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stgex2.c 36 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. #if defined(_WIN64)
  18. typedef long long BLASLONG;
  19. typedef unsigned long long BLASULONG;
  20. #else
  21. typedef long BLASLONG;
  22. typedef unsigned long BLASULONG;
  23. #endif
  24. #ifdef LAPACK_ILP64
  25. typedef BLASLONG blasint;
  26. #if defined(_WIN64)
  27. #define blasabs(x) llabs(x)
  28. #else
  29. #define blasabs(x) labs(x)
  30. #endif
  31. #else
  32. typedef int blasint;
  33. #define blasabs(x) abs(x)
  34. #endif
  35. typedef blasint integer;
  36. typedef unsigned int uinteger;
  37. typedef char *address;
  38. typedef short int shortint;
  39. typedef float real;
  40. typedef double doublereal;
  41. typedef struct { real r, i; } complex;
  42. typedef struct { doublereal r, i; } doublecomplex;
  43. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  44. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  45. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  46. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  47. #define pCf(z) (*_pCf(z))
  48. #define pCd(z) (*_pCd(z))
  49. typedef int logical;
  50. typedef short int shortlogical;
  51. typedef char logical1;
  52. typedef char integer1;
  53. #define TRUE_ (1)
  54. #define FALSE_ (0)
  55. /* Extern is for use with -E */
  56. #ifndef Extern
  57. #define Extern extern
  58. #endif
  59. /* I/O stuff */
  60. typedef int flag;
  61. typedef int ftnlen;
  62. typedef int ftnint;
  63. /*external read, write*/
  64. typedef struct
  65. { flag cierr;
  66. ftnint ciunit;
  67. flag ciend;
  68. char *cifmt;
  69. ftnint cirec;
  70. } cilist;
  71. /*internal read, write*/
  72. typedef struct
  73. { flag icierr;
  74. char *iciunit;
  75. flag iciend;
  76. char *icifmt;
  77. ftnint icirlen;
  78. ftnint icirnum;
  79. } icilist;
  80. /*open*/
  81. typedef struct
  82. { flag oerr;
  83. ftnint ounit;
  84. char *ofnm;
  85. ftnlen ofnmlen;
  86. char *osta;
  87. char *oacc;
  88. char *ofm;
  89. ftnint orl;
  90. char *oblnk;
  91. } olist;
  92. /*close*/
  93. typedef struct
  94. { flag cerr;
  95. ftnint cunit;
  96. char *csta;
  97. } cllist;
  98. /*rewind, backspace, endfile*/
  99. typedef struct
  100. { flag aerr;
  101. ftnint aunit;
  102. } alist;
  103. /* inquire */
  104. typedef struct
  105. { flag inerr;
  106. ftnint inunit;
  107. char *infile;
  108. ftnlen infilen;
  109. ftnint *inex; /*parameters in standard's order*/
  110. ftnint *inopen;
  111. ftnint *innum;
  112. ftnint *innamed;
  113. char *inname;
  114. ftnlen innamlen;
  115. char *inacc;
  116. ftnlen inacclen;
  117. char *inseq;
  118. ftnlen inseqlen;
  119. char *indir;
  120. ftnlen indirlen;
  121. char *infmt;
  122. ftnlen infmtlen;
  123. char *inform;
  124. ftnint informlen;
  125. char *inunf;
  126. ftnlen inunflen;
  127. ftnint *inrecl;
  128. ftnint *innrec;
  129. char *inblank;
  130. ftnlen inblanklen;
  131. } inlist;
  132. #define VOID void
  133. union Multitype { /* for multiple entry points */
  134. integer1 g;
  135. shortint h;
  136. integer i;
  137. /* longint j; */
  138. real r;
  139. doublereal d;
  140. complex c;
  141. doublecomplex z;
  142. };
  143. typedef union Multitype Multitype;
  144. struct Vardesc { /* for Namelist */
  145. char *name;
  146. char *addr;
  147. ftnlen *dims;
  148. int type;
  149. };
  150. typedef struct Vardesc Vardesc;
  151. struct Namelist {
  152. char *name;
  153. Vardesc **vars;
  154. int nvars;
  155. };
  156. typedef struct Namelist Namelist;
  157. #define abs(x) ((x) >= 0 ? (x) : -(x))
  158. #define dabs(x) (fabs(x))
  159. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  160. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  161. #define dmin(a,b) (f2cmin(a,b))
  162. #define dmax(a,b) (f2cmax(a,b))
  163. #define bit_test(a,b) ((a) >> (b) & 1)
  164. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  165. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  166. #define abort_() { sig_die("Fortran abort routine called", 1); }
  167. #define c_abs(z) (cabsf(Cf(z)))
  168. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  169. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  170. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  171. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  172. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  173. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  174. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  175. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  176. #define d_abs(x) (fabs(*(x)))
  177. #define d_acos(x) (acos(*(x)))
  178. #define d_asin(x) (asin(*(x)))
  179. #define d_atan(x) (atan(*(x)))
  180. #define d_atn2(x, y) (atan2(*(x),*(y)))
  181. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  182. #define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
  183. #define d_cos(x) (cos(*(x)))
  184. #define d_cosh(x) (cosh(*(x)))
  185. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  186. #define d_exp(x) (exp(*(x)))
  187. #define d_imag(z) (cimag(Cd(z)))
  188. #define r_imag(z) (cimag(Cf(z)))
  189. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  190. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  191. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  192. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  193. #define d_log(x) (log(*(x)))
  194. #define d_mod(x, y) (fmod(*(x), *(y)))
  195. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  196. #define d_nint(x) u_nint(*(x))
  197. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  198. #define d_sign(a,b) u_sign(*(a),*(b))
  199. #define r_sign(a,b) u_sign(*(a),*(b))
  200. #define d_sin(x) (sin(*(x)))
  201. #define d_sinh(x) (sinh(*(x)))
