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zgesdd.c 104 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 doublecomplex c_b1 = {0.,0.};
  485. static doublecomplex c_b2 = {1.,0.};
  486. static integer c_n1 = -1;
  487. static integer c__0 = 0;
  488. static integer c__1 = 1;
  489. /* > \brief \b ZGESDD */
  490. /* =========== DOCUMENTATION =========== */
  491. /* Online html documentation available at */
  492. /* http://www.netlib.org/lapack/explore-html/ */
  493. /* > \htmlonly */
  494. /* > Download ZGESDD + dependencies */
  495. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgesdd.
  496. f"> */
  497. /* > [TGZ]</a> */
  498. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgesdd.
  499. f"> */
  500. /* > [ZIP]</a> */
  501. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgesdd.
  502. f"> */
  503. /* > [TXT]</a> */
  504. /* > \endhtmlonly */
  505. /* Definition: */
  506. /* =========== */
  507. /* SUBROUTINE ZGESDD( 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. /* DOUBLE PRECISION RWORK( * ), S( * ) */
  513. /* COMPLEX*16 A( LDA, * ), U( LDU, * ), VT( LDVT, * ), */
  514. /* $ WORK( * ) */
  515. /* > \par Purpose: */
  516. /* ============= */
  517. /* > */
  518. /* > \verbatim */
  519. /* > */
  520. /* > ZGESDD 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*16 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 DOUBLE PRECISION 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*16 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*16 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*16 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 DOUBLE PRECISION 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 DBDSDC 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 complex16GEsing */
  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 zgesdd_(char *jobz, integer *m, integer *n,
  699. doublecomplex *a, integer *lda, doublereal *s, doublecomplex *u,
  700. integer *ldu, doublecomplex *vt, integer *ldvt, doublecomplex *work,
  701. integer *lwork, doublereal *rwork, integer *iwork, 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_zgebrd_mm__, lwork_zgebrd_mn__, lwork_zgebrd_nn__,
  708. lwork_zgelqf_mn__, lwork_zgeqrf_mn__;
  709. doublecomplex cdum[1];
  710. integer iscl;
  711. doublereal anrm;
  712. integer idum[1], ierr, itau, lwork_zunglq_mn__, lwork_zunglq_nn__,
  713. lwork_zungqr_mm__, lwork_zungqr_mn__, irvt, lwork_zunmbr_prc_mm__,
  714. lwork_zunmbr_prc_mn__, lwork_zunmbr_prc_nn__,
  715. lwork_zunmbr_qln_mm__, lwork_zunmbr_qln_mn__,
  716. lwork_zunmbr_qln_nn__, i__;
  717. extern logical lsame_(char *, char *);
  718. integer chunk, minmn;
  719. extern /* Subroutine */ void zgemm_(char *, char *, integer *, integer *,
  720. integer *, doublecomplex *, doublecomplex *, integer *,
  721. doublecomplex *, integer *, doublecomplex *, doublecomplex *,
  722. integer *);
  723. integer wrkbl, itaup, itauq;
  724. logical wntqa;
  725. integer nwork;
  726. logical wntqn, wntqo, wntqs;
  727. extern /* Subroutine */ void zlacp2_(char *, integer *, integer *,
  728. doublereal *, integer *, doublecomplex *, integer *);
  729. integer mnthr1, mnthr2, ie;
  730. extern /* Subroutine */ void dbdsdc_(char *, char *, integer *, doublereal
  731. *, doublereal *, doublereal *, integer *, doublereal *, integer *,
  732. doublereal *, integer *, doublereal *, integer *, integer *);
  733. integer il;
  734. extern doublereal dlamch_(char *);
  735. integer ir, iu;
  736. extern /* Subroutine */ void dlascl_(char *, integer *, integer *,
  737. doublereal *, doublereal *, integer *, integer *, doublereal *,
  738. integer *, integer *);
  739. integer lwork_zungbr_p_mn__, lwork_zungbr_p_nn__, lwork_zungbr_q_mn__,
  740. lwork_zungbr_q_mm__;
  741. extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
  742. doublereal bignum;
  743. extern /* Subroutine */ void zgebrd_(integer *, integer *, doublecomplex *,
  744. integer *, doublereal *, doublereal *, doublecomplex *,
  745. doublecomplex *, doublecomplex *, integer *, integer *);
  746. extern logical disnan_(doublereal *);
  747. extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
  748. integer *, doublereal *);
  749. extern /* Subroutine */ void zgelqf_(integer *, integer *, doublecomplex *,
  750. integer *, doublecomplex *, doublecomplex *, integer *, integer *
  751. ), zlacrm_(integer *, integer *, doublecomplex *, integer *,
  752. doublereal *, integer *, doublecomplex *, integer *, doublereal *)
  753. , zlarcm_(integer *, integer *, doublereal *, integer *,
  754. doublecomplex *, integer *, doublecomplex *, integer *,
  755. doublereal *), zlascl_(char *, integer *, integer *, doublereal *,
  756. doublereal *, integer *, integer *, doublecomplex *, integer *,
  757. integer *), zgeqrf_(integer *, integer *, doublecomplex *,
  758. integer *, doublecomplex *, doublecomplex *, integer *, integer *
  759. );
  760. integer ldwrkl;
  761. extern /* Subroutine */ void zlacpy_(char *, integer *, integer *,
  762. doublecomplex *, integer *, doublecomplex *, integer *),
  763. zlaset_(char *, integer *, integer *, doublecomplex *,
  764. doublecomplex *, doublecomplex *, integer *);
  765. integer ldwrkr, minwrk, ldwrku, maxwrk;
  766. extern /* Subroutine */ void zungbr_(char *, integer *, integer *, integer
  767. *, doublecomplex *, integer *, doublecomplex *, doublecomplex *,
  768. integer *, integer *);
  769. integer ldwkvt;
  770. doublereal smlnum;
  771. logical wntqas;
  772. extern /* Subroutine */ void zunmbr_(char *, char *, char *, integer *,
  773. integer *, integer *, doublecomplex *, integer *, doublecomplex *,
  774. doublecomplex *, integer *, doublecomplex *, integer *, integer *
  775. ), zunglq_(integer *, integer *, integer *
  776. , doublecomplex *, integer *, doublecomplex *, doublecomplex *,
  777. integer *, integer *);
  778. logical lquery;
  779. integer nrwork;
  780. extern /* Subroutine */ void zungqr_(integer *, integer *, integer *,
  781. doublecomplex *, integer *, doublecomplex *, doublecomplex *,
  782. integer *, integer *);
  783. integer blk;
  784. doublereal dum[1], eps;
  785. integer iru, ivt;
  786. /* -- LAPACK driver routine (version 3.7.0) -- */
  787. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  788. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  789. /* June 2016 */
  790. /* ===================================================================== */
  791. /* Test the input arguments */
  792. /* Parameter adjustments */
  793. a_dim1 = *lda;
  794. a_offset = 1 + a_dim1 * 1;
  795. a -= a_offset;
  796. --s;
  797. u_dim1 = *ldu;
  798. u_offset = 1 + u_dim1 * 1;
  799. u -= u_offset;
  800. vt_dim1 = *ldvt;
  801. vt_offset = 1 + vt_dim1 * 1;
  802. vt -= vt_offset;
  803. --work;
  804. --rwork;
  805. --iwork;
  806. /* Function Body */
  807. *info = 0;
  808. minmn = f2cmin(*m,*n);
  809. mnthr1 = (integer) (minmn * 17. / 9.);
  810. mnthr2 = (integer) (minmn * 5. / 3.);
  811. wntqa = lsame_(jobz, "A");
  812. wntqs = lsame_(jobz, "S");
  813. wntqas = wntqa || wntqs;
  814. wntqo = lsame_(jobz, "O");
  815. wntqn = lsame_(jobz, "N");
  816. lquery = *lwork == -1;
  817. minwrk = 1;
  818. maxwrk = 1;
  819. if (! (wntqa || wntqs || wntqo || wntqn)) {
  820. *info = -1;
  821. } else if (*m < 0) {
  822. *info = -2;
  823. } else if (*n < 0) {
  824. *info = -3;
  825. } else if (*lda < f2cmax(1,*m)) {
  826. *info = -5;
  827. } else if (*ldu < 1 || wntqas && *ldu < *m || wntqo && *m < *n && *ldu < *
  828. m) {
  829. *info = -8;
  830. } else if (*ldvt < 1 || wntqa && *ldvt < *n || wntqs && *ldvt < minmn ||
  831. wntqo && *m >= *n && *ldvt < *n) {
  832. *info = -10;
  833. }
  834. /* Compute workspace */
  835. /* Note: Comments in the code beginning "Workspace:" describe the */
  836. /* minimal amount of workspace allocated at that point in the code, */
  837. /* as well as the preferred amount for good performance. */
  838. /* CWorkspace refers to complex workspace, and RWorkspace to */
  839. /* real workspace. NB refers to the optimal block size for the */
  840. /* immediately following subroutine, as returned by ILAENV.) */
  841. if (*info == 0) {
  842. minwrk = 1;
  843. maxwrk = 1;
  844. if (*m >= *n && minmn > 0) {
  845. /* There is no complex work space needed for bidiagonal SVD */
  846. /* The real work space needed for bidiagonal SVD (dbdsdc) is */
  847. /* BDSPAC = 3*N*N + 4*N for singular values and vectors; */
  848. /* BDSPAC = 4*N for singular values only; */
  849. /* not including e, RU, and RVT matrices. */
  850. /* Compute space preferred for each routine */
  851. zgebrd_(m, n, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
  852. lwork_zgebrd_mn__ = (integer) cdum[0].r;
  853. zgebrd_(n, n, cdum, n, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
  854. lwork_zgebrd_nn__ = (integer) cdum[0].r;
  855. zgeqrf_(m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  856. lwork_zgeqrf_mn__ = (integer) cdum[0].r;
  857. zungbr_("P", n, n, n, cdum, n, cdum, cdum, &c_n1, &ierr);
  858. lwork_zungbr_p_nn__ = (integer) cdum[0].r;
  859. zungbr_("Q", m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  860. lwork_zungbr_q_mm__ = (integer) cdum[0].r;
  861. zungbr_("Q", m, n, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  862. lwork_zungbr_q_mn__ = (integer) cdum[0].r;
  863. zungqr_(m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  864. lwork_zungqr_mm__ = (integer) cdum[0].r;
  865. zungqr_(m, n, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  866. lwork_zungqr_mn__ = (integer) cdum[0].r;
  867. zunmbr_("P", "R", "C", n, n, n, cdum, n, cdum, cdum, n, cdum, &
  868. c_n1, &ierr);
  869. lwork_zunmbr_prc_nn__ = (integer) cdum[0].r;
  870. zunmbr_("Q", "L", "N", m, m, n, cdum, m, cdum, cdum, m, cdum, &
  871. c_n1, &ierr);
  872. lwork_zunmbr_qln_mm__ = (integer) cdum[0].r;
  873. zunmbr_("Q", "L", "N", m, n, n, cdum, m, cdum, cdum, m, cdum, &
  874. c_n1, &ierr);
  875. lwork_zunmbr_qln_mn__ = (integer) cdum[0].r;
  876. zunmbr_("Q", "L", "N", n, n, n, cdum, n, cdum, cdum, n, cdum, &
  877. c_n1, &ierr);
  878. lwork_zunmbr_qln_nn__ = (integer) cdum[0].r;
  879. if (*m >= mnthr1) {
  880. if (wntqn) {
