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zlatm5.c 31 kB

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  1. #include <math.h>
  2. #include <stdlib.h>
  3. #include <string.h>
  4. #include <stdio.h>
  5. #include <complex.h>
  6. #ifdef complex
  7. #undef complex
  8. #endif
  9. #ifdef I
  10. #undef I
  11. #endif
  12. #if defined(_WIN64)
  13. typedef long long BLASLONG;
  14. typedef unsigned long long BLASULONG;
  15. #else
  16. typedef long BLASLONG;
  17. typedef unsigned long BLASULONG;
  18. #endif
  19. #ifdef LAPACK_ILP64
  20. typedef BLASLONG blasint;
  21. #if defined(_WIN64)
  22. #define blasabs(x) llabs(x)
  23. #else
  24. #define blasabs(x) labs(x)
  25. #endif
  26. #else
  27. typedef int blasint;
  28. #define blasabs(x) abs(x)
  29. #endif
  30. typedef blasint integer;
  31. typedef unsigned int uinteger;
  32. typedef char *address;
  33. typedef short int shortint;
  34. typedef float real;
  35. typedef double doublereal;
  36. typedef struct { real r, i; } complex;
  37. typedef struct { doublereal r, i; } doublecomplex;
  38. #ifdef _MSC_VER
  39. static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
  40. static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
  41. static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
  42. static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
  43. #else
  44. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  45. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  46. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  47. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  48. #endif
  49. #define pCf(z) (*_pCf(z))
  50. #define pCd(z) (*_pCd(z))
  51. typedef int logical;
  52. typedef short int shortlogical;
  53. typedef char logical1;
  54. typedef char integer1;
  55. #define TRUE_ (1)
  56. #define FALSE_ (0)
  57. /* Extern is for use with -E */
  58. #ifndef Extern
  59. #define Extern extern
  60. #endif
  61. /* I/O stuff */
  62. typedef int flag;
  63. typedef int ftnlen;
  64. typedef int ftnint;
  65. /*external read, write*/
  66. typedef struct
  67. { flag cierr;
  68. ftnint ciunit;
  69. flag ciend;
  70. char *cifmt;
  71. ftnint cirec;
  72. } cilist;
  73. /*internal read, write*/
  74. typedef struct
  75. { flag icierr;
  76. char *iciunit;
  77. flag iciend;
  78. char *icifmt;
  79. ftnint icirlen;
  80. ftnint icirnum;
  81. } icilist;
  82. /*open*/
  83. typedef struct
  84. { flag oerr;
  85. ftnint ounit;
  86. char *ofnm;
  87. ftnlen ofnmlen;
  88. char *osta;
  89. char *oacc;
  90. char *ofm;
  91. ftnint orl;
  92. char *oblnk;
  93. } olist;
  94. /*close*/
  95. typedef struct
  96. { flag cerr;
  97. ftnint cunit;
  98. char *csta;
  99. } cllist;
  100. /*rewind, backspace, endfile*/
  101. typedef struct
  102. { flag aerr;
  103. ftnint aunit;
  104. } alist;
  105. /* inquire */
  106. typedef struct
  107. { flag inerr;
  108. ftnint inunit;
  109. char *infile;
  110. ftnlen infilen;
  111. ftnint *inex; /*parameters in standard's order*/
  112. ftnint *inopen;
  113. ftnint *innum;
  114. ftnint *innamed;
  115. char *inname;
  116. ftnlen innamlen;
  117. char *inacc;
  118. ftnlen inacclen;
  119. char *inseq;
  120. ftnlen inseqlen;
  121. char *indir;
  122. ftnlen indirlen;
  123. char *infmt;
  124. ftnlen infmtlen;
  125. char *inform;
  126. ftnint informlen;
  127. char *inunf;
  128. ftnlen inunflen;
  129. ftnint *inrecl;
  130. ftnint *innrec;
  131. char *inblank;
  132. ftnlen inblanklen;
  133. } inlist;
  134. #define VOID void
  135. union Multitype { /* for multiple entry points */
  136. integer1 g;
  137. shortint h;
  138. integer i;
  139. /* longint j; */
  140. real r;
  141. doublereal d;
  142. complex c;
  143. doublecomplex z;
  144. };
  145. typedef union Multitype Multitype;
  146. struct Vardesc { /* for Namelist */
  147. char *name;
  148. char *addr;
  149. ftnlen *dims;
  150. int type;
  151. };
  152. typedef struct Vardesc Vardesc;
  153. struct Namelist {
  154. char *name;
  155. Vardesc **vars;
  156. int nvars;
  157. };
  158. typedef struct Namelist Namelist;
  159. #define abs(x) ((x) >= 0 ? (x) : -(x))
  160. #define dabs(x) (fabs(x))
  161. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  162. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  163. #define dmin(a,b) (f2cmin(a,b))
  164. #define dmax(a,b) (f2cmax(a,b))
  165. #define bit_test(a,b) ((a) >> (b) & 1)
  166. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  167. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  168. #define abort_() { sig_die("Fortran abort routine called", 1); }
