lwork - iwork + 1;
  3127. cungbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq],
  3128. &work[iwork], &i__2, &ierr);
  3129. irwork = ie + *m;
  3130. /* Perform bidiagonal QR iteration, computing left */
  3131. /* singular vectors of A in A and computing right */
  3132. /* singular vectors of A in VT */
  3133. /* (CWorkspace: 0) */
  3134. /* (RWorkspace: need BDSPAC) */
  3135. cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
  3136. vt_offset], ldvt, &a[a_offset], lda, cdum, &
  3137. c__1, &rwork[irwork], info);
  3138. }
  3139. } else if (wntuas) {
  3140. /* Path 6t(N much larger than M, JOBU='S' or 'A', */
  3141. /* JOBVT='S') */
  3142. /* M right singular vectors to be computed in VT and */
  3143. /* M left singular vectors to be computed in U */
  3144. if (*lwork >= *m * *m + *m * 3) {
  3145. /* Sufficient workspace for a fast algorithm */
  3146. iu = 1;
  3147. if (*lwork >= wrkbl + *lda * *m) {
  3148. /* WORK(IU) is LDA by N */
  3149. ldwrku = *lda;
  3150. } else {
  3151. /* WORK(IU) is LDA by M */
  3152. ldwrku = *m;
  3153. }
  3154. itau = iu + ldwrku * *m;
  3155. iwork = itau + *m;
  3156. /* Compute A=L*Q */
  3157. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  3158. /* (RWorkspace: 0) */
  3159. i__2 = *lwork - iwork + 1;
  3160. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3161. iwork], &i__2, &ierr);
  3162. /* Copy L to WORK(IU), zeroing out above it */
  3163. clacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
  3164. ldwrku);
  3165. i__2 = *m - 1;
  3166. i__3 = *m - 1;
  3167. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
  3168. ldwrku], &ldwrku);
  3169. /* Generate Q in A */
  3170. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  3171. /* (RWorkspace: 0) */
  3172. i__2 = *lwork - iwork + 1;
  3173. cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &
  3174. work[iwork], &i__2, &ierr);
  3175. ie = 1;
  3176. itauq = itau;
  3177. itaup = itauq + *m;
  3178. iwork = itaup + *m;
  3179. /* Bidiagonalize L in WORK(IU), copying result to U */
  3180. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
  3181. /* (RWorkspace: need M) */
  3182. i__2 = *lwork - iwork + 1;
  3183. cgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  3184. work[itauq], &work[itaup], &work[iwork], &
  3185. i__2, &ierr);
  3186. clacpy_("L", m, m, &work[iu], &ldwrku, &u[u_offset],
  3187. ldu);
  3188. /* Generate right bidiagonalizing vectors in WORK(IU) */
  3189. /* (CWorkspace: need M*M+3*M-1, */
  3190. /* prefer M*M+2*M+(M-1)*NB) */
  3191. /* (RWorkspace: 0) */
  3192. i__2 = *lwork - iwork + 1;
  3193. cungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
  3194. , &work[iwork], &i__2, &ierr);
  3195. /* Generate left bidiagonalizing vectors in U */
  3196. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
  3197. /* (RWorkspace: 0) */
  3198. i__2 = *lwork - iwork + 1;
  3199. cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
  3200. &work[iwork], &i__2, &ierr);
  3201. irwork = ie + *m;
  3202. /* Perform bidiagonal QR iteration, computing left */
  3203. /* singular vectors of L in U and computing right */
  3204. /* singular vectors of L in WORK(IU) */
  3205. /* (CWorkspace: need M*M) */
  3206. /* (RWorkspace: need BDSPAC) */
  3207. cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
  3208. iu], &ldwrku, &u[u_offset], ldu, cdum, &c__1,
  3209. &rwork[irwork], info);
  3210. /* Multiply right singular vectors of L in WORK(IU) by */
  3211. /* Q in A, storing result in VT */