  202. #define d_sqrt(x) (sqrt(*(x)))
  203. #define d_tan(x) (tan(*(x)))
  204. #define d_tanh(x) (tanh(*(x)))
  205. #define i_abs(x) abs(*(x))
  206. #define i_dnnt(x) ((integer)u_nint(*(x)))
  207. #define i_len(s, n) (n)
  208. #define i_nint(x) ((integer)u_nint(*(x)))
  209. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  210. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  211. #define pow_si(B,E) spow_ui(*(B),*(E))
  212. #define pow_ri(B,E) spow_ui(*(B),*(E))
  213. #define pow_di(B,E) dpow_ui(*(B),*(E))
  214. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  215. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  216. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  217. #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++ = ' '; }
  218. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  219. #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]; }
  220. #define sig_die(s, kill) { exit(1); }
  221. #define s_stop(s, n) {exit(0);}
  222. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  223. #define z_abs(z) (cabs(Cd(z)))
  224. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  225. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  226. #define myexit_() break;
  227. #define mycycle() continue;
  228. #define myceiling(w) {ceil(w)}
  229. #define myhuge(w) {HUGE_VAL}
  230. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  231. #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  232. /* procedure parameter types for -A and -C++ */
  233. #define F2C_proc_par_types 1
  234. #ifdef __cplusplus
  235. typedef logical (*L_fp)(...);
  236. #else
  237. typedef logical (*L_fp)();
  238. #endif
  239. static float spow_ui(float x, integer n) {
  240. float pow=1.0; unsigned long int u;
  241. if(n != 0) {
  242. if(n < 0) n = -n, x = 1/x;
  243. for(u = n; ; ) {
  244. if(u & 01) pow *= x;
  245. if(u >>= 1) x *= x;
  246. else break;
  247. }
  248. }
  249. return pow;
  250. }
  251. static double dpow_ui(double x, integer n) {
  252. double pow=1.0; unsigned long int u;
  253. if(n != 0) {
  254. if(n < 0) n = -n, x = 1/x;
  255. for(u = n; ; ) {
  256. if(u & 01) pow *= x;
  257. if(u >>= 1) x *= x;
  258. else break;
  259. }
  260. }
  261. return pow;
  262. }
  263. static _Complex float cpow_ui(_Complex float x, integer n) {
  264. _Complex float pow=1.0; unsigned long int u;
  265. if(n != 0) {
  266. if(n < 0) n = -n, x = 1/x;
  267. for(u = n; ; ) {
  268. if(u & 01) pow *= x;
  269. if(u >>= 1) x *= x;
  270. else break;
  271. }
  272. }
  273. return pow;
  274. }
  275. static _Complex double zpow_ui(_Complex double x, integer n) {
  276. _Complex double pow=1.0; unsigned long int u;
  277. if(n != 0) {
  278. if(n < 0) n = -n, x = 1/x;
  279. for(u = n; ; ) {
  280. if(u & 01) pow *= x;
  281. if(u >>= 1) x *= x;
  282. else break;
  283. }
  284. }
  285. return pow;
  286. }
  287. static integer pow_ii(integer x, integer n) {
  288. integer pow; unsigned long int u;
  289. if (n <= 0) {
  290. if (n == 0 || x == 1) pow = 1;
  291. else if (x != -1) pow = x == 0 ? 1/x : 0;
  292. else n = -n;
  293. }
  294. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  295. u = n;
  296. for(pow = 1; ; ) {
  297. if(u & 01) pow *= x;
  298. if(u >>= 1) x *= x;
  299. else break;
  300. }
  301. }
  302. return pow;
  303. }
  304. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  305. {
  306. double m; integer i, mi;
  307. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  308. if (w[i-1]>m) mi=i ,m=w[i-1];
  309. return mi-s+1;
  310. }
  311. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  312. {
  313. float m; integer i, mi;
  314. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  315. if (w[i-1]>m) mi=i ,m=w[i-1];
  316. return mi-s+1;
  317. }
  318. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  319. integer n = *n_, incx = *incx_, incy = *incy_, i;
  320. _Complex float zdotc = 0.0;
  321. if (incx == 1 && incy == 1) {
  322. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  323. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  324. }
  325. } else {
  326. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  327. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  328. }
  329. }
  330. pCf(z) = zdotc;
  331. }
  332. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  333. integer n = *n_, incx = *incx_, incy = *incy_, i;
  334. _Complex double zdotc = 0.0;
  335. if (incx == 1 && incy == 1) {
  336. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  337. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  338. }
  339. } else {
  340. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  341. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  342. }
  343. }
  344. pCd(z) = zdotc;
  345. }
  346. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  347. integer n = *n_, incx = *incx_, incy = *incy_, i;
  348. _Complex float zdotc = 0.0;
  349. if (incx == 1 && incy == 1) {
  350. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  351. zdotc += Cf(&x[i]) * Cf(&y[i]);
  352. }
  353. } else {
  354. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  355. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  356. }
  357. }
  358. pCf(z) = zdotc;
  359. }
  360. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  361. integer n = *n_, incx = *incx_, incy = *incy_, i;
  362. _Complex double zdotc = 0.0;
  363. if (incx == 1 && incy == 1) {
  364. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  365. zdotc += Cd(&x[i]) * Cd(&y[i]);
  366. }
  367. } else {
  368. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  369. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  370. }
  371. }
  372. pCd(z) = zdotc;
  373. }
  374. #endif
  375. /* -- translated by f2c (version 20000121).