  881. /* Path 1 (M >> N, JOBZ='N') */
  882. maxwrk = *n + lwork_zgeqrf_mn__;
  883. /* Computing MAX */
  884. i__1 = maxwrk, i__2 = (*n << 1) + lwork_zgebrd_nn__;
  885. maxwrk = f2cmax(i__1,i__2);
  886. minwrk = *n * 3;
  887. } else if (wntqo) {
  888. /* Path 2 (M >> N, JOBZ='O') */
  889. wrkbl = *n + lwork_zgeqrf_mn__;
  890. /* Computing MAX */
  891. i__1 = wrkbl, i__2 = *n + lwork_zungqr_mn__;
  892. wrkbl = f2cmax(i__1,i__2);
  893. /* Computing MAX */
  894. i__1 = wrkbl, i__2 = (*n << 1) + lwork_zgebrd_nn__;
  895. wrkbl = f2cmax(i__1,i__2);
  896. /* Computing MAX */
  897. i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_qln_nn__;
  898. wrkbl = f2cmax(i__1,i__2);
  899. /* Computing MAX */
  900. i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__;
  901. wrkbl = f2cmax(i__1,i__2);
  902. maxwrk = *m * *n + *n * *n + wrkbl;
  903. minwrk = (*n << 1) * *n + *n * 3;
  904. } else if (wntqs) {
  905. /* Path 3 (M >> N, JOBZ='S') */
  906. wrkbl = *n + lwork_zgeqrf_mn__;
  907. /* Computing MAX */
  908. i__1 = wrkbl, i__2 = *n + lwork_zungqr_mn__;
  909. wrkbl = f2cmax(i__1,i__2);
  910. /* Computing MAX */
  911. i__1 = wrkbl, i__2 = (*n << 1) + lwork_zgebrd_nn__;
  912. wrkbl = f2cmax(i__1,i__2);
  913. /* Computing MAX */
  914. i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_qln_nn__;
  915. wrkbl = f2cmax(i__1,i__2);
  916. /* Computing MAX */
  917. i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__;
  918. wrkbl = f2cmax(i__1,i__2);
  919. maxwrk = *n * *n + wrkbl;
  920. minwrk = *n * *n + *n * 3;
  921. } else if (wntqa) {
  922. /* Path 4 (M >> N, JOBZ='A') */
  923. wrkbl = *n + lwork_zgeqrf_mn__;
  924. /* Computing MAX */
  925. i__1 = wrkbl, i__2 = *n + lwork_zungqr_mm__;
  926. wrkbl = f2cmax(i__1,i__2);
  927. /* Computing MAX */
  928. i__1 = wrkbl, i__2 = (*n << 1) + lwork_zgebrd_nn__;
  929. wrkbl = f2cmax(i__1,i__2);
  930. /* Computing MAX */
  931. i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_qln_nn__;
  932. wrkbl = f2cmax(i__1,i__2);
  933. /* Computing MAX */
  934. i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__;
  935. wrkbl = f2cmax(i__1,i__2);
  936. maxwrk = *n * *n + wrkbl;
  937. /* Computing MAX */
  938. i__1 = *n * 3, i__2 = *n + *m;
  939. minwrk = *n * *n + f2cmax(i__1,i__2);
  940. }
  941. } else if (*m >= mnthr2) {
  942. /* Path 5 (M >> N, but not as much as MNTHR1) */
  943. maxwrk = (*n << 1) + lwork_zgebrd_mn__;
  944. minwrk = (*n << 1) + *m;
  945. if (wntqo) {
  946. /* Path 5o (M >> N, JOBZ='O') */
  947. /* Computing MAX */
  948. i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_p_nn__;
  949. maxwrk = f2cmax(i__1,i__2);
  950. /* Computing MAX */
  951. i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_q_mn__;
  952. maxwrk = f2cmax(i__1,i__2);
  953. maxwrk += *m * *n;
  954. minwrk += *n * *n;
  955. } else if (wntqs) {
  956. /* Path 5s (M >> N, JOBZ='S') */
  957. /* Computing MAX */
  958. i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_p_nn__;
  959. maxwrk = f2cmax(i__1,i__2);
  960. /* Computing MAX */
  961. i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_q_mn__;
  962. maxwrk = f2cmax(i__1,i__2);
  963. } else if (wntqa) {
  964. /* Path 5a (M >> N, JOBZ='A') */
  965. /* Computing MAX */
  966. i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_p_nn__;
  967. maxwrk = f2cmax(i__1,i__2);
  968. /* Computing MAX */
  969. i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_q_mm__;
  970. maxwrk = f2cmax(i__1,i__2);
  971. }
  972. } else {
  973. /* Path 6 (M >= N, but not much larger) */
  974. maxwrk = (*n << 1) + lwork_zgebrd_mn__;
  975. minwrk = (*n << 1) + *m;
  976. if (wntqo) {
  977. /* Path 6o (M >= N, JOBZ='O') */
  978. /* Computing MAX */
  979. i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__;
  980. maxwrk = f2cmax(i__1,i__2);
  981. /* Computing MAX */
  982. i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_qln_mn__;
  983. maxwrk = f2cmax(i__1,i__2);
  984. maxwrk += *m * *n;
  985. minwrk += *n * *n;
  986. } else if (wntqs) {
  987. /* Path 6s (M >= N, JOBZ='S') */
  988. /* Computing MAX */
  989. i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_qln_mn__;
  990. maxwrk = f2cmax(i__1,i__2);
  991. /* Computing MAX */
  992. i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__;
  993. maxwrk = f2cmax(i__1,i__2);
  994. } else if (wntqa) {
  995. /* Path 6a (M >= N, JOBZ='A') */
  996. /* Computing MAX */
  997. i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_qln_mm__;
  998. maxwrk = f2cmax(i__1,i__2);
  999. /* Computing MAX */
  1000. i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__;
  1001. maxwrk = f2cmax(i__1,i__2);
  1002. }
  1003. }
  1004. } else if (minmn > 0) {
  1005. /* There is no complex work space needed for bidiagonal SVD */
  1006. /* The real work space needed for bidiagonal SVD (dbdsdc) is */
  1007. /* BDSPAC = 3*M*M + 4*M for singular values and vectors; */
  1008. /* BDSPAC = 4*M for singular values only; */
  1009. /* not including e, RU, and RVT matrices. */
  1010. /* Compute space preferred for each routine */
  1011. zgebrd_(m, n, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
  1012. lwork_zgebrd_mn__ = (integer) cdum[0].r;
  1013. zgebrd_(m, m, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
  1014. lwork_zgebrd_mm__ = (integer) cdum[0].r;
  1015. zgelqf_(m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  1016. lwork_zgelqf_mn__ = (integer) cdum[0].r;
  1017. zungbr_("P", m, n, m, cdum, m, cdum, cdum, &c_n1, &ierr);
  1018. lwork_zungbr_p_mn__ = (integer) cdum[0].r;
  1019. zungbr_("P", n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
  1020. lwork_zungbr_p_nn__ = (integer) cdum[0].r;
  1021. zungbr_("Q", m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  1022. lwork_zungbr_q_mm__ = (integer) cdum[0].r;
  1023. zunglq_(m, n, m, cdum, m, cdum, cdum, &c_n1, &ierr);
  1024. lwork_zunglq_mn__ = (integer) cdum[0].r;
  1025. zunglq_(n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
  1026. lwork_zunglq_nn__ = (integer) cdum[0].r;
  1027. zunmbr_("P", "R", "C", m, m, m, cdum, m, cdum, cdum, m, cdum, &
  1028. c_n1, &ierr);
  1029. lwork_zunmbr_prc_mm__ = (integer) cdum[0].r;
  1030. zunmbr_("P", "R", "C", m, n, m, cdum, m, cdum, cdum, m, cdum, &
  1031. c_n1, &ierr);
  1032. lwork_zunmbr_prc_mn__ = (integer) cdum[0].r;
  1033. zunmbr_("P", "R", "C", n, n, m, cdum, n, cdum, cdum, n, cdum, &
  1034. c_n1, &ierr);
  1035. lwork_zunmbr_prc_nn__ = (integer) cdum[0].r;
  1036. zunmbr_("Q", "L", "N", m, m, m, cdum, m, cdum, cdum, m, cdum, &
  1037. c_n1, &ierr);
  1038. lwork_zunmbr_qln_mm__ = (integer) cdum[0].r;
  1039. if (*n >= mnthr1) {
  1040. if (wntqn) {
  1041. /* Path 1t (N >> M, JOBZ='N') */
  1042. maxwrk = *m + lwork_zgelqf_mn__;
  1043. /* Computing MAX */
  1044. i__1 = maxwrk, i__2 = (*m << 1) + lwork_zgebrd_mm__;
  1045. maxwrk = f2cmax(i__1,i__2);
  1046. minwrk = *m * 3;
  1047. } else if (wntqo) {
  1048. /* Path 2t (N >> M, JOBZ='O') */
  1049. wrkbl = *m + lwork_zgelqf_mn__;
  1050. /* Computing MAX */
  1051. i__1 = wrkbl, i__2 = *m + lwork_zunglq_mn__;
  1052. wrkbl = f2cmax(i__1,i__2);
  1053. /* Computing MAX */
  1054. i__1 = wrkbl, i__2 = (*m << 1) + lwork_zgebrd_mm__;
  1055. wrkbl = f2cmax(i__1,i__2);
  1056. /* Computing MAX */
  1057. i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__;
  1058. wrkbl = f2cmax(i__1,i__2);
  1059. /* Computing MAX */
  1060. i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_prc_mm__;
  1061. wrkbl = f2cmax(i__1,i__2);
  1062. maxwrk = *m * *n + *m * *m + wrkbl;
  1063. minwrk = (*m << 1) * *m + *m * 3;
  1064. } else if (wntqs) {
  1065. /* Path 3t (N >> M, JOBZ='S') */
  1066. wrkbl = *m + lwork_zgelqf_mn__;
  1067. /* Computing MAX */
  1068. i__1 = wrkbl, i__2 = *m + lwork_zunglq_mn__;
  1069. wrkbl = f2cmax(i__1,i__2);
  1070. /* Computing MAX */
  1071. i__1 = wrkbl, i__2 = (*m << 1) + lwork_zgebrd_mm__;
  1072. wrkbl = f2cmax(i__1,i__2);
  1073. /* Computing MAX */
  1074. i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__;
  1075. wrkbl = f2cmax(i__1,i__2);
  1076. /* Computing MAX */
  1077. i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_prc_mm__;
  1078. wrkbl = f2cmax(i__1,i__2);
  1079. maxwrk = *m * *m + wrkbl;
  1080. minwrk = *m * *m + *m * 3;
  1081. } else if (wntqa) {
  1082. /* Path 4t (N >> M, JOBZ='A') */
  1083. wrkbl = *m + lwork_zgelqf_mn__;
  1084. /* Computing MAX */
  1085. i__1 = wrkbl, i__2 = *m + lwork_zunglq_nn__;
  1086. wrkbl = f2cmax(i__1,i__2);
  1087. /* Computing MAX */
  1088. i__1 = wrkbl, i__2 = (*m << 1) + lwork_zgebrd_mm__;
  1089. wrkbl = f2cmax(i__1,i__2);
  1090. /* Computing MAX */
  1091. i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__;
  1092. wrkbl = f2cmax(i__1,i__2);
  1093. /* Computing MAX */
  1094. i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_prc_mm__;
  1095. wrkbl = f2cmax(i__1,i__2);
  1096. maxwrk = *m * *m + wrkbl;
  1097. /* Computing MAX */
  1098. i__1 = *m * 3, i__2 = *m + *n;
  1099. minwrk = *m * *m + f2cmax(i__1,i__2);
  1100. }
  1101. } else if (*n >= mnthr2) {
  1102. /* Path 5t (N >> M, but not as much as MNTHR1) */
  1103. maxwrk = (*m << 1) + lwork_zgebrd_mn__;
  1104. minwrk = (*m << 1) + *n;
  1105. if (wntqo) {
  1106. /* Path 5to (N >> M, JOBZ='O') */
  1107. /* Computing MAX */
  1108. i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_q_mm__;
  1109. maxwrk = f2cmax(i__1,i__2);
  1110. /* Computing MAX */
  1111. i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_p_mn__;
  1112. maxwrk = f2cmax(i__1,i__2);
  1113. maxwrk += *m * *n;
  1114. minwrk += *m * *m;
  1115. } else if (wntqs) {
  1116. /* Path 5ts (N >> M, JOBZ='S') */
  1117. /* Computing MAX */
  1118. i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_q_mm__;
  1119. maxwrk = f2cmax(i__1,i__2);
  1120. /* Computing MAX */
  1121. i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_p_mn__;
  1122. maxwrk = f2cmax(i__1,i__2);
  1123. } else if (wntqa) {
  1124. /* Path 5ta (N >> M, JOBZ='A') */
  1125. /* Computing MAX */
  1126. i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_q_mm__;
  1127. maxwrk = f2cmax(i__1,i__2);
  1128. /* Computing MAX */
