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cgesdd.c 100 kB

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  1. /* f2c.h -- Standard Fortran to C header file */
  2. /** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed."
  3. - From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
  4. #ifndef F2C_INCLUDE
  5. #define F2C_INCLUDE
  6. #include <math.h>
  7. #include <stdlib.h>
  8. #include <string.h>
  9. #include <stdio.h>
  10. #include <complex.h>
  11. #ifdef complex
  12. #undef complex
  13. #endif
  14. #ifdef I
  15. #undef I
  16. #endif
  17. typedef int integer;
  18. typedef unsigned int uinteger;
  19. typedef char *address;
  20. typedef short int shortint;
  21. typedef float real;
  22. typedef double doublereal;
  23. typedef struct { real r, i; } complex;
  24. typedef struct { doublereal r, i; } doublecomplex;
  25. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  26. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  27. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  28. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  29. #define pCf(z) (*_pCf(z))
  30. #define pCd(z) (*_pCd(z))
  31. typedef int logical;
  32. typedef short int shortlogical;
  33. typedef char logical1;
  34. typedef char integer1;
  35. #define TRUE_ (1)
  36. #define FALSE_ (0)
  37. /* Extern is for use with -E */
  38. #ifndef Extern
  39. #define Extern extern
  40. #endif
  41. /* I/O stuff */
  42. typedef int flag;
  43. typedef int ftnlen;
  44. typedef int ftnint;
  45. /*external read, write*/
  46. typedef struct
  47. { flag cierr;
  48. ftnint ciunit;
  49. flag ciend;
  50. char *cifmt;
  51. ftnint cirec;
  52. } cilist;
  53. /*internal read, write*/
  54. typedef struct
  55. { flag icierr;
  56. char *iciunit;
  57. flag iciend;
  58. char *icifmt;
  59. ftnint icirlen;
  60. ftnint icirnum;
  61. } icilist;
  62. /*open*/
  63. typedef struct
  64. { flag oerr;
  65. ftnint ounit;
  66. char *ofnm;
  67. ftnlen ofnmlen;
  68. char *osta;
  69. char *oacc;
  70. char *ofm;
  71. ftnint orl;
  72. char *oblnk;
  73. } olist;
  74. /*close*/
  75. typedef struct
  76. { flag cerr;
  77. ftnint cunit;
  78. char *csta;
  79. } cllist;
  80. /*rewind, backspace, endfile*/
  81. typedef struct
  82. { flag aerr;
  83. ftnint aunit;
  84. } alist;
  85. /* inquire */
  86. typedef struct
  87. { flag inerr;
  88. ftnint inunit;
  89. char *infile;
  90. ftnlen infilen;
  91. ftnint *inex; /*parameters in standard's order*/
  92. ftnint *inopen;
  93. ftnint *innum;
  94. ftnint *innamed;
  95. char *inname;
  96. ftnlen innamlen;
  97. char *inacc;
  98. ftnlen inacclen;
  99. char *inseq;
  100. ftnlen inseqlen;
  101. char *indir;
  102. ftnlen indirlen;
  103. char *infmt;
  104. ftnlen infmtlen;
  105. char *inform;
  106. ftnint informlen;
  107. char *inunf;
  108. ftnlen inunflen;
  109. ftnint *inrecl;
  110. ftnint *innrec;
  111. char *inblank;
  112. ftnlen inblanklen;
  113. } inlist;
  114. #define VOID void
  115. union Multitype { /* for multiple entry points */
  116. integer1 g;
  117. shortint h;
  118. integer i;
  119. /* longint j; */
  120. real r;
  121. doublereal d;
  122. complex c;
  123. doublecomplex z;
  124. };
  125. typedef union Multitype Multitype;
  126. struct Vardesc { /* for Namelist */
  127. char *name;
  128. char *addr;
  129. ftnlen *dims;
  130. int type;
  131. };
  132. typedef struct Vardesc Vardesc;
  133. struct Namelist {
  134. char *name;
  135. Vardesc **vars;
  136. int nvars;
  137. };
  138. typedef struct Namelist Namelist;
  139. #define abs(x) ((x) >= 0 ? (x) : -(x))
  140. #define dabs(x) (fabs(x))
  141. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  142. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  143. #define dmin(a,b) (f2cmin(a,b))
  144. #define dmax(a,b) (f2cmax(a,b))
  145. #define bit_test(a,b) ((a) >> (b) & 1)
  146. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  147. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  148. #define abort_() { sig_die("Fortran abort routine called", 1); }
  149. #define c_abs(z) (cabsf(Cf(z)))
  150. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  151. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  152. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  153. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  154. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  155. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  156. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  157. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  158. #define d_abs(x) (fabs(*(x)))
  159. #define d_acos(x) (acos(*(x)))
  160. #define d_asin(x) (asin(*(x)))
  161. #define d_atan(x) (atan(*(x)))
  162. #define d_atn2(x, y) (atan2(*(x),*(y)))
  163. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  164. #define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
  165. #define d_cos(x) (cos(*(x)))
  166. #define d_cosh(x) (cosh(*(x)))
  167. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  168. #define d_exp(x) (exp(*(x)))
  169. #define d_imag(z) (cimag(Cd(z)))
  170. #define r_imag(z) (cimag(Cf(z)))
  171. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  172. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  173. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  174. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  175. #define d_log(x) (log(*(x)))
  176. #define d_mod(x, y) (fmod(*(x), *(y)))
  177. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  178. #define d_nint(x) u_nint(*(x))
  179. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  180. #define d_sign(a,b) u_sign(*(a),*(b))
  181. #define r_sign(a,b) u_sign(*(a),*(b))
  182. #define d_sin(x) (sin(*(x)))
  183. #define d_sinh(x) (sinh(*(x)))
  184. #define d_sqrt(x) (sqrt(*(x)))
  185. #define d_tan(x) (tan(*(x)))
  186. #define d_tanh(x) (tanh(*(x)))
  187. #define i_abs(x) abs(*(x))
  188. #define i_dnnt(x) ((integer)u_nint(*(x)))
  189. #define i_len(s, n) (n)
  190. #define i_nint(x) ((integer)u_nint(*(x)))
  191. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  192. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  193. #define pow_si(B,E) spow_ui(*(B),*(E))
  194. #define pow_ri(B,E) spow_ui(*(B),*(E))
  195. #define pow_di(B,E) dpow_ui(*(B),*(E))
  196. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  197. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  198. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  199. #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++ = ' '; }
  200. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  201. #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]; }
  202. #define sig_die(s, kill) { exit(1); }
  203. #define s_stop(s, n) {exit(0);}
  204. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  205. #define z_abs(z) (cabs(Cd(z)))
  206. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  207. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  208. #define myexit_() break;
  209. #define mycycle() continue;
  210. #define myceiling(w) {ceil(w)}
  211. #define myhuge(w) {HUGE_VAL}
  212. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  213. #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  214. /* procedure parameter types for -A and -C++ */
  215. #define F2C_proc_par_types 1
  216. #ifdef __cplusplus
  217. typedef logical (*L_fp)(...);
  218. #else
  219. typedef logical (*L_fp)();
  220. #endif
  221. static float spow_ui(float x, integer n) {
  222. float pow=1.0; unsigned long int u;
  223. if(n != 0) {
  224. if(n < 0) n = -n, x = 1/x;
  225. for(u = n; ; ) {
  226. if(u & 01) pow *= x;
  227. if(u >>= 1) x *= x;
  228. else break;
  229. }
  230. }
  231. return pow;
  232. }
  233. static double dpow_ui(double x, integer n) {
  234. double pow=1.0; unsigned long int u;
  235. if(n != 0) {
  236. if(n < 0) n = -n, x = 1/x;
  237. for(u = n; ; ) {
  238. if(u & 01) pow *= x;
  239. if(u >>= 1) x *= x;
  240. else break;
  241. }
  242. }
  243. return pow;
  244. }
  245. static _Complex float cpow_ui(_Complex float x, integer n) {
  246. _Complex float pow=1.0; unsigned long int u;
  247. if(n != 0) {
  248. if(n < 0) n = -n, x = 1/x;
  249. for(u = n; ; ) {
  250. if(u & 01) pow *= x;
  251. if(u >>= 1) x *= x;
  252. else break;
  253. }
  254. }
  255. return pow;
  256. }
  257. static _Complex double zpow_ui(_Complex double x, integer n) {
  258. _Complex double pow=1.0; unsigned long int u;
  259. if(n != 0) {
  260. if(n < 0) n = -n, x = 1/x;
  261. for(u = n; ; ) {
  262. if(u & 01) pow *= x;
  263. if(u >>= 1) x *= x;
  264. else break;
  265. }
  266. }
  267. return pow;
  268. }
  269. static integer pow_ii(integer x, integer n) {
  270. integer pow; unsigned long int u;
  271. if (n <= 0) {
  272. if (n == 0 || x == 1) pow = 1;
  273. else if (x != -1) pow = x == 0 ? 1/x : 0;
  274. else n = -n;
  275. }
  276. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  277. u = n;
  278. for(pow = 1; ; ) {
  279. if(u & 01) pow *= x;
  280. if(u >>= 1) x *= x;
  281. else break;
  282. }
  283. }
  284. return pow;
  285. }
  286. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  287. {
  288. double m; integer i, mi;
  289. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  290. if (w[i-1]>m) mi=i ,m=w[i-1];
  291. return mi-s+1;
  292. }
  293. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  294. {
  295. float m; integer i, mi;
  296. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  297. if (w[i-1]>m) mi=i ,m=w[i-1];
  298. return mi-s+1;
  299. }
  300. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  301. integer n = *n_, incx = *incx_, incy = *incy_, i;
  302. _Complex float zdotc = 0.0;
  303. if (incx == 1 && incy == 1) {
  304. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  305. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  306. }
  307. } else {
  308. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  309. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  310. }
  311. }
  312. pCf(z) = zdotc;
  313. }
  314. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  315. integer n = *n_, incx = *incx_, incy = *incy_, i;
  316. _Complex double zdotc = 0.0;
  317. if (incx == 1 && incy == 1) {
  318. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  319. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  320. }
  321. } else {
  322. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  323. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  324. }
  325. }
  326. pCd(z) = zdotc;
  327. }
  328. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  329. integer n = *n_, incx = *incx_, incy = *incy_, i;
  330. _Complex float zdotc = 0.0;
  331. if (incx == 1 && incy == 1) {
  332. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  333. zdotc += Cf(&x[i]) * Cf(&y[i]);
  334. }
  335. } else {
  336. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  337. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  338. }
  339. }
  340. pCf(z) = zdotc;
  341. }
  342. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  343. integer n = *n_, incx = *incx_, incy = *incy_, i;
  344. _Complex double zdotc = 0.0;
  345. if (incx == 1 && incy == 1) {
  346. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  347. zdotc += Cd(&x[i]) * Cd(&y[i]);
  348. }
  349. } else {
  350. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  351. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  352. }
  353. }
  354. pCd(z) = zdotc;
  355. }
  356. #endif
  357. /* -- translated by f2c (version 20000121).
  358. You must link the resulting object file with the libraries:
  359. -lf2c -lm (in that order)
  360. */
  361. /* Table of constant values */
  362. static complex c_b1 = {0.f,0.f};
  363. static complex c_b2 = {1.f,0.f};
  364. static integer c_n1 = -1;
  365. static integer c__0 = 0;
  366. static integer c__1 = 1;
  367. /* > \brief \b CGESDD */
  368. /* =========== DOCUMENTATION =========== */
  369. /* Online html documentation available at */
  370. /* http://www.netlib.org/lapack/explore-html/ */
  371. /* > \htmlonly */
  372. /* > Download CGESDD + dependencies */
  373. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgesdd.
  374. f"> */
  375. /* > [TGZ]</a> */
  376. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgesdd.
  377. f"> */
  378. /* > [ZIP]</a> */
  379. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgesdd.