  169. #define c_abs(z) (cabsf(Cf(z)))
  170. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  171. #ifdef _MSC_VER
  172. #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
  173. #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/Cd(b)._Val[1]);}
  174. #else
  175. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  176. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  177. #endif
  178. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  179. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  180. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  181. #define z_sin(R, Z) {pCd(R) = csin(Cd(Z));}
  182. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  183. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  184. #define d_abs(x) (fabs(*(x)))
  185. #define d_acos(x) (acos(*(x)))
  186. #define d_asin(x) (asin(*(x)))
  187. #define d_atan(x) (atan(*(x)))
  188. #define d_atn2(x, y) (atan2(*(x),*(y)))
  189. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  190. #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
  191. #define d_cos(x) (cos(*(x)))
  192. #define d_cosh(x) (cosh(*(x)))
  193. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  194. #define d_exp(x) (exp(*(x)))
  195. #define d_imag(z) (cimag(Cd(z)))
  196. #define r_imag(z) (cimagf(Cf(z)))
  197. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  198. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  199. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  200. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  201. #define d_log(x) (log(*(x)))
  202. #define d_mod(x, y) (fmod(*(x), *(y)))
  203. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  204. #define d_nint(x) u_nint(*(x))
  205. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  206. #define d_sign(a,b) u_sign(*(a),*(b))
  207. #define r_sign(a,b) u_sign(*(a),*(b))
  208. #define d_sin(x) (sin(*(x)))
  209. #define d_sinh(x) (sinh(*(x)))
  210. #define d_sqrt(x) (sqrt(*(x)))
  211. #define d_tan(x) (tan(*(x)))
  212. #define d_tanh(x) (tanh(*(x)))
  213. #define i_abs(x) abs(*(x))
  214. #define i_dnnt(x) ((integer)u_nint(*(x)))
  215. #define i_len(s, n) (n)
  216. #define i_nint(x) ((integer)u_nint(*(x)))
  217. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  218. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  219. #define pow_si(B,E) spow_ui(*(B),*(E))
  220. #define pow_ri(B,E) spow_ui(*(B),*(E))
  221. #define pow_di(B,E) dpow_ui(*(B),*(E))
  222. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  223. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  224. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  225. #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++ = ' '; }
  226. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  227. #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]; }
  228. #define sig_die(s, kill) { exit(1); }
  229. #define s_stop(s, n) {exit(0);}
  230. #define z_abs(z) (cabs(Cd(z)))
  231. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  232. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  233. #define myexit_() break;
  234. #define mycycle_() continue;
  235. #define myceiling_(w) {ceil(w)}
  236. #define myhuge_(w) {HUGE_VAL}
  237. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  238. #define mymaxloc_(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  239. /* procedure parameter types for -A and -C++ */
  240. #define F2C_proc_par_types 1
  241. /* Table of constant values */
  242. static doublecomplex c_b1 = {1.,0.};
  243. static doublecomplex c_b3 = {0.,0.};
  244. static doublecomplex c_b5 = {20.,0.};
  245. /* > \brief \b ZLATM5 */
  246. /* =========== DOCUMENTATION =========== */
  247. /* Online html documentation available at */
  248. /* http://www.netlib.org/lapack/explore-html/ */
  249. /* Definition: */
  250. /* =========== */
  251. /* SUBROUTINE ZLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, */
  252. /* E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, */
  253. /* QBLCKB ) */
  254. /* INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, */
  255. /* $ PRTYPE, QBLCKA, QBLCKB */
  256. /* DOUBLE PRECISION ALPHA */
  257. /* COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * ), */
  258. /* $ D( LDD, * ), E( LDE, * ), F( LDF, * ), */
  259. /* $ L( LDL, * ), R( LDR, * ) */
  260. /* > \par Purpose: */
  261. /* ============= */
  262. /* > */
  263. /* > \verbatim */
  264. /* > */
  265. /* > ZLATM5 generates matrices involved in the Generalized Sylvester */