  1129. i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_p_nn__;
  1130. maxwrk = f2cmax(i__1,i__2);
  1131. }
  1132. } else {
  1133. /* Path 6t (N > M, but not much larger) */
  1134. maxwrk = (*m << 1) + lwork_zgebrd_mn__;
  1135. minwrk = (*m << 1) + *n;
  1136. if (wntqo) {
  1137. /* Path 6to (N > M, JOBZ='O') */
  1138. /* Computing MAX */
  1139. i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__;
  1140. maxwrk = f2cmax(i__1,i__2);
  1141. /* Computing MAX */
  1142. i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_prc_mn__;
  1143. maxwrk = f2cmax(i__1,i__2);
  1144. maxwrk += *m * *n;
  1145. minwrk += *m * *m;
  1146. } else if (wntqs) {
  1147. /* Path 6ts (N > M, JOBZ='S') */
  1148. /* Computing MAX */
  1149. i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__;
  1150. maxwrk = f2cmax(i__1,i__2);
  1151. /* Computing MAX */
  1152. i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_prc_mn__;
  1153. maxwrk = f2cmax(i__1,i__2);
  1154. } else if (wntqa) {
  1155. /* Path 6ta (N > M, JOBZ='A') */
  1156. /* Computing MAX */
  1157. i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__;
  1158. maxwrk = f2cmax(i__1,i__2);
  1159. /* Computing MAX */
  1160. i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_prc_nn__;
  1161. maxwrk = f2cmax(i__1,i__2);
  1162. }
  1163. }
  1164. }
  1165. maxwrk = f2cmax(maxwrk,minwrk);
  1166. }
  1167. if (*info == 0) {
  1168. work[1].r = (doublereal) maxwrk, work[1].i = 0.;
  1169. if (*lwork < minwrk && ! lquery) {
  1170. *info = -12;
  1171. }
  1172. }
  1173. if (*info != 0) {
  1174. i__1 = -(*info);
  1175. xerbla_("ZGESDD", &i__1, (ftnlen)6);
  1176. return;
  1177. } else if (lquery) {
  1178. return;
  1179. }
  1180. /* Quick return if possible */
  1181. if (*m == 0 || *n == 0) {
  1182. return;
  1183. }
  1184. /* Get machine constants */
  1185. eps = dlamch_("P");
  1186. smlnum = sqrt(dlamch_("S")) / eps;
  1187. bignum = 1. / smlnum;
  1188. /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
  1189. anrm = zlange_("M", m, n, &a[a_offset], lda, dum);
  1190. if (disnan_(&anrm)) {
  1191. *info = -4;
  1192. return;
  1193. }
  1194. iscl = 0;
  1195. if (anrm > 0. && anrm < smlnum) {
  1196. iscl = 1;
  1197. zlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
  1198. ierr);
  1199. } else if (anrm > bignum) {
  1200. iscl = 1;
  1201. zlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &
  1202. ierr);
  1203. }
  1204. if (*m >= *n) {
  1205. /* A has at least as many rows as columns. If A has sufficiently */
  1206. /* more rows than columns, first reduce using the QR */
  1207. /* decomposition (if sufficient workspace available) */
  1208. if (*m >= mnthr1) {
  1209. if (wntqn) {
  1210. /* Path 1 (M >> N, JOBZ='N') */
  1211. /* No singular vectors to be computed */
  1212. itau = 1;
  1213. nwork = itau + *n;
  1214. /* Compute A=Q*R */
  1215. /* CWorkspace: need N [tau] + N [work] */
  1216. /* CWorkspace: prefer N [tau] + N*NB [work] */
  1217. /* RWorkspace: need 0 */
  1218. i__1 = *lwork - nwork + 1;
  1219. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1220. i__1, &ierr);
  1221. /* Zero out below R */
  1222. i__1 = *n - 1;
  1223. i__2 = *n - 1;
  1224. zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &a[a_dim1 + 2], lda);
  1225. ie = 1;
  1226. itauq = 1;
  1227. itaup = itauq + *n;
  1228. nwork = itaup + *n;
  1229. /* Bidiagonalize R in A */
  1230. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1231. /* CWorkspace: prefer 2*N [tauq, taup] + 2*N*NB [work] */
  1232. /* RWorkspace: need N [e] */
  1233. i__1 = *lwork - nwork + 1;
  1234. zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1235. itauq], &work[itaup], &work[nwork], &i__1, &ierr);
  1236. nrwork = ie + *n;
  1237. /* Perform bidiagonal SVD, compute singular values only */
  1238. /* CWorkspace: need 0 */
  1239. /* RWorkspace: need N [e] + BDSPAC */
  1240. dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
  1241. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  1242. } else if (wntqo) {
  1243. /* Path 2 (M >> N, JOBZ='O') */
  1244. /* N left singular vectors to be overwritten on A and */
  1245. /* N right singular vectors to be computed in VT */
  1246. iu = 1;
  1247. /* WORK(IU) is N by N */
  1248. ldwrku = *n;
  1249. ir = iu + ldwrku * *n;
  1250. if (*lwork >= *m * *n + *n * *n + *n * 3) {
  1251. /* WORK(IR) is M by N */
  1252. ldwrkr = *m;
  1253. } else {
  1254. ldwrkr = (*lwork - *n * *n - *n * 3) / *n;
  1255. }
  1256. itau = ir + ldwrkr * *n;
  1257. nwork = itau + *n;
  1258. /* Compute A=Q*R */
  1259. /* CWorkspace: need N*N [U] + N*N [R] + N [tau] + N [work] */
  1260. /* CWorkspace: prefer N*N [U] + N*N [R] + N [tau] + N*NB [work] */
  1261. /* RWorkspace: need 0 */
  1262. i__1 = *lwork - nwork + 1;
  1263. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1264. i__1, &ierr);
  1265. /* Copy R to WORK( IR ), zeroing out below it */
  1266. zlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
  1267. i__1 = *n - 1;
  1268. i__2 = *n - 1;
  1269. zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &work[ir + 1], &
  1270. ldwrkr);
  1271. /* Generate Q in A */
  1272. /* CWorkspace: need N*N [U] + N*N [R] + N [tau] + N [work] */
  1273. /* CWorkspace: prefer N*N [U] + N*N [R] + N [tau] + N*NB [work] */
  1274. /* RWorkspace: need 0 */
  1275. i__1 = *lwork - nwork + 1;
  1276. zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
  1277. &i__1, &ierr);
  1278. ie = 1;
  1279. itauq = itau;
  1280. itaup = itauq + *n;
  1281. nwork = itaup + *n;
  1282. /* Bidiagonalize R in WORK(IR) */
  1283. /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
  1284. /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + 2*N*NB [work] */
  1285. /* RWorkspace: need N [e] */
  1286. i__1 = *lwork - nwork + 1;
  1287. zgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[
  1288. itauq], &work[itaup], &work[nwork], &i__1, &ierr);
  1289. /* Perform bidiagonal SVD, computing left singular vectors */
  1290. /* of R in WORK(IRU) and computing right singular vectors */
  1291. /* of R in WORK(IRVT) */
  1292. /* CWorkspace: need 0 */
  1293. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1294. iru = ie + *n;
  1295. irvt = iru + *n * *n;
  1296. nrwork = irvt + *n * *n;
  1297. dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1298. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1299. info);
  1300. /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
  1301. /* Overwrite WORK(IU) by the left singular vectors of R */
  1302. /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
  1303. /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + N*NB [work] */
  1304. /* RWorkspace: need 0 */
  1305. zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
  1306. i__1 = *lwork - nwork + 1;
  1307. zunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
  1308. itauq], &work[iu], &ldwrku, &work[nwork], &i__1, &
  1309. ierr);
  1310. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1311. /* Overwrite VT by the right singular vectors of R */
  1312. /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
  1313. /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + N*NB [work] */
  1314. /* RWorkspace: need 0 */
  1315. zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1316. i__1 = *lwork - nwork + 1;
  1317. zunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[
  1318. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  1319. ierr);
  1320. /* Multiply Q in A by left singular vectors of R in */
  1321. /* WORK(IU), storing result in WORK(IR) and copying to A */
  1322. /* CWorkspace: need N*N [U] + N*N [R] */
  1323. /* CWorkspace: prefer N*N [U] + M*N [R] */
  1324. /* RWorkspace: need 0 */
  1325. i__1 = *m;
  1326. i__2 = ldwrkr;
  1327. for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
  1328. i__2) {
  1329. /* Computing MIN */
  1330. i__3 = *m - i__ + 1;
  1331. chunk = f2cmin(i__3,ldwrkr);
  1332. zgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1],
  1333. lda, &work[iu], &ldwrku, &c_b1, &work[ir], &
  1334. ldwrkr);
  1335. zlacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ +
  1336. a_dim1], lda);
  1337. /* L10: */
  1338. }
  1339. } else if (wntqs) {
  1340. /* Path 3 (M >> N, JOBZ='S') */
  1341. /* N left singular vectors to be computed in U and */
  1342. /* N right singular vectors to be computed in VT */
  1343. ir = 1;
  1344. /* WORK(IR) is N by N */
  1345. ldwrkr = *n;
  1346. itau = ir + ldwrkr * *n;
  1347. nwork = itau + *n;
  1348. /* Compute A=Q*R */
  1349. /* CWorkspace: need N*N [R] + N [tau] + N [work] */
  1350. /* CWorkspace: prefer N*N [R] + N [tau] + N*NB [work] */
  1351. /* RWorkspace: need 0 */
  1352. i__2 = *lwork - nwork + 1;
  1353. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1354. i__2, &ierr);
  1355. /* Copy R to WORK(IR), zeroing out below it */
  1356. zlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
  1357. i__2 = *n - 1;
  1358. i__1 = *n - 1;
  1359. zlaset_("L", &i__2, &i__1, &c_b1, &c_b1, &work[ir + 1], &
  1360. ldwrkr);
  1361. /* Generate Q in A */
  1362. /* CWorkspace: need N*N [R] + N [tau] + N [work] */
  1363. /* CWorkspace: prefer N*N [R] + N [tau] + N*NB [work] */
  1364. /* RWorkspace: need 0 */
  1365. i__2 = *lwork - nwork + 1;
  1366. zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
  1367. &i__2, &ierr);
  1368. ie = 1;
  1369. itauq = itau;
  1370. itaup = itauq + *n;
  1371. nwork = itaup + *n;
  1372. /* Bidiagonalize R in WORK(IR) */
  1373. /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
  1374. /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + 2*N*NB [work] */
  1375. /* RWorkspace: need N [e] */
  1376. i__2 = *lwork - nwork + 1;
  1377. zgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[
  1378. itauq], &work[itaup], &work[nwork], &i__2, &ierr);
  1379. /* Perform bidiagonal SVD, computing left singular vectors */
  1380. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1381. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1382. /* CWorkspace: need 0 */
  1383. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1384. iru = ie + *n;
  1385. irvt = iru + *n * *n;
  1386. nrwork = irvt + *n * *n;