  3212. /* (CWorkspace: need M*M) */
  3213. /* (RWorkspace: 0) */
  3214. cgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
  3215. a[a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
  3216. } else {
  3217. /* Insufficient workspace for a fast algorithm */
  3218. itau = 1;
  3219. iwork = itau + *m;
  3220. /* Compute A=L*Q, copying result to VT */
  3221. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3222. /* (RWorkspace: 0) */
  3223. i__2 = *lwork - iwork + 1;
  3224. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3225. iwork], &i__2, &ierr);
  3226. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3227. ldvt);
  3228. /* Generate Q in VT */
  3229. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3230. /* (RWorkspace: 0) */
  3231. i__2 = *lwork - iwork + 1;
  3232. cunglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3233. work[iwork], &i__2, &ierr);
  3234. /* Copy L to U, zeroing out above it */
  3235. clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset],
  3236. ldu);
  3237. i__2 = *m - 1;
  3238. i__3 = *m - 1;
  3239. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &u[(u_dim1 <<
  3240. 1) + 1], ldu);
  3241. ie = 1;
  3242. itauq = itau;
  3243. itaup = itauq + *m;
  3244. iwork = itaup + *m;
  3245. /* Bidiagonalize L in U */
  3246. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  3247. /* (RWorkspace: need M) */
  3248. i__2 = *lwork - iwork + 1;
  3249. cgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &
  3250. work[itauq], &work[itaup], &work[iwork], &
  3251. i__2, &ierr);
  3252. /* Multiply right bidiagonalizing vectors in U by Q */
  3253. /* in VT */
  3254. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  3255. /* (RWorkspace: 0) */
  3256. i__2 = *lwork - iwork + 1;
  3257. cunmbr_("P", "L", "C", m, n, m, &u[u_offset], ldu, &
  3258. work[itaup], &vt[vt_offset], ldvt, &work[
  3259. iwork], &i__2, &ierr);
  3260. /* Generate left bidiagonalizing vectors in U */
  3261. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  3262. /* (RWorkspace: 0) */
  3263. i__2 = *lwork - iwork + 1;
  3264. cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
  3265. &work[iwork], &i__2, &ierr);
  3266. irwork = ie + *m;
  3267. /* Perform bidiagonal QR iteration, computing left */
  3268. /* singular vectors of A in U and computing right */
  3269. /* singular vectors of A in VT */
  3270. /* (CWorkspace: 0) */
  3271. /* (RWorkspace: need BDSPAC) */
  3272. cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
  3273. vt_offset], ldvt, &u[u_offset], ldu, cdum, &
  3274. c__1, &rwork[irwork], info);
  3275. }
  3276. }
  3277. } else if (wntva) {
  3278. if (wntun) {
  3279. /* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
  3280. /* N right singular vectors to be computed in VT and */
  3281. /* no left singular vectors to be computed */
  3282. /* Computing MAX */
  3283. i__2 = *n + *m, i__3 = *m * 3;
  3284. if (*lwork >= *m * *m + f2cmax(i__2,i__3)) {
  3285. /* Sufficient workspace for a fast algorithm */
  3286. ir = 1;
  3287. if (*lwork >= wrkbl + *lda * *m) {
  3288. /* WORK(IR) is LDA by M */
  3289. ldwrkr = *lda;
  3290. } else {
  3291. /* WORK(IR) is M by M */
  3292. ldwrkr = *m;
  3293. }
  3294. itau = ir + ldwrkr * *m;
  3295. iwork = itau + *m;
  3296. /* Compute A=L*Q, copying result to VT */
  3297. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  3298. /* (RWorkspace: 0) */
  3299. i__2 = *lwork - iwork + 1;