  376. You must link the resulting object file with the libraries:
  377. -lf2c -lm (in that order)
  378. */
  379. /* Table of constant values */
  380. static integer c__4 = 4;
  381. static real c_b5 = 0.f;
  382. static integer c__1 = 1;
  383. static integer c__2 = 2;
  384. static real c_b42 = 1.f;
  385. static real c_b48 = -1.f;
  386. static integer c__0 = 0;
  387. /* > \brief \b STGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogon
  388. al equivalence transformation. */
  389. /* =========== DOCUMENTATION =========== */
  390. /* Online html documentation available at */
  391. /* http://www.netlib.org/lapack/explore-html/ */
  392. /* > \htmlonly */
  393. /* > Download STGEX2 + dependencies */
  394. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/stgex2.
  395. f"> */
  396. /* > [TGZ]</a> */
  397. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stgex2.
  398. f"> */
  399. /* > [ZIP]</a> */
  400. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stgex2.
  401. f"> */
  402. /* > [TXT]</a> */
  403. /* > \endhtmlonly */
  404. /* Definition: */
  405. /* =========== */
  406. /* SUBROUTINE STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, */
  407. /* LDZ, J1, N1, N2, WORK, LWORK, INFO ) */
  408. /* LOGICAL WANTQ, WANTZ */
  409. /* INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2 */
  410. /* REAL A( LDA, * ), B( LDB, * ), Q( LDQ, * ), */
  411. /* $ WORK( * ), Z( LDZ, * ) */
  412. /* > \par Purpose: */
  413. /* ============= */
  414. /* > */
  415. /* > \verbatim */
  416. /* > */
  417. /* > STGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22) */
  418. /* > of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair */
  419. /* > (A, B) by an orthogonal equivalence transformation. */
  420. /* > */
  421. /* > (A, B) must be in generalized real Schur canonical form (as returned */
  422. /* > by SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 */
  423. /* > diagonal blocks. B is upper triangular. */
  424. /* > */
  425. /* > Optionally, the matrices Q and Z of generalized Schur vectors are */
  426. /* > updated. */
  427. /* > */
  428. /* > Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T */
  429. /* > Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T */
  430. /* > */
  431. /* > \endverbatim */
  432. /* Arguments: */
  433. /* ========== */
  434. /* > \param[in] WANTQ */
  435. /* > \verbatim */
  436. /* > WANTQ is LOGICAL */
  437. /* > .TRUE. : update the left transformation matrix Q; */
  438. /* > .FALSE.: do not update Q. */
  439. /* > \endverbatim */
  440. /* > */
  441. /* > \param[in] WANTZ */
  442. /* > \verbatim */
  443. /* > WANTZ is LOGICAL */
  444. /* > .TRUE. : update the right transformation matrix Z; */
  445. /* > .FALSE.: do not update Z. */
  446. /* > \endverbatim */
  447. /* > */
  448. /* > \param[in] N */
  449. /* > \verbatim */
  450. /* > N is INTEGER */
  451. /* > The order of the matrices A and B. N >= 0. */
  452. /* > \endverbatim */
  453. /* > */
  454. /* > \param[in,out] A */
  455. /* > \verbatim */
  456. /* > A is REAL array, dimension (LDA,N) */
  457. /* > On entry, the matrix A in the pair (A, B). */
  458. /* > On exit, the updated matrix A. */
  459. /* > \endverbatim */
  460. /* > */
  461. /* > \param[in] LDA */
  462. /* > \verbatim */
  463. /* > LDA is INTEGER */
  464. /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
  465. /* > \endverbatim */
  466. /* > */
  467. /* > \param[in,out] B */
  468. /* > \verbatim */
  469. /* > B is REAL array, dimension (LDB,N) */
  470. /* > On entry, the matrix B in the pair (A, B). */
  471. /* > On exit, the updated matrix B. */
  472. /* > \endverbatim */
  473. /* > */
  474. /* > \param[in] LDB */
  475. /* > \verbatim */
  476. /* > LDB is INTEGER */
  477. /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
  478. /* > \endverbatim */
  479. /* > */
  480. /* > \param[in,out] Q */
  481. /* > \verbatim */
  482. /* > Q is REAL array, dimension (LDQ,N) */
  483. /* > On entry, if WANTQ = .TRUE., the orthogonal matrix Q. */
  484. /* > On exit, the updated matrix Q. */
  485. /* > Not referenced if WANTQ = .FALSE.. */
  486. /* > \endverbatim */
  487. /* > */
  488. /* > \param[in] LDQ */
  489. /* > \verbatim */
  490. /* > LDQ is INTEGER */
  491. /* > The leading dimension of the array Q. LDQ >= 1. */
  492. /* > If WANTQ = .TRUE., LDQ >= N. */
  493. /* > \endverbatim */
  494. /* > */
  495. /* > \param[in,out] Z */
  496. /* > \verbatim */
  497. /* > Z is REAL array, dimension (LDZ,N) */
  498. /* > On entry, if WANTZ =.TRUE., the orthogonal matrix Z. */