  1387. dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1388. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1389. info);
  1390. /* Copy real matrix RWORK(IRU) to complex matrix U */
  1391. /* Overwrite U by left singular vectors of R */
  1392. /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
  1393. /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + N*NB [work] */
  1394. /* RWorkspace: need 0 */
  1395. zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
  1396. i__2 = *lwork - nwork + 1;
  1397. zunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
  1398. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  1399. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1400. /* Overwrite VT by right singular vectors of R */
  1401. /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
  1402. /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + N*NB [work] */
  1403. /* RWorkspace: need 0 */
  1404. zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1405. i__2 = *lwork - nwork + 1;
  1406. zunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[
  1407. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
  1408. ierr);
  1409. /* Multiply Q in A by left singular vectors of R in */
  1410. /* WORK(IR), storing result in U */
  1411. /* CWorkspace: need N*N [R] */
  1412. /* RWorkspace: need 0 */
  1413. zlacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr);
  1414. zgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &work[ir],
  1415. &ldwrkr, &c_b1, &u[u_offset], ldu);
  1416. } else if (wntqa) {
  1417. /* Path 4 (M >> N, JOBZ='A') */
  1418. /* M left singular vectors to be computed in U and */
  1419. /* N right singular vectors to be computed in VT */
  1420. iu = 1;
  1421. /* WORK(IU) is N by N */
  1422. ldwrku = *n;
  1423. itau = iu + ldwrku * *n;
  1424. nwork = itau + *n;
  1425. /* Compute A=Q*R, copying result to U */
  1426. /* CWorkspace: need N*N [U] + N [tau] + N [work] */
  1427. /* CWorkspace: prefer N*N [U] + N [tau] + N*NB [work] */
  1428. /* RWorkspace: need 0 */
  1429. i__2 = *lwork - nwork + 1;
  1430. zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1431. i__2, &ierr);
  1432. zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1433. /* Generate Q in U */
  1434. /* CWorkspace: need N*N [U] + N [tau] + M [work] */
  1435. /* CWorkspace: prefer N*N [U] + N [tau] + M*NB [work] */
  1436. /* RWorkspace: need 0 */
  1437. i__2 = *lwork - nwork + 1;
  1438. zungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork],
  1439. &i__2, &ierr);
  1440. /* Produce R in A, zeroing out below it */
  1441. i__2 = *n - 1;
  1442. i__1 = *n - 1;
  1443. zlaset_("L", &i__2, &i__1, &c_b1, &c_b1, &a[a_dim1 + 2], lda);
  1444. ie = 1;
  1445. itauq = itau;
  1446. itaup = itauq + *n;
  1447. nwork = itaup + *n;
  1448. /* Bidiagonalize R in A */
  1449. /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
  1450. /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + 2*N*NB [work] */
  1451. /* RWorkspace: need N [e] */
  1452. i__2 = *lwork - nwork + 1;
  1453. zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1454. itauq], &work[itaup], &work[nwork], &i__2, &ierr);
  1455. iru = ie + *n;
  1456. irvt = iru + *n * *n;
  1457. nrwork = irvt + *n * *n;
  1458. /* Perform bidiagonal SVD, computing left singular vectors */
  1459. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1460. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1461. /* CWorkspace: need 0 */
  1462. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1463. dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1464. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1465. info);
  1466. /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
  1467. /* Overwrite WORK(IU) by left singular vectors of R */
  1468. /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
  1469. /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + N*NB [work] */
  1470. /* RWorkspace: need 0 */
  1471. zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
  1472. i__2 = *lwork - nwork + 1;
  1473. zunmbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[
  1474. itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
  1475. ierr);
  1476. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1477. /* Overwrite VT by right singular vectors of R */
  1478. /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
  1479. /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + N*NB [work] */
  1480. /* RWorkspace: need 0 */
  1481. zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1482. i__2 = *lwork - nwork + 1;
  1483. zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
  1484. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
  1485. ierr);
  1486. /* Multiply Q in U by left singular vectors of R in */
  1487. /* WORK(IU), storing result in A */
  1488. /* CWorkspace: need N*N [U] */
  1489. /* RWorkspace: need 0 */
  1490. zgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &work[iu],
  1491. &ldwrku, &c_b1, &a[a_offset], lda);
  1492. /* Copy left singular vectors of A from A to U */
  1493. zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1494. }
  1495. } else if (*m >= mnthr2) {
  1496. /* MNTHR2 <= M < MNTHR1 */
  1497. /* Path 5 (M >> N, but not as much as MNTHR1) */
  1498. /* Reduce to bidiagonal form without QR decomposition, use */
  1499. /* ZUNGBR and matrix multiplication to compute singular vectors */
  1500. ie = 1;
  1501. nrwork = ie + *n;
  1502. itauq = 1;
  1503. itaup = itauq + *n;
  1504. nwork = itaup + *n;
  1505. /* Bidiagonalize A */
  1506. /* CWorkspace: need 2*N [tauq, taup] + M [work] */
  1507. /* CWorkspace: prefer 2*N [tauq, taup] + (M+N)*NB [work] */
  1508. /* RWorkspace: need N [e] */
  1509. i__2 = *lwork - nwork + 1;
  1510. zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  1511. &work[itaup], &work[nwork], &i__2, &ierr);
  1512. if (wntqn) {
  1513. /* Path 5n (M >> N, JOBZ='N') */
  1514. /* Compute singular values only */
  1515. /* CWorkspace: need 0 */
  1516. /* RWorkspace: need N [e] + BDSPAC */
  1517. dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
  1518. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  1519. } else if (wntqo) {
  1520. iu = nwork;
  1521. iru = nrwork;
  1522. irvt = iru + *n * *n;
  1523. nrwork = irvt + *n * *n;
  1524. /* Path 5o (M >> N, JOBZ='O') */
  1525. /* Copy A to VT, generate P**H */
  1526. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1527. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1528. /* RWorkspace: need 0 */
  1529. zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1530. i__2 = *lwork - nwork + 1;
  1531. zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
  1532. work[nwork], &i__2, &ierr);
  1533. /* Generate Q in A */
  1534. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1535. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1536. /* RWorkspace: need 0 */
  1537. i__2 = *lwork - nwork + 1;
  1538. zungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[
  1539. nwork], &i__2, &ierr);
  1540. if (*lwork >= *m * *n + *n * 3) {
  1541. /* WORK( IU ) is M by N */
  1542. ldwrku = *m;
  1543. } else {
  1544. /* WORK(IU) is LDWRKU by N */
  1545. ldwrku = (*lwork - *n * 3) / *n;
  1546. }
  1547. nwork = iu + ldwrku * *n;
  1548. /* Perform bidiagonal SVD, computing left singular vectors */
  1549. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1550. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1551. /* CWorkspace: need 0 */
  1552. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1553. dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1554. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1555. info);
  1556. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  1557. /* storing the result in WORK(IU), copying to VT */
  1558. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
  1559. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
  1560. zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &work[iu]
  1561. , &ldwrku, &rwork[nrwork]);
  1562. zlacpy_("F", n, n, &work[iu], &ldwrku, &vt[vt_offset], ldvt);
  1563. /* Multiply Q in A by real matrix RWORK(IRU), storing the */
  1564. /* result in WORK(IU), copying to A */
  1565. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
  1566. /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] */
  1567. /* RWorkspace: need N [e] + N*N [RU] + 2*N*N [rwork] */
  1568. /* RWorkspace: prefer N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
  1569. nrwork = irvt;
  1570. i__2 = *m;
  1571. i__1 = ldwrku;
  1572. for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
  1573. i__1) {
  1574. /* Computing MIN */
  1575. i__3 = *m - i__ + 1;
  1576. chunk = f2cmin(i__3,ldwrku);
  1577. zlacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru], n,
  1578. &work[iu], &ldwrku, &rwork[nrwork]);
  1579. zlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
  1580. a_dim1], lda);
  1581. /* L20: */
  1582. }
  1583. } else if (wntqs) {
  1584. /* Path 5s (M >> N, JOBZ='S') */
  1585. /* Copy A to VT, generate P**H */
  1586. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1587. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1588. /* RWorkspace: need 0 */
  1589. zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1590. i__1 = *lwork - nwork + 1;
  1591. zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
  1592. work[nwork], &i__1, &ierr);
  1593. /* Copy A to U, generate Q */
  1594. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1595. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1596. /* RWorkspace: need 0 */
  1597. zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1598. i__1 = *lwork - nwork + 1;
  1599. zungbr_("Q", m, n, n, &u[u_offset], ldu, &work[itauq], &work[
  1600. nwork], &i__1, &ierr);
  1601. /* Perform bidiagonal SVD, computing left singular vectors */
  1602. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1603. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1604. /* CWorkspace: need 0 */
  1605. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1606. iru = nrwork;
  1607. irvt = iru + *n * *n;
  1608. nrwork = irvt + *n * *n;