  3300. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3301. iwork], &i__2, &ierr);
  3302. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3303. ldvt);
  3304. /* Copy L to WORK(IR), zeroing out above it */
  3305. clacpy_("L", m, m, &a[a_offset], lda, &work[ir], &
  3306. ldwrkr);
  3307. i__2 = *m - 1;
  3308. i__3 = *m - 1;
  3309. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[ir +
  3310. ldwrkr], &ldwrkr);
  3311. /* Generate Q in VT */
  3312. /* (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB) */
  3313. /* (RWorkspace: 0) */
  3314. i__2 = *lwork - iwork + 1;
  3315. cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3316. work[iwork], &i__2, &ierr);
  3317. ie = 1;
  3318. itauq = itau;
  3319. itaup = itauq + *m;
  3320. iwork = itaup + *m;
  3321. /* Bidiagonalize L in WORK(IR) */
  3322. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
  3323. /* (RWorkspace: need M) */
  3324. i__2 = *lwork - iwork + 1;
  3325. cgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
  3326. work[itauq], &work[itaup], &work[iwork], &
  3327. i__2, &ierr);
  3328. /* Generate right bidiagonalizing vectors in WORK(IR) */
  3329. /* (CWorkspace: need M*M+3*M-1, */
  3330. /* prefer M*M+2*M+(M-1)*NB) */
  3331. /* (RWorkspace: 0) */
  3332. i__2 = *lwork - iwork + 1;
  3333. cungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
  3334. , &work[iwork], &i__2, &ierr);
  3335. irwork = ie + *m;
  3336. /* Perform bidiagonal QR iteration, computing right */
  3337. /* singular vectors of L in WORK(IR) */
  3338. /* (CWorkspace: need M*M) */
  3339. /* (RWorkspace: need BDSPAC) */
  3340. cbdsqr_("U", m, m, &c__0, &c__0, &s[1], &rwork[ie], &
  3341. work[ir], &ldwrkr, cdum, &c__1, cdum, &c__1, &
  3342. rwork[irwork], info);
  3343. /* Multiply right singular vectors of L in WORK(IR) by */
  3344. /* Q in VT, storing result in A */
  3345. /* (CWorkspace: need M*M) */
  3346. /* (RWorkspace: 0) */
  3347. cgemm_("N", "N", m, n, m, &c_b2, &work[ir], &ldwrkr, &
  3348. vt[vt_offset], ldvt, &c_b1, &a[a_offset], lda);
  3349. /* Copy right singular vectors of A from A to VT */
  3350. clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
  3351. ldvt);
  3352. } else {
  3353. /* Insufficient workspace for a fast algorithm */
  3354. itau = 1;
  3355. iwork = itau + *m;
  3356. /* Compute A=L*Q, copying result to VT */
  3357. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3358. /* (RWorkspace: 0) */
  3359. i__2 = *lwork - iwork + 1;
  3360. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3361. iwork], &i__2, &ierr);
  3362. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3363. ldvt);
  3364. /* Generate Q in VT */
  3365. /* (CWorkspace: need M+N, prefer M+N*NB) */
  3366. /* (RWorkspace: 0) */
  3367. i__2 = *lwork - iwork + 1;
  3368. cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3369. work[iwork], &i__2, &ierr);
  3370. ie = 1;
  3371. itauq = itau;
  3372. itaup = itauq + *m;
  3373. iwork = itaup + *m;
  3374. /* Zero out above L in A */
  3375. i__2 = *m - 1;
  3376. i__3 = *m - 1;
  3377. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
  3378. 1) + 1], lda);
  3379. /* Bidiagonalize L in A */
  3380. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  3381. /* (RWorkspace: need M) */
  3382. i__2 = *lwork - iwork + 1;
  3383. cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
  3384. work[itauq], &work[itaup], &work[iwork], &
  3385. i__2, &ierr);
  3386. /* Multiply right bidiagonalizing vectors in A by Q */
  3387. /* in VT */
  3388. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  3389. /* (RWorkspace: 0) */
  3390. i__2 = *lwork - iwork + 1;
  3391. cunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
  3392. work[itaup], &vt[vt_offset], ldvt, &work[
  3393. iwork], &i__2, &ierr);
  3394. irwork = ie + *m;
  3395. /* Perform bidiagonal QR iteration, computing right */
  3396. /* singular vectors of A in VT */
  3397. /* (CWorkspace: 0) */
  3398. /* (RWorkspace: need BDSPAC) */
  3399. cbdsqr_("U", m, n, &c__0, &c__0, &s[1], &rwork[ie], &
  3400. vt[vt_offset], ldvt, cdum, &c__1, cdum, &c__1,
  3401. &rwork[irwork], info);
  3402. }
  3403. } else if (wntuo) {
  3404. /* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
  3405. /* N right singular vectors to be computed in VT and */
  3406. /* M left singular vectors to be overwritten on A */
  3407. /* Computing MAX */
  3408. i__2 = *n + *m, i__3 = *m * 3;
  3409. if (*lwork >= (*m << 1) * *m + f2cmax(i__2,i__3)) {
  3410. /* Sufficient workspace for a fast algorithm */
  3411. iu = 1;
  3412. if (*lwork >= wrkbl + (*lda << 1) * *m) {
  3413. /* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
  3414. ldwrku = *lda;
  3415. ir = iu + ldwrku * *m;
  3416. ldwrkr = *lda;
  3417. } else if (*lwork >= wrkbl + (*lda + *m) * *m) {
  3418. /* WORK(IU) is LDA by M and WORK(IR) is M by M */
  3419. ldwrku = *lda;
  3420. ir = iu + ldwrku * *m;
  3421. ldwrkr = *m;
  3422. } else {
  3423. /* WORK(IU) is M by M and WORK(IR) is M by M */
  3424. ldwrku = *m;
  3425. ir = iu + ldwrku * *m;
  3426. ldwrkr = *m;
  3427. }
  3428. itau = ir + ldwrkr * *m;
  3429. iwork = itau + *m;
  3430. /* Compute A=L*Q, copying result to VT */
  3431. /* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
  3432. /* (RWorkspace: 0) */
  3433. i__2 = *lwork - iwork + 1;
  3434. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3435. iwork], &i__2, &ierr);
  3436. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3437. ldvt);
  3438. /* Generate Q in VT */
  3439. /* (CWorkspace: need 2*M*M+M+N, prefer 2*M*M+M+N*NB) */
  3440. /* (RWorkspace: 0) */
  3441. i__2 = *lwork - iwork + 1;
  3442. cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3443. work[iwork], &i__2, &ierr);
  3444. /* Copy L to WORK(IU), zeroing out above it */
  3445. clacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
  3446. ldwrku);
  3447. i__2 = *m - 1;
  3448. i__3 = *m - 1;
  3449. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
  3450. ldwrku], &ldwrku);
  3451. ie = 1;
  3452. itauq = itau;
  3453. itaup = itauq + *m;
  3454. iwork = itaup + *m;
  3455. /* Bidiagonalize L in WORK(IU), copying result to */
  3456. /* WORK(IR) */
  3457. /* (CWorkspace: need 2*M*M+3*M, */
  3458. /* prefer 2*M*M+2*M+2*M*NB) */
  3459. /* (RWorkspace: need M) */
  3460. i__2 = *lwork - iwork + 1;
  3461. cgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  3462. work[itauq], &work[itaup], &work[iwork], &
  3463. i__2, &ierr);
  3464. clacpy_("L", m, m, &work[iu], &ldwrku, &work[ir], &
  3465. ldwrkr);
  3466. /* Generate right bidiagonalizing vectors in WORK(IU) */
  3467. /* (CWorkspace: need 2*M*M+3*M-1, */
  3468. /* prefer 2*M*M+2*M+(M-1)*NB) */
  3469. /* (RWorkspace: 0) */
  3470. i__2 = *lwork - iwork + 1;
  3471. cungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
  3472. , &work[iwork], &i__2, &ierr);
  3473. /* Generate left bidiagonalizing vectors in WORK(IR) */
  3474. /* (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) */
  3475. /* (RWorkspace: 0) */
  3476. i__2 = *lwork - iwork + 1;
  3477. cungbr_("Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
  3478. , &work[iwork], &i__2, &ierr);
  3479. irwork = ie + *m;
  3480. /* Perform bidiagonal QR iteration, computing left */
  3481. /* singular vectors of L in WORK(IR) and computing */
  3482. /* right singular vectors of L in WORK(IU) */
  3483. /* (CWorkspace: need 2*M*M) */
  3484. /* (RWorkspace: need BDSPAC) */
  3485. cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
  3486. iu], &ldwrku, &work[ir], &ldwrkr, cdum, &c__1,
  3487. &rwork[irwork], info);
  3488. /* Multiply right singular vectors of L in WORK(IU) by */
  3489. /* Q in VT, storing result in A */
  3490. /* (CWorkspace: need M*M) */
  3491. /* (RWorkspace: 0) */
  3492. cgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
  3493. vt[vt_offset], ldvt, &c_b1, &a[a_offset], lda);
  3494. /* Copy right singular vectors of A from A to VT */
  3495. clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
  3496. ldvt);
  3497. /* Copy left singular vectors of A from WORK(IR) to A */
  3498. clacpy_("F", m, m, &work[ir], &ldwrkr, &a[a_offset],
  3499. lda);
  3500. } else {
  3501. /* Insufficient workspace for a fast algorithm */
  3502. itau = 1;
  3503. iwork = itau + *m;
  3504. /* Compute A=L*Q, copying result to VT */
  3505. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3506. /* (RWorkspace: 0) */
  3507. i__2 = *lwork - iwork + 1;
  3508. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3509. iwork], &i__2, &ierr);
  3510. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3511. ldvt);
  3512. /* Generate Q in VT */
  3513. /* (CWorkspace: need M+N, prefer M+N*NB) */
  3514. /* (RWorkspace: 0) */
  3515. i__2 = *lwork - iwork + 1;
  3516. cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3517. work[iwork], &i__2, &ierr);
  3518. ie = 1;
  3519. itauq = itau;
  3520. itaup = itauq + *m;
  3521. iwork = itaup + *m;
  3522. /* Zero out above L in A */
  3523. i__2 = *m - 1;
  3524. i__3 = *m - 1;
  3525. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
  3526. 1) + 1], lda);
  3527. /* Bidiagonalize L in A */
  3528. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  3529. /* (RWorkspace: need M) */
  3530. i__2 = *lwork - iwork + 1;
  3531. cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
  3532. work[itauq], &work[itaup], &work[iwork], &
  3533. i__2, &ierr);
  3534. /* Multiply right bidiagonalizing vectors in A by Q */
  3535. /* in VT */
  3536. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  3537. /* (RWorkspace: 0) */
  3538. i__2 = *lwork - iwork + 1;
  3539. cunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
  3540. work[itaup], &vt[vt_offset], ldvt, &work[
  3541. iwork], &i__2, &ierr);
  3542. /* Generate left bidiagonalizing vectors in A */
  3543. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  3544. /* (RWorkspace: 0) */
  3545. i__2 = *lwork - iwork + 1;
  3546. cungbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq],
  3547. &work[iwork], &i__2, &ierr);
  3548. irwork = ie + *m;
  3549. /* Perform bidiagonal QR iteration, computing left */
  3550. /* singular vectors of A in A and computing right */
  3551. /* singular vectors of A in VT */
  3552. /* (CWorkspace: 0) */
  3553. /* (RWorkspace: need BDSPAC) */
  3554. cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
  3555. vt_offset], ldvt, &a[a_offset], lda, cdum, &
  3556. c__1, &rwork[irwork], info);
  3557. }
  3558. } else if (wntuas) {
  3559. /* Path 9t(N much larger than M, JOBU='S' or 'A', */
  3560. /* JOBVT='A') */
  3561. /* N right singular vectors to be computed in VT and */
  3562. /* M left singular vectors to be computed in U */
  3563. /* Computing MAX */
  3564. i__2 = *n + *m, i__3 = *m * 3;
  3565. if (*lwork >= *m * *m + f2cmax(i__2,i__3)) {
  3566. /* Sufficient workspace for a fast algorithm */
  3567. iu = 1;
  3568. if (*lwork >= wrkbl + *lda * *m) {
  3569. /* WORK(IU) is LDA by M */
  3570. ldwrku = *lda;
  3571. } else {
  3572. /* WORK(IU) is M by M */
  3573. ldwrku = *m;
  3574. }
  3575. itau = iu + ldwrku * *m;
  3576. iwork = itau + *m;
  3577. /* Compute A=L*Q, copying result to VT */
  3578. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  3579. /* (RWorkspace: 0) */
  3580. i__2 = *lwork - iwork + 1;
  3581. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3582. iwork], &i__2, &ierr);
  3583. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3584. ldvt);
  3585. /* Generate Q in VT */
  3586. /* (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB) */
  3587. /* (RWorkspace: 0) */
  3588. i__2 = *lwork - iwork + 1;
  3589. cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3590. work[iwork], &i__2, &ierr);
  3591. /* Copy L to WORK(IU), zeroing out above it */
  3592. clacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
  3593. ldwrku);
  3594. i__2 = *m - 1;
  3595. i__3 = *m - 1;
  3596. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
  3597. ldwrku], &ldwrku);
  3598. ie = 1;
  3599. itauq = itau;
  3600. itaup = itauq + *m;
  3601. iwork = itaup + *m;
  3602. /* Bidiagonalize L in WORK(IU), copying result to U */
  3603. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
  3604. /* (RWorkspace: need M) */
  3605. i__2 = *lwork - iwork + 1;
  3606. cgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  3607. work[itauq], &work[itaup], &work[iwork], &
  3608. i__2, &ierr);
  3609. clacpy_("L", m, m, &work[iu], &ldwrku, &u[u_offset],
  3610. ldu);
  3611. /* Generate right bidiagonalizing vectors in WORK(IU) */
  3612. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB) */
  3613. /* (RWorkspace: 0) */
  3614. i__2 = *lwork - iwork + 1;
  3615. cungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
  3616. , &work[iwork], &i__2, &ierr);
  3617. /* Generate left bidiagonalizing vectors in U */
  3618. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
  3619. /* (RWorkspace: 0) */
  3620. i__2 = *lwork - iwork + 1;
  3621. cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
  3622. &work[iwork], &i__2, &ierr);
  3623. irwork = ie + *m;
  3624. /* Perform bidiagonal QR iteration, computing left */
  3625. /* singular vectors of L in U and computing right */
  3626. /* singular vectors of L in WORK(IU) */
  3627. /* (CWorkspace: need M*M) */
  3628. /* (RWorkspace: need BDSPAC) */
  3629. cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
  3630. iu], &ldwrku, &u[u_offset], ldu, cdum, &c__1,
  3631. &rwork[irwork], info);
  3632. /* Multiply right singular vectors of L in WORK(IU) by */
  3633. /* Q in VT, storing result in A */
  3634. /* (CWorkspace: need M*M) */
  3635. /* (RWorkspace: 0) */
  3636. cgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
  3637. vt[vt_offset], ldvt, &c_b1, &a[a_offset], lda);
  3638. /* Copy right singular vectors of A from A to VT */
  3639. clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
  3640. ldvt);
  3641. } else {
  3642. /* Insufficient workspace for a fast algorithm */
  3643. itau = 1;
  3644. iwork = itau + *m;
  3645. /* Compute A=L*Q, copying result to VT */
  3646. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3647. /* (RWorkspace: 0) */
  3648. i__2 = *lwork - iwork + 1;
  3649. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3650. iwork], &i__2, &ierr);
  3651. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3652. ldvt);
  3653. /* Generate Q in VT */
  3654. /* (CWorkspace: need M+N, prefer M+N*NB) */
  3655. /* (RWorkspace: 0) */
  3656. i__2 = *lwork - iwork + 1;
  3657. cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3658. work[iwork], &i__2, &ierr);
  3659. /* Copy L to U, zeroing out above it */
  3660. clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset],
  3661. ldu);
  3662. i__2 = *m - 1;
  3663. i__3 = *m - 1;
  3664. claset_("U", &i__2, &i__3, &c_b1, &c_b1, &u[(u_dim1 <<
  3665. 1) + 1], ldu);
  3666. ie = 1;
  3667. itauq = itau;
  3668. itaup = itauq + *m;
  3669. iwork = itaup + *m;
  3670. /* Bidiagonalize L in U */
  3671. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  3672. /* (RWorkspace: need M) */
  3673. i__2 = *lwork - iwork + 1;
  3674. cgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &
  3675. work[itauq], &work[itaup], &work[iwork], &
  3676. i__2, &ierr);
  3677. /* Multiply right bidiagonalizing vectors in U by Q */
  3678. /* in VT */
  3679. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  3680. /* (RWorkspace: 0) */
  3681. i__2 = *lwork - iwork + 1;
  3682. cunmbr_("P", "L", "C", m, n, m, &u[u_offset], ldu, &
  3683. work[itaup], &vt[vt_offset], ldvt, &work[
  3684. iwork], &i__2, &ierr);
  3685. /* Generate left bidiagonalizing vectors in U */
  3686. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  3687. /* (RWorkspace: 0) */
  3688. i__2 = *lwork - iwork + 1;
  3689. cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
  3690. &work[iwork], &i__2, &ierr);
  3691. irwork = ie + *m;
  3692. /* Perform bidiagonal QR iteration, computing left */
  3693. /* singular vectors of A in U and computing right */
  3694. /* singular vectors of A in VT */
  3695. /* (CWorkspace: 0) */
  3696. /* (RWorkspace: need BDSPAC) */
  3697. cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
  3698. vt_offset], ldvt, &u[u_offset], ldu, cdum, &
  3699. c__1, &rwork[irwork], info);
  3700. }
  3701. }
  3702. }
  3703. } else {
  3704. /* N .LT. MNTHR */
  3705. /* Path 10t(N greater than M, but not much larger) */
  3706. /* Reduce to bidiagonal form without LQ decomposition */
  3707. ie = 1;
  3708. itauq = 1;
  3709. itaup = itauq + *m;
  3710. iwork = itaup + *m;
  3711. /* Bidiagonalize A */
  3712. /* (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) */
  3713. /* (RWorkspace: M) */
  3714. i__2 = *lwork - iwork + 1;
  3715. cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  3716. &work[itaup], &work[iwork], &i__2, &ierr);
  3717. if (wntuas) {
  3718. /* If left singular vectors desired in U, copy result to U */
  3719. /* and generate left bidiagonalizing vectors in U */
  3720. /* (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB) */
  3721. /* (RWorkspace: 0) */
  3722. clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  3723. i__2 = *lwork - iwork + 1;
  3724. cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  3725. iwork], &i__2, &ierr);
  3726. }
  3727. if (wntvas) {
  3728. /* If right singular vectors desired in VT, copy result to */
  3729. /* VT and generate right bidiagonalizing vectors in VT */
  3730. /* (CWorkspace: need 2*M+NRVT, prefer 2*M+NRVT*NB) */
  3731. /* (RWorkspace: 0) */
  3732. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  3733. if (wntva) {
  3734. nrvt = *n;
  3735. }
  3736. if (wntvs) {
  3737. nrvt = *m;
  3738. }
  3739. i__2 = *lwork - iwork + 1;
  3740. cungbr_("P", &nrvt, n, m, &vt[vt_offset], ldvt, &work[itaup],
  3741. &work[iwork], &i__2, &ierr);
  3742. }
  3743. if (wntuo) {
  3744. /* If left singular vectors desired in A, generate left */
  3745. /* bidiagonalizing vectors in A */
  3746. /* (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB) */
  3747. /* (RWorkspace: 0) */
  3748. i__2 = *lwork - iwork + 1;
  3749. cungbr_("Q", m, m, n, &a[a_offset], lda, &work[itauq], &work[
  3750. iwork], &i__2, &ierr);
  3751. }
  3752. if (wntvo) {
  3753. /* If right singular vectors desired in A, generate right */
  3754. /* bidiagonalizing vectors in A */
  3755. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  3756. /* (RWorkspace: 0) */
  3757. i__2 = *lwork - iwork + 1;
  3758. cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
  3759. iwork], &i__2, &ierr);
  3760. }
  3761. irwork = ie + *m;
  3762. if (wntuas || wntuo) {
  3763. nru = *m;
  3764. }
  3765. if (wntun) {
  3766. nru = 0;
  3767. }
  3768. if (wntvas || wntvo) {
  3769. ncvt = *n;
  3770. }
  3771. if (wntvn) {
  3772. ncvt = 0;
  3773. }
  3774. if (! wntuo && ! wntvo) {
  3775. /* Perform bidiagonal QR iteration, if desired, computing */
  3776. /* left singular vectors in U and computing right singular */
  3777. /* vectors in VT */
  3778. /* (CWorkspace: 0) */
  3779. /* (RWorkspace: need BDSPAC) */
  3780. cbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
  3781. vt_offset], ldvt, &u[u_offset], ldu, cdum, &c__1, &
  3782. rwork[irwork], info);
  3783. } else if (! wntuo && wntvo) {
  3784. /* Perform bidiagonal QR iteration, if desired, computing */
  3785. /* left singular vectors in U and computing right singular */
  3786. /* vectors in A */
  3787. /* (CWorkspace: 0) */
  3788. /* (RWorkspace: need BDSPAC) */
  3789. cbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &a[
  3790. a_offset], lda, &u[u_offset], ldu, cdum, &c__1, &
  3791. rwork[irwork], info);
  3792. } else {
  3793. /* Perform bidiagonal QR iteration, if desired, computing */
  3794. /* left singular vectors in A and computing right singular */
  3795. /* vectors in VT */
  3796. /* (CWorkspace: 0) */
  3797. /* (RWorkspace: need BDSPAC) */
  3798. cbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
  3799. vt_offset], ldvt, &a[a_offset], lda, cdum, &c__1, &
  3800. rwork[irwork], info);
  3801. }
  3802. }
  3803. }
  3804. /* Undo scaling if necessary */
  3805. if (iscl == 1) {
  3806. if (anrm > bignum) {
  3807. slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
  3808. minmn, &ierr);
  3809. }
  3810. if (*info != 0 && anrm > bignum) {
  3811. i__2 = minmn - 1;
  3812. slascl_("G", &c__0, &c__0, &bignum, &anrm, &i__2, &c__1, &rwork[
  3813. ie], &minmn, &ierr);
  3814. }
  3815. if (anrm < smlnum) {
  3816. slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
  3817. minmn, &ierr);
  3818. }
  3819. if (*info != 0 && anrm < smlnum) {
  3820. i__2 = minmn - 1;
  3821. slascl_("G", &c__0, &c__0, &smlnum, &anrm, &i__2, &c__1, &rwork[
  3822. ie], &minmn, &ierr);
  3823. }
  3824. }
  3825. /* Return optimal workspace in WORK(1) */
  3826. work[1].r = (real) maxwrk, work[1].i = 0.f;
  3827. return 0;
  3828. /* End of CGESVD */
  3829. } /* cgesvd_ */