  499. /* > On exit, the updated matrix Z. */
  500. /* > Not referenced if WANTZ = .FALSE.. */
  501. /* > \endverbatim */
  502. /* > */
  503. /* > \param[in] LDZ */
  504. /* > \verbatim */
  505. /* > LDZ is INTEGER */
  506. /* > The leading dimension of the array Z. LDZ >= 1. */
  507. /* > If WANTZ = .TRUE., LDZ >= N. */
  508. /* > \endverbatim */
  509. /* > */
  510. /* > \param[in] J1 */
  511. /* > \verbatim */
  512. /* > J1 is INTEGER */
  513. /* > The index to the first block (A11, B11). 1 <= J1 <= N. */
  514. /* > \endverbatim */
  515. /* > */
  516. /* > \param[in] N1 */
  517. /* > \verbatim */
  518. /* > N1 is INTEGER */
  519. /* > The order of the first block (A11, B11). N1 = 0, 1 or 2. */
  520. /* > \endverbatim */
  521. /* > */
  522. /* > \param[in] N2 */
  523. /* > \verbatim */
  524. /* > N2 is INTEGER */
  525. /* > The order of the second block (A22, B22). N2 = 0, 1 or 2. */
  526. /* > \endverbatim */
  527. /* > */
  528. /* > \param[out] WORK */
  529. /* > \verbatim */
  530. /* > WORK is REAL array, dimension (MAX(1,LWORK)). */
  531. /* > \endverbatim */
  532. /* > */
  533. /* > \param[in] LWORK */
  534. /* > \verbatim */
  535. /* > LWORK is INTEGER */
  536. /* > The dimension of the array WORK. */
  537. /* > LWORK >= MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 ) */
  538. /* > \endverbatim */
  539. /* > */
  540. /* > \param[out] INFO */
  541. /* > \verbatim */
  542. /* > INFO is INTEGER */
  543. /* > =0: Successful exit */
  544. /* > >0: If INFO = 1, the transformed matrix (A, B) would be */
  545. /* > too far from generalized Schur form; the blocks are */
  546. /* > not swapped and (A, B) and (Q, Z) are unchanged. */
  547. /* > The problem of swapping is too ill-conditioned. */
  548. /* > <0: If INFO = -16: LWORK is too small. Appropriate value */
  549. /* > for LWORK is returned in WORK(1). */
  550. /* > \endverbatim */
  551. /* Authors: */
  552. /* ======== */
  553. /* > \author Univ. of Tennessee */
  554. /* > \author Univ. of California Berkeley */
  555. /* > \author Univ. of Colorado Denver */
  556. /* > \author NAG Ltd. */
  557. /* > \date June 2017 */
  558. /* > \ingroup realGEauxiliary */
  559. /* > \par Further Details: */
  560. /* ===================== */
  561. /* > */
  562. /* > In the current code both weak and strong stability tests are */
  563. /* > performed. The user can omit the strong stability test by changing */
  564. /* > the internal logical parameter WANDS to .FALSE.. See ref. [2] for */
  565. /* > details. */
  566. /* > \par Contributors: */
  567. /* ================== */
  568. /* > */
  569. /* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
  570. /* > Umea University, S-901 87 Umea, Sweden. */
  571. /* > \par References: */
  572. /* ================ */
  573. /* > */
  574. /* > \verbatim */
  575. /* > */
  576. /* > [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */
  577. /* > Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */
  578. /* > M.S. Moonen et al (eds), Linear Algebra for Large Scale and */
  579. /* > Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */
  580. /* > */
  581. /* > [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */
  582. /* > Eigenvalues of a Regular Matrix Pair (A, B) and Condition */
  583. /* > Estimation: Theory, Algorithms and Software, */
  584. /* > Report UMINF - 94.04, Department of Computing Science, Umea */
  585. /* > University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working */
  586. /* > Note 87. To appear in Numerical Algorithms, 1996. */
  587. /* > \endverbatim */
  588. /* > */
  589. /* ===================================================================== */
  590. /* Subroutine */ int stgex2_(logical *wantq, logical *wantz, integer *n, real
  591. *a, integer *lda, real *b, integer *ldb, real *q, integer *ldq, real *
  592. z__, integer *ldz, integer *j1, integer *n1, integer *n2, real *work,
  593. integer *lwork, integer *info)
  594. {
  595. /* System generated locals */
  596. integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1,
  597. z_offset, i__1, i__2;
  598. real r__1;
  599. /* Local variables */
  600. logical weak;
  601. real ddum;
  602. integer idum;
  603. real taul[4], dsum, taur[4], scpy[16] /* was [4][4] */, tcpy[16]
  604. /* was [4][4] */;
  605. extern /* Subroutine */ int srot_(integer *, real *, integer *, real *,
  606. integer *, real *, real *);
  607. real f, g;
  608. integer i__, m;
  609. real s[16] /* was [4][4] */, t[16] /* was [4][4] */, scale, bqra21,
  610. brqa21;