  380. f"> */
  381. /* > [TXT]</a> */
  382. /* > \endhtmlonly */
  383. /* Definition: */
  384. /* =========== */
  385. /* SUBROUTINE CGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, */
  386. /* WORK, LWORK, RWORK, IWORK, INFO ) */
  387. /* CHARACTER JOBZ */
  388. /* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */
  389. /* INTEGER IWORK( * ) */
  390. /* REAL RWORK( * ), S( * ) */
  391. /* COMPLEX A( LDA, * ), U( LDU, * ), VT( LDVT, * ), */
  392. /* $ WORK( * ) */
  393. /* > \par Purpose: */
  394. /* ============= */
  395. /* > */
  396. /* > \verbatim */
  397. /* > */
  398. /* > CGESDD computes the singular value decomposition (SVD) of a complex */
  399. /* > M-by-N matrix A, optionally computing the left and/or right singular */
  400. /* > vectors, by using divide-and-conquer method. The SVD is written */
  401. /* > */
  402. /* > A = U * SIGMA * conjugate-transpose(V) */
  403. /* > */
  404. /* > where SIGMA is an M-by-N matrix which is zero except for its */
  405. /* > f2cmin(m,n) diagonal elements, U is an M-by-M unitary matrix, and */
  406. /* > V is an N-by-N unitary matrix. The diagonal elements of SIGMA */
  407. /* > are the singular values of A; they are real and non-negative, and */
  408. /* > are returned in descending order. The first f2cmin(m,n) columns of */
  409. /* > U and V are the left and right singular vectors of A. */
  410. /* > */
  411. /* > Note that the routine returns VT = V**H, not V. */
  412. /* > */
  413. /* > The divide and conquer algorithm makes very mild assumptions about */
  414. /* > floating point arithmetic. It will work on machines with a guard */
  415. /* > digit in add/subtract, or on those binary machines without guard */
  416. /* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
  417. /* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */
  418. /* > without guard digits, but we know of none. */
  419. /* > \endverbatim */
  420. /* Arguments: */
  421. /* ========== */
  422. /* > \param[in] JOBZ */
  423. /* > \verbatim */
  424. /* > JOBZ is CHARACTER*1 */
  425. /* > Specifies options for computing all or part of the matrix U: */
  426. /* > = 'A': all M columns of U and all N rows of V**H are */
  427. /* > returned in the arrays U and VT; */
  428. /* > = 'S': the first f2cmin(M,N) columns of U and the first */
  429. /* > f2cmin(M,N) rows of V**H are returned in the arrays U */
  430. /* > and VT; */
  431. /* > = 'O': If M >= N, the first N columns of U are overwritten */
  432. /* > in the array A and all rows of V**H are returned in */
  433. /* > the array VT; */
  434. /* > otherwise, all columns of U are returned in the */
  435. /* > array U and the first M rows of V**H are overwritten */
  436. /* > in the array A; */
  437. /* > = 'N': no columns of U or rows of V**H are computed. */
  438. /* > \endverbatim */
  439. /* > */
  440. /* > \param[in] M */
  441. /* > \verbatim */
  442. /* > M is INTEGER */
  443. /* > The number of rows of the input matrix A. M >= 0. */
  444. /* > \endverbatim */
  445. /* > */
  446. /* > \param[in] N */
  447. /* > \verbatim */
  448. /* > N is INTEGER */
  449. /* > The number of columns of the input matrix A. N >= 0. */
  450. /* > \endverbatim */
  451. /* > */
  452. /* > \param[in,out] A */
  453. /* > \verbatim */
  454. /* > A is COMPLEX array, dimension (LDA,N) */
  455. /* > On entry, the M-by-N matrix A. */
  456. /* > On exit, */
  457. /* > if JOBZ = 'O', A is overwritten with the first N columns */
  458. /* > of U (the left singular vectors, stored */
  459. /* > columnwise) if M >= N; */
  460. /* > A is overwritten with the first M rows */
  461. /* > of V**H (the right singular vectors, stored */
  462. /* > rowwise) otherwise. */
  463. /* > if JOBZ .ne. 'O', the contents of A are destroyed. */
  464. /* > \endverbatim */
  465. /* > */
  466. /* > \param[in] LDA */
  467. /* > \verbatim */
  468. /* > LDA is INTEGER */
  469. /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
  470. /* > \endverbatim */
  471. /* > */
  472. /* > \param[out] S */
  473. /* > \verbatim */
  474. /* > S is REAL array, dimension (f2cmin(M,N)) */
  475. /* > The singular values of A, sorted so that S(i) >= S(i+1). */
  476. /* > \endverbatim */
  477. /* > */
  478. /* > \param[out] U */
  479. /* > \verbatim */
  480. /* > U is COMPLEX array, dimension (LDU,UCOL) */
  481. /* > UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; */
  482. /* > UCOL = f2cmin(M,N) if JOBZ = 'S'. */
  483. /* > If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M */
  484. /* > unitary matrix U; */
  485. /* > if JOBZ = 'S', U contains the first f2cmin(M,N) columns of U */
  486. /* > (the left singular vectors, stored columnwise); */
  487. /* > if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. */
  488. /* > \endverbatim */
  489. /* > */
  490. /* > \param[in] LDU */
  491. /* > \verbatim */
  492. /* > LDU is INTEGER */
  493. /* > The leading dimension of the array U. LDU >= 1; */
  494. /* > if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. */
  495. /* > \endverbatim */
  496. /* > */
  497. /* > \param[out] VT */
  498. /* > \verbatim */
  499. /* > VT is COMPLEX array, dimension (LDVT,N) */
  500. /* > If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the */
  501. /* > N-by-N unitary matrix V**H; */
  502. /* > if JOBZ = 'S', VT contains the first f2cmin(M,N) rows of */
  503. /* > V**H (the right singular vectors, stored rowwise); */
  504. /* > if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. */
  505. /* > \endverbatim */
  506. /* > */
  507. /* > \param[in] LDVT */
  508. /* > \verbatim */
  509. /* > LDVT is INTEGER */
  510. /* > The leading dimension of the array VT. LDVT >= 1; */
  511. /* > if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; */
  512. /* > if JOBZ = 'S', LDVT >= f2cmin(M,N). */
  513. /* > \endverbatim */
  514. /* > */
  515. /* > \param[out] WORK */
  516. /* > \verbatim */
  517. /* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
  518. /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
  519. /* > \endverbatim */
  520. /* > */
  521. /* > \param[in] LWORK */
  522. /* > \verbatim */
  523. /* > LWORK is INTEGER */
  524. /* > The dimension of the array WORK. LWORK >= 1. */
  525. /* > If LWORK = -1, a workspace query is assumed. The optimal */
  526. /* > size for the WORK array is calculated and stored in WORK(1), */
  527. /* > and no other work except argument checking is performed. */
  528. /* > */
  529. /* > Let mx = f2cmax(M,N) and mn = f2cmin(M,N). */
  530. /* > If JOBZ = 'N', LWORK >= 2*mn + mx. */
  531. /* > If JOBZ = 'O', LWORK >= 2*mn*mn + 2*mn + mx. */
  532. /* > If JOBZ = 'S', LWORK >= mn*mn + 3*mn. */
  533. /* > If JOBZ = 'A', LWORK >= mn*mn + 2*mn + mx. */
  534. /* > These are not tight minimums in all cases; see comments inside code. */
  535. /* > For good performance, LWORK should generally be larger; */
  536. /* > a query is recommended. */
  537. /* > \endverbatim */
  538. /* > */
  539. /* > \param[out] RWORK */
  540. /* > \verbatim */
  541. /* > RWORK is REAL array, dimension (MAX(1,LRWORK)) */
  542. /* > Let mx = f2cmax(M,N) and mn = f2cmin(M,N). */
  543. /* > If JOBZ = 'N', LRWORK >= 5*mn (LAPACK <= 3.6 needs 7*mn); */
  544. /* > else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn; */
  545. /* > else LRWORK >= f2cmax( 5*mn*mn + 5*mn, */
  546. /* > 2*mx*mn + 2*mn*mn + mn ). */
  547. /* > \endverbatim */
  548. /* > */
  549. /* > \param[out] IWORK */
  550. /* > \verbatim */
  551. /* > IWORK is INTEGER array, dimension (8*f2cmin(M,N)) */
  552. /* > \endverbatim */
  553. /* > */
  554. /* > \param[out] INFO */
  555. /* > \verbatim */
  556. /* > INFO is INTEGER */
  557. /* > = 0: successful exit. */
  558. /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
  559. /* > > 0: The updating process of SBDSDC did not converge. */
  560. /* > \endverbatim */
  561. /* Authors: */
  562. /* ======== */
  563. /* > \author Univ. of Tennessee */
  564. /* > \author Univ. of California Berkeley */
  565. /* > \author Univ. of Colorado Denver */
  566. /* > \author NAG Ltd. */
  567. /* > \date June 2016 */
  568. /* > \ingroup complexGEsing */
  569. /* > \par Contributors: */
  570. /* ================== */
  571. /* > */
  572. /* > Ming Gu and Huan Ren, Computer Science Division, University of */
  573. /* > California at Berkeley, USA */
  574. /* > */
  575. /* ===================================================================== */
  576. /* Subroutine */ int cgesdd_(char *jobz, integer *m, integer *n, complex *a,
  577. integer *lda, real *s, complex *u, integer *ldu, complex *vt, integer
  578. *ldvt, complex *work, integer *lwork, real *rwork, integer *iwork,
  579. integer *info)
  580. {
  581. /* System generated locals */
  582. integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
  583. i__2, i__3;
  584. /* Local variables */
  585. integer lwork_cunglq_mn__, lwork_cunglq_nn__, lwork_cungqr_mm__,
  586. lwork_cungqr_mn__;
  587. complex cdum[1];
  588. integer iscl, lwork_cunmbr_prc_mm__, lwork_cunmbr_prc_mn__,
  589. lwork_cunmbr_prc_nn__;
  590. real anrm;
  591. integer ierr, itau, lwork_cunmbr_qln_mm__, lwork_cunmbr_qln_mn__,
  592. lwork_cunmbr_qln_nn__, idum[1], irvt, i__;
  593. extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
  594. integer *, complex *, complex *, integer *, complex *, integer *,
  595. complex *, complex *, integer *);
  596. extern logical lsame_(char *, char *);
  597. integer chunk, minmn, wrkbl, itaup, itauq;
  598. logical wntqa;
  599. integer nwork;
  600. extern /* Subroutine */ int clacp2_(char *, integer *, integer *, real *,
  601. integer *, complex *, integer *);
  602. logical wntqn, wntqo, wntqs;
  603. integer mnthr1, mnthr2, ie, lwork_cungbr_p_mn__, il, lwork_cungbr_p_nn__,
  604. lwork_cungbr_q_mn__, lwork_cungbr_q_mm__;
  605. extern /* Subroutine */ int cgebrd_(integer *, integer *, complex *,
  606. integer *, real *, real *, complex *, complex *, complex *,
  607. integer *, integer *);
  608. integer ir;
  609. extern real clange_(char *, integer *, integer *, complex *, integer *,
  610. real *);
  611. integer iu;
  612. extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *,
  613. integer *, complex *, complex *, integer *, integer *), clacrm_(
  614. integer *, integer *, complex *, integer *, real *, integer *,
  615. complex *, integer *, real *), clarcm_(integer *, integer *, real
  616. *, integer *, complex *, integer *, complex *, integer *, real *),
  617. clascl_(char *, integer *, integer *, real *, real *, integer *,
  618. integer *, complex *, integer *, integer *), sbdsdc_(char
  619. *, char *, integer *, real *, real *, real *, integer *, real *,
  620. integer *, real *, integer *, real *, integer *, integer *), cgeqrf_(integer *, integer *, complex *, integer
  621. *, complex *, complex *, integer *, integer *);
  622. extern real slamch_(char *);
  623. extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
  624. *, integer *, complex *, integer *), claset_(char *,
  625. integer *, integer *, complex *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen), cungbr_(char *,
  626. integer *, integer *, integer *, complex *, integer *, complex *,
  627. complex *, integer *, integer *);
  628. real bignum;
  629. extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
  630. real *, integer *, integer *, real *, integer *, integer *), cunmbr_(char *, char *, char *, integer *, integer *,
  631. integer *, complex *, integer *, complex *, complex *, integer *,
  632. complex *, integer *, integer *), cunglq_(
  633. integer *, integer *, integer *, complex *, integer *, complex *,
  634. complex *, integer *, integer *);
  635. extern logical sisnan_(real *);
  636. integer ldwrkl;
  637. extern /* Subroutine */ int cungqr_(integer *, integer *, integer *,
  638. complex *, integer *, complex *, complex *, integer *, integer *);
  639. integer ldwrkr, minwrk, ldwrku, maxwrk, ldwkvt;
  640. real smlnum;
  641. logical wntqas, lquery;
  642. integer nrwork, blk;
  643. real dum[1], eps;
  644. integer iru, ivt, lwork_cgebrd_mm__, lwork_cgebrd_mn__, lwork_cgebrd_nn__,
  645. lwork_cgelqf_mn__, lwork_cgeqrf_mn__;
  646. /* -- LAPACK driver routine (version 3.7.0) -- */
  647. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  648. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  649. /* June 2016 */
  650. /* ===================================================================== */
  651. /* Test the input arguments */