  1609. dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1610. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1611. info);
  1612. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  1613. /* storing the result in A, copying to VT */
  1614. /* CWorkspace: need 0 */
  1615. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
  1616. zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[
  1617. a_offset], lda, &rwork[nrwork]);
  1618. zlacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1619. /* Multiply Q in U by real matrix RWORK(IRU), storing the */
  1620. /* result in A, copying to U */
  1621. /* CWorkspace: need 0 */
  1622. /* RWorkspace: need N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
  1623. nrwork = irvt;
  1624. zlacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset],
  1625. lda, &rwork[nrwork]);
  1626. zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1627. } else {
  1628. /* Path 5a (M >> N, JOBZ='A') */
  1629. /* Copy A to VT, generate P**H */
  1630. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1631. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1632. /* RWorkspace: need 0 */
  1633. zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1634. i__1 = *lwork - nwork + 1;
  1635. zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
  1636. work[nwork], &i__1, &ierr);
  1637. /* Copy A to U, generate Q */
  1638. /* CWorkspace: need 2*N [tauq, taup] + M [work] */
  1639. /* CWorkspace: prefer 2*N [tauq, taup] + M*NB [work] */
  1640. /* RWorkspace: need 0 */
  1641. zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1642. i__1 = *lwork - nwork + 1;
  1643. zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  1644. nwork], &i__1, &ierr);
  1645. /* Perform bidiagonal SVD, computing left singular vectors */
  1646. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1647. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1648. /* CWorkspace: need 0 */
  1649. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1650. iru = nrwork;
  1651. irvt = iru + *n * *n;
  1652. nrwork = irvt + *n * *n;
  1653. dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1654. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1655. info);
  1656. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  1657. /* storing the result in A, copying to VT */
  1658. /* CWorkspace: need 0 */
  1659. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
  1660. zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[
  1661. a_offset], lda, &rwork[nrwork]);
  1662. zlacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1663. /* Multiply Q in U by real matrix RWORK(IRU), storing the */
  1664. /* result in A, copying to U */
  1665. /* CWorkspace: need 0 */
  1666. /* RWorkspace: need N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
  1667. nrwork = irvt;
  1668. zlacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset],
  1669. lda, &rwork[nrwork]);
  1670. zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1671. }
  1672. } else {
  1673. /* M .LT. MNTHR2 */
  1674. /* Path 6 (M >= N, but not much larger) */
  1675. /* Reduce to bidiagonal form without QR decomposition */
  1676. /* Use ZUNMBR to compute singular vectors */
  1677. ie = 1;
  1678. nrwork = ie + *n;
  1679. itauq = 1;
  1680. itaup = itauq + *n;
  1681. nwork = itaup + *n;
  1682. /* Bidiagonalize A */
  1683. /* CWorkspace: need 2*N [tauq, taup] + M [work] */
  1684. /* CWorkspace: prefer 2*N [tauq, taup] + (M+N)*NB [work] */
  1685. /* RWorkspace: need N [e] */
  1686. i__1 = *lwork - nwork + 1;
  1687. zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  1688. &work[itaup], &work[nwork], &i__1, &ierr);
  1689. if (wntqn) {
  1690. /* Path 6n (M >= N, JOBZ='N') */
  1691. /* Compute singular values only */
  1692. /* CWorkspace: need 0 */
  1693. /* RWorkspace: need N [e] + BDSPAC */
  1694. dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
  1695. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  1696. } else if (wntqo) {
  1697. iu = nwork;
  1698. iru = nrwork;
  1699. irvt = iru + *n * *n;
  1700. nrwork = irvt + *n * *n;
  1701. if (*lwork >= *m * *n + *n * 3) {
  1702. /* WORK( IU ) is M by N */
  1703. ldwrku = *m;
  1704. } else {
  1705. /* WORK( IU ) is LDWRKU by N */
  1706. ldwrku = (*lwork - *n * 3) / *n;
  1707. }
  1708. nwork = iu + ldwrku * *n;
  1709. /* Path 6o (M >= N, JOBZ='O') */
  1710. /* Perform bidiagonal SVD, computing left singular vectors */
  1711. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1712. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1713. /* CWorkspace: need 0 */
  1714. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1715. dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1716. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1717. info);
  1718. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1719. /* Overwrite VT by right singular vectors of A */
  1720. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] + N [work] */
  1721. /* CWorkspace: prefer 2*N [tauq, taup] + N*N [U] + N*NB [work] */
  1722. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1723. zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1724. i__1 = *lwork - nwork + 1;
  1725. zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
  1726. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  1727. ierr);
  1728. if (*lwork >= *m * *n + *n * 3) {
  1729. /* Path 6o-fast */
  1730. /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
  1731. /* Overwrite WORK(IU) by left singular vectors of A, copying */
  1732. /* to A */
  1733. /* CWorkspace: need 2*N [tauq, taup] + M*N [U] + N [work] */
  1734. /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] + N*NB [work] */
  1735. /* RWorkspace: need N [e] + N*N [RU] */
  1736. zlaset_("F", m, n, &c_b1, &c_b1, &work[iu], &ldwrku);
  1737. zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
  1738. i__1 = *lwork - nwork + 1;
  1739. zunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
  1740. itauq], &work[iu], &ldwrku, &work[nwork], &i__1, &
  1741. ierr);
  1742. zlacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda);
  1743. } else {
  1744. /* Path 6o-slow */
  1745. /* Generate Q in A */
  1746. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] + N [work] */
  1747. /* CWorkspace: prefer 2*N [tauq, taup] + N*N [U] + N*NB [work] */
  1748. /* RWorkspace: need 0 */
  1749. i__1 = *lwork - nwork + 1;
  1750. zungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
  1751. work[nwork], &i__1, &ierr);
  1752. /* Multiply Q in A by real matrix RWORK(IRU), storing the */
  1753. /* result in WORK(IU), copying to A */
  1754. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
  1755. /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] */
  1756. /* RWorkspace: need N [e] + N*N [RU] + 2*N*N [rwork] */
  1757. /* RWorkspace: prefer N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
  1758. nrwork = irvt;
  1759. i__1 = *m;
  1760. i__2 = ldwrku;
  1761. for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
  1762. i__2) {
  1763. /* Computing MIN */
  1764. i__3 = *m - i__ + 1;
  1765. chunk = f2cmin(i__3,ldwrku);
  1766. zlacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru],
  1767. n, &work[iu], &ldwrku, &rwork[nrwork]);
  1768. zlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
  1769. a_dim1], lda);
  1770. /* L30: */
  1771. }
  1772. }
  1773. } else if (wntqs) {
  1774. /* Path 6s (M >= N, JOBZ='S') */
  1775. /* Perform bidiagonal SVD, computing left singular vectors */
  1776. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1777. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1778. /* CWorkspace: need 0 */
  1779. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1780. iru = nrwork;
  1781. irvt = iru + *n * *n;
  1782. nrwork = irvt + *n * *n;
  1783. dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1784. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1785. info);
  1786. /* Copy real matrix RWORK(IRU) to complex matrix U */
  1787. /* Overwrite U by left singular vectors of A */
  1788. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1789. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1790. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1791. zlaset_("F", m, n, &c_b1, &c_b1, &u[u_offset], ldu)
  1792. ;
  1793. zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
  1794. i__2 = *lwork - nwork + 1;
  1795. zunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
  1796. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  1797. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1798. /* Overwrite VT by right singular vectors of A */
  1799. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1800. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1801. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1802. zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1803. i__2 = *lwork - nwork + 1;
  1804. zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
  1805. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
  1806. ierr);
  1807. } else {
  1808. /* Path 6a (M >= N, JOBZ='A') */
  1809. /* Perform bidiagonal SVD, computing left singular vectors */
  1810. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1811. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1812. /* CWorkspace: need 0 */
  1813. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1814. iru = nrwork;
  1815. irvt = iru + *n * *n;
  1816. nrwork = irvt + *n * *n;
  1817. dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1818. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1819. info);
  1820. /* Set the right corner of U to identity matrix */
  1821. zlaset_("F", m, m, &c_b1, &c_b1, &u[u_offset], ldu)
  1822. ;
  1823. if (*m > *n) {
  1824. i__2 = *m - *n;
  1825. i__1 = *m - *n;
  1826. zlaset_("F", &i__2, &i__1, &c_b1, &c_b2, &u[*n + 1 + (*n
  1827. + 1) * u_dim1], ldu);
  1828. }
  1829. /* Copy real matrix RWORK(IRU) to complex matrix U */
  1830. /* Overwrite U by left singular vectors of A */
  1831. /* CWorkspace: need 2*N [tauq, taup] + M [work] */
  1832. /* CWorkspace: prefer 2*N [tauq, taup] + M*NB [work] */
  1833. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1834. zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
