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cuncsd2by1.c 46 kB

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  1. #include <math.h>
  2. #include <stdlib.h>
  3. #include <string.h>
  4. #include <stdio.h>
  5. #include <complex.h>
  6. #ifdef complex
  7. #undef complex
  8. #endif
  9. #ifdef I
  10. #undef I
  11. #endif
  12. #if defined(_WIN64)
  13. typedef long long BLASLONG;
  14. typedef unsigned long long BLASULONG;
  15. #else
  16. typedef long BLASLONG;
  17. typedef unsigned long BLASULONG;
  18. #endif
  19. #ifdef LAPACK_ILP64
  20. typedef BLASLONG blasint;
  21. #if defined(_WIN64)
  22. #define blasabs(x) llabs(x)
  23. #else
  24. #define blasabs(x) labs(x)
  25. #endif
  26. #else
  27. typedef int blasint;
  28. #define blasabs(x) abs(x)
  29. #endif
  30. typedef blasint integer;
  31. typedef unsigned int uinteger;
  32. typedef char *address;
  33. typedef short int shortint;
  34. typedef float real;
  35. typedef double doublereal;
  36. typedef struct { real r, i; } complex;
  37. typedef struct { doublereal r, i; } doublecomplex;
  38. #ifdef _MSC_VER
  39. static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
  40. static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
  41. static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
  42. static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
  43. #else
  44. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  45. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  46. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  47. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  48. #endif
  49. #define pCf(z) (*_pCf(z))
  50. #define pCd(z) (*_pCd(z))
  51. typedef int logical;
  52. typedef short int shortlogical;
  53. typedef char logical1;
  54. typedef char integer1;
  55. #define TRUE_ (1)
  56. #define FALSE_ (0)
  57. /* Extern is for use with -E */
  58. #ifndef Extern
  59. #define Extern extern
  60. #endif
  61. /* I/O stuff */
  62. typedef int flag;
  63. typedef int ftnlen;
  64. typedef int ftnint;
  65. /*external read, write*/
  66. typedef struct
  67. { flag cierr;
  68. ftnint ciunit;
  69. flag ciend;
  70. char *cifmt;
  71. ftnint cirec;
  72. } cilist;
  73. /*internal read, write*/
  74. typedef struct
  75. { flag icierr;
  76. char *iciunit;
  77. flag iciend;
  78. char *icifmt;
  79. ftnint icirlen;
  80. ftnint icirnum;
  81. } icilist;
  82. /*open*/
  83. typedef struct
  84. { flag oerr;
  85. ftnint ounit;
  86. char *ofnm;
  87. ftnlen ofnmlen;
  88. char *osta;
  89. char *oacc;
  90. char *ofm;
  91. ftnint orl;
  92. char *oblnk;
  93. } olist;
  94. /*close*/
  95. typedef struct
  96. { flag cerr;
  97. ftnint cunit;
  98. char *csta;
  99. } cllist;
  100. /*rewind, backspace, endfile*/
  101. typedef struct
  102. { flag aerr;
  103. ftnint aunit;
  104. } alist;
  105. /* inquire */
  106. typedef struct
  107. { flag inerr;
  108. ftnint inunit;
  109. char *infile;
  110. ftnlen infilen;
  111. ftnint *inex; /*parameters in standard's order*/
  112. ftnint *inopen;
  113. ftnint *innum;
  114. ftnint *innamed;
  115. char *inname;
  116. ftnlen innamlen;
  117. char *inacc;
  118. ftnlen inacclen;
  119. char *inseq;
  120. ftnlen inseqlen;
  121. char *indir;
  122. ftnlen indirlen;
  123. char *infmt;
  124. ftnlen infmtlen;
  125. char *inform;
  126. ftnint informlen;
  127. char *inunf;
  128. ftnlen inunflen;
  129. ftnint *inrecl;
  130. ftnint *innrec;
  131. char *inblank;
  132. ftnlen inblanklen;
  133. } inlist;
  134. #define VOID void
  135. union Multitype { /* for multiple entry points */
  136. integer1 g;
  137. shortint h;
  138. integer i;
  139. /* longint j; */
  140. real r;
  141. doublereal d;
  142. complex c;
  143. doublecomplex z;
  144. };
  145. typedef union Multitype Multitype;
  146. struct Vardesc { /* for Namelist */
  147. char *name;
  148. char *addr;
  149. ftnlen *dims;
  150. int type;
  151. };
  152. typedef struct Vardesc Vardesc;
  153. struct Namelist {
  154. char *name;
  155. Vardesc **vars;
  156. int nvars;
  157. };
  158. typedef struct Namelist Namelist;
  159. #define abs(x) ((x) >= 0 ? (x) : -(x))
  160. #define dabs(x) (fabs(x))
  161. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  162. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  163. #define dmin(a,b) (f2cmin(a,b))
  164. #define dmax(a,b) (f2cmax(a,b))
  165. #define bit_test(a,b) ((a) >> (b) & 1)
  166. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  167. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  168. #define abort_() { sig_die("Fortran abort routine called", 1); }
  169. #define c_abs(z) (cabsf(Cf(z)))
  170. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  171. #ifdef _MSC_VER
  172. #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
  173. #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
  174. #else
  175. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  176. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  177. #endif
  178. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  179. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  180. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  181. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  182. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  183. #define d_abs(x) (fabs(*(x)))
  184. #define d_acos(x) (acos(*(x)))
  185. #define d_asin(x) (asin(*(x)))
  186. #define d_atan(x) (atan(*(x)))
  187. #define d_atn2(x, y) (atan2(*(x),*(y)))
  188. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  189. #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
  190. #define d_cos(x) (cos(*(x)))
  191. #define d_cosh(x) (cosh(*(x)))
  192. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  193. #define d_exp(x) (exp(*(x)))
  194. #define d_imag(z) (cimag(Cd(z)))
  195. #define r_imag(z) (cimagf(Cf(z)))
  196. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  197. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  198. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  199. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  200. #define d_log(x) (log(*(x)))
  201. #define d_mod(x, y) (fmod(*(x), *(y)))
  202. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  203. #define d_nint(x) u_nint(*(x))
  204. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  205. #define d_sign(a,b) u_sign(*(a),*(b))
  206. #define r_sign(a,b) u_sign(*(a),*(b))
  207. #define d_sin(x) (sin(*(x)))
  208. #define d_sinh(x) (sinh(*(x)))
  209. #define d_sqrt(x) (sqrt(*(x)))
  210. #define d_tan(x) (tan(*(x)))
  211. #define d_tanh(x) (tanh(*(x)))
  212. #define i_abs(x) abs(*(x))
  213. #define i_dnnt(x) ((integer)u_nint(*(x)))
  214. #define i_len(s, n) (n)
  215. #define i_nint(x) ((integer)u_nint(*(x)))
  216. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  217. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  218. #define pow_si(B,E) spow_ui(*(B),*(E))
  219. #define pow_ri(B,E) spow_ui(*(B),*(E))
  220. #define pow_di(B,E) dpow_ui(*(B),*(E))
  221. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  222. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  223. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  224. #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
  225. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  226. #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
  227. #define sig_die(s, kill) { exit(1); }
  228. #define s_stop(s, n) {exit(0);}
  229. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  230. #define z_abs(z) (cabs(Cd(z)))
  231. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  232. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  233. #define myexit_() break;