  652. /* Parameter adjustments */
  653. a_dim1 = *lda;
  654. a_offset = 1 + a_dim1 * 1;
  655. a -= a_offset;
  656. --s;
  657. u_dim1 = *ldu;
  658. u_offset = 1 + u_dim1 * 1;
  659. u -= u_offset;
  660. vt_dim1 = *ldvt;
  661. vt_offset = 1 + vt_dim1 * 1;
  662. vt -= vt_offset;
  663. --work;
  664. --rwork;
  665. --iwork;
  666. /* Function Body */
  667. *info = 0;
  668. minmn = f2cmin(*m,*n);
  669. mnthr1 = (integer) (minmn * 17.f / 9.f);
  670. mnthr2 = (integer) (minmn * 5.f / 3.f);
  671. wntqa = lsame_(jobz, "A");
  672. wntqs = lsame_(jobz, "S");
  673. wntqas = wntqa || wntqs;
  674. wntqo = lsame_(jobz, "O");
  675. wntqn = lsame_(jobz, "N");
  676. lquery = *lwork == -1;
  677. minwrk = 1;
  678. maxwrk = 1;
  679. if (! (wntqa || wntqs || wntqo || wntqn)) {
  680. *info = -1;
  681. } else if (*m < 0) {
  682. *info = -2;
  683. } else if (*n < 0) {
  684. *info = -3;
  685. } else if (*lda < f2cmax(1,*m)) {
  686. *info = -5;
  687. } else if (*ldu < 1 || wntqas && *ldu < *m || wntqo && *m < *n && *ldu < *
  688. m) {
  689. *info = -8;
  690. } else if (*ldvt < 1 || wntqa && *ldvt < *n || wntqs && *ldvt < minmn ||
  691. wntqo && *m >= *n && *ldvt < *n) {
  692. *info = -10;
  693. }
  694. /* Compute workspace */
  695. /* Note: Comments in the code beginning "Workspace:" describe the */
  696. /* minimal amount of workspace allocated at that point in the code, */
  697. /* as well as the preferred amount for good performance. */
  698. /* CWorkspace refers to complex workspace, and RWorkspace to */
  699. /* real workspace. NB refers to the optimal block size for the */
  700. /* immediately following subroutine, as returned by ILAENV.) */
  701. if (*info == 0) {
  702. minwrk = 1;
  703. maxwrk = 1;
  704. if (*m >= *n && minmn > 0) {
  705. /* There is no complex work space needed for bidiagonal SVD */
  706. /* The real work space needed for bidiagonal SVD (sbdsdc) is */
  707. /* BDSPAC = 3*N*N + 4*N for singular values and vectors; */
  708. /* BDSPAC = 4*N for singular values only; */
  709. /* not including e, RU, and RVT matrices. */
  710. /* Compute space preferred for each routine */
  711. cgebrd_(m, n, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
  712. lwork_cgebrd_mn__ = (integer) cdum[0].r;
  713. cgebrd_(n, n, cdum, n, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
  714. lwork_cgebrd_nn__ = (integer) cdum[0].r;
  715. cgeqrf_(m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  716. lwork_cgeqrf_mn__ = (integer) cdum[0].r;
  717. cungbr_("P", n, n, n, cdum, n, cdum, cdum, &c_n1, &ierr);
  718. lwork_cungbr_p_nn__ = (integer) cdum[0].r;
  719. cungbr_("Q", m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  720. lwork_cungbr_q_mm__ = (integer) cdum[0].r;
  721. cungbr_("Q", m, n, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  722. lwork_cungbr_q_mn__ = (integer) cdum[0].r;
  723. cungqr_(m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  724. lwork_cungqr_mm__ = (integer) cdum[0].r;
  725. cungqr_(m, n, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  726. lwork_cungqr_mn__ = (integer) cdum[0].r;
  727. cunmbr_("P", "R", "C", n, n, n, cdum, n, cdum, cdum, n, cdum, &
  728. c_n1, &ierr);
  729. lwork_cunmbr_prc_nn__ = (integer) cdum[0].r;
  730. cunmbr_("Q", "L", "N", m, m, n, cdum, m, cdum, cdum, m, cdum, &
  731. c_n1, &ierr);
  732. lwork_cunmbr_qln_mm__ = (integer) cdum[0].r;
  733. cunmbr_("Q", "L", "N", m, n, n, cdum, m, cdum, cdum, m, cdum, &
  734. c_n1, &ierr);
  735. lwork_cunmbr_qln_mn__ = (integer) cdum[0].r;
  736. cunmbr_("Q", "L", "N", n, n, n, cdum, n, cdum, cdum, n, cdum, &
  737. c_n1, &ierr);
  738. lwork_cunmbr_qln_nn__ = (integer) cdum[0].r;
  739. if (*m >= mnthr1) {
  740. if (wntqn) {
  741. /* Path 1 (M >> N, JOBZ='N') */
  742. maxwrk = *n + lwork_cgeqrf_mn__;
  743. /* Computing MAX */
  744. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cgebrd_nn__;
  745. maxwrk = f2cmax(i__1,i__2);
  746. minwrk = *n * 3;
  747. } else if (wntqo) {
  748. /* Path 2 (M >> N, JOBZ='O') */
  749. wrkbl = *n + lwork_cgeqrf_mn__;
  750. /* Computing MAX */
  751. i__1 = wrkbl, i__2 = *n + lwork_cungqr_mn__;
  752. wrkbl = f2cmax(i__1,i__2);
  753. /* Computing MAX */
  754. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cgebrd_nn__;
  755. wrkbl = f2cmax(i__1,i__2);
  756. /* Computing MAX */
  757. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_qln_nn__;
  758. wrkbl = f2cmax(i__1,i__2);
  759. /* Computing MAX */
  760. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
  761. wrkbl = f2cmax(i__1,i__2);
  762. maxwrk = *m * *n + *n * *n + wrkbl;
  763. minwrk = (*n << 1) * *n + *n * 3;
  764. } else if (wntqs) {
  765. /* Path 3 (M >> N, JOBZ='S') */
  766. wrkbl = *n + lwork_cgeqrf_mn__;
  767. /* Computing MAX */
  768. i__1 = wrkbl, i__2 = *n + lwork_cungqr_mn__;
  769. wrkbl = f2cmax(i__1,i__2);
  770. /* Computing MAX */
  771. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cgebrd_nn__;
  772. wrkbl = f2cmax(i__1,i__2);
  773. /* Computing MAX */
  774. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_qln_nn__;
  775. wrkbl = f2cmax(i__1,i__2);
  776. /* Computing MAX */
  777. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
  778. wrkbl = f2cmax(i__1,i__2);
  779. maxwrk = *n * *n + wrkbl;
  780. minwrk = *n * *n + *n * 3;
  781. } else if (wntqa) {
  782. /* Path 4 (M >> N, JOBZ='A') */
  783. wrkbl = *n + lwork_cgeqrf_mn__;
  784. /* Computing MAX */
  785. i__1 = wrkbl, i__2 = *n + lwork_cungqr_mm__;
  786. wrkbl = f2cmax(i__1,i__2);
  787. /* Computing MAX */
  788. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cgebrd_nn__;
  789. wrkbl = f2cmax(i__1,i__2);
  790. /* Computing MAX */
  791. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_qln_nn__;
  792. wrkbl = f2cmax(i__1,i__2);
  793. /* Computing MAX */
  794. i__1 = wrkbl, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
  795. wrkbl = f2cmax(i__1,i__2);
  796. maxwrk = *n * *n + wrkbl;
  797. /* Computing MAX */
  798. i__1 = *n * 3, i__2 = *n + *m;
  799. minwrk = *n * *n + f2cmax(i__1,i__2);
  800. }
  801. } else if (*m >= mnthr2) {
  802. /* Path 5 (M >> N, but not as much as MNTHR1) */
  803. maxwrk = (*n << 1) + lwork_cgebrd_mn__;
  804. minwrk = (*n << 1) + *m;
  805. if (wntqo) {
  806. /* Path 5o (M >> N, JOBZ='O') */
  807. /* Computing MAX */
  808. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_p_nn__;
  809. maxwrk = f2cmax(i__1,i__2);
  810. /* Computing MAX */
  811. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_q_mn__;
  812. maxwrk = f2cmax(i__1,i__2);
  813. maxwrk += *m * *n;
  814. minwrk += *n * *n;
  815. } else if (wntqs) {
  816. /* Path 5s (M >> N, JOBZ='S') */
  817. /* Computing MAX */
  818. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_p_nn__;
  819. maxwrk = f2cmax(i__1,i__2);
  820. /* Computing MAX */
  821. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_q_mn__;
  822. maxwrk = f2cmax(i__1,i__2);
  823. } else if (wntqa) {
  824. /* Path 5a (M >> N, JOBZ='A') */
  825. /* Computing MAX */
  826. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_p_nn__;
  827. maxwrk = f2cmax(i__1,i__2);
  828. /* Computing MAX */
  829. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cungbr_q_mm__;
  830. maxwrk = f2cmax(i__1,i__2);
  831. }
  832. } else {
  833. /* Path 6 (M >= N, but not much larger) */
  834. maxwrk = (*n << 1) + lwork_cgebrd_mn__;
  835. minwrk = (*n << 1) + *m;
  836. if (wntqo) {
  837. /* Path 6o (M >= N, JOBZ='O') */
  838. /* Computing MAX */
  839. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
  840. maxwrk = f2cmax(i__1,i__2);
  841. /* Computing MAX */
  842. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_qln_mn__;
  843. maxwrk = f2cmax(i__1,i__2);
  844. maxwrk += *m * *n;
  845. minwrk += *n * *n;
  846. } else if (wntqs) {
  847. /* Path 6s (M >= N, JOBZ='S') */
  848. /* Computing MAX */
  849. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_qln_mn__;
  850. maxwrk = f2cmax(i__1,i__2);
  851. /* Computing MAX */
  852. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
  853. maxwrk = f2cmax(i__1,i__2);
  854. } else if (wntqa) {
  855. /* Path 6a (M >= N, JOBZ='A') */
  856. /* Computing MAX */
  857. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_qln_mm__;
  858. maxwrk = f2cmax(i__1,i__2);
  859. /* Computing MAX */
  860. i__1 = maxwrk, i__2 = (*n << 1) + lwork_cunmbr_prc_nn__;
  861. maxwrk = f2cmax(i__1,i__2);
  862. }
  863. }
  864. } else if (minmn > 0) {
  865. /* There is no complex work space needed for bidiagonal SVD */
  866. /* The real work space needed for bidiagonal SVD (sbdsdc) is */
  867. /* BDSPAC = 3*M*M + 4*M for singular values and vectors; */
  868. /* BDSPAC = 4*M for singular values only; */
  869. /* not including e, RU, and RVT matrices. */
  870. /* Compute space preferred for each routine */
  871. cgebrd_(m, n, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
  872. lwork_cgebrd_mn__ = (integer) cdum[0].r;
  873. cgebrd_(m, m, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
  874. lwork_cgebrd_mm__ = (integer) cdum[0].r;
  875. cgelqf_(m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  876. lwork_cgelqf_mn__ = (integer) cdum[0].r;
  877. cungbr_("P", m, n, m, cdum, m, cdum, cdum, &c_n1, &ierr);
  878. lwork_cungbr_p_mn__ = (integer) cdum[0].r;
  879. cungbr_("P", n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
  880. lwork_cungbr_p_nn__ = (integer) cdum[0].r;
  881. cungbr_("Q", m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
  882. lwork_cungbr_q_mm__ = (integer) cdum[0].r;
  883. cunglq_(m, n, m, cdum, m, cdum, cdum, &c_n1, &ierr);
  884. lwork_cunglq_mn__ = (integer) cdum[0].r;
  885. cunglq_(n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
  886. lwork_cunglq_nn__ = (integer) cdum[0].r;
  887. cunmbr_("P", "R", "C", m, m, m, cdum, m, cdum, cdum, m, cdum, &
  888. c_n1, &ierr);
  889. lwork_cunmbr_prc_mm__ = (integer) cdum[0].r;
  890. cunmbr_("P", "R", "C", m, n, m, cdum, m, cdum, cdum, m, cdum, &
  891. c_n1, &ierr);
  892. lwork_cunmbr_prc_mn__ = (integer) cdum[0].r;
  893. cunmbr_("P", "R", "C", n, n, m, cdum, n, cdum, cdum, n, cdum, &
  894. c_n1, &ierr);
  895. lwork_cunmbr_prc_nn__ = (integer) cdum[0].r;
  896. cunmbr_("Q", "L", "N", m, m, m, cdum, m, cdum, cdum, m, cdum, &
  897. c_n1, &ierr);
  898. lwork_cunmbr_qln_mm__ = (integer) cdum[0].r;
  899. if (*n >= mnthr1) {
  900. if (wntqn) {
  901. /* Path 1t (N >> M, JOBZ='N') */
  902. maxwrk = *m + lwork_cgelqf_mn__;
  903. /* Computing MAX */
  904. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cgebrd_mm__;
  905. maxwrk = f2cmax(i__1,i__2);
  906. minwrk = *m * 3;
  907. } else if (wntqo) {
  908. /* Path 2t (N >> M, JOBZ='O') */
  909. wrkbl = *m + lwork_cgelqf_mn__;
  910. /* Computing MAX */
  911. i__1 = wrkbl, i__2 = *m + lwork_cunglq_mn__;
  912. wrkbl = f2cmax(i__1,i__2);
  913. /* Computing MAX */
  914. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cgebrd_mm__;
  915. wrkbl = f2cmax(i__1,i__2);
  916. /* Computing MAX */
  917. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
  918. wrkbl = f2cmax(i__1,i__2);
  919. /* Computing MAX */
  920. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_prc_mm__;
  921. wrkbl = f2cmax(i__1,i__2);
  922. maxwrk = *m * *n + *m * *m + wrkbl;
  923. minwrk = (*m << 1) * *m + *m * 3;
  924. } else if (wntqs) {
  925. /* Path 3t (N >> M, JOBZ='S') */
  926. wrkbl = *m + lwork_cgelqf_mn__;
  927. /* Computing MAX */
  928. i__1 = wrkbl, i__2 = *m + lwork_cunglq_mn__;
  929. wrkbl = f2cmax(i__1,i__2);
  930. /* Computing MAX */
  931. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cgebrd_mm__;
  932. wrkbl = f2cmax(i__1,i__2);
  933. /* Computing MAX */
  934. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
  935. wrkbl = f2cmax(i__1,i__2);
  936. /* Computing MAX */
  937. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_prc_mm__;
  938. wrkbl = f2cmax(i__1,i__2);
  939. maxwrk = *m * *m + wrkbl;
  940. minwrk = *m * *m + *m * 3;
  941. } else if (wntqa) {
  942. /* Path 4t (N >> M, JOBZ='A') */
  943. wrkbl = *m + lwork_cgelqf_mn__;
  944. /* Computing MAX */
  945. i__1 = wrkbl, i__2 = *m + lwork_cunglq_nn__;
  946. wrkbl = f2cmax(i__1,i__2);
  947. /* Computing MAX */
  948. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cgebrd_mm__;
  949. wrkbl = f2cmax(i__1,i__2);
  950. /* Computing MAX */
  951. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
  952. wrkbl = f2cmax(i__1,i__2);
  953. /* Computing MAX */
  954. i__1 = wrkbl, i__2 = (*m << 1) + lwork_cunmbr_prc_mm__;