  1835. i__2 = *lwork - nwork + 1;
  1836. zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
  1837. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  1838. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1839. /* Overwrite VT by right singular vectors of A */
  1840. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1841. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1842. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1843. zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1844. i__2 = *lwork - nwork + 1;
  1845. zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
  1846. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
  1847. ierr);
  1848. }
  1849. }
  1850. } else {
  1851. /* A has more columns than rows. If A has sufficiently more */
  1852. /* columns than rows, first reduce using the LQ decomposition (if */
  1853. /* sufficient workspace available) */
  1854. if (*n >= mnthr1) {
  1855. if (wntqn) {
  1856. /* Path 1t (N >> M, JOBZ='N') */
  1857. /* No singular vectors to be computed */
  1858. itau = 1;
  1859. nwork = itau + *m;
  1860. /* Compute A=L*Q */
  1861. /* CWorkspace: need M [tau] + M [work] */
  1862. /* CWorkspace: prefer M [tau] + M*NB [work] */
  1863. /* RWorkspace: need 0 */
  1864. i__2 = *lwork - nwork + 1;
  1865. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1866. i__2, &ierr);
  1867. /* Zero out above L */
  1868. i__2 = *m - 1;
  1869. i__1 = *m - 1;
  1870. zlaset_("U", &i__2, &i__1, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
  1871. , lda);
  1872. ie = 1;
  1873. itauq = 1;
  1874. itaup = itauq + *m;
  1875. nwork = itaup + *m;
  1876. /* Bidiagonalize L in A */
  1877. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  1878. /* CWorkspace: prefer 2*M [tauq, taup] + 2*M*NB [work] */
  1879. /* RWorkspace: need M [e] */
  1880. i__2 = *lwork - nwork + 1;
  1881. zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1882. itauq], &work[itaup], &work[nwork], &i__2, &ierr);
  1883. nrwork = ie + *m;
  1884. /* Perform bidiagonal SVD, compute singular values only */
  1885. /* CWorkspace: need 0 */
  1886. /* RWorkspace: need M [e] + BDSPAC */
  1887. dbdsdc_("U", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
  1888. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  1889. } else if (wntqo) {
  1890. /* Path 2t (N >> M, JOBZ='O') */
  1891. /* M right singular vectors to be overwritten on A and */
  1892. /* M left singular vectors to be computed in U */
  1893. ivt = 1;
  1894. ldwkvt = *m;
  1895. /* WORK(IVT) is M by M */
  1896. il = ivt + ldwkvt * *m;
  1897. if (*lwork >= *m * *n + *m * *m + *m * 3) {
  1898. /* WORK(IL) M by N */
  1899. ldwrkl = *m;
  1900. chunk = *n;
  1901. } else {
  1902. /* WORK(IL) is M by CHUNK */
  1903. ldwrkl = *m;
  1904. chunk = (*lwork - *m * *m - *m * 3) / *m;
  1905. }
  1906. itau = il + ldwrkl * chunk;
  1907. nwork = itau + *m;
  1908. /* Compute A=L*Q */
  1909. /* CWorkspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
  1910. /* CWorkspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
  1911. /* RWorkspace: need 0 */
  1912. i__2 = *lwork - nwork + 1;
  1913. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1914. i__2, &ierr);
  1915. /* Copy L to WORK(IL), zeroing about above it */
  1916. zlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
  1917. i__2 = *m - 1;
  1918. i__1 = *m - 1;
  1919. zlaset_("U", &i__2, &i__1, &c_b1, &c_b1, &work[il + ldwrkl], &
  1920. ldwrkl);
  1921. /* Generate Q in A */
  1922. /* CWorkspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
  1923. /* CWorkspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
  1924. /* RWorkspace: need 0 */
  1925. i__2 = *lwork - nwork + 1;
  1926. zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
  1927. &i__2, &ierr);
  1928. ie = 1;
  1929. itauq = itau;
  1930. itaup = itauq + *m;
  1931. nwork = itaup + *m;
  1932. /* Bidiagonalize L in WORK(IL) */
  1933. /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
  1934. /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + 2*M*NB [work] */
  1935. /* RWorkspace: need M [e] */
  1936. i__2 = *lwork - nwork + 1;
  1937. zgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[
  1938. itauq], &work[itaup], &work[nwork], &i__2, &ierr);
  1939. /* Perform bidiagonal SVD, computing left singular vectors */
  1940. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1941. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1942. /* CWorkspace: need 0 */
  1943. /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
  1944. iru = ie + *m;
  1945. irvt = iru + *m * *m;
  1946. nrwork = irvt + *m * *m;
  1947. dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  1948. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  1949. info);
  1950. /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
  1951. /* Overwrite WORK(IU) by the left singular vectors of L */
  1952. /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
  1953. /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + M*NB [work] */
  1954. /* RWorkspace: need 0 */
  1955. zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  1956. i__2 = *lwork - nwork + 1;
  1957. zunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
  1958. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  1959. /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
  1960. /* Overwrite WORK(IVT) by the right singular vectors of L */
  1961. /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
  1962. /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + M*NB [work] */
  1963. /* RWorkspace: need 0 */
  1964. zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
  1965. i__2 = *lwork - nwork + 1;
  1966. zunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[
  1967. itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &
  1968. ierr);
  1969. /* Multiply right singular vectors of L in WORK(IL) by Q */
  1970. /* in A, storing result in WORK(IL) and copying to A */
  1971. /* CWorkspace: need M*M [VT] + M*M [L] */
  1972. /* CWorkspace: prefer M*M [VT] + M*N [L] */
  1973. /* RWorkspace: need 0 */
  1974. i__2 = *n;
  1975. i__1 = chunk;
  1976. for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
  1977. i__1) {
  1978. /* Computing MIN */
  1979. i__3 = *n - i__ + 1;
  1980. blk = f2cmin(i__3,chunk);
  1981. zgemm_("N", "N", m, &blk, m, &c_b2, &work[ivt], m, &a[i__
  1982. * a_dim1 + 1], lda, &c_b1, &work[il], &ldwrkl);
  1983. zlacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1
  1984. + 1], lda);
  1985. /* L40: */
  1986. }
  1987. } else if (wntqs) {
  1988. /* Path 3t (N >> M, JOBZ='S') */
  1989. /* M right singular vectors to be computed in VT and */
  1990. /* M left singular vectors to be computed in U */
  1991. il = 1;
  1992. /* WORK(IL) is M by M */
  1993. ldwrkl = *m;
  1994. itau = il + ldwrkl * *m;
  1995. nwork = itau + *m;
  1996. /* Compute A=L*Q */
  1997. /* CWorkspace: need M*M [L] + M [tau] + M [work] */
  1998. /* CWorkspace: prefer M*M [L] + M [tau] + M*NB [work] */
  1999. /* RWorkspace: need 0 */
  2000. i__1 = *lwork - nwork + 1;
  2001. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  2002. i__1, &ierr);
  2003. /* Copy L to WORK(IL), zeroing out above it */
  2004. zlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
  2005. i__1 = *m - 1;
  2006. i__2 = *m - 1;
  2007. zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &work[il + ldwrkl], &
  2008. ldwrkl);
  2009. /* Generate Q in A */
  2010. /* CWorkspace: need M*M [L] + M [tau] + M [work] */
  2011. /* CWorkspace: prefer M*M [L] + M [tau] + M*NB [work] */
  2012. /* RWorkspace: need 0 */
  2013. i__1 = *lwork - nwork + 1;
  2014. zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
  2015. &i__1, &ierr);
  2016. ie = 1;
  2017. itauq = itau;
  2018. itaup = itauq + *m;
  2019. nwork = itaup + *m;
  2020. /* Bidiagonalize L in WORK(IL) */
  2021. /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
  2022. /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + 2*M*NB [work] */
  2023. /* RWorkspace: need M [e] */
  2024. i__1 = *lwork - nwork + 1;
  2025. zgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[
  2026. itauq], &work[itaup], &work[nwork], &i__1, &ierr);
  2027. /* Perform bidiagonal SVD, computing left singular vectors */
  2028. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2029. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2030. /* CWorkspace: need 0 */
  2031. /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
  2032. iru = ie + *m;
  2033. irvt = iru + *m * *m;
  2034. nrwork = irvt + *m * *m;
  2035. dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2036. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2037. info);
  2038. /* Copy real matrix RWORK(IRU) to complex matrix U */
  2039. /* Overwrite U by left singular vectors of L */
  2040. /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
  2041. /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + M*NB [work] */
  2042. /* RWorkspace: need 0 */
  2043. zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  2044. i__1 = *lwork - nwork + 1;
  2045. zunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
  2046. itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
  2047. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  2048. /* Overwrite VT by left singular vectors of L */
  2049. /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
  2050. /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + M*NB [work] */
  2051. /* RWorkspace: need 0 */
  2052. zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
  2053. i__1 = *lwork - nwork + 1;
  2054. zunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[
  2055. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  2056. ierr);
  2057. /* Copy VT to WORK(IL), multiply right singular vectors of L */
  2058. /* in WORK(IL) by Q in A, storing result in VT */
  2059. /* CWorkspace: need M*M [L] */
  2060. /* RWorkspace: need 0 */
  2061. zlacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl);
  2062. zgemm_("N", "N", m, n, m, &c_b2, &work[il], &ldwrkl, &a[
  2063. a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
  2064. } else if (wntqa) {