  266. /* > equation: */
  267. /* > */
  268. /* > A * R - L * B = C */
  269. /* > D * R - L * E = F */
  270. /* > */
  271. /* > They also satisfy (the diagonalization condition) */
  272. /* > */
  273. /* > [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] ) */
  274. /* > [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] ) */
  275. /* > */
  276. /* > \endverbatim */
  277. /* Arguments: */
  278. /* ========== */
  279. /* > \param[in] PRTYPE */
  280. /* > \verbatim */
  281. /* > PRTYPE is INTEGER */
  282. /* > "Points" to a certain type of the matrices to generate */
  283. /* > (see further details). */
  284. /* > \endverbatim */
  285. /* > */
  286. /* > \param[in] M */
  287. /* > \verbatim */
  288. /* > M is INTEGER */
  289. /* > Specifies the order of A and D and the number of rows in */
  290. /* > C, F, R and L. */
  291. /* > \endverbatim */
  292. /* > */
  293. /* > \param[in] N */
  294. /* > \verbatim */
  295. /* > N is INTEGER */
  296. /* > Specifies the order of B and E and the number of columns in */
  297. /* > C, F, R and L. */
  298. /* > \endverbatim */
  299. /* > */
  300. /* > \param[out] A */
  301. /* > \verbatim */
  302. /* > A is COMPLEX*16 array, dimension (LDA, M). */
  303. /* > On exit A M-by-M is initialized according to PRTYPE. */
  304. /* > \endverbatim */
  305. /* > */
  306. /* > \param[in] LDA */
  307. /* > \verbatim */
  308. /* > LDA is INTEGER */
  309. /* > The leading dimension of A. */
  310. /* > \endverbatim */
  311. /* > */
  312. /* > \param[out] B */
  313. /* > \verbatim */
  314. /* > B is COMPLEX*16 array, dimension (LDB, N). */
  315. /* > On exit B N-by-N is initialized according to PRTYPE. */
  316. /* > \endverbatim */
  317. /* > */
  318. /* > \param[in] LDB */
  319. /* > \verbatim */
  320. /* > LDB is INTEGER */
  321. /* > The leading dimension of B. */
  322. /* > \endverbatim */
  323. /* > */
  324. /* > \param[out] C */
  325. /* > \verbatim */
  326. /* > C is COMPLEX*16 array, dimension (LDC, N). */
  327. /* > On exit C M-by-N is initialized according to PRTYPE. */
  328. /* > \endverbatim */
  329. /* > */
  330. /* > \param[in] LDC */
  331. /* > \verbatim */
  332. /* > LDC is INTEGER */
  333. /* > The leading dimension of C. */
  334. /* > \endverbatim */
  335. /* > */
  336. /* > \param[out] D */
  337. /* > \verbatim */
  338. /* > D is COMPLEX*16 array, dimension (LDD, M). */
  339. /* > On exit D M-by-M is initialized according to PRTYPE. */
  340. /* > \endverbatim */
  341. /* > */
  342. /* > \param[in] LDD */
  343. /* > \verbatim */
  344. /* > LDD is INTEGER */
  345. /* > The leading dimension of D. */
  346. /* > \endverbatim */
  347. /* > */
  348. /* > \param[out] E */
  349. /* > \verbatim */
  350. /* > E is COMPLEX*16 array, dimension (LDE, N). */
  351. /* > On exit E N-by-N is initialized according to PRTYPE. */
  352. /* > \endverbatim */
  353. /* > */
  354. /* > \param[in] LDE */
  355. /* > \verbatim */
  356. /* > LDE is INTEGER */
  357. /* > The leading dimension of E. */
  358. /* > \endverbatim */
  359. /* > */
  360. /* > \param[out] F */
  361. /* > \verbatim */
  362. /* > F is COMPLEX*16 array, dimension (LDF, N). */
  363. /* > On exit F M-by-N is initialized according to PRTYPE. */
  364. /* > \endverbatim */
  365. /* > */
  366. /* > \param[in] LDF */
  367. /* > \verbatim */
  368. /* > LDF is INTEGER */
  369. /* > The leading dimension of F. */
  370. /* > \endverbatim */
  371. /* > */
  372. /* > \param[out] R */
  373. /* > \verbatim */
  374. /* > R is COMPLEX*16 array, dimension (LDR, N). */
  375. /* > On exit R M-by-N is initialized according to PRTYPE. */
  376. /* > \endverbatim */
  377. /* > */
  378. /* > \param[in] LDR */
  379. /* > \verbatim */
  380. /* > LDR is INTEGER */
  381. /* > The leading dimension of R. */
  382. /* > \endverbatim */
  383. /* > */
  384. /* > \param[out] L */
  385. /* > \verbatim */
  386. /* > L is COMPLEX*16 array, dimension (LDL, N). */
  387. /* > On exit L M-by-N is initialized according to PRTYPE. */
  388. /* > \endverbatim */
  389. /* > */
  390. /* > \param[in] LDL */
  391. /* > \verbatim */
  392. /* > LDL is INTEGER */
  393. /* > The leading dimension of L. */
  394. /* > \endverbatim */
  395. /* > */
  396. /* > \param[in] ALPHA */
  397. /* > \verbatim */
  398. /* > ALPHA is DOUBLE PRECISION */
  399. /* > Parameter used in generating PRTYPE = 1 and 5 matrices. */
  400. /* > \endverbatim */
  401. /* > */
  402. /* > \param[in] QBLCKA */
  403. /* > \verbatim */
  404. /* > QBLCKA is INTEGER */
  405. /* > When PRTYPE = 3, specifies the distance between 2-by-2 */
  406. /* > blocks on the diagonal in A. Otherwise, QBLCKA is not */
  407. /* > referenced. QBLCKA > 1. */
  408. /* > \endverbatim */
  409. /* > */
  410. /* > \param[in] QBLCKB */
  411. /* > \verbatim */
  412. /* > QBLCKB is INTEGER */
  413. /* > When PRTYPE = 3, specifies the distance between 2-by-2 */
  414. /* > blocks on the diagonal in B. Otherwise, QBLCKB is not */
  415. /* > referenced. QBLCKB > 1. */
  416. /* > \endverbatim */
  417. /* Authors: */
  418. /* ======== */
  419. /* > \author Univ. of Tennessee */
  420. /* > \author Univ. of California Berkeley */
  421. /* > \author Univ. of Colorado Denver */
  422. /* > \author NAG Ltd. */
  423. /* > \date June 2016 */
  424. /* > \ingroup complex16_matgen */
  425. /* > \par Further Details: */
  426. /* ===================== */
  427. /* > */
  428. /* > \verbatim */
  429. /* > */
  430. /* > PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices */
  431. /* > */
  432. /* > A : if (i == j) then A(i, j) = 1.0 */
  433. /* > if (j == i + 1) then A(i, j) = -1.0 */
  434. /* > else A(i, j) = 0.0, i, j = 1...M */
  435. /* > */
  436. /* > B : if (i == j) then B(i, j) = 1.0 - ALPHA */
  437. /* > if (j == i + 1) then B(i, j) = 1.0 */
  438. /* > else B(i, j) = 0.0, i, j = 1...N */
  439. /* > */
  440. /* > D : if (i == j) then D(i, j) = 1.0 */
  441. /* > else D(i, j) = 0.0, i, j = 1...M */
  442. /* > */
  443. /* > E : if (i == j) then E(i, j) = 1.0 */
  444. /* > else E(i, j) = 0.0, i, j = 1...N */
  445. /* > */
  446. /* > L = R are chosen from [-10...10], */
  447. /* > which specifies the right hand sides (C, F). */
  448. /* > */
  449. /* > PRTYPE = 2 or 3: Triangular and/or quasi- triangular. */
  450. /* > */
  451. /* > A : if (i <= j) then A(i, j) = [-1...1] */
  452. /* > else A(i, j) = 0.0, i, j = 1...M */
  453. /* > */
  454. /* > if (PRTYPE = 3) then */
  455. /* > A(k + 1, k + 1) = A(k, k) */
  456. /* > A(k + 1, k) = [-1...1] */
  457. /* > sign(A(k, k + 1) = -(sin(A(k + 1, k)) */
  458. /* > k = 1, M - 1, QBLCKA */
  459. /* > */
  460. /* > B : if (i <= j) then B(i, j) = [-1...1] */
  461. /* > else B(i, j) = 0.0, i, j = 1...N */
  462. /* > */
  463. /* > if (PRTYPE = 3) then */
  464. /* > B(k + 1, k + 1) = B(k, k) */
  465. /* > B(k + 1, k) = [-1...1] */
  466. /* > sign(B(k, k + 1) = -(sign(B(k + 1, k)) */
  467. /* > k = 1, N - 1, QBLCKB */
  468. /* > */
  469. /* > D : if (i <= j) then D(i, j) = [-1...1]. */
  470. /* > else D(i, j) = 0.0, i, j = 1...M */
  471. /* > */
  472. /* > */
  473. /* > E : if (i <= j) then D(i, j) = [-1...1] */
  474. /* > else E(i, j) = 0.0, i, j = 1...N */
  475. /* > */
  476. /* > L, R are chosen from [-10...10], */
  477. /* > which specifies the right hand sides (C, F). */
  478. /* > */
  479. /* > PRTYPE = 4 Full */
  480. /* > A(i, j) = [-10...10] */
  481. /* > D(i, j) = [-1...1] i,j = 1...M */
  482. /* > B(i, j) = [-10...10] */
  483. /* > E(i, j) = [-1...1] i,j = 1...N */
  484. /* > R(i, j) = [-10...10] */
  485. /* > L(i, j) = [-1...1] i = 1..M ,j = 1...N */
  486. /* > */
  487. /* > L, R specifies the right hand sides (C, F). */
  488. /* > */
  489. /* > PRTYPE = 5 special case common and/or close eigs. */
  490. /* > \endverbatim */
  491. /* > */
  492. /* ===================================================================== */
  493. /* Subroutine */ void zlatm5_(integer *prtype, integer *m, integer *n,
  494. doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb,
  495. doublecomplex *c__, integer *ldc, doublecomplex *d__, integer *ldd,
  496. doublecomplex *e, integer *lde, doublecomplex *f, integer *ldf,
  497. doublecomplex *r__, integer *ldr, doublecomplex *l, integer *ldl,
  498. doublereal *alpha, integer *qblcka, integer *qblckb)
  499. {
  500. /* System generated locals */
  501. integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, d_dim1,
  502. d_offset, e_dim1, e_offset, f_dim1, f_offset, l_dim1, l_offset,
  503. r_dim1, r_offset, i__1, i__2, i__3, i__4;
  504. doublereal d__1;
  505. doublecomplex z__1, z__2, z__3, z__4, z__5;
  506. /* Local variables */
  507. integer i__, j, k;
  508. doublecomplex imeps, reeps;
  509. extern /* Subroutine */ void zgemm_(char *, char *, integer *, integer *,
  510. integer *, doublecomplex *, doublecomplex *, integer *,
  511. doublecomplex *, integer *, doublecomplex *, doublecomplex *,
  512. integer *);
  513. /* -- LAPACK computational routine (version 3.7.0) -- */
  514. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  515. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  516. /* June 2016 */
  517. /* ===================================================================== */
  518. /* Parameter adjustments */
  519. a_dim1 = *lda;
  520. a_offset = 1 + a_dim1 * 1;
  521. a -= a_offset;
  522. b_dim1 = *ldb;
  523. b_offset = 1 + b_dim1 * 1;
  524. b -= b_offset;
  525. c_dim1 = *ldc;
  526. c_offset = 1 + c_dim1 * 1;
  527. c__ -= c_offset;
  528. d_dim1 = *ldd;
  529. d_offset = 1 + d_dim1 * 1;
  530. d__ -= d_offset;
  531. e_dim1 = *lde;
  532. e_offset = 1 + e_dim1 * 1;
  533. e -= e_offset;
  534. f_dim1 = *ldf;
  535. f_offset = 1 + f_dim1 * 1;
  536. f -= f_offset;
  537. r_dim1 = *ldr;
  538. r_offset = 1 + r_dim1 * 1;
  539. r__ -= r_offset;
  540. l_dim1 = *ldl;
  541. l_offset = 1 + l_dim1 * 1;
  542. l -= l_offset;
  543. /* Function Body */
  544. if (*prtype == 1) {
  545. i__1 = *m;
  546. for (i__ = 1; i__ <= i__1; ++i__) {
  547. i__2 = *m;
  548. for (j = 1; j <= i__2; ++j) {
  549. if (i__ == j) {
  550. i__3 = i__ + j * a_dim1;
  551. a[i__3].r = 1., a[i__3].i = 0.;
  552. i__3 = i__ + j * d_dim1;
  553. d__[i__3].r = 1., d__[i__3].i = 0.;
  554. } else if (i__ == j - 1) {
  555. i__3 = i__ + j * a_dim1;
  556. z__1.r = -1., z__1.i = 0.;
  557. a[i__3].r = z__1.r, a[i__3].i = z__1.i;
  558. i__3 = i__ + j * d_dim1;
  559. d__[i__3].r = 0., d__[i__3].i = 0.;
  560. } else {
  561. i__3 = i__ + j * a_dim1;
  562. a[i__3].r = 0., a[i__3].i = 0.;
  563. i__3 = i__ + j * d_dim1;
  564. d__[i__3].r = 0., d__[i__3].i = 0.;
  565. }
  566. /* L10: */
  567. }
  568. /* L20: */
  569. }
  570. i__1 = *n;
  571. for (i__ = 1; i__ <= i__1; ++i__) {
  572. i__2 = *n;
  573. for (j = 1; j <= i__2; ++j) {
  574. if (i__ == j) {
  575. i__3 = i__ + j * b_dim1;
  576. z__1.r = 1. - *alpha, z__1.i = 0.;
  577. b[i__3].r = z__1.r, b[i__3].i = z__1.i;
  578. i__3 = i__ + j * e_dim1;
  579. e[i__3].r = 1., e[i__3].i = 0.;
  580. } else if (i__ == j - 1) {
  581. i__3 = i__ + j * b_dim1;
  582. b[i__3].r = 1., b[i__3].i = 0.;
  583. i__3 = i__ + j * e_dim1;
  584. e[i__3].r = 0., e[i__3].i = 0.;
  585. } else {
  586. i__3 = i__ + j * b_dim1;
  587. b[i__3].r = 0., b[i__3].i = 0.;
  588. i__3 = i__ + j * e_dim1;
  589. e[i__3].r = 0., e[i__3].i = 0.;
  590. }
  591. /* L30: */
  592. }
  593. /* L40: */
  594. }
  595. i__1 = *m;
  596. for (i__ = 1; i__ <= i__1; ++i__) {
  597. i__2 = *n;
  598. for (j = 1; j <= i__2; ++j) {
  599. i__3 = i__ + j * r_dim1;
  600. i__4 = i__ / j;
  601. z__4.r = (doublereal) i__4, z__4.i = 0.;
  602. z_sin(&z__3, &z__4);
  603. z__2.r = .5 - z__3.r, z__2.i = 0. - z__3.i;
  604. z__1.r = z__2.r * 20. - z__2.i * 0., z__1.i = z__2.r * 0. +
  605. z__2.i * 20.;
  606. r__[i__3].r = z__1.r, r__[i__3].i = z__1.i;
  607. i__3 = i__ + j * l_dim1;
  608. i__4 = i__ + j * r_dim1;
  609. l[i__3].r = r__[i__4].r, l[i__3].i = r__[i__4].i;
  610. /* L50: */
  611. }
  612. /* L60: */
  613. }
  614. } else if (*prtype == 2 || *prtype == 3) {
  615. i__1 = *m;
  616. for (i__ = 1; i__ <= i__1; ++i__) {
  617. i__2 = *m;
  618. for (j = 1; j <= i__2; ++j) {
  619. if (i__ <= j) {
  620. i__3 = i__ + j * a_dim1;
  621. z__4.r = (doublereal) i__, z__4.i = 0.;
  622. z_sin(&z__3, &z__4);
  623. z__2.r = .5 - z__3.r, z__2.i = 0. - z__3.i;
  624. z__1.r = z__2.r * 2. - z__2.i * 0., z__1.i = z__2.r * 0.
  625. + z__2.i * 2.;
  626. a[i__3].r = z__1.r, a[i__3].i = z__1.i;
  627. i__3 = i__ + j * d_dim1;
  628. i__4 = i__ * j;
  629. z__4.r = (doublereal) i__4, z__4.i = 0.;
  630. z_sin(&z__3, &z__4);
  631. z__2.r = .5 - z__3.r, z__2.i = 0. - z__3.i;
  632. z__1.r = z__2.r * 2. - z__2.i * 0., z__1.i = z__2.r * 0.
  633. + z__2.i * 2.;
  634. d__[i__3].r = z__1.r, d__[i__3].i = z__1.i;
  635. } else {
  636. i__3 = i__ + j * a_dim1;
  637. a[i__3].r = 0., a[i__3].i = 0.;
  638. i__3 = i__ + j * d_dim1;
  639. d__[i__3].r = 0., d__[i__3].i = 0.;
  640. }
  641. /* L70: */
  642. }
  643. /* L80: */
  644. }
  645. i__1 = *n;
  646. for (i__ = 1; i__ <= i__1; ++i__) {
  647. i__2 = *n;
  648. for (j = 1; j <= i__2; ++j) {
  649. if (i__ <= j) {
  650. i__3 = i__ + j * b_dim1;
  651. i__4 = i__ + j;
  652. z__4.r = (doublereal) i__4, z__4.i = 0.;
  653. z_sin(&z__3, &z__4);
  654. z__2.r = .5 - z__3.r, z__2.i = 0. - z__3.i;
  655. z__1.r = z__2.r * 2. - z__2.i * 0., z__1.i = z__2.r * 0.
  656. + z__2.i * 2.;
  657. b[i__3].r = z__1.r, b[i__3].i = z__1.i;
  658. i__3 = i__ + j * e_dim1;
  659. z__4.r = (doublereal) j, z__4.i = 0.;
  660. z_sin(&z__3, &z__4);
  661. z__2.r = .5 - z__3.r, z__2.i = 0. - z__3.i;
  662. z__1.r = z__2.r * 2. - z__2.i * 0., z__1.i = z__2.r * 0.
  663. + z__2.i * 2.;
  664. e[i__3].r = z__1.r, e[i__3].i = z__1.i;
  665. } else {
  666. i__3 = i__ + j * b_dim1;
  667. b[i__3].r = 0., b[i__3].i = 0.;
  668. i__3 = i__ + j * e_dim1;
  669. e[i__3].r = 0., e[i__3].i = 0.;
  670. }
  671. /* L90: */
  672. }
  673. /* L100: */
  674. }
  675. i__1 = *m;
  676. for (i__ = 1; i__ <= i__1; ++i__) {
  677. i__2 = *n;
  678. for (j = 1; j <= i__2; ++j) {
  679. i__3 = i__ + j * r_dim1;
  680. i__4 = i__ * j;
  681. z__4.r = (doublereal) i__4, z__4.i = 0.;
  682. z_sin(&z__3, &z__4);
  683. z__2.r = .5 - z__3.r, z__2.i = 0. - z__3.i;
  684. z__1.r = z__2.r * 20. - z__2.i * 0., z__1.i = z__2.r * 0. +
  685. z__2.i * 20.;
  686. r__[i__3].r = z__1.r, r__[i__3].i = z__1.i;
  687. i__3 = i__ + j * l_dim1;
  688. i__4 = i__ + j;
  689. z__4.r = (doublereal) i__4, z__4.i = 0.;
  690. z_sin(&z__3, &z__4);
  691. z__2.r = .5 - z__3.r, z__2.i = 0. - z__3.i;
  692. z__1.r = z__2.r * 20. - z__2.i * 0., z__1.i = z__2.r * 0. +
  693. z__2.i * 20.;
  694. l[i__3].r = z__1.r, l[i__3].i = z__1.i;
  695. /* L110: */
  696. }
  697. /* L120: */
  698. }
  699. if (*prtype == 3) {
  700. if (*qblcka <= 1) {
  701. *qblcka = 2;
  702. }
  703. i__1 = *m - 1;
  704. i__2 = *qblcka;
  705. for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
  706. i__3 = k + 1 + (k + 1) * a_dim1;
  707. i__4 = k + k * a_dim1;
  708. a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i;
  709. i__3 = k + 1 + k * a_dim1;
  710. z_sin(&z__2, &a[k + (k + 1) * a_dim1]);
  711. z__1.r = -z__2.r, z__1.i = -z__2.i;
  712. a[i__3].r = z__1.r, a[i__3].i = z__1.i;
  713. /* L130: */
  714. }
  715. if (*qblckb <= 1) {
  716. *qblckb = 2;
  717. }
  718. i__2 = *n - 1;
  719. i__1 = *qblckb;
  720. for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
  721. i__3 = k + 1 + (k + 1) * b_dim1;
  722. i__4 = k + k * b_dim1;
  723. b[i__3].r = b[i__4].r, b[i__3].i = b[i__4].i;
  724. i__3 = k + 1 + k * b_dim1;
  725. z_sin(&z__2, &b[k + (k + 1) * b_dim1]);
  726. z__1.r = -z__2.r, z__1.i = -z__2.i;
  727. b[i__3].r = z__1.r, b[i__3].i = z__1.i;
  728. /* L140: */
  729. }
  730. }
  731. } else if (*prtype == 4) {
  732. i__1 = *m;
  733. for (i__ = 1; i__ <= i__1; ++i__) {
  734. i__2 = *m;
  735. for (j = 1; j <= i__2; ++j) {
  736. i__3 = i__ + j * a_dim1;
  737. i__4 = i__ * j;
  738. z__4.r = (doublereal) i__4, z__4.i = 0.;
  739. z_sin(&z__3, &z__4);
  740. z__2.r = .5 - z__3.r, z__2.i = 0. - z__3.i;
  741. z__1.r = z__2.r * 20. - z__2.i * 0., z__1.i = z__2.r * 0. +
  742. z__2.i * 20.;
  743. a[i__3].r = z__1.r, a[i__3].i = z__1.i;
  744. i__3 = i__ + j * d_dim1;
  745. i__4 = i__ + j;
  746. z__4.r = (doublereal) i__4, z__4.i = 0.;
  747. z_sin(&z__3, &z__4);
  748. z__2.r = .5 - z__3.r, z__2.i = 0. - z__3.i;
  749. z__1.r = z__2.r * 2. - z__2.i * 0., z__1.i = z__2.r * 0. +
  750. z__2.i * 2.;
  751. d__[i__3].r = z__1.r, d__[i__3].i = z__1.i;
  752. /* L150: */
  753. }
  754. /* L160: */
  755. }
  756. i__1 = *n;
  757. for (i__ = 1; i__ <= i__1; ++i__) {
  758. i__2 = *n;
  759. for (j = 1; j <= i__2; ++j) {
  760. i__3 = i__ + j * b_dim1;
  761. i__4 = i__ + j;
  762. z__4.r = (doublereal) i__4, z__4.i = 0.;
  763. z_sin(&z__3, &z__4);
  764. z__2.r = .5 - z__3.r, z__2.i = 0. - z__3.i;
  765. z__1.r = z__2.r * 20. - z__2.i * 0., z__1.i = z__2.r * 0. +
  766. z__2.i * 20.;
  767. b[i__3].r = z__1.r, b[i__3].i = z__1.i;
  768. i__3 = i__ + j * e_dim1;
  769. i__4 = i__ * j;
  770. z__4.r = (doublereal) i__4, z__4.i = 0.;
  771. z_sin(&z__3, &z__4);
  772. z__2.r = .5 - z__3.r, z__2.i = 0. - z__3.i;
  773. z__1.r = z__2.r * 2. - z__2.i * 0., z__1.i = z__2.r * 0. +
  774. z__2.i * 2.;
  775. e[i__3].r = z__1.r, e[i__3].i = z__1.i;
  776. /* L170: */
  777. }
  778. /* L180: */
  779. }
  780. i__1 = *m;
  781. for (i__ = 1; i__ <= i__1; ++i__) {
  782. i__2 = *n;
  783. for (j = 1; j <= i__2; ++j) {
  784. i__3 = i__ + j * r_dim1;
  785. i__4 = j / i__;
  786. z__4.r = (doublereal) i__4, z__4.i = 0.;
  787. z_sin(&z__3, &z__4);
  788. z__2.r = .5 - z__3.r, z__2.i = 0. - z__3.i;
  789. z__1.r = z__2.r * 20. - z__2.i * 0., z__1.i = z__2.r * 0. +
  790. z__2.i * 20.;
  791. r__[i__3].r = z__1.r, r__[i__3].i = z__1.i;
  792. i__3 = i__ + j * l_dim1;
  793. i__4 = i__ * j;
  794. z__4.r = (doublereal) i__4, z__4.i = 0.;
  795. z_sin(&z__3, &z__4);
  796. z__2.r = .5 - z__3.r, z__2.i = 0. - z__3.i;
  797. z__1.r = z__2.r * 2. - z__2.i * 0., z__1.i = z__2.r * 0. +
  798. z__2.i * 2.;
  799. l[i__3].r = z__1.r, l[i__3].i = z__1.i;
  800. /* L190: */
  801. }
  802. /* L200: */
  803. }
  804. } else if (*prtype >= 5) {
  805. z__3.r = 1., z__3.i = 0.;
  806. z__2.r = z__3.r * 20. - z__3.i * 0., z__2.i = z__3.r * 0. + z__3.i *
  807. 20.;
  808. z__1.r = z__2.r / *alpha, z__1.i = z__2.i / *alpha;
  809. reeps.r = z__1.r, reeps.i = z__1.i;
  810. z__2.r = -1.5, z__2.i = 0.;
  811. z__1.r = z__2.r / *alpha, z__1.i = z__2.i / *alpha;
  812. imeps.r = z__1.r, imeps.i = z__1.i;
  813. i__1 = *m;
  814. for (i__ = 1; i__ <= i__1; ++i__) {
  815. i__2 = *n;
  816. for (j = 1; j <= i__2; ++j) {
  817. i__3 = i__ + j * r_dim1;
  818. i__4 = i__ * j;
  819. z__5.r = (doublereal) i__4, z__5.i = 0.;
  820. z_sin(&z__4, &z__5);
  821. z__3.r = .5 - z__4.r, z__3.i = 0. - z__4.i;
  822. z__2.r = *alpha * z__3.r, z__2.i = *alpha * z__3.i;
  823. z_div(&z__1, &z__2, &c_b5);
  824. r__[i__3].r = z__1.r, r__[i__3].i = z__1.i;
  825. i__3 = i__ + j * l_dim1;
  826. i__4 = i__ + j;
  827. z__5.r = (doublereal) i__4, z__5.i = 0.;
  828. z_sin(&z__4, &z__5);
  829. z__3.r = .5 - z__4.r, z__3.i = 0. - z__4.i;
  830. z__2.r = *alpha * z__3.r, z__2.i = *alpha * z__3.i;
  831. z_div(&z__1, &z__2, &c_b5);
  832. l[i__3].r = z__1.r, l[i__3].i = z__1.i;
  833. /* L210: */
  834. }
  835. /* L220: */
  836. }
  837. i__1 = *m;
  838. for (i__ = 1; i__ <= i__1; ++i__) {
  839. i__2 = i__ + i__ * d_dim1;
  840. d__[i__2].r = 1., d__[i__2].i = 0.;
  841. /* L230: */
  842. }
  843. i__1 = *m;
  844. for (i__ = 1; i__ <= i__1; ++i__) {
  845. if (i__ <= 4) {
  846. i__2 = i__ + i__ * a_dim1;
  847. a[i__2].r = 1., a[i__2].i = 0.;
  848. if (i__ > 2) {
  849. i__2 = i__ + i__ * a_dim1;
  850. z__1.r = reeps.r + 1., z__1.i = reeps.i + 0.;
  851. a[i__2].r = z__1.r, a[i__2].i = z__1.i;
  852. }
  853. if (i__ % 2 != 0 && i__ < *m) {
  854. i__2 = i__ + (i__ + 1) * a_dim1;
  855. a[i__2].r = imeps.r, a[i__2].i = imeps.i;
  856. } else if (i__ > 1) {
  857. i__2 = i__ + (i__ - 1) * a_dim1;
  858. z__1.r = -imeps.r, z__1.i = -imeps.i;
  859. a[i__2].r = z__1.r, a[i__2].i = z__1.i;
  860. }
  861. } else if (i__ <= 8) {
  862. if (i__ <= 6) {
  863. i__2 = i__ + i__ * a_dim1;
  864. a[i__2].r = reeps.r, a[i__2].i = reeps.i;
  865. } else {
  866. i__2 = i__ + i__ * a_dim1;
  867. z__1.r = -reeps.r, z__1.i = -reeps.i;
  868. a[i__2].r = z__1.r, a[i__2].i = z__1.i;
  869. }
  870. if (i__ % 2 != 0 && i__ < *m) {
  871. i__2 = i__ + (i__ + 1) * a_dim1;
  872. a[i__2].r = 1., a[i__2].i = 0.;
  873. } else if (i__ > 1) {
  874. i__2 = i__ + (i__ - 1) * a_dim1;
  875. z__1.r = -1., z__1.i = 0.;
  876. a[i__2].r = z__1.r, a[i__2].i = z__1.i;
  877. }
  878. } else {
  879. i__2 = i__ + i__ * a_dim1;
  880. a[i__2].r = 1., a[i__2].i = 0.;
  881. if (i__ % 2 != 0 && i__ < *m) {
  882. i__2 = i__ + (i__ + 1) * a_dim1;
  883. d__1 = 2.;
  884. z__1.r = d__1 * imeps.r, z__1.i = d__1 * imeps.i;
  885. a[i__2].r = z__1.r, a[i__2].i = z__1.i;
  886. } else if (i__ > 1) {
  887. i__2 = i__ + (i__ - 1) * a_dim1;
  888. z__2.r = -imeps.r, z__2.i = -imeps.i;
  889. d__1 = 2.;
  890. z__1.r = d__1 * z__2.r, z__1.i = d__1 * z__2.i;
  891. a[i__2].r = z__1.r, a[i__2].i = z__1.i;
  892. }
  893. }
  894. /* L240: */
  895. }
  896. i__1 = *n;
  897. for (i__ = 1; i__ <= i__1; ++i__) {
  898. i__2 = i__ + i__ * e_dim1;
  899. e[i__2].r = 1., e[i__2].i = 0.;
  900. if (i__ <= 4) {
  901. i__2 = i__ + i__ * b_dim1;
  902. z__1.r = -1., z__1.i = 0.;
  903. b[i__2].r = z__1.r, b[i__2].i = z__1.i;
  904. if (i__ > 2) {
  905. i__2 = i__ + i__ * b_dim1;
  906. z__1.r = 1. - reeps.r, z__1.i = 0. - reeps.i;
  907. b[i__2].r = z__1.r, b[i__2].i = z__1.i;
  908. }
  909. if (i__ % 2 != 0 && i__ < *n) {
  910. i__2 = i__ + (i__ + 1) * b_dim1;
  911. b[i__2].r = imeps.r, b[i__2].i = imeps.i;
  912. } else if (i__ > 1) {
  913. i__2 = i__ + (i__ - 1) * b_dim1;
  914. z__1.r = -imeps.r, z__1.i = -imeps.i;
  915. b[i__2].r = z__1.r, b[i__2].i = z__1.i;
  916. }
  917. } else if (i__ <= 8) {
  918. if (i__ <= 6) {
  919. i__2 = i__ + i__ * b_dim1;
  920. b[i__2].r = reeps.r, b[i__2].i = reeps.i;
  921. } else {
  922. i__2 = i__ + i__ * b_dim1;
  923. z__1.r = -reeps.r, z__1.i = -reeps.i;
  924. b[i__2].r = z__1.r, b[i__2].i = z__1.i;
  925. }
  926. if (i__ % 2 != 0 && i__ < *n) {
  927. i__2 = i__ + (i__ + 1) * b_dim1;
  928. z__1.r = imeps.r + 1., z__1.i = imeps.i + 0.;
  929. b[i__2].r = z__1.r, b[i__2].i = z__1.i;
  930. } else if (i__ > 1) {
  931. i__2 = i__ + (i__ - 1) * b_dim1;
  932. z__2.r = -1., z__2.i = 0.;
  933. z__1.r = z__2.r - imeps.r, z__1.i = z__2.i - imeps.i;
  934. b[i__2].r = z__1.r, b[i__2].i = z__1.i;
  935. }
  936. } else {
  937. i__2 = i__ + i__ * b_dim1;
  938. z__1.r = 1. - reeps.r, z__1.i = 0. - reeps.i;
  939. b[i__2].r = z__1.r, b[i__2].i = z__1.i;
  940. if (i__ % 2 != 0 && i__ < *n) {
  941. i__2 = i__ + (i__ + 1) * b_dim1;
  942. d__1 = 2.;
  943. z__1.r = d__1 * imeps.r, z__1.i = d__1 * imeps.i;
  944. b[i__2].r = z__1.r, b[i__2].i = z__1.i;
  945. } else if (i__ > 1) {
  946. i__2 = i__ + (i__ - 1) * b_dim1;
  947. z__2.r = -imeps.r, z__2.i = -imeps.i;
  948. d__1 = 2.;
  949. z__1.r = d__1 * z__2.r, z__1.i = d__1 * z__2.i;
  950. b[i__2].r = z__1.r, b[i__2].i = z__1.i;
  951. }
  952. }
  953. /* L250: */
  954. }
  955. }
  956. /* Compute rhs (C, F) */
  957. zgemm_("N", "N", m, n, m, &c_b1, &a[a_offset], lda, &r__[r_offset], ldr, &
  958. c_b3, &c__[c_offset], ldc);
  959. z__1.r = -1., z__1.i = 0.;
  960. zgemm_("N", "N", m, n, n, &z__1, &l[l_offset], ldl, &b[b_offset], ldb, &
  961. c_b1, &c__[c_offset], ldc);
  962. zgemm_("N", "N", m, n, m, &c_b1, &d__[d_offset], ldd, &r__[r_offset], ldr,
  963. &c_b3, &f[f_offset], ldf);
  964. z__1.r = -1., z__1.i = 0.;
  965. zgemm_("N", "N", m, n, n, &z__1, &l[l_offset], ldl, &e[e_offset], lde, &
  966. c_b1, &f[f_offset], ldf);
  967. /* End of ZLATM5 */
  968. return;
  969. } /* zlatm5_ */