  955. wrkbl = f2cmax(i__1,i__2);
  956. maxwrk = *m * *m + wrkbl;
  957. /* Computing MAX */
  958. i__1 = *m * 3, i__2 = *m + *n;
  959. minwrk = *m * *m + f2cmax(i__1,i__2);
  960. }
  961. } else if (*n >= mnthr2) {
  962. /* Path 5t (N >> M, but not as much as MNTHR1) */
  963. maxwrk = (*m << 1) + lwork_cgebrd_mn__;
  964. minwrk = (*m << 1) + *n;
  965. if (wntqo) {
  966. /* Path 5to (N >> M, JOBZ='O') */
  967. /* Computing MAX */
  968. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_q_mm__;
  969. maxwrk = f2cmax(i__1,i__2);
  970. /* Computing MAX */
  971. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_p_mn__;
  972. maxwrk = f2cmax(i__1,i__2);
  973. maxwrk += *m * *n;
  974. minwrk += *m * *m;
  975. } else if (wntqs) {
  976. /* Path 5ts (N >> M, JOBZ='S') */
  977. /* Computing MAX */
  978. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_q_mm__;
  979. maxwrk = f2cmax(i__1,i__2);
  980. /* Computing MAX */
  981. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_p_mn__;
  982. maxwrk = f2cmax(i__1,i__2);
  983. } else if (wntqa) {
  984. /* Path 5ta (N >> M, JOBZ='A') */
  985. /* Computing MAX */
  986. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_q_mm__;
  987. maxwrk = f2cmax(i__1,i__2);
  988. /* Computing MAX */
  989. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cungbr_p_nn__;
  990. maxwrk = f2cmax(i__1,i__2);
  991. }
  992. } else {
  993. /* Path 6t (N > M, but not much larger) */
  994. maxwrk = (*m << 1) + lwork_cgebrd_mn__;
  995. minwrk = (*m << 1) + *n;
  996. if (wntqo) {
  997. /* Path 6to (N > M, JOBZ='O') */
  998. /* Computing MAX */
  999. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
  1000. maxwrk = f2cmax(i__1,i__2);
  1001. /* Computing MAX */
  1002. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_prc_mn__;
  1003. maxwrk = f2cmax(i__1,i__2);
  1004. maxwrk += *m * *n;
  1005. minwrk += *m * *m;
  1006. } else if (wntqs) {
  1007. /* Path 6ts (N > M, JOBZ='S') */
  1008. /* Computing MAX */
  1009. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
  1010. maxwrk = f2cmax(i__1,i__2);
  1011. /* Computing MAX */
  1012. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_prc_mn__;
  1013. maxwrk = f2cmax(i__1,i__2);
  1014. } else if (wntqa) {
  1015. /* Path 6ta (N > M, JOBZ='A') */
  1016. /* Computing MAX */
  1017. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_qln_mm__;
  1018. maxwrk = f2cmax(i__1,i__2);
  1019. /* Computing MAX */
  1020. i__1 = maxwrk, i__2 = (*m << 1) + lwork_cunmbr_prc_nn__;
  1021. maxwrk = f2cmax(i__1,i__2);
  1022. }
  1023. }
  1024. }
  1025. maxwrk = f2cmax(maxwrk,minwrk);
  1026. }
  1027. if (*info == 0) {
  1028. work[1].r = (real) maxwrk, work[1].i = 0.f;
  1029. if (*lwork < minwrk && ! lquery) {
  1030. *info = -12;
  1031. }
  1032. }
  1033. if (*info != 0) {
  1034. i__1 = -(*info);
  1035. xerbla_("CGESDD", &i__1, (ftnlen)6);
  1036. return 0;
  1037. } else if (lquery) {
  1038. return 0;
  1039. }
  1040. /* Quick return if possible */
  1041. if (*m == 0 || *n == 0) {
  1042. return 0;
  1043. }
  1044. /* Get machine constants */
  1045. eps = slamch_("P");
  1046. smlnum = sqrt(slamch_("S")) / eps;
  1047. bignum = 1.f / smlnum;
  1048. /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
  1049. anrm = clange_("M", m, n, &a[a_offset], lda, dum);
  1050. if (sisnan_(&anrm)) {
  1051. *info = -4;
  1052. return 0;
  1053. }
  1054. iscl = 0;
  1055. if (anrm > 0.f && anrm < smlnum) {
  1056. iscl = 1;
  1057. clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
  1058. ierr);
  1059. } else if (anrm > bignum) {
  1060. iscl = 1;
  1061. clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &
  1062. ierr);
  1063. }
  1064. if (*m >= *n) {
  1065. /* A has at least as many rows as columns. If A has sufficiently */
  1066. /* more rows than columns, first reduce using the QR */
  1067. /* decomposition (if sufficient workspace available) */
  1068. if (*m >= mnthr1) {
  1069. if (wntqn) {
  1070. /* Path 1 (M >> N, JOBZ='N') */
  1071. /* No singular vectors to be computed */
  1072. itau = 1;
  1073. nwork = itau + *n;
  1074. /* Compute A=Q*R */
  1075. /* CWorkspace: need N [tau] + N [work] */
  1076. /* CWorkspace: prefer N [tau] + N*NB [work] */
  1077. /* RWorkspace: need 0 */
  1078. i__1 = *lwork - nwork + 1;
  1079. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1080. i__1, &ierr);
  1081. /* Zero out below R */
  1082. i__1 = *n - 1;
  1083. i__2 = *n - 1;
  1084. claset_("L", &i__1, &i__2, &c_b1, &c_b1, &a[a_dim1 + 2], lda);
  1085. ie = 1;
  1086. itauq = 1;
  1087. itaup = itauq + *n;
  1088. nwork = itaup + *n;
  1089. /* Bidiagonalize R in A */
  1090. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1091. /* CWorkspace: prefer 2*N [tauq, taup] + 2*N*NB [work] */
  1092. /* RWorkspace: need N [e] */
  1093. i__1 = *lwork - nwork + 1;
  1094. cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1095. itauq], &work[itaup], &work[nwork], &i__1, &ierr);
  1096. nrwork = ie + *n;
  1097. /* Perform bidiagonal SVD, compute singular values only */
  1098. /* CWorkspace: need 0 */
  1099. /* RWorkspace: need N [e] + BDSPAC */
  1100. sbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
  1101. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  1102. } else if (wntqo) {
  1103. /* Path 2 (M >> N, JOBZ='O') */
  1104. /* N left singular vectors to be overwritten on A and */
  1105. /* N right singular vectors to be computed in VT */
  1106. iu = 1;
  1107. /* WORK(IU) is N by N */
  1108. ldwrku = *n;
  1109. ir = iu + ldwrku * *n;
  1110. if (*lwork >= *m * *n + *n * *n + *n * 3) {
  1111. /* WORK(IR) is M by N */
  1112. ldwrkr = *m;
  1113. } else {
  1114. ldwrkr = (*lwork - *n * *n - *n * 3) / *n;
  1115. }
  1116. itau = ir + ldwrkr * *n;
  1117. nwork = itau + *n;
  1118. /* Compute A=Q*R */
  1119. /* CWorkspace: need N*N [U] + N*N [R] + N [tau] + N [work] */
  1120. /* CWorkspace: prefer N*N [U] + N*N [R] + N [tau] + N*NB [work] */
  1121. /* RWorkspace: need 0 */
  1122. i__1 = *lwork - nwork + 1;
  1123. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1124. i__1, &ierr);
  1125. /* Copy R to WORK( IR ), zeroing out below it */
  1126. clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
  1127. i__1 = *n - 1;
  1128. i__2 = *n - 1;
  1129. claset_("L", &i__1, &i__2, &c_b1, &c_b1, &work[ir + 1], &
  1130. ldwrkr);
  1131. /* Generate Q in A */
  1132. /* CWorkspace: need N*N [U] + N*N [R] + N [tau] + N [work] */
  1133. /* CWorkspace: prefer N*N [U] + N*N [R] + N [tau] + N*NB [work] */
  1134. /* RWorkspace: need 0 */
  1135. i__1 = *lwork - nwork + 1;
  1136. cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
  1137. &i__1, &ierr);
  1138. ie = 1;
  1139. itauq = itau;
  1140. itaup = itauq + *n;
  1141. nwork = itaup + *n;
  1142. /* Bidiagonalize R in WORK(IR) */
  1143. /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
  1144. /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + 2*N*NB [work] */
  1145. /* RWorkspace: need N [e] */
  1146. i__1 = *lwork - nwork + 1;
  1147. cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[
  1148. itauq], &work[itaup], &work[nwork], &i__1, &ierr);
  1149. /* Perform bidiagonal SVD, computing left singular vectors */
  1150. /* of R in WORK(IRU) and computing right singular vectors */
  1151. /* of R in WORK(IRVT) */
  1152. /* CWorkspace: need 0 */
  1153. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1154. iru = ie + *n;
  1155. irvt = iru + *n * *n;
  1156. nrwork = irvt + *n * *n;
  1157. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1158. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1159. info);
  1160. /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
  1161. /* Overwrite WORK(IU) by the left singular vectors of R */
  1162. /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
  1163. /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + N*NB [work] */
  1164. /* RWorkspace: need 0 */
  1165. clacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
  1166. i__1 = *lwork - nwork + 1;
  1167. cunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
  1168. itauq], &work[iu], &ldwrku, &work[nwork], &i__1, &
  1169. ierr);
  1170. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1171. /* Overwrite VT by the right singular vectors of R */
  1172. /* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
  1173. /* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + N*NB [work] */
  1174. /* RWorkspace: need 0 */
  1175. clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1176. i__1 = *lwork - nwork + 1;
  1177. cunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[
  1178. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  1179. ierr);
  1180. /* Multiply Q in A by left singular vectors of R in */
  1181. /* WORK(IU), storing result in WORK(IR) and copying to A */
  1182. /* CWorkspace: need N*N [U] + N*N [R] */
  1183. /* CWorkspace: prefer N*N [U] + M*N [R] */
  1184. /* RWorkspace: need 0 */
  1185. i__1 = *m;
  1186. i__2 = ldwrkr;
  1187. for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
  1188. i__2) {
  1189. /* Computing MIN */
  1190. i__3 = *m - i__ + 1;
  1191. chunk = f2cmin(i__3,ldwrkr);
  1192. cgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1],
  1193. lda, &work[iu], &ldwrku, &c_b1, &work[ir], &
  1194. ldwrkr);
  1195. clacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ +
  1196. a_dim1], lda);
  1197. /* L10: */
  1198. }
  1199. } else if (wntqs) {
  1200. /* Path 3 (M >> N, JOBZ='S') */
  1201. /* N left singular vectors to be computed in U and */
  1202. /* N right singular vectors to be computed in VT */
  1203. ir = 1;
  1204. /* WORK(IR) is N by N */
  1205. ldwrkr = *n;
  1206. itau = ir + ldwrkr * *n;
  1207. nwork = itau + *n;
  1208. /* Compute A=Q*R */
  1209. /* CWorkspace: need N*N [R] + N [tau] + N [work] */
  1210. /* CWorkspace: prefer N*N [R] + N [tau] + N*NB [work] */
  1211. /* RWorkspace: need 0 */
  1212. i__2 = *lwork - nwork + 1;
  1213. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1214. i__2, &ierr);
  1215. /* Copy R to WORK(IR), zeroing out below it */
  1216. clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
  1217. i__2 = *n - 1;
  1218. i__1 = *n - 1;
  1219. claset_("L", &i__2, &i__1, &c_b1, &c_b1, &work[ir + 1], &
  1220. ldwrkr);
  1221. /* Generate Q in A */
  1222. /* CWorkspace: need N*N [R] + N [tau] + N [work] */
  1223. /* CWorkspace: prefer N*N [R] + N [tau] + N*NB [work] */
  1224. /* RWorkspace: need 0 */
  1225. i__2 = *lwork - nwork + 1;
  1226. cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
  1227. &i__2, &ierr);
  1228. ie = 1;
  1229. itauq = itau;
  1230. itaup = itauq + *n;
  1231. nwork = itaup + *n;
  1232. /* Bidiagonalize R in WORK(IR) */
  1233. /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
  1234. /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + 2*N*NB [work] */
  1235. /* RWorkspace: need N [e] */
  1236. i__2 = *lwork - nwork + 1;
  1237. cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[
  1238. itauq], &work[itaup], &work[nwork], &i__2, &ierr);
  1239. /* Perform bidiagonal SVD, computing left singular vectors */
  1240. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1241. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1242. /* CWorkspace: need 0 */
  1243. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1244. iru = ie + *n;
  1245. irvt = iru + *n * *n;
  1246. nrwork = irvt + *n * *n;
  1247. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1248. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1249. info);
  1250. /* Copy real matrix RWORK(IRU) to complex matrix U */
  1251. /* Overwrite U by left singular vectors of R */
  1252. /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
  1253. /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + N*NB [work] */
  1254. /* RWorkspace: need 0 */
  1255. clacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
  1256. i__2 = *lwork - nwork + 1;
  1257. cunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
  1258. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  1259. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1260. /* Overwrite VT by right singular vectors of R */
  1261. /* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
  1262. /* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + N*NB [work] */
  1263. /* RWorkspace: need 0 */
  1264. clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1265. i__2 = *lwork - nwork + 1;
  1266. cunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[
