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