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cgesdd.c 103 kB

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  1. #include <math.h>
  2. #include <stdlib.h>
  3. #include <string.h>
  4. #include <stdio.h>
  5. #include <complex.h>
  6. #ifdef complex
  7. #undef complex
  8. #endif
  9. #ifdef I
  10. #undef I
  11. #endif
  12. #if defined(_WIN64)
  13. typedef long long BLASLONG;
  14. typedef unsigned long long BLASULONG;
  15. #else
  16. typedef long BLASLONG;
  17. typedef unsigned long BLASULONG;
  18. #endif
  19. #ifdef LAPACK_ILP64
  20. typedef BLASLONG blasint;
  21. #if defined(_WIN64)
  22. #define blasabs(x) llabs(x)
  23. #else
  24. #define blasabs(x) labs(x)
  25. #endif
  26. #else
  27. typedef int blasint;
  28. #define blasabs(x) abs(x)
  29. #endif
  30. typedef blasint integer;
  31. typedef unsigned int uinteger;
  32. typedef char *address;
  33. typedef short int shortint;
  34. typedef float real;
  35. typedef double doublereal;
  36. typedef struct { real r, i; } complex;
  37. typedef struct { doublereal r, i; } doublecomplex;
  38. #ifdef _MSC_VER
  39. static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
  40. static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
  41. static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
  42. static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
  43. #else
  44. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  45. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  46. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  47. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  48. #endif
  49. #define pCf(z) (*_pCf(z))
  50. #define pCd(z) (*_pCd(z))
  51. typedef int logical;
  52. typedef short int shortlogical;
  53. typedef char logical1;
  54. typedef char integer1;
  55. #define TRUE_ (1)
  56. #define FALSE_ (0)
  57. /* Extern is for use with -E */
  58. #ifndef Extern
  59. #define Extern extern
  60. #endif
  61. /* I/O stuff */
  62. typedef int flag;
  63. typedef int ftnlen;
  64. typedef int ftnint;
  65. /*external read, write*/
  66. typedef struct
  67. { flag cierr;
  68. ftnint ciunit;
  69. flag ciend;
  70. char *cifmt;
  71. ftnint cirec;
  72. } cilist;
  73. /*internal read, write*/
  74. typedef struct
  75. { flag icierr;
  76. char *iciunit;
  77. flag iciend;
  78. char *icifmt;
  79. ftnint icirlen;
  80. ftnint icirnum;
  81. } icilist;
  82. /*open*/
  83. typedef struct
  84. { flag oerr;
  85. ftnint ounit;
  86. char *ofnm;
  87. ftnlen ofnmlen;
  88. char *osta;
  89. char *oacc;
  90. char *ofm;
  91. ftnint orl;
  92. char *oblnk;
  93. } olist;
  94. /*close*/
  95. typedef struct
  96. { flag cerr;
  97. ftnint cunit;
  98. char *csta;
  99. } cllist;
  100. /*rewind, backspace, endfile*/
  101. typedef struct
  102. { flag aerr;
  103. ftnint aunit;
  104. } alist;
  105. /* inquire */
  106. typedef struct
  107. { flag inerr;
  108. ftnint inunit;
  109. char *infile;
  110. ftnlen infilen;
  111. ftnint *inex; /*parameters in standard's order*/
  112. ftnint *inopen;
  113. ftnint *innum;
  114. ftnint *innamed;
  115. char *inname;
  116. ftnlen innamlen;
  117. char *inacc;
  118. ftnlen inacclen;
  119. char *inseq;
  120. ftnlen inseqlen;
  121. char *indir;
  122. ftnlen indirlen;
  123. char *infmt;
  124. ftnlen infmtlen;
  125. char *inform;
  126. ftnint informlen;
  127. char *inunf;
  128. ftnlen inunflen;
  129. ftnint *inrecl;
  130. ftnint *innrec;
  131. char *inblank;
  132. ftnlen inblanklen;
  133. } inlist;
  134. #define VOID void
  135. union Multitype { /* for multiple entry points */
  136. integer1 g;
  137. shortint h;
  138. integer i;
  139. /* longint j; */
  140. real r;
  141. doublereal d;
  142. complex c;
  143. doublecomplex z;
  144. };
  145. typedef union Multitype Multitype;
  146. struct Vardesc { /* for Namelist */
  147. char *name;
  148. char *addr;
  149. ftnlen *dims;
  150. int type;
  151. };
  152. typedef struct Vardesc Vardesc;
  153. struct Namelist {
  154. char *name;
  155. Vardesc **vars;
  156. int nvars;
  157. };
  158. typedef struct Namelist Namelist;
  159. #define abs(x) ((x) >= 0 ? (x) : -(x))
  160. #define dabs(x) (fabs(x))
  161. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  162. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  163. #define dmin(a,b) (f2cmin(a,b))
  164. #define dmax(a,b) (f2cmax(a,b))
  165. #define bit_test(a,b) ((a) >> (b) & 1)
  166. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  167. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  168. #define abort_() { sig_die("Fortran abort routine called", 1); }
  169. #define c_abs(z) (cabsf(Cf(z)))
  170. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  171. #ifdef _MSC_VER
  172. #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
  173. #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
  174. #else
  175. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  176. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  177. #endif
  178. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  179. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  180. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  181. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  182. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  183. #define d_abs(x) (fabs(*(x)))
  184. #define d_acos(x) (acos(*(x)))
  185. #define d_asin(x) (asin(*(x)))
  186. #define d_atan(x) (atan(*(x)))
  187. #define d_atn2(x, y) (atan2(*(x),*(y)))
  188. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  189. #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
  190. #define d_cos(x) (cos(*(x)))
  191. #define d_cosh(x) (cosh(*(x)))
  192. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  193. #define d_exp(x) (exp(*(x)))
  194. #define d_imag(z) (cimag(Cd(z)))
  195. #define r_imag(z) (cimagf(Cf(z)))
  196. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  197. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  198. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  199. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  200. #define d_log(x) (log(*(x)))
  201. #define d_mod(x, y) (fmod(*(x), *(y)))
  202. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  203. #define d_nint(x) u_nint(*(x))
  204. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  205. #define d_sign(a,b) u_sign(*(a),*(b))
  206. #define r_sign(a,b) u_sign(*(a),*(b))
  207. #define d_sin(x) (sin(*(x)))
  208. #define d_sinh(x) (sinh(*(x)))
  209. #define d_sqrt(x) (sqrt(*(x)))
  210. #define d_tan(x) (tan(*(x)))
  211. #define d_tanh(x) (tanh(*(x)))
  212. #define i_abs(x) abs(*(x))
  213. #define i_dnnt(x) ((integer)u_nint(*(x)))
  214. #define i_len(s, n) (n)
  215. #define i_nint(x) ((integer)u_nint(*(x)))
  216. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  217. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  218. #define pow_si(B,E) spow_ui(*(B),*(E))
  219. #define pow_ri(B,E) spow_ui(*(B),*(E))
  220. #define pow_di(B,E) dpow_ui(*(B),*(E))
  221. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  222. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  223. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  224. #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
  225. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  226. #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
  227. #define sig_die(s, kill) { exit(1); }
  228. #define s_stop(s, n) {exit(0);}
  229. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  230. #define z_abs(z) (cabs(Cd(z)))
  231. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  232. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  233. #define myexit_() break;
  234. #define mycycle() continue;
  235. #define myceiling(w) {ceil(w)}
  236. #define myhuge(w) {HUGE_VAL}
  237. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  238. #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  239. /* procedure parameter types for -A and -C++ */
  240. #define F2C_proc_par_types 1
  241. #ifdef __cplusplus
  242. typedef logical (*L_fp)(...);
  243. #else
  244. typedef logical (*L_fp)();
  245. #endif
  246. static float spow_ui(float x, integer n) {
  247. float pow=1.0; unsigned long int u;
  248. if(n != 0) {
  249. if(n < 0) n = -n, x = 1/x;
  250. for(u = n; ; ) {
  251. if(u & 01) pow *= x;
  252. if(u >>= 1) x *= x;
  253. else break;
  254. }
  255. }
  256. return pow;
  257. }
  258. static double dpow_ui(double x, integer n) {
  259. double pow=1.0; unsigned long int u;
  260. if(n != 0) {
  261. if(n < 0) n = -n, x = 1/x;
  262. for(u = n; ; ) {
  263. if(u & 01) pow *= x;
  264. if(u >>= 1) x *= x;
  265. else break;
  266. }
  267. }
  268. return pow;
  269. }
  270. #ifdef _MSC_VER
  271. static _Fcomplex cpow_ui(complex x, integer n) {
  272. complex pow={1.0,0.0}; unsigned long int u;
  273. if(n != 0) {
  274. if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
  275. for(u = n; ; ) {
  276. if(u & 01) pow.r *= x.r, pow.i *= x.i;
  277. if(u >>= 1) x.r *= x.r, x.i *= x.i;
  278. else break;
  279. }
  280. }
  281. _Fcomplex p={pow.r, pow.i};
  282. return p;
  283. }
  284. #else
  285. static _Complex float cpow_ui(_Complex float x, integer n) {
  286. _Complex float pow=1.0; unsigned long int u;
  287. if(n != 0) {
  288. if(n < 0) n = -n, x = 1/x;
  289. for(u = n; ; ) {
  290. if(u & 01) pow *= x;
  291. if(u >>= 1) x *= x;
  292. else break;
  293. }
  294. }
  295. return pow;
  296. }
  297. #endif
  298. #ifdef _MSC_VER
  299. static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
  300. _Dcomplex pow={1.0,0.0}; unsigned long int u;
  301. if(n != 0) {
  302. if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
  303. for(u = n; ; ) {
  304. if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
  305. if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
  306. else break;
  307. }
  308. }
  309. _Dcomplex p = {pow._Val[0], pow._Val[1]};
  310. return p;
  311. }
  312. #else
  313. static _Complex double zpow_ui(_Complex double x, integer n) {
  314. _Complex double pow=1.0; unsigned long int u;
  315. if(n != 0) {
  316. if(n < 0) n = -n, x = 1/x;
  317. for(u = n; ; ) {
  318. if(u & 01) pow *= x;
  319. if(u >>= 1) x *= x;
  320. else break;
  321. }
  322. }
  323. return pow;
  324. }
  325. #endif
  326. static integer pow_ii(integer x, integer n) {
  327. integer pow; unsigned long int u;
  328. if (n <= 0) {
  329. if (n == 0 || x == 1) pow = 1;
  330. else if (x != -1) pow = x == 0 ? 1/x : 0;
  331. else n = -n;
  332. }
  333. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  334. u = n;
  335. for(pow = 1; ; ) {
  336. if(u & 01) pow *= x;
  337. if(u >>= 1) x *= x;
  338. else break;
  339. }
  340. }
  341. return pow;
  342. }
  343. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  344. {
  345. double m; integer i, mi;
  346. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  347. if (w[i-1]>m) mi=i ,m=w[i-1];
  348. return mi-s+1;
  349. }
  350. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  351. {
  352. float m; integer i, mi;
  353. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  354. if (w[i-1]>m) mi=i ,m=w[i-1];
  355. return mi-s+1;
  356. }
  357. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  358. integer n = *n_, incx = *incx_, incy = *incy_, i;
  359. #ifdef _MSC_VER
  360. _Fcomplex zdotc = {0.0, 0.0};
  361. if (incx == 1 && incy == 1) {
  362. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  363. zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
  364. zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
  365. }
  366. } else {
  367. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  368. zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
  369. zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
  370. }
  371. }
  372. pCf(z) = zdotc;
  373. }
  374. #else
  375. _Complex float zdotc = 0.0;
  376. if (incx == 1 && incy == 1) {
  377. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  378. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  379. }
  380. } else {
  381. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  382. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  383. }
  384. }
  385. pCf(z) = zdotc;
  386. }
  387. #endif
  388. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  389. integer n = *n_, incx = *incx_, incy = *incy_, i;
  390. #ifdef _MSC_VER
  391. _Dcomplex zdotc = {0.0, 0.0};
  392. if (incx == 1 && incy == 1) {
  393. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  394. zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
  395. zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
  396. }
  397. } else {
  398. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  399. zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
  400. zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
  401. }
  402. }
  403. pCd(z) = zdotc;
  404. }
  405. #else
  406. _Complex double zdotc = 0.0;
  407. if (incx == 1 && incy == 1) {
  408. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  409. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  410. }
  411. } else {
  412. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  413. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  414. }
  415. }
  416. pCd(z) = zdotc;
  417. }
  418. #endif
  419. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  420. integer n = *n_, incx = *incx_, incy = *incy_, i;
  421. #ifdef _MSC_VER
  422. _Fcomplex zdotc = {0.0, 0.0};
  423. if (incx == 1 && incy == 1) {
  424. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  425. zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
  426. zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
  427. }
  428. } else {
  429. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  430. zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
  431. zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
  432. }
  433. }
  434. pCf(z) = zdotc;
  435. }
  436. #else
  437. _Complex float zdotc = 0.0;
  438. if (incx == 1 && incy == 1) {
  439. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  440. zdotc += Cf(&x[i]) * Cf(&y[i]);
  441. }
  442. } else {
  443. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  444. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  445. }
  446. }
  447. pCf(z) = zdotc;
  448. }
  449. #endif
  450. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  451. integer n = *n_, incx = *incx_, incy = *incy_, i;
  452. #ifdef _MSC_VER
  453. _Dcomplex zdotc = {0.0, 0.0};
  454. if (incx == 1 && incy == 1) {
  455. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  456. zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
  457. zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
  458. }
  459. } else {
  460. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  461. zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
  462. zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
  463. }
  464. }
  465. pCd(z) = zdotc;
  466. }
  467. #else
  468. _Complex double zdotc = 0.0;
  469. if (incx == 1 && incy == 1) {
  470. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  471. zdotc += Cd(&x[i]) * Cd(&y[i]);
  472. }
  473. } else {
  474. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  475. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  476. }
  477. }
  478. pCd(z) = zdotc;
  479. }
  480. #endif
  481. /* -- translated by f2c (version 20000121).
  482. You must link the resulting object file with the libraries:
  483. -lf2c -lm (in that order)
  484. */
  485. /* Table of constant values */
  486. static complex c_b1 = {0.f,0.f};
  487. static complex c_b2 = {1.f,0.f};
  488. static integer c_n1 = -1;
  489. static integer c__0 = 0;
  490. static integer c__1 = 1;
  491. /* > \brief \b CGESDD */
  492. /* =========== DOCUMENTATION =========== */
  493. /* Online html documentation available at */
  494. /* http://www.netlib.org/lapack/explore-html/ */
  495. /* > \htmlonly */
  496. /* > Download CGESDD + dependencies */
  497. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgesdd.
  498. f"> */
  499. /* > [TGZ]</a> */
  500. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgesdd.
  501. f"> */
  502. /* > [ZIP]</a> */
  503. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgesdd.
  504. f"> */
  505. /* > [TXT]</a> */
  506. /* > \endhtmlonly */
  507. /* Definition: */
  508. /* =========== */
  509. /* SUBROUTINE CGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, */
  510. /* WORK, LWORK, RWORK, IWORK, INFO ) */
  511. /* CHARACTER JOBZ */
  512. /* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */
  513. /* INTEGER IWORK( * ) */
  514. /* REAL RWORK( * ), S( * ) */
  515. /* COMPLEX A( LDA, * ), U( LDU, * ), VT( LDVT, * ), */
  516. /* $ WORK( * ) */
  517. /* > \par Purpose: */
  518. /* ============= */
  519. /* > */
  520. /* > \verbatim */
  521. /* > */
  522. /* > CGESDD computes the singular value decomposition (SVD) of a complex */
  523. /* > M-by-N matrix A, optionally computing the left and/or right singular */
  524. /* > vectors, by using divide-and-conquer method. The SVD is written */
  525. /* > */
  526. /* > A = U * SIGMA * conjugate-transpose(V) */
  527. /* > */
  528. /* > where SIGMA is an M-by-N matrix which is zero except for its */
  529. /* > f2cmin(m,n) diagonal elements, U is an M-by-M unitary matrix, and */
  530. /* > V is an N-by-N unitary matrix. The diagonal elements of SIGMA */
  531. /* > are the singular values of A; they are real and non-negative, and */
  532. /* > are returned in descending order. The first f2cmin(m,n) columns of */
  533. /* > U and V are the left and right singular vectors of A. */
  534. /* > */
  535. /* > Note that the routine returns VT = V**H, not V. */
  536. /* > */
  537. /* > The divide and conquer algorithm makes very mild assumptions about */
  538. /* > floating point arithmetic. It will work on machines with a guard */
  539. /* > digit in add/subtract, or on those binary machines without guard */
  540. /* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
  541. /* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */
  542. /* > without guard digits, but we know of none. */
  543. /* > \endverbatim */
  544. /* Arguments: */
  545. /* ========== */
  546. /* > \param[in] JOBZ */
  547. /* > \verbatim */
  548. /* > JOBZ is CHARACTER*1 */
  549. /* > Specifies options for computing all or part of the matrix U: */
  550. /* > = 'A': all M columns of U and all N rows of V**H are */
  551. /* > returned in the arrays U and VT; */
  552. /* > = 'S': the first f2cmin(M,N) columns of U and the first */
  553. /* > f2cmin(M,N) rows of V**H are returned in the arrays U */
  554. /* > and VT; */
  555. /* > = 'O': If M >= N, the first N columns of U are overwritten */
  556. /* > in the array A and all rows of V**H are returned in */
  557. /* > the array VT; */
  558. /* > otherwise, all columns of U are returned in the */
  559. /* > array U and the first M rows of V**H are overwritten */
  560. /* > in the array A; */
  561. /* > = 'N': no columns of U or rows of V**H are computed. */
  562. /* > \endverbatim */
  563. /* > */
  564. /* > \param[in] M */
  565. /* > \verbatim */
  566. /* > M is INTEGER */
  567. /* > The number of rows of the input matrix A. M >= 0. */
  568. /* > \endverbatim */
  569. /* > */
  570. /* > \param[in] N */
  571. /* > \verbatim */
  572. /* > N is INTEGER */
  573. /* > The number of columns of the input matrix A. N >= 0. */
  574. /* > \endverbatim */
  575. /* > */
  576. /* > \param[in,out] A */
  577. /* > \verbatim */
  578. /* > A is COMPLEX array, dimension (LDA,N) */
  579. /* > On entry, the M-by-N matrix A. */
  580. /* > On exit, */
  581. /* > if JOBZ = 'O', A is overwritten with the first N columns */
  582. /* > of U (the left singular vectors, stored */
  583. /* > columnwise) if M >= N; */
  584. /* > A is overwritten with the first M rows */
  585. /* > of V**H (the right singular vectors, stored */
  586. /* > rowwise) otherwise. */
  587. /* > if JOBZ .ne. 'O', the contents of A are destroyed. */
  588. /* > \endverbatim */
  589. /* > */
  590. /* > \param[in] LDA */
  591. /* > \verbatim */
  592. /* > LDA is INTEGER */
  593. /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
  594. /* > \endverbatim */
  595. /* > */
  596. /* > \param[out] S */
  597. /* > \verbatim */
  598. /* > S is REAL array, dimension (f2cmin(M,N)) */
  599. /* > The singular values of A, sorted so that S(i) >= S(i+1). */
  600. /* > \endverbatim */
  601. /* > */
  602. /* > \param[out] U */
  603. /* > \verbatim */
  604. /* > U is COMPLEX array, dimension (LDU,UCOL) */
  605. /* > UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; */
  606. /* > UCOL = f2cmin(M,N) if JOBZ = 'S'. */
  607. /* > If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M */
  608. /* > unitary matrix U; */
  609. /* > if JOBZ = 'S', U contains the first f2cmin(M,N) columns of U */
  610. /* > (the left singular vectors, stored columnwise); */
  611. /* > if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. */
  612. /* > \endverbatim */
  613. /* > */
  614. /* > \param[in] LDU */
  615. /* > \verbatim */
  616. /* > LDU is INTEGER */
  617. /* > The leading dimension of the array U. LDU >= 1; */
  618. /* > if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. */
  619. /* > \endverbatim */
  620. /* > */
  621. /* > \param[out] VT */
  622. /* > \verbatim */
  623. /* > VT is COMPLEX array, dimension (LDVT,N) */
  624. /* > If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the */
  625. /* > N-by-N unitary matrix V**H; */
  626. /* > if JOBZ = 'S', VT contains the first f2cmin(M,N) rows of */
  627. /* > V**H (the right singular vectors, stored rowwise); */
  628. /* > if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. */
  629. /* > \endverbatim */
  630. /* > */
  631. /* > \param[in] LDVT */
  632. /* > \verbatim */
  633. /* > LDVT is INTEGER */
  634. /* > The leading dimension of the array VT. LDVT >= 1; */
  635. /* > if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; */
  636. /* > if JOBZ = 'S', LDVT >= f2cmin(M,N). */
  637. /* > \endverbatim */
  638. /* > */
  639. /* > \param[out] WORK */
  640. /* > \verbatim */
  641. /* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
  642. /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
  643. /* > \endverbatim */
  644. /* > */
  645. /* > \param[in] LWORK */
  646. /* > \verbatim */
  647. /* > LWORK is INTEGER */
  648. /* > The dimension of the array WORK. LWORK >= 1. */
  649. /* > If LWORK = -1, a workspace query is assumed. The optimal */
  650. /* > size for the WORK array is calculated and stored in WORK(1), */
  651. /* > and no other work except argument checking is performed. */
  652. /* > */
  653. /* > Let mx = f2cmax(M,N) and mn = f2cmin(M,N). */
  654. /* > If JOBZ = 'N', LWORK >= 2*mn + mx. */
  655. /* > If JOBZ = 'O', LWORK >= 2*mn*mn + 2*mn + mx. */
  656. /* > If JOBZ = 'S', LWORK >= mn*mn + 3*mn. */
  657. /* > If JOBZ = 'A', LWORK >= mn*mn + 2*mn + mx. */
  658. /* > These are not tight minimums in all cases; see comments inside code. */
  659. /* > For good performance, LWORK should generally be larger; */
  660. /* > a query is recommended. */
  661. /* > \endverbatim */
  662. /* > */
  663. /* > \param[out] RWORK */
  664. /* > \verbatim */
  665. /* > RWORK is REAL array, dimension (MAX(1,LRWORK)) */
  666. /* > Let mx = f2cmax(M,N) and mn = f2cmin(M,N). */
  667. /* > If JOBZ = 'N', LRWORK >= 5*mn (LAPACK <= 3.6 needs 7*mn); */
  668. /* > else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn; */
  669. /* > else LRWORK >= f2cmax( 5*mn*mn + 5*mn, */
  670. /* > 2*mx*mn + 2*mn*mn + mn ). */
  671. /* > \endverbatim */
  672. /* > */
  673. /* > \param[out] IWORK */
  674. /* > \verbatim */
  675. /* > IWORK is INTEGER array, dimension (8*f2cmin(M,N)) */
  676. /* > \endverbatim */
  677. /* > */
  678. /* > \param[out] INFO */
  679. /* > \verbatim */
  680. /* > INFO is INTEGER */
  681. /* > = 0: successful exit. */
  682. /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
  683. /* > > 0: The updating process of SBDSDC did not converge. */
  684. /* > \endverbatim */
  685. /* Authors: */
  686. /* ======== */
  687. /* > \author Univ. of Tennessee */
  688. /* > \author Univ. of California Berkeley */
  689. /* > \author Univ. of Colorado Denver */
  690. /* > \author NAG Ltd. */
  691. /* > \date June 2016 */
  692. /* > \ingroup complexGEsing */
  693. /* > \par Contributors: */
  694. /* ================== */
  695. /* > */
  696. /* > Ming Gu and Huan Ren, Computer Science Division, University of */
  697. /* > California at Berkeley, USA */
  698. /* > */
  699. /* ===================================================================== */
  700. /* Subroutine */ void cgesdd_(char *jobz, integer *m, integer *n, complex *a,
  701. integer *lda, real *s, complex *u, integer *ldu, complex *vt, integer
  702. *ldvt, complex *work, integer *lwork, real *rwork, integer *iwork,
  703. integer *info)
  704. {
  705. /* System generated locals */
  706. integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
  707. i__2, i__3;
  708. /* Local variables */
  709. integer lwork_cunglq_mn__, lwork_cunglq_nn__, lwork_cungqr_mm__,
  710. lwork_cungqr_mn__;
  711. complex cdum[1];
  712. integer iscl, lwork_cunmbr_prc_mm__, lwork_cunmbr_prc_mn__,
  713. lwork_cunmbr_prc_nn__;
  714. real anrm;
  715. integer ierr, itau, lwork_cunmbr_qln_mm__, lwork_cunmbr_qln_mn__,
  716. lwork_cunmbr_qln_nn__, idum[1], irvt, i__;
  717. extern /* Subroutine */ void cgemm_(char *, char *, integer *, integer *,
  718. integer *, complex *, complex *, integer *, complex *, integer *,
  719. complex *, complex *, integer *);
  720. extern logical lsame_(char *, char *);
  721. integer chunk, minmn, wrkbl, itaup, itauq;
  722. logical wntqa;
  723. integer nwork;
  724. extern /* Subroutine */ void clacp2_(char *, integer *, integer *, real *,
  725. integer *, complex *, integer *);
  726. logical wntqn, wntqo, wntqs;
  727. integer mnthr1, mnthr2, ie, lwork_cungbr_p_mn__, il, lwork_cungbr_p_nn__,
  728. lwork_cungbr_q_mn__, lwork_cungbr_q_mm__;
  729. extern /* Subroutine */ void cgebrd_(integer *, integer *, complex *,
  730. integer *, real *, real *, complex *, complex *, complex *,
  731. integer *, integer *);
  732. integer ir;
  733. extern real clange_(char *, integer *, integer *, complex *, integer *,
  734. real *);
  735. integer iu;
  736. extern /* Subroutine */ void cgelqf_(integer *, integer *, complex *,
  737. integer *, complex *, complex *, integer *, integer *), clacrm_(
  738. integer *, integer *, complex *, integer *, real *, integer *,
  739. complex *, integer *, real *), clarcm_(integer *, integer *, real
  740. *, integer *, complex *, integer *, complex *, integer *, real *),
  741. clascl_(char *, integer *, integer *, real *, real *, integer *,
  742. integer *, complex *, integer *, integer *), sbdsdc_(char
  743. *, char *, integer *, real *, real *, real *, integer *, real *,
  744. integer *, real *, integer *, real *, integer *, integer *), cgeqrf_(integer *, integer *, complex *, integer
  745. *, complex *, complex *, integer *, integer *);
  746. extern real slamch_(char *);
  747. extern /* Subroutine */ void clacpy_(char *, integer *, integer *, complex
  748. *, integer *, complex *, integer *), claset_(char *,
  749. integer *, integer *, complex *, complex *, complex *, integer *);
  750. extern int xerbla_(char *, integer *, ftnlen);
  751. extern void cungbr_(char *,
  752. integer *, integer *, integer *, complex *, integer *, complex *,
  753. complex *, integer *, integer *);
  754. real bignum;
  755. extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *,
  756. real *, integer *, integer *, real *, integer *, integer *), cunmbr_(char *, char *, char *, integer *, integer *,
  757. integer *, complex *, integer *, complex *, complex *, integer *,
  758. complex *, integer *, integer *), cunglq_(
  759. integer *, integer *, integer *, complex *, integer *, complex *,
  760. complex *, integer *, integer *);
  761. extern logical sisnan_(real *);
  762. integer ldwrkl;
  763. extern /* Subroutine */ void cungqr_(integer *, integer *, integer *,
  764. complex *, integer *, complex *, complex *, integer *, integer *);
  765. integer ldwrkr, minwrk, ldwrku, maxwrk, ldwkvt;
  766. real smlnum;
  767. logical wntqas, lquery;
  768. integer nrwork, blk;
  769. real dum[1], eps;
  770. integer iru, ivt, lwork_cgebrd_mm__, lwork_cgebrd_mn__, lwork_cgebrd_nn__,
  771. lwork_cgelqf_mn__, lwork_cgeqrf_mn__;
  772. /* -- LAPACK driver routine (version 3.7.0) -- */
  773. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  774. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  775. /* June 2016 */
  776. /* ===================================================================== */
  777. /* Test the input arguments */
  778. /* Parameter adjustments */
  779. a_dim1 = *lda;
  780. a_offset = 1 + a_dim1 * 1;
  781. a -= a_offset;
  782. --s;
  783. u_dim1 = *ldu;
  784. u_offset = 1 + u_dim1 * 1;
  785. u -= u_offset;
  786. vt_dim1 = *ldvt;
  787. vt_offset = 1 + vt_dim1 * 1;
  788. vt -= vt_offset;
  789. --work;
  790. --rwork;
  791. --iwork;
  792. /* Function Body */
  793. *info = 0;
  794. minmn = f2cmin(*m,*n);
  795. mnthr1 = (integer) (minmn * 17.f / 9.f);
  796. mnthr2 = (integer) (minmn * 5.f / 3.f);
  797. wntqa = lsame_(jobz, "A");
  798. wntqs = lsame_(jobz, "S");
  799. wntqas = wntqa || wntqs;
  800. wntqo = lsame_(jobz, "O");
  801. wntqn = lsame_(jobz, "N");
  802. lquery = *lwork == -1;
  803. minwrk = 1;
  804. maxwrk = 1;
  805. if (! (wntqa || wntqs || wntqo || wntqn)) {
  806. *info = -1;
  807. } else if (*m < 0) {
  808. *info = -2;
  809. } else if (*n < 0) {
  810. *info = -3;
  811. } else if (*lda < f2cmax(1,*m)) {
  812. *info = -5;
  813. } else if (*ldu < 1 || wntqas && *ldu < *m || wntqo && *m < *n && *ldu < *
  814. m) {
  815. *info = -8;
  816. } else if (*ldvt < 1 || wntqa && *ldvt < *n || wntqs && *ldvt < minmn ||
  817. wntqo && *m >= *n && *ldvt < *n) {
  818. *info = -10;
  819. }
  820. /* Compute workspace */
  821. /* Note: Comments in the code beginning "Workspace:" describe the */
  822. /* minimal amount of workspace allocated at that point in the code, */
  823. /* as well as the preferred amount for good performance. */
  824. /* CWorkspace refers to complex workspace, and RWorkspace to */
  825. /* real workspace. NB refers to the optimal block size for the */
  826. /* immediately following subroutine, as returned by ILAENV.) */
  827. if (*info == 0) {
  828. minwrk = 1;
  829. maxwrk = 1;
  830. if (*m >= *n && minmn > 0) {
  831. /* There is no complex work space needed for bidiagonal SVD */
  832. /* The real work space needed for bidiagonal SVD (sbdsdc) is */
  833. /* BDSPAC = 3*N*N + 4*N for singular values and vectors; */
  834. /* BDSPAC = 4*N for singular values only; */
  835. /* not including e, RU, and RVT matrices. */
  836. /* Compute space preferred for each routine */
  837. cgebrd_(m, n, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
  838. lwork_cgebrd_mn__ = (integer) cdum[0].r;
  839. cgebrd_(n, n, cdum, n, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
  840. lwork_cgebrd_nn__ = (integer) cdum[0].r;
  841. cgeqrf_(m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  842. lwork_cgeqrf_mn__ = (integer) cdum[0].r;
  843. cungbr_("P", n, n, n, cdum, n, cdum, cdum, &c_n1, &ierr);
  844. lwork_cungbr_p_nn__ = (integer) cdum[0].r;
  845. cungbr_("Q", m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  846. lwork_cungbr_q_mm__ = (integer) cdum[0].r;
  847. cungbr_("Q", m, n, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  848. lwork_cungbr_q_mn__ = (integer) cdum[0].r;
  849. cungqr_(m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  850. lwork_cungqr_mm__ = (integer) cdum[0].r;
  851. cungqr_(m, n, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  852. lwork_cungqr_mn__ = (integer) cdum[0].r;
  853. cunmbr_("P", "R", "C", n, n, n, cdum, n, cdum, cdum, n, cdum, &
  854. c_n1, &ierr);
  855. lwork_cunmbr_prc_nn__ = (integer) cdum[0].r;
  856. cunmbr_("Q", "L", "N", m, m, n, cdum, m, cdum, cdum, m, cdum, &
  857. c_n1, &ierr);
  858. lwork_cunmbr_qln_mm__ = (integer) cdum[0].r;
  859. cunmbr_("Q", "L", "N", m, n, n, cdum, m, cdum, cdum, m, cdum, &
  860. c_n1, &ierr);
  861. lwork_cunmbr_qln_mn__ = (integer) cdum[0].r;
  862. cunmbr_("Q", "L", "N", n, n, n, cdum, n, cdum, cdum, n, cdum, &
  863. c_n1, &ierr);
  864. lwork_cunmbr_qln_nn__ = (integer) cdum[0].r;
  865. if (*m >= mnthr1) {
  866. if (wntqn) {
  867. /* Path 1 (M >> N, JOBZ='N') */
  868. maxwrk = *n + lwork_cgeqrf_mn__;
  869. /* Computing MAX */
  870. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cgebrd_nn__;
  871. maxwrk = f2cmax(i__1,i__2);
  872. minwrk = *n * 3;
  873. } else if (wntqo) {
  874. /* Path 2 (M >> N, JOBZ='O') */
  875. wrkbl = *n + lwork_cgeqrf_mn__;
  876. /* Computing MAX */
  877. i__1 = wrkbl, i__2 = *n + lwork_cungqr_mn__;
  878. wrkbl = f2cmax(i__1,i__2);
  879. /* Computing MAX */
  880. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cgebrd_nn__;
  881. wrkbl = f2cmax(i__1,i__2);
  882. /* Computing MAX */
  883. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_qln_nn__;
  884. wrkbl = f2cmax(i__1,i__2);
  885. /* Computing MAX */
  886. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
  887. wrkbl = f2cmax(i__1,i__2);
  888. maxwrk = *m * *n + *n * *n + wrkbl;
  889. minwrk = (*n << 1) * *n + *n * 3;
  890. } else if (wntqs) {
  891. /* Path 3 (M >> N, JOBZ='S') */
  892. wrkbl = *n + lwork_cgeqrf_mn__;
  893. /* Computing MAX */
  894. i__1 = wrkbl, i__2 = *n + lwork_cungqr_mn__;
  895. wrkbl = f2cmax(i__1,i__2);
  896. /* Computing MAX */
  897. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cgebrd_nn__;
  898. wrkbl = f2cmax(i__1,i__2);
  899. /* Computing MAX */
  900. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_qln_nn__;
  901. wrkbl = f2cmax(i__1,i__2);
  902. /* Computing MAX */
  903. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
  904. wrkbl = f2cmax(i__1,i__2);
  905. maxwrk = *n * *n + wrkbl;
  906. minwrk = *n * *n + *n * 3;
  907. } else if (wntqa) {
  908. /* Path 4 (M >> N, JOBZ='A') */
  909. wrkbl = *n + lwork_cgeqrf_mn__;
  910. /* Computing MAX */
  911. i__1 = wrkbl, i__2 = *n + lwork_cungqr_mm__;
  912. wrkbl = f2cmax(i__1,i__2);
  913. /* Computing MAX */
  914. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cgebrd_nn__;
  915. wrkbl = f2cmax(i__1,i__2);
  916. /* Computing MAX */
  917. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_qln_nn__;
  918. wrkbl = f2cmax(i__1,i__2);
  919. /* Computing MAX */
  920. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
  921. wrkbl = f2cmax(i__1,i__2);
  922. maxwrk = *n * *n + wrkbl;
  923. /* Computing MAX */
  924. i__1 = *n * 3, i__2 = *n + *m;
  925. minwrk = *n * *n + f2cmax(i__1,i__2);
  926. }
  927. } else if (*m >= mnthr2) {
  928. /* Path 5 (M >> N, but not as much as MNTHR1) */
  929. maxwrk = (*n << 1) + lwork_cgebrd_mn__;
  930. minwrk = (*n << 1) + *m;
  931. if (wntqo) {
  932. /* Path 5o (M >> N, JOBZ='O') */
  933. /* Computing MAX */
  934. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_p_nn__;
  935. maxwrk = f2cmax(i__1,i__2);
  936. /* Computing MAX */
  937. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_q_mn__;
  938. maxwrk = f2cmax(i__1,i__2);
  939. maxwrk += *m * *n;
  940. minwrk += *n * *n;
  941. } else if (wntqs) {
  942. /* Path 5s (M >> N, JOBZ='S') */
  943. /* Computing MAX */
  944. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_p_nn__;
  945. maxwrk = f2cmax(i__1,i__2);
  946. /* Computing MAX */
  947. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_q_mn__;
  948. maxwrk = f2cmax(i__1,i__2);
  949. } else if (wntqa) {
  950. /* Path 5a (M >> N, JOBZ='A') */
  951. /* Computing MAX */
  952. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_p_nn__;
  953. maxwrk = f2cmax(i__1,i__2);
  954. /* Computing MAX */
  955. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_q_mm__;
  956. maxwrk = f2cmax(i__1,i__2);
  957. }
  958. } else {
  959. /* Path 6 (M >= N, but not much larger) */
  960. maxwrk = (*n << 1) + lwork_cgebrd_mn__;
  961. minwrk = (*n << 1) + *m;
  962. if (wntqo) {
  963. /* Path 6o (M >= N, JOBZ='O') */
  964. /* Computing MAX */
  965. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
  966. maxwrk = f2cmax(i__1,i__2);
  967. /* Computing MAX */
  968. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_qln_mn__;
  969. maxwrk = f2cmax(i__1,i__2);
  970. maxwrk += *m * *n;
  971. minwrk += *n * *n;
  972. } else if (wntqs) {
  973. /* Path 6s (M >= N, JOBZ='S') */
  974. /* Computing MAX */
  975. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_qln_mn__;
  976. maxwrk = f2cmax(i__1,i__2);
  977. /* Computing MAX */
  978. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
  979. maxwrk = f2cmax(i__1,i__2);
  980. } else if (wntqa) {
  981. /* Path 6a (M >= N, JOBZ='A') */
  982. /* Computing MAX */
  983. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_qln_mm__;
  984. maxwrk = f2cmax(i__1,i__2);
  985. /* Computing MAX */
  986. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
  987. maxwrk = f2cmax(i__1,i__2);
  988. }
  989. }
  990. } else if (minmn > 0) {
  991. /* There is no complex work space needed for bidiagonal SVD */
  992. /* The real work space needed for bidiagonal SVD (sbdsdc) is */
  993. /* BDSPAC = 3*M*M + 4*M for singular values and vectors; */
  994. /* BDSPAC = 4*M for singular values only; */
  995. /* not including e, RU, and RVT matrices. */
  996. /* Compute space preferred for each routine */
  997. cgebrd_(m, n, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
  998. lwork_cgebrd_mn__ = (integer) cdum[0].r;
  999. cgebrd_(m, m, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
  1000. lwork_cgebrd_mm__ = (integer) cdum[0].r;
  1001. cgelqf_(m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  1002. lwork_cgelqf_mn__ = (integer) cdum[0].r;
  1003. cungbr_("P", m, n, m, cdum, m, cdum, cdum, &c_n1, &ierr);
  1004. lwork_cungbr_p_mn__ = (integer) cdum[0].r;
  1005. cungbr_("P", n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
  1006. lwork_cungbr_p_nn__ = (integer) cdum[0].r;
  1007. cungbr_("Q", m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  1008. lwork_cungbr_q_mm__ = (integer) cdum[0].r;
  1009. cunglq_(m, n, m, cdum, m, cdum, cdum, &c_n1, &ierr);
  1010. lwork_cunglq_mn__ = (integer) cdum[0].r;
  1011. cunglq_(n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
  1012. lwork_cunglq_nn__ = (integer) cdum[0].r;
  1013. cunmbr_("P", "R", "C", m, m, m, cdum, m, cdum, cdum, m, cdum, &
  1014. c_n1, &ierr);
  1015. lwork_cunmbr_prc_mm__ = (integer) cdum[0].r;
  1016. cunmbr_("P", "R", "C", m, n, m, cdum, m, cdum, cdum, m, cdum, &
  1017. c_n1, &ierr);
  1018. lwork_cunmbr_prc_mn__ = (integer) cdum[0].r;
  1019. cunmbr_("P", "R", "C", n, n, m, cdum, n, cdum, cdum, n, cdum, &
  1020. c_n1, &ierr);
  1021. lwork_cunmbr_prc_nn__ = (integer) cdum[0].r;
  1022. cunmbr_("Q", "L", "N", m, m, m, cdum, m, cdum, cdum, m, cdum, &
  1023. c_n1, &ierr);
  1024. lwork_cunmbr_qln_mm__ = (integer) cdum[0].r;
  1025. if (*n >= mnthr1) {
  1026. if (wntqn) {
  1027. /* Path 1t (N >> M, JOBZ='N') */
  1028. maxwrk = *m + lwork_cgelqf_mn__;
  1029. /* Computing MAX */
  1030. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cgebrd_mm__;
  1031. maxwrk = f2cmax(i__1,i__2);
  1032. minwrk = *m * 3;
  1033. } else if (wntqo) {
  1034. /* Path 2t (N >> M, JOBZ='O') */
  1035. wrkbl = *m + lwork_cgelqf_mn__;
  1036. /* Computing MAX */
  1037. i__1 = wrkbl, i__2 = *m + lwork_cunglq_mn__;
  1038. wrkbl = f2cmax(i__1,i__2);
  1039. /* Computing MAX */
  1040. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cgebrd_mm__;
  1041. wrkbl = f2cmax(i__1,i__2);
  1042. /* Computing MAX */
  1043. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
  1044. wrkbl = f2cmax(i__1,i__2);
  1045. /* Computing MAX */
  1046. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_prc_mm__;
  1047. wrkbl = f2cmax(i__1,i__2);
  1048. maxwrk = *m * *n + *m * *m + wrkbl;
  1049. minwrk = (*m << 1) * *m + *m * 3;
  1050. } else if (wntqs) {
  1051. /* Path 3t (N >> M, JOBZ='S') */
  1052. wrkbl = *m + lwork_cgelqf_mn__;
  1053. /* Computing MAX */
  1054. i__1 = wrkbl, i__2 = *m + lwork_cunglq_mn__;
  1055. wrkbl = f2cmax(i__1,i__2);
  1056. /* Computing MAX */
  1057. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cgebrd_mm__;
  1058. wrkbl = f2cmax(i__1,i__2);
  1059. /* Computing MAX */
  1060. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
  1061. wrkbl = f2cmax(i__1,i__2);
  1062. /* Computing MAX */
  1063. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_prc_mm__;
  1064. wrkbl = f2cmax(i__1,i__2);
  1065. maxwrk = *m * *m + wrkbl;
  1066. minwrk = *m * *m + *m * 3;
  1067. } else if (wntqa) {
  1068. /* Path 4t (N >> M, JOBZ='A') */
  1069. wrkbl = *m + lwork_cgelqf_mn__;
  1070. /* Computing MAX */
  1071. i__1 = wrkbl, i__2 = *m + lwork_cunglq_nn__;
  1072. wrkbl = f2cmax(i__1,i__2);
  1073. /* Computing MAX */
  1074. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cgebrd_mm__;
  1075. wrkbl = f2cmax(i__1,i__2);
  1076. /* Computing MAX */
  1077. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
  1078. wrkbl = f2cmax(i__1,i__2);
  1079. /* Computing MAX */
  1080. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_prc_mm__;
  1081. wrkbl = f2cmax(i__1,i__2);
  1082. maxwrk = *m * *m + wrkbl;
  1083. /* Computing MAX */
  1084. i__1 = *m * 3, i__2 = *m + *n;
  1085. minwrk = *m * *m + f2cmax(i__1,i__2);
  1086. }
  1087. } else if (*n >= mnthr2) {
  1088. /* Path 5t (N >> M, but not as much as MNTHR1) */
  1089. maxwrk = (*m << 1) + lwork_cgebrd_mn__;
  1090. minwrk = (*m << 1) + *n;
  1091. if (wntqo) {
  1092. /* Path 5to (N >> M, JOBZ='O') */
  1093. /* Computing MAX */
  1094. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_q_mm__;
  1095. maxwrk = f2cmax(i__1,i__2);
  1096. /* Computing MAX */
  1097. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_p_mn__;
  1098. maxwrk = f2cmax(i__1,i__2);
  1099. maxwrk += *m * *n;
  1100. minwrk += *m * *m;
  1101. } else if (wntqs) {
  1102. /* Path 5ts (N >> M, JOBZ='S') */
  1103. /* Computing MAX */
  1104. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_q_mm__;
  1105. maxwrk = f2cmax(i__1,i__2);
  1106. /* Computing MAX */
  1107. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_p_mn__;
  1108. maxwrk = f2cmax(i__1,i__2);
  1109. } else if (wntqa) {
  1110. /* Path 5ta (N >> M, JOBZ='A') */
  1111. /* Computing MAX */
  1112. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_q_mm__;
  1113. maxwrk = f2cmax(i__1,i__2);
  1114. /* Computing MAX */
  1115. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_p_nn__;
  1116. maxwrk = f2cmax(i__1,i__2);
  1117. }
  1118. } else {
  1119. /* Path 6t (N > M, but not much larger) */
  1120. maxwrk = (*m << 1) + lwork_cgebrd_mn__;
  1121. minwrk = (*m << 1) + *n;
  1122. if (wntqo) {
  1123. /* Path 6to (N > M, JOBZ='O') */
  1124. /* Computing MAX */
  1125. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
  1126. maxwrk = f2cmax(i__1,i__2);
  1127. /* Computing MAX */
  1128. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_prc_mn__;
  1129. maxwrk = f2cmax(i__1,i__2);
  1130. maxwrk += *m * *n;
  1131. minwrk += *m * *m;
  1132. } else if (wntqs) {
  1133. /* Path 6ts (N > M, JOBZ='S') */
  1134. /* Computing MAX */
  1135. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
  1136. maxwrk = f2cmax(i__1,i__2);
  1137. /* Computing MAX */
  1138. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_prc_mn__;
  1139. maxwrk = f2cmax(i__1,i__2);
  1140. } else if (wntqa) {
  1141. /* Path 6ta (N > M, JOBZ='A') */
  1142. /* Computing MAX */
  1143. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
  1144. maxwrk = f2cmax(i__1,i__2);
  1145. /* Computing MAX */
  1146. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_prc_nn__;
  1147. maxwrk = f2cmax(i__1,i__2);
  1148. }
  1149. }
  1150. }
  1151. maxwrk = f2cmax(maxwrk,minwrk);
  1152. }
  1153. if (*info == 0) {
  1154. work[1].r = (real) maxwrk, work[1].i = 0.f;
  1155. if (*lwork < minwrk && ! lquery) {
  1156. *info = -12;
  1157. }
  1158. }
  1159. if (*info != 0) {
  1160. i__1 = -(*info);
  1161. xerbla_("CGESDD", &i__1, (ftnlen)6);
  1162. return;
  1163. } else if (lquery) {
  1164. return;
  1165. }
  1166. /* Quick return if possible */
  1167. if (*m == 0 || *n == 0) {
  1168. return;
  1169. }
  1170. /* Get machine constants */
  1171. eps = slamch_("P");
  1172. smlnum = sqrt(slamch_("S")) / eps;
  1173. bignum = 1.f / smlnum;
  1174. /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
  1175. anrm = clange_("M", m, n, &a[a_offset], lda, dum);
  1176. if (sisnan_(&anrm)) {
  1177. *info = -4;
  1178. return;
  1179. }
  1180. iscl = 0;
  1181. if (anrm > 0.f && anrm < smlnum) {
  1182. iscl = 1;
  1183. clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
  1184. ierr);
  1185. } else if (anrm > bignum) {
  1186. iscl = 1;
  1187. clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &
  1188. ierr);
  1189. }
  1190. if (*m >= *n) {
  1191. /* A has at least as many rows as columns. If A has sufficiently */
  1192. /* more rows than columns, first reduce using the QR */
  1193. /* decomposition (if sufficient workspace available) */
  1194. if (*m >= mnthr1) {
  1195. if (wntqn) {
  1196. /* Path 1 (M >> N, JOBZ='N') */
  1197. /* No singular vectors to be computed */
  1198. itau = 1;
  1199. nwork = itau + *n;
  1200. /* Compute A=Q*R */
  1201. /* CWorkspace: need N [tau] + N [work] */
  1202. /* CWorkspace: prefer N [tau] + N*NB [work] */
  1203. /* RWorkspace: need 0 */
  1204. i__1 = *lwork - nwork + 1;
  1205. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1206. i__1, &ierr);
  1207. /* Zero out below R */
  1208. i__1 = *n - 1;
  1209. i__2 = *n - 1;
  1210. claset_("L", &i__1, &i__2, &c_b1, &c_b1, &a[a_dim1 + 2], lda);
  1211. ie = 1;
  1212. itauq = 1;
  1213. itaup = itauq + *n;
  1214. nwork = itaup + *n;
  1215. /* Bidiagonalize R in A */
  1216. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1217. /* CWorkspace: prefer 2*N [tauq, taup] + 2*N*NB [work] */
  1218. /* RWorkspace: need N [e] */
  1219. i__1 = *lwork - nwork + 1;
  1220. cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1221. itauq], &work[itaup], &work[nwork], &i__1, &ierr);
  1222. nrwork = ie + *n;
  1223. /* Perform bidiagonal SVD, compute singular values only */
  1224. /* CWorkspace: need 0 */
  1225. /* RWorkspace: need N [e] + BDSPAC */
  1226. sbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
  1227. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  1228. } else if (wntqo) {
  1229. /* Path 2 (M >> N, JOBZ='O') */
  1230. /* N left singular vectors to be overwritten on A and */
  1231. /* N right singular vectors to be computed in VT */
  1232. iu = 1;
  1233. /* WORK(IU) is N by N */
  1234. ldwrku = *n;
  1235. ir = iu + ldwrku * *n;
  1236. if (*lwork >= *m * *n + *n * *n + *n * 3) {
  1237. /* WORK(IR) is M by N */
  1238. ldwrkr = *m;
  1239. } else {
  1240. ldwrkr = (*lwork - *n * *n - *n * 3) / *n;
  1241. }
  1242. itau = ir + ldwrkr * *n;
  1243. nwork = itau + *n;
  1244. /* Compute A=Q*R */
  1245. /* CWorkspace: need N*N [U] + N*N [R] + N [tau] + N [work] */
  1246. /* CWorkspace: prefer N*N [U] + N*N [R] + N [tau] + N*NB [work] */
  1247. /* RWorkspace: need 0 */
  1248. i__1 = *lwork - nwork + 1;
  1249. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1250. i__1, &ierr);
  1251. /* Copy R to WORK( IR ), zeroing out below it */
  1252. clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
  1253. i__1 = *n - 1;
  1254. i__2 = *n - 1;
  1255. claset_("L", &i__1, &i__2, &c_b1, &c_b1, &work[ir + 1], &
  1256. ldwrkr);
  1257. /* Generate Q in A */
  1258. /* CWorkspace: need N*N [U] + N*N [R] + N [tau] + N [work] */
  1259. /* CWorkspace: prefer N*N [U] + N*N [R] + N [tau] + N*NB [work] */
  1260. /* RWorkspace: need 0 */
  1261. i__1 = *lwork - nwork + 1;
  1262. cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
  1263. &i__1, &ierr);
  1264. ie = 1;
  1265. itauq = itau;
  1266. itaup = itauq + *n;
  1267. nwork = itaup + *n;
  1268. /* Bidiagonalize R in WORK(IR) */
  1269. /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
  1270. /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + 2*N*NB [work] */
  1271. /* RWorkspace: need N [e] */
  1272. i__1 = *lwork - nwork + 1;
  1273. cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[
  1274. itauq], &work[itaup], &work[nwork], &i__1, &ierr);
  1275. /* Perform bidiagonal SVD, computing left singular vectors */
  1276. /* of R in WORK(IRU) and computing right singular vectors */
  1277. /* of R in WORK(IRVT) */
  1278. /* CWorkspace: need 0 */
  1279. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1280. iru = ie + *n;
  1281. irvt = iru + *n * *n;
  1282. nrwork = irvt + *n * *n;
  1283. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1284. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1285. info);
  1286. /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
  1287. /* Overwrite WORK(IU) by the left singular vectors of R */
  1288. /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
  1289. /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + N*NB [work] */
  1290. /* RWorkspace: need 0 */
  1291. clacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
  1292. i__1 = *lwork - nwork + 1;
  1293. cunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
  1294. itauq], &work[iu], &ldwrku, &work[nwork], &i__1, &
  1295. ierr);
  1296. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1297. /* Overwrite VT by the right singular vectors of R */
  1298. /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
  1299. /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + N*NB [work] */
  1300. /* RWorkspace: need 0 */
  1301. clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1302. i__1 = *lwork - nwork + 1;
  1303. cunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[
  1304. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  1305. ierr);
  1306. /* Multiply Q in A by left singular vectors of R in */
  1307. /* WORK(IU), storing result in WORK(IR) and copying to A */
  1308. /* CWorkspace: need N*N [U] + N*N [R] */
  1309. /* CWorkspace: prefer N*N [U] + M*N [R] */
  1310. /* RWorkspace: need 0 */
  1311. i__1 = *m;
  1312. i__2 = ldwrkr;
  1313. for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
  1314. i__2) {
  1315. /* Computing MIN */
  1316. i__3 = *m - i__ + 1;
  1317. chunk = f2cmin(i__3,ldwrkr);
  1318. cgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1],
  1319. lda, &work[iu], &ldwrku, &c_b1, &work[ir], &
  1320. ldwrkr);
  1321. clacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ +
  1322. a_dim1], lda);
  1323. /* L10: */
  1324. }
  1325. } else if (wntqs) {
  1326. /* Path 3 (M >> N, JOBZ='S') */
  1327. /* N left singular vectors to be computed in U and */
  1328. /* N right singular vectors to be computed in VT */
  1329. ir = 1;
  1330. /* WORK(IR) is N by N */
  1331. ldwrkr = *n;
  1332. itau = ir + ldwrkr * *n;
  1333. nwork = itau + *n;
  1334. /* Compute A=Q*R */
  1335. /* CWorkspace: need N*N [R] + N [tau] + N [work] */
  1336. /* CWorkspace: prefer N*N [R] + N [tau] + N*NB [work] */
  1337. /* RWorkspace: need 0 */
  1338. i__2 = *lwork - nwork + 1;
  1339. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1340. i__2, &ierr);
  1341. /* Copy R to WORK(IR), zeroing out below it */
  1342. clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
  1343. i__2 = *n - 1;
  1344. i__1 = *n - 1;
  1345. claset_("L", &i__2, &i__1, &c_b1, &c_b1, &work[ir + 1], &
  1346. ldwrkr);
  1347. /* Generate Q in A */
  1348. /* CWorkspace: need N*N [R] + N [tau] + N [work] */
  1349. /* CWorkspace: prefer N*N [R] + N [tau] + N*NB [work] */
  1350. /* RWorkspace: need 0 */
  1351. i__2 = *lwork - nwork + 1;
  1352. cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
  1353. &i__2, &ierr);
  1354. ie = 1;
  1355. itauq = itau;
  1356. itaup = itauq + *n;
  1357. nwork = itaup + *n;
  1358. /* Bidiagonalize R in WORK(IR) */
  1359. /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
  1360. /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + 2*N*NB [work] */
  1361. /* RWorkspace: need N [e] */
  1362. i__2 = *lwork - nwork + 1;
  1363. cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[
  1364. itauq], &work[itaup], &work[nwork], &i__2, &ierr);
  1365. /* Perform bidiagonal SVD, computing left singular vectors */
  1366. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1367. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1368. /* CWorkspace: need 0 */
  1369. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1370. iru = ie + *n;
  1371. irvt = iru + *n * *n;
  1372. nrwork = irvt + *n * *n;
  1373. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1374. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1375. info);
  1376. /* Copy real matrix RWORK(IRU) to complex matrix U */
  1377. /* Overwrite U by left singular vectors of R */
  1378. /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
  1379. /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + N*NB [work] */
  1380. /* RWorkspace: need 0 */
  1381. clacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
  1382. i__2 = *lwork - nwork + 1;
  1383. cunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
  1384. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  1385. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1386. /* Overwrite VT by right singular vectors of R */
  1387. /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
  1388. /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + N*NB [work] */
  1389. /* RWorkspace: need 0 */
  1390. clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1391. i__2 = *lwork - nwork + 1;
  1392. cunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[
  1393. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
  1394. ierr);
  1395. /* Multiply Q in A by left singular vectors of R in */
  1396. /* WORK(IR), storing result in U */
  1397. /* CWorkspace: need N*N [R] */
  1398. /* RWorkspace: need 0 */
  1399. clacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr);
  1400. cgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &work[ir],
  1401. &ldwrkr, &c_b1, &u[u_offset], ldu);
  1402. } else if (wntqa) {
  1403. /* Path 4 (M >> N, JOBZ='A') */
  1404. /* M left singular vectors to be computed in U and */
  1405. /* N right singular vectors to be computed in VT */
  1406. iu = 1;
  1407. /* WORK(IU) is N by N */
  1408. ldwrku = *n;
  1409. itau = iu + ldwrku * *n;
  1410. nwork = itau + *n;
  1411. /* Compute A=Q*R, copying result to U */
  1412. /* CWorkspace: need N*N [U] + N [tau] + N [work] */
  1413. /* CWorkspace: prefer N*N [U] + N [tau] + N*NB [work] */
  1414. /* RWorkspace: need 0 */
  1415. i__2 = *lwork - nwork + 1;
  1416. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1417. i__2, &ierr);
  1418. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1419. /* Generate Q in U */
  1420. /* CWorkspace: need N*N [U] + N [tau] + M [work] */
  1421. /* CWorkspace: prefer N*N [U] + N [tau] + M*NB [work] */
  1422. /* RWorkspace: need 0 */
  1423. i__2 = *lwork - nwork + 1;
  1424. cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork],
  1425. &i__2, &ierr);
  1426. /* Produce R in A, zeroing out below it */
  1427. i__2 = *n - 1;
  1428. i__1 = *n - 1;
  1429. claset_("L", &i__2, &i__1, &c_b1, &c_b1, &a[a_dim1 + 2], lda);
  1430. ie = 1;
  1431. itauq = itau;
  1432. itaup = itauq + *n;
  1433. nwork = itaup + *n;
  1434. /* Bidiagonalize R in A */
  1435. /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
  1436. /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + 2*N*NB [work] */
  1437. /* RWorkspace: need N [e] */
  1438. i__2 = *lwork - nwork + 1;
  1439. cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1440. itauq], &work[itaup], &work[nwork], &i__2, &ierr);
  1441. iru = ie + *n;
  1442. irvt = iru + *n * *n;
  1443. nrwork = irvt + *n * *n;
  1444. /* Perform bidiagonal SVD, computing left singular vectors */
  1445. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1446. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1447. /* CWorkspace: need 0 */
  1448. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1449. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1450. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1451. info);
  1452. /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
  1453. /* Overwrite WORK(IU) by left singular vectors of R */
  1454. /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
  1455. /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + N*NB [work] */
  1456. /* RWorkspace: need 0 */
  1457. clacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
  1458. i__2 = *lwork - nwork + 1;
  1459. cunmbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[
  1460. itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
  1461. ierr);
  1462. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1463. /* Overwrite VT by right singular vectors of R */
  1464. /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
  1465. /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + N*NB [work] */
  1466. /* RWorkspace: need 0 */
  1467. clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1468. i__2 = *lwork - nwork + 1;
  1469. cunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
  1470. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
  1471. ierr);
  1472. /* Multiply Q in U by left singular vectors of R in */
  1473. /* WORK(IU), storing result in A */
  1474. /* CWorkspace: need N*N [U] */
  1475. /* RWorkspace: need 0 */
  1476. cgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &work[iu],
  1477. &ldwrku, &c_b1, &a[a_offset], lda);
  1478. /* Copy left singular vectors of A from A to U */
  1479. clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1480. }
  1481. } else if (*m >= mnthr2) {
  1482. /* MNTHR2 <= M < MNTHR1 */
  1483. /* Path 5 (M >> N, but not as much as MNTHR1) */
  1484. /* Reduce to bidiagonal form without QR decomposition, use */
  1485. /* CUNGBR and matrix multiplication to compute singular vectors */
  1486. ie = 1;
  1487. nrwork = ie + *n;
  1488. itauq = 1;
  1489. itaup = itauq + *n;
  1490. nwork = itaup + *n;
  1491. /* Bidiagonalize A */
  1492. /* CWorkspace: need 2*N [tauq, taup] + M [work] */
  1493. /* CWorkspace: prefer 2*N [tauq, taup] + (M+N)*NB [work] */
  1494. /* RWorkspace: need N [e] */
  1495. i__2 = *lwork - nwork + 1;
  1496. cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  1497. &work[itaup], &work[nwork], &i__2, &ierr);
  1498. if (wntqn) {
  1499. /* Path 5n (M >> N, JOBZ='N') */
  1500. /* Compute singular values only */
  1501. /* CWorkspace: need 0 */
  1502. /* RWorkspace: need N [e] + BDSPAC */
  1503. sbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
  1504. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  1505. } else if (wntqo) {
  1506. iu = nwork;
  1507. iru = nrwork;
  1508. irvt = iru + *n * *n;
  1509. nrwork = irvt + *n * *n;
  1510. /* Path 5o (M >> N, JOBZ='O') */
  1511. /* Copy A to VT, generate P**H */
  1512. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1513. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1514. /* RWorkspace: need 0 */
  1515. clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1516. i__2 = *lwork - nwork + 1;
  1517. cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
  1518. work[nwork], &i__2, &ierr);
  1519. /* Generate Q in A */
  1520. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1521. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1522. /* RWorkspace: need 0 */
  1523. i__2 = *lwork - nwork + 1;
  1524. cungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[
  1525. nwork], &i__2, &ierr);
  1526. if (*lwork >= *m * *n + *n * 3) {
  1527. /* WORK( IU ) is M by N */
  1528. ldwrku = *m;
  1529. } else {
  1530. /* WORK(IU) is LDWRKU by N */
  1531. ldwrku = (*lwork - *n * 3) / *n;
  1532. }
  1533. nwork = iu + ldwrku * *n;
  1534. /* Perform bidiagonal SVD, computing left singular vectors */
  1535. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1536. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1537. /* CWorkspace: need 0 */
  1538. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1539. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1540. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1541. info);
  1542. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  1543. /* storing the result in WORK(IU), copying to VT */
  1544. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
  1545. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
  1546. clarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &work[iu]
  1547. , &ldwrku, &rwork[nrwork]);
  1548. clacpy_("F", n, n, &work[iu], &ldwrku, &vt[vt_offset], ldvt);
  1549. /* Multiply Q in A by real matrix RWORK(IRU), storing the */
  1550. /* result in WORK(IU), copying to A */
  1551. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
  1552. /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] */
  1553. /* RWorkspace: need N [e] + N*N [RU] + 2*N*N [rwork] */
  1554. /* RWorkspace: prefer N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
  1555. nrwork = irvt;
  1556. i__2 = *m;
  1557. i__1 = ldwrku;
  1558. for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
  1559. i__1) {
  1560. /* Computing MIN */
  1561. i__3 = *m - i__ + 1;
  1562. chunk = f2cmin(i__3,ldwrku);
  1563. clacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru], n,
  1564. &work[iu], &ldwrku, &rwork[nrwork]);
  1565. clacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
  1566. a_dim1], lda);
  1567. /* L20: */
  1568. }
  1569. } else if (wntqs) {
  1570. /* Path 5s (M >> N, JOBZ='S') */
  1571. /* Copy A to VT, generate P**H */
  1572. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1573. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1574. /* RWorkspace: need 0 */
  1575. clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1576. i__1 = *lwork - nwork + 1;
  1577. cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
  1578. work[nwork], &i__1, &ierr);
  1579. /* Copy A to U, generate Q */
  1580. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1581. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1582. /* RWorkspace: need 0 */
  1583. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1584. i__1 = *lwork - nwork + 1;
  1585. cungbr_("Q", m, n, n, &u[u_offset], ldu, &work[itauq], &work[
  1586. nwork], &i__1, &ierr);
  1587. /* Perform bidiagonal SVD, computing left singular vectors */
  1588. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1589. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1590. /* CWorkspace: need 0 */
  1591. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1592. iru = nrwork;
  1593. irvt = iru + *n * *n;
  1594. nrwork = irvt + *n * *n;
  1595. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1596. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1597. info);
  1598. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  1599. /* storing the result in A, copying to VT */
  1600. /* CWorkspace: need 0 */
  1601. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
  1602. clarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[
  1603. a_offset], lda, &rwork[nrwork]);
  1604. clacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1605. /* Multiply Q in U by real matrix RWORK(IRU), storing the */
  1606. /* result in A, copying to U */
  1607. /* CWorkspace: need 0 */
  1608. /* RWorkspace: need N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
  1609. nrwork = irvt;
  1610. clacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset],
  1611. lda, &rwork[nrwork]);
  1612. clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1613. } else {
  1614. /* Path 5a (M >> N, JOBZ='A') */
  1615. /* Copy A to VT, generate P**H */
  1616. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1617. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1618. /* RWorkspace: need 0 */
  1619. clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1620. i__1 = *lwork - nwork + 1;
  1621. cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
  1622. work[nwork], &i__1, &ierr);
  1623. /* Copy A to U, generate Q */
  1624. /* CWorkspace: need 2*N [tauq, taup] + M [work] */
  1625. /* CWorkspace: prefer 2*N [tauq, taup] + M*NB [work] */
  1626. /* RWorkspace: need 0 */
  1627. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1628. i__1 = *lwork - nwork + 1;
  1629. cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  1630. nwork], &i__1, &ierr);
  1631. /* Perform bidiagonal SVD, computing left singular vectors */
  1632. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1633. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1634. /* CWorkspace: need 0 */
  1635. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1636. iru = nrwork;
  1637. irvt = iru + *n * *n;
  1638. nrwork = irvt + *n * *n;
  1639. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1640. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1641. info);
  1642. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  1643. /* storing the result in A, copying to VT */
  1644. /* CWorkspace: need 0 */
  1645. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
  1646. clarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[
  1647. a_offset], lda, &rwork[nrwork]);
  1648. clacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1649. /* Multiply Q in U by real matrix RWORK(IRU), storing the */
  1650. /* result in A, copying to U */
  1651. /* CWorkspace: need 0 */
  1652. /* RWorkspace: need N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
  1653. nrwork = irvt;
  1654. clacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset],
  1655. lda, &rwork[nrwork]);
  1656. clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1657. }
  1658. } else {
  1659. /* M .LT. MNTHR2 */
  1660. /* Path 6 (M >= N, but not much larger) */
  1661. /* Reduce to bidiagonal form without QR decomposition */
  1662. /* Use CUNMBR to compute singular vectors */
  1663. ie = 1;
  1664. nrwork = ie + *n;
  1665. itauq = 1;
  1666. itaup = itauq + *n;
  1667. nwork = itaup + *n;
  1668. /* Bidiagonalize A */
  1669. /* CWorkspace: need 2*N [tauq, taup] + M [work] */
  1670. /* CWorkspace: prefer 2*N [tauq, taup] + (M+N)*NB [work] */
  1671. /* RWorkspace: need N [e] */
  1672. i__1 = *lwork - nwork + 1;
  1673. cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  1674. &work[itaup], &work[nwork], &i__1, &ierr);
  1675. if (wntqn) {
  1676. /* Path 6n (M >= N, JOBZ='N') */
  1677. /* Compute singular values only */
  1678. /* CWorkspace: need 0 */
  1679. /* RWorkspace: need N [e] + BDSPAC */
  1680. sbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
  1681. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  1682. } else if (wntqo) {
  1683. iu = nwork;
  1684. iru = nrwork;
  1685. irvt = iru + *n * *n;
  1686. nrwork = irvt + *n * *n;
  1687. if (*lwork >= *m * *n + *n * 3) {
  1688. /* WORK( IU ) is M by N */
  1689. ldwrku = *m;
  1690. } else {
  1691. /* WORK( IU ) is LDWRKU by N */
  1692. ldwrku = (*lwork - *n * 3) / *n;
  1693. }
  1694. nwork = iu + ldwrku * *n;
  1695. /* Path 6o (M >= N, JOBZ='O') */
  1696. /* Perform bidiagonal SVD, computing left singular vectors */
  1697. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1698. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1699. /* CWorkspace: need 0 */
  1700. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1701. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1702. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1703. info);
  1704. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1705. /* Overwrite VT by right singular vectors of A */
  1706. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] + N [work] */
  1707. /* CWorkspace: prefer 2*N [tauq, taup] + N*N [U] + N*NB [work] */
  1708. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1709. clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1710. i__1 = *lwork - nwork + 1;
  1711. cunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
  1712. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  1713. ierr);
  1714. if (*lwork >= *m * *n + *n * 3) {
  1715. /* Path 6o-fast */
  1716. /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
  1717. /* Overwrite WORK(IU) by left singular vectors of A, copying */
  1718. /* to A */
  1719. /* CWorkspace: need 2*N [tauq, taup] + M*N [U] + N [work] */
  1720. /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] + N*NB [work] */
  1721. /* RWorkspace: need N [e] + N*N [RU] */
  1722. claset_("F", m, n, &c_b1, &c_b1, &work[iu], &ldwrku);
  1723. clacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
  1724. i__1 = *lwork - nwork + 1;
  1725. cunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
  1726. itauq], &work[iu], &ldwrku, &work[nwork], &i__1, &
  1727. ierr);
  1728. clacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda);
  1729. } else {
  1730. /* Path 6o-slow */
  1731. /* Generate Q in A */
  1732. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] + N [work] */
  1733. /* CWorkspace: prefer 2*N [tauq, taup] + N*N [U] + N*NB [work] */
  1734. /* RWorkspace: need 0 */
  1735. i__1 = *lwork - nwork + 1;
  1736. cungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
  1737. work[nwork], &i__1, &ierr);
  1738. /* Multiply Q in A by real matrix RWORK(IRU), storing the */
  1739. /* result in WORK(IU), copying to A */
  1740. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
  1741. /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] */
  1742. /* RWorkspace: need N [e] + N*N [RU] + 2*N*N [rwork] */
  1743. /* RWorkspace: prefer N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
  1744. nrwork = irvt;
  1745. i__1 = *m;
  1746. i__2 = ldwrku;
  1747. for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
  1748. i__2) {
  1749. /* Computing MIN */
  1750. i__3 = *m - i__ + 1;
  1751. chunk = f2cmin(i__3,ldwrku);
  1752. clacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru],
  1753. n, &work[iu], &ldwrku, &rwork[nrwork]);
  1754. clacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
  1755. a_dim1], lda);
  1756. /* L30: */
  1757. }
  1758. }
  1759. } else if (wntqs) {
  1760. /* Path 6s (M >= N, JOBZ='S') */
  1761. /* Perform bidiagonal SVD, computing left singular vectors */
  1762. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1763. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1764. /* CWorkspace: need 0 */
  1765. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1766. iru = nrwork;
  1767. irvt = iru + *n * *n;
  1768. nrwork = irvt + *n * *n;
  1769. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1770. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1771. info);
  1772. /* Copy real matrix RWORK(IRU) to complex matrix U */
  1773. /* Overwrite U by left singular vectors of A */
  1774. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1775. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1776. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1777. claset_("F", m, n, &c_b1, &c_b1, &u[u_offset], ldu)
  1778. ;
  1779. clacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
  1780. i__2 = *lwork - nwork + 1;
  1781. cunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
  1782. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  1783. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1784. /* Overwrite VT by right singular vectors of A */
  1785. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1786. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1787. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1788. clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1789. i__2 = *lwork - nwork + 1;
  1790. cunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
  1791. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
  1792. ierr);
  1793. } else {
  1794. /* Path 6a (M >= N, JOBZ='A') */
  1795. /* Perform bidiagonal SVD, computing left singular vectors */
  1796. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1797. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1798. /* CWorkspace: need 0 */
  1799. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1800. iru = nrwork;
  1801. irvt = iru + *n * *n;
  1802. nrwork = irvt + *n * *n;
  1803. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1804. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1805. info);
  1806. /* Set the right corner of U to identity matrix */
  1807. claset_("F", m, m, &c_b1, &c_b1, &u[u_offset], ldu)
  1808. ;
  1809. if (*m > *n) {
  1810. i__2 = *m - *n;
  1811. i__1 = *m - *n;
  1812. claset_("F", &i__2, &i__1, &c_b1, &c_b2, &u[*n + 1 + (*n
  1813. + 1) * u_dim1], ldu);
  1814. }
  1815. /* Copy real matrix RWORK(IRU) to complex matrix U */
  1816. /* Overwrite U by left singular vectors of A */
  1817. /* CWorkspace: need 2*N [tauq, taup] + M [work] */
  1818. /* CWorkspace: prefer 2*N [tauq, taup] + M*NB [work] */
  1819. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1820. clacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
  1821. i__2 = *lwork - nwork + 1;
  1822. cunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
  1823. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  1824. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1825. /* Overwrite VT by right singular vectors of A */
  1826. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1827. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1828. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1829. clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1830. i__2 = *lwork - nwork + 1;
  1831. cunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
  1832. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
  1833. ierr);
  1834. }
  1835. }
  1836. } else {
  1837. /* A has more columns than rows. If A has sufficiently more */
  1838. /* columns than rows, first reduce using the LQ decomposition (if */
  1839. /* sufficient workspace available) */
  1840. if (*n >= mnthr1) {
  1841. if (wntqn) {
  1842. /* Path 1t (N >> M, JOBZ='N') */
  1843. /* No singular vectors to be computed */
  1844. itau = 1;
  1845. nwork = itau + *m;
  1846. /* Compute A=L*Q */
  1847. /* CWorkspace: need M [tau] + M [work] */
  1848. /* CWorkspace: prefer M [tau] + M*NB [work] */
  1849. /* RWorkspace: need 0 */
  1850. i__2 = *lwork - nwork + 1;
  1851. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1852. i__2, &ierr);
  1853. /* Zero out above L */
  1854. i__2 = *m - 1;
  1855. i__1 = *m - 1;
  1856. claset_("U", &i__2, &i__1, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
  1857. , lda);
  1858. ie = 1;
  1859. itauq = 1;
  1860. itaup = itauq + *m;
  1861. nwork = itaup + *m;
  1862. /* Bidiagonalize L in A */
  1863. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  1864. /* CWorkspace: prefer 2*M [tauq, taup] + 2*M*NB [work] */
  1865. /* RWorkspace: need M [e] */
  1866. i__2 = *lwork - nwork + 1;
  1867. cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1868. itauq], &work[itaup], &work[nwork], &i__2, &ierr);
  1869. nrwork = ie + *m;
  1870. /* Perform bidiagonal SVD, compute singular values only */
  1871. /* CWorkspace: need 0 */
  1872. /* RWorkspace: need M [e] + BDSPAC */
  1873. sbdsdc_("U", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
  1874. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  1875. } else if (wntqo) {
  1876. /* Path 2t (N >> M, JOBZ='O') */
  1877. /* M right singular vectors to be overwritten on A and */
  1878. /* M left singular vectors to be computed in U */
  1879. ivt = 1;
  1880. ldwkvt = *m;
  1881. /* WORK(IVT) is M by M */
  1882. il = ivt + ldwkvt * *m;
  1883. if (*lwork >= *m * *n + *m * *m + *m * 3) {
  1884. /* WORK(IL) M by N */
  1885. ldwrkl = *m;
  1886. chunk = *n;
  1887. } else {
  1888. /* WORK(IL) is M by CHUNK */
  1889. ldwrkl = *m;
  1890. chunk = (*lwork - *m * *m - *m * 3) / *m;
  1891. }
  1892. itau = il + ldwrkl * chunk;
  1893. nwork = itau + *m;
  1894. /* Compute A=L*Q */
  1895. /* CWorkspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
  1896. /* CWorkspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
  1897. /* RWorkspace: need 0 */
  1898. i__2 = *lwork - nwork + 1;
  1899. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1900. i__2, &ierr);
  1901. /* Copy L to WORK(IL), zeroing about above it */
  1902. clacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
  1903. i__2 = *m - 1;
  1904. i__1 = *m - 1;
  1905. claset_("U", &i__2, &i__1, &c_b1, &c_b1, &work[il + ldwrkl], &
  1906. ldwrkl);
  1907. /* Generate Q in A */
  1908. /* CWorkspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
  1909. /* CWorkspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
  1910. /* RWorkspace: need 0 */
  1911. i__2 = *lwork - nwork + 1;
  1912. cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
  1913. &i__2, &ierr);
  1914. ie = 1;
  1915. itauq = itau;
  1916. itaup = itauq + *m;
  1917. nwork = itaup + *m;
  1918. /* Bidiagonalize L in WORK(IL) */
  1919. /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
  1920. /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + 2*M*NB [work] */
  1921. /* RWorkspace: need M [e] */
  1922. i__2 = *lwork - nwork + 1;
  1923. cgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[
  1924. itauq], &work[itaup], &work[nwork], &i__2, &ierr);
  1925. /* Perform bidiagonal SVD, computing left singular vectors */
  1926. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1927. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1928. /* CWorkspace: need 0 */
  1929. /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
  1930. iru = ie + *m;
  1931. irvt = iru + *m * *m;
  1932. nrwork = irvt + *m * *m;
  1933. sbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  1934. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  1935. info);
  1936. /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
  1937. /* Overwrite WORK(IU) by the left singular vectors of L */
  1938. /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
  1939. /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + M*NB [work] */
  1940. /* RWorkspace: need 0 */
  1941. clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  1942. i__2 = *lwork - nwork + 1;
  1943. cunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
  1944. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  1945. /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
  1946. /* Overwrite WORK(IVT) by the right singular vectors of L */
  1947. /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
  1948. /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + M*NB [work] */
  1949. /* RWorkspace: need 0 */
  1950. clacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
  1951. i__2 = *lwork - nwork + 1;
  1952. cunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[
  1953. itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &
  1954. ierr);
  1955. /* Multiply right singular vectors of L in WORK(IL) by Q */
  1956. /* in A, storing result in WORK(IL) and copying to A */
  1957. /* CWorkspace: need M*M [VT] + M*M [L] */
  1958. /* CWorkspace: prefer M*M [VT] + M*N [L] */
  1959. /* RWorkspace: need 0 */
  1960. i__2 = *n;
  1961. i__1 = chunk;
  1962. for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
  1963. i__1) {
  1964. /* Computing MIN */
  1965. i__3 = *n - i__ + 1;
  1966. blk = f2cmin(i__3,chunk);
  1967. cgemm_("N", "N", m, &blk, m, &c_b2, &work[ivt], m, &a[i__
  1968. * a_dim1 + 1], lda, &c_b1, &work[il], &ldwrkl);
  1969. clacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1
  1970. + 1], lda);
  1971. /* L40: */
  1972. }
  1973. } else if (wntqs) {
  1974. /* Path 3t (N >> M, JOBZ='S') */
  1975. /* M right singular vectors to be computed in VT and */
  1976. /* M left singular vectors to be computed in U */
  1977. il = 1;
  1978. /* WORK(IL) is M by M */
  1979. ldwrkl = *m;
  1980. itau = il + ldwrkl * *m;
  1981. nwork = itau + *m;
  1982. /* Compute A=L*Q */
  1983. /* CWorkspace: need M*M [L] + M [tau] + M [work] */
  1984. /* CWorkspace: prefer M*M [L] + M [tau] + M*NB [work] */
  1985. /* RWorkspace: need 0 */
  1986. i__1 = *lwork - nwork + 1;
  1987. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1988. i__1, &ierr);
  1989. /* Copy L to WORK(IL), zeroing out above it */
  1990. clacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
  1991. i__1 = *m - 1;
  1992. i__2 = *m - 1;
  1993. claset_("U", &i__1, &i__2, &c_b1, &c_b1, &work[il + ldwrkl], &
  1994. ldwrkl);
  1995. /* Generate Q in A */
  1996. /* CWorkspace: need M*M [L] + M [tau] + M [work] */
  1997. /* CWorkspace: prefer M*M [L] + M [tau] + M*NB [work] */
  1998. /* RWorkspace: need 0 */
  1999. i__1 = *lwork - nwork + 1;
  2000. cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
  2001. &i__1, &ierr);
  2002. ie = 1;
  2003. itauq = itau;
  2004. itaup = itauq + *m;
  2005. nwork = itaup + *m;
  2006. /* Bidiagonalize L in WORK(IL) */
  2007. /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
  2008. /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + 2*M*NB [work] */
  2009. /* RWorkspace: need M [e] */
  2010. i__1 = *lwork - nwork + 1;
  2011. cgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[
  2012. itauq], &work[itaup], &work[nwork], &i__1, &ierr);
  2013. /* Perform bidiagonal SVD, computing left singular vectors */
  2014. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2015. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2016. /* CWorkspace: need 0 */
  2017. /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
  2018. iru = ie + *m;
  2019. irvt = iru + *m * *m;
  2020. nrwork = irvt + *m * *m;
  2021. sbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2022. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2023. info);
  2024. /* Copy real matrix RWORK(IRU) to complex matrix U */
  2025. /* Overwrite U by left singular vectors of L */
  2026. /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
  2027. /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + M*NB [work] */
  2028. /* RWorkspace: need 0 */
  2029. clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  2030. i__1 = *lwork - nwork + 1;
  2031. cunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
  2032. itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
  2033. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  2034. /* Overwrite VT by left singular vectors of L */
  2035. /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
  2036. /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + M*NB [work] */
  2037. /* RWorkspace: need 0 */
  2038. clacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
  2039. i__1 = *lwork - nwork + 1;
  2040. cunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[
  2041. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  2042. ierr);
  2043. /* Copy VT to WORK(IL), multiply right singular vectors of L */
  2044. /* in WORK(IL) by Q in A, storing result in VT */
  2045. /* CWorkspace: need M*M [L] */
  2046. /* RWorkspace: need 0 */
  2047. clacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl);
  2048. cgemm_("N", "N", m, n, m, &c_b2, &work[il], &ldwrkl, &a[
  2049. a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
  2050. } else if (wntqa) {
  2051. /* Path 4t (N >> M, JOBZ='A') */
  2052. /* N right singular vectors to be computed in VT and */
  2053. /* M left singular vectors to be computed in U */
  2054. ivt = 1;
  2055. /* WORK(IVT) is M by M */
  2056. ldwkvt = *m;
  2057. itau = ivt + ldwkvt * *m;
  2058. nwork = itau + *m;
  2059. /* Compute A=L*Q, copying result to VT */
  2060. /* CWorkspace: need M*M [VT] + M [tau] + M [work] */
  2061. /* CWorkspace: prefer M*M [VT] + M [tau] + M*NB [work] */
  2062. /* RWorkspace: need 0 */
  2063. i__1 = *lwork - nwork + 1;
  2064. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  2065. i__1, &ierr);
  2066. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2067. /* Generate Q in VT */
  2068. /* CWorkspace: need M*M [VT] + M [tau] + N [work] */
  2069. /* CWorkspace: prefer M*M [VT] + M [tau] + N*NB [work] */
  2070. /* RWorkspace: need 0 */
  2071. i__1 = *lwork - nwork + 1;
  2072. cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[
  2073. nwork], &i__1, &ierr);
  2074. /* Produce L in A, zeroing out above it */
  2075. i__1 = *m - 1;
  2076. i__2 = *m - 1;
  2077. claset_("U", &i__1, &i__2, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
  2078. , lda);
  2079. ie = 1;
  2080. itauq = itau;
  2081. itaup = itauq + *m;
  2082. nwork = itaup + *m;
  2083. /* Bidiagonalize L in A */
  2084. /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
  2085. /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + 2*M*NB [work] */
  2086. /* RWorkspace: need M [e] */
  2087. i__1 = *lwork - nwork + 1;
  2088. cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  2089. itauq], &work[itaup], &work[nwork], &i__1, &ierr);
  2090. /* Perform bidiagonal SVD, computing left singular vectors */
  2091. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2092. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2093. /* CWorkspace: need 0 */
  2094. /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
  2095. iru = ie + *m;
  2096. irvt = iru + *m * *m;
  2097. nrwork = irvt + *m * *m;
  2098. sbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2099. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2100. info);
  2101. /* Copy real matrix RWORK(IRU) to complex matrix U */
  2102. /* Overwrite U by left singular vectors of L */
  2103. /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
  2104. /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + M*NB [work] */
  2105. /* RWorkspace: need 0 */
  2106. clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  2107. i__1 = *lwork - nwork + 1;
  2108. cunmbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[
  2109. itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
  2110. /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
  2111. /* Overwrite WORK(IVT) by right singular vectors of L */
  2112. /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
  2113. /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + M*NB [work] */
  2114. /* RWorkspace: need 0 */
  2115. clacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
  2116. i__1 = *lwork - nwork + 1;
  2117. cunmbr_("P", "R", "C", m, m, m, &a[a_offset], lda, &work[
  2118. itaup], &work[ivt], &ldwkvt, &work[nwork], &i__1, &
  2119. ierr);
  2120. /* Multiply right singular vectors of L in WORK(IVT) by */
  2121. /* Q in VT, storing result in A */
  2122. /* CWorkspace: need M*M [VT] */
  2123. /* RWorkspace: need 0 */
  2124. cgemm_("N", "N", m, n, m, &c_b2, &work[ivt], &ldwkvt, &vt[
  2125. vt_offset], ldvt, &c_b1, &a[a_offset], lda);
  2126. /* Copy right singular vectors of A from A to VT */
  2127. clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2128. }
  2129. } else if (*n >= mnthr2) {
  2130. /* MNTHR2 <= N < MNTHR1 */
  2131. /* Path 5t (N >> M, but not as much as MNTHR1) */
  2132. /* Reduce to bidiagonal form without QR decomposition, use */
  2133. /* CUNGBR and matrix multiplication to compute singular vectors */
  2134. ie = 1;
  2135. nrwork = ie + *m;
  2136. itauq = 1;
  2137. itaup = itauq + *m;
  2138. nwork = itaup + *m;
  2139. /* Bidiagonalize A */
  2140. /* CWorkspace: need 2*M [tauq, taup] + N [work] */
  2141. /* CWorkspace: prefer 2*M [tauq, taup] + (M+N)*NB [work] */
  2142. /* RWorkspace: need M [e] */
  2143. i__1 = *lwork - nwork + 1;
  2144. cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  2145. &work[itaup], &work[nwork], &i__1, &ierr);
  2146. if (wntqn) {
  2147. /* Path 5tn (N >> M, JOBZ='N') */
  2148. /* Compute singular values only */
  2149. /* CWorkspace: need 0 */
  2150. /* RWorkspace: need M [e] + BDSPAC */
  2151. sbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
  2152. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  2153. } else if (wntqo) {
  2154. irvt = nrwork;
  2155. iru = irvt + *m * *m;
  2156. nrwork = iru + *m * *m;
  2157. ivt = nwork;
  2158. /* Path 5to (N >> M, JOBZ='O') */
  2159. /* Copy A to U, generate Q */
  2160. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2161. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2162. /* RWorkspace: need 0 */
  2163. clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2164. i__1 = *lwork - nwork + 1;
  2165. cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  2166. nwork], &i__1, &ierr);
  2167. /* Generate P**H in A */
  2168. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2169. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2170. /* RWorkspace: need 0 */
  2171. i__1 = *lwork - nwork + 1;
  2172. cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
  2173. nwork], &i__1, &ierr);
  2174. ldwkvt = *m;
  2175. if (*lwork >= *m * *n + *m * 3) {
  2176. /* WORK( IVT ) is M by N */
  2177. nwork = ivt + ldwkvt * *n;
  2178. chunk = *n;
  2179. } else {
  2180. /* WORK( IVT ) is M by CHUNK */
  2181. chunk = (*lwork - *m * 3) / *m;
  2182. nwork = ivt + ldwkvt * chunk;
  2183. }
  2184. /* Perform bidiagonal SVD, computing left singular vectors */
  2185. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2186. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2187. /* CWorkspace: need 0 */
  2188. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2189. sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2190. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2191. info);
  2192. /* Multiply Q in U by real matrix RWORK(IRVT) */
  2193. /* storing the result in WORK(IVT), copying to U */
  2194. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
  2195. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
  2196. clacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &work[ivt], &
  2197. ldwkvt, &rwork[nrwork]);
  2198. clacpy_("F", m, m, &work[ivt], &ldwkvt, &u[u_offset], ldu);
  2199. /* Multiply RWORK(IRVT) by P**H in A, storing the */
  2200. /* result in WORK(IVT), copying to A */
  2201. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
  2202. /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] */
  2203. /* RWorkspace: need M [e] + M*M [RVT] + 2*M*M [rwork] */
  2204. /* RWorkspace: prefer M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
  2205. nrwork = iru;
  2206. i__1 = *n;
  2207. i__2 = chunk;
  2208. for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
  2209. i__2) {
  2210. /* Computing MIN */
  2211. i__3 = *n - i__ + 1;
  2212. blk = f2cmin(i__3,chunk);
  2213. clarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1],
  2214. lda, &work[ivt], &ldwkvt, &rwork[nrwork]);
  2215. clacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ *
  2216. a_dim1 + 1], lda);
  2217. /* L50: */
  2218. }
  2219. } else if (wntqs) {
  2220. /* Path 5ts (N >> M, JOBZ='S') */
  2221. /* Copy A to U, generate Q */
  2222. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2223. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2224. /* RWorkspace: need 0 */
  2225. clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2226. i__2 = *lwork - nwork + 1;
  2227. cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  2228. nwork], &i__2, &ierr);
  2229. /* Copy A to VT, generate P**H */
  2230. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2231. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2232. /* RWorkspace: need 0 */
  2233. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2234. i__2 = *lwork - nwork + 1;
  2235. cungbr_("P", m, n, m, &vt[vt_offset], ldvt, &work[itaup], &
  2236. work[nwork], &i__2, &ierr);
  2237. /* Perform bidiagonal SVD, computing left singular vectors */
  2238. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2239. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2240. /* CWorkspace: need 0 */
  2241. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2242. irvt = nrwork;
  2243. iru = irvt + *m * *m;
  2244. nrwork = iru + *m * *m;
  2245. sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2246. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2247. info);
  2248. /* Multiply Q in U by real matrix RWORK(IRU), storing the */
  2249. /* result in A, copying to U */
  2250. /* CWorkspace: need 0 */
  2251. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
  2252. clacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset],
  2253. lda, &rwork[nrwork]);
  2254. clacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2255. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  2256. /* storing the result in A, copying to VT */
  2257. /* CWorkspace: need 0 */
  2258. /* RWorkspace: need M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
  2259. nrwork = iru;
  2260. clarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[
  2261. a_offset], lda, &rwork[nrwork]);
  2262. clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2263. } else {
  2264. /* Path 5ta (N >> M, JOBZ='A') */
  2265. /* Copy A to U, generate Q */
  2266. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2267. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2268. /* RWorkspace: need 0 */
  2269. clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2270. i__2 = *lwork - nwork + 1;
  2271. cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  2272. nwork], &i__2, &ierr);
  2273. /* Copy A to VT, generate P**H */
  2274. /* CWorkspace: need 2*M [tauq, taup] + N [work] */
  2275. /* CWorkspace: prefer 2*M [tauq, taup] + N*NB [work] */
  2276. /* RWorkspace: need 0 */
  2277. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2278. i__2 = *lwork - nwork + 1;
  2279. cungbr_("P", n, n, m, &vt[vt_offset], ldvt, &work[itaup], &
  2280. work[nwork], &i__2, &ierr);
  2281. /* Perform bidiagonal SVD, computing left singular vectors */
  2282. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2283. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2284. /* CWorkspace: need 0 */
  2285. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2286. irvt = nrwork;
  2287. iru = irvt + *m * *m;
  2288. nrwork = iru + *m * *m;
  2289. sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2290. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2291. info);
  2292. /* Multiply Q in U by real matrix RWORK(IRU), storing the */
  2293. /* result in A, copying to U */
  2294. /* CWorkspace: need 0 */
  2295. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
  2296. clacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset],
  2297. lda, &rwork[nrwork]);
  2298. clacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2299. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  2300. /* storing the result in A, copying to VT */
  2301. /* CWorkspace: need 0 */
  2302. /* RWorkspace: need M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
  2303. nrwork = iru;
  2304. clarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[
  2305. a_offset], lda, &rwork[nrwork]);
  2306. clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2307. }
  2308. } else {
  2309. /* N .LT. MNTHR2 */
  2310. /* Path 6t (N > M, but not much larger) */
  2311. /* Reduce to bidiagonal form without LQ decomposition */
  2312. /* Use CUNMBR to compute singular vectors */
  2313. ie = 1;
  2314. nrwork = ie + *m;
  2315. itauq = 1;
  2316. itaup = itauq + *m;
  2317. nwork = itaup + *m;
  2318. /* Bidiagonalize A */
  2319. /* CWorkspace: need 2*M [tauq, taup] + N [work] */
  2320. /* CWorkspace: prefer 2*M [tauq, taup] + (M+N)*NB [work] */
  2321. /* RWorkspace: need M [e] */
  2322. i__2 = *lwork - nwork + 1;
  2323. cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  2324. &work[itaup], &work[nwork], &i__2, &ierr);
  2325. if (wntqn) {
  2326. /* Path 6tn (N > M, JOBZ='N') */
  2327. /* Compute singular values only */
  2328. /* CWorkspace: need 0 */
  2329. /* RWorkspace: need M [e] + BDSPAC */
  2330. sbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
  2331. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  2332. } else if (wntqo) {
  2333. /* Path 6to (N > M, JOBZ='O') */
  2334. ldwkvt = *m;
  2335. ivt = nwork;
  2336. if (*lwork >= *m * *n + *m * 3) {
  2337. /* WORK( IVT ) is M by N */
  2338. claset_("F", m, n, &c_b1, &c_b1, &work[ivt], &ldwkvt);
  2339. nwork = ivt + ldwkvt * *n;
  2340. } else {
  2341. /* WORK( IVT ) is M by CHUNK */
  2342. chunk = (*lwork - *m * 3) / *m;
  2343. nwork = ivt + ldwkvt * chunk;
  2344. }
  2345. /* Perform bidiagonal SVD, computing left singular vectors */
  2346. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2347. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2348. /* CWorkspace: need 0 */
  2349. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2350. irvt = nrwork;
  2351. iru = irvt + *m * *m;
  2352. nrwork = iru + *m * *m;
  2353. sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2354. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2355. info);
  2356. /* Copy real matrix RWORK(IRU) to complex matrix U */
  2357. /* Overwrite U by left singular vectors of A */
  2358. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] + M [work] */
  2359. /* CWorkspace: prefer 2*M [tauq, taup] + M*M [VT] + M*NB [work] */
  2360. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
  2361. clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  2362. i__2 = *lwork - nwork + 1;
  2363. cunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
  2364. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  2365. if (*lwork >= *m * *n + *m * 3) {
  2366. /* Path 6to-fast */
  2367. /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
  2368. /* Overwrite WORK(IVT) by right singular vectors of A, */
  2369. /* copying to A */
  2370. /* CWorkspace: need 2*M [tauq, taup] + M*N [VT] + M [work] */
  2371. /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] + M*NB [work] */
  2372. /* RWorkspace: need M [e] + M*M [RVT] */
  2373. clacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
  2374. i__2 = *lwork - nwork + 1;
  2375. cunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[
  2376. itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2,
  2377. &ierr);
  2378. clacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda);
  2379. } else {
  2380. /* Path 6to-slow */
  2381. /* Generate P**H in A */
  2382. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] + M [work] */
  2383. /* CWorkspace: prefer 2*M [tauq, taup] + M*M [VT] + M*NB [work] */
  2384. /* RWorkspace: need 0 */
  2385. i__2 = *lwork - nwork + 1;
  2386. cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
  2387. work[nwork], &i__2, &ierr);
  2388. /* Multiply Q in A by real matrix RWORK(IRU), storing the */
  2389. /* result in WORK(IU), copying to A */
  2390. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
  2391. /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] */
  2392. /* RWorkspace: need M [e] + M*M [RVT] + 2*M*M [rwork] */
  2393. /* RWorkspace: prefer M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
  2394. nrwork = iru;
  2395. i__2 = *n;
  2396. i__1 = chunk;
  2397. for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
  2398. i__1) {
  2399. /* Computing MIN */
  2400. i__3 = *n - i__ + 1;
  2401. blk = f2cmin(i__3,chunk);
  2402. clarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1]
  2403. , lda, &work[ivt], &ldwkvt, &rwork[nrwork]);
  2404. clacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ *
  2405. a_dim1 + 1], lda);
  2406. /* L60: */
  2407. }
  2408. }
  2409. } else if (wntqs) {
  2410. /* Path 6ts (N > M, JOBZ='S') */
  2411. /* Perform bidiagonal SVD, computing left singular vectors */
  2412. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2413. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2414. /* CWorkspace: need 0 */
  2415. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2416. irvt = nrwork;
  2417. iru = irvt + *m * *m;
  2418. nrwork = iru + *m * *m;
  2419. sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2420. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2421. info);
  2422. /* Copy real matrix RWORK(IRU) to complex matrix U */
  2423. /* Overwrite U by left singular vectors of A */
  2424. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2425. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2426. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
  2427. clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  2428. i__1 = *lwork - nwork + 1;
  2429. cunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
  2430. itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
  2431. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  2432. /* Overwrite VT by right singular vectors of A */
  2433. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2434. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2435. /* RWorkspace: need M [e] + M*M [RVT] */
  2436. claset_("F", m, n, &c_b1, &c_b1, &vt[vt_offset], ldvt);
  2437. clacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
  2438. i__1 = *lwork - nwork + 1;
  2439. cunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[
  2440. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  2441. ierr);
  2442. } else {
  2443. /* Path 6ta (N > M, JOBZ='A') */
  2444. /* Perform bidiagonal SVD, computing left singular vectors */
  2445. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2446. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2447. /* CWorkspace: need 0 */
  2448. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2449. irvt = nrwork;
  2450. iru = irvt + *m * *m;
  2451. nrwork = iru + *m * *m;
  2452. sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2453. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2454. info);
  2455. /* Copy real matrix RWORK(IRU) to complex matrix U */
  2456. /* Overwrite U by left singular vectors of A */
  2457. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2458. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2459. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
  2460. clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  2461. i__1 = *lwork - nwork + 1;
  2462. cunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
  2463. itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
  2464. /* Set all of VT to identity matrix */
  2465. claset_("F", n, n, &c_b1, &c_b2, &vt[vt_offset], ldvt);
  2466. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  2467. /* Overwrite VT by right singular vectors of A */
  2468. /* CWorkspace: need 2*M [tauq, taup] + N [work] */
  2469. /* CWorkspace: prefer 2*M [tauq, taup] + N*NB [work] */
  2470. /* RWorkspace: need M [e] + M*M [RVT] */
  2471. clacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
  2472. i__1 = *lwork - nwork + 1;
  2473. cunmbr_("P", "R", "C", n, n, m, &a[a_offset], lda, &work[
  2474. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  2475. ierr);
  2476. }
  2477. }
  2478. }
  2479. /* Undo scaling if necessary */
  2480. if (iscl == 1) {
  2481. if (anrm > bignum) {
  2482. slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
  2483. minmn, &ierr);
  2484. }
  2485. if (*info != 0 && anrm > bignum) {
  2486. i__1 = minmn - 1;
  2487. slascl_("G", &c__0, &c__0, &bignum, &anrm, &i__1, &c__1, &rwork[
  2488. ie], &minmn, &ierr);
  2489. }
  2490. if (anrm < smlnum) {
  2491. slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
  2492. minmn, &ierr);
  2493. }
  2494. if (*info != 0 && anrm < smlnum) {
  2495. i__1 = minmn - 1;
  2496. slascl_("G", &c__0, &c__0, &smlnum, &anrm, &i__1, &c__1, &rwork[
  2497. ie], &minmn, &ierr);
  2498. }
  2499. }
  2500. /* Return optimal workspace in WORK(1) */
  2501. work[1].r = (real) maxwrk, work[1].i = 0.f;
  2502. return;
  2503. /* End of CGESDD */
  2504. } /* cgesdd_ */