  1267. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
  1268. ierr);
  1269. /* Multiply Q in A by left singular vectors of R in */
  1270. /* WORK(IR), storing result in U */
  1271. /* CWorkspace: need N*N [R] */
  1272. /* RWorkspace: need 0 */
  1273. clacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr);
  1274. cgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &work[ir],
  1275. &ldwrkr, &c_b1, &u[u_offset], ldu);
  1276. } else if (wntqa) {
  1277. /* Path 4 (M >> N, JOBZ='A') */
  1278. /* M left singular vectors to be computed in U and */
  1279. /* N right singular vectors to be computed in VT */
  1280. iu = 1;
  1281. /* WORK(IU) is N by N */
  1282. ldwrku = *n;
  1283. itau = iu + ldwrku * *n;
  1284. nwork = itau + *n;
  1285. /* Compute A=Q*R, copying result to U */
  1286. /* CWorkspace: need N*N [U] + N [tau] + N [work] */
  1287. /* CWorkspace: prefer N*N [U] + N [tau] + N*NB [work] */
  1288. /* RWorkspace: need 0 */
  1289. i__2 = *lwork - nwork + 1;
  1290. cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1291. i__2, &ierr);
  1292. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1293. /* Generate Q in U */
  1294. /* CWorkspace: need N*N [U] + N [tau] + M [work] */
  1295. /* CWorkspace: prefer N*N [U] + N [tau] + M*NB [work] */
  1296. /* RWorkspace: need 0 */
  1297. i__2 = *lwork - nwork + 1;
  1298. cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork],
  1299. &i__2, &ierr);
  1300. /* Produce R in A, zeroing out below it */
  1301. i__2 = *n - 1;
  1302. i__1 = *n - 1;
  1303. claset_("L", &i__2, &i__1, &c_b1, &c_b1, &a[a_dim1 + 2], lda);
  1304. ie = 1;
  1305. itauq = itau;
  1306. itaup = itauq + *n;
  1307. nwork = itaup + *n;
  1308. /* Bidiagonalize R in A */
  1309. /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
  1310. /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + 2*N*NB [work] */
  1311. /* RWorkspace: need N [e] */
  1312. i__2 = *lwork - nwork + 1;
  1313. cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1314. itauq], &work[itaup], &work[nwork], &i__2, &ierr);
  1315. iru = ie + *n;
  1316. irvt = iru + *n * *n;
  1317. nrwork = irvt + *n * *n;
  1318. /* Perform bidiagonal SVD, computing left singular vectors */
  1319. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1320. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1321. /* CWorkspace: need 0 */
  1322. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1323. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1324. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1325. info);
  1326. /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
  1327. /* Overwrite WORK(IU) by left singular vectors of R */
  1328. /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
  1329. /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + N*NB [work] */
  1330. /* RWorkspace: need 0 */
  1331. clacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
  1332. i__2 = *lwork - nwork + 1;
  1333. cunmbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[
  1334. itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
  1335. ierr);
  1336. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1337. /* Overwrite VT by right singular vectors of R */
  1338. /* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
  1339. /* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + N*NB [work] */
  1340. /* RWorkspace: need 0 */
  1341. clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1342. i__2 = *lwork - nwork + 1;
  1343. cunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
  1344. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
  1345. ierr);
  1346. /* Multiply Q in U by left singular vectors of R in */
  1347. /* WORK(IU), storing result in A */
  1348. /* CWorkspace: need N*N [U] */
  1349. /* RWorkspace: need 0 */
  1350. cgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &work[iu],
  1351. &ldwrku, &c_b1, &a[a_offset], lda);
  1352. /* Copy left singular vectors of A from A to U */
  1353. clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1354. }
  1355. } else if (*m >= mnthr2) {
  1356. /* MNTHR2 <= M < MNTHR1 */
  1357. /* Path 5 (M >> N, but not as much as MNTHR1) */
  1358. /* Reduce to bidiagonal form without QR decomposition, use */
  1359. /* CUNGBR and matrix multiplication to compute singular vectors */
  1360. ie = 1;
  1361. nrwork = ie + *n;
  1362. itauq = 1;
  1363. itaup = itauq + *n;
  1364. nwork = itaup + *n;
  1365. /* Bidiagonalize A */
  1366. /* CWorkspace: need 2*N [tauq, taup] + M [work] */
  1367. /* CWorkspace: prefer 2*N [tauq, taup] + (M+N)*NB [work] */
  1368. /* RWorkspace: need N [e] */
  1369. i__2 = *lwork - nwork + 1;
  1370. cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  1371. &work[itaup], &work[nwork], &i__2, &ierr);
  1372. if (wntqn) {
  1373. /* Path 5n (M >> N, JOBZ='N') */
  1374. /* Compute singular values only */
  1375. /* CWorkspace: need 0 */
  1376. /* RWorkspace: need N [e] + BDSPAC */
  1377. sbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
  1378. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  1379. } else if (wntqo) {
  1380. iu = nwork;
  1381. iru = nrwork;
  1382. irvt = iru + *n * *n;
  1383. nrwork = irvt + *n * *n;
  1384. /* Path 5o (M >> N, JOBZ='O') */
  1385. /* Copy A to VT, generate P**H */
  1386. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1387. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1388. /* RWorkspace: need 0 */
  1389. clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1390. i__2 = *lwork - nwork + 1;
  1391. cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
  1392. work[nwork], &i__2, &ierr);
  1393. /* Generate Q in A */
  1394. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1395. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1396. /* RWorkspace: need 0 */
  1397. i__2 = *lwork - nwork + 1;
  1398. cungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[
  1399. nwork], &i__2, &ierr);
  1400. if (*lwork >= *m * *n + *n * 3) {
  1401. /* WORK( IU ) is M by N */
  1402. ldwrku = *m;
  1403. } else {
  1404. /* WORK(IU) is LDWRKU by N */
  1405. ldwrku = (*lwork - *n * 3) / *n;
  1406. }
  1407. nwork = iu + ldwrku * *n;
  1408. /* Perform bidiagonal SVD, computing left singular vectors */
  1409. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1410. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1411. /* CWorkspace: need 0 */
  1412. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1413. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1414. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1415. info);
  1416. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  1417. /* storing the result in WORK(IU), copying to VT */
  1418. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
  1419. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
  1420. clarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &work[iu]
  1421. , &ldwrku, &rwork[nrwork]);
  1422. clacpy_("F", n, n, &work[iu], &ldwrku, &vt[vt_offset], ldvt);
  1423. /* Multiply Q in A by real matrix RWORK(IRU), storing the */
  1424. /* result in WORK(IU), copying to A */
  1425. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
  1426. /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] */
  1427. /* RWorkspace: need N [e] + N*N [RU] + 2*N*N [rwork] */
  1428. /* RWorkspace: prefer N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
  1429. nrwork = irvt;
  1430. i__2 = *m;
  1431. i__1 = ldwrku;
  1432. for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
  1433. i__1) {
  1434. /* Computing MIN */
  1435. i__3 = *m - i__ + 1;
  1436. chunk = f2cmin(i__3,ldwrku);
  1437. clacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru], n,
  1438. &work[iu], &ldwrku, &rwork[nrwork]);
  1439. clacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
  1440. a_dim1], lda);
  1441. /* L20: */
  1442. }
  1443. } else if (wntqs) {
  1444. /* Path 5s (M >> N, JOBZ='S') */
  1445. /* Copy A to VT, generate P**H */
  1446. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1447. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1448. /* RWorkspace: need 0 */
  1449. clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1450. i__1 = *lwork - nwork + 1;
  1451. cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
  1452. work[nwork], &i__1, &ierr);
  1453. /* Copy A to U, generate Q */
  1454. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1455. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1456. /* RWorkspace: need 0 */
  1457. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1458. i__1 = *lwork - nwork + 1;
  1459. cungbr_("Q", m, n, n, &u[u_offset], ldu, &work[itauq], &work[
  1460. nwork], &i__1, &ierr);
  1461. /* Perform bidiagonal SVD, computing left singular vectors */
  1462. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1463. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1464. /* CWorkspace: need 0 */
  1465. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1466. iru = nrwork;
  1467. irvt = iru + *n * *n;
  1468. nrwork = irvt + *n * *n;
  1469. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1470. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1471. info);
  1472. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  1473. /* storing the result in A, copying to VT */
  1474. /* CWorkspace: need 0 */
  1475. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
  1476. clarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[
  1477. a_offset], lda, &rwork[nrwork]);
  1478. clacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1479. /* Multiply Q in U by real matrix RWORK(IRU), storing the */
  1480. /* result in A, copying to U */
  1481. /* CWorkspace: need 0 */
  1482. /* RWorkspace: need N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
  1483. nrwork = irvt;
  1484. clacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset],
  1485. lda, &rwork[nrwork]);
  1486. clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1487. } else {
  1488. /* Path 5a (M >> N, JOBZ='A') */
  1489. /* Copy A to VT, generate P**H */
  1490. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1491. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1492. /* RWorkspace: need 0 */
  1493. clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1494. i__1 = *lwork - nwork + 1;
  1495. cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
  1496. work[nwork], &i__1, &ierr);
  1497. /* Copy A to U, generate Q */
  1498. /* CWorkspace: need 2*N [tauq, taup] + M [work] */
  1499. /* CWorkspace: prefer 2*N [tauq, taup] + M*NB [work] */
  1500. /* RWorkspace: need 0 */
  1501. clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1502. i__1 = *lwork - nwork + 1;
  1503. cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  1504. nwork], &i__1, &ierr);
  1505. /* Perform bidiagonal SVD, computing left singular vectors */
  1506. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1507. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1508. /* CWorkspace: need 0 */
  1509. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1510. iru = nrwork;
  1511. irvt = iru + *n * *n;
  1512. nrwork = irvt + *n * *n;
  1513. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1514. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1515. info);
  1516. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  1517. /* storing the result in A, copying to VT */
  1518. /* CWorkspace: need 0 */
  1519. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
  1520. clarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[
  1521. a_offset], lda, &rwork[nrwork]);
  1522. clacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1523. /* Multiply Q in U by real matrix RWORK(IRU), storing the */
  1524. /* result in A, copying to U */
  1525. /* CWorkspace: need 0 */
  1526. /* RWorkspace: need N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
  1527. nrwork = irvt;
  1528. clacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset],
  1529. lda, &rwork[nrwork]);
  1530. clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
  1531. }
  1532. } else {
  1533. /* M .LT. MNTHR2 */
  1534. /* Path 6 (M >= N, but not much larger) */
  1535. /* Reduce to bidiagonal form without QR decomposition */
  1536. /* Use CUNMBR to compute singular vectors */
  1537. ie = 1;
  1538. nrwork = ie + *n;
  1539. itauq = 1;
  1540. itaup = itauq + *n;
  1541. nwork = itaup + *n;
  1542. /* Bidiagonalize A */
  1543. /* CWorkspace: need 2*N [tauq, taup] + M [work] */
