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slaqtr.c 36 kB

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  1. #include <math.h>
  2. #include <stdlib.h>
  3. #include <string.h>
  4. #include <stdio.h>
  5. #include <complex.h>
  6. #ifdef complex
  7. #undef complex
  8. #endif
  9. #ifdef I
  10. #undef I
  11. #endif
  12. #if defined(_WIN64)
  13. typedef long long BLASLONG;
  14. typedef unsigned long long BLASULONG;
  15. #else
  16. typedef long BLASLONG;
  17. typedef unsigned long BLASULONG;
  18. #endif
  19. #ifdef LAPACK_ILP64
  20. typedef BLASLONG blasint;
  21. #if defined(_WIN64)
  22. #define blasabs(x) llabs(x)
  23. #else
  24. #define blasabs(x) labs(x)
  25. #endif
  26. #else
  27. typedef int blasint;
  28. #define blasabs(x) abs(x)
  29. #endif
  30. typedef blasint integer;
  31. typedef unsigned int uinteger;
  32. typedef char *address;
  33. typedef short int shortint;
  34. typedef float real;
  35. typedef double doublereal;
  36. typedef struct { real r, i; } complex;
  37. typedef struct { doublereal r, i; } doublecomplex;
  38. #ifdef _MSC_VER
  39. static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
  40. static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
  41. static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
  42. static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
  43. #else
  44. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  45. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  46. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  47. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  48. #endif
  49. #define pCf(z) (*_pCf(z))
  50. #define pCd(z) (*_pCd(z))
  51. typedef int logical;
  52. typedef short int shortlogical;
  53. typedef char logical1;
  54. typedef char integer1;
  55. #define TRUE_ (1)
  56. #define FALSE_ (0)
  57. /* Extern is for use with -E */
  58. #ifndef Extern
  59. #define Extern extern
  60. #endif
  61. /* I/O stuff */
  62. typedef int flag;
  63. typedef int ftnlen;
  64. typedef int ftnint;
  65. /*external read, write*/
  66. typedef struct
  67. { flag cierr;
  68. ftnint ciunit;
  69. flag ciend;
  70. char *cifmt;
  71. ftnint cirec;
  72. } cilist;
  73. /*internal read, write*/
  74. typedef struct
  75. { flag icierr;
  76. char *iciunit;
  77. flag iciend;
  78. char *icifmt;
  79. ftnint icirlen;
  80. ftnint icirnum;
  81. } icilist;
  82. /*open*/
  83. typedef struct
  84. { flag oerr;
  85. ftnint ounit;
  86. char *ofnm;
  87. ftnlen ofnmlen;
  88. char *osta;
  89. char *oacc;
  90. char *ofm;
  91. ftnint orl;
  92. char *oblnk;
  93. } olist;
  94. /*close*/
  95. typedef struct
  96. { flag cerr;
  97. ftnint cunit;
  98. char *csta;
  99. } cllist;
  100. /*rewind, backspace, endfile*/
  101. typedef struct
  102. { flag aerr;
  103. ftnint aunit;
  104. } alist;
  105. /* inquire */
  106. typedef struct
  107. { flag inerr;
  108. ftnint inunit;
  109. char *infile;
  110. ftnlen infilen;
  111. ftnint *inex; /*parameters in standard's order*/
  112. ftnint *inopen;
  113. ftnint *innum;
  114. ftnint *innamed;
  115. char *inname;
  116. ftnlen innamlen;
  117. char *inacc;
  118. ftnlen inacclen;
  119. char *inseq;
  120. ftnlen inseqlen;
  121. char *indir;
  122. ftnlen indirlen;
  123. char *infmt;
  124. ftnlen infmtlen;
  125. char *inform;
  126. ftnint informlen;
  127. char *inunf;
  128. ftnlen inunflen;
  129. ftnint *inrecl;
  130. ftnint *innrec;
  131. char *inblank;
  132. ftnlen inblanklen;
  133. } inlist;
  134. #define VOID void
  135. union Multitype { /* for multiple entry points */
  136. integer1 g;
  137. shortint h;
  138. integer i;
  139. /* longint j; */
  140. real r;
  141. doublereal d;
  142. complex c;
  143. doublecomplex z;
  144. };
  145. typedef union Multitype Multitype;
  146. struct Vardesc { /* for Namelist */
  147. char *name;
  148. char *addr;
  149. ftnlen *dims;
  150. int type;
  151. };
  152. typedef struct Vardesc Vardesc;
  153. struct Namelist {
  154. char *name;
  155. Vardesc **vars;
  156. int nvars;
  157. };
  158. typedef struct Namelist Namelist;
  159. #define abs(x) ((x) >= 0 ? (x) : -(x))
  160. #define dabs(x) (fabs(x))