  2065. /* Path 4t (N >> M, JOBZ='A') */
  2066. /* N right singular vectors to be computed in VT and */
  2067. /* M left singular vectors to be computed in U */
  2068. ivt = 1;
  2069. /* WORK(IVT) is M by M */
  2070. ldwkvt = *m;
  2071. itau = ivt + ldwkvt * *m;
  2072. nwork = itau + *m;
  2073. /* Compute A=L*Q, copying result to VT */
  2074. /* CWorkspace: need M*M [VT] + M [tau] + M [work] */
  2075. /* CWorkspace: prefer M*M [VT] + M [tau] + M*NB [work] */
  2076. /* RWorkspace: need 0 */
  2077. i__1 = *lwork - nwork + 1;
  2078. zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  2079. i__1, &ierr);
  2080. zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2081. /* Generate Q in VT */
  2082. /* CWorkspace: need M*M [VT] + M [tau] + N [work] */
  2083. /* CWorkspace: prefer M*M [VT] + M [tau] + N*NB [work] */
  2084. /* RWorkspace: need 0 */
  2085. i__1 = *lwork - nwork + 1;
  2086. zunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[
  2087. nwork], &i__1, &ierr);
  2088. /* Produce L in A, zeroing out above it */
  2089. i__1 = *m - 1;
  2090. i__2 = *m - 1;
  2091. zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
  2092. , lda);
  2093. ie = 1;
  2094. itauq = itau;
  2095. itaup = itauq + *m;
  2096. nwork = itaup + *m;
  2097. /* Bidiagonalize L in A */
  2098. /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
  2099. /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + 2*M*NB [work] */
  2100. /* RWorkspace: need M [e] */
  2101. i__1 = *lwork - nwork + 1;
  2102. zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  2103. itauq], &work[itaup], &work[nwork], &i__1, &ierr);
  2104. /* Perform bidiagonal SVD, computing left singular vectors */
  2105. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2106. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2107. /* CWorkspace: need 0 */
  2108. /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
  2109. iru = ie + *m;
  2110. irvt = iru + *m * *m;
  2111. nrwork = irvt + *m * *m;
  2112. dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2113. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2114. info);
  2115. /* Copy real matrix RWORK(IRU) to complex matrix U */
  2116. /* Overwrite U by left singular vectors of L */
  2117. /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
  2118. /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + M*NB [work] */
  2119. /* RWorkspace: need 0 */
  2120. zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  2121. i__1 = *lwork - nwork + 1;
  2122. zunmbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[
  2123. itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
  2124. /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
  2125. /* Overwrite WORK(IVT) by right singular vectors of L */
  2126. /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
  2127. /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + M*NB [work] */
  2128. /* RWorkspace: need 0 */
  2129. zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
  2130. i__1 = *lwork - nwork + 1;
  2131. zunmbr_("P", "R", "C", m, m, m, &a[a_offset], lda, &work[
  2132. itaup], &work[ivt], &ldwkvt, &work[nwork], &i__1, &
  2133. ierr);
  2134. /* Multiply right singular vectors of L in WORK(IVT) by */
  2135. /* Q in VT, storing result in A */
  2136. /* CWorkspace: need M*M [VT] */
  2137. /* RWorkspace: need 0 */
  2138. zgemm_("N", "N", m, n, m, &c_b2, &work[ivt], &ldwkvt, &vt[
  2139. vt_offset], ldvt, &c_b1, &a[a_offset], lda);
  2140. /* Copy right singular vectors of A from A to VT */
  2141. zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2142. }
  2143. } else if (*n >= mnthr2) {
  2144. /* MNTHR2 <= N < MNTHR1 */
  2145. /* Path 5t (N >> M, but not as much as MNTHR1) */
  2146. /* Reduce to bidiagonal form without QR decomposition, use */
  2147. /* ZUNGBR and matrix multiplication to compute singular vectors */
  2148. ie = 1;
  2149. nrwork = ie + *m;
  2150. itauq = 1;
  2151. itaup = itauq + *m;
  2152. nwork = itaup + *m;
  2153. /* Bidiagonalize A */
  2154. /* CWorkspace: need 2*M [tauq, taup] + N [work] */
  2155. /* CWorkspace: prefer 2*M [tauq, taup] + (M+N)*NB [work] */
  2156. /* RWorkspace: need M [e] */
  2157. i__1 = *lwork - nwork + 1;
  2158. zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  2159. &work[itaup], &work[nwork], &i__1, &ierr);
  2160. if (wntqn) {
  2161. /* Path 5tn (N >> M, JOBZ='N') */
  2162. /* Compute singular values only */
  2163. /* CWorkspace: need 0 */
  2164. /* RWorkspace: need M [e] + BDSPAC */
  2165. dbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
  2166. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  2167. } else if (wntqo) {
  2168. irvt = nrwork;
  2169. iru = irvt + *m * *m;
  2170. nrwork = iru + *m * *m;
  2171. ivt = nwork;
  2172. /* Path 5to (N >> M, JOBZ='O') */
  2173. /* Copy A to U, generate Q */
  2174. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2175. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2176. /* RWorkspace: need 0 */
  2177. zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2178. i__1 = *lwork - nwork + 1;
  2179. zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  2180. nwork], &i__1, &ierr);
  2181. /* Generate P**H in A */
  2182. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2183. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2184. /* RWorkspace: need 0 */
  2185. i__1 = *lwork - nwork + 1;
  2186. zungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
  2187. nwork], &i__1, &ierr);
  2188. ldwkvt = *m;
  2189. if (*lwork >= *m * *n + *m * 3) {
  2190. /* WORK( IVT ) is M by N */
  2191. nwork = ivt + ldwkvt * *n;
  2192. chunk = *n;
  2193. } else {
  2194. /* WORK( IVT ) is M by CHUNK */
  2195. chunk = (*lwork - *m * 3) / *m;
  2196. nwork = ivt + ldwkvt * chunk;
  2197. }
  2198. /* Perform bidiagonal SVD, computing left singular vectors */
  2199. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2200. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2201. /* CWorkspace: need 0 */
  2202. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2203. dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2204. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2205. info);
  2206. /* Multiply Q in U by real matrix RWORK(IRVT) */
  2207. /* storing the result in WORK(IVT), copying to U */
  2208. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
  2209. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
  2210. zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &work[ivt], &
  2211. ldwkvt, &rwork[nrwork]);
  2212. zlacpy_("F", m, m, &work[ivt], &ldwkvt, &u[u_offset], ldu);
  2213. /* Multiply RWORK(IRVT) by P**H in A, storing the */
  2214. /* result in WORK(IVT), copying to A */
  2215. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
  2216. /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] */
  2217. /* RWorkspace: need M [e] + M*M [RVT] + 2*M*M [rwork] */
  2218. /* RWorkspace: prefer M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
  2219. nrwork = iru;
  2220. i__1 = *n;
  2221. i__2 = chunk;
  2222. for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
  2223. i__2) {
  2224. /* Computing MIN */
  2225. i__3 = *n - i__ + 1;
  2226. blk = f2cmin(i__3,chunk);
  2227. zlarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1],
  2228. lda, &work[ivt], &ldwkvt, &rwork[nrwork]);
  2229. zlacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ *
  2230. a_dim1 + 1], lda);
  2231. /* L50: */
  2232. }
  2233. } else if (wntqs) {
  2234. /* Path 5ts (N >> M, JOBZ='S') */
  2235. /* Copy A to U, generate Q */
  2236. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2237. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2238. /* RWorkspace: need 0 */
  2239. zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2240. i__2 = *lwork - nwork + 1;
  2241. zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  2242. nwork], &i__2, &ierr);
  2243. /* Copy A to VT, generate P**H */
  2244. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2245. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2246. /* RWorkspace: need 0 */
  2247. zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2248. i__2 = *lwork - nwork + 1;
  2249. zungbr_("P", m, n, m, &vt[vt_offset], ldvt, &work[itaup], &
  2250. work[nwork], &i__2, &ierr);
  2251. /* Perform bidiagonal SVD, computing left singular vectors */
  2252. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2253. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2254. /* CWorkspace: need 0 */
  2255. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2256. irvt = nrwork;
  2257. iru = irvt + *m * *m;
  2258. nrwork = iru + *m * *m;
  2259. dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2260. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2261. info);
  2262. /* Multiply Q in U by real matrix RWORK(IRU), storing the */
  2263. /* result in A, copying to U */
  2264. /* CWorkspace: need 0 */
  2265. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
  2266. zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset],
  2267. lda, &rwork[nrwork]);
  2268. zlacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2269. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  2270. /* storing the result in A, copying to VT */
  2271. /* CWorkspace: need 0 */
  2272. /* RWorkspace: need M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
  2273. nrwork = iru;
  2274. zlarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[
  2275. a_offset], lda, &rwork[nrwork]);
  2276. zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2277. } else {
  2278. /* Path 5ta (N >> M, JOBZ='A') */
  2279. /* Copy A to U, generate Q */
  2280. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2281. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2282. /* RWorkspace: need 0 */
  2283. zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2284. i__2 = *lwork - nwork + 1;
  2285. zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  2286. nwork], &i__2, &ierr);
  2287. /* Copy A to VT, generate P**H */
  2288. /* CWorkspace: need 2*M [tauq, taup] + N [work] */
  2289. /* CWorkspace: prefer 2*M [tauq, taup] + N*NB [work] */
  2290. /* RWorkspace: need 0 */
  2291. zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2292. i__2 = *lwork - nwork + 1;
  2293. zungbr_("P", n, n, m, &vt[vt_offset], ldvt, &work[itaup], &
  2294. work[nwork], &i__2, &ierr);
  2295. /* Perform bidiagonal SVD, computing left singular vectors */
  2296. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2297. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2298. /* CWorkspace: need 0 */
  2299. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2300. irvt = nrwork;
  2301. iru = irvt + *m * *m;
  2302. nrwork = iru + *m * *m;
  2303. dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2304. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2305. info);
  2306. /* Multiply Q in U by real matrix RWORK(IRU), storing the */
  2307. /* result in A, copying to U */
  2308. /* CWorkspace: need 0 */
  2309. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
  2310. zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset],
  2311. lda, &rwork[nrwork]);
  2312. zlacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2313. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  2314. /* storing the result in A, copying to VT */
  2315. /* CWorkspace: need 0 */
  2316. /* RWorkspace: need M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
  2317. nrwork = iru;
  2318. zlarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[
  2319. a_offset], lda, &rwork[nrwork]);
  2320. zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2321. }
  2322. } else {
  2323. /* N .LT. MNTHR2 */
  2324. /* Path 6t (N > M, but not much larger) */
  2325. /* Reduce to bidiagonal form without LQ decomposition */
  2326. /* Use ZUNMBR to compute singular vectors */
  2327. ie = 1;
  2328. nrwork = ie + *m;
  2329. itauq = 1;
  2330. itaup = itauq + *m;
  2331. nwork = itaup + *m;
  2332. /* Bidiagonalize A */
  2333. /* CWorkspace: need 2*M [tauq, taup] + N [work] */
  2334. /* CWorkspace: prefer 2*M [tauq, taup] + (M+N)*NB [work] */
  2335. /* RWorkspace: need M [e] */
  2336. i__2 = *lwork - nwork + 1;
  2337. zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  2338. &work[itaup], &work[nwork], &i__2, &ierr);
  2339. if (wntqn) {
  2340. /* Path 6tn (N > M, JOBZ='N') */
  2341. /* Compute singular values only */
  2342. /* CWorkspace: need 0 */
  2343. /* RWorkspace: need M [e] + BDSPAC */
  2344. dbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
  2345. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  2346. } else if (wntqo) {
  2347. /* Path 6to (N > M, JOBZ='O') */
  2348. ldwkvt = *m;
  2349. ivt = nwork;
  2350. if (*lwork >= *m * *n + *m * 3) {
  2351. /* WORK( IVT ) is M by N */
  2352. zlaset_("F", m, n, &c_b1, &c_b1, &work[ivt], &ldwkvt);
  2353. nwork = ivt + ldwkvt * *n;
  2354. } else {
  2355. /* WORK( IVT ) is M by CHUNK */
  2356. chunk = (*lwork - *m * 3) / *m;
  2357. nwork = ivt + ldwkvt * chunk;
  2358. }
  2359. /* Perform bidiagonal SVD, computing left singular vectors */
  2360. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2361. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2362. /* CWorkspace: need 0 */
  2363. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2364. irvt = nrwork;
  2365. iru = irvt + *m * *m;
  2366. nrwork = iru + *m * *m;
  2367. dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2368. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2369. info);
  2370. /* Copy real matrix RWORK(IRU) to complex matrix U */
  2371. /* Overwrite U by left singular vectors of A */
  2372. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] + M [work] */
  2373. /* CWorkspace: prefer 2*M [tauq, taup] + M*M [VT] + M*NB [work] */
  2374. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
  2375. zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  2376. i__2 = *lwork - nwork + 1;
  2377. zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
  2378. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  2379. if (*lwork >= *m * *n + *m * 3) {
  2380. /* Path 6to-fast */
  2381. /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
  2382. /* Overwrite WORK(IVT) by right singular vectors of A, */
  2383. /* copying to A */
  2384. /* CWorkspace: need 2*M [tauq, taup] + M*N [VT] + M [work] */
  2385. /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] + M*NB [work] */
  2386. /* RWorkspace: need M [e] + M*M [RVT] */
  2387. zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
  2388. i__2 = *lwork - nwork + 1;
  2389. zunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[
  2390. itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2,
  2391. &ierr);
  2392. zlacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda);
  2393. } else {
  2394. /* Path 6to-slow */
  2395. /* Generate P**H in A */
  2396. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] + M [work] */
  2397. /* CWorkspace: prefer 2*M [tauq, taup] + M*M [VT] + M*NB [work] */
  2398. /* RWorkspace: need 0 */
  2399. i__2 = *lwork - nwork + 1;
  2400. zungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
  2401. work[nwork], &i__2, &ierr);
  2402. /* Multiply Q in A by real matrix RWORK(IRU), storing the */
  2403. /* result in WORK(IU), copying to A */
  2404. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
  2405. /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] */
  2406. /* RWorkspace: need M [e] + M*M [RVT] + 2*M*M [rwork] */
  2407. /* RWorkspace: prefer M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
  2408. nrwork = iru;
  2409. i__2 = *n;
  2410. i__1 = chunk;
  2411. for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
  2412. i__1) {
  2413. /* Computing MIN */
  2414. i__3 = *n - i__ + 1;
  2415. blk = f2cmin(i__3,chunk);
  2416. zlarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1]
  2417. , lda, &work[ivt], &ldwkvt, &rwork[nrwork]);
  2418. zlacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ *
  2419. a_dim1 + 1], lda);
  2420. /* L60: */
  2421. }
  2422. }
  2423. } else if (wntqs) {
  2424. /* Path 6ts (N > M, JOBZ='S') */
  2425. /* Perform bidiagonal SVD, computing left singular vectors */
  2426. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2427. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2428. /* CWorkspace: need 0 */
  2429. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2430. irvt = nrwork;
  2431. iru = irvt + *m * *m;
  2432. nrwork = iru + *m * *m;
  2433. dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2434. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2435. info);
  2436. /* Copy real matrix RWORK(IRU) to complex matrix U */
  2437. /* Overwrite U by left singular vectors of A */
  2438. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2439. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2440. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
  2441. zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  2442. i__1 = *lwork - nwork + 1;
  2443. zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
  2444. itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
  2445. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  2446. /* Overwrite VT by right singular vectors of A */
  2447. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2448. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2449. /* RWorkspace: need M [e] + M*M [RVT] */
  2450. zlaset_("F", m, n, &c_b1, &c_b1, &vt[vt_offset], ldvt);
  2451. zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
  2452. i__1 = *lwork - nwork + 1;
  2453. zunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[
  2454. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  2455. ierr);
  2456. } else {
  2457. /* Path 6ta (N > M, JOBZ='A') */
  2458. /* Perform bidiagonal SVD, computing left singular vectors */
  2459. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2460. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2461. /* CWorkspace: need 0 */
  2462. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2463. irvt = nrwork;
  2464. iru = irvt + *m * *m;
  2465. nrwork = iru + *m * *m;
  2466. dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2467. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2468. info);
  2469. /* Copy real matrix RWORK(IRU) to complex matrix U */
  2470. /* Overwrite U by left singular vectors of A */
  2471. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2472. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2473. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
  2474. zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  2475. i__1 = *lwork - nwork + 1;
  2476. zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
  2477. itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
  2478. /* Set all of VT to identity matrix */
  2479. zlaset_("F", n, n, &c_b1, &c_b2, &vt[vt_offset], ldvt);
  2480. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  2481. /* Overwrite VT by right singular vectors of A */
  2482. /* CWorkspace: need 2*M [tauq, taup] + N [work] */
  2483. /* CWorkspace: prefer 2*M [tauq, taup] + N*NB [work] */
  2484. /* RWorkspace: need M [e] + M*M [RVT] */
  2485. zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
  2486. i__1 = *lwork - nwork + 1;
  2487. zunmbr_("P", "R", "C", n, n, m, &a[a_offset], lda, &work[
  2488. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  2489. ierr);
  2490. }
  2491. }
  2492. }
  2493. /* Undo scaling if necessary */
  2494. if (iscl == 1) {
  2495. if (anrm > bignum) {
  2496. dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
  2497. minmn, &ierr);
  2498. }
  2499. if (*info != 0 && anrm > bignum) {
  2500. i__1 = minmn - 1;
  2501. dlascl_("G", &c__0, &c__0, &bignum, &anrm, &i__1, &c__1, &rwork[
  2502. ie], &minmn, &ierr);
  2503. }
  2504. if (anrm < smlnum) {
  2505. dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
  2506. minmn, &ierr);
  2507. }
  2508. if (*info != 0 && anrm < smlnum) {
  2509. i__1 = minmn - 1;
  2510. dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &i__1, &c__1, &rwork[
  2511. ie], &minmn, &ierr);
  2512. }
  2513. }
  2514. /* Return optimal workspace in WORK(1) */
  2515. work[1].r = (doublereal) maxwrk, work[1].i = 0.;
  2516. return;
  2517. /* End of ZGESDD */
  2518. } /* zgesdd_ */