  1544. /* CWorkspace: prefer 2*N [tauq, taup] + (M+N)*NB [work] */
  1545. /* RWorkspace: need N [e] */
  1546. i__1 = *lwork - nwork + 1;
  1547. cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  1548. &work[itaup], &work[nwork], &i__1, &ierr);
  1549. if (wntqn) {
  1550. /* Path 6n (M >= N, JOBZ='N') */
  1551. /* Compute singular values only */
  1552. /* CWorkspace: need 0 */
  1553. /* RWorkspace: need N [e] + BDSPAC */
  1554. sbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
  1555. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  1556. } else if (wntqo) {
  1557. iu = nwork;
  1558. iru = nrwork;
  1559. irvt = iru + *n * *n;
  1560. nrwork = irvt + *n * *n;
  1561. if (*lwork >= *m * *n + *n * 3) {
  1562. /* WORK( IU ) is M by N */
  1563. ldwrku = *m;
  1564. } else {
  1565. /* WORK( IU ) is LDWRKU by N */
  1566. ldwrku = (*lwork - *n * 3) / *n;
  1567. }
  1568. nwork = iu + ldwrku * *n;
  1569. /* Path 6o (M >= N, JOBZ='O') */
  1570. /* Perform bidiagonal SVD, computing left singular vectors */
  1571. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1572. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1573. /* CWorkspace: need 0 */
  1574. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1575. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1576. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1577. info);
  1578. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1579. /* Overwrite VT by right singular vectors of A */
  1580. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] + N [work] */
  1581. /* CWorkspace: prefer 2*N [tauq, taup] + N*N [U] + N*NB [work] */
  1582. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1583. clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1584. i__1 = *lwork - nwork + 1;
  1585. cunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
  1586. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  1587. ierr);
  1588. if (*lwork >= *m * *n + *n * 3) {
  1589. /* Path 6o-fast */
  1590. /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
  1591. /* Overwrite WORK(IU) by left singular vectors of A, copying */
  1592. /* to A */
  1593. /* CWorkspace: need 2*N [tauq, taup] + M*N [U] + N [work] */
  1594. /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] + N*NB [work] */
  1595. /* RWorkspace: need N [e] + N*N [RU] */
  1596. claset_("F", m, n, &c_b1, &c_b1, &work[iu], &ldwrku);
  1597. clacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
  1598. i__1 = *lwork - nwork + 1;
  1599. cunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
  1600. itauq], &work[iu], &ldwrku, &work[nwork], &i__1, &
  1601. ierr);
  1602. clacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda);
  1603. } else {
  1604. /* Path 6o-slow */
  1605. /* Generate Q in A */
  1606. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] + N [work] */
  1607. /* CWorkspace: prefer 2*N [tauq, taup] + N*N [U] + N*NB [work] */
  1608. /* RWorkspace: need 0 */
  1609. i__1 = *lwork - nwork + 1;
  1610. cungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
  1611. work[nwork], &i__1, &ierr);
  1612. /* Multiply Q in A by real matrix RWORK(IRU), storing the */
  1613. /* result in WORK(IU), copying to A */
  1614. /* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
  1615. /* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] */
  1616. /* RWorkspace: need N [e] + N*N [RU] + 2*N*N [rwork] */
  1617. /* RWorkspace: prefer N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
  1618. nrwork = irvt;
  1619. i__1 = *m;
  1620. i__2 = ldwrku;
  1621. for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
  1622. i__2) {
  1623. /* Computing MIN */
  1624. i__3 = *m - i__ + 1;
  1625. chunk = f2cmin(i__3,ldwrku);
  1626. clacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru],
  1627. n, &work[iu], &ldwrku, &rwork[nrwork]);
  1628. clacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
  1629. a_dim1], lda);
  1630. /* L30: */
  1631. }
  1632. }
  1633. } else if (wntqs) {
  1634. /* Path 6s (M >= N, JOBZ='S') */
  1635. /* Perform bidiagonal SVD, computing left singular vectors */
  1636. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1637. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1638. /* CWorkspace: need 0 */
  1639. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1640. iru = nrwork;
  1641. irvt = iru + *n * *n;
  1642. nrwork = irvt + *n * *n;
  1643. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1644. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1645. info);
  1646. /* Copy real matrix RWORK(IRU) to complex matrix U */
  1647. /* Overwrite U by left singular vectors of A */
  1648. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1649. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1650. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1651. claset_("F", m, n, &c_b1, &c_b1, &u[u_offset], ldu)
  1652. ;
  1653. clacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
  1654. i__2 = *lwork - nwork + 1;
  1655. cunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
  1656. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  1657. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1658. /* Overwrite VT by right singular vectors of A */
  1659. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1660. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1661. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1662. clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1663. i__2 = *lwork - nwork + 1;
  1664. cunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
  1665. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
  1666. ierr);
  1667. } else {
  1668. /* Path 6a (M >= N, JOBZ='A') */
  1669. /* Perform bidiagonal SVD, computing left singular vectors */
  1670. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1671. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1672. /* CWorkspace: need 0 */
  1673. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
  1674. iru = nrwork;
  1675. irvt = iru + *n * *n;
  1676. nrwork = irvt + *n * *n;
  1677. sbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
  1678. rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
  1679. info);
  1680. /* Set the right corner of U to identity matrix */
  1681. claset_("F", m, m, &c_b1, &c_b1, &u[u_offset], ldu)
  1682. ;
  1683. if (*m > *n) {
  1684. i__2 = *m - *n;
  1685. i__1 = *m - *n;
  1686. claset_("F", &i__2, &i__1, &c_b1, &c_b2, &u[*n + 1 + (*n
  1687. + 1) * u_dim1], ldu);
  1688. }
  1689. /* Copy real matrix RWORK(IRU) to complex matrix U */
  1690. /* Overwrite U by left singular vectors of A */
  1691. /* CWorkspace: need 2*N [tauq, taup] + M [work] */
  1692. /* CWorkspace: prefer 2*N [tauq, taup] + M*NB [work] */
  1693. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1694. clacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
  1695. i__2 = *lwork - nwork + 1;
  1696. cunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
  1697. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  1698. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1699. /* Overwrite VT by right singular vectors of A */
  1700. /* CWorkspace: need 2*N [tauq, taup] + N [work] */
  1701. /* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
  1702. /* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
  1703. clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
  1704. i__2 = *lwork - nwork + 1;
  1705. cunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
  1706. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
  1707. ierr);
  1708. }
  1709. }
  1710. } else {
  1711. /* A has more columns than rows. If A has sufficiently more */
  1712. /* columns than rows, first reduce using the LQ decomposition (if */
  1713. /* sufficient workspace available) */
  1714. if (*n >= mnthr1) {
  1715. if (wntqn) {
  1716. /* Path 1t (N >> M, JOBZ='N') */
  1717. /* No singular vectors to be computed */
  1718. itau = 1;
  1719. nwork = itau + *m;
  1720. /* Compute A=L*Q */
  1721. /* CWorkspace: need M [tau] + M [work] */
  1722. /* CWorkspace: prefer M [tau] + M*NB [work] */
  1723. /* RWorkspace: need 0 */
  1724. i__2 = *lwork - nwork + 1;
  1725. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1726. i__2, &ierr);
  1727. /* Zero out above L */
  1728. i__2 = *m - 1;
  1729. i__1 = *m - 1;
  1730. claset_("U", &i__2, &i__1, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
  1731. , lda);
  1732. ie = 1;
  1733. itauq = 1;
  1734. itaup = itauq + *m;
  1735. nwork = itaup + *m;
  1736. /* Bidiagonalize L in A */
  1737. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  1738. /* CWorkspace: prefer 2*M [tauq, taup] + 2*M*NB [work] */
  1739. /* RWorkspace: need M [e] */
  1740. i__2 = *lwork - nwork + 1;
  1741. cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1742. itauq], &work[itaup], &work[nwork], &i__2, &ierr);
  1743. nrwork = ie + *m;
  1744. /* Perform bidiagonal SVD, compute singular values only */
  1745. /* CWorkspace: need 0 */
  1746. /* RWorkspace: need M [e] + BDSPAC */
  1747. sbdsdc_("U", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
  1748. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  1749. } else if (wntqo) {
  1750. /* Path 2t (N >> M, JOBZ='O') */
  1751. /* M right singular vectors to be overwritten on A and */
  1752. /* M left singular vectors to be computed in U */
  1753. ivt = 1;
  1754. ldwkvt = *m;
  1755. /* WORK(IVT) is M by M */
  1756. il = ivt + ldwkvt * *m;
  1757. if (*lwork >= *m * *n + *m * *m + *m * 3) {
  1758. /* WORK(IL) M by N */
  1759. ldwrkl = *m;
  1760. chunk = *n;
  1761. } else {
  1762. /* WORK(IL) is M by CHUNK */
  1763. ldwrkl = *m;
  1764. chunk = (*lwork - *m * *m - *m * 3) / *m;
  1765. }
  1766. itau = il + ldwrkl * chunk;
  1767. nwork = itau + *m;
  1768. /* Compute A=L*Q */
  1769. /* CWorkspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
  1770. /* CWorkspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
  1771. /* RWorkspace: need 0 */
  1772. i__2 = *lwork - nwork + 1;
  1773. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1774. i__2, &ierr);
  1775. /* Copy L to WORK(IL), zeroing about above it */
  1776. clacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
  1777. i__2 = *m - 1;
  1778. i__1 = *m - 1;
  1779. claset_("U", &i__2, &i__1, &c_b1, &c_b1, &work[il + ldwrkl], &
  1780. ldwrkl);
  1781. /* Generate Q in A */
  1782. /* CWorkspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
  1783. /* CWorkspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
  1784. /* RWorkspace: need 0 */
  1785. i__2 = *lwork - nwork + 1;
  1786. cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
  1787. &i__2, &ierr);
  1788. ie = 1;
  1789. itauq = itau;
  1790. itaup = itauq + *m;
  1791. nwork = itaup + *m;
  1792. /* Bidiagonalize L in WORK(IL) */
  1793. /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
  1794. /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + 2*M*NB [work] */
  1795. /* RWorkspace: need M [e] */
  1796. i__2 = *lwork - nwork + 1;
  1797. cgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[
  1798. itauq], &work[itaup], &work[nwork], &i__2, &ierr);
  1799. /* Perform bidiagonal SVD, computing left singular vectors */
  1800. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1801. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1802. /* CWorkspace: need 0 */
  1803. /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
  1804. iru = ie + *m;
  1805. irvt = iru + *m * *m;
  1806. nrwork = irvt + *m * *m;
  1807. sbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  1808. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  1809. info);
  1810. /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
  1811. /* Overwrite WORK(IU) by the left singular vectors of L */
  1812. /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
  1813. /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + M*NB [work] */
  1814. /* RWorkspace: need 0 */
  1815. clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  1816. i__2 = *lwork - nwork + 1;
  1817. cunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
  1818. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  1819. /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
  1820. /* Overwrite WORK(IVT) by the right singular vectors of L */
  1821. /* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
  1822. /* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + M*NB [work] */
  1823. /* RWorkspace: need 0 */
  1824. clacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