  161. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  162. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  163. #define dmin(a,b) (f2cmin(a,b))
  164. #define dmax(a,b) (f2cmax(a,b))
  165. #define bit_test(a,b) ((a) >> (b) & 1)
  166. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  167. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  168. #define abort_() { sig_die("Fortran abort routine called", 1); }
  169. #define c_abs(z) (cabsf(Cf(z)))
  170. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  171. #ifdef _MSC_VER
  172. #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
  173. #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
  174. #else
  175. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  176. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  177. #endif
  178. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  179. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  180. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  181. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  182. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  183. #define d_abs(x) (fabs(*(x)))
  184. #define d_acos(x) (acos(*(x)))
  185. #define d_asin(x) (asin(*(x)))
  186. #define d_atan(x) (atan(*(x)))
  187. #define d_atn2(x, y) (atan2(*(x),*(y)))
  188. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  189. #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
  190. #define d_cos(x) (cos(*(x)))
  191. #define d_cosh(x) (cosh(*(x)))
  192. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  193. #define d_exp(x) (exp(*(x)))
  194. #define d_imag(z) (cimag(Cd(z)))
  195. #define r_imag(z) (cimagf(Cf(z)))
  196. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  197. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  198. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  199. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  200. #define d_log(x) (log(*(x)))
  201. #define d_mod(x, y) (fmod(*(x), *(y)))
  202. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  203. #define d_nint(x) u_nint(*(x))
  204. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  205. #define d_sign(a,b) u_sign(*(a),*(b))
  206. #define r_sign(a,b) u_sign(*(a),*(b))
  207. #define d_sin(x) (sin(*(x)))
  208. #define d_sinh(x) (sinh(*(x)))
  209. #define d_sqrt(x) (sqrt(*(x)))
  210. #define d_tan(x) (tan(*(x)))
  211. #define d_tanh(x) (tanh(*(x)))
  212. #define i_abs(x) abs(*(x))
  213. #define i_dnnt(x) ((integer)u_nint(*(x)))
  214. #define i_len(s, n) (n)
  215. #define i_nint(x) ((integer)u_nint(*(x)))
  216. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  217. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  218. #define pow_si(B,E) spow_ui(*(B),*(E))
  219. #define pow_ri(B,E) spow_ui(*(B),*(E))
  220. #define pow_di(B,E) dpow_ui(*(B),*(E))
  221. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  222. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  223. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  224. #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
  225. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  226. #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
  227. #define sig_die(s, kill) { exit(1); }
  228. #define s_stop(s, n) {exit(0);}
  229. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  230. #define z_abs(z) (cabs(Cd(z)))
  231. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  232. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  233. #define myexit_() break;
  234. #define mycycle() continue;
  235. #define myceiling(w) {ceil(w)}
  236. #define myhuge(w) {HUGE_VAL}
  237. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  238. #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  239. /* procedure parameter types for -A and -C++ */
  240. #define F2C_proc_par_types 1
  241. #ifdef __cplusplus
  242. typedef logical (*L_fp)(...);
  243. #else
  244. typedef logical (*L_fp)();
  245. #endif
  246. static float spow_ui(float x, integer n) {
  247. float pow=1.0; unsigned long int u;
  248. if(n != 0) {
  249. if(n < 0) n = -n, x = 1/x;
  250. for(u = n; ; ) {
  251. if(u & 01) pow *= x;
  252. if(u >>= 1) x *= x;
  253. else break;
  254. }
  255. }
  256. return pow;
  257. }