  611. extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
  612. real licop[16] /* was [4][4] */;
  613. integer linfo;
  614. extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
  615. integer *, real *, real *, integer *, real *, integer *, real *,
  616. real *, integer *);
  617. real ircop[16] /* was [4][4] */, dnorm;
  618. integer iwork[4];
  619. extern /* Subroutine */ int slagv2_(real *, integer *, real *, integer *,
  620. real *, real *, real *, real *, real *, real *, real *), sgeqr2_(
  621. integer *, integer *, real *, integer *, real *, real *, integer *
  622. ), sgerq2_(integer *, integer *, real *, integer *, real *, real *
  623. , integer *);
  624. real be[2], ai[2];
  625. extern /* Subroutine */ int sorg2r_(integer *, integer *, integer *, real
  626. *, integer *, real *, real *, integer *), sorgr2_(integer *,
  627. integer *, integer *, real *, integer *, real *, real *, integer *
  628. );
  629. real ar[2], sa, sb, li[16] /* was [4][4] */;
  630. extern /* Subroutine */ int sorm2r_(char *, char *, integer *, integer *,
  631. integer *, real *, integer *, real *, real *, integer *, real *,
  632. integer *), sormr2_(char *, char *, integer *,
  633. integer *, integer *, real *, integer *, real *, real *, integer *
  634. , real *, integer *);
  635. real dscale, ir[16] /* was [4][4] */;
  636. extern /* Subroutine */ int stgsy2_(char *, integer *, integer *, integer
  637. *, real *, integer *, real *, integer *, real *, integer *, real *
  638. , integer *, real *, integer *, real *, integer *, real *, real *,
  639. real *, integer *, integer *, integer *);
  640. real ss;
  641. extern real slamch_(char *);
  642. real ws;
  643. extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
  644. integer *, real *, integer *), slartg_(real *, real *,
  645. real *, real *, real *);
  646. real thresh;
  647. extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *,
  648. real *, real *, integer *), slassq_(integer *, real *,
  649. integer *, real *, real *);
  650. real smlnum;
  651. logical strong;
  652. real eps;
  653. /* -- LAPACK auxiliary routine (version 3.7.1) -- */
  654. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  655. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  656. /* June 2017 */
  657. /* ===================================================================== */
  658. /* Replaced various illegal calls to SCOPY by calls to SLASET, or by DO */
  659. /* loops. Sven Hammarling, 1/5/02. */
  660. /* Parameter adjustments */
  661. a_dim1 = *lda;
  662. a_offset = 1 + a_dim1 * 1;
  663. a -= a_offset;
  664. b_dim1 = *ldb;
  665. b_offset = 1 + b_dim1 * 1;
  666. b -= b_offset;
  667. q_dim1 = *ldq;
  668. q_offset = 1 + q_dim1 * 1;
  669. q -= q_offset;
  670. z_dim1 = *ldz;
  671. z_offset = 1 + z_dim1 * 1;
  672. z__ -= z_offset;
  673. --work;
  674. /* Function Body */
  675. *info = 0;
  676. /* Quick return if possible */
  677. if (*n <= 1 || *n1 <= 0 || *n2 <= 0) {
  678. return 0;
  679. }
  680. if (*n1 > *n || *j1 + *n1 > *n) {
  681. return 0;
  682. }
  683. m = *n1 + *n2;
  684. /* Computing MAX */
  685. i__1 = *n * m, i__2 = m * m << 1;
  686. if (*lwork < f2cmax(i__1,i__2)) {
  687. *info = -16;
  688. /* Computing MAX */
  689. i__1 = *n * m, i__2 = m * m << 1;
  690. work[1] = (real) f2cmax(i__1,i__2);
  691. return 0;
  692. }
  693. weak = FALSE_;
  694. strong = FALSE_;
  695. /* Make a local copy of selected block */
  696. slaset_("Full", &c__4, &c__4, &c_b5, &c_b5, li, &c__4);
  697. slaset_("Full", &c__4, &c__4, &c_b5, &c_b5, ir, &c__4);
  698. slacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, s, &c__4);
  699. slacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, t, &c__4);
  700. /* Compute threshold for testing acceptance of swapping. */
  701. eps = slamch_("P");
  702. smlnum = slamch_("S") / eps;
  703. dscale = 0.f;
  704. dsum = 1.f;
  705. slacpy_("Full", &m, &m, s, &c__4, &work[1], &m);
  706. i__1 = m * m;
  707. slassq_(&i__1, &work[1], &c__1, &dscale, &dsum);
  708. slacpy_("Full", &m, &m, t, &c__4, &work[1], &m);
  709. i__1 = m * m;
  710. slassq_(&i__1, &work[1], &c__1, &dscale, &dsum);
  711. dnorm = dscale * sqrt(dsum);
  712. /* THRES has been changed from */
  713. /* THRESH = MAX( TEN*EPS*SA, SMLNUM ) */
  714. /* to */
  715. /* THRESH = MAX( TWENTY*EPS*SA, SMLNUM ) */
  716. /* on 04/01/10. */
  717. /* "Bug" reported by Ondra Kamenik, confirmed by Julie Langou, fixed by */
  718. /* Jim Demmel and Guillaume Revy. See forum post 1783. */
  719. /* Computing MAX */
  720. r__1 = eps * 20.f * dnorm;
  721. thresh = f2cmax(r__1,smlnum);
  722. if (m == 2) {
  723. /* CASE 1: Swap 1-by-1 and 1-by-1 blocks. */
  724. /* Compute orthogonal QL and RQ that swap 1-by-1 and 1-by-1 blocks */
  725. /* using Givens rotations and perform the swap tentatively. */
  726. f = s[5] * t[0] - t[5] * s[0];
  727. g = s[5] * t[4] - t[5] * s[4];
  728. sb = abs(t[5]);
  729. sa = abs(s[5]);
  730. slartg_(&f, &g, &ir[4], ir, &ddum);
  731. ir[1] = -ir[4];
  732. ir[5] = ir[0];
  733. srot_(&c__2, s, &c__1, &s[4], &c__1, ir, &ir[1]);
  734. srot_(&c__2, t, &c__1, &t[4], &c__1, ir, &ir[1]);
  735. if (sa >= sb) {
  736. slartg_(s, &s[1], li, &li[1], &ddum);
  737. } else {
  738. slartg_(t, &t[1], li, &li[1], &ddum);
  739. }
  740. srot_(&c__2, s, &c__4, &s[1], &c__4, li, &li[1]);
  741. srot_(&c__2, t, &c__4, &t[1], &c__4, li, &li[1]);
  742. li[5] = li[0];
  743. li[4] = -li[1];
  744. /* Weak stability test: */
  745. /* |S21| + |T21| <= O(EPS * F-norm((S, T))) */
  746. ws = abs(s[1]) + abs(t[1]);
  747. weak = ws <= thresh;
  748. if (! weak) {
  749. goto L70;
  750. }
  751. if (TRUE_) {
  752. /* Strong stability test: */
  753. /* F-norm((A-QL**T*S*QR, B-QL**T*T*QR)) <= O(EPS*F-norm((A, B))) */
  754. slacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, &work[m * m
  755. + 1], &m);
  756. sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, s, &c__4, &c_b5, &
  757. work[1], &m);
  758. sgemm_("N", "T", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, &
  759. c_b42, &work[m * m + 1], &m);
  760. dscale = 0.f;
  761. dsum = 1.f;
  762. i__1 = m * m;
  763. slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
  764. slacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, &work[m * m
  765. + 1], &m);
  766. sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, t, &c__4, &c_b5, &
  767. work[1], &m);
  768. sgemm_("N", "T", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, &
  769. c_b42, &work[m * m + 1], &m);
  770. i__1 = m * m;
  771. slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
  772. ss = dscale * sqrt(dsum);
  773. strong = ss <= thresh;
  774. if (! strong) {
  775. goto L70;
  776. }
  777. }
  778. /* Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and */
  779. /* (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). */
  780. i__1 = *j1 + 1;
  781. srot_(&i__1, &a[*j1 * a_dim1 + 1], &c__1, &a[(*j1 + 1) * a_dim1 + 1],
  782. &c__1, ir, &ir[1]);
  783. i__1 = *j1 + 1;
  784. srot_(&i__1, &b[*j1 * b_dim1 + 1], &c__1, &b[(*j1 + 1) * b_dim1 + 1],
  785. &c__1, ir, &ir[1]);
  786. i__1 = *n - *j1 + 1;
  787. srot_(&i__1, &a[*j1 + *j1 * a_dim1], lda, &a[*j1 + 1 + *j1 * a_dim1],
  788. lda, li, &li[1]);
  789. i__1 = *n - *j1 + 1;
  790. srot_(&i__1, &b[*j1 + *j1 * b_dim1], ldb, &b[*j1 + 1 + *j1 * b_dim1],
  791. ldb, li, &li[1]);
  792. /* Set N1-by-N2 (2,1) - blocks to ZERO. */
  793. a[*j1 + 1 + *j1 * a_dim1] = 0.f;
  794. b[*j1 + 1 + *j1 * b_dim1] = 0.f;
  795. /* Accumulate transformations into Q and Z if requested. */
  796. if (*wantz) {
  797. srot_(n, &z__[*j1 * z_dim1 + 1], &c__1, &z__[(*j1 + 1) * z_dim1 +
  798. 1], &c__1, ir, &ir[1]);
  799. }
  800. if (*wantq) {
  801. srot_(n, &q[*j1 * q_dim1 + 1], &c__1, &q[(*j1 + 1) * q_dim1 + 1],
  802. &c__1, li, &li[1]);
  803. }
  804. /* Exit with INFO = 0 if swap was successfully performed. */
  805. return 0;
  806. } else {
  807. /* CASE 2: Swap 1-by-1 and 2-by-2 blocks, or 2-by-2 */
  808. /* and 2-by-2 blocks. */
  809. /* Solve the generalized Sylvester equation */
  810. /* S11 * R - L * S22 = SCALE * S12 */
  811. /* T11 * R - L * T22 = SCALE * T12 */
  812. /* for R and L. Solutions in LI and IR. */
  813. slacpy_("Full", n1, n2, &t[(*n1 + 1 << 2) - 4], &c__4, li, &c__4);
  814. slacpy_("Full", n1, n2, &s[(*n1 + 1 << 2) - 4], &c__4, &ir[*n2 + 1 + (
  815. *n1 + 1 << 2) - 5], &c__4);
  816. stgsy2_("N", &c__0, n1, n2, s, &c__4, &s[*n1 + 1 + (*n1 + 1 << 2) - 5]
  817. , &c__4, &ir[*n2 + 1 + (*n1 + 1 << 2) - 5], &c__4, t, &c__4, &
  818. t[*n1 + 1 + (*n1 + 1 << 2) - 5], &c__4, li, &c__4, &scale, &
  819. dsum, &dscale, iwork, &idum, &linfo);
  820. /* Compute orthogonal matrix QL: */
  821. /* QL**T * LI = [ TL ] */
  822. /* [ 0 ] */
  823. /* where */
  824. /* LI = [ -L ] */
  825. /* [ SCALE * identity(N2) ] */
  826. i__1 = *n2;
  827. for (i__ = 1; i__ <= i__1; ++i__) {
  828. sscal_(n1, &c_b48, &li[(i__ << 2) - 4], &c__1);
  829. li[*n1 + i__ + (i__ << 2) - 5] = scale;
  830. /* L10: */
  831. }
  832. sgeqr2_(&m, n2, li, &c__4, taul, &work[1], &linfo);
  833. if (linfo != 0) {
  834. goto L70;
  835. }
  836. sorg2r_(&m, &m, n2, li, &c__4, taul, &work[1], &linfo);
  837. if (linfo != 0) {
  838. goto L70;
  839. }
  840. /* Compute orthogonal matrix RQ: */
  841. /* IR * RQ**T = [ 0 TR], */
  842. /* where IR = [ SCALE * identity(N1), R ] */
  843. i__1 = *n1;
  844. for (i__ = 1; i__ <= i__1; ++i__) {
  845. ir[*n2 + i__ + (i__ << 2) - 5] = scale;
  846. /* L20: */
  847. }
  848. sgerq2_(n1, &m, &ir[*n2], &c__4, taur, &work[1], &linfo);
  849. if (linfo != 0) {
  850. goto L70;
  851. }
  852. sorgr2_(&m, &m, n1, ir, &c__4, taur, &work[1], &linfo);
  853. if (linfo != 0) {
  854. goto L70;
  855. }
  856. /* Perform the swapping tentatively: */
  857. sgemm_("T", "N", &m, &m, &m, &c_b42, li, &c__4, s, &c__4, &c_b5, &
  858. work[1], &m);
  859. sgemm_("N", "T", &m, &m, &m, &c_b42, &work[1], &m, ir, &c__4, &c_b5,
  860. s, &c__4);
  861. sgemm_("T", "N", &m, &m, &m, &c_b42, li, &c__4, t, &c__4, &c_b5, &
  862. work[1], &m);
  863. sgemm_("N", "T", &m, &m, &m, &c_b42, &work[1], &m, ir, &c__4, &c_b5,
  864. t, &c__4);
  865. slacpy_("F", &m, &m, s, &c__4, scpy, &c__4);
  866. slacpy_("F", &m, &m, t, &c__4, tcpy, &c__4);
  867. slacpy_("F", &m, &m, ir, &c__4, ircop, &c__4);
  868. slacpy_("F", &m, &m, li, &c__4, licop, &c__4);
  869. /* Triangularize the B-part by an RQ factorization. */
  870. /* Apply transformation (from left) to A-part, giving S. */
  871. sgerq2_(&m, &m, t, &c__4, taur, &work[1], &linfo);
  872. if (linfo != 0) {
  873. goto L70;
  874. }
  875. sormr2_("R", "T", &m, &m, &m, t, &c__4, taur, s, &c__4, &work[1], &
  876. linfo);
  877. if (linfo != 0) {
  878. goto L70;
  879. }
  880. sormr2_("L", "N", &m, &m, &m, t, &c__4, taur, ir, &c__4, &work[1], &
  881. linfo);
  882. if (linfo != 0) {
  883. goto L70;
  884. }
  885. /* Compute F-norm(S21) in BRQA21. (T21 is 0.) */
  886. dscale = 0.f;
  887. dsum = 1.f;
  888. i__1 = *n2;
  889. for (i__ = 1; i__ <= i__1; ++i__) {
  890. slassq_(n1, &s[*n2 + 1 + (i__ << 2) - 5], &c__1, &dscale, &dsum);
  891. /* L30: */
  892. }
  893. brqa21 = dscale * sqrt(dsum);
  894. /* Triangularize the B-part by a QR factorization. */
  895. /* Apply transformation (from right) to A-part, giving S. */
  896. sgeqr2_(&m, &m, tcpy, &c__4, taul, &work[1], &linfo);
  897. if (linfo != 0) {
  898. goto L70;
  899. }
  900. sorm2r_("L", "T", &m, &m, &m, tcpy, &c__4, taul, scpy, &c__4, &work[1]
  901. , info);
  902. sorm2r_("R", "N", &m, &m, &m, tcpy, &c__4, taul, licop, &c__4, &work[
  903. 1], info);
  904. if (linfo != 0) {
  905. goto L70;
  906. }
  907. /* Compute F-norm(S21) in BQRA21. (T21 is 0.) */
  908. dscale = 0.f;
  909. dsum = 1.f;
  910. i__1 = *n2;
  911. for (i__ = 1; i__ <= i__1; ++i__) {
  912. slassq_(n1, &scpy[*n2 + 1 + (i__ << 2) - 5], &c__1, &dscale, &
  913. dsum);
  914. /* L40: */
  915. }
  916. bqra21 = dscale * sqrt(dsum);
  917. /* Decide which method to use. */
  918. /* Weak stability test: */
  919. /* F-norm(S21) <= O(EPS * F-norm((S, T))) */
  920. if (bqra21 <= brqa21 && bqra21 <= thresh) {
  921. slacpy_("F", &m, &m, scpy, &c__4, s, &c__4);
  922. slacpy_("F", &m, &m, tcpy, &c__4, t, &c__4);
  923. slacpy_("F", &m, &m, ircop, &c__4, ir, &c__4);
  924. slacpy_("F", &m, &m, licop, &c__4, li, &c__4);
  925. } else if (brqa21 >= thresh) {
  926. goto L70;
  927. }
  928. /* Set lower triangle of B-part to zero */
  929. i__1 = m - 1;
  930. i__2 = m - 1;
  931. slaset_("Lower", &i__1, &i__2, &c_b5, &c_b5, &t[1], &c__4);
  932. if (TRUE_) {
  933. /* Strong stability test: */
  934. /* F-norm((A-QL*S*QR**T, B-QL*T*QR**T)) <= O(EPS*F-norm((A,B))) */
  935. slacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, &work[m * m
  936. + 1], &m);
  937. sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, s, &c__4, &c_b5, &
  938. work[1], &m);
  939. sgemm_("N", "N", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, &
  940. c_b42, &work[m * m + 1], &m);
  941. dscale = 0.f;
  942. dsum = 1.f;
  943. i__1 = m * m;
  944. slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
  945. slacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, &work[m * m
  946. + 1], &m);
  947. sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, t, &c__4, &c_b5, &
  948. work[1], &m);
  949. sgemm_("N", "N", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, &
  950. c_b42, &work[m * m + 1], &m);
  951. i__1 = m * m;
  952. slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
  953. ss = dscale * sqrt(dsum);
  954. strong = ss <= thresh;
  955. if (! strong) {
  956. goto L70;
  957. }
  958. }
  959. /* If the swap is accepted ("weakly" and "strongly"), apply the */
  960. /* transformations and set N1-by-N2 (2,1)-block to zero. */
