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cgebd2.c 23 kB

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  1. /* f2c.h -- Standard Fortran to C header file */
  2. /** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed."
  3. - From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
  4. #ifndef F2C_INCLUDE
  5. #define F2C_INCLUDE
  6. #include <math.h>
  7. #include <stdlib.h>
  8. #include <string.h>
  9. #include <stdio.h>
  10. #include <complex.h>
  11. #ifdef complex
  12. #undef complex
  13. #endif
  14. #ifdef I
  15. #undef I
  16. #endif
  17. typedef int integer;
  18. typedef unsigned int uinteger;
  19. typedef char *address;
  20. typedef short int shortint;
  21. typedef float real;
  22. typedef double doublereal;
  23. typedef struct { real r, i; } complex;
  24. typedef struct { doublereal r, i; } doublecomplex;
  25. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  26. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  27. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  28. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  29. #define pCf(z) (*_pCf(z))
  30. #define pCd(z) (*_pCd(z))
  31. typedef int logical;
  32. typedef short int shortlogical;
  33. typedef char logical1;
  34. typedef char integer1;
  35. #define TRUE_ (1)
  36. #define FALSE_ (0)
  37. /* Extern is for use with -E */
  38. #ifndef Extern
  39. #define Extern extern
  40. #endif
  41. /* I/O stuff */
  42. typedef int flag;
  43. typedef int ftnlen;
  44. typedef int ftnint;
  45. /*external read, write*/
  46. typedef struct
  47. { flag cierr;
  48. ftnint ciunit;
  49. flag ciend;
  50. char *cifmt;
  51. ftnint cirec;
  52. } cilist;
  53. /*internal read, write*/
  54. typedef struct
  55. { flag icierr;
  56. char *iciunit;
  57. flag iciend;
  58. char *icifmt;
  59. ftnint icirlen;
  60. ftnint icirnum;
  61. } icilist;
  62. /*open*/
  63. typedef struct
  64. { flag oerr;
  65. ftnint ounit;
  66. char *ofnm;
  67. ftnlen ofnmlen;
  68. char *osta;
  69. char *oacc;
  70. char *ofm;
  71. ftnint orl;
  72. char *oblnk;
  73. } olist;
  74. /*close*/
  75. typedef struct
  76. { flag cerr;
  77. ftnint cunit;
  78. char *csta;
  79. } cllist;
  80. /*rewind, backspace, endfile*/
  81. typedef struct
  82. { flag aerr;
  83. ftnint aunit;
  84. } alist;
  85. /* inquire */
  86. typedef struct
  87. { flag inerr;
  88. ftnint inunit;
  89. char *infile;
  90. ftnlen infilen;
  91. ftnint *inex; /*parameters in standard's order*/
  92. ftnint *inopen;
  93. ftnint *innum;
  94. ftnint *innamed;
  95. char *inname;
  96. ftnlen innamlen;
  97. char *inacc;
  98. ftnlen inacclen;
  99. char *inseq;
  100. ftnlen inseqlen;
  101. char *indir;
  102. ftnlen indirlen;
  103. char *infmt;
  104. ftnlen infmtlen;
  105. char *inform;
  106. ftnint informlen;
  107. char *inunf;
  108. ftnlen inunflen;
  109. ftnint *inrecl;
  110. ftnint *innrec;
  111. char *inblank;
  112. ftnlen inblanklen;
  113. } inlist;
  114. #define VOID void
  115. union Multitype { /* for multiple entry points */
  116. integer1 g;
  117. shortint h;
  118. integer i;
  119. /* longint j; */
  120. real r;
  121. doublereal d;
  122. complex c;
  123. doublecomplex z;
  124. };
  125. typedef union Multitype Multitype;
  126. struct Vardesc { /* for Namelist */
  127. char *name;
  128. char *addr;
  129. ftnlen *dims;
  130. int type;
  131. };
  132. typedef struct Vardesc Vardesc;
  133. struct Namelist {
  134. char *name;
  135. Vardesc **vars;
  136. int nvars;
  137. };
  138. typedef struct Namelist Namelist;
  139. #define abs(x) ((x) >= 0 ? (x) : -(x))
  140. #define dabs(x) (fabs(x))
  141. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  142. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  143. #define dmin(a,b) (f2cmin(a,b))
  144. #define dmax(a,b) (f2cmax(a,b))
  145. #define bit_test(a,b) ((a) >> (b) & 1)
  146. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  147. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  148. #define abort_() { sig_die("Fortran abort routine called", 1); }
  149. #define c_abs(z) (cabsf(Cf(z)))
  150. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  151. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  152. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  153. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  154. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  155. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  156. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  157. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  158. #define d_abs(x) (fabs(*(x)))
  159. #define d_acos(x) (acos(*(x)))
  160. #define d_asin(x) (asin(*(x)))
  161. #define d_atan(x) (atan(*(x)))
  162. #define d_atn2(x, y) (atan2(*(x),*(y)))
  163. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  164. #define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
  165. #define d_cos(x) (cos(*(x)))
  166. #define d_cosh(x) (cosh(*(x)))
  167. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  168. #define d_exp(x) (exp(*(x)))
  169. #define d_imag(z) (cimag(Cd(z)))
  170. #define r_imag(z) (cimag(Cf(z)))
  171. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  172. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  173. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  174. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  175. #define d_log(x) (log(*(x)))
  176. #define d_mod(x, y) (fmod(*(x), *(y)))
  177. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  178. #define d_nint(x) u_nint(*(x))
  179. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  180. #define d_sign(a,b) u_sign(*(a),*(b))
  181. #define r_sign(a,b) u_sign(*(a),*(b))
  182. #define d_sin(x) (sin(*(x)))
  183. #define d_sinh(x) (sinh(*(x)))
  184. #define d_sqrt(x) (sqrt(*(x)))
  185. #define d_tan(x) (tan(*(x)))
  186. #define d_tanh(x) (tanh(*(x)))
  187. #define i_abs(x) abs(*(x))
  188. #define i_dnnt(x) ((integer)u_nint(*(x)))
  189. #define i_len(s, n) (n)
  190. #define i_nint(x) ((integer)u_nint(*(x)))
  191. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  192. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  193. #define pow_si(B,E) spow_ui(*(B),*(E))
  194. #define pow_ri(B,E) spow_ui(*(B),*(E))
  195. #define pow_di(B,E) dpow_ui(*(B),*(E))
  196. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  197. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  198. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  199. #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
  200. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  201. #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
  202. #define sig_die(s, kill) { exit(1); }
  203. #define s_stop(s, n) {exit(0);}
  204. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  205. #define z_abs(z) (cabs(Cd(z)))
  206. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  207. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  208. #define myexit_() break;
  209. #define mycycle() continue;
  210. #define myceiling(w) {ceil(w)}
  211. #define myhuge(w) {HUGE_VAL}
  212. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  213. #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  214. /* procedure parameter types for -A and -C++ */
  215. #define F2C_proc_par_types 1
  216. #ifdef __cplusplus
  217. typedef logical (*L_fp)(...);
  218. #else
  219. typedef logical (*L_fp)();
  220. #endif
  221. static float spow_ui(float x, integer n) {
  222. float pow=1.0; unsigned long int u;
  223. if(n != 0) {
  224. if(n < 0) n = -n, x = 1/x;
  225. for(u = n; ; ) {
  226. if(u & 01) pow *= x;
  227. if(u >>= 1) x *= x;
  228. else break;
  229. }
  230. }
  231. return pow;
  232. }
  233. static double dpow_ui(double x, integer n) {
  234. double pow=1.0; unsigned long int u;
  235. if(n != 0) {
  236. if(n < 0) n = -n, x = 1/x;
  237. for(u = n; ; ) {
  238. if(u & 01) pow *= x;
  239. if(u >>= 1) x *= x;
  240. else break;
  241. }
  242. }
  243. return pow;
  244. }
  245. static _Complex float cpow_ui(_Complex float x, integer n) {
  246. _Complex float pow=1.0; unsigned long int u;
  247. if(n != 0) {
  248. if(n < 0) n = -n, x = 1/x;
  249. for(u = n; ; ) {
