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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 doublecomplex c_b1 = {0.,0.};
  487. static doublecomplex c_b2 = {1.,0.};
  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> ZGESVD 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 ZGESVD + dependencies */
  499. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgesvd.
  500. f"> */
  501. /* > [TGZ]</a> */
  502. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgesvd.
  503. f"> */
  504. /* > [ZIP]</a> */
  505. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgesvd.
  506. f"> */
  507. /* > [TXT]</a> */
  508. /* > \endhtmlonly */
  509. /* Definition: */
  510. /* =========== */
  511. /* SUBROUTINE ZGESVD( 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. /* DOUBLE PRECISION RWORK( * ), S( * ) */
  516. /* COMPLEX*16 A( LDA, * ), U( LDU, * ), VT( LDVT, * ), */
  517. /* $ WORK( * ) */
  518. /* > \par Purpose: */
  519. /* ============= */
  520. /* > */
  521. /* > \verbatim */
  522. /* > */
  523. /* > ZGESVD 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*16 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 DOUBLE PRECISION 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*16 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*16 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*16 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 DOUBLE PRECISION 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 ZBDSQR 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 complex16GEsing */
  689. /* ===================================================================== */
  690. /* Subroutine */ void zgesvd_(char *jobu, char *jobvt, integer *m, integer *n,
  691. doublecomplex *a, integer *lda, doublereal *s, doublecomplex *u,
  692. integer *ldu, doublecomplex *vt, integer *ldvt, doublecomplex *work,
  693. integer *lwork, doublereal *rwork, 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. doublecomplex cdum[1];
  702. integer iscl;
  703. doublereal anrm;
  704. integer ierr, itau, ncvt, nrvt, lwork_zgebrd__, lwork_zgelqf__, i__,
  705. lwork_zgeqrf__;
  706. extern logical lsame_(char *, char *);
  707. integer chunk, minmn;
  708. extern /* Subroutine */ void zgemm_(char *, char *, integer *, integer *,
  709. integer *, doublecomplex *, doublecomplex *, integer *,
  710. doublecomplex *, integer *, doublecomplex *, doublecomplex *,
  711. integer *);
  712. integer wrkbl, itaup, itauq, mnthr, iwork;
  713. logical wntua, wntva, wntun, wntuo, wntvn, wntvo, wntus, wntvs;
  714. integer ie;
  715. extern doublereal dlamch_(char *);
  716. integer ir, iu;
  717. extern /* Subroutine */ void dlascl_(char *, integer *, integer *,
  718. doublereal *, doublereal *, integer *, integer *, doublereal *,
  719. integer *, integer *);
  720. extern int xerbla_(char *, integer *, ftnlen);
  721. extern void zgebrd_(integer *, integer *, doublecomplex *, integer *,
  722. doublereal *, doublereal *, doublecomplex *, doublecomplex *,
  723. doublecomplex *, integer *, integer *);
  724. extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
  725. integer *, integer *, ftnlen, ftnlen);
  726. extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
  727. integer *, doublereal *);
  728. doublereal bignum;
  729. extern /* Subroutine */ void zgelqf_(integer *, integer *, doublecomplex *,
  730. integer *, doublecomplex *, doublecomplex *, integer *, integer *
  731. ), zlascl_(char *, integer *, integer *, doublereal *, doublereal
  732. *, integer *, integer *, doublecomplex *, integer *, integer *), zgeqrf_(integer *, integer *, doublecomplex *, integer *,
  733. doublecomplex *, doublecomplex *, integer *, integer *), zlacpy_(
  734. char *, integer *, integer *, doublecomplex *, integer *,
  735. doublecomplex *, integer *), zlaset_(char *, integer *,
  736. integer *, doublecomplex *, doublecomplex *, doublecomplex *,
  737. integer *);
  738. integer ldwrkr;
  739. extern /* Subroutine */ void zbdsqr_(char *, integer *, integer *, integer
  740. *, integer *, doublereal *, doublereal *, doublecomplex *,
  741. integer *, doublecomplex *, integer *, doublecomplex *, integer *,
  742. doublereal *, integer *);
  743. integer minwrk, ldwrku, maxwrk;
  744. extern /* Subroutine */ void zungbr_(char *, integer *, integer *, integer
  745. *, doublecomplex *, integer *, doublecomplex *, doublecomplex *,
  746. integer *, integer *);
  747. doublereal smlnum;
  748. integer irwork;
  749. extern /* Subroutine */ void zunmbr_(char *, char *, char *, integer *,
  750. integer *, integer *, doublecomplex *, integer *, doublecomplex *,
  751. doublecomplex *, integer *, doublecomplex *, integer *, integer *
  752. ), zunglq_(integer *, integer *, integer *
  753. , doublecomplex *, integer *, doublecomplex *, doublecomplex *,
  754. integer *, integer *);
  755. logical lquery, wntuas, wntvas;
  756. extern /* Subroutine */ void zungqr_(integer *, integer *, integer *,
  757. doublecomplex *, integer *, doublecomplex *, doublecomplex *,
  758. integer *, integer *);
  759. integer blk, lwork_zungbr_p__, lwork_zungbr_q__, ncu;
  760. doublereal dum[1];
  761. integer lwork_zunglq_m__, lwork_zunglq_n__;
  762. doublereal eps;
  763. integer lwork_zungqr_m__, lwork_zungqr_n__, nru;
  764. /* -- LAPACK driver routine (version 3.7.0) -- */
  765. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  766. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  767. /* April 2012 */
  768. /* ===================================================================== */
  769. /* Test the input arguments */
  770. /* Parameter adjustments */
  771. a_dim1 = *lda;
  772. a_offset = 1 + a_dim1 * 1;
  773. a -= a_offset;
  774. --s;
  775. u_dim1 = *ldu;
  776. u_offset = 1 + u_dim1 * 1;
  777. u -= u_offset;
  778. vt_dim1 = *ldvt;
  779. vt_offset = 1 + vt_dim1 * 1;
  780. vt -= vt_offset;
  781. --work;
  782. --rwork;
  783. /* Function Body */
  784. *info = 0;
  785. minmn = f2cmin(*m,*n);
  786. wntua = lsame_(jobu, "A");
  787. wntus = lsame_(jobu, "S");
  788. wntuas = wntua || wntus;
  789. wntuo = lsame_(jobu, "O");
  790. wntun = lsame_(jobu, "N");
  791. wntva = lsame_(jobvt, "A");
  792. wntvs = lsame_(jobvt, "S");
  793. wntvas = wntva || wntvs;
  794. wntvo = lsame_(jobvt, "O");
  795. wntvn = lsame_(jobvt, "N");
  796. lquery = *lwork == -1;
  797. if (! (wntua || wntus || wntuo || wntun)) {
  798. *info = -1;
  799. } else if (! (wntva || wntvs || wntvo || wntvn) || wntvo && wntuo) {
  800. *info = -2;
  801. } else if (*m < 0) {
  802. *info = -3;
  803. } else if (*n < 0) {
  804. *info = -4;
  805. } else if (*lda < f2cmax(1,*m)) {
  806. *info = -6;
  807. } else if (*ldu < 1 || wntuas && *ldu < *m) {
  808. *info = -9;
  809. } else if (*ldvt < 1 || wntva && *ldvt < *n || wntvs && *ldvt < minmn) {
  810. *info = -11;
  811. }
  812. /* Compute workspace */
  813. /* (Note: Comments in the code beginning "Workspace:" describe the */
  814. /* minimal amount of workspace needed at that point in the code, */
  815. /* as well as the preferred amount for good performance. */
  816. /* CWorkspace refers to complex workspace, and RWorkspace to */
  817. /* real workspace. NB refers to the optimal block size for the */
  818. /* immediately following subroutine, as returned by ILAENV.) */
  819. if (*info == 0) {
  820. minwrk = 1;
  821. maxwrk = 1;
  822. if (*m >= *n && minmn > 0) {
  823. /* Space needed for ZBDSQR is BDSPAC = 5*N */
  824. /* Writing concatenation */
  825. i__1[0] = 1, a__1[0] = jobu;
  826. i__1[1] = 1, a__1[1] = jobvt;
  827. s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
  828. mnthr = ilaenv_(&c__6, "ZGESVD", ch__1, m, n, &c__0, &c__0, (
  829. ftnlen)6, (ftnlen)2);
  830. /* Compute space needed for ZGEQRF */
  831. zgeqrf_(m, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  832. lwork_zgeqrf__ = (integer) cdum[0].r;
  833. /* Compute space needed for ZUNGQR */
  834. zungqr_(m, n, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  835. lwork_zungqr_n__ = (integer) cdum[0].r;
  836. zungqr_(m, m, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  837. lwork_zungqr_m__ = (integer) cdum[0].r;
  838. /* Compute space needed for ZGEBRD */
  839. zgebrd_(n, n, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum, &
  840. c_n1, &ierr);
  841. lwork_zgebrd__ = (integer) cdum[0].r;
  842. /* Compute space needed for ZUNGBR */
  843. zungbr_("P", n, n, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  844. lwork_zungbr_p__ = (integer) cdum[0].r;
  845. zungbr_("Q", n, n, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  846. lwork_zungbr_q__ = (integer) cdum[0].r;
  847. if (*m >= mnthr) {
  848. if (wntun) {
  849. /* Path 1 (M much larger than N, JOBU='N') */
  850. maxwrk = *n + lwork_zgeqrf__;
  851. /* Computing MAX */
  852. i__2 = maxwrk, i__3 = (*n << 1) + lwork_zgebrd__;
  853. maxwrk = f2cmax(i__2,i__3);
  854. if (wntvo || wntvas) {
  855. /* Computing MAX */
  856. i__2 = maxwrk, i__3 = (*n << 1) + lwork_zungbr_p__;
  857. maxwrk = f2cmax(i__2,i__3);
  858. }
  859. minwrk = *n * 3;
  860. } else if (wntuo && wntvn) {
  861. /* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
  862. wrkbl = *n + lwork_zgeqrf__;
  863. /* Computing MAX */
  864. i__2 = wrkbl, i__3 = *n + lwork_zungqr_n__;
  865. wrkbl = f2cmax(i__2,i__3);
  866. /* Computing MAX */
  867. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zgebrd__;
  868. wrkbl = f2cmax(i__2,i__3);
  869. /* Computing MAX */
  870. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zungbr_q__;
  871. wrkbl = f2cmax(i__2,i__3);
  872. /* Computing MAX */
  873. i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n;
  874. maxwrk = f2cmax(i__2,i__3);
  875. minwrk = (*n << 1) + *m;
  876. } else if (wntuo && wntvas) {
  877. /* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or */
  878. /* 'A') */
  879. wrkbl = *n + lwork_zgeqrf__;
  880. /* Computing MAX */
  881. i__2 = wrkbl, i__3 = *n + lwork_zungqr_n__;
  882. wrkbl = f2cmax(i__2,i__3);
  883. /* Computing MAX */
  884. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zgebrd__;
  885. wrkbl = f2cmax(i__2,i__3);
  886. /* Computing MAX */
  887. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zungbr_q__;
  888. wrkbl = f2cmax(i__2,i__3);
  889. /* Computing MAX */
  890. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zungbr_p__;
  891. wrkbl = f2cmax(i__2,i__3);
  892. /* Computing MAX */
  893. i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n;
  894. maxwrk = f2cmax(i__2,i__3);
  895. minwrk = (*n << 1) + *m;
  896. } else if (wntus && wntvn) {
  897. /* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
  898. wrkbl = *n + lwork_zgeqrf__;
  899. /* Computing MAX */
  900. i__2 = wrkbl, i__3 = *n + lwork_zungqr_n__;
  901. wrkbl = f2cmax(i__2,i__3);
  902. /* Computing MAX */
  903. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zgebrd__;
  904. wrkbl = f2cmax(i__2,i__3);
  905. /* Computing MAX */
  906. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zungbr_q__;
  907. wrkbl = f2cmax(i__2,i__3);
  908. maxwrk = *n * *n + wrkbl;
  909. minwrk = (*n << 1) + *m;
  910. } else if (wntus && wntvo) {
  911. /* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
  912. wrkbl = *n + lwork_zgeqrf__;
  913. /* Computing MAX */
  914. i__2 = wrkbl, i__3 = *n + lwork_zungqr_n__;
  915. wrkbl = f2cmax(i__2,i__3);
  916. /* Computing MAX */
  917. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zgebrd__;
  918. wrkbl = f2cmax(i__2,i__3);
  919. /* Computing MAX */
  920. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zungbr_q__;
  921. wrkbl = f2cmax(i__2,i__3);
  922. /* Computing MAX */
  923. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zungbr_p__;
  924. wrkbl = f2cmax(i__2,i__3);
  925. maxwrk = (*n << 1) * *n + wrkbl;
  926. minwrk = (*n << 1) + *m;
  927. } else if (wntus && wntvas) {
  928. /* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or */
  929. /* 'A') */
  930. wrkbl = *n + lwork_zgeqrf__;
  931. /* Computing MAX */
  932. i__2 = wrkbl, i__3 = *n + lwork_zungqr_n__;
  933. wrkbl = f2cmax(i__2,i__3);
  934. /* Computing MAX */
  935. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zgebrd__;
  936. wrkbl = f2cmax(i__2,i__3);
  937. /* Computing MAX */
  938. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zungbr_q__;
  939. wrkbl = f2cmax(i__2,i__3);
  940. /* Computing MAX */
  941. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zungbr_p__;
  942. wrkbl = f2cmax(i__2,i__3);
  943. maxwrk = *n * *n + wrkbl;
  944. minwrk = (*n << 1) + *m;
  945. } else if (wntua && wntvn) {
  946. /* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
  947. wrkbl = *n + lwork_zgeqrf__;
  948. /* Computing MAX */
  949. i__2 = wrkbl, i__3 = *n + lwork_zungqr_m__;
  950. wrkbl = f2cmax(i__2,i__3);
  951. /* Computing MAX */
  952. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zgebrd__;
  953. wrkbl = f2cmax(i__2,i__3);
  954. /* Computing MAX */
  955. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zungbr_q__;
  956. wrkbl = f2cmax(i__2,i__3);
  957. maxwrk = *n * *n + wrkbl;
  958. minwrk = (*n << 1) + *m;
  959. } else if (wntua && wntvo) {
  960. /* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
  961. wrkbl = *n + lwork_zgeqrf__;
  962. /* Computing MAX */
  963. i__2 = wrkbl, i__3 = *n + lwork_zungqr_m__;
  964. wrkbl = f2cmax(i__2,i__3);
  965. /* Computing MAX */
  966. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zgebrd__;
  967. wrkbl = f2cmax(i__2,i__3);
  968. /* Computing MAX */
  969. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zungbr_q__;
  970. wrkbl = f2cmax(i__2,i__3);
  971. /* Computing MAX */
  972. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zungbr_p__;
  973. wrkbl = f2cmax(i__2,i__3);
  974. maxwrk = (*n << 1) * *n + wrkbl;
  975. minwrk = (*n << 1) + *m;
  976. } else if (wntua && wntvas) {
  977. /* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or */
  978. /* 'A') */
  979. wrkbl = *n + lwork_zgeqrf__;
  980. /* Computing MAX */
  981. i__2 = wrkbl, i__3 = *n + lwork_zungqr_m__;
  982. wrkbl = f2cmax(i__2,i__3);
  983. /* Computing MAX */
  984. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zgebrd__;
  985. wrkbl = f2cmax(i__2,i__3);
  986. /* Computing MAX */
  987. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zungbr_q__;
  988. wrkbl = f2cmax(i__2,i__3);
  989. /* Computing MAX */
  990. i__2 = wrkbl, i__3 = (*n << 1) + lwork_zungbr_p__;
  991. wrkbl = f2cmax(i__2,i__3);
  992. maxwrk = *n * *n + wrkbl;
  993. minwrk = (*n << 1) + *m;
  994. }
  995. } else {
  996. /* Path 10 (M at least N, but not much larger) */
  997. zgebrd_(m, n, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum,
  998. &c_n1, &ierr);
  999. lwork_zgebrd__ = (integer) cdum[0].r;
  1000. maxwrk = (*n << 1) + lwork_zgebrd__;
  1001. if (wntus || wntuo) {
  1002. zungbr_("Q", m, n, n, &a[a_offset], lda, cdum, cdum, &
  1003. c_n1, &ierr);
  1004. lwork_zungbr_q__ = (integer) cdum[0].r;
  1005. /* Computing MAX */
  1006. i__2 = maxwrk, i__3 = (*n << 1) + lwork_zungbr_q__;
  1007. maxwrk = f2cmax(i__2,i__3);
  1008. }
  1009. if (wntua) {
  1010. zungbr_("Q", m, m, n, &a[a_offset], lda, cdum, cdum, &
  1011. c_n1, &ierr);
  1012. lwork_zungbr_q__ = (integer) cdum[0].r;
  1013. /* Computing MAX */
  1014. i__2 = maxwrk, i__3 = (*n << 1) + lwork_zungbr_q__;
  1015. maxwrk = f2cmax(i__2,i__3);
  1016. }
  1017. if (! wntvn) {
  1018. /* Computing MAX */
  1019. i__2 = maxwrk, i__3 = (*n << 1) + lwork_zungbr_p__;
  1020. maxwrk = f2cmax(i__2,i__3);
  1021. }
  1022. minwrk = (*n << 1) + *m;
  1023. }
  1024. } else if (minmn > 0) {
  1025. /* Space needed for ZBDSQR is BDSPAC = 5*M */
  1026. /* Writing concatenation */
  1027. i__1[0] = 1, a__1[0] = jobu;
  1028. i__1[1] = 1, a__1[1] = jobvt;
  1029. s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
  1030. mnthr = ilaenv_(&c__6, "ZGESVD", ch__1, m, n, &c__0, &c__0, (
  1031. ftnlen)6, (ftnlen)2);
  1032. /* Compute space needed for ZGELQF */
  1033. zgelqf_(m, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  1034. lwork_zgelqf__ = (integer) cdum[0].r;
  1035. /* Compute space needed for ZUNGLQ */
  1036. zunglq_(n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
  1037. lwork_zunglq_n__ = (integer) cdum[0].r;
  1038. zunglq_(m, n, m, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
  1039. lwork_zunglq_m__ = (integer) cdum[0].r;
  1040. /* Compute space needed for ZGEBRD */
  1041. zgebrd_(m, m, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum, &
  1042. c_n1, &ierr);
  1043. lwork_zgebrd__ = (integer) cdum[0].r;
  1044. /* Compute space needed for ZUNGBR P */
  1045. zungbr_("P", m, m, m, &a[a_offset], n, cdum, cdum, &c_n1, &ierr);
  1046. lwork_zungbr_p__ = (integer) cdum[0].r;
  1047. /* Compute space needed for ZUNGBR Q */
  1048. zungbr_("Q", m, m, m, &a[a_offset], n, cdum, cdum, &c_n1, &ierr);
  1049. lwork_zungbr_q__ = (integer) cdum[0].r;
  1050. if (*n >= mnthr) {
  1051. if (wntvn) {
  1052. /* Path 1t(N much larger than M, JOBVT='N') */
  1053. maxwrk = *m + lwork_zgelqf__;
  1054. /* Computing MAX */
  1055. i__2 = maxwrk, i__3 = (*m << 1) + lwork_zgebrd__;
  1056. maxwrk = f2cmax(i__2,i__3);
  1057. if (wntuo || wntuas) {
  1058. /* Computing MAX */
  1059. i__2 = maxwrk, i__3 = (*m << 1) + lwork_zungbr_q__;
  1060. maxwrk = f2cmax(i__2,i__3);
  1061. }
  1062. minwrk = *m * 3;
  1063. } else if (wntvo && wntun) {
  1064. /* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
  1065. wrkbl = *m + lwork_zgelqf__;
  1066. /* Computing MAX */
  1067. i__2 = wrkbl, i__3 = *m + lwork_zunglq_m__;
  1068. wrkbl = f2cmax(i__2,i__3);
  1069. /* Computing MAX */
  1070. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zgebrd__;
  1071. wrkbl = f2cmax(i__2,i__3);
  1072. /* Computing MAX */
  1073. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zungbr_p__;
  1074. wrkbl = f2cmax(i__2,i__3);
  1075. /* Computing MAX */
  1076. i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n;
  1077. maxwrk = f2cmax(i__2,i__3);
  1078. minwrk = (*m << 1) + *n;
  1079. } else if (wntvo && wntuas) {
  1080. /* Path 3t(N much larger than M, JOBU='S' or 'A', */
  1081. /* JOBVT='O') */
  1082. wrkbl = *m + lwork_zgelqf__;
  1083. /* Computing MAX */
  1084. i__2 = wrkbl, i__3 = *m + lwork_zunglq_m__;
  1085. wrkbl = f2cmax(i__2,i__3);
  1086. /* Computing MAX */
  1087. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zgebrd__;
  1088. wrkbl = f2cmax(i__2,i__3);
  1089. /* Computing MAX */
  1090. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zungbr_p__;
  1091. wrkbl = f2cmax(i__2,i__3);
  1092. /* Computing MAX */
  1093. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zungbr_q__;
  1094. wrkbl = f2cmax(i__2,i__3);
  1095. /* Computing MAX */
  1096. i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n;
  1097. maxwrk = f2cmax(i__2,i__3);
  1098. minwrk = (*m << 1) + *n;
  1099. } else if (wntvs && wntun) {
  1100. /* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
  1101. wrkbl = *m + lwork_zgelqf__;
  1102. /* Computing MAX */
  1103. i__2 = wrkbl, i__3 = *m + lwork_zunglq_m__;
  1104. wrkbl = f2cmax(i__2,i__3);
  1105. /* Computing MAX */
  1106. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zgebrd__;
  1107. wrkbl = f2cmax(i__2,i__3);
  1108. /* Computing MAX */
  1109. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zungbr_p__;
  1110. wrkbl = f2cmax(i__2,i__3);
  1111. maxwrk = *m * *m + wrkbl;
  1112. minwrk = (*m << 1) + *n;
  1113. } else if (wntvs && wntuo) {
  1114. /* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
  1115. wrkbl = *m + lwork_zgelqf__;
  1116. /* Computing MAX */
  1117. i__2 = wrkbl, i__3 = *m + lwork_zunglq_m__;
  1118. wrkbl = f2cmax(i__2,i__3);
  1119. /* Computing MAX */
  1120. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zgebrd__;
  1121. wrkbl = f2cmax(i__2,i__3);
  1122. /* Computing MAX */
  1123. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zungbr_p__;
  1124. wrkbl = f2cmax(i__2,i__3);
  1125. /* Computing MAX */
  1126. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zungbr_q__;
  1127. wrkbl = f2cmax(i__2,i__3);
  1128. maxwrk = (*m << 1) * *m + wrkbl;
  1129. minwrk = (*m << 1) + *n;
  1130. } else if (wntvs && wntuas) {
  1131. /* Path 6t(N much larger than M, JOBU='S' or 'A', */
  1132. /* JOBVT='S') */
  1133. wrkbl = *m + lwork_zgelqf__;
  1134. /* Computing MAX */
  1135. i__2 = wrkbl, i__3 = *m + lwork_zunglq_m__;
  1136. wrkbl = f2cmax(i__2,i__3);
  1137. /* Computing MAX */
  1138. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zgebrd__;
  1139. wrkbl = f2cmax(i__2,i__3);
  1140. /* Computing MAX */
  1141. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zungbr_p__;
  1142. wrkbl = f2cmax(i__2,i__3);
  1143. /* Computing MAX */
  1144. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zungbr_q__;
  1145. wrkbl = f2cmax(i__2,i__3);
  1146. maxwrk = *m * *m + wrkbl;
  1147. minwrk = (*m << 1) + *n;
  1148. } else if (wntva && wntun) {
  1149. /* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
  1150. wrkbl = *m + lwork_zgelqf__;
  1151. /* Computing MAX */
  1152. i__2 = wrkbl, i__3 = *m + lwork_zunglq_n__;
  1153. wrkbl = f2cmax(i__2,i__3);
  1154. /* Computing MAX */
  1155. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zgebrd__;
  1156. wrkbl = f2cmax(i__2,i__3);
  1157. /* Computing MAX */
  1158. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zungbr_p__;
  1159. wrkbl = f2cmax(i__2,i__3);
  1160. maxwrk = *m * *m + wrkbl;
  1161. minwrk = (*m << 1) + *n;
  1162. } else if (wntva && wntuo) {
  1163. /* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
  1164. wrkbl = *m + lwork_zgelqf__;
  1165. /* Computing MAX */
  1166. i__2 = wrkbl, i__3 = *m + lwork_zunglq_n__;
  1167. wrkbl = f2cmax(i__2,i__3);
  1168. /* Computing MAX */
  1169. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zgebrd__;
  1170. wrkbl = f2cmax(i__2,i__3);
  1171. /* Computing MAX */
  1172. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zungbr_p__;
  1173. wrkbl = f2cmax(i__2,i__3);
  1174. /* Computing MAX */
  1175. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zungbr_q__;
  1176. wrkbl = f2cmax(i__2,i__3);
  1177. maxwrk = (*m << 1) * *m + wrkbl;
  1178. minwrk = (*m << 1) + *n;
  1179. } else if (wntva && wntuas) {
  1180. /* Path 9t(N much larger than M, JOBU='S' or 'A', */
  1181. /* JOBVT='A') */
  1182. wrkbl = *m + lwork_zgelqf__;
  1183. /* Computing MAX */
  1184. i__2 = wrkbl, i__3 = *m + lwork_zunglq_n__;
  1185. wrkbl = f2cmax(i__2,i__3);
  1186. /* Computing MAX */
  1187. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zgebrd__;
  1188. wrkbl = f2cmax(i__2,i__3);
  1189. /* Computing MAX */
  1190. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zungbr_p__;
  1191. wrkbl = f2cmax(i__2,i__3);
  1192. /* Computing MAX */
  1193. i__2 = wrkbl, i__3 = (*m << 1) + lwork_zungbr_q__;
  1194. wrkbl = f2cmax(i__2,i__3);
  1195. maxwrk = *m * *m + wrkbl;
  1196. minwrk = (*m << 1) + *n;
  1197. }
  1198. } else {
  1199. /* Path 10t(N greater than M, but not much larger) */
  1200. zgebrd_(m, n, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum,
  1201. &c_n1, &ierr);
  1202. lwork_zgebrd__ = (integer) cdum[0].r;
  1203. maxwrk = (*m << 1) + lwork_zgebrd__;
  1204. if (wntvs || wntvo) {
  1205. /* Compute space needed for ZUNGBR P */
  1206. zungbr_("P", m, n, m, &a[a_offset], n, cdum, cdum, &c_n1,
  1207. &ierr);
  1208. lwork_zungbr_p__ = (integer) cdum[0].r;
  1209. /* Computing MAX */
  1210. i__2 = maxwrk, i__3 = (*m << 1) + lwork_zungbr_p__;
  1211. maxwrk = f2cmax(i__2,i__3);
  1212. }
  1213. if (wntva) {
  1214. zungbr_("P", n, n, m, &a[a_offset], n, cdum, cdum, &c_n1,
  1215. &ierr);
  1216. lwork_zungbr_p__ = (integer) cdum[0].r;
  1217. /* Computing MAX */
  1218. i__2 = maxwrk, i__3 = (*m << 1) + lwork_zungbr_p__;
  1219. maxwrk = f2cmax(i__2,i__3);
  1220. }
  1221. if (! wntun) {
  1222. /* Computing MAX */
  1223. i__2 = maxwrk, i__3 = (*m << 1) + lwork_zungbr_q__;
  1224. maxwrk = f2cmax(i__2,i__3);
  1225. }
  1226. minwrk = (*m << 1) + *n;
  1227. }
  1228. }
  1229. maxwrk = f2cmax(maxwrk,minwrk);
  1230. work[1].r = (doublereal) maxwrk, work[1].i = 0.;
  1231. if (*lwork < minwrk && ! lquery) {
  1232. *info = -13;
  1233. }
  1234. }
  1235. if (*info != 0) {
  1236. i__2 = -(*info);
  1237. xerbla_("ZGESVD", &i__2, (ftnlen)6);
  1238. return;
  1239. } else if (lquery) {
  1240. return;
  1241. }
  1242. /* Quick return if possible */
  1243. if (*m == 0 || *n == 0) {
  1244. return;
  1245. }
  1246. /* Get machine constants */
  1247. eps = dlamch_("P");
  1248. smlnum = sqrt(dlamch_("S")) / eps;
  1249. bignum = 1. / smlnum;
  1250. /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
  1251. anrm = zlange_("M", m, n, &a[a_offset], lda, dum);
  1252. iscl = 0;
  1253. if (anrm > 0. && anrm < smlnum) {
  1254. iscl = 1;
  1255. zlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
  1256. ierr);
  1257. } else if (anrm > bignum) {
  1258. iscl = 1;
  1259. zlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &
  1260. ierr);
  1261. }
  1262. if (*m >= *n) {
  1263. /* A has at least as many rows as columns. If A has sufficiently */
  1264. /* more rows than columns, first reduce using the QR */
  1265. /* decomposition (if sufficient workspace available) */
  1266. if (*m >= mnthr) {
  1267. if (wntun) {
  1268. /* Path 1 (M much larger than N, JOBU='N') */
  1269. /* No left singular vectors to be computed */
  1270. itau = 1;
  1271. iwork = itau + *n;
  1272. /* Compute A=Q*R */
  1273. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1274. /* (RWorkspace: need 0) */
  1275. i__2 = *lwork - iwork + 1;
  1276. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
  1277. i__2, &ierr);
  1278. /* Zero out below R */
  1279. if (*n > 1) {
  1280. i__2 = *n - 1;
  1281. i__3 = *n - 1;
  1282. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[a_dim1 + 2],
  1283. lda);
  1284. }
  1285. ie = 1;
  1286. itauq = 1;
  1287. itaup = itauq + *n;
  1288. iwork = itaup + *n;
  1289. /* Bidiagonalize R in A */
  1290. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  1291. /* (RWorkspace: need N) */
  1292. i__2 = *lwork - iwork + 1;
  1293. zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1294. itauq], &work[itaup], &work[iwork], &i__2, &ierr);
  1295. ncvt = 0;
  1296. if (wntvo || wntvas) {
  1297. /* If right singular vectors desired, generate P'. */
  1298. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  1299. /* (RWorkspace: 0) */
  1300. i__2 = *lwork - iwork + 1;
  1301. zungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &
  1302. work[iwork], &i__2, &ierr);
  1303. ncvt = *n;
  1304. }
  1305. irwork = ie + *n;
  1306. /* Perform bidiagonal QR iteration, computing right */
  1307. /* singular vectors of A in A if desired */
  1308. /* (CWorkspace: 0) */
  1309. /* (RWorkspace: need BDSPAC) */
  1310. zbdsqr_("U", n, &ncvt, &c__0, &c__0, &s[1], &rwork[ie], &a[
  1311. a_offset], lda, cdum, &c__1, cdum, &c__1, &rwork[
  1312. irwork], info);
  1313. /* If right singular vectors desired in VT, copy them there */
  1314. if (wntvas) {
  1315. zlacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset],
  1316. ldvt);
  1317. }
  1318. } else if (wntuo && wntvn) {
  1319. /* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
  1320. /* N left singular vectors to be overwritten on A and */
  1321. /* no right singular vectors to be computed */
  1322. if (*lwork >= *n * *n + *n * 3) {
  1323. /* Sufficient workspace for a fast algorithm */
  1324. ir = 1;
  1325. /* Computing MAX */
  1326. i__2 = wrkbl, i__3 = *lda * *n;
  1327. if (*lwork >= f2cmax(i__2,i__3) + *lda * *n) {
  1328. /* WORK(IU) is LDA by N, WORK(IR) is LDA by N */
  1329. ldwrku = *lda;
  1330. ldwrkr = *lda;
  1331. } else /* if(complicated condition) */ {
  1332. /* Computing MAX */
  1333. i__2 = wrkbl, i__3 = *lda * *n;
  1334. if (*lwork >= f2cmax(i__2,i__3) + *n * *n) {
  1335. /* WORK(IU) is LDA by N, WORK(IR) is N by N */
  1336. ldwrku = *lda;
  1337. ldwrkr = *n;
  1338. } else {
  1339. /* WORK(IU) is LDWRKU by N, WORK(IR) is N by N */
  1340. ldwrku = (*lwork - *n * *n) / *n;
  1341. ldwrkr = *n;
  1342. }
  1343. }
  1344. itau = ir + ldwrkr * *n;
  1345. iwork = itau + *n;
  1346. /* Compute A=Q*R */
  1347. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1348. /* (RWorkspace: 0) */
  1349. i__2 = *lwork - iwork + 1;
  1350. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
  1351. , &i__2, &ierr);
  1352. /* Copy R to WORK(IR) and zero out below it */
  1353. zlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
  1354. i__2 = *n - 1;
  1355. i__3 = *n - 1;
  1356. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[ir + 1], &
  1357. ldwrkr);
  1358. /* Generate Q in A */
  1359. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1360. /* (RWorkspace: 0) */
  1361. i__2 = *lwork - iwork + 1;
  1362. zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
  1363. iwork], &i__2, &ierr);
  1364. ie = 1;
  1365. itauq = itau;
  1366. itaup = itauq + *n;
  1367. iwork = itaup + *n;
  1368. /* Bidiagonalize R in WORK(IR) */
  1369. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
  1370. /* (RWorkspace: need N) */
  1371. i__2 = *lwork - iwork + 1;
  1372. zgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
  1373. work[itauq], &work[itaup], &work[iwork], &i__2, &
  1374. ierr);
  1375. /* Generate left vectors bidiagonalizing R */
  1376. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
  1377. /* (RWorkspace: need 0) */
  1378. i__2 = *lwork - iwork + 1;
  1379. zungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
  1380. work[iwork], &i__2, &ierr);
  1381. irwork = ie + *n;
  1382. /* Perform bidiagonal QR iteration, computing left */
  1383. /* singular vectors of R in WORK(IR) */
  1384. /* (CWorkspace: need N*N) */
  1385. /* (RWorkspace: need BDSPAC) */
  1386. zbdsqr_("U", n, &c__0, n, &c__0, &s[1], &rwork[ie], cdum,
  1387. &c__1, &work[ir], &ldwrkr, cdum, &c__1, &rwork[
  1388. irwork], info);
  1389. iu = itauq;
  1390. /* Multiply Q in A by left singular vectors of R in */
  1391. /* WORK(IR), storing result in WORK(IU) and copying to A */
  1392. /* (CWorkspace: need N*N+N, prefer N*N+M*N) */
  1393. /* (RWorkspace: 0) */
  1394. i__2 = *m;
  1395. i__3 = ldwrku;
  1396. for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
  1397. i__3) {
  1398. /* Computing MIN */
  1399. i__4 = *m - i__ + 1;
  1400. chunk = f2cmin(i__4,ldwrku);
  1401. zgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1]
  1402. , lda, &work[ir], &ldwrkr, &c_b1, &work[iu], &
  1403. ldwrku);
  1404. zlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
  1405. a_dim1], lda);
  1406. /* L10: */
  1407. }
  1408. } else {
  1409. /* Insufficient workspace for a fast algorithm */
  1410. ie = 1;
  1411. itauq = 1;
  1412. itaup = itauq + *n;
  1413. iwork = itaup + *n;
  1414. /* Bidiagonalize A */
  1415. /* (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) */
  1416. /* (RWorkspace: N) */
  1417. i__3 = *lwork - iwork + 1;
  1418. zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1419. itauq], &work[itaup], &work[iwork], &i__3, &ierr);
  1420. /* Generate left vectors bidiagonalizing A */
  1421. /* (CWorkspace: need 3*N, prefer 2*N+N*NB) */
  1422. /* (RWorkspace: 0) */
  1423. i__3 = *lwork - iwork + 1;
  1424. zungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
  1425. work[iwork], &i__3, &ierr);
  1426. irwork = ie + *n;
  1427. /* Perform bidiagonal QR iteration, computing left */
  1428. /* singular vectors of A in A */
  1429. /* (CWorkspace: need 0) */
  1430. /* (RWorkspace: need BDSPAC) */
  1431. zbdsqr_("U", n, &c__0, m, &c__0, &s[1], &rwork[ie], cdum,
  1432. &c__1, &a[a_offset], lda, cdum, &c__1, &rwork[
  1433. irwork], info);
  1434. }
  1435. } else if (wntuo && wntvas) {
  1436. /* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A') */
  1437. /* N left singular vectors to be overwritten on A and */
  1438. /* N right singular vectors to be computed in VT */
  1439. if (*lwork >= *n * *n + *n * 3) {
  1440. /* Sufficient workspace for a fast algorithm */
  1441. ir = 1;
  1442. /* Computing MAX */
  1443. i__3 = wrkbl, i__2 = *lda * *n;
  1444. if (*lwork >= f2cmax(i__3,i__2) + *lda * *n) {
  1445. /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
  1446. ldwrku = *lda;
  1447. ldwrkr = *lda;
  1448. } else /* if(complicated condition) */ {
  1449. /* Computing MAX */
  1450. i__3 = wrkbl, i__2 = *lda * *n;
  1451. if (*lwork >= f2cmax(i__3,i__2) + *n * *n) {
  1452. /* WORK(IU) is LDA by N and WORK(IR) is N by N */
  1453. ldwrku = *lda;
  1454. ldwrkr = *n;
  1455. } else {
  1456. /* WORK(IU) is LDWRKU by N and WORK(IR) is N by N */
  1457. ldwrku = (*lwork - *n * *n) / *n;
  1458. ldwrkr = *n;
  1459. }
  1460. }
  1461. itau = ir + ldwrkr * *n;
  1462. iwork = itau + *n;
  1463. /* Compute A=Q*R */
  1464. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1465. /* (RWorkspace: 0) */
  1466. i__3 = *lwork - iwork + 1;
  1467. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
  1468. , &i__3, &ierr);
  1469. /* Copy R to VT, zeroing out below it */
  1470. zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
  1471. ldvt);
  1472. if (*n > 1) {
  1473. i__3 = *n - 1;
  1474. i__2 = *n - 1;
  1475. zlaset_("L", &i__3, &i__2, &c_b1, &c_b1, &vt[vt_dim1
  1476. + 2], ldvt);
  1477. }
  1478. /* Generate Q in A */
  1479. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1480. /* (RWorkspace: 0) */
  1481. i__3 = *lwork - iwork + 1;
  1482. zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
  1483. iwork], &i__3, &ierr);
  1484. ie = 1;
  1485. itauq = itau;
  1486. itaup = itauq + *n;
  1487. iwork = itaup + *n;
  1488. /* Bidiagonalize R in VT, copying result to WORK(IR) */
  1489. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
  1490. /* (RWorkspace: need N) */
  1491. i__3 = *lwork - iwork + 1;
  1492. zgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie], &
  1493. work[itauq], &work[itaup], &work[iwork], &i__3, &
  1494. ierr);
  1495. zlacpy_("L", n, n, &vt[vt_offset], ldvt, &work[ir], &
  1496. ldwrkr);
  1497. /* Generate left vectors bidiagonalizing R in WORK(IR) */
  1498. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
  1499. /* (RWorkspace: 0) */
  1500. i__3 = *lwork - iwork + 1;
  1501. zungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
  1502. work[iwork], &i__3, &ierr);
  1503. /* Generate right vectors bidiagonalizing R in VT */
  1504. /* (CWorkspace: need N*N+3*N-1, prefer N*N+2*N+(N-1)*NB) */
  1505. /* (RWorkspace: 0) */
  1506. i__3 = *lwork - iwork + 1;
  1507. zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
  1508. &work[iwork], &i__3, &ierr);
  1509. irwork = ie + *n;
  1510. /* Perform bidiagonal QR iteration, computing left */
  1511. /* singular vectors of R in WORK(IR) and computing right */
  1512. /* singular vectors of R in VT */
  1513. /* (CWorkspace: need N*N) */
  1514. /* (RWorkspace: need BDSPAC) */
  1515. zbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &vt[
  1516. vt_offset], ldvt, &work[ir], &ldwrkr, cdum, &c__1,
  1517. &rwork[irwork], info);
  1518. iu = itauq;
  1519. /* Multiply Q in A by left singular vectors of R in */
  1520. /* WORK(IR), storing result in WORK(IU) and copying to A */
  1521. /* (CWorkspace: need N*N+N, prefer N*N+M*N) */
  1522. /* (RWorkspace: 0) */
  1523. i__3 = *m;
  1524. i__2 = ldwrku;
  1525. for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
  1526. i__2) {
  1527. /* Computing MIN */
  1528. i__4 = *m - i__ + 1;
  1529. chunk = f2cmin(i__4,ldwrku);
  1530. zgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1]
  1531. , lda, &work[ir], &ldwrkr, &c_b1, &work[iu], &
  1532. ldwrku);
  1533. zlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
  1534. a_dim1], lda);
  1535. /* L20: */
  1536. }
  1537. } else {
  1538. /* Insufficient workspace for a fast algorithm */
  1539. itau = 1;
  1540. iwork = itau + *n;
  1541. /* Compute A=Q*R */
  1542. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1543. /* (RWorkspace: 0) */
  1544. i__2 = *lwork - iwork + 1;
  1545. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
  1546. , &i__2, &ierr);
  1547. /* Copy R to VT, zeroing out below it */
  1548. zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
  1549. ldvt);
  1550. if (*n > 1) {
  1551. i__2 = *n - 1;
  1552. i__3 = *n - 1;
  1553. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &vt[vt_dim1
  1554. + 2], ldvt);
  1555. }
  1556. /* Generate Q in A */
  1557. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1558. /* (RWorkspace: 0) */
  1559. i__2 = *lwork - iwork + 1;
  1560. zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
  1561. iwork], &i__2, &ierr);
  1562. ie = 1;
  1563. itauq = itau;
  1564. itaup = itauq + *n;
  1565. iwork = itaup + *n;
  1566. /* Bidiagonalize R in VT */
  1567. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  1568. /* (RWorkspace: N) */
  1569. i__2 = *lwork - iwork + 1;
  1570. zgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie], &
  1571. work[itauq], &work[itaup], &work[iwork], &i__2, &
  1572. ierr);
  1573. /* Multiply Q in A by left vectors bidiagonalizing R */
  1574. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  1575. /* (RWorkspace: 0) */
  1576. i__2 = *lwork - iwork + 1;
  1577. zunmbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt, &
  1578. work[itauq], &a[a_offset], lda, &work[iwork], &
  1579. i__2, &ierr);
  1580. /* Generate right vectors bidiagonalizing R in VT */
  1581. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  1582. /* (RWorkspace: 0) */
  1583. i__2 = *lwork - iwork + 1;
  1584. zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
  1585. &work[iwork], &i__2, &ierr);
  1586. irwork = ie + *n;
  1587. /* Perform bidiagonal QR iteration, computing left */
  1588. /* singular vectors of A in A and computing right */
  1589. /* singular vectors of A in VT */
  1590. /* (CWorkspace: 0) */
  1591. /* (RWorkspace: need BDSPAC) */
  1592. zbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &vt[
  1593. vt_offset], ldvt, &a[a_offset], lda, cdum, &c__1,
  1594. &rwork[irwork], info);
  1595. }
  1596. } else if (wntus) {
  1597. if (wntvn) {
  1598. /* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
  1599. /* N left singular vectors to be computed in U and */
  1600. /* no right singular vectors to be computed */
  1601. if (*lwork >= *n * *n + *n * 3) {
  1602. /* Sufficient workspace for a fast algorithm */
  1603. ir = 1;
  1604. if (*lwork >= wrkbl + *lda * *n) {
  1605. /* WORK(IR) is LDA by N */
  1606. ldwrkr = *lda;
  1607. } else {
  1608. /* WORK(IR) is N by N */
  1609. ldwrkr = *n;
  1610. }
  1611. itau = ir + ldwrkr * *n;
  1612. iwork = itau + *n;
  1613. /* Compute A=Q*R */
  1614. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1615. /* (RWorkspace: 0) */
  1616. i__2 = *lwork - iwork + 1;
  1617. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  1618. iwork], &i__2, &ierr);
  1619. /* Copy R to WORK(IR), zeroing out below it */
  1620. zlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &
  1621. ldwrkr);
  1622. i__2 = *n - 1;
  1623. i__3 = *n - 1;
  1624. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[ir + 1]
  1625. , &ldwrkr);
  1626. /* Generate Q in A */
  1627. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1628. /* (RWorkspace: 0) */
  1629. i__2 = *lwork - iwork + 1;
  1630. zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &
  1631. work[iwork], &i__2, &ierr);
  1632. ie = 1;
  1633. itauq = itau;
  1634. itaup = itauq + *n;
  1635. iwork = itaup + *n;
  1636. /* Bidiagonalize R in WORK(IR) */
  1637. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
  1638. /* (RWorkspace: need N) */
  1639. i__2 = *lwork - iwork + 1;
  1640. zgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
  1641. work[itauq], &work[itaup], &work[iwork], &
  1642. i__2, &ierr);
  1643. /* Generate left vectors bidiagonalizing R in WORK(IR) */
  1644. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
  1645. /* (RWorkspace: 0) */
  1646. i__2 = *lwork - iwork + 1;
  1647. zungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
  1648. , &work[iwork], &i__2, &ierr);
  1649. irwork = ie + *n;
  1650. /* Perform bidiagonal QR iteration, computing left */
  1651. /* singular vectors of R in WORK(IR) */
  1652. /* (CWorkspace: need N*N) */
  1653. /* (RWorkspace: need BDSPAC) */
  1654. zbdsqr_("U", n, &c__0, n, &c__0, &s[1], &rwork[ie],
  1655. cdum, &c__1, &work[ir], &ldwrkr, cdum, &c__1,
  1656. &rwork[irwork], info);
  1657. /* Multiply Q in A by left singular vectors of R in */
  1658. /* WORK(IR), storing result in U */
  1659. /* (CWorkspace: need N*N) */
  1660. /* (RWorkspace: 0) */
  1661. zgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &
  1662. work[ir], &ldwrkr, &c_b1, &u[u_offset], ldu);
  1663. } else {
  1664. /* Insufficient workspace for a fast algorithm */
  1665. itau = 1;
  1666. iwork = itau + *n;
  1667. /* Compute A=Q*R, copying result to U */
  1668. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1669. /* (RWorkspace: 0) */
  1670. i__2 = *lwork - iwork + 1;
  1671. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  1672. iwork], &i__2, &ierr);
  1673. zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  1674. ldu);
  1675. /* Generate Q in U */
  1676. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1677. /* (RWorkspace: 0) */
  1678. i__2 = *lwork - iwork + 1;
  1679. zungqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
  1680. work[iwork], &i__2, &ierr);
  1681. ie = 1;
  1682. itauq = itau;
  1683. itaup = itauq + *n;
  1684. iwork = itaup + *n;
  1685. /* Zero out below R in A */
  1686. if (*n > 1) {
  1687. i__2 = *n - 1;
  1688. i__3 = *n - 1;
  1689. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
  1690. a_dim1 + 2], lda);
  1691. }
  1692. /* Bidiagonalize R in A */
  1693. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  1694. /* (RWorkspace: need N) */
  1695. i__2 = *lwork - iwork + 1;
  1696. zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
  1697. work[itauq], &work[itaup], &work[iwork], &
  1698. i__2, &ierr);
  1699. /* Multiply Q in U by left vectors bidiagonalizing R */
  1700. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  1701. /* (RWorkspace: 0) */
  1702. i__2 = *lwork - iwork + 1;
  1703. zunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
  1704. work[itauq], &u[u_offset], ldu, &work[iwork],
  1705. &i__2, &ierr)
  1706. ;
  1707. irwork = ie + *n;
  1708. /* Perform bidiagonal QR iteration, computing left */
  1709. /* singular vectors of A in U */
  1710. /* (CWorkspace: 0) */
  1711. /* (RWorkspace: need BDSPAC) */
  1712. zbdsqr_("U", n, &c__0, m, &c__0, &s[1], &rwork[ie],
  1713. cdum, &c__1, &u[u_offset], ldu, cdum, &c__1, &
  1714. rwork[irwork], info);
  1715. }
  1716. } else if (wntvo) {
  1717. /* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
  1718. /* N left singular vectors to be computed in U and */
  1719. /* N right singular vectors to be overwritten on A */
  1720. if (*lwork >= (*n << 1) * *n + *n * 3) {
  1721. /* Sufficient workspace for a fast algorithm */
  1722. iu = 1;
  1723. if (*lwork >= wrkbl + (*lda << 1) * *n) {
  1724. /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
  1725. ldwrku = *lda;
  1726. ir = iu + ldwrku * *n;
  1727. ldwrkr = *lda;
  1728. } else if (*lwork >= wrkbl + (*lda + *n) * *n) {
  1729. /* WORK(IU) is LDA by N and WORK(IR) is N by N */
  1730. ldwrku = *lda;
  1731. ir = iu + ldwrku * *n;
  1732. ldwrkr = *n;
  1733. } else {
  1734. /* WORK(IU) is N by N and WORK(IR) is N by N */
  1735. ldwrku = *n;
  1736. ir = iu + ldwrku * *n;
  1737. ldwrkr = *n;
  1738. }
  1739. itau = ir + ldwrkr * *n;
  1740. iwork = itau + *n;
  1741. /* Compute A=Q*R */
  1742. /* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
  1743. /* (RWorkspace: 0) */
  1744. i__2 = *lwork - iwork + 1;
  1745. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  1746. iwork], &i__2, &ierr);
  1747. /* Copy R to WORK(IU), zeroing out below it */
  1748. zlacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
  1749. ldwrku);
  1750. i__2 = *n - 1;
  1751. i__3 = *n - 1;
  1752. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
  1753. , &ldwrku);
  1754. /* Generate Q in A */
  1755. /* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
  1756. /* (RWorkspace: 0) */
  1757. i__2 = *lwork - iwork + 1;
  1758. zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &
  1759. work[iwork], &i__2, &ierr);
  1760. ie = 1;
  1761. itauq = itau;
  1762. itaup = itauq + *n;
  1763. iwork = itaup + *n;
  1764. /* Bidiagonalize R in WORK(IU), copying result to */
  1765. /* WORK(IR) */
  1766. /* (CWorkspace: need 2*N*N+3*N, */
  1767. /* prefer 2*N*N+2*N+2*N*NB) */
  1768. /* (RWorkspace: need N) */
  1769. i__2 = *lwork - iwork + 1;
  1770. zgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  1771. work[itauq], &work[itaup], &work[iwork], &
  1772. i__2, &ierr);
  1773. zlacpy_("U", n, n, &work[iu], &ldwrku, &work[ir], &
  1774. ldwrkr);
  1775. /* Generate left bidiagonalizing vectors in WORK(IU) */
  1776. /* (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) */
  1777. /* (RWorkspace: 0) */
  1778. i__2 = *lwork - iwork + 1;
  1779. zungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
  1780. , &work[iwork], &i__2, &ierr);
  1781. /* Generate right bidiagonalizing vectors in WORK(IR) */
  1782. /* (CWorkspace: need 2*N*N+3*N-1, */
  1783. /* prefer 2*N*N+2*N+(N-1)*NB) */
  1784. /* (RWorkspace: 0) */
  1785. i__2 = *lwork - iwork + 1;
  1786. zungbr_("P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
  1787. , &work[iwork], &i__2, &ierr);
  1788. irwork = ie + *n;
  1789. /* Perform bidiagonal QR iteration, computing left */
  1790. /* singular vectors of R in WORK(IU) and computing */
  1791. /* right singular vectors of R in WORK(IR) */
  1792. /* (CWorkspace: need 2*N*N) */
  1793. /* (RWorkspace: need BDSPAC) */
  1794. zbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &work[
  1795. ir], &ldwrkr, &work[iu], &ldwrku, cdum, &c__1,
  1796. &rwork[irwork], info);
  1797. /* Multiply Q in A by left singular vectors of R in */
  1798. /* WORK(IU), storing result in U */
  1799. /* (CWorkspace: need N*N) */
  1800. /* (RWorkspace: 0) */
  1801. zgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &
  1802. work[iu], &ldwrku, &c_b1, &u[u_offset], ldu);
  1803. /* Copy right singular vectors of R to A */
  1804. /* (CWorkspace: need N*N) */
  1805. /* (RWorkspace: 0) */
  1806. zlacpy_("F", n, n, &work[ir], &ldwrkr, &a[a_offset],
  1807. lda);
  1808. } else {
  1809. /* Insufficient workspace for a fast algorithm */
  1810. itau = 1;
  1811. iwork = itau + *n;
  1812. /* Compute A=Q*R, copying result to U */
  1813. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1814. /* (RWorkspace: 0) */
  1815. i__2 = *lwork - iwork + 1;
  1816. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  1817. iwork], &i__2, &ierr);
  1818. zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  1819. ldu);
  1820. /* Generate Q in U */
  1821. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1822. /* (RWorkspace: 0) */
  1823. i__2 = *lwork - iwork + 1;
  1824. zungqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
  1825. work[iwork], &i__2, &ierr);
  1826. ie = 1;
  1827. itauq = itau;
  1828. itaup = itauq + *n;
  1829. iwork = itaup + *n;
  1830. /* Zero out below R in A */
  1831. if (*n > 1) {
  1832. i__2 = *n - 1;
  1833. i__3 = *n - 1;
  1834. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
  1835. a_dim1 + 2], lda);
  1836. }
  1837. /* Bidiagonalize R in A */
  1838. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  1839. /* (RWorkspace: need N) */
  1840. i__2 = *lwork - iwork + 1;
  1841. zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
  1842. work[itauq], &work[itaup], &work[iwork], &
  1843. i__2, &ierr);
  1844. /* Multiply Q in U by left vectors bidiagonalizing R */
  1845. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  1846. /* (RWorkspace: 0) */
  1847. i__2 = *lwork - iwork + 1;
  1848. zunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
  1849. work[itauq], &u[u_offset], ldu, &work[iwork],
  1850. &i__2, &ierr)
  1851. ;
  1852. /* Generate right vectors bidiagonalizing R in A */
  1853. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  1854. /* (RWorkspace: 0) */
  1855. i__2 = *lwork - iwork + 1;
  1856. zungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup],
  1857. &work[iwork], &i__2, &ierr);
  1858. irwork = ie + *n;
  1859. /* Perform bidiagonal QR iteration, computing left */
  1860. /* singular vectors of A in U and computing right */
  1861. /* singular vectors of A in A */
  1862. /* (CWorkspace: 0) */
  1863. /* (RWorkspace: need BDSPAC) */
  1864. zbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &a[
  1865. a_offset], lda, &u[u_offset], ldu, cdum, &
  1866. c__1, &rwork[irwork], info);
  1867. }
  1868. } else if (wntvas) {
  1869. /* Path 6 (M much larger than N, JOBU='S', JOBVT='S' */
  1870. /* or 'A') */
  1871. /* N left singular vectors to be computed in U and */
  1872. /* N right singular vectors to be computed in VT */
  1873. if (*lwork >= *n * *n + *n * 3) {
  1874. /* Sufficient workspace for a fast algorithm */
  1875. iu = 1;
  1876. if (*lwork >= wrkbl + *lda * *n) {
  1877. /* WORK(IU) is LDA by N */
  1878. ldwrku = *lda;
  1879. } else {
  1880. /* WORK(IU) is N by N */
  1881. ldwrku = *n;
  1882. }
  1883. itau = iu + ldwrku * *n;
  1884. iwork = itau + *n;
  1885. /* Compute A=Q*R */
  1886. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1887. /* (RWorkspace: 0) */
  1888. i__2 = *lwork - iwork + 1;
  1889. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  1890. iwork], &i__2, &ierr);
  1891. /* Copy R to WORK(IU), zeroing out below it */
  1892. zlacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
  1893. ldwrku);
  1894. i__2 = *n - 1;
  1895. i__3 = *n - 1;
  1896. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
  1897. , &ldwrku);
  1898. /* Generate Q in A */
  1899. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  1900. /* (RWorkspace: 0) */
  1901. i__2 = *lwork - iwork + 1;
  1902. zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &
  1903. work[iwork], &i__2, &ierr);
  1904. ie = 1;
  1905. itauq = itau;
  1906. itaup = itauq + *n;
  1907. iwork = itaup + *n;
  1908. /* Bidiagonalize R in WORK(IU), copying result to VT */
  1909. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
  1910. /* (RWorkspace: need N) */
  1911. i__2 = *lwork - iwork + 1;
  1912. zgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  1913. work[itauq], &work[itaup], &work[iwork], &
  1914. i__2, &ierr);
  1915. zlacpy_("U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
  1916. ldvt);
  1917. /* Generate left bidiagonalizing vectors in WORK(IU) */
  1918. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
  1919. /* (RWorkspace: 0) */
  1920. i__2 = *lwork - iwork + 1;
  1921. zungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
  1922. , &work[iwork], &i__2, &ierr);
  1923. /* Generate right bidiagonalizing vectors in VT */
  1924. /* (CWorkspace: need N*N+3*N-1, */
  1925. /* prefer N*N+2*N+(N-1)*NB) */
  1926. /* (RWorkspace: 0) */
  1927. i__2 = *lwork - iwork + 1;
  1928. zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
  1929. itaup], &work[iwork], &i__2, &ierr)
  1930. ;
  1931. irwork = ie + *n;
  1932. /* Perform bidiagonal QR iteration, computing left */
  1933. /* singular vectors of R in WORK(IU) and computing */
  1934. /* right singular vectors of R in VT */
  1935. /* (CWorkspace: need N*N) */
  1936. /* (RWorkspace: need BDSPAC) */
  1937. zbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &vt[
  1938. vt_offset], ldvt, &work[iu], &ldwrku, cdum, &
  1939. c__1, &rwork[irwork], info);
  1940. /* Multiply Q in A by left singular vectors of R in */
  1941. /* WORK(IU), storing result in U */
  1942. /* (CWorkspace: need N*N) */
  1943. /* (RWorkspace: 0) */
  1944. zgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &
  1945. work[iu], &ldwrku, &c_b1, &u[u_offset], ldu);
  1946. } else {
  1947. /* Insufficient workspace for a fast algorithm */
  1948. itau = 1;
  1949. iwork = itau + *n;
  1950. /* Compute A=Q*R, copying result to U */
  1951. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1952. /* (RWorkspace: 0) */
  1953. i__2 = *lwork - iwork + 1;
  1954. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  1955. iwork], &i__2, &ierr);
  1956. zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  1957. ldu);
  1958. /* Generate Q in U */
  1959. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  1960. /* (RWorkspace: 0) */
  1961. i__2 = *lwork - iwork + 1;
  1962. zungqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
  1963. work[iwork], &i__2, &ierr);
  1964. /* Copy R to VT, zeroing out below it */
  1965. zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
  1966. ldvt);
  1967. if (*n > 1) {
  1968. i__2 = *n - 1;
  1969. i__3 = *n - 1;
  1970. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &vt[
  1971. vt_dim1 + 2], ldvt);
  1972. }
  1973. ie = 1;
  1974. itauq = itau;
  1975. itaup = itauq + *n;
  1976. iwork = itaup + *n;
  1977. /* Bidiagonalize R in VT */
  1978. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  1979. /* (RWorkspace: need N) */
  1980. i__2 = *lwork - iwork + 1;
  1981. zgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie],
  1982. &work[itauq], &work[itaup], &work[iwork], &
  1983. i__2, &ierr);
  1984. /* Multiply Q in U by left bidiagonalizing vectors */
  1985. /* in VT */
  1986. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  1987. /* (RWorkspace: 0) */
  1988. i__2 = *lwork - iwork + 1;
  1989. zunmbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt,
  1990. &work[itauq], &u[u_offset], ldu, &work[iwork],
  1991. &i__2, &ierr);
  1992. /* Generate right bidiagonalizing vectors in VT */
  1993. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  1994. /* (RWorkspace: 0) */
  1995. i__2 = *lwork - iwork + 1;
  1996. zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
  1997. itaup], &work[iwork], &i__2, &ierr)
  1998. ;
  1999. irwork = ie + *n;
  2000. /* Perform bidiagonal QR iteration, computing left */
  2001. /* singular vectors of A in U and computing right */
  2002. /* singular vectors of A in VT */
  2003. /* (CWorkspace: 0) */
  2004. /* (RWorkspace: need BDSPAC) */
  2005. zbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &vt[
  2006. vt_offset], ldvt, &u[u_offset], ldu, cdum, &
  2007. c__1, &rwork[irwork], info);
  2008. }
  2009. }
  2010. } else if (wntua) {
  2011. if (wntvn) {
  2012. /* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
  2013. /* M left singular vectors to be computed in U and */
  2014. /* no right singular vectors to be computed */
  2015. /* Computing MAX */
  2016. i__2 = *n + *m, i__3 = *n * 3;
  2017. if (*lwork >= *n * *n + f2cmax(i__2,i__3)) {
  2018. /* Sufficient workspace for a fast algorithm */
  2019. ir = 1;
  2020. if (*lwork >= wrkbl + *lda * *n) {
  2021. /* WORK(IR) is LDA by N */
  2022. ldwrkr = *lda;
  2023. } else {
  2024. /* WORK(IR) is N by N */
  2025. ldwrkr = *n;
  2026. }
  2027. itau = ir + ldwrkr * *n;
  2028. iwork = itau + *n;
  2029. /* Compute A=Q*R, copying result to U */
  2030. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  2031. /* (RWorkspace: 0) */
  2032. i__2 = *lwork - iwork + 1;
  2033. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2034. iwork], &i__2, &ierr);
  2035. zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  2036. ldu);
  2037. /* Copy R to WORK(IR), zeroing out below it */
  2038. zlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &
  2039. ldwrkr);
  2040. i__2 = *n - 1;
  2041. i__3 = *n - 1;
  2042. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[ir + 1]
  2043. , &ldwrkr);
  2044. /* Generate Q in U */
  2045. /* (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB) */
  2046. /* (RWorkspace: 0) */
  2047. i__2 = *lwork - iwork + 1;
  2048. zungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
  2049. work[iwork], &i__2, &ierr);
  2050. ie = 1;
  2051. itauq = itau;
  2052. itaup = itauq + *n;
  2053. iwork = itaup + *n;
  2054. /* Bidiagonalize R in WORK(IR) */
  2055. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
  2056. /* (RWorkspace: need N) */
  2057. i__2 = *lwork - iwork + 1;
  2058. zgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
  2059. work[itauq], &work[itaup], &work[iwork], &
  2060. i__2, &ierr);
  2061. /* Generate left bidiagonalizing vectors in WORK(IR) */
  2062. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
  2063. /* (RWorkspace: 0) */
  2064. i__2 = *lwork - iwork + 1;
  2065. zungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
  2066. , &work[iwork], &i__2, &ierr);
  2067. irwork = ie + *n;
  2068. /* Perform bidiagonal QR iteration, computing left */
  2069. /* singular vectors of R in WORK(IR) */
  2070. /* (CWorkspace: need N*N) */
  2071. /* (RWorkspace: need BDSPAC) */
  2072. zbdsqr_("U", n, &c__0, n, &c__0, &s[1], &rwork[ie],
  2073. cdum, &c__1, &work[ir], &ldwrkr, cdum, &c__1,
  2074. &rwork[irwork], info);
  2075. /* Multiply Q in U by left singular vectors of R in */
  2076. /* WORK(IR), storing result in A */
  2077. /* (CWorkspace: need N*N) */
  2078. /* (RWorkspace: 0) */
  2079. zgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &
  2080. work[ir], &ldwrkr, &c_b1, &a[a_offset], lda);
  2081. /* Copy left singular vectors of A from A to U */
  2082. zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
  2083. ldu);
  2084. } else {
  2085. /* Insufficient workspace for a fast algorithm */
  2086. itau = 1;
  2087. iwork = itau + *n;
  2088. /* Compute A=Q*R, copying result to U */
  2089. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  2090. /* (RWorkspace: 0) */
  2091. i__2 = *lwork - iwork + 1;
  2092. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2093. iwork], &i__2, &ierr);
  2094. zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  2095. ldu);
  2096. /* Generate Q in U */
  2097. /* (CWorkspace: need N+M, prefer N+M*NB) */
  2098. /* (RWorkspace: 0) */
  2099. i__2 = *lwork - iwork + 1;
  2100. zungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
  2101. work[iwork], &i__2, &ierr);
  2102. ie = 1;
  2103. itauq = itau;
  2104. itaup = itauq + *n;
  2105. iwork = itaup + *n;
  2106. /* Zero out below R in A */
  2107. if (*n > 1) {
  2108. i__2 = *n - 1;
  2109. i__3 = *n - 1;
  2110. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
  2111. a_dim1 + 2], lda);
  2112. }
  2113. /* Bidiagonalize R in A */
  2114. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  2115. /* (RWorkspace: need N) */
  2116. i__2 = *lwork - iwork + 1;
  2117. zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
  2118. work[itauq], &work[itaup], &work[iwork], &
  2119. i__2, &ierr);
  2120. /* Multiply Q in U by left bidiagonalizing vectors */
  2121. /* in A */
  2122. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  2123. /* (RWorkspace: 0) */
  2124. i__2 = *lwork - iwork + 1;
  2125. zunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
  2126. work[itauq], &u[u_offset], ldu, &work[iwork],
  2127. &i__2, &ierr)
  2128. ;
  2129. irwork = ie + *n;
  2130. /* Perform bidiagonal QR iteration, computing left */
  2131. /* singular vectors of A in U */
  2132. /* (CWorkspace: 0) */
  2133. /* (RWorkspace: need BDSPAC) */
  2134. zbdsqr_("U", n, &c__0, m, &c__0, &s[1], &rwork[ie],
  2135. cdum, &c__1, &u[u_offset], ldu, cdum, &c__1, &
  2136. rwork[irwork], info);
  2137. }
  2138. } else if (wntvo) {
  2139. /* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
  2140. /* M left singular vectors to be computed in U and */
  2141. /* N right singular vectors to be overwritten on A */
  2142. /* Computing MAX */
  2143. i__2 = *n + *m, i__3 = *n * 3;
  2144. if (*lwork >= (*n << 1) * *n + f2cmax(i__2,i__3)) {
  2145. /* Sufficient workspace for a fast algorithm */
  2146. iu = 1;
  2147. if (*lwork >= wrkbl + (*lda << 1) * *n) {
  2148. /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
  2149. ldwrku = *lda;
  2150. ir = iu + ldwrku * *n;
  2151. ldwrkr = *lda;
  2152. } else if (*lwork >= wrkbl + (*lda + *n) * *n) {
  2153. /* WORK(IU) is LDA by N and WORK(IR) is N by N */
  2154. ldwrku = *lda;
  2155. ir = iu + ldwrku * *n;
  2156. ldwrkr = *n;
  2157. } else {
  2158. /* WORK(IU) is N by N and WORK(IR) is N by N */
  2159. ldwrku = *n;
  2160. ir = iu + ldwrku * *n;
  2161. ldwrkr = *n;
  2162. }
  2163. itau = ir + ldwrkr * *n;
  2164. iwork = itau + *n;
  2165. /* Compute A=Q*R, copying result to U */
  2166. /* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
  2167. /* (RWorkspace: 0) */
  2168. i__2 = *lwork - iwork + 1;
  2169. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2170. iwork], &i__2, &ierr);
  2171. zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  2172. ldu);
  2173. /* Generate Q in U */
  2174. /* (CWorkspace: need 2*N*N+N+M, prefer 2*N*N+N+M*NB) */
  2175. /* (RWorkspace: 0) */
  2176. i__2 = *lwork - iwork + 1;
  2177. zungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
  2178. work[iwork], &i__2, &ierr);
  2179. /* Copy R to WORK(IU), zeroing out below it */
  2180. zlacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
  2181. ldwrku);
  2182. i__2 = *n - 1;
  2183. i__3 = *n - 1;
  2184. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
  2185. , &ldwrku);
  2186. ie = 1;
  2187. itauq = itau;
  2188. itaup = itauq + *n;
  2189. iwork = itaup + *n;
  2190. /* Bidiagonalize R in WORK(IU), copying result to */
  2191. /* WORK(IR) */
  2192. /* (CWorkspace: need 2*N*N+3*N, */
  2193. /* prefer 2*N*N+2*N+2*N*NB) */
  2194. /* (RWorkspace: need N) */
  2195. i__2 = *lwork - iwork + 1;
  2196. zgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  2197. work[itauq], &work[itaup], &work[iwork], &
  2198. i__2, &ierr);
  2199. zlacpy_("U", n, n, &work[iu], &ldwrku, &work[ir], &
  2200. ldwrkr);
  2201. /* Generate left bidiagonalizing vectors in WORK(IU) */
  2202. /* (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) */
  2203. /* (RWorkspace: 0) */
  2204. i__2 = *lwork - iwork + 1;
  2205. zungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
  2206. , &work[iwork], &i__2, &ierr);
  2207. /* Generate right bidiagonalizing vectors in WORK(IR) */
  2208. /* (CWorkspace: need 2*N*N+3*N-1, */
  2209. /* prefer 2*N*N+2*N+(N-1)*NB) */
  2210. /* (RWorkspace: 0) */
  2211. i__2 = *lwork - iwork + 1;
  2212. zungbr_("P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
  2213. , &work[iwork], &i__2, &ierr);
  2214. irwork = ie + *n;
  2215. /* Perform bidiagonal QR iteration, computing left */
  2216. /* singular vectors of R in WORK(IU) and computing */
  2217. /* right singular vectors of R in WORK(IR) */
  2218. /* (CWorkspace: need 2*N*N) */
  2219. /* (RWorkspace: need BDSPAC) */
  2220. zbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &work[
  2221. ir], &ldwrkr, &work[iu], &ldwrku, cdum, &c__1,
  2222. &rwork[irwork], info);
  2223. /* Multiply Q in U by left singular vectors of R in */
  2224. /* WORK(IU), storing result in A */
  2225. /* (CWorkspace: need N*N) */
  2226. /* (RWorkspace: 0) */
  2227. zgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &
  2228. work[iu], &ldwrku, &c_b1, &a[a_offset], lda);
  2229. /* Copy left singular vectors of A from A to U */
  2230. zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
  2231. ldu);
  2232. /* Copy right singular vectors of R from WORK(IR) to A */
  2233. zlacpy_("F", n, n, &work[ir], &ldwrkr, &a[a_offset],
  2234. lda);
  2235. } else {
  2236. /* Insufficient workspace for a fast algorithm */
  2237. itau = 1;
  2238. iwork = itau + *n;
  2239. /* Compute A=Q*R, copying result to U */
  2240. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  2241. /* (RWorkspace: 0) */
  2242. i__2 = *lwork - iwork + 1;
  2243. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2244. iwork], &i__2, &ierr);
  2245. zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  2246. ldu);
  2247. /* Generate Q in U */
  2248. /* (CWorkspace: need N+M, prefer N+M*NB) */
  2249. /* (RWorkspace: 0) */
  2250. i__2 = *lwork - iwork + 1;
  2251. zungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
  2252. work[iwork], &i__2, &ierr);
  2253. ie = 1;
  2254. itauq = itau;
  2255. itaup = itauq + *n;
  2256. iwork = itaup + *n;
  2257. /* Zero out below R in A */
  2258. if (*n > 1) {
  2259. i__2 = *n - 1;
  2260. i__3 = *n - 1;
  2261. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
  2262. a_dim1 + 2], lda);
  2263. }
  2264. /* Bidiagonalize R in A */
  2265. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  2266. /* (RWorkspace: need N) */
  2267. i__2 = *lwork - iwork + 1;
  2268. zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
  2269. work[itauq], &work[itaup], &work[iwork], &
  2270. i__2, &ierr);
  2271. /* Multiply Q in U by left bidiagonalizing vectors */
  2272. /* in A */
  2273. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  2274. /* (RWorkspace: 0) */
  2275. i__2 = *lwork - iwork + 1;
  2276. zunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
  2277. work[itauq], &u[u_offset], ldu, &work[iwork],
  2278. &i__2, &ierr)
  2279. ;
  2280. /* Generate right bidiagonalizing vectors in A */
  2281. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  2282. /* (RWorkspace: 0) */
  2283. i__2 = *lwork - iwork + 1;
  2284. zungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup],
  2285. &work[iwork], &i__2, &ierr);
  2286. irwork = ie + *n;
  2287. /* Perform bidiagonal QR iteration, computing left */
  2288. /* singular vectors of A in U and computing right */
  2289. /* singular vectors of A in A */
  2290. /* (CWorkspace: 0) */
  2291. /* (RWorkspace: need BDSPAC) */
  2292. zbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &a[
  2293. a_offset], lda, &u[u_offset], ldu, cdum, &
  2294. c__1, &rwork[irwork], info);
  2295. }
  2296. } else if (wntvas) {
  2297. /* Path 9 (M much larger than N, JOBU='A', JOBVT='S' */
  2298. /* or 'A') */
  2299. /* M left singular vectors to be computed in U and */
  2300. /* N right singular vectors to be computed in VT */
  2301. /* Computing MAX */
  2302. i__2 = *n + *m, i__3 = *n * 3;
  2303. if (*lwork >= *n * *n + f2cmax(i__2,i__3)) {
  2304. /* Sufficient workspace for a fast algorithm */
  2305. iu = 1;
  2306. if (*lwork >= wrkbl + *lda * *n) {
  2307. /* WORK(IU) is LDA by N */
  2308. ldwrku = *lda;
  2309. } else {
  2310. /* WORK(IU) is N by N */
  2311. ldwrku = *n;
  2312. }
  2313. itau = iu + ldwrku * *n;
  2314. iwork = itau + *n;
  2315. /* Compute A=Q*R, copying result to U */
  2316. /* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
  2317. /* (RWorkspace: 0) */
  2318. i__2 = *lwork - iwork + 1;
  2319. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2320. iwork], &i__2, &ierr);
  2321. zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  2322. ldu);
  2323. /* Generate Q in U */
  2324. /* (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB) */
  2325. /* (RWorkspace: 0) */
  2326. i__2 = *lwork - iwork + 1;
  2327. zungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
  2328. work[iwork], &i__2, &ierr);
  2329. /* Copy R to WORK(IU), zeroing out below it */
  2330. zlacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
  2331. ldwrku);
  2332. i__2 = *n - 1;
  2333. i__3 = *n - 1;
  2334. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
  2335. , &ldwrku);
  2336. ie = 1;
  2337. itauq = itau;
  2338. itaup = itauq + *n;
  2339. iwork = itaup + *n;
  2340. /* Bidiagonalize R in WORK(IU), copying result to VT */
  2341. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
  2342. /* (RWorkspace: need N) */
  2343. i__2 = *lwork - iwork + 1;
  2344. zgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  2345. work[itauq], &work[itaup], &work[iwork], &
  2346. i__2, &ierr);
  2347. zlacpy_("U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
  2348. ldvt);
  2349. /* Generate left bidiagonalizing vectors in WORK(IU) */
  2350. /* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
  2351. /* (RWorkspace: 0) */
  2352. i__2 = *lwork - iwork + 1;
  2353. zungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
  2354. , &work[iwork], &i__2, &ierr);
  2355. /* Generate right bidiagonalizing vectors in VT */
  2356. /* (CWorkspace: need N*N+3*N-1, */
  2357. /* prefer N*N+2*N+(N-1)*NB) */
  2358. /* (RWorkspace: need 0) */
  2359. i__2 = *lwork - iwork + 1;
  2360. zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
  2361. itaup], &work[iwork], &i__2, &ierr)
  2362. ;
  2363. irwork = ie + *n;
  2364. /* Perform bidiagonal QR iteration, computing left */
  2365. /* singular vectors of R in WORK(IU) and computing */
  2366. /* right singular vectors of R in VT */
  2367. /* (CWorkspace: need N*N) */
  2368. /* (RWorkspace: need BDSPAC) */
  2369. zbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &vt[
  2370. vt_offset], ldvt, &work[iu], &ldwrku, cdum, &
  2371. c__1, &rwork[irwork], info);
  2372. /* Multiply Q in U by left singular vectors of R in */
  2373. /* WORK(IU), storing result in A */
  2374. /* (CWorkspace: need N*N) */
  2375. /* (RWorkspace: 0) */
  2376. zgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &
  2377. work[iu], &ldwrku, &c_b1, &a[a_offset], lda);
  2378. /* Copy left singular vectors of A from A to U */
  2379. zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
  2380. ldu);
  2381. } else {
  2382. /* Insufficient workspace for a fast algorithm */
  2383. itau = 1;
  2384. iwork = itau + *n;
  2385. /* Compute A=Q*R, copying result to U */
  2386. /* (CWorkspace: need 2*N, prefer N+N*NB) */
  2387. /* (RWorkspace: 0) */
  2388. i__2 = *lwork - iwork + 1;
  2389. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2390. iwork], &i__2, &ierr);
  2391. zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
  2392. ldu);
  2393. /* Generate Q in U */
  2394. /* (CWorkspace: need N+M, prefer N+M*NB) */
  2395. /* (RWorkspace: 0) */
  2396. i__2 = *lwork - iwork + 1;
  2397. zungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
  2398. work[iwork], &i__2, &ierr);
  2399. /* Copy R from A to VT, zeroing out below it */
  2400. zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
  2401. ldvt);
  2402. if (*n > 1) {
  2403. i__2 = *n - 1;
  2404. i__3 = *n - 1;
  2405. zlaset_("L", &i__2, &i__3, &c_b1, &c_b1, &vt[
  2406. vt_dim1 + 2], ldvt);
  2407. }
  2408. ie = 1;
  2409. itauq = itau;
  2410. itaup = itauq + *n;
  2411. iwork = itaup + *n;
  2412. /* Bidiagonalize R in VT */
  2413. /* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
  2414. /* (RWorkspace: need N) */
  2415. i__2 = *lwork - iwork + 1;
  2416. zgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie],
  2417. &work[itauq], &work[itaup], &work[iwork], &
  2418. i__2, &ierr);
  2419. /* Multiply Q in U by left bidiagonalizing vectors */
  2420. /* in VT */
  2421. /* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
  2422. /* (RWorkspace: 0) */
  2423. i__2 = *lwork - iwork + 1;
  2424. zunmbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt,
  2425. &work[itauq], &u[u_offset], ldu, &work[iwork],
  2426. &i__2, &ierr);
  2427. /* Generate right bidiagonalizing vectors in VT */
  2428. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  2429. /* (RWorkspace: 0) */
  2430. i__2 = *lwork - iwork + 1;
  2431. zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
  2432. itaup], &work[iwork], &i__2, &ierr)
  2433. ;
  2434. irwork = ie + *n;
  2435. /* Perform bidiagonal QR iteration, computing left */
  2436. /* singular vectors of A in U and computing right */
  2437. /* singular vectors of A in VT */
  2438. /* (CWorkspace: 0) */
  2439. /* (RWorkspace: need BDSPAC) */
  2440. zbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &vt[
  2441. vt_offset], ldvt, &u[u_offset], ldu, cdum, &
  2442. c__1, &rwork[irwork], info);
  2443. }
  2444. }
  2445. }
  2446. } else {
  2447. /* M .LT. MNTHR */
  2448. /* Path 10 (M at least N, but not much larger) */
  2449. /* Reduce to bidiagonal form without QR decomposition */
  2450. ie = 1;
  2451. itauq = 1;
  2452. itaup = itauq + *n;
  2453. iwork = itaup + *n;
  2454. /* Bidiagonalize A */
  2455. /* (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) */
  2456. /* (RWorkspace: need N) */
  2457. i__2 = *lwork - iwork + 1;
  2458. zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  2459. &work[itaup], &work[iwork], &i__2, &ierr);
  2460. if (wntuas) {
  2461. /* If left singular vectors desired in U, copy result to U */
  2462. /* and generate left bidiagonalizing vectors in U */
  2463. /* (CWorkspace: need 2*N+NCU, prefer 2*N+NCU*NB) */
  2464. /* (RWorkspace: 0) */
  2465. zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  2466. if (wntus) {
  2467. ncu = *n;
  2468. }
  2469. if (wntua) {
  2470. ncu = *m;
  2471. }
  2472. i__2 = *lwork - iwork + 1;
  2473. zungbr_("Q", m, &ncu, n, &u[u_offset], ldu, &work[itauq], &
  2474. work[iwork], &i__2, &ierr);
  2475. }
  2476. if (wntvas) {
  2477. /* If right singular vectors desired in VT, copy result to */
  2478. /* VT and generate right bidiagonalizing vectors in VT */
  2479. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  2480. /* (RWorkspace: 0) */
  2481. zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2482. i__2 = *lwork - iwork + 1;
  2483. zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
  2484. work[iwork], &i__2, &ierr);
  2485. }
  2486. if (wntuo) {
  2487. /* If left singular vectors desired in A, generate left */
  2488. /* bidiagonalizing vectors in A */
  2489. /* (CWorkspace: need 3*N, prefer 2*N+N*NB) */
  2490. /* (RWorkspace: 0) */
  2491. i__2 = *lwork - iwork + 1;
  2492. zungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[
  2493. iwork], &i__2, &ierr);
  2494. }
  2495. if (wntvo) {
  2496. /* If right singular vectors desired in A, generate right */
  2497. /* bidiagonalizing vectors in A */
  2498. /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
  2499. /* (RWorkspace: 0) */
  2500. i__2 = *lwork - iwork + 1;
  2501. zungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[
  2502. iwork], &i__2, &ierr);
  2503. }
  2504. irwork = ie + *n;
  2505. if (wntuas || wntuo) {
  2506. nru = *m;
  2507. }
  2508. if (wntun) {
  2509. nru = 0;
  2510. }
  2511. if (wntvas || wntvo) {
  2512. ncvt = *n;
  2513. }
  2514. if (wntvn) {
  2515. ncvt = 0;
  2516. }
  2517. if (! wntuo && ! wntvo) {
  2518. /* Perform bidiagonal QR iteration, if desired, computing */
  2519. /* left singular vectors in U and computing right singular */
  2520. /* vectors in VT */
  2521. /* (CWorkspace: 0) */
  2522. /* (RWorkspace: need BDSPAC) */
  2523. zbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
  2524. vt_offset], ldvt, &u[u_offset], ldu, cdum, &c__1, &
  2525. rwork[irwork], info);
  2526. } else if (! wntuo && wntvo) {
  2527. /* Perform bidiagonal QR iteration, if desired, computing */
  2528. /* left singular vectors in U and computing right singular */
  2529. /* vectors in A */
  2530. /* (CWorkspace: 0) */
  2531. /* (RWorkspace: need BDSPAC) */
  2532. zbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &a[
  2533. a_offset], lda, &u[u_offset], ldu, cdum, &c__1, &
  2534. rwork[irwork], info);
  2535. } else {
  2536. /* Perform bidiagonal QR iteration, if desired, computing */
  2537. /* left singular vectors in A and computing right singular */
  2538. /* vectors in VT */
  2539. /* (CWorkspace: 0) */
  2540. /* (RWorkspace: need BDSPAC) */
  2541. zbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
  2542. vt_offset], ldvt, &a[a_offset], lda, cdum, &c__1, &
  2543. rwork[irwork], info);
  2544. }
  2545. }
  2546. } else {
  2547. /* A has more columns than rows. If A has sufficiently more */
  2548. /* columns than rows, first reduce using the LQ decomposition (if */
  2549. /* sufficient workspace available) */
  2550. if (*n >= mnthr) {
  2551. if (wntvn) {
  2552. /* Path 1t(N much larger than M, JOBVT='N') */
  2553. /* No right singular vectors to be computed */
  2554. itau = 1;
  2555. iwork = itau + *m;
  2556. /* Compute A=L*Q */
  2557. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  2558. /* (RWorkspace: 0) */
  2559. i__2 = *lwork - iwork + 1;
  2560. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
  2561. i__2, &ierr);
  2562. /* Zero out above L */
  2563. i__2 = *m - 1;
  2564. i__3 = *m - 1;
  2565. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
  2566. , lda);
  2567. ie = 1;
  2568. itauq = 1;
  2569. itaup = itauq + *m;
  2570. iwork = itaup + *m;
  2571. /* Bidiagonalize L in A */
  2572. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  2573. /* (RWorkspace: need M) */
  2574. i__2 = *lwork - iwork + 1;
  2575. zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  2576. itauq], &work[itaup], &work[iwork], &i__2, &ierr);
  2577. if (wntuo || wntuas) {
  2578. /* If left singular vectors desired, generate Q */
  2579. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  2580. /* (RWorkspace: 0) */
  2581. i__2 = *lwork - iwork + 1;
  2582. zungbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq], &
  2583. work[iwork], &i__2, &ierr);
  2584. }
  2585. irwork = ie + *m;
  2586. nru = 0;
  2587. if (wntuo || wntuas) {
  2588. nru = *m;
  2589. }
  2590. /* Perform bidiagonal QR iteration, computing left singular */
  2591. /* vectors of A in A if desired */
  2592. /* (CWorkspace: 0) */
  2593. /* (RWorkspace: need BDSPAC) */
  2594. zbdsqr_("U", m, &c__0, &nru, &c__0, &s[1], &rwork[ie], cdum, &
  2595. c__1, &a[a_offset], lda, cdum, &c__1, &rwork[irwork],
  2596. info);
  2597. /* If left singular vectors desired in U, copy them there */
  2598. if (wntuas) {
  2599. zlacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2600. }
  2601. } else if (wntvo && wntun) {
  2602. /* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
  2603. /* M right singular vectors to be overwritten on A and */
  2604. /* no left singular vectors to be computed */
  2605. if (*lwork >= *m * *m + *m * 3) {
  2606. /* Sufficient workspace for a fast algorithm */
  2607. ir = 1;
  2608. /* Computing MAX */
  2609. i__2 = wrkbl, i__3 = *lda * *n;
  2610. if (*lwork >= f2cmax(i__2,i__3) + *lda * *m) {
  2611. /* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
  2612. ldwrku = *lda;
  2613. chunk = *n;
  2614. ldwrkr = *lda;
  2615. } else /* if(complicated condition) */ {
  2616. /* Computing MAX */
  2617. i__2 = wrkbl, i__3 = *lda * *n;
  2618. if (*lwork >= f2cmax(i__2,i__3) + *m * *m) {
  2619. /* WORK(IU) is LDA by N and WORK(IR) is M by M */
  2620. ldwrku = *lda;
  2621. chunk = *n;
  2622. ldwrkr = *m;
  2623. } else {
  2624. /* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
  2625. ldwrku = *m;
  2626. chunk = (*lwork - *m * *m) / *m;
  2627. ldwrkr = *m;
  2628. }
  2629. }
  2630. itau = ir + ldwrkr * *m;
  2631. iwork = itau + *m;
  2632. /* Compute A=L*Q */
  2633. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  2634. /* (RWorkspace: 0) */
  2635. i__2 = *lwork - iwork + 1;
  2636. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
  2637. , &i__2, &ierr);
  2638. /* Copy L to WORK(IR) and zero out above it */
  2639. zlacpy_("L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr);
  2640. i__2 = *m - 1;
  2641. i__3 = *m - 1;
  2642. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[ir +
  2643. ldwrkr], &ldwrkr);
  2644. /* Generate Q in A */
  2645. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  2646. /* (RWorkspace: 0) */
  2647. i__2 = *lwork - iwork + 1;
  2648. zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
  2649. iwork], &i__2, &ierr);
  2650. ie = 1;
  2651. itauq = itau;
  2652. itaup = itauq + *m;
  2653. iwork = itaup + *m;
  2654. /* Bidiagonalize L in WORK(IR) */
  2655. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
  2656. /* (RWorkspace: need M) */
  2657. i__2 = *lwork - iwork + 1;
  2658. zgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
  2659. work[itauq], &work[itaup], &work[iwork], &i__2, &
  2660. ierr);
  2661. /* Generate right vectors bidiagonalizing L */
  2662. /* (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB) */
  2663. /* (RWorkspace: 0) */
  2664. i__2 = *lwork - iwork + 1;
  2665. zungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
  2666. work[iwork], &i__2, &ierr);
  2667. irwork = ie + *m;
  2668. /* Perform bidiagonal QR iteration, computing right */
  2669. /* singular vectors of L in WORK(IR) */
  2670. /* (CWorkspace: need M*M) */
  2671. /* (RWorkspace: need BDSPAC) */
  2672. zbdsqr_("U", m, m, &c__0, &c__0, &s[1], &rwork[ie], &work[
  2673. ir], &ldwrkr, cdum, &c__1, cdum, &c__1, &rwork[
  2674. irwork], info);
  2675. iu = itauq;
  2676. /* Multiply right singular vectors of L in WORK(IR) by Q */
  2677. /* in A, storing result in WORK(IU) and copying to A */
  2678. /* (CWorkspace: need M*M+M, prefer M*M+M*N) */
  2679. /* (RWorkspace: 0) */
  2680. i__2 = *n;
  2681. i__3 = chunk;
  2682. for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
  2683. i__3) {
  2684. /* Computing MIN */
  2685. i__4 = *n - i__ + 1;
  2686. blk = f2cmin(i__4,chunk);
  2687. zgemm_("N", "N", m, &blk, m, &c_b2, &work[ir], &
  2688. ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b1, &
  2689. work[iu], &ldwrku);
  2690. zlacpy_("F", m, &blk, &work[iu], &ldwrku, &a[i__ *
  2691. a_dim1 + 1], lda);
  2692. /* L30: */
  2693. }
  2694. } else {
  2695. /* Insufficient workspace for a fast algorithm */
  2696. ie = 1;
  2697. itauq = 1;
  2698. itaup = itauq + *m;
  2699. iwork = itaup + *m;
  2700. /* Bidiagonalize A */
  2701. /* (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) */
  2702. /* (RWorkspace: need M) */
  2703. i__3 = *lwork - iwork + 1;
  2704. zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  2705. itauq], &work[itaup], &work[iwork], &i__3, &ierr);
  2706. /* Generate right vectors bidiagonalizing A */
  2707. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  2708. /* (RWorkspace: 0) */
  2709. i__3 = *lwork - iwork + 1;
  2710. zungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
  2711. work[iwork], &i__3, &ierr);
  2712. irwork = ie + *m;
  2713. /* Perform bidiagonal QR iteration, computing right */
  2714. /* singular vectors of A in A */
  2715. /* (CWorkspace: 0) */
  2716. /* (RWorkspace: need BDSPAC) */
  2717. zbdsqr_("L", m, n, &c__0, &c__0, &s[1], &rwork[ie], &a[
  2718. a_offset], lda, cdum, &c__1, cdum, &c__1, &rwork[
  2719. irwork], info);
  2720. }
  2721. } else if (wntvo && wntuas) {
  2722. /* Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O') */
  2723. /* M right singular vectors to be overwritten on A and */
  2724. /* M left singular vectors to be computed in U */
  2725. if (*lwork >= *m * *m + *m * 3) {
  2726. /* Sufficient workspace for a fast algorithm */
  2727. ir = 1;
  2728. /* Computing MAX */
  2729. i__3 = wrkbl, i__2 = *lda * *n;
  2730. if (*lwork >= f2cmax(i__3,i__2) + *lda * *m) {
  2731. /* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
  2732. ldwrku = *lda;
  2733. chunk = *n;
  2734. ldwrkr = *lda;
  2735. } else /* if(complicated condition) */ {
  2736. /* Computing MAX */
  2737. i__3 = wrkbl, i__2 = *lda * *n;
  2738. if (*lwork >= f2cmax(i__3,i__2) + *m * *m) {
  2739. /* WORK(IU) is LDA by N and WORK(IR) is M by M */
  2740. ldwrku = *lda;
  2741. chunk = *n;
  2742. ldwrkr = *m;
  2743. } else {
  2744. /* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
  2745. ldwrku = *m;
  2746. chunk = (*lwork - *m * *m) / *m;
  2747. ldwrkr = *m;
  2748. }
  2749. }
  2750. itau = ir + ldwrkr * *m;
  2751. iwork = itau + *m;
  2752. /* Compute A=L*Q */
  2753. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  2754. /* (RWorkspace: 0) */
  2755. i__3 = *lwork - iwork + 1;
  2756. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
  2757. , &i__3, &ierr);
  2758. /* Copy L to U, zeroing about above it */
  2759. zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2760. i__3 = *m - 1;
  2761. i__2 = *m - 1;
  2762. zlaset_("U", &i__3, &i__2, &c_b1, &c_b1, &u[(u_dim1 << 1)
  2763. + 1], ldu);
  2764. /* Generate Q in A */
  2765. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  2766. /* (RWorkspace: 0) */
  2767. i__3 = *lwork - iwork + 1;
  2768. zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
  2769. iwork], &i__3, &ierr);
  2770. ie = 1;
  2771. itauq = itau;
  2772. itaup = itauq + *m;
  2773. iwork = itaup + *m;
  2774. /* Bidiagonalize L in U, copying result to WORK(IR) */
  2775. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
  2776. /* (RWorkspace: need M) */
  2777. i__3 = *lwork - iwork + 1;
  2778. zgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &work[
  2779. itauq], &work[itaup], &work[iwork], &i__3, &ierr);
  2780. zlacpy_("U", m, m, &u[u_offset], ldu, &work[ir], &ldwrkr);
  2781. /* Generate right vectors bidiagonalizing L in WORK(IR) */
  2782. /* (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB) */
  2783. /* (RWorkspace: 0) */
  2784. i__3 = *lwork - iwork + 1;
  2785. zungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
  2786. work[iwork], &i__3, &ierr);
  2787. /* Generate left vectors bidiagonalizing L in U */
  2788. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
  2789. /* (RWorkspace: 0) */
  2790. i__3 = *lwork - iwork + 1;
  2791. zungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
  2792. work[iwork], &i__3, &ierr);
  2793. irwork = ie + *m;
  2794. /* Perform bidiagonal QR iteration, computing left */
  2795. /* singular vectors of L in U, and computing right */
  2796. /* singular vectors of L in WORK(IR) */
  2797. /* (CWorkspace: need M*M) */
  2798. /* (RWorkspace: need BDSPAC) */
  2799. zbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[ir],
  2800. &ldwrkr, &u[u_offset], ldu, cdum, &c__1, &rwork[
  2801. irwork], info);
  2802. iu = itauq;
  2803. /* Multiply right singular vectors of L in WORK(IR) by Q */
  2804. /* in A, storing result in WORK(IU) and copying to A */
  2805. /* (CWorkspace: need M*M+M, prefer M*M+M*N)) */
  2806. /* (RWorkspace: 0) */
  2807. i__3 = *n;
  2808. i__2 = chunk;
  2809. for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
  2810. i__2) {
  2811. /* Computing MIN */
  2812. i__4 = *n - i__ + 1;
  2813. blk = f2cmin(i__4,chunk);
  2814. zgemm_("N", "N", m, &blk, m, &c_b2, &work[ir], &
  2815. ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b1, &
  2816. work[iu], &ldwrku);
  2817. zlacpy_("F", m, &blk, &work[iu], &ldwrku, &a[i__ *
  2818. a_dim1 + 1], lda);
  2819. /* L40: */
  2820. }
  2821. } else {
  2822. /* Insufficient workspace for a fast algorithm */
  2823. itau = 1;
  2824. iwork = itau + *m;
  2825. /* Compute A=L*Q */
  2826. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  2827. /* (RWorkspace: 0) */
  2828. i__2 = *lwork - iwork + 1;
  2829. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
  2830. , &i__2, &ierr);
  2831. /* Copy L to U, zeroing out above it */
  2832. zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2833. i__2 = *m - 1;
  2834. i__3 = *m - 1;
  2835. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &u[(u_dim1 << 1)
  2836. + 1], ldu);
  2837. /* Generate Q in A */
  2838. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  2839. /* (RWorkspace: 0) */
  2840. i__2 = *lwork - iwork + 1;
  2841. zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
  2842. iwork], &i__2, &ierr);
  2843. ie = 1;
  2844. itauq = itau;
  2845. itaup = itauq + *m;
  2846. iwork = itaup + *m;
  2847. /* Bidiagonalize L in U */
  2848. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  2849. /* (RWorkspace: need M) */
  2850. i__2 = *lwork - iwork + 1;
  2851. zgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &work[
  2852. itauq], &work[itaup], &work[iwork], &i__2, &ierr);
  2853. /* Multiply right vectors bidiagonalizing L by Q in A */
  2854. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  2855. /* (RWorkspace: 0) */
  2856. i__2 = *lwork - iwork + 1;
  2857. zunmbr_("P", "L", "C", m, n, m, &u[u_offset], ldu, &work[
  2858. itaup], &a[a_offset], lda, &work[iwork], &i__2, &
  2859. ierr);
  2860. /* Generate left vectors bidiagonalizing L in U */
  2861. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  2862. /* (RWorkspace: 0) */
  2863. i__2 = *lwork - iwork + 1;
  2864. zungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
  2865. work[iwork], &i__2, &ierr);
  2866. irwork = ie + *m;
  2867. /* Perform bidiagonal QR iteration, computing left */
  2868. /* singular vectors of A in U and computing right */
  2869. /* singular vectors of A in A */
  2870. /* (CWorkspace: 0) */
  2871. /* (RWorkspace: need BDSPAC) */
  2872. zbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &a[
  2873. a_offset], lda, &u[u_offset], ldu, cdum, &c__1, &
  2874. rwork[irwork], info);
  2875. }
  2876. } else if (wntvs) {
  2877. if (wntun) {
  2878. /* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
  2879. /* M right singular vectors to be computed in VT and */
  2880. /* no left singular vectors to be computed */
  2881. if (*lwork >= *m * *m + *m * 3) {
  2882. /* Sufficient workspace for a fast algorithm */
  2883. ir = 1;
  2884. if (*lwork >= wrkbl + *lda * *m) {
  2885. /* WORK(IR) is LDA by M */
  2886. ldwrkr = *lda;
  2887. } else {
  2888. /* WORK(IR) is M by M */
  2889. ldwrkr = *m;
  2890. }
  2891. itau = ir + ldwrkr * *m;
  2892. iwork = itau + *m;
  2893. /* Compute A=L*Q */
  2894. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  2895. /* (RWorkspace: 0) */
  2896. i__2 = *lwork - iwork + 1;
  2897. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2898. iwork], &i__2, &ierr);
  2899. /* Copy L to WORK(IR), zeroing out above it */
  2900. zlacpy_("L", m, m, &a[a_offset], lda, &work[ir], &
  2901. ldwrkr);
  2902. i__2 = *m - 1;
  2903. i__3 = *m - 1;
  2904. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[ir +
  2905. ldwrkr], &ldwrkr);
  2906. /* Generate Q in A */
  2907. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  2908. /* (RWorkspace: 0) */
  2909. i__2 = *lwork - iwork + 1;
  2910. zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &
  2911. work[iwork], &i__2, &ierr);
  2912. ie = 1;
  2913. itauq = itau;
  2914. itaup = itauq + *m;
  2915. iwork = itaup + *m;
  2916. /* Bidiagonalize L in WORK(IR) */
  2917. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
  2918. /* (RWorkspace: need M) */
  2919. i__2 = *lwork - iwork + 1;
  2920. zgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
  2921. work[itauq], &work[itaup], &work[iwork], &
  2922. i__2, &ierr);
  2923. /* Generate right vectors bidiagonalizing L in */
  2924. /* WORK(IR) */
  2925. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB) */
  2926. /* (RWorkspace: 0) */
  2927. i__2 = *lwork - iwork + 1;
  2928. zungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
  2929. , &work[iwork], &i__2, &ierr);
  2930. irwork = ie + *m;
  2931. /* Perform bidiagonal QR iteration, computing right */
  2932. /* singular vectors of L in WORK(IR) */
  2933. /* (CWorkspace: need M*M) */
  2934. /* (RWorkspace: need BDSPAC) */
  2935. zbdsqr_("U", m, m, &c__0, &c__0, &s[1], &rwork[ie], &
  2936. work[ir], &ldwrkr, cdum, &c__1, cdum, &c__1, &
  2937. rwork[irwork], info);
  2938. /* Multiply right singular vectors of L in WORK(IR) by */
  2939. /* Q in A, storing result in VT */
  2940. /* (CWorkspace: need M*M) */
  2941. /* (RWorkspace: 0) */
  2942. zgemm_("N", "N", m, n, m, &c_b2, &work[ir], &ldwrkr, &
  2943. a[a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
  2944. } else {
  2945. /* Insufficient workspace for a fast algorithm */
  2946. itau = 1;
  2947. iwork = itau + *m;
  2948. /* Compute A=L*Q */
  2949. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  2950. /* (RWorkspace: 0) */
  2951. i__2 = *lwork - iwork + 1;
  2952. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  2953. iwork], &i__2, &ierr);
  2954. /* Copy result to VT */
  2955. zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  2956. ldvt);
  2957. /* Generate Q in VT */
  2958. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  2959. /* (RWorkspace: 0) */
  2960. i__2 = *lwork - iwork + 1;
  2961. zunglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
  2962. work[iwork], &i__2, &ierr);
  2963. ie = 1;
  2964. itauq = itau;
  2965. itaup = itauq + *m;
  2966. iwork = itaup + *m;
  2967. /* Zero out above L in A */
  2968. i__2 = *m - 1;
  2969. i__3 = *m - 1;
  2970. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
  2971. 1) + 1], lda);
  2972. /* Bidiagonalize L in A */
  2973. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  2974. /* (RWorkspace: need M) */
  2975. i__2 = *lwork - iwork + 1;
  2976. zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
  2977. work[itauq], &work[itaup], &work[iwork], &
  2978. i__2, &ierr);
  2979. /* Multiply right vectors bidiagonalizing L by Q in VT */
  2980. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  2981. /* (RWorkspace: 0) */
  2982. i__2 = *lwork - iwork + 1;
  2983. zunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
  2984. work[itaup], &vt[vt_offset], ldvt, &work[
  2985. iwork], &i__2, &ierr);
  2986. irwork = ie + *m;
  2987. /* Perform bidiagonal QR iteration, computing right */
  2988. /* singular vectors of A in VT */
  2989. /* (CWorkspace: 0) */
  2990. /* (RWorkspace: need BDSPAC) */
  2991. zbdsqr_("U", m, n, &c__0, &c__0, &s[1], &rwork[ie], &
  2992. vt[vt_offset], ldvt, cdum, &c__1, cdum, &c__1,
  2993. &rwork[irwork], info);
  2994. }
  2995. } else if (wntuo) {
  2996. /* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
  2997. /* M right singular vectors to be computed in VT and */
  2998. /* M left singular vectors to be overwritten on A */
  2999. if (*lwork >= (*m << 1) * *m + *m * 3) {
  3000. /* Sufficient workspace for a fast algorithm */
  3001. iu = 1;
  3002. if (*lwork >= wrkbl + (*lda << 1) * *m) {
  3003. /* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
  3004. ldwrku = *lda;
  3005. ir = iu + ldwrku * *m;
  3006. ldwrkr = *lda;
  3007. } else if (*lwork >= wrkbl + (*lda + *m) * *m) {
  3008. /* WORK(IU) is LDA by M and WORK(IR) is M by M */
  3009. ldwrku = *lda;
  3010. ir = iu + ldwrku * *m;
  3011. ldwrkr = *m;
  3012. } else {
  3013. /* WORK(IU) is M by M and WORK(IR) is M by M */
  3014. ldwrku = *m;
  3015. ir = iu + ldwrku * *m;
  3016. ldwrkr = *m;
  3017. }
  3018. itau = ir + ldwrkr * *m;
  3019. iwork = itau + *m;
  3020. /* Compute A=L*Q */
  3021. /* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
  3022. /* (RWorkspace: 0) */
  3023. i__2 = *lwork - iwork + 1;
  3024. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3025. iwork], &i__2, &ierr);
  3026. /* Copy L to WORK(IU), zeroing out below it */
  3027. zlacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
  3028. ldwrku);
  3029. i__2 = *m - 1;
  3030. i__3 = *m - 1;
  3031. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
  3032. ldwrku], &ldwrku);
  3033. /* Generate Q in A */
  3034. /* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
  3035. /* (RWorkspace: 0) */
  3036. i__2 = *lwork - iwork + 1;
  3037. zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &
  3038. work[iwork], &i__2, &ierr);
  3039. ie = 1;
  3040. itauq = itau;
  3041. itaup = itauq + *m;
  3042. iwork = itaup + *m;
  3043. /* Bidiagonalize L in WORK(IU), copying result to */
  3044. /* WORK(IR) */
  3045. /* (CWorkspace: need 2*M*M+3*M, */
  3046. /* prefer 2*M*M+2*M+2*M*NB) */
  3047. /* (RWorkspace: need M) */
  3048. i__2 = *lwork - iwork + 1;
  3049. zgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  3050. work[itauq], &work[itaup], &work[iwork], &
  3051. i__2, &ierr);
  3052. zlacpy_("L", m, m, &work[iu], &ldwrku, &work[ir], &
  3053. ldwrkr);
  3054. /* Generate right bidiagonalizing vectors in WORK(IU) */
  3055. /* (CWorkspace: need 2*M*M+3*M-1, */
  3056. /* prefer 2*M*M+2*M+(M-1)*NB) */
  3057. /* (RWorkspace: 0) */
  3058. i__2 = *lwork - iwork + 1;
  3059. zungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
  3060. , &work[iwork], &i__2, &ierr);
  3061. /* Generate left bidiagonalizing vectors in WORK(IR) */
  3062. /* (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) */
  3063. /* (RWorkspace: 0) */
  3064. i__2 = *lwork - iwork + 1;
  3065. zungbr_("Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
  3066. , &work[iwork], &i__2, &ierr);
  3067. irwork = ie + *m;
  3068. /* Perform bidiagonal QR iteration, computing left */
  3069. /* singular vectors of L in WORK(IR) and computing */
  3070. /* right singular vectors of L in WORK(IU) */
  3071. /* (CWorkspace: need 2*M*M) */
  3072. /* (RWorkspace: need BDSPAC) */
  3073. zbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
  3074. iu], &ldwrku, &work[ir], &ldwrkr, cdum, &c__1,
  3075. &rwork[irwork], info);
  3076. /* Multiply right singular vectors of L in WORK(IU) by */
  3077. /* Q in A, storing result in VT */
  3078. /* (CWorkspace: need M*M) */
  3079. /* (RWorkspace: 0) */
  3080. zgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
  3081. a[a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
  3082. /* Copy left singular vectors of L to A */
  3083. /* (CWorkspace: need M*M) */
  3084. /* (RWorkspace: 0) */
  3085. zlacpy_("F", m, m, &work[ir], &ldwrkr, &a[a_offset],
  3086. lda);
  3087. } else {
  3088. /* Insufficient workspace for a fast algorithm */
  3089. itau = 1;
  3090. iwork = itau + *m;
  3091. /* Compute A=L*Q, copying result to VT */
  3092. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3093. /* (RWorkspace: 0) */
  3094. i__2 = *lwork - iwork + 1;
  3095. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3096. iwork], &i__2, &ierr);
  3097. zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3098. ldvt);
  3099. /* Generate Q in VT */
  3100. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3101. /* (RWorkspace: 0) */
  3102. i__2 = *lwork - iwork + 1;
  3103. zunglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3104. work[iwork], &i__2, &ierr);
  3105. ie = 1;
  3106. itauq = itau;
  3107. itaup = itauq + *m;
  3108. iwork = itaup + *m;
  3109. /* Zero out above L in A */
  3110. i__2 = *m - 1;
  3111. i__3 = *m - 1;
  3112. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
  3113. 1) + 1], lda);
  3114. /* Bidiagonalize L in A */
  3115. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  3116. /* (RWorkspace: need M) */
  3117. i__2 = *lwork - iwork + 1;
  3118. zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
  3119. work[itauq], &work[itaup], &work[iwork], &
  3120. i__2, &ierr);
  3121. /* Multiply right vectors bidiagonalizing L by Q in VT */
  3122. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  3123. /* (RWorkspace: 0) */
  3124. i__2 = *lwork - iwork + 1;
  3125. zunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
  3126. work[itaup], &vt[vt_offset], ldvt, &work[
  3127. iwork], &i__2, &ierr);
  3128. /* Generate left bidiagonalizing vectors of L in A */
  3129. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  3130. /* (RWorkspace: 0) */
  3131. i__2 = *lwork - iwork + 1;
  3132. zungbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq],
  3133. &work[iwork], &i__2, &ierr);
  3134. irwork = ie + *m;
  3135. /* Perform bidiagonal QR iteration, computing left */
  3136. /* singular vectors of A in A and computing right */
  3137. /* singular vectors of A in VT */
  3138. /* (CWorkspace: 0) */
  3139. /* (RWorkspace: need BDSPAC) */
  3140. zbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
  3141. vt_offset], ldvt, &a[a_offset], lda, cdum, &
  3142. c__1, &rwork[irwork], info);
  3143. }
  3144. } else if (wntuas) {
  3145. /* Path 6t(N much larger than M, JOBU='S' or 'A', */
  3146. /* JOBVT='S') */
  3147. /* M right singular vectors to be computed in VT and */
  3148. /* M left singular vectors to be computed in U */
  3149. if (*lwork >= *m * *m + *m * 3) {
  3150. /* Sufficient workspace for a fast algorithm */
  3151. iu = 1;
  3152. if (*lwork >= wrkbl + *lda * *m) {
  3153. /* WORK(IU) is LDA by N */
  3154. ldwrku = *lda;
  3155. } else {
  3156. /* WORK(IU) is LDA by M */
  3157. ldwrku = *m;
  3158. }
  3159. itau = iu + ldwrku * *m;
  3160. iwork = itau + *m;
  3161. /* Compute A=L*Q */
  3162. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  3163. /* (RWorkspace: 0) */
  3164. i__2 = *lwork - iwork + 1;
  3165. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3166. iwork], &i__2, &ierr);
  3167. /* Copy L to WORK(IU), zeroing out above it */
  3168. zlacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
  3169. ldwrku);
  3170. i__2 = *m - 1;
  3171. i__3 = *m - 1;
  3172. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
  3173. ldwrku], &ldwrku);
  3174. /* Generate Q in A */
  3175. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  3176. /* (RWorkspace: 0) */
  3177. i__2 = *lwork - iwork + 1;
  3178. zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &
  3179. work[iwork], &i__2, &ierr);
  3180. ie = 1;
  3181. itauq = itau;
  3182. itaup = itauq + *m;
  3183. iwork = itaup + *m;
  3184. /* Bidiagonalize L in WORK(IU), copying result to U */
  3185. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
  3186. /* (RWorkspace: need M) */
  3187. i__2 = *lwork - iwork + 1;
  3188. zgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  3189. work[itauq], &work[itaup], &work[iwork], &
  3190. i__2, &ierr);
  3191. zlacpy_("L", m, m, &work[iu], &ldwrku, &u[u_offset],
  3192. ldu);
  3193. /* Generate right bidiagonalizing vectors in WORK(IU) */
  3194. /* (CWorkspace: need M*M+3*M-1, */
  3195. /* prefer M*M+2*M+(M-1)*NB) */
  3196. /* (RWorkspace: 0) */
  3197. i__2 = *lwork - iwork + 1;
  3198. zungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
  3199. , &work[iwork], &i__2, &ierr);
  3200. /* Generate left bidiagonalizing vectors in U */
  3201. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
  3202. /* (RWorkspace: 0) */
  3203. i__2 = *lwork - iwork + 1;
  3204. zungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
  3205. &work[iwork], &i__2, &ierr);
  3206. irwork = ie + *m;
  3207. /* Perform bidiagonal QR iteration, computing left */
  3208. /* singular vectors of L in U and computing right */
  3209. /* singular vectors of L in WORK(IU) */
  3210. /* (CWorkspace: need M*M) */
  3211. /* (RWorkspace: need BDSPAC) */
  3212. zbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
  3213. iu], &ldwrku, &u[u_offset], ldu, cdum, &c__1,
  3214. &rwork[irwork], info);
  3215. /* Multiply right singular vectors of L in WORK(IU) by */
  3216. /* Q in A, storing result in VT */
  3217. /* (CWorkspace: need M*M) */
  3218. /* (RWorkspace: 0) */
  3219. zgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
  3220. a[a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
  3221. } else {
  3222. /* Insufficient workspace for a fast algorithm */
  3223. itau = 1;
  3224. iwork = itau + *m;
  3225. /* Compute A=L*Q, copying result to VT */
  3226. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3227. /* (RWorkspace: 0) */
  3228. i__2 = *lwork - iwork + 1;
  3229. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3230. iwork], &i__2, &ierr);
  3231. zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3232. ldvt);
  3233. /* Generate Q in VT */
  3234. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3235. /* (RWorkspace: 0) */
  3236. i__2 = *lwork - iwork + 1;
  3237. zunglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3238. work[iwork], &i__2, &ierr);
  3239. /* Copy L to U, zeroing out above it */
  3240. zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset],
  3241. ldu);
  3242. i__2 = *m - 1;
  3243. i__3 = *m - 1;
  3244. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &u[(u_dim1 <<
  3245. 1) + 1], ldu);
  3246. ie = 1;
  3247. itauq = itau;
  3248. itaup = itauq + *m;
  3249. iwork = itaup + *m;
  3250. /* Bidiagonalize L in U */
  3251. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  3252. /* (RWorkspace: need M) */
  3253. i__2 = *lwork - iwork + 1;
  3254. zgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &
  3255. work[itauq], &work[itaup], &work[iwork], &
  3256. i__2, &ierr);
  3257. /* Multiply right bidiagonalizing vectors in U by Q */
  3258. /* in VT */
  3259. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  3260. /* (RWorkspace: 0) */
  3261. i__2 = *lwork - iwork + 1;
  3262. zunmbr_("P", "L", "C", m, n, m, &u[u_offset], ldu, &
  3263. work[itaup], &vt[vt_offset], ldvt, &work[
  3264. iwork], &i__2, &ierr);
  3265. /* Generate left bidiagonalizing vectors in U */
  3266. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  3267. /* (RWorkspace: 0) */
  3268. i__2 = *lwork - iwork + 1;
  3269. zungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
  3270. &work[iwork], &i__2, &ierr);
  3271. irwork = ie + *m;
  3272. /* Perform bidiagonal QR iteration, computing left */
  3273. /* singular vectors of A in U and computing right */
  3274. /* singular vectors of A in VT */
  3275. /* (CWorkspace: 0) */
  3276. /* (RWorkspace: need BDSPAC) */
  3277. zbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
  3278. vt_offset], ldvt, &u[u_offset], ldu, cdum, &
  3279. c__1, &rwork[irwork], info);
  3280. }
  3281. }
  3282. } else if (wntva) {
  3283. if (wntun) {
  3284. /* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
  3285. /* N right singular vectors to be computed in VT and */
  3286. /* no left singular vectors to be computed */
  3287. /* Computing MAX */
  3288. i__2 = *n + *m, i__3 = *m * 3;
  3289. if (*lwork >= *m * *m + f2cmax(i__2,i__3)) {
  3290. /* Sufficient workspace for a fast algorithm */
  3291. ir = 1;
  3292. if (*lwork >= wrkbl + *lda * *m) {
  3293. /* WORK(IR) is LDA by M */
  3294. ldwrkr = *lda;
  3295. } else {
  3296. /* WORK(IR) is M by M */
  3297. ldwrkr = *m;
  3298. }
  3299. itau = ir + ldwrkr * *m;
  3300. iwork = itau + *m;
  3301. /* Compute A=L*Q, copying result to VT */
  3302. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  3303. /* (RWorkspace: 0) */
  3304. i__2 = *lwork - iwork + 1;
  3305. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3306. iwork], &i__2, &ierr);
  3307. zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3308. ldvt);
  3309. /* Copy L to WORK(IR), zeroing out above it */
  3310. zlacpy_("L", m, m, &a[a_offset], lda, &work[ir], &
  3311. ldwrkr);
  3312. i__2 = *m - 1;
  3313. i__3 = *m - 1;
  3314. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[ir +
  3315. ldwrkr], &ldwrkr);
  3316. /* Generate Q in VT */
  3317. /* (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB) */
  3318. /* (RWorkspace: 0) */
  3319. i__2 = *lwork - iwork + 1;
  3320. zunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3321. work[iwork], &i__2, &ierr);
  3322. ie = 1;
  3323. itauq = itau;
  3324. itaup = itauq + *m;
  3325. iwork = itaup + *m;
  3326. /* Bidiagonalize L in WORK(IR) */
  3327. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
  3328. /* (RWorkspace: need M) */
  3329. i__2 = *lwork - iwork + 1;
  3330. zgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
  3331. work[itauq], &work[itaup], &work[iwork], &
  3332. i__2, &ierr);
  3333. /* Generate right bidiagonalizing vectors in WORK(IR) */
  3334. /* (CWorkspace: need M*M+3*M-1, */
  3335. /* prefer M*M+2*M+(M-1)*NB) */
  3336. /* (RWorkspace: 0) */
  3337. i__2 = *lwork - iwork + 1;
  3338. zungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
  3339. , &work[iwork], &i__2, &ierr);
  3340. irwork = ie + *m;
  3341. /* Perform bidiagonal QR iteration, computing right */
  3342. /* singular vectors of L in WORK(IR) */
  3343. /* (CWorkspace: need M*M) */
  3344. /* (RWorkspace: need BDSPAC) */
  3345. zbdsqr_("U", m, m, &c__0, &c__0, &s[1], &rwork[ie], &
  3346. work[ir], &ldwrkr, cdum, &c__1, cdum, &c__1, &
  3347. rwork[irwork], info);
  3348. /* Multiply right singular vectors of L in WORK(IR) by */
  3349. /* Q in VT, storing result in A */
  3350. /* (CWorkspace: need M*M) */
  3351. /* (RWorkspace: 0) */
  3352. zgemm_("N", "N", m, n, m, &c_b2, &work[ir], &ldwrkr, &
  3353. vt[vt_offset], ldvt, &c_b1, &a[a_offset], lda);
  3354. /* Copy right singular vectors of A from A to VT */
  3355. zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
  3356. ldvt);
  3357. } else {
  3358. /* Insufficient workspace for a fast algorithm */
  3359. itau = 1;
  3360. iwork = itau + *m;
  3361. /* Compute A=L*Q, copying result to VT */
  3362. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3363. /* (RWorkspace: 0) */
  3364. i__2 = *lwork - iwork + 1;
  3365. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3366. iwork], &i__2, &ierr);
  3367. zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3368. ldvt);
  3369. /* Generate Q in VT */
  3370. /* (CWorkspace: need M+N, prefer M+N*NB) */
  3371. /* (RWorkspace: 0) */
  3372. i__2 = *lwork - iwork + 1;
  3373. zunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3374. work[iwork], &i__2, &ierr);
  3375. ie = 1;
  3376. itauq = itau;
  3377. itaup = itauq + *m;
  3378. iwork = itaup + *m;
  3379. /* Zero out above L in A */
  3380. i__2 = *m - 1;
  3381. i__3 = *m - 1;
  3382. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
  3383. 1) + 1], lda);
  3384. /* Bidiagonalize L in A */
  3385. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  3386. /* (RWorkspace: need M) */
  3387. i__2 = *lwork - iwork + 1;
  3388. zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
  3389. work[itauq], &work[itaup], &work[iwork], &
  3390. i__2, &ierr);
  3391. /* Multiply right bidiagonalizing vectors in A by Q */
  3392. /* in VT */
  3393. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  3394. /* (RWorkspace: 0) */
  3395. i__2 = *lwork - iwork + 1;
  3396. zunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
  3397. work[itaup], &vt[vt_offset], ldvt, &work[
  3398. iwork], &i__2, &ierr);
  3399. irwork = ie + *m;
  3400. /* Perform bidiagonal QR iteration, computing right */
  3401. /* singular vectors of A in VT */
  3402. /* (CWorkspace: 0) */
  3403. /* (RWorkspace: need BDSPAC) */
  3404. zbdsqr_("U", m, n, &c__0, &c__0, &s[1], &rwork[ie], &
  3405. vt[vt_offset], ldvt, cdum, &c__1, cdum, &c__1,
  3406. &rwork[irwork], info);
  3407. }
  3408. } else if (wntuo) {
  3409. /* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
  3410. /* N right singular vectors to be computed in VT and */
  3411. /* M left singular vectors to be overwritten on A */
  3412. /* Computing MAX */
  3413. i__2 = *n + *m, i__3 = *m * 3;
  3414. if (*lwork >= (*m << 1) * *m + f2cmax(i__2,i__3)) {
  3415. /* Sufficient workspace for a fast algorithm */
  3416. iu = 1;
  3417. if (*lwork >= wrkbl + (*lda << 1) * *m) {
  3418. /* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
  3419. ldwrku = *lda;
  3420. ir = iu + ldwrku * *m;
  3421. ldwrkr = *lda;
  3422. } else if (*lwork >= wrkbl + (*lda + *m) * *m) {
  3423. /* WORK(IU) is LDA by M and WORK(IR) is M by M */
  3424. ldwrku = *lda;
  3425. ir = iu + ldwrku * *m;
  3426. ldwrkr = *m;
  3427. } else {
  3428. /* WORK(IU) is M by M and WORK(IR) is M by M */
  3429. ldwrku = *m;
  3430. ir = iu + ldwrku * *m;
  3431. ldwrkr = *m;
  3432. }
  3433. itau = ir + ldwrkr * *m;
  3434. iwork = itau + *m;
  3435. /* Compute A=L*Q, copying result to VT */
  3436. /* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
  3437. /* (RWorkspace: 0) */
  3438. i__2 = *lwork - iwork + 1;
  3439. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3440. iwork], &i__2, &ierr);
  3441. zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3442. ldvt);
  3443. /* Generate Q in VT */
  3444. /* (CWorkspace: need 2*M*M+M+N, prefer 2*M*M+M+N*NB) */
  3445. /* (RWorkspace: 0) */
  3446. i__2 = *lwork - iwork + 1;
  3447. zunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3448. work[iwork], &i__2, &ierr);
  3449. /* Copy L to WORK(IU), zeroing out above it */
  3450. zlacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
  3451. ldwrku);
  3452. i__2 = *m - 1;
  3453. i__3 = *m - 1;
  3454. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
  3455. ldwrku], &ldwrku);
  3456. ie = 1;
  3457. itauq = itau;
  3458. itaup = itauq + *m;
  3459. iwork = itaup + *m;
  3460. /* Bidiagonalize L in WORK(IU), copying result to */
  3461. /* WORK(IR) */
  3462. /* (CWorkspace: need 2*M*M+3*M, */
  3463. /* prefer 2*M*M+2*M+2*M*NB) */
  3464. /* (RWorkspace: need M) */
  3465. i__2 = *lwork - iwork + 1;
  3466. zgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  3467. work[itauq], &work[itaup], &work[iwork], &
  3468. i__2, &ierr);
  3469. zlacpy_("L", m, m, &work[iu], &ldwrku, &work[ir], &
  3470. ldwrkr);
  3471. /* Generate right bidiagonalizing vectors in WORK(IU) */
  3472. /* (CWorkspace: need 2*M*M+3*M-1, */
  3473. /* prefer 2*M*M+2*M+(M-1)*NB) */
  3474. /* (RWorkspace: 0) */
  3475. i__2 = *lwork - iwork + 1;
  3476. zungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
  3477. , &work[iwork], &i__2, &ierr);
  3478. /* Generate left bidiagonalizing vectors in WORK(IR) */
  3479. /* (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) */
  3480. /* (RWorkspace: 0) */
  3481. i__2 = *lwork - iwork + 1;
  3482. zungbr_("Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
  3483. , &work[iwork], &i__2, &ierr);
  3484. irwork = ie + *m;
  3485. /* Perform bidiagonal QR iteration, computing left */
  3486. /* singular vectors of L in WORK(IR) and computing */
  3487. /* right singular vectors of L in WORK(IU) */
  3488. /* (CWorkspace: need 2*M*M) */
  3489. /* (RWorkspace: need BDSPAC) */
  3490. zbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
  3491. iu], &ldwrku, &work[ir], &ldwrkr, cdum, &c__1,
  3492. &rwork[irwork], info);
  3493. /* Multiply right singular vectors of L in WORK(IU) by */
  3494. /* Q in VT, storing result in A */
  3495. /* (CWorkspace: need M*M) */
  3496. /* (RWorkspace: 0) */
  3497. zgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
  3498. vt[vt_offset], ldvt, &c_b1, &a[a_offset], lda);
  3499. /* Copy right singular vectors of A from A to VT */
  3500. zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
  3501. ldvt);
  3502. /* Copy left singular vectors of A from WORK(IR) to A */
  3503. zlacpy_("F", m, m, &work[ir], &ldwrkr, &a[a_offset],
  3504. lda);
  3505. } else {
  3506. /* Insufficient workspace for a fast algorithm */
  3507. itau = 1;
  3508. iwork = itau + *m;
  3509. /* Compute A=L*Q, copying result to VT */
  3510. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3511. /* (RWorkspace: 0) */
  3512. i__2 = *lwork - iwork + 1;
  3513. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3514. iwork], &i__2, &ierr);
  3515. zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3516. ldvt);
  3517. /* Generate Q in VT */
  3518. /* (CWorkspace: need M+N, prefer M+N*NB) */
  3519. /* (RWorkspace: 0) */
  3520. i__2 = *lwork - iwork + 1;
  3521. zunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3522. work[iwork], &i__2, &ierr);
  3523. ie = 1;
  3524. itauq = itau;
  3525. itaup = itauq + *m;
  3526. iwork = itaup + *m;
  3527. /* Zero out above L in A */
  3528. i__2 = *m - 1;
  3529. i__3 = *m - 1;
  3530. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
  3531. 1) + 1], lda);
  3532. /* Bidiagonalize L in A */
  3533. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  3534. /* (RWorkspace: need M) */
  3535. i__2 = *lwork - iwork + 1;
  3536. zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
  3537. work[itauq], &work[itaup], &work[iwork], &
  3538. i__2, &ierr);
  3539. /* Multiply right bidiagonalizing vectors in A by Q */
  3540. /* in VT */
  3541. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  3542. /* (RWorkspace: 0) */
  3543. i__2 = *lwork - iwork + 1;
  3544. zunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
  3545. work[itaup], &vt[vt_offset], ldvt, &work[
  3546. iwork], &i__2, &ierr);
  3547. /* Generate left bidiagonalizing vectors in A */
  3548. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  3549. /* (RWorkspace: 0) */
  3550. i__2 = *lwork - iwork + 1;
  3551. zungbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq],
  3552. &work[iwork], &i__2, &ierr);
  3553. irwork = ie + *m;
  3554. /* Perform bidiagonal QR iteration, computing left */
  3555. /* singular vectors of A in A and computing right */
  3556. /* singular vectors of A in VT */
  3557. /* (CWorkspace: 0) */
  3558. /* (RWorkspace: need BDSPAC) */
  3559. zbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
  3560. vt_offset], ldvt, &a[a_offset], lda, cdum, &
  3561. c__1, &rwork[irwork], info);
  3562. }
  3563. } else if (wntuas) {
  3564. /* Path 9t(N much larger than M, JOBU='S' or 'A', */
  3565. /* JOBVT='A') */
  3566. /* N right singular vectors to be computed in VT and */
  3567. /* M left singular vectors to be computed in U */
  3568. /* Computing MAX */
  3569. i__2 = *n + *m, i__3 = *m * 3;
  3570. if (*lwork >= *m * *m + f2cmax(i__2,i__3)) {
  3571. /* Sufficient workspace for a fast algorithm */
  3572. iu = 1;
  3573. if (*lwork >= wrkbl + *lda * *m) {
  3574. /* WORK(IU) is LDA by M */
  3575. ldwrku = *lda;
  3576. } else {
  3577. /* WORK(IU) is M by M */
  3578. ldwrku = *m;
  3579. }
  3580. itau = iu + ldwrku * *m;
  3581. iwork = itau + *m;
  3582. /* Compute A=L*Q, copying result to VT */
  3583. /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
  3584. /* (RWorkspace: 0) */
  3585. i__2 = *lwork - iwork + 1;
  3586. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3587. iwork], &i__2, &ierr);
  3588. zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3589. ldvt);
  3590. /* Generate Q in VT */
  3591. /* (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB) */
  3592. /* (RWorkspace: 0) */
  3593. i__2 = *lwork - iwork + 1;
  3594. zunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3595. work[iwork], &i__2, &ierr);
  3596. /* Copy L to WORK(IU), zeroing out above it */
  3597. zlacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
  3598. ldwrku);
  3599. i__2 = *m - 1;
  3600. i__3 = *m - 1;
  3601. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
  3602. ldwrku], &ldwrku);
  3603. ie = 1;
  3604. itauq = itau;
  3605. itaup = itauq + *m;
  3606. iwork = itaup + *m;
  3607. /* Bidiagonalize L in WORK(IU), copying result to U */
  3608. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
  3609. /* (RWorkspace: need M) */
  3610. i__2 = *lwork - iwork + 1;
  3611. zgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
  3612. work[itauq], &work[itaup], &work[iwork], &
  3613. i__2, &ierr);
  3614. zlacpy_("L", m, m, &work[iu], &ldwrku, &u[u_offset],
  3615. ldu);
  3616. /* Generate right bidiagonalizing vectors in WORK(IU) */
  3617. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB) */
  3618. /* (RWorkspace: 0) */
  3619. i__2 = *lwork - iwork + 1;
  3620. zungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
  3621. , &work[iwork], &i__2, &ierr);
  3622. /* Generate left bidiagonalizing vectors in U */
  3623. /* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
  3624. /* (RWorkspace: 0) */
  3625. i__2 = *lwork - iwork + 1;
  3626. zungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
  3627. &work[iwork], &i__2, &ierr);
  3628. irwork = ie + *m;
  3629. /* Perform bidiagonal QR iteration, computing left */
  3630. /* singular vectors of L in U and computing right */
  3631. /* singular vectors of L in WORK(IU) */
  3632. /* (CWorkspace: need M*M) */
  3633. /* (RWorkspace: need BDSPAC) */
  3634. zbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
  3635. iu], &ldwrku, &u[u_offset], ldu, cdum, &c__1,
  3636. &rwork[irwork], info);
  3637. /* Multiply right singular vectors of L in WORK(IU) by */
  3638. /* Q in VT, storing result in A */
  3639. /* (CWorkspace: need M*M) */
  3640. /* (RWorkspace: 0) */
  3641. zgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
  3642. vt[vt_offset], ldvt, &c_b1, &a[a_offset], lda);
  3643. /* Copy right singular vectors of A from A to VT */
  3644. zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
  3645. ldvt);
  3646. } else {
  3647. /* Insufficient workspace for a fast algorithm */
  3648. itau = 1;
  3649. iwork = itau + *m;
  3650. /* Compute A=L*Q, copying result to VT */
  3651. /* (CWorkspace: need 2*M, prefer M+M*NB) */
  3652. /* (RWorkspace: 0) */
  3653. i__2 = *lwork - iwork + 1;
  3654. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
  3655. iwork], &i__2, &ierr);
  3656. zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
  3657. ldvt);
  3658. /* Generate Q in VT */
  3659. /* (CWorkspace: need M+N, prefer M+N*NB) */
  3660. /* (RWorkspace: 0) */
  3661. i__2 = *lwork - iwork + 1;
  3662. zunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
  3663. work[iwork], &i__2, &ierr);
  3664. /* Copy L to U, zeroing out above it */
  3665. zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset],
  3666. ldu);
  3667. i__2 = *m - 1;
  3668. i__3 = *m - 1;
  3669. zlaset_("U", &i__2, &i__3, &c_b1, &c_b1, &u[(u_dim1 <<
  3670. 1) + 1], ldu);
  3671. ie = 1;
  3672. itauq = itau;
  3673. itaup = itauq + *m;
  3674. iwork = itaup + *m;
  3675. /* Bidiagonalize L in U */
  3676. /* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
  3677. /* (RWorkspace: need M) */
  3678. i__2 = *lwork - iwork + 1;
  3679. zgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &
  3680. work[itauq], &work[itaup], &work[iwork], &
  3681. i__2, &ierr);
  3682. /* Multiply right bidiagonalizing vectors in U by Q */
  3683. /* in VT */
  3684. /* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
  3685. /* (RWorkspace: 0) */
  3686. i__2 = *lwork - iwork + 1;
  3687. zunmbr_("P", "L", "C", m, n, m, &u[u_offset], ldu, &
  3688. work[itaup], &vt[vt_offset], ldvt, &work[
  3689. iwork], &i__2, &ierr);
  3690. /* Generate left bidiagonalizing vectors in U */
  3691. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  3692. /* (RWorkspace: 0) */
  3693. i__2 = *lwork - iwork + 1;
  3694. zungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
  3695. &work[iwork], &i__2, &ierr);
  3696. irwork = ie + *m;
  3697. /* Perform bidiagonal QR iteration, computing left */
  3698. /* singular vectors of A in U and computing right */
  3699. /* singular vectors of A in VT */
  3700. /* (CWorkspace: 0) */
  3701. /* (RWorkspace: need BDSPAC) */
  3702. zbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
  3703. vt_offset], ldvt, &u[u_offset], ldu, cdum, &
  3704. c__1, &rwork[irwork], info);
  3705. }
  3706. }
  3707. }
  3708. } else {
  3709. /* N .LT. MNTHR */
  3710. /* Path 10t(N greater than M, but not much larger) */
  3711. /* Reduce to bidiagonal form without LQ decomposition */
  3712. ie = 1;
  3713. itauq = 1;
  3714. itaup = itauq + *m;
  3715. iwork = itaup + *m;
  3716. /* Bidiagonalize A */
  3717. /* (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) */
  3718. /* (RWorkspace: M) */
  3719. i__2 = *lwork - iwork + 1;
  3720. zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  3721. &work[itaup], &work[iwork], &i__2, &ierr);
  3722. if (wntuas) {
  3723. /* If left singular vectors desired in U, copy result to U */
  3724. /* and generate left bidiagonalizing vectors in U */
  3725. /* (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB) */
  3726. /* (RWorkspace: 0) */
  3727. zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  3728. i__2 = *lwork - iwork + 1;
  3729. zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  3730. iwork], &i__2, &ierr);
  3731. }
  3732. if (wntvas) {
  3733. /* If right singular vectors desired in VT, copy result to */
  3734. /* VT and generate right bidiagonalizing vectors in VT */
  3735. /* (CWorkspace: need 2*M+NRVT, prefer 2*M+NRVT*NB) */
  3736. /* (RWorkspace: 0) */
  3737. zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  3738. if (wntva) {
  3739. nrvt = *n;
  3740. }
  3741. if (wntvs) {
  3742. nrvt = *m;
  3743. }
  3744. i__2 = *lwork - iwork + 1;
  3745. zungbr_("P", &nrvt, n, m, &vt[vt_offset], ldvt, &work[itaup],
  3746. &work[iwork], &i__2, &ierr);
  3747. }
  3748. if (wntuo) {
  3749. /* If left singular vectors desired in A, generate left */
  3750. /* bidiagonalizing vectors in A */
  3751. /* (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB) */
  3752. /* (RWorkspace: 0) */
  3753. i__2 = *lwork - iwork + 1;
  3754. zungbr_("Q", m, m, n, &a[a_offset], lda, &work[itauq], &work[
  3755. iwork], &i__2, &ierr);
  3756. }
  3757. if (wntvo) {
  3758. /* If right singular vectors desired in A, generate right */
  3759. /* bidiagonalizing vectors in A */
  3760. /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
  3761. /* (RWorkspace: 0) */
  3762. i__2 = *lwork - iwork + 1;
  3763. zungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
  3764. iwork], &i__2, &ierr);
  3765. }
  3766. irwork = ie + *m;
  3767. if (wntuas || wntuo) {
  3768. nru = *m;
  3769. }
  3770. if (wntun) {
  3771. nru = 0;
  3772. }
  3773. if (wntvas || wntvo) {
  3774. ncvt = *n;
  3775. }
  3776. if (wntvn) {
  3777. ncvt = 0;
  3778. }
  3779. if (! wntuo && ! wntvo) {
  3780. /* Perform bidiagonal QR iteration, if desired, computing */
  3781. /* left singular vectors in U and computing right singular */
  3782. /* vectors in VT */
  3783. /* (CWorkspace: 0) */
  3784. /* (RWorkspace: need BDSPAC) */
  3785. zbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
  3786. vt_offset], ldvt, &u[u_offset], ldu, cdum, &c__1, &
  3787. rwork[irwork], info);
  3788. } else if (! wntuo && wntvo) {
  3789. /* Perform bidiagonal QR iteration, if desired, computing */
  3790. /* left singular vectors in U and computing right singular */
  3791. /* vectors in A */
  3792. /* (CWorkspace: 0) */
  3793. /* (RWorkspace: need BDSPAC) */
  3794. zbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &a[
  3795. a_offset], lda, &u[u_offset], ldu, cdum, &c__1, &
  3796. rwork[irwork], info);
  3797. } else {
  3798. /* Perform bidiagonal QR iteration, if desired, computing */
  3799. /* left singular vectors in A and computing right singular */
  3800. /* vectors in VT */
  3801. /* (CWorkspace: 0) */
  3802. /* (RWorkspace: need BDSPAC) */
  3803. zbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
  3804. vt_offset], ldvt, &a[a_offset], lda, cdum, &c__1, &
  3805. rwork[irwork], info);
  3806. }
  3807. }
  3808. }
  3809. /* Undo scaling if necessary */
  3810. if (iscl == 1) {
  3811. if (anrm > bignum) {
  3812. dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
  3813. minmn, &ierr);
  3814. }
  3815. if (*info != 0 && anrm > bignum) {
  3816. i__2 = minmn - 1;
  3817. dlascl_("G", &c__0, &c__0, &bignum, &anrm, &i__2, &c__1, &rwork[
  3818. ie], &minmn, &ierr);
  3819. }
  3820. if (anrm < smlnum) {
  3821. dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
  3822. minmn, &ierr);
  3823. }
  3824. if (*info != 0 && anrm < smlnum) {
  3825. i__2 = minmn - 1;
  3826. dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &i__2, &c__1, &rwork[
  3827. ie], &minmn, &ierr);
  3828. }
  3829. }
  3830. /* Return optimal workspace in WORK(1) */
  3831. work[1].r = (doublereal) maxwrk, work[1].i = 0.;
  3832. return;
  3833. /* End of ZGESVD */
  3834. } /* zgesvd_ */