  1825. i__2 = *lwork - nwork + 1;
  1826. cunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[
  1827. itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &
  1828. ierr);
  1829. /* Multiply right singular vectors of L in WORK(IL) by Q */
  1830. /* in A, storing result in WORK(IL) and copying to A */
  1831. /* CWorkspace: need M*M [VT] + M*M [L] */
  1832. /* CWorkspace: prefer M*M [VT] + M*N [L] */
  1833. /* RWorkspace: need 0 */
  1834. i__2 = *n;
  1835. i__1 = chunk;
  1836. for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
  1837. i__1) {
  1838. /* Computing MIN */
  1839. i__3 = *n - i__ + 1;
  1840. blk = f2cmin(i__3,chunk);
  1841. cgemm_("N", "N", m, &blk, m, &c_b2, &work[ivt], m, &a[i__
  1842. * a_dim1 + 1], lda, &c_b1, &work[il], &ldwrkl);
  1843. clacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1
  1844. + 1], lda);
  1845. /* L40: */
  1846. }
  1847. } else if (wntqs) {
  1848. /* Path 3t (N >> M, JOBZ='S') */
  1849. /* M right singular vectors to be computed in VT and */
  1850. /* M left singular vectors to be computed in U */
  1851. il = 1;
  1852. /* WORK(IL) is M by M */
  1853. ldwrkl = *m;
  1854. itau = il + ldwrkl * *m;
  1855. nwork = itau + *m;
  1856. /* Compute A=L*Q */
  1857. /* CWorkspace: need M*M [L] + M [tau] + M [work] */
  1858. /* CWorkspace: prefer M*M [L] + M [tau] + M*NB [work] */
  1859. /* RWorkspace: need 0 */
  1860. i__1 = *lwork - nwork + 1;
  1861. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1862. i__1, &ierr);
  1863. /* Copy L to WORK(IL), zeroing out above it */
  1864. clacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
  1865. i__1 = *m - 1;
  1866. i__2 = *m - 1;
  1867. claset_("U", &i__1, &i__2, &c_b1, &c_b1, &work[il + ldwrkl], &
  1868. ldwrkl);
  1869. /* Generate Q in A */
  1870. /* CWorkspace: need M*M [L] + M [tau] + M [work] */
  1871. /* CWorkspace: prefer M*M [L] + M [tau] + M*NB [work] */
  1872. /* RWorkspace: need 0 */
  1873. i__1 = *lwork - nwork + 1;
  1874. cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
  1875. &i__1, &ierr);
  1876. ie = 1;
  1877. itauq = itau;
  1878. itaup = itauq + *m;
  1879. nwork = itaup + *m;
  1880. /* Bidiagonalize L in WORK(IL) */
  1881. /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
  1882. /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + 2*M*NB [work] */
  1883. /* RWorkspace: need M [e] */
  1884. i__1 = *lwork - nwork + 1;
  1885. cgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[
  1886. itauq], &work[itaup], &work[nwork], &i__1, &ierr);
  1887. /* Perform bidiagonal SVD, computing left singular vectors */
  1888. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1889. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1890. /* CWorkspace: need 0 */
  1891. /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
  1892. iru = ie + *m;
  1893. irvt = iru + *m * *m;
  1894. nrwork = irvt + *m * *m;
  1895. sbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  1896. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  1897. info);
  1898. /* Copy real matrix RWORK(IRU) to complex matrix U */
  1899. /* Overwrite U by left singular vectors of L */
  1900. /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
  1901. /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + M*NB [work] */
  1902. /* RWorkspace: need 0 */
  1903. clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  1904. i__1 = *lwork - nwork + 1;
  1905. cunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
  1906. itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
  1907. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  1908. /* Overwrite VT by left singular vectors of L */
  1909. /* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
  1910. /* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + M*NB [work] */
  1911. /* RWorkspace: need 0 */
  1912. clacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
  1913. i__1 = *lwork - nwork + 1;
  1914. cunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[
  1915. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  1916. ierr);
  1917. /* Copy VT to WORK(IL), multiply right singular vectors of L */
  1918. /* in WORK(IL) by Q in A, storing result in VT */
  1919. /* CWorkspace: need M*M [L] */
  1920. /* RWorkspace: need 0 */
  1921. clacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl);
  1922. cgemm_("N", "N", m, n, m, &c_b2, &work[il], &ldwrkl, &a[
  1923. a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
  1924. } else if (wntqa) {
  1925. /* Path 4t (N >> M, JOBZ='A') */
  1926. /* N right singular vectors to be computed in VT and */
  1927. /* M left singular vectors to be computed in U */
  1928. ivt = 1;
  1929. /* WORK(IVT) is M by M */
  1930. ldwkvt = *m;
  1931. itau = ivt + ldwkvt * *m;
  1932. nwork = itau + *m;
  1933. /* Compute A=L*Q, copying result to VT */
  1934. /* CWorkspace: need M*M [VT] + M [tau] + M [work] */
  1935. /* CWorkspace: prefer M*M [VT] + M [tau] + M*NB [work] */
  1936. /* RWorkspace: need 0 */
  1937. i__1 = *lwork - nwork + 1;
  1938. cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
  1939. i__1, &ierr);
  1940. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  1941. /* Generate Q in VT */
  1942. /* CWorkspace: need M*M [VT] + M [tau] + N [work] */
  1943. /* CWorkspace: prefer M*M [VT] + M [tau] + N*NB [work] */
  1944. /* RWorkspace: need 0 */
  1945. i__1 = *lwork - nwork + 1;
  1946. cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[
  1947. nwork], &i__1, &ierr);
  1948. /* Produce L in A, zeroing out above it */
  1949. i__1 = *m - 1;
  1950. i__2 = *m - 1;
  1951. claset_("U", &i__1, &i__2, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
  1952. , lda);
  1953. ie = 1;
  1954. itauq = itau;
  1955. itaup = itauq + *m;
  1956. nwork = itaup + *m;
  1957. /* Bidiagonalize L in A */
  1958. /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
  1959. /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + 2*M*NB [work] */
  1960. /* RWorkspace: need M [e] */
  1961. i__1 = *lwork - nwork + 1;
  1962. cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
  1963. itauq], &work[itaup], &work[nwork], &i__1, &ierr);
  1964. /* Perform bidiagonal SVD, computing left singular vectors */
  1965. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  1966. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  1967. /* CWorkspace: need 0 */
  1968. /* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
  1969. iru = ie + *m;
  1970. irvt = iru + *m * *m;
  1971. nrwork = irvt + *m * *m;
  1972. sbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  1973. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  1974. info);
  1975. /* Copy real matrix RWORK(IRU) to complex matrix U */
  1976. /* Overwrite U by left singular vectors of L */
  1977. /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
  1978. /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + M*NB [work] */
  1979. /* RWorkspace: need 0 */
  1980. clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  1981. i__1 = *lwork - nwork + 1;
  1982. cunmbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[
  1983. itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
  1984. /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
  1985. /* Overwrite WORK(IVT) by right singular vectors of L */
  1986. /* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
  1987. /* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + M*NB [work] */
  1988. /* RWorkspace: need 0 */
  1989. clacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
  1990. i__1 = *lwork - nwork + 1;
  1991. cunmbr_("P", "R", "C", m, m, m, &a[a_offset], lda, &work[
  1992. itaup], &work[ivt], &ldwkvt, &work[nwork], &i__1, &
  1993. ierr);
  1994. /* Multiply right singular vectors of L in WORK(IVT) by */
  1995. /* Q in VT, storing result in A */
  1996. /* CWorkspace: need M*M [VT] */
  1997. /* RWorkspace: need 0 */
  1998. cgemm_("N", "N", m, n, m, &c_b2, &work[ivt], &ldwkvt, &vt[
  1999. vt_offset], ldvt, &c_b1, &a[a_offset], lda);
  2000. /* Copy right singular vectors of A from A to VT */
  2001. clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2002. }
  2003. } else if (*n >= mnthr2) {
  2004. /* MNTHR2 <= N < MNTHR1 */
  2005. /* Path 5t (N >> M, but not as much as MNTHR1) */
  2006. /* Reduce to bidiagonal form without QR decomposition, use */
  2007. /* CUNGBR and matrix multiplication to compute singular vectors */
  2008. ie = 1;
  2009. nrwork = ie + *m;
  2010. itauq = 1;
  2011. itaup = itauq + *m;
  2012. nwork = itaup + *m;
  2013. /* Bidiagonalize A */
  2014. /* CWorkspace: need 2*M [tauq, taup] + N [work] */
  2015. /* CWorkspace: prefer 2*M [tauq, taup] + (M+N)*NB [work] */
  2016. /* RWorkspace: need M [e] */
  2017. i__1 = *lwork - nwork + 1;
  2018. cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  2019. &work[itaup], &work[nwork], &i__1, &ierr);
  2020. if (wntqn) {
  2021. /* Path 5tn (N >> M, JOBZ='N') */
  2022. /* Compute singular values only */
  2023. /* CWorkspace: need 0 */
  2024. /* RWorkspace: need M [e] + BDSPAC */
  2025. sbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
  2026. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  2027. } else if (wntqo) {
  2028. irvt = nrwork;
  2029. iru = irvt + *m * *m;
  2030. nrwork = iru + *m * *m;
  2031. ivt = nwork;
  2032. /* Path 5to (N >> M, JOBZ='O') */
  2033. /* Copy A to U, generate Q */
  2034. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2035. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2036. /* RWorkspace: need 0 */
  2037. clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2038. i__1 = *lwork - nwork + 1;
  2039. cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  2040. nwork], &i__1, &ierr);
  2041. /* Generate P**H in A */
  2042. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2043. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2044. /* RWorkspace: need 0 */
  2045. i__1 = *lwork - nwork + 1;
  2046. cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
  2047. nwork], &i__1, &ierr);
  2048. ldwkvt = *m;
  2049. if (*lwork >= *m * *n + *m * 3) {
  2050. /* WORK( IVT ) is M by N */
  2051. nwork = ivt + ldwkvt * *n;
  2052. chunk = *n;
  2053. } else {
  2054. /* WORK( IVT ) is M by CHUNK */
  2055. chunk = (*lwork - *m * 3) / *m;
  2056. nwork = ivt + ldwkvt * chunk;
  2057. }
  2058. /* Perform bidiagonal SVD, computing left singular vectors */
  2059. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2060. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2061. /* CWorkspace: need 0 */
  2062. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2063. sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2064. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2065. info);
  2066. /* Multiply Q in U by real matrix RWORK(IRVT) */
  2067. /* storing the result in WORK(IVT), copying to U */
  2068. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
  2069. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
  2070. clacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &work[ivt], &
  2071. ldwkvt, &rwork[nrwork]);
  2072. clacpy_("F", m, m, &work[ivt], &ldwkvt, &u[u_offset], ldu);
  2073. /* Multiply RWORK(IRVT) by P**H in A, storing the */
  2074. /* result in WORK(IVT), copying to A */
  2075. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
  2076. /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] */
  2077. /* RWorkspace: need M [e] + M*M [RVT] + 2*M*M [rwork] */
  2078. /* RWorkspace: prefer M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
  2079. nrwork = iru;
  2080. i__1 = *n;
  2081. i__2 = chunk;
  2082. for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
  2083. i__2) {
  2084. /* Computing MIN */
  2085. i__3 = *n - i__ + 1;
  2086. blk = f2cmin(i__3,chunk);
  2087. clarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1],
  2088. lda, &work[ivt], &ldwkvt, &rwork[nrwork]);
  2089. clacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ *
  2090. a_dim1 + 1], lda);
  2091. /* L50: */
  2092. }
  2093. } else if (wntqs) {
  2094. /* Path 5ts (N >> M, JOBZ='S') */
  2095. /* Copy A to U, generate Q */
  2096. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2097. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2098. /* RWorkspace: need 0 */
  2099. clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2100. i__2 = *lwork - nwork + 1;
  2101. cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  2102. nwork], &i__2, &ierr);
  2103. /* Copy A to VT, generate P**H */
  2104. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2105. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2106. /* RWorkspace: need 0 */
  2107. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2108. i__2 = *lwork - nwork + 1;
  2109. cungbr_("P", m, n, m, &vt[vt_offset], ldvt, &work[itaup], &
  2110. work[nwork], &i__2, &ierr);
  2111. /* Perform bidiagonal SVD, computing left singular vectors */
  2112. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2113. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2114. /* CWorkspace: need 0 */
  2115. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2116. irvt = nrwork;
  2117. iru = irvt + *m * *m;
  2118. nrwork = iru + *m * *m;
  2119. sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2120. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2121. info);
  2122. /* Multiply Q in U by real matrix RWORK(IRU), storing the */
  2123. /* result in A, copying to U */
  2124. /* CWorkspace: need 0 */
  2125. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
  2126. clacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset],
  2127. lda, &rwork[nrwork]);
  2128. clacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2129. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  2130. /* storing the result in A, copying to VT */
  2131. /* CWorkspace: need 0 */
  2132. /* RWorkspace: need M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
  2133. nrwork = iru;
  2134. clarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[
  2135. a_offset], lda, &rwork[nrwork]);
  2136. clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2137. } else {
  2138. /* Path 5ta (N >> M, JOBZ='A') */
  2139. /* Copy A to U, generate Q */
  2140. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2141. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2142. /* RWorkspace: need 0 */
  2143. clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2144. i__2 = *lwork - nwork + 1;
  2145. cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
  2146. nwork], &i__2, &ierr);
  2147. /* Copy A to VT, generate P**H */
  2148. /* CWorkspace: need 2*M [tauq, taup] + N [work] */
  2149. /* CWorkspace: prefer 2*M [tauq, taup] + N*NB [work] */
  2150. /* RWorkspace: need 0 */
  2151. clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2152. i__2 = *lwork - nwork + 1;
  2153. cungbr_("P", n, n, m, &vt[vt_offset], ldvt, &work[itaup], &
  2154. work[nwork], &i__2, &ierr);
  2155. /* Perform bidiagonal SVD, computing left singular vectors */
  2156. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2157. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2158. /* CWorkspace: need 0 */
  2159. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2160. irvt = nrwork;
  2161. iru = irvt + *m * *m;
  2162. nrwork = iru + *m * *m;
  2163. sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2164. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2165. info);
  2166. /* Multiply Q in U by real matrix RWORK(IRU), storing the */
  2167. /* result in A, copying to U */
  2168. /* CWorkspace: need 0 */
  2169. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
  2170. clacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset],
  2171. lda, &rwork[nrwork]);
  2172. clacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
  2173. /* Multiply real matrix RWORK(IRVT) by P**H in VT, */
  2174. /* storing the result in A, copying to VT */
  2175. /* CWorkspace: need 0 */
  2176. /* RWorkspace: need M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
  2177. nrwork = iru;
  2178. clarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[
  2179. a_offset], lda, &rwork[nrwork]);
  2180. clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
  2181. }
  2182. } else {
  2183. /* N .LT. MNTHR2 */
  2184. /* Path 6t (N > M, but not much larger) */
  2185. /* Reduce to bidiagonal form without LQ decomposition */
  2186. /* Use CUNMBR to compute singular vectors */
  2187. ie = 1;
  2188. nrwork = ie + *m;
  2189. itauq = 1;
  2190. itaup = itauq + *m;
  2191. nwork = itaup + *m;
  2192. /* Bidiagonalize A */
  2193. /* CWorkspace: need 2*M [tauq, taup] + N [work] */
  2194. /* CWorkspace: prefer 2*M [tauq, taup] + (M+N)*NB [work] */
  2195. /* RWorkspace: need M [e] */
  2196. i__2 = *lwork - nwork + 1;
  2197. cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
  2198. &work[itaup], &work[nwork], &i__2, &ierr);
  2199. if (wntqn) {
  2200. /* Path 6tn (N > M, JOBZ='N') */
  2201. /* Compute singular values only */
  2202. /* CWorkspace: need 0 */
  2203. /* RWorkspace: need M [e] + BDSPAC */
  2204. sbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
  2205. c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
  2206. } else if (wntqo) {
  2207. /* Path 6to (N > M, JOBZ='O') */
  2208. ldwkvt = *m;
  2209. ivt = nwork;
  2210. if (*lwork >= *m * *n + *m * 3) {
  2211. /* WORK( IVT ) is M by N */
  2212. claset_("F", m, n, &c_b1, &c_b1, &work[ivt], &ldwkvt);
  2213. nwork = ivt + ldwkvt * *n;
  2214. } else {
  2215. /* WORK( IVT ) is M by CHUNK */
  2216. chunk = (*lwork - *m * 3) / *m;
  2217. nwork = ivt + ldwkvt * chunk;
  2218. }
  2219. /* Perform bidiagonal SVD, computing left singular vectors */
  2220. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2221. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2222. /* CWorkspace: need 0 */
  2223. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2224. irvt = nrwork;
  2225. iru = irvt + *m * *m;
  2226. nrwork = iru + *m * *m;
  2227. sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2228. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2229. info);
  2230. /* Copy real matrix RWORK(IRU) to complex matrix U */
  2231. /* Overwrite U by left singular vectors of A */
  2232. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] + M [work] */
  2233. /* CWorkspace: prefer 2*M [tauq, taup] + M*M [VT] + M*NB [work] */
  2234. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
  2235. clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  2236. i__2 = *lwork - nwork + 1;
  2237. cunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
  2238. itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
  2239. if (*lwork >= *m * *n + *m * 3) {
  2240. /* Path 6to-fast */
  2241. /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
  2242. /* Overwrite WORK(IVT) by right singular vectors of A, */
  2243. /* copying to A */
  2244. /* CWorkspace: need 2*M [tauq, taup] + M*N [VT] + M [work] */
  2245. /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] + M*NB [work] */
  2246. /* RWorkspace: need M [e] + M*M [RVT] */
  2247. clacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
  2248. i__2 = *lwork - nwork + 1;
  2249. cunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[
  2250. itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2,
  2251. &ierr);
  2252. clacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda);
  2253. } else {
  2254. /* Path 6to-slow */
  2255. /* Generate P**H in A */
  2256. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] + M [work] */
  2257. /* CWorkspace: prefer 2*M [tauq, taup] + M*M [VT] + M*NB [work] */
  2258. /* RWorkspace: need 0 */
  2259. i__2 = *lwork - nwork + 1;
  2260. cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
  2261. work[nwork], &i__2, &ierr);
  2262. /* Multiply Q in A by real matrix RWORK(IRU), storing the */
  2263. /* result in WORK(IU), copying to A */
  2264. /* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
  2265. /* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] */
  2266. /* RWorkspace: need M [e] + M*M [RVT] + 2*M*M [rwork] */
  2267. /* RWorkspace: prefer M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
  2268. nrwork = iru;
  2269. i__2 = *n;
  2270. i__1 = chunk;
  2271. for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
  2272. i__1) {
  2273. /* Computing MIN */
  2274. i__3 = *n - i__ + 1;
  2275. blk = f2cmin(i__3,chunk);
  2276. clarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1]
  2277. , lda, &work[ivt], &ldwkvt, &rwork[nrwork]);
  2278. clacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ *
  2279. a_dim1 + 1], lda);
  2280. /* L60: */
  2281. }
  2282. }
  2283. } else if (wntqs) {
  2284. /* Path 6ts (N > M, JOBZ='S') */
  2285. /* Perform bidiagonal SVD, computing left singular vectors */
  2286. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2287. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2288. /* CWorkspace: need 0 */
  2289. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2290. irvt = nrwork;
  2291. iru = irvt + *m * *m;
  2292. nrwork = iru + *m * *m;
  2293. sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2294. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2295. info);
  2296. /* Copy real matrix RWORK(IRU) to complex matrix U */
  2297. /* Overwrite U by left singular vectors of A */
  2298. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2299. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2300. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
  2301. clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  2302. i__1 = *lwork - nwork + 1;
  2303. cunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
  2304. itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
  2305. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  2306. /* Overwrite VT by right singular vectors of A */
  2307. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2308. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2309. /* RWorkspace: need M [e] + M*M [RVT] */
  2310. claset_("F", m, n, &c_b1, &c_b1, &vt[vt_offset], ldvt);
  2311. clacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
  2312. i__1 = *lwork - nwork + 1;
  2313. cunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[
  2314. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  2315. ierr);
  2316. } else {
  2317. /* Path 6ta (N > M, JOBZ='A') */
  2318. /* Perform bidiagonal SVD, computing left singular vectors */
  2319. /* of bidiagonal matrix in RWORK(IRU) and computing right */
  2320. /* singular vectors of bidiagonal matrix in RWORK(IRVT) */
  2321. /* CWorkspace: need 0 */
  2322. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
  2323. irvt = nrwork;
  2324. iru = irvt + *m * *m;
  2325. nrwork = iru + *m * *m;
  2326. sbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
  2327. rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
  2328. info);
  2329. /* Copy real matrix RWORK(IRU) to complex matrix U */
  2330. /* Overwrite U by left singular vectors of A */
  2331. /* CWorkspace: need 2*M [tauq, taup] + M [work] */
  2332. /* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
  2333. /* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
  2334. clacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
  2335. i__1 = *lwork - nwork + 1;
  2336. cunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
  2337. itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
  2338. /* Set all of VT to identity matrix */
  2339. claset_("F", n, n, &c_b1, &c_b2, &vt[vt_offset], ldvt);
  2340. /* Copy real matrix RWORK(IRVT) to complex matrix VT */
  2341. /* Overwrite VT by right singular vectors of A */
  2342. /* CWorkspace: need 2*M [tauq, taup] + N [work] */
  2343. /* CWorkspace: prefer 2*M [tauq, taup] + N*NB [work] */
  2344. /* RWorkspace: need M [e] + M*M [RVT] */
  2345. clacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
  2346. i__1 = *lwork - nwork + 1;
  2347. cunmbr_("P", "R", "C", n, n, m, &a[a_offset], lda, &work[
  2348. itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
  2349. ierr);
  2350. }
  2351. }
  2352. }
  2353. /* Undo scaling if necessary */
  2354. if (iscl == 1) {
  2355. if (anrm > bignum) {
  2356. slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
  2357. minmn, &ierr);
  2358. }
  2359. if (*info != 0 && anrm > bignum) {
  2360. i__1 = minmn - 1;
  2361. slascl_("G", &c__0, &c__0, &bignum, &anrm, &i__1, &c__1, &rwork[
  2362. ie], &minmn, &ierr);
  2363. }
  2364. if (anrm < smlnum) {
  2365. slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
  2366. minmn, &ierr);
  2367. }
  2368. if (*info != 0 && anrm < smlnum) {
  2369. i__1 = minmn - 1;
  2370. slascl_("G", &c__0, &c__0, &smlnum, &anrm, &i__1, &c__1, &rwork[
  2371. ie], &minmn, &ierr);
  2372. }
  2373. }
  2374. /* Return optimal workspace in WORK(1) */
  2375. work[1].r = (real) maxwrk, work[1].i = 0.f;
  2376. return 0;
  2377. /* End of CGESDD */
  2378. } /* cgesdd_ */