  250. if(u & 01) pow *= x;
  251. if(u >>= 1) x *= x;
  252. else break;
  253. }
  254. }
  255. return pow;
  256. }
  257. static _Complex double zpow_ui(_Complex double x, integer n) {
  258. _Complex double pow=1.0; unsigned long int u;
  259. if(n != 0) {
  260. if(n < 0) n = -n, x = 1/x;
  261. for(u = n; ; ) {
  262. if(u & 01) pow *= x;
  263. if(u >>= 1) x *= x;
  264. else break;
  265. }
  266. }
  267. return pow;
  268. }
  269. static integer pow_ii(integer x, integer n) {
  270. integer pow; unsigned long int u;
  271. if (n <= 0) {
  272. if (n == 0 || x == 1) pow = 1;
  273. else if (x != -1) pow = x == 0 ? 1/x : 0;
  274. else n = -n;
  275. }
  276. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  277. u = n;
  278. for(pow = 1; ; ) {
  279. if(u & 01) pow *= x;
  280. if(u >>= 1) x *= x;
  281. else break;
  282. }
  283. }
  284. return pow;
  285. }
  286. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  287. {
  288. double m; integer i, mi;
  289. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  290. if (w[i-1]>m) mi=i ,m=w[i-1];
  291. return mi-s+1;
  292. }
  293. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  294. {
  295. float m; integer i, mi;
  296. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  297. if (w[i-1]>m) mi=i ,m=w[i-1];
  298. return mi-s+1;
  299. }
  300. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  301. integer n = *n_, incx = *incx_, incy = *incy_, i;
  302. _Complex float zdotc = 0.0;
  303. if (incx == 1 && incy == 1) {
  304. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  305. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  306. }
  307. } else {
  308. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  309. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  310. }
  311. }
  312. pCf(z) = zdotc;
  313. }
  314. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  315. integer n = *n_, incx = *incx_, incy = *incy_, i;
  316. _Complex double zdotc = 0.0;
  317. if (incx == 1 && incy == 1) {
  318. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  319. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  320. }
  321. } else {
  322. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  323. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  324. }
  325. }
  326. pCd(z) = zdotc;
  327. }
  328. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  329. integer n = *n_, incx = *incx_, incy = *incy_, i;
  330. _Complex float zdotc = 0.0;
  331. if (incx == 1 && incy == 1) {
  332. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  333. zdotc += Cf(&x[i]) * Cf(&y[i]);
  334. }
  335. } else {
  336. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  337. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  338. }
  339. }
  340. pCf(z) = zdotc;
  341. }
  342. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  343. integer n = *n_, incx = *incx_, incy = *incy_, i;
  344. _Complex double zdotc = 0.0;
  345. if (incx == 1 && incy == 1) {
  346. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  347. zdotc += Cd(&x[i]) * Cd(&y[i]);
  348. }
  349. } else {
  350. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  351. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  352. }
  353. }
  354. pCd(z) = zdotc;
  355. }
  356. #endif
  357. /* -- translated by f2c (version 20000121).
  358. You must link the resulting object file with the libraries:
  359. -lf2c -lm (in that order)
  360. */
  361. /* Table of constant values */
  362. static integer c__1 = 1;
  363. /* > \brief \b CGEBD2 reduces a general matrix to bidiagonal form using an unblocked algorithm. */
  364. /* =========== DOCUMENTATION =========== */
  365. /* Online html documentation available at */
  366. /* http://www.netlib.org/lapack/explore-html/ */
  367. /* > \htmlonly */
  368. /* > Download CGEBD2 + dependencies */
  369. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgebd2.
  370. f"> */
  371. /* > [TGZ]</a> */
  372. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgebd2.
  373. f"> */
  374. /* > [ZIP]</a> */
  375. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgebd2.
  376. f"> */
  377. /* > [TXT]</a> */
  378. /* > \endhtmlonly */
  379. /* Definition: */
  380. /* =========== */
  381. /* SUBROUTINE CGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO ) */
  382. /* INTEGER INFO, LDA, M, N */
  383. /* REAL D( * ), E( * ) */
  384. /* COMPLEX A( LDA, * ), TAUP( * ), TAUQ( * ), WORK( * ) */
  385. /* > \par Purpose: */
  386. /* ============= */
  387. /* > */
  388. /* > \verbatim */
  389. /* > */
  390. /* > CGEBD2 reduces a complex general m by n matrix A to upper or lower */
  391. /* > real bidiagonal form B by a unitary transformation: Q**H * A * P = B. */
  392. /* > */
  393. /* > If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */
  394. /* > \endverbatim */
  395. /* Arguments: */
  396. /* ========== */
  397. /* > \param[in] M */
  398. /* > \verbatim */
  399. /* > M is INTEGER */
  400. /* > The number of rows in the matrix A. M >= 0. */
  401. /* > \endverbatim */
  402. /* > */
  403. /* > \param[in] N */
  404. /* > \verbatim */
  405. /* > N is INTEGER */
  406. /* > The number of columns in the matrix A. N >= 0. */
  407. /* > \endverbatim */
  408. /* > */
  409. /* > \param[in,out] A */
  410. /* > \verbatim */
  411. /* > A is COMPLEX array, dimension (LDA,N) */
  412. /* > On entry, the m by n general matrix to be reduced. */
  413. /* > On exit, */
  414. /* > if m >= n, the diagonal and the first superdiagonal are */
  415. /* > overwritten with the upper bidiagonal matrix B; the */
  416. /* > elements below the diagonal, with the array TAUQ, represent */
  417. /* > the unitary matrix Q as a product of elementary */
  418. /* > reflectors, and the elements above the first superdiagonal, */
  419. /* > with the array TAUP, represent the unitary matrix P as */
  420. /* > a product of elementary reflectors; */
  421. /* > if m < n, the diagonal and the first subdiagonal are */
  422. /* > overwritten with the lower bidiagonal matrix B; the */
  423. /* > elements below the first subdiagonal, with the array TAUQ, */
  424. /* > represent the unitary matrix Q as a product of */
  425. /* > elementary reflectors, and the elements above the diagonal, */
  426. /* > with the array TAUP, represent the unitary matrix P as */
  427. /* > a product of elementary reflectors. */
  428. /* > See Further Details. */
  429. /* > \endverbatim */
  430. /* > */
  431. /* > \param[in] LDA */
  432. /* > \verbatim */
  433. /* > LDA is INTEGER */
  434. /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
  435. /* > \endverbatim */
  436. /* > */
  437. /* > \param[out] D */
  438. /* > \verbatim */
  439. /* > D is REAL array, dimension (f2cmin(M,N)) */
  440. /* > The diagonal elements of the bidiagonal matrix B: */
  441. /* > D(i) = A(i,i). */
  442. /* > \endverbatim */
  443. /* > */
  444. /* > \param[out] E */
  445. /* > \verbatim */
  446. /* > E is REAL array, dimension (f2cmin(M,N)-1) */
  447. /* > The off-diagonal elements of the bidiagonal matrix B: */
  448. /* > if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */
  449. /* > if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */
  450. /* > \endverbatim */
  451. /* > */
  452. /* > \param[out] TAUQ */
  453. /* > \verbatim */
  454. /* > TAUQ is COMPLEX array, dimension (f2cmin(M,N)) */
  455. /* > The scalar factors of the elementary reflectors which */
  456. /* > represent the unitary matrix Q. See Further Details. */
  457. /* > \endverbatim */
  458. /* > */
  459. /* > \param[out] TAUP */
  460. /* > \verbatim */
  461. /* > TAUP is COMPLEX array, dimension (f2cmin(M,N)) */
  462. /* > The scalar factors of the elementary reflectors which */
  463. /* > represent the unitary matrix P. See Further Details. */
  464. /* > \endverbatim */
  465. /* > */
  466. /* > \param[out] WORK */
  467. /* > \verbatim */
  468. /* > WORK is COMPLEX array, dimension (f2cmax(M,N)) */
  469. /* > \endverbatim */
  470. /* > */
  471. /* > \param[out] INFO */
  472. /* > \verbatim */
  473. /* > INFO is INTEGER */
  474. /* > = 0: successful exit */
  475. /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
  476. /* > \endverbatim */
  477. /* Authors: */
  478. /* ======== */
  479. /* > \author Univ. of Tennessee */
  480. /* > \author Univ. of California Berkeley */
  481. /* > \author Univ. of Colorado Denver */
  482. /* > \author NAG Ltd. */
  483. /* > \date June 2017 */
  484. /* > \ingroup complexGEcomputational */
  485. /* @precisions normal c -> s d z */
  486. /* > \par Further Details: */
  487. /* ===================== */
  488. /* > */
  489. /* > \verbatim */
  490. /* > */
  491. /* > The matrices Q and P are represented as products of elementary */
  492. /* > reflectors: */
  493. /* > */
  494. /* > If m >= n, */
  495. /* > */
  496. /* > Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) */
  497. /* > */
  498. /* > Each H(i) and G(i) has the form: */
  499. /* > */
  500. /* > H(i) = I - tauq * v * v**H and G(i) = I - taup * u * u**H */
  501. /* > */
  502. /* > where tauq and taup are complex scalars, and v and u are complex */
  503. /* > vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in */
  504. /* > A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in */
  505. /* > A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
  506. /* > */
  507. /* > If m < n, */
  508. /* > */
  509. /* > Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) */
  510. /* > */
  511. /* > Each H(i) and G(i) has the form: */
  512. /* > */
  513. /* > H(i) = I - tauq * v * v**H and G(i) = I - taup * u * u**H */
  514. /* > */
  515. /* > where tauq and taup are complex scalars, v and u are complex vectors; */
  516. /* > v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); */
  517. /* > u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); */
  518. /* > tauq is stored in TAUQ(i) and taup in TAUP(i). */
  519. /* > */
  520. /* > The contents of A on exit are illustrated by the following examples: */
  521. /* > */
  522. /* > m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */
  523. /* > */
  524. /* > ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) */
  525. /* > ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) */
  526. /* > ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) */
  527. /* > ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) */
  528. /* > ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) */
  529. /* > ( v1 v2 v3 v4 v5 ) */
  530. /* > */
  531. /* > where d and e denote diagonal and off-diagonal elements of B, vi */
  532. /* > denotes an element of the vector defining H(i), and ui an element of */
  533. /* > the vector defining G(i). */
  534. /* > \endverbatim */
  535. /* > */
  536. /* ===================================================================== */
  537. /* Subroutine */ int cgebd2_(integer *m, integer *n, complex *a, integer *lda,
  538. real *d__, real *e, complex *tauq, complex *taup, complex *work,
  539. integer *info)
  540. {
  541. /* System generated locals */
  542. integer a_dim1, a_offset, i__1, i__2, i__3;
  543. complex q__1;
  544. /* Local variables */
  545. integer i__;
  546. complex alpha;
  547. extern /* Subroutine */ int clarf_(char *, integer *, integer *, complex *
  548. , integer *, complex *, complex *, integer *, complex *),
  549. clarfg_(integer *, complex *, complex *, integer *, complex *),
  550. clacgv_(integer *, complex *, integer *), xerbla_(char *, integer
  551. *, ftnlen);
  552. /* -- LAPACK computational routine (version 3.7.1) -- */
  553. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  554. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  555. /* June 2017 */
  556. /* ===================================================================== */
  557. /* Test the input parameters */
  558. /* Parameter adjustments */
  559. a_dim1 = *lda;
  560. a_offset = 1 + a_dim1 * 1;
  561. a -= a_offset;
  562. --d__;
  563. --e;
  564. --tauq;
  565. --taup;
  566. --work;
  567. /* Function Body */
  568. *info = 0;
  569. if (*m < 0) {
  570. *info = -1;
  571. } else if (*n < 0) {
  572. *info = -2;
  573. } else if (*lda < f2cmax(1,*m)) {
  574. *info = -4;
  575. }
  576. if (*info < 0) {
  577. i__1 = -(*info);
  578. xerbla_("CGEBD2", &i__1, (ftnlen)6);
  579. return 0;
  580. }
  581. if (*m >= *n) {
  582. /* Reduce to upper bidiagonal form */
  583. i__1 = *n;
  584. for (i__ = 1; i__ <= i__1; ++i__) {
  585. /* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */
  586. i__2 = i__ + i__ * a_dim1;
  587. alpha.r = a[i__2].r, alpha.i = a[i__2].i;
  588. i__2 = *m - i__ + 1;
  589. /* Computing MIN */
  590. i__3 = i__ + 1;
  591. clarfg_(&i__2, &alpha, &a[f2cmin(i__3,*m) + i__ * a_dim1], &c__1, &
  592. tauq[i__]);
  593. i__2 = i__;
  594. d__[i__2] = alpha.r;
  595. i__2 = i__ + i__ * a_dim1;
  596. a[i__2].r = 1.f, a[i__2].i = 0.f;
  597. /* Apply H(i)**H to A(i:m,i+1:n) from the left */
  598. if (i__ < *n) {
  599. i__2 = *m - i__ + 1;
  600. i__3 = *n - i__;
  601. r_cnjg(&q__1, &tauq[i__]);
  602. clarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &
  603. q__1, &a[i__ + (i__ + 1) * a_dim1], lda, &work[1]);
  604. }
  605. i__2 = i__ + i__ * a_dim1;
  606. i__3 = i__;
  607. a[i__2].r = d__[i__3], a[i__2].i = 0.f;
  608. if (i__ < *n) {
  609. /* Generate elementary reflector G(i) to annihilate */
  610. /* A(i,i+2:n) */
  611. i__2 = *n - i__;
  612. clacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
  613. i__2 = i__ + (i__ + 1) * a_dim1;
  614. alpha.r = a[i__2].r, alpha.i = a[i__2].i;
  615. i__2 = *n - i__;
  616. /* Computing MIN */
  617. i__3 = i__ + 2;
  618. clarfg_(&i__2, &alpha, &a[i__ + f2cmin(i__3,*n) * a_dim1], lda, &
  619. taup[i__]);
  620. i__2 = i__;
  621. e[i__2] = alpha.r;
  622. i__2 = i__ + (i__ + 1) * a_dim1;
  623. a[i__2].r = 1.f, a[i__2].i = 0.f;
  624. /* Apply G(i) to A(i+1:m,i+1:n) from the right */
  625. i__2 = *m - i__;
  626. i__3 = *n - i__;
  627. clarf_("Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1],
  628. lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1],
  629. lda, &work[1]);
  630. i__2 = *n - i__;
  631. clacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
  632. i__2 = i__ + (i__ + 1) * a_dim1;
  633. i__3 = i__;
  634. a[i__2].r = e[i__3], a[i__2].i = 0.f;
  635. } else {
  636. i__2 = i__;
  637. taup[i__2].r = 0.f, taup[i__2].i = 0.f;
  638. }
  639. /* L10: */
  640. }
  641. } else {
  642. /* Reduce to lower bidiagonal form */
  643. i__1 = *m;
  644. for (i__ = 1; i__ <= i__1; ++i__) {
  645. /* Generate elementary reflector G(i) to annihilate A(i,i+1:n) */
  646. i__2 = *n - i__ + 1;
  647. clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
  648. i__2 = i__ + i__ * a_dim1;
  649. alpha.r = a[i__2].r, alpha.i = a[i__2].i;
  650. i__2 = *n - i__ + 1;
  651. /* Computing MIN */
  652. i__3 = i__ + 1;
  653. clarfg_(&i__2, &alpha, &a[i__ + f2cmin(i__3,*n) * a_dim1], lda, &
  654. taup[i__]);
  655. i__2 = i__;
  656. d__[i__2] = alpha.r;
  657. i__2 = i__ + i__ * a_dim1;
  658. a[i__2].r = 1.f, a[i__2].i = 0.f;
  659. /* Apply G(i) to A(i+1:m,i:n) from the right */
  660. if (i__ < *m) {
  661. i__2 = *m - i__;
  662. i__3 = *n - i__ + 1;
  663. clarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &
  664. taup[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1]);
  665. }
  666. i__2 = *n - i__ + 1;
  667. clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
  668. i__2 = i__ + i__ * a_dim1;
  669. i__3 = i__;
  670. a[i__2].r = d__[i__3], a[i__2].i = 0.f;
  671. if (i__ < *m) {
  672. /* Generate elementary reflector H(i) to annihilate */
  673. /* A(i+2:m,i) */
  674. i__2 = i__ + 1 + i__ * a_dim1;
  675. alpha.r = a[i__2].r, alpha.i = a[i__2].i;
  676. i__2 = *m - i__;
  677. /* Computing MIN */
  678. i__3 = i__ + 2;
  679. clarfg_(&i__2, &alpha, &a[f2cmin(i__3,*m) + i__ * a_dim1], &c__1,
  680. &tauq[i__]);
  681. i__2 = i__;
  682. e[i__2] = alpha.r;
  683. i__2 = i__ + 1 + i__ * a_dim1;
  684. a[i__2].r = 1.f, a[i__2].i = 0.f;
  685. /* Apply H(i)**H to A(i+1:m,i+1:n) from the left */
  686. i__2 = *m - i__;
  687. i__3 = *n - i__;
  688. r_cnjg(&q__1, &tauq[i__]);
  689. clarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], &
  690. c__1, &q__1, &a[i__ + 1 + (i__ + 1) * a_dim1], lda, &
  691. work[1]);
  692. i__2 = i__ + 1 + i__ * a_dim1;
  693. i__3 = i__;
  694. a[i__2].r = e[i__3], a[i__2].i = 0.f;
  695. } else {
  696. i__2 = i__;
  697. tauq[i__2].r = 0.f, tauq[i__2].i = 0.f;
  698. }
  699. /* L20: */
  700. }
  701. }
  702. return 0;
  703. /* End of CGEBD2 */
  704. } /* cgebd2_ */