  961. slaset_("Full", n1, n2, &c_b5, &c_b5, &s[*n2], &c__4);
  962. /* copy back M-by-M diagonal block starting at index J1 of (A, B) */
  963. slacpy_("F", &m, &m, s, &c__4, &a[*j1 + *j1 * a_dim1], lda)
  964. ;
  965. slacpy_("F", &m, &m, t, &c__4, &b[*j1 + *j1 * b_dim1], ldb)
  966. ;
  967. slaset_("Full", &c__4, &c__4, &c_b5, &c_b5, t, &c__4);
  968. /* Standardize existing 2-by-2 blocks. */
  969. slaset_("Full", &m, &m, &c_b5, &c_b5, &work[1], &m);
  970. work[1] = 1.f;
  971. t[0] = 1.f;
  972. idum = *lwork - m * m - 2;
  973. if (*n2 > 1) {
  974. slagv2_(&a[*j1 + *j1 * a_dim1], lda, &b[*j1 + *j1 * b_dim1], ldb,
  975. ar, ai, be, &work[1], &work[2], t, &t[1]);
  976. work[m + 1] = -work[2];
  977. work[m + 2] = work[1];
  978. t[*n2 + (*n2 << 2) - 5] = t[0];
  979. t[4] = -t[1];
  980. }
  981. work[m * m] = 1.f;
  982. t[m + (m << 2) - 5] = 1.f;
  983. if (*n1 > 1) {
  984. slagv2_(&a[*j1 + *n2 + (*j1 + *n2) * a_dim1], lda, &b[*j1 + *n2 +
  985. (*j1 + *n2) * b_dim1], ldb, taur, taul, &work[m * m + 1],
  986. &work[*n2 * m + *n2 + 1], &work[*n2 * m + *n2 + 2], &t[*
  987. n2 + 1 + (*n2 + 1 << 2) - 5], &t[m + (m - 1 << 2) - 5]);
  988. work[m * m] = work[*n2 * m + *n2 + 1];
  989. work[m * m - 1] = -work[*n2 * m + *n2 + 2];
  990. t[m + (m << 2) - 5] = t[*n2 + 1 + (*n2 + 1 << 2) - 5];
  991. t[m - 1 + (m << 2) - 5] = -t[m + (m - 1 << 2) - 5];
  992. }
  993. sgemm_("T", "N", n2, n1, n2, &c_b42, &work[1], &m, &a[*j1 + (*j1 + *
  994. n2) * a_dim1], lda, &c_b5, &work[m * m + 1], n2);
  995. slacpy_("Full", n2, n1, &work[m * m + 1], n2, &a[*j1 + (*j1 + *n2) *
  996. a_dim1], lda);
  997. sgemm_("T", "N", n2, n1, n2, &c_b42, &work[1], &m, &b[*j1 + (*j1 + *
  998. n2) * b_dim1], ldb, &c_b5, &work[m * m + 1], n2);
  999. slacpy_("Full", n2, n1, &work[m * m + 1], n2, &b[*j1 + (*j1 + *n2) *
  1000. b_dim1], ldb);
  1001. sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, &work[1], &m, &c_b5, &
  1002. work[m * m + 1], &m);
  1003. slacpy_("Full", &m, &m, &work[m * m + 1], &m, li, &c__4);
  1004. sgemm_("N", "N", n2, n1, n1, &c_b42, &a[*j1 + (*j1 + *n2) * a_dim1],
  1005. lda, &t[*n2 + 1 + (*n2 + 1 << 2) - 5], &c__4, &c_b5, &work[1],
  1006. n2);
  1007. slacpy_("Full", n2, n1, &work[1], n2, &a[*j1 + (*j1 + *n2) * a_dim1],
  1008. lda);
  1009. sgemm_("N", "N", n2, n1, n1, &c_b42, &b[*j1 + (*j1 + *n2) * b_dim1],
  1010. ldb, &t[*n2 + 1 + (*n2 + 1 << 2) - 5], &c__4, &c_b5, &work[1],
  1011. n2);
  1012. slacpy_("Full", n2, n1, &work[1], n2, &b[*j1 + (*j1 + *n2) * b_dim1],
  1013. ldb);
  1014. sgemm_("T", "N", &m, &m, &m, &c_b42, ir, &c__4, t, &c__4, &c_b5, &
  1015. work[1], &m);
  1016. slacpy_("Full", &m, &m, &work[1], &m, ir, &c__4);
  1017. /* Accumulate transformations into Q and Z if requested. */
  1018. if (*wantq) {
  1019. sgemm_("N", "N", n, &m, &m, &c_b42, &q[*j1 * q_dim1 + 1], ldq, li,
  1020. &c__4, &c_b5, &work[1], n);
  1021. slacpy_("Full", n, &m, &work[1], n, &q[*j1 * q_dim1 + 1], ldq);
  1022. }
  1023. if (*wantz) {
  1024. sgemm_("N", "N", n, &m, &m, &c_b42, &z__[*j1 * z_dim1 + 1], ldz,
  1025. ir, &c__4, &c_b5, &work[1], n);
  1026. slacpy_("Full", n, &m, &work[1], n, &z__[*j1 * z_dim1 + 1], ldz);
  1027. }
  1028. /* Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and */
  1029. /* (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). */
  1030. i__ = *j1 + m;
  1031. if (i__ <= *n) {
  1032. i__1 = *n - i__ + 1;
  1033. sgemm_("T", "N", &m, &i__1, &m, &c_b42, li, &c__4, &a[*j1 + i__ *
  1034. a_dim1], lda, &c_b5, &work[1], &m);
  1035. i__1 = *n - i__ + 1;
  1036. slacpy_("Full", &m, &i__1, &work[1], &m, &a[*j1 + i__ * a_dim1],
  1037. lda);
  1038. i__1 = *n - i__ + 1;
  1039. sgemm_("T", "N", &m, &i__1, &m, &c_b42, li, &c__4, &b[*j1 + i__ *
  1040. b_dim1], ldb, &c_b5, &work[1], &m);
  1041. i__1 = *n - i__ + 1;
  1042. slacpy_("Full", &m, &i__1, &work[1], &m, &b[*j1 + i__ * b_dim1],
  1043. ldb);
  1044. }
  1045. i__ = *j1 - 1;
  1046. if (i__ > 0) {
  1047. sgemm_("N", "N", &i__, &m, &m, &c_b42, &a[*j1 * a_dim1 + 1], lda,
  1048. ir, &c__4, &c_b5, &work[1], &i__);
  1049. slacpy_("Full", &i__, &m, &work[1], &i__, &a[*j1 * a_dim1 + 1],
  1050. lda);
  1051. sgemm_("N", "N", &i__, &m, &m, &c_b42, &b[*j1 * b_dim1 + 1], ldb,
  1052. ir, &c__4, &c_b5, &work[1], &i__);
  1053. slacpy_("Full", &i__, &m, &work[1], &i__, &b[*j1 * b_dim1 + 1],
  1054. ldb);
  1055. }
  1056. /* Exit with INFO = 0 if swap was successfully performed. */
  1057. return 0;
  1058. }
  1059. /* Exit with INFO = 1 if swap was rejected. */
  1060. L70:
  1061. *info = 1;
  1062. return 0;
  1063. /* End of STGEX2 */
  1064. } /* stgex2_ */