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