  234. #define mycycle() continue;
  235. #define myceiling(w) {ceil(w)}
  236. #define myhuge(w) {HUGE_VAL}
  237. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  238. #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  239. /* procedure parameter types for -A and -C++ */
  240. #define F2C_proc_par_types 1
  241. #ifdef __cplusplus
  242. typedef logical (*L_fp)(...);
  243. #else
  244. typedef logical (*L_fp)();
  245. #endif
  246. static float spow_ui(float x, integer n) {
  247. float pow=1.0; unsigned long int u;
  248. if(n != 0) {
  249. if(n < 0) n = -n, x = 1/x;
  250. for(u = n; ; ) {
  251. if(u & 01) pow *= x;
  252. if(u >>= 1) x *= x;
  253. else break;
  254. }
  255. }
  256. return pow;
  257. }
  258. static double dpow_ui(double x, integer n) {
  259. double pow=1.0; unsigned long int u;
  260. if(n != 0) {
  261. if(n < 0) n = -n, x = 1/x;
  262. for(u = n; ; ) {
  263. if(u & 01) pow *= x;
  264. if(u >>= 1) x *= x;
  265. else break;
  266. }
  267. }
  268. return pow;
  269. }
  270. #ifdef _MSC_VER
  271. static _Fcomplex cpow_ui(complex x, integer n) {
  272. complex pow={1.0,0.0}; unsigned long int u;
  273. if(n != 0) {
  274. if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
  275. for(u = n; ; ) {
  276. if(u & 01) pow.r *= x.r, pow.i *= x.i;
  277. if(u >>= 1) x.r *= x.r, x.i *= x.i;
  278. else break;
  279. }
  280. }
  281. _Fcomplex p={pow.r, pow.i};
  282. return p;
  283. }
  284. #else
  285. static _Complex float cpow_ui(_Complex float x, integer n) {
  286. _Complex float pow=1.0; unsigned long int u;
  287. if(n != 0) {
  288. if(n < 0) n = -n, x = 1/x;
  289. for(u = n; ; ) {
  290. if(u & 01) pow *= x;
  291. if(u >>= 1) x *= x;
  292. else break;
  293. }
  294. }
  295. return pow;
  296. }
  297. #endif
  298. #ifdef _MSC_VER
  299. static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
  300. _Dcomplex pow={1.0,0.0}; unsigned long int u;
  301. if(n != 0) {
  302. if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
  303. for(u = n; ; ) {
  304. if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
  305. if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
  306. else break;
  307. }
  308. }
  309. _Dcomplex p = {pow._Val[0], pow._Val[1]};
  310. return p;
  311. }
  312. #else
  313. static _Complex double zpow_ui(_Complex double x, integer n) {
  314. _Complex double pow=1.0; unsigned long int u;
  315. if(n != 0) {
  316. if(n < 0) n = -n, x = 1/x;
  317. for(u = n; ; ) {
  318. if(u & 01) pow *= x;
  319. if(u >>= 1) x *= x;
  320. else break;
  321. }
  322. }
  323. return pow;
  324. }
  325. #endif
  326. static integer pow_ii(integer x, integer n) {
  327. integer pow; unsigned long int u;
  328. if (n <= 0) {
  329. if (n == 0 || x == 1) pow = 1;
  330. else if (x != -1) pow = x == 0 ? 1/x : 0;
  331. else n = -n;
  332. }
  333. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  334. u = n;
  335. for(pow = 1; ; ) {
  336. if(u & 01) pow *= x;
  337. if(u >>= 1) x *= x;
  338. else break;
  339. }
  340. }
  341. return pow;
  342. }
  343. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  344. {
  345. double m; integer i, mi;
  346. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  347. if (w[i-1]>m) mi=i ,m=w[i-1];
  348. return mi-s+1;
  349. }
  350. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  351. {
  352. float m; integer i, mi;
  353. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  354. if (w[i-1]>m) mi=i ,m=w[i-1];
  355. return mi-s+1;
  356. }
  357. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  358. integer n = *n_, incx = *incx_, incy = *incy_, i;
  359. #ifdef _MSC_VER
  360. _Fcomplex zdotc = {0.0, 0.0};
  361. if (incx == 1 && incy == 1) {
  362. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  363. zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
  364. zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
  365. }
  366. } else {
  367. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  368. zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
  369. zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
  370. }
  371. }
  372. pCf(z) = zdotc;
  373. }
  374. #else
  375. _Complex float zdotc = 0.0;
  376. if (incx == 1 && incy == 1) {
  377. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  378. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  379. }
  380. } else {
  381. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  382. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  383. }
  384. }
  385. pCf(z) = zdotc;
  386. }
  387. #endif
  388. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  389. integer n = *n_, incx = *incx_, incy = *incy_, i;
  390. #ifdef _MSC_VER
  391. _Dcomplex zdotc = {0.0, 0.0};
  392. if (incx == 1 && incy == 1) {
  393. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  394. zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
  395. zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
  396. }
  397. } else {
  398. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  399. zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
  400. zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
  401. }
  402. }
  403. pCd(z) = zdotc;
  404. }
  405. #else
  406. _Complex double zdotc = 0.0;
  407. if (incx == 1 && incy == 1) {
  408. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  409. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  410. }
  411. } else {
  412. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  413. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  414. }
  415. }
  416. pCd(z) = zdotc;
  417. }
  418. #endif
  419. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  420. integer n = *n_, incx = *incx_, incy = *incy_, i;
  421. #ifdef _MSC_VER
  422. _Fcomplex zdotc = {0.0, 0.0};
  423. if (incx == 1 && incy == 1) {
  424. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  425. zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
  426. zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
  427. }
  428. } else {
  429. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  430. zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
  431. zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
  432. }
  433. }
  434. pCf(z) = zdotc;
  435. }
  436. #else
  437. _Complex float zdotc = 0.0;
  438. if (incx == 1 && incy == 1) {
  439. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  440. zdotc += Cf(&x[i]) * Cf(&y[i]);
  441. }
  442. } else {
  443. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  444. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  445. }
  446. }
  447. pCf(z) = zdotc;
  448. }
  449. #endif
  450. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  451. integer n = *n_, incx = *incx_, incy = *incy_, i;
  452. #ifdef _MSC_VER
  453. _Dcomplex zdotc = {0.0, 0.0};
  454. if (incx == 1 && incy == 1) {
  455. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  456. zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
  457. zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
  458. }
  459. } else {
  460. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  461. zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
  462. zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
  463. }
  464. }
  465. pCd(z) = zdotc;
  466. }
  467. #else
  468. _Complex double zdotc = 0.0;
  469. if (incx == 1 && incy == 1) {
  470. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  471. zdotc += Cd(&x[i]) * Cd(&y[i]);
  472. }
  473. } else {
  474. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  475. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  476. }
  477. }
  478. pCd(z) = zdotc;
  479. }
  480. #endif
  481. /* -- translated by f2c (version 20000121).
  482. You must link the resulting object file with the libraries:
  483. -lf2c -lm (in that order)
  484. */
  485. /* Table of constant values */
  486. static integer c_n1 = -1;
  487. static integer c__1 = 1;
  488. static logical c_false = FALSE_;
  489. /* > \brief \b CUNCSD2BY1 */
  490. /* =========== DOCUMENTATION =========== */
  491. /* Online html documentation available at */
  492. /* http://www.netlib.org/lapack/explore-html/ */
  493. /* > \htmlonly */
  494. /* > Download CUNCSD2BY1 + dependencies */
  495. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cuncsd2
  496. by1.f"> */
  497. /* > [TGZ]</a> */
  498. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cuncsd2
  499. by1.f"> */
  500. /* > [ZIP]</a> */
  501. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cuncsd2
  502. by1.f"> */
  503. /* > [TXT]</a> */
  504. /* > \endhtmlonly */
  505. /* Definition: */
  506. /* =========== */
  507. /* SUBROUTINE CUNCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, */
  508. /* X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, */
  509. /* LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, */
  510. /* INFO ) */
  511. /* CHARACTER JOBU1, JOBU2, JOBV1T */
  512. /* INTEGER INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21, */
  513. /* $ M, P, Q */
  514. /* INTEGER LRWORK, LRWORKMIN, LRWORKOPT */
  515. /* REAL RWORK(*) */
  516. /* REAL THETA(*) */
  517. /* COMPLEX U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*), */
  518. /* $ X11(LDX11,*), X21(LDX21,*) */
  519. /* INTEGER IWORK(*) */
  520. /* > \par Purpose: */
  521. /* ============= */
  522. /* > */
  523. /* >\verbatim */
  524. /* > */
  525. /* > CUNCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with */
  526. /* > orthonormal columns that has been partitioned into a 2-by-1 block */
  527. /* > structure: */
  528. /* > */
  529. /* > [ I1 0 0 ] */
  530. /* > [ 0 C 0 ] */
  531. /* > [ X11 ] [ U1 | ] [ 0 0 0 ] */
  532. /* > X = [-----] = [---------] [----------] V1**T . */
  533. /* > [ X21 ] [ | U2 ] [ 0 0 0 ] */
  534. /* > [ 0 S 0 ] */
  535. /* > [ 0 0 I2] */
  536. /* > */
  537. /* > X11 is P-by-Q. The unitary matrices U1, U2, and V1 are P-by-P, */
  538. /* > (M-P)-by-(M-P), and Q-by-Q, respectively. C and S are R-by-R */
  539. /* > nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which */
  540. /* > R = MIN(P,M-P,Q,M-Q). I1 is a K1-by-K1 identity matrix and I2 is a */
  541. /* > K2-by-K2 identity matrix, where K1 = MAX(Q+P-M,0), K2 = MAX(Q-P,0). */
  542. /* > */
  543. /* > \endverbatim */
  544. /* Arguments: */
  545. /* ========== */
  546. /* > \param[in] JOBU1 */
  547. /* > \verbatim */
  548. /* > JOBU1 is CHARACTER */
  549. /* > = 'Y': U1 is computed; */
  550. /* > otherwise: U1 is not computed. */
  551. /* > \endverbatim */
  552. /* > */
  553. /* > \param[in] JOBU2 */
  554. /* > \verbatim */
  555. /* > JOBU2 is CHARACTER */
  556. /* > = 'Y': U2 is computed; */
  557. /* > otherwise: U2 is not computed. */
  558. /* > \endverbatim */
  559. /* > */
  560. /* > \param[in] JOBV1T */
  561. /* > \verbatim */
  562. /* > JOBV1T is CHARACTER */
  563. /* > = 'Y': V1T is computed; */
  564. /* > otherwise: V1T is not computed. */
  565. /* > \endverbatim */
  566. /* > */
  567. /* > \param[in] M */
  568. /* > \verbatim */
  569. /* > M is INTEGER */
  570. /* > The number of rows in X. */
  571. /* > \endverbatim */
  572. /* > */
  573. /* > \param[in] P */
  574. /* > \verbatim */
  575. /* > P is INTEGER */
  576. /* > The number of rows in X11. 0 <= P <= M. */
  577. /* > \endverbatim */
  578. /* > */
  579. /* > \param[in] Q */
  580. /* > \verbatim */
  581. /* > Q is INTEGER */
  582. /* > The number of columns in X11 and X21. 0 <= Q <= M. */
  583. /* > \endverbatim */
  584. /* > */
  585. /* > \param[in,out] X11 */
  586. /* > \verbatim */
  587. /* > X11 is COMPLEX array, dimension (LDX11,Q) */
  588. /* > On entry, part of the unitary matrix whose CSD is desired. */
  589. /* > \endverbatim */
  590. /* > */
  591. /* > \param[in] LDX11 */
  592. /* > \verbatim */
  593. /* > LDX11 is INTEGER */
  594. /* > The leading dimension of X11. LDX11 >= MAX(1,P). */
  595. /* > \endverbatim */
  596. /* > */
  597. /* > \param[in,out] X21 */
  598. /* > \verbatim */
  599. /* > X21 is COMPLEX array, dimension (LDX21,Q) */
  600. /* > On entry, part of the unitary matrix whose CSD is desired. */
  601. /* > \endverbatim */
  602. /* > */
  603. /* > \param[in] LDX21 */
  604. /* > \verbatim */
  605. /* > LDX21 is INTEGER */
  606. /* > The leading dimension of X21. LDX21 >= MAX(1,M-P). */
  607. /* > \endverbatim */
  608. /* > */
  609. /* > \param[out] THETA */
  610. /* > \verbatim */
  611. /* > THETA is REAL array, dimension (R), in which R = */
  612. /* > MIN(P,M-P,Q,M-Q). */
  613. /* > C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and */
  614. /* > S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ). */
  615. /* > \endverbatim */
  616. /* > */
  617. /* > \param[out] U1 */
  618. /* > \verbatim */
  619. /* > U1 is COMPLEX array, dimension (P) */
  620. /* > If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1. */
  621. /* > \endverbatim */
  622. /* > */
  623. /* > \param[in] LDU1 */
  624. /* > \verbatim */
  625. /* > LDU1 is INTEGER */
  626. /* > The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= */
  627. /* > MAX(1,P). */
  628. /* > \endverbatim */
  629. /* > */
  630. /* > \param[out] U2 */
  631. /* > \verbatim */
  632. /* > U2 is COMPLEX array, dimension (M-P) */
  633. /* > If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary */
  634. /* > matrix U2. */
  635. /* > \endverbatim */
  636. /* > */
  637. /* > \param[in] LDU2 */
  638. /* > \verbatim */
  639. /* > LDU2 is INTEGER */
  640. /* > The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= */
  641. /* > MAX(1,M-P). */
  642. /* > \endverbatim */
  643. /* > */
  644. /* > \param[out] V1T */
  645. /* > \verbatim */
  646. /* > V1T is COMPLEX array, dimension (Q) */
  647. /* > If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary */
  648. /* > matrix V1**T. */
  649. /* > \endverbatim */
  650. /* > */
  651. /* > \param[in] LDV1T */
  652. /* > \verbatim */
  653. /* > LDV1T is INTEGER */
  654. /* > The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= */
  655. /* > MAX(1,Q). */
  656. /* > \endverbatim */
  657. /* > */
  658. /* > \param[out] WORK */
  659. /* > \verbatim */
  660. /* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
  661. /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
  662. /* > \endverbatim */
  663. /* > */
  664. /* > \param[in] LWORK */
  665. /* > \verbatim */
  666. /* > LWORK is INTEGER */
  667. /* > The dimension of the array WORK. */
  668. /* > */
  669. /* > If LWORK = -1, then a workspace query is assumed; the routine */
  670. /* > only calculates the optimal size of the WORK array, returns */
  671. /* > this value as the first entry of the work array, and no error */
  672. /* > message related to LWORK is issued by XERBLA. */
  673. /* > \endverbatim */
  674. /* > */
  675. /* > \param[out] RWORK */
  676. /* > \verbatim */
  677. /* > RWORK is REAL array, dimension (MAX(1,LRWORK)) */
  678. /* > On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */
  679. /* > If INFO > 0 on exit, RWORK(2:R) contains the values PHI(1), */
  680. /* > ..., PHI(R-1) that, together with THETA(1), ..., THETA(R), */
  681. /* > define the matrix in intermediate bidiagonal-block form */
  682. /* > remaining after nonconvergence. INFO specifies the number */
  683. /* > of nonzero PHI's. */
  684. /* > \endverbatim */
  685. /* > */
  686. /* > \param[in] LRWORK */
  687. /* > \verbatim */
  688. /* > LRWORK is INTEGER */
  689. /* > The dimension of the array RWORK. */
  690. /* > */
  691. /* > If LRWORK = -1, then a workspace query is assumed; the routine */
  692. /* > only calculates the optimal size of the RWORK array, returns */
  693. /* > this value as the first entry of the work array, and no error */
  694. /* > message related to LRWORK is issued by XERBLA. */
  695. /* > \endverbatim */
  696. /* > \param[out] IWORK */
  697. /* > \verbatim */
  698. /* > IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q)) */
  699. /* > \endverbatim */
  700. /* > */
  701. /* > \param[out] INFO */
  702. /* > \verbatim */
  703. /* > INFO is INTEGER */
  704. /* > = 0: successful exit. */
  705. /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
  706. /* > > 0: CBBCSD did not converge. See the description of WORK */
  707. /* > above for details. */
  708. /* > \endverbatim */
  709. /* > \par References: */
  710. /* ================ */
  711. /* > */
  712. /* > [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. */
  713. /* > Algorithms, 50(1):33-65, 2009. */
  714. /* Authors: */
  715. /* ======== */
  716. /* > \author Univ. of Tennessee */
  717. /* > \author Univ. of California Berkeley */
  718. /* > \author Univ. of Colorado Denver */
  719. /* > \author NAG Ltd. */
  720. /* > \date June 2016 */
  721. /* > \ingroup complexOTHERcomputational */
  722. /* ===================================================================== */
  723. /* Subroutine */ int cuncsd2by1_(char *jobu1, char *jobu2, char *jobv1t,
  724. integer *m, integer *p, integer *q, complex *x11, integer *ldx11,
  725. complex *x21, integer *ldx21, real *theta, complex *u1, integer *ldu1,
  726. complex *u2, integer *ldu2, complex *v1t, integer *ldv1t, complex *
  727. work, integer *lwork, real *rwork, integer *lrwork, integer *iwork,
  728. integer *info)
  729. {
  730. /* System generated locals */
  731. integer u1_dim1, u1_offset, u2_dim1, u2_offset, v1t_dim1, v1t_offset,
  732. x11_dim1, x11_offset, x21_dim1, x21_offset, i__1, i__2, i__3;
  733. /* Local variables */
  734. integer ib11d, ib11e, ib12d, ib12e, ib21d, ib21e, ib22d, ib22e;
  735. complex cdum[1] /* was [1][1] */;
  736. integer iphi, lworkmin, lworkopt, i__, j, r__;
  737. extern logical lsame_(char *, char *);
  738. extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
  739. complex *, integer *);
  740. integer childinfo, lorglqmin, lorgqrmin, lorglqopt, lrworkmin, itaup1,
  741. itaup2, itauq1, lorgqropt;
  742. logical wantu1, wantu2;
  743. extern /* Subroutine */ int cbbcsd_(char *, char *, char *, char *, char *
  744. , integer *, integer *, integer *, real *, real *, complex *,
  745. integer *, complex *, integer *, complex *, integer *, complex *,
  746. integer *, real *, real *, real *, real *, real *, real *, real *,
  747. real *, real *, integer *, integer *);
  748. integer lrworkopt, ibbcsd, lbbcsd, iorbdb, lorbdb;
  749. extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
  750. *, integer *, complex *, integer *), xerbla_(char *,
  751. integer *, ftnlen), clapmr_(logical *, integer *, integer *,
  752. complex *, integer *, integer *), clapmt_(logical *, integer *,
  753. integer *, complex *, integer *, integer *), cunglq_(integer *,
  754. integer *, integer *, complex *, integer *, complex *, complex *,
  755. integer *, integer *);
  756. integer iorglq;
  757. extern /* Subroutine */ int cungqr_(integer *, integer *, integer *,
  758. complex *, integer *, complex *, complex *, integer *, integer *);
  759. integer lorglq, iorgqr, lorgqr;
  760. extern /* Subroutine */ int cunbdb1_(integer *, integer *, integer *,
  761. complex *, integer *, complex *, integer *, real *, real *,
  762. complex *, complex *, complex *, complex *, integer *, integer *),
  763. cunbdb2_(integer *, integer *, integer *, complex *, integer *,
  764. complex *, integer *, real *, real *, complex *, complex *,
  765. complex *, complex *, integer *, integer *);
  766. logical lquery;
  767. extern /* Subroutine */ int cunbdb3_(integer *, integer *, integer *,
  768. complex *, integer *, complex *, integer *, real *, real *,
  769. complex *, complex *, complex *, complex *, integer *, integer *),
  770. cunbdb4_(integer *, integer *, integer *, complex *, integer *,
  771. complex *, integer *, real *, real *, complex *, complex *,
  772. complex *, complex *, complex *, integer *, integer *);
  773. logical wantv1t;
  774. real dum[1];
  775. /* -- LAPACK computational routine (version 3.7.1) -- */
  776. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  777. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  778. /* June 2016 */
  779. /* ===================================================================== */
  780. /* Test input arguments */
  781. /* Parameter adjustments */
  782. x11_dim1 = *ldx11;
  783. x11_offset = 1 + x11_dim1 * 1;
  784. x11 -= x11_offset;
  785. x21_dim1 = *ldx21;
  786. x21_offset = 1 + x21_dim1 * 1;
  787. x21 -= x21_offset;
  788. --theta;
  789. u1_dim1 = *ldu1;
  790. u1_offset = 1 + u1_dim1 * 1;
  791. u1 -= u1_offset;
  792. u2_dim1 = *ldu2;
  793. u2_offset = 1 + u2_dim1 * 1;
  794. u2 -= u2_offset;
  795. v1t_dim1 = *ldv1t;
  796. v1t_offset = 1 + v1t_dim1 * 1;
  797. v1t -= v1t_offset;
  798. --work;
  799. --rwork;
  800. --iwork;
  801. /* Function Body */
  802. *info = 0;
  803. wantu1 = lsame_(jobu1, "Y");
  804. wantu2 = lsame_(jobu2, "Y");
  805. wantv1t = lsame_(jobv1t, "Y");
  806. lquery = *lwork == -1;
  807. if (*m < 0) {
  808. *info = -4;
  809. } else if (*p < 0 || *p > *m) {
  810. *info = -5;
  811. } else if (*q < 0 || *q > *m) {
  812. *info = -6;
  813. } else if (*ldx11 < f2cmax(1,*p)) {
  814. *info = -8;
  815. } else /* if(complicated condition) */ {
  816. /* Computing MAX */
  817. i__1 = 1, i__2 = *m - *p;
  818. if (*ldx21 < f2cmax(i__1,i__2)) {
  819. *info = -10;
  820. } else if (wantu1 && *ldu1 < f2cmax(1,*p)) {
  821. *info = -13;
  822. } else /* if(complicated condition) */ {
  823. /* Computing MAX */
  824. i__1 = 1, i__2 = *m - *p;
  825. if (wantu2 && *ldu2 < f2cmax(i__1,i__2)) {
  826. *info = -15;
  827. } else if (wantv1t && *ldv1t < f2cmax(1,*q)) {
  828. *info = -17;
  829. }
  830. }
  831. }
  832. /* Computing MIN */
  833. i__1 = *p, i__2 = *m - *p, i__1 = f2cmin(i__1,i__2), i__1 = f2cmin(i__1,*q),
  834. i__2 = *m - *q;
  835. r__ = f2cmin(i__1,i__2);
  836. /* Compute workspace */
  837. /* WORK layout: */
  838. /* |-----------------------------------------| */
  839. /* | LWORKOPT (1) | */
  840. /* |-----------------------------------------| */
  841. /* | TAUP1 (MAX(1,P)) | */
  842. /* | TAUP2 (MAX(1,M-P)) | */
  843. /* | TAUQ1 (MAX(1,Q)) | */
  844. /* |-----------------------------------------| */
  845. /* | CUNBDB WORK | CUNGQR WORK | CUNGLQ WORK | */
  846. /* | | | | */
  847. /* | | | | */
  848. /* | | | | */
  849. /* | | | | */
  850. /* |-----------------------------------------| */
  851. /* RWORK layout: */
  852. /* |------------------| */
  853. /* | LRWORKOPT (1) | */
  854. /* |------------------| */
  855. /* | PHI (MAX(1,R-1)) | */
  856. /* |------------------| */
  857. /* | B11D (R) | */
  858. /* | B11E (R-1) | */
  859. /* | B12D (R) | */
  860. /* | B12E (R-1) | */
  861. /* | B21D (R) | */
  862. /* | B21E (R-1) | */
  863. /* | B22D (R) | */
  864. /* | B22E (R-1) | */
  865. /* | CBBCSD RWORK | */
  866. /* |------------------| */
  867. if (*info == 0) {
  868. iphi = 2;
  869. /* Computing MAX */
  870. i__1 = 1, i__2 = r__ - 1;
  871. ib11d = iphi + f2cmax(i__1,i__2);
  872. ib11e = ib11d + f2cmax(1,r__);
  873. /* Computing MAX */
  874. i__1 = 1, i__2 = r__ - 1;
  875. ib12d = ib11e + f2cmax(i__1,i__2);
  876. ib12e = ib12d + f2cmax(1,r__);
  877. /* Computing MAX */
  878. i__1 = 1, i__2 = r__ - 1;
  879. ib21d = ib12e + f2cmax(i__1,i__2);
  880. ib21e = ib21d + f2cmax(1,r__);
  881. /* Computing MAX */
  882. i__1 = 1, i__2 = r__ - 1;
  883. ib22d = ib21e + f2cmax(i__1,i__2);
  884. ib22e = ib22d + f2cmax(1,r__);
  885. /* Computing MAX */
  886. i__1 = 1, i__2 = r__ - 1;
  887. ibbcsd = ib22e + f2cmax(i__1,i__2);
  888. itaup1 = 2;
  889. itaup2 = itaup1 + f2cmax(1,*p);
  890. /* Computing MAX */
  891. i__1 = 1, i__2 = *m - *p;
  892. itauq1 = itaup2 + f2cmax(i__1,i__2);
  893. iorbdb = itauq1 + f2cmax(1,*q);
  894. iorgqr = itauq1 + f2cmax(1,*q);
  895. iorglq = itauq1 + f2cmax(1,*q);
  896. lorgqrmin = 1;
  897. lorgqropt = 1;
  898. lorglqmin = 1;
  899. lorglqopt = 1;
  900. if (r__ == *q) {
  901. cunbdb1_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset],
  902. ldx21, &theta[1], dum, cdum, cdum, cdum, &work[1], &c_n1,
  903. &childinfo);
  904. lorbdb = (integer) work[1].r;
  905. if (wantu1 && *p > 0) {
  906. cungqr_(p, p, q, &u1[u1_offset], ldu1, cdum, &work[1], &c_n1,
  907. &childinfo);
  908. lorgqrmin = f2cmax(lorgqrmin,*p);
  909. /* Computing MAX */
  910. i__1 = lorgqropt, i__2 = (integer) work[1].r;
  911. lorgqropt = f2cmax(i__1,i__2);
  912. }
  913. if (wantu2 && *m - *p > 0) {
  914. i__1 = *m - *p;
  915. i__2 = *m - *p;
  916. cungqr_(&i__1, &i__2, q, &u2[u2_offset], ldu2, cdum, &work[1],
  917. &c_n1, &childinfo);
  918. /* Computing MAX */
  919. i__1 = lorgqrmin, i__2 = *m - *p;
  920. lorgqrmin = f2cmax(i__1,i__2);
  921. /* Computing MAX */
  922. i__1 = lorgqropt, i__2 = (integer) work[1].r;
  923. lorgqropt = f2cmax(i__1,i__2);
  924. }
  925. if (wantv1t && *q > 0) {
  926. i__1 = *q - 1;
  927. i__2 = *q - 1;
  928. i__3 = *q - 1;
  929. cunglq_(&i__1, &i__2, &i__3, &v1t[v1t_offset], ldv1t, cdum, &
  930. work[1], &c_n1, &childinfo);
  931. /* Computing MAX */
  932. i__1 = lorglqmin, i__2 = *q - 1;
  933. lorglqmin = f2cmax(i__1,i__2);
  934. /* Computing MAX */
  935. i__1 = lorglqopt, i__2 = (integer) work[1].r;
  936. lorglqopt = f2cmax(i__1,i__2);
  937. }
  938. cbbcsd_(jobu1, jobu2, jobv1t, "N", "N", m, p, q, &theta[1], dum, &
  939. u1[u1_offset], ldu1, &u2[u2_offset], ldu2, &v1t[
  940. v1t_offset], ldv1t, cdum, &c__1, dum, dum, dum, dum, dum,
  941. dum, dum, dum, &rwork[1], &c_n1, &childinfo);
  942. lbbcsd = (integer) rwork[1];
  943. } else if (r__ == *p) {
  944. cunbdb2_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset],
  945. ldx21, &theta[1], dum, cdum, cdum, cdum, &work[1], &c_n1,
  946. &childinfo);
  947. lorbdb = (integer) work[1].r;
  948. if (wantu1 && *p > 0) {
  949. i__1 = *p - 1;
  950. i__2 = *p - 1;
  951. i__3 = *p - 1;
  952. cungqr_(&i__1, &i__2, &i__3, &u1[(u1_dim1 << 1) + 2], ldu1,
  953. cdum, &work[1], &c_n1, &childinfo);
  954. /* Computing MAX */
  955. i__1 = lorgqrmin, i__2 = *p - 1;
  956. lorgqrmin = f2cmax(i__1,i__2);
  957. /* Computing MAX */
  958. i__1 = lorgqropt, i__2 = (integer) work[1].r;
  959. lorgqropt = f2cmax(i__1,i__2);
  960. }
  961. if (wantu2 && *m - *p > 0) {
  962. i__1 = *m - *p;
  963. i__2 = *m - *p;
  964. cungqr_(&i__1, &i__2, q, &u2[u2_offset], ldu2, cdum, &work[1],
  965. &c_n1, &childinfo);
  966. /* Computing MAX */
  967. i__1 = lorgqrmin, i__2 = *m - *p;
  968. lorgqrmin = f2cmax(i__1,i__2);
  969. /* Computing MAX */
  970. i__1 = lorgqropt, i__2 = (integer) work[1].r;
  971. lorgqropt = f2cmax(i__1,i__2);
  972. }
  973. if (wantv1t && *q > 0) {
  974. cunglq_(q, q, &r__, &v1t[v1t_offset], ldv1t, cdum, &work[1], &
  975. c_n1, &childinfo);
  976. lorglqmin = f2cmax(lorglqmin,*q);
  977. /* Computing MAX */
  978. i__1 = lorglqopt, i__2 = (integer) work[1].r;
  979. lorglqopt = f2cmax(i__1,i__2);
  980. }
  981. cbbcsd_(jobv1t, "N", jobu1, jobu2, "T", m, q, p, &theta[1], dum, &
  982. v1t[v1t_offset], ldv1t, cdum, &c__1, &u1[u1_offset], ldu1,
  983. &u2[u2_offset], ldu2, dum, dum, dum, dum, dum, dum, dum,
  984. dum, &rwork[1], &c_n1, &childinfo);
  985. lbbcsd = (integer) rwork[1];
  986. } else if (r__ == *m - *p) {
  987. cunbdb3_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset],
  988. ldx21, &theta[1], dum, cdum, cdum, cdum, &work[1], &c_n1,
  989. &childinfo);
  990. lorbdb = (integer) work[1].r;
  991. if (wantu1 && *p > 0) {
  992. cungqr_(p, p, q, &u1[u1_offset], ldu1, cdum, &work[1], &c_n1,
  993. &childinfo);
  994. lorgqrmin = f2cmax(lorgqrmin,*p);
  995. /* Computing MAX */
  996. i__1 = lorgqropt, i__2 = (integer) work[1].r;
  997. lorgqropt = f2cmax(i__1,i__2);
  998. }
  999. if (wantu2 && *m - *p > 0) {
  1000. i__1 = *m - *p - 1;
  1001. i__2 = *m - *p - 1;
  1002. i__3 = *m - *p - 1;
  1003. cungqr_(&i__1, &i__2, &i__3, &u2[(u2_dim1 << 1) + 2], ldu2,
  1004. cdum, &work[1], &c_n1, &childinfo);
  1005. /* Computing MAX */
  1006. i__1 = lorgqrmin, i__2 = *m - *p - 1;
  1007. lorgqrmin = f2cmax(i__1,i__2);
  1008. /* Computing MAX */
  1009. i__1 = lorgqropt, i__2 = (integer) work[1].r;
  1010. lorgqropt = f2cmax(i__1,i__2);
  1011. }
  1012. if (wantv1t && *q > 0) {
  1013. cunglq_(q, q, &r__, &v1t[v1t_offset], ldv1t, cdum, &work[1], &
  1014. c_n1, &childinfo);
  1015. lorglqmin = f2cmax(lorglqmin,*q);
  1016. /* Computing MAX */
  1017. i__1 = lorglqopt, i__2 = (integer) work[1].r;
  1018. lorglqopt = f2cmax(i__1,i__2);
  1019. }
  1020. i__1 = *m - *q;
  1021. i__2 = *m - *p;
  1022. cbbcsd_("N", jobv1t, jobu2, jobu1, "T", m, &i__1, &i__2, &theta[1]
  1023. , dum, cdum, &c__1, &v1t[v1t_offset], ldv1t, &u2[
  1024. u2_offset], ldu2, &u1[u1_offset], ldu1, dum, dum, dum,
  1025. dum, dum, dum, dum, dum, &rwork[1], &c_n1, &childinfo);
  1026. lbbcsd = (integer) rwork[1];
  1027. } else {
  1028. cunbdb4_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset],
  1029. ldx21, &theta[1], dum, cdum, cdum, cdum, cdum, &work[1], &
  1030. c_n1, &childinfo);
  1031. lorbdb = *m + (integer) work[1].r;
  1032. if (wantu1 && *p > 0) {
  1033. i__1 = *m - *q;
  1034. cungqr_(p, p, &i__1, &u1[u1_offset], ldu1, cdum, &work[1], &
  1035. c_n1, &childinfo);
  1036. lorgqrmin = f2cmax(lorgqrmin,*p);
  1037. /* Computing MAX */
  1038. i__1 = lorgqropt, i__2 = (integer) work[1].r;
  1039. lorgqropt = f2cmax(i__1,i__2);
  1040. }
  1041. if (wantu2 && *m - *p > 0) {
  1042. i__1 = *m - *p;
  1043. i__2 = *m - *p;
  1044. i__3 = *m - *q;
  1045. cungqr_(&i__1, &i__2, &i__3, &u2[u2_offset], ldu2, cdum, &
  1046. work[1], &c_n1, &childinfo);
  1047. /* Computing MAX */
  1048. i__1 = lorgqrmin, i__2 = *m - *p;
  1049. lorgqrmin = f2cmax(i__1,i__2);
  1050. /* Computing MAX */
  1051. i__1 = lorgqropt, i__2 = (integer) work[1].r;
  1052. lorgqropt = f2cmax(i__1,i__2);
  1053. }
  1054. if (wantv1t && *q > 0) {
  1055. cunglq_(q, q, q, &v1t[v1t_offset], ldv1t, cdum, &work[1], &
  1056. c_n1, &childinfo);
  1057. lorglqmin = f2cmax(lorglqmin,*q);
  1058. /* Computing MAX */
  1059. i__1 = lorglqopt, i__2 = (integer) work[1].r;
  1060. lorglqopt = f2cmax(i__1,i__2);
  1061. }
  1062. i__1 = *m - *p;
  1063. i__2 = *m - *q;
  1064. cbbcsd_(jobu2, jobu1, "N", jobv1t, "N", m, &i__1, &i__2, &theta[1]
  1065. , dum, &u2[u2_offset], ldu2, &u1[u1_offset], ldu1, cdum, &
  1066. c__1, &v1t[v1t_offset], ldv1t, dum, dum, dum, dum, dum,
  1067. dum, dum, dum, &rwork[1], &c_n1, &childinfo);
  1068. lbbcsd = (integer) rwork[1];
  1069. }
  1070. lrworkmin = ibbcsd + lbbcsd - 1;
  1071. lrworkopt = lrworkmin;
  1072. rwork[1] = (real) lrworkopt;
  1073. /* Computing MAX */
  1074. i__1 = iorbdb + lorbdb - 1, i__2 = iorgqr + lorgqrmin - 1, i__1 = f2cmax(
  1075. i__1,i__2), i__2 = iorglq + lorglqmin - 1;
  1076. lworkmin = f2cmax(i__1,i__2);
  1077. /* Computing MAX */
  1078. i__1 = iorbdb + lorbdb - 1, i__2 = iorgqr + lorgqropt - 1, i__1 = f2cmax(
  1079. i__1,i__2), i__2 = iorglq + lorglqopt - 1;
  1080. lworkopt = f2cmax(i__1,i__2);
  1081. work[1].r = (real) lworkopt, work[1].i = 0.f;
  1082. if (*lwork < lworkmin && ! lquery) {
  1083. *info = -19;
  1084. }
  1085. }
  1086. if (*info != 0) {
  1087. i__1 = -(*info);
  1088. xerbla_("CUNCSD2BY1", &i__1, (ftnlen)10);
  1089. return 0;
  1090. } else if (lquery) {
  1091. return 0;
  1092. }
  1093. lorgqr = *lwork - iorgqr + 1;
  1094. lorglq = *lwork - iorglq + 1;
  1095. /* Handle four cases separately: R = Q, R = P, R = M-P, and R = M-Q, */
  1096. /* in which R = MIN(P,M-P,Q,M-Q) */
  1097. if (r__ == *q) {
  1098. /* Case 1: R = Q */
  1099. /* Simultaneously bidiagonalize X11 and X21 */
  1100. cunbdb1_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, &
  1101. theta[1], &rwork[iphi], &work[itaup1], &work[itaup2], &work[
  1102. itauq1], &work[iorbdb], &lorbdb, &childinfo);
  1103. /* Accumulate Householder reflectors */
  1104. if (wantu1 && *p > 0) {
  1105. clacpy_("L", p, q, &x11[x11_offset], ldx11, &u1[u1_offset], ldu1);
  1106. cungqr_(p, p, q, &u1[u1_offset], ldu1, &work[itaup1], &work[
  1107. iorgqr], &lorgqr, &childinfo);
  1108. }
  1109. if (wantu2 && *m - *p > 0) {
  1110. i__1 = *m - *p;
  1111. clacpy_("L", &i__1, q, &x21[x21_offset], ldx21, &u2[u2_offset],
  1112. ldu2);
  1113. i__1 = *m - *p;
  1114. i__2 = *m - *p;
  1115. cungqr_(&i__1, &i__2, q, &u2[u2_offset], ldu2, &work[itaup2], &
  1116. work[iorgqr], &lorgqr, &childinfo);
  1117. }
  1118. if (wantv1t && *q > 0) {
  1119. i__1 = v1t_dim1 + 1;
  1120. v1t[i__1].r = 1.f, v1t[i__1].i = 0.f;
  1121. i__1 = *q;
  1122. for (j = 2; j <= i__1; ++j) {
  1123. i__2 = j * v1t_dim1 + 1;
  1124. v1t[i__2].r = 0.f, v1t[i__2].i = 0.f;
  1125. i__2 = j + v1t_dim1;
  1126. v1t[i__2].r = 0.f, v1t[i__2].i = 0.f;
  1127. }
  1128. i__1 = *q - 1;
  1129. i__2 = *q - 1;
  1130. clacpy_("U", &i__1, &i__2, &x21[(x21_dim1 << 1) + 1], ldx21, &v1t[
  1131. (v1t_dim1 << 1) + 2], ldv1t);
  1132. i__1 = *q - 1;
  1133. i__2 = *q - 1;
  1134. i__3 = *q - 1;
  1135. cunglq_(&i__1, &i__2, &i__3, &v1t[(v1t_dim1 << 1) + 2], ldv1t, &
  1136. work[itauq1], &work[iorglq], &lorglq, &childinfo);
  1137. }
  1138. /* Simultaneously diagonalize X11 and X21. */
  1139. cbbcsd_(jobu1, jobu2, jobv1t, "N", "N", m, p, q, &theta[1], &rwork[
  1140. iphi], &u1[u1_offset], ldu1, &u2[u2_offset], ldu2, &v1t[
  1141. v1t_offset], ldv1t, cdum, &c__1, &rwork[ib11d], &rwork[ib11e],
  1142. &rwork[ib12d], &rwork[ib12e], &rwork[ib21d], &rwork[ib21e], &
  1143. rwork[ib22d], &rwork[ib22e], &rwork[ibbcsd], &lbbcsd, &
  1144. childinfo);
  1145. /* Permute rows and columns to place zero submatrices in */
  1146. /* preferred positions */
  1147. if (*q > 0 && wantu2) {
  1148. i__1 = *q;
  1149. for (i__ = 1; i__ <= i__1; ++i__) {
  1150. iwork[i__] = *m - *p - *q + i__;
  1151. }
  1152. i__1 = *m - *p;
  1153. for (i__ = *q + 1; i__ <= i__1; ++i__) {
  1154. iwork[i__] = i__ - *q;
  1155. }
  1156. i__1 = *m - *p;
  1157. i__2 = *m - *p;
  1158. clapmt_(&c_false, &i__1, &i__2, &u2[u2_offset], ldu2, &iwork[1]);
  1159. }
  1160. } else if (r__ == *p) {
  1161. /* Case 2: R = P */
  1162. /* Simultaneously bidiagonalize X11 and X21 */
  1163. cunbdb2_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, &
  1164. theta[1], &rwork[iphi], &work[itaup1], &work[itaup2], &work[
  1165. itauq1], &work[iorbdb], &lorbdb, &childinfo);
  1166. /* Accumulate Householder reflectors */
  1167. if (wantu1 && *p > 0) {
  1168. i__1 = u1_dim1 + 1;
  1169. u1[i__1].r = 1.f, u1[i__1].i = 0.f;
  1170. i__1 = *p;
  1171. for (j = 2; j <= i__1; ++j) {
  1172. i__2 = j * u1_dim1 + 1;
  1173. u1[i__2].r = 0.f, u1[i__2].i = 0.f;
  1174. i__2 = j + u1_dim1;
  1175. u1[i__2].r = 0.f, u1[i__2].i = 0.f;
  1176. }
  1177. i__1 = *p - 1;
  1178. i__2 = *p - 1;
  1179. clacpy_("L", &i__1, &i__2, &x11[x11_dim1 + 2], ldx11, &u1[(
  1180. u1_dim1 << 1) + 2], ldu1);
  1181. i__1 = *p - 1;
  1182. i__2 = *p - 1;
  1183. i__3 = *p - 1;
  1184. cungqr_(&i__1, &i__2, &i__3, &u1[(u1_dim1 << 1) + 2], ldu1, &work[
  1185. itaup1], &work[iorgqr], &lorgqr, &childinfo);
  1186. }
  1187. if (wantu2 && *m - *p > 0) {
  1188. i__1 = *m - *p;
  1189. clacpy_("L", &i__1, q, &x21[x21_offset], ldx21, &u2[u2_offset],
  1190. ldu2);
  1191. i__1 = *m - *p;
  1192. i__2 = *m - *p;
  1193. cungqr_(&i__1, &i__2, q, &u2[u2_offset], ldu2, &work[itaup2], &
  1194. work[iorgqr], &lorgqr, &childinfo);
  1195. }
  1196. if (wantv1t && *q > 0) {
  1197. clacpy_("U", p, q, &x11[x11_offset], ldx11, &v1t[v1t_offset],
  1198. ldv1t);
  1199. cunglq_(q, q, &r__, &v1t[v1t_offset], ldv1t, &work[itauq1], &work[
  1200. iorglq], &lorglq, &childinfo);
  1201. }
  1202. /* Simultaneously diagonalize X11 and X21. */
  1203. cbbcsd_(jobv1t, "N", jobu1, jobu2, "T", m, q, p, &theta[1], &rwork[
  1204. iphi], &v1t[v1t_offset], ldv1t, cdum, &c__1, &u1[u1_offset],
  1205. ldu1, &u2[u2_offset], ldu2, &rwork[ib11d], &rwork[ib11e], &
  1206. rwork[ib12d], &rwork[ib12e], &rwork[ib21d], &rwork[ib21e], &
  1207. rwork[ib22d], &rwork[ib22e], &rwork[ibbcsd], &lbbcsd, &
  1208. childinfo);
  1209. /* Permute rows and columns to place identity submatrices in */
  1210. /* preferred positions */
  1211. if (*q > 0 && wantu2) {
  1212. i__1 = *q;
  1213. for (i__ = 1; i__ <= i__1; ++i__) {
  1214. iwork[i__] = *m - *p - *q + i__;
  1215. }
  1216. i__1 = *m - *p;
  1217. for (i__ = *q + 1; i__ <= i__1; ++i__) {
  1218. iwork[i__] = i__ - *q;
  1219. }
  1220. i__1 = *m - *p;
  1221. i__2 = *m - *p;
  1222. clapmt_(&c_false, &i__1, &i__2, &u2[u2_offset], ldu2, &iwork[1]);
  1223. }
  1224. } else if (r__ == *m - *p) {
  1225. /* Case 3: R = M-P */
  1226. /* Simultaneously bidiagonalize X11 and X21 */
  1227. cunbdb3_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, &
  1228. theta[1], &rwork[iphi], &work[itaup1], &work[itaup2], &work[
  1229. itauq1], &work[iorbdb], &lorbdb, &childinfo);
  1230. /* Accumulate Householder reflectors */
  1231. if (wantu1 && *p > 0) {
  1232. clacpy_("L", p, q, &x11[x11_offset], ldx11, &u1[u1_offset], ldu1);
  1233. cungqr_(p, p, q, &u1[u1_offset], ldu1, &work[itaup1], &work[
  1234. iorgqr], &lorgqr, &childinfo);
  1235. }
  1236. if (wantu2 && *m - *p > 0) {
  1237. i__1 = u2_dim1 + 1;
  1238. u2[i__1].r = 1.f, u2[i__1].i = 0.f;
  1239. i__1 = *m - *p;
  1240. for (j = 2; j <= i__1; ++j) {
  1241. i__2 = j * u2_dim1 + 1;
  1242. u2[i__2].r = 0.f, u2[i__2].i = 0.f;
  1243. i__2 = j + u2_dim1;
  1244. u2[i__2].r = 0.f, u2[i__2].i = 0.f;
  1245. }
  1246. i__1 = *m - *p - 1;
  1247. i__2 = *m - *p - 1;
  1248. clacpy_("L", &i__1, &i__2, &x21[x21_dim1 + 2], ldx21, &u2[(
  1249. u2_dim1 << 1) + 2], ldu2);
  1250. i__1 = *m - *p - 1;
  1251. i__2 = *m - *p - 1;
  1252. i__3 = *m - *p - 1;
  1253. cungqr_(&i__1, &i__2, &i__3, &u2[(u2_dim1 << 1) + 2], ldu2, &work[
  1254. itaup2], &work[iorgqr], &lorgqr, &childinfo);
  1255. }
  1256. if (wantv1t && *q > 0) {
  1257. i__1 = *m - *p;
  1258. clacpy_("U", &i__1, q, &x21[x21_offset], ldx21, &v1t[v1t_offset],
  1259. ldv1t);
  1260. cunglq_(q, q, &r__, &v1t[v1t_offset], ldv1t, &work[itauq1], &work[
  1261. iorglq], &lorglq, &childinfo);
  1262. }
  1263. /* Simultaneously diagonalize X11 and X21. */
  1264. i__1 = *m - *q;
  1265. i__2 = *m - *p;
  1266. cbbcsd_("N", jobv1t, jobu2, jobu1, "T", m, &i__1, &i__2, &theta[1], &
  1267. rwork[iphi], cdum, &c__1, &v1t[v1t_offset], ldv1t, &u2[
  1268. u2_offset], ldu2, &u1[u1_offset], ldu1, &rwork[ib11d], &rwork[
  1269. ib11e], &rwork[ib12d], &rwork[ib12e], &rwork[ib21d], &rwork[
  1270. ib21e], &rwork[ib22d], &rwork[ib22e], &rwork[ibbcsd], &lbbcsd,
  1271. &childinfo);
  1272. /* Permute rows and columns to place identity submatrices in */
  1273. /* preferred positions */
  1274. if (*q > r__) {
  1275. i__1 = r__;
  1276. for (i__ = 1; i__ <= i__1; ++i__) {
  1277. iwork[i__] = *q - r__ + i__;
  1278. }
  1279. i__1 = *q;
  1280. for (i__ = r__ + 1; i__ <= i__1; ++i__) {
  1281. iwork[i__] = i__ - r__;
  1282. }
  1283. if (wantu1) {
  1284. clapmt_(&c_false, p, q, &u1[u1_offset], ldu1, &iwork[1]);
  1285. }
  1286. if (wantv1t) {
  1287. clapmr_(&c_false, q, q, &v1t[v1t_offset], ldv1t, &iwork[1]);
  1288. }
  1289. }
  1290. } else {
  1291. /* Case 4: R = M-Q */
  1292. /* Simultaneously bidiagonalize X11 and X21 */
  1293. i__1 = lorbdb - *m;
  1294. cunbdb4_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, &
  1295. theta[1], &rwork[iphi], &work[itaup1], &work[itaup2], &work[
  1296. itauq1], &work[iorbdb], &work[iorbdb + *m], &i__1, &childinfo)
  1297. ;
  1298. /* Accumulate Householder reflectors */
  1299. if (wantu1 && *p > 0) {
  1300. ccopy_(p, &work[iorbdb], &c__1, &u1[u1_offset], &c__1);
  1301. i__1 = *p;
  1302. for (j = 2; j <= i__1; ++j) {
  1303. i__2 = j * u1_dim1 + 1;
  1304. u1[i__2].r = 0.f, u1[i__2].i = 0.f;
  1305. }
  1306. i__1 = *p - 1;
  1307. i__2 = *m - *q - 1;
  1308. clacpy_("L", &i__1, &i__2, &x11[x11_dim1 + 2], ldx11, &u1[(
  1309. u1_dim1 << 1) + 2], ldu1);
  1310. i__1 = *m - *q;
  1311. cungqr_(p, p, &i__1, &u1[u1_offset], ldu1, &work[itaup1], &work[
  1312. iorgqr], &lorgqr, &childinfo);
  1313. }
  1314. if (wantu2 && *m - *p > 0) {
  1315. i__1 = *m - *p;
  1316. ccopy_(&i__1, &work[iorbdb + *p], &c__1, &u2[u2_offset], &c__1);
  1317. i__1 = *m - *p;
  1318. for (j = 2; j <= i__1; ++j) {
  1319. i__2 = j * u2_dim1 + 1;
  1320. u2[i__2].r = 0.f, u2[i__2].i = 0.f;
  1321. }
  1322. i__1 = *m - *p - 1;
  1323. i__2 = *m - *q - 1;
  1324. clacpy_("L", &i__1, &i__2, &x21[x21_dim1 + 2], ldx21, &u2[(
  1325. u2_dim1 << 1) + 2], ldu2);
  1326. i__1 = *m - *p;
  1327. i__2 = *m - *p;
  1328. i__3 = *m - *q;
  1329. cungqr_(&i__1, &i__2, &i__3, &u2[u2_offset], ldu2, &work[itaup2],
  1330. &work[iorgqr], &lorgqr, &childinfo);
  1331. }
  1332. if (wantv1t && *q > 0) {
  1333. i__1 = *m - *q;
  1334. clacpy_("U", &i__1, q, &x21[x21_offset], ldx21, &v1t[v1t_offset],
  1335. ldv1t);
  1336. i__1 = *p - (*m - *q);
  1337. i__2 = *q - (*m - *q);
  1338. clacpy_("U", &i__1, &i__2, &x11[*m - *q + 1 + (*m - *q + 1) *
  1339. x11_dim1], ldx11, &v1t[*m - *q + 1 + (*m - *q + 1) *
  1340. v1t_dim1], ldv1t);
  1341. i__1 = -(*p) + *q;
  1342. i__2 = *q - *p;
  1343. clacpy_("U", &i__1, &i__2, &x21[*m - *q + 1 + (*p + 1) * x21_dim1]
  1344. , ldx21, &v1t[*p + 1 + (*p + 1) * v1t_dim1], ldv1t);
  1345. cunglq_(q, q, q, &v1t[v1t_offset], ldv1t, &work[itauq1], &work[
  1346. iorglq], &lorglq, &childinfo);
  1347. }
  1348. /* Simultaneously diagonalize X11 and X21. */
  1349. i__1 = *m - *p;
  1350. i__2 = *m - *q;
  1351. cbbcsd_(jobu2, jobu1, "N", jobv1t, "N", m, &i__1, &i__2, &theta[1], &
  1352. rwork[iphi], &u2[u2_offset], ldu2, &u1[u1_offset], ldu1, cdum,
  1353. &c__1, &v1t[v1t_offset], ldv1t, &rwork[ib11d], &rwork[ib11e],
  1354. &rwork[ib12d], &rwork[ib12e], &rwork[ib21d], &rwork[ib21e], &
  1355. rwork[ib22d], &rwork[ib22e], &rwork[ibbcsd], &lbbcsd, &
  1356. childinfo);
  1357. /* Permute rows and columns to place identity submatrices in */
  1358. /* preferred positions */
  1359. if (*p > r__) {
  1360. i__1 = r__;
  1361. for (i__ = 1; i__ <= i__1; ++i__) {
  1362. iwork[i__] = *p - r__ + i__;
  1363. }
  1364. i__1 = *p;
  1365. for (i__ = r__ + 1; i__ <= i__1; ++i__) {
  1366. iwork[i__] = i__ - r__;
  1367. }
  1368. if (wantu1) {
  1369. clapmt_(&c_false, p, p, &u1[u1_offset], ldu1, &iwork[1]);
  1370. }
  1371. if (wantv1t) {
  1372. clapmr_(&c_false, p, q, &v1t[v1t_offset], ldv1t, &iwork[1]);
  1373. }
  1374. }
  1375. }
  1376. return 0;
  1377. /* End of CUNCSD2BY1 */
  1378. } /* cuncsd2by1_ */