  258. static double dpow_ui(double x, integer n) {
  259. double pow=1.0; unsigned long int u;
  260. if(n != 0) {
  261. if(n < 0) n = -n, x = 1/x;
  262. for(u = n; ; ) {
  263. if(u & 01) pow *= x;
  264. if(u >>= 1) x *= x;
  265. else break;
  266. }
  267. }
  268. return pow;
  269. }
  270. #ifdef _MSC_VER
  271. static _Fcomplex cpow_ui(complex x, integer n) {
  272. complex pow={1.0,0.0}; unsigned long int u;
  273. if(n != 0) {
  274. if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
  275. for(u = n; ; ) {
  276. if(u & 01) pow.r *= x.r, pow.i *= x.i;
  277. if(u >>= 1) x.r *= x.r, x.i *= x.i;
  278. else break;
  279. }
  280. }
  281. _Fcomplex p={pow.r, pow.i};
  282. return p;
  283. }
  284. #else
  285. static _Complex float cpow_ui(_Complex float x, integer n) {
  286. _Complex float pow=1.0; unsigned long int u;
  287. if(n != 0) {
  288. if(n < 0) n = -n, x = 1/x;
  289. for(u = n; ; ) {
  290. if(u & 01) pow *= x;
  291. if(u >>= 1) x *= x;
  292. else break;
  293. }
  294. }
  295. return pow;
  296. }
  297. #endif
  298. #ifdef _MSC_VER
  299. static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
  300. _Dcomplex pow={1.0,0.0}; unsigned long int u;
  301. if(n != 0) {
  302. if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
  303. for(u = n; ; ) {
  304. if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
  305. if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
  306. else break;
  307. }
  308. }
  309. _Dcomplex p = {pow._Val[0], pow._Val[1]};
  310. return p;
  311. }
  312. #else
  313. static _Complex double zpow_ui(_Complex double x, integer n) {
  314. _Complex double pow=1.0; unsigned long int u;
  315. if(n != 0) {
  316. if(n < 0) n = -n, x = 1/x;
  317. for(u = n; ; ) {
  318. if(u & 01) pow *= x;
  319. if(u >>= 1) x *= x;
  320. else break;
  321. }
  322. }
  323. return pow;
  324. }
  325. #endif
  326. static integer pow_ii(integer x, integer n) {
  327. integer pow; unsigned long int u;
  328. if (n <= 0) {
  329. if (n == 0 || x == 1) pow = 1;
  330. else if (x != -1) pow = x == 0 ? 1/x : 0;
  331. else n = -n;
  332. }
  333. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  334. u = n;
  335. for(pow = 1; ; ) {
  336. if(u & 01) pow *= x;
  337. if(u >>= 1) x *= x;
  338. else break;
  339. }
  340. }
  341. return pow;
  342. }
  343. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  344. {
  345. double m; integer i, mi;
  346. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  347. if (w[i-1]>m) mi=i ,m=w[i-1];
  348. return mi-s+1;
  349. }
  350. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  351. {
  352. float m; integer i, mi;
  353. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  354. if (w[i-1]>m) mi=i ,m=w[i-1];
  355. return mi-s+1;
  356. }
  357. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  358. integer n = *n_, incx = *incx_, incy = *incy_, i;
  359. #ifdef _MSC_VER
  360. _Fcomplex zdotc = {0.0, 0.0};
  361. if (incx == 1 && incy == 1) {
  362. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  363. zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
  364. zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
  365. }
  366. } else {
  367. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  368. zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
  369. zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
  370. }
  371. }
  372. pCf(z) = zdotc;
  373. }
  374. #else
  375. _Complex float zdotc = 0.0;
  376. if (incx == 1 && incy == 1) {
  377. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  378. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  379. }
  380. } else {
  381. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  382. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  383. }
  384. }
  385. pCf(z) = zdotc;
  386. }
  387. #endif
  388. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  389. integer n = *n_, incx = *incx_, incy = *incy_, i;
  390. #ifdef _MSC_VER
  391. _Dcomplex zdotc = {0.0, 0.0};
  392. if (incx == 1 && incy == 1) {
  393. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  394. zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
  395. zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
  396. }
  397. } else {
  398. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  399. zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
  400. zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
  401. }
  402. }
  403. pCd(z) = zdotc;
  404. }
  405. #else
  406. _Complex double zdotc = 0.0;
  407. if (incx == 1 && incy == 1) {
  408. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  409. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  410. }
  411. } else {
  412. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  413. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  414. }
  415. }
  416. pCd(z) = zdotc;
  417. }
  418. #endif
  419. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  420. integer n = *n_, incx = *incx_, incy = *incy_, i;
  421. #ifdef _MSC_VER
  422. _Fcomplex zdotc = {0.0, 0.0};
  423. if (incx == 1 && incy == 1) {
  424. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  425. zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
  426. zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
  427. }
  428. } else {
  429. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  430. zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
  431. zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
  432. }
  433. }
  434. pCf(z) = zdotc;
  435. }
  436. #else
  437. _Complex float zdotc = 0.0;
  438. if (incx == 1 && incy == 1) {
  439. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  440. zdotc += Cf(&x[i]) * Cf(&y[i]);
  441. }
  442. } else {
  443. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  444. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  445. }
  446. }
  447. pCf(z) = zdotc;
  448. }
  449. #endif
  450. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  451. integer n = *n_, incx = *incx_, incy = *incy_, i;
  452. #ifdef _MSC_VER
  453. _Dcomplex zdotc = {0.0, 0.0};
  454. if (incx == 1 && incy == 1) {
  455. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  456. zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
  457. zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
  458. }
  459. } else {
  460. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  461. zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
  462. zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
  463. }
  464. }
  465. pCd(z) = zdotc;
  466. }
  467. #else
  468. _Complex double zdotc = 0.0;
  469. if (incx == 1 && incy == 1) {
  470. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  471. zdotc += Cd(&x[i]) * Cd(&y[i]);
  472. }
  473. } else {
  474. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  475. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  476. }
  477. }
  478. pCd(z) = zdotc;
  479. }
  480. #endif
  481. /* -- translated by f2c (version 20000121).
  482. You must link the resulting object file with the libraries:
  483. -lf2c -lm (in that order)
  484. */
  485. /* Table of constant values */
  486. static integer c__1 = 1;
  487. static logical c_false = FALSE_;
  488. static integer c__2 = 2;
  489. static real c_b21 = 1.f;
  490. static real c_b25 = 0.f;
  491. static logical c_true = TRUE_;
  492. /* > \brief \b SLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system
  493. of special form, in real arithmetic. */
  494. /* =========== DOCUMENTATION =========== */
  495. /* Online html documentation available at */
  496. /* http://www.netlib.org/lapack/explore-html/ */
  497. /* > \htmlonly */
  498. /* > Download SLAQTR + dependencies */
  499. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slaqtr.
  500. f"> */
  501. /* > [TGZ]</a> */
  502. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slaqtr.
  503. f"> */
  504. /* > [ZIP]</a> */
  505. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slaqtr.
  506. f"> */
  507. /* > [TXT]</a> */
  508. /* > \endhtmlonly */
  509. /* Definition: */
  510. /* =========== */
  511. /* SUBROUTINE SLAQTR( LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, */
  512. /* INFO ) */
  513. /* LOGICAL LREAL, LTRAN */
  514. /* INTEGER INFO, LDT, N */
  515. /* REAL SCALE, W */
  516. /* REAL B( * ), T( LDT, * ), WORK( * ), X( * ) */
  517. /* > \par Purpose: */
  518. /* ============= */
  519. /* > */
  520. /* > \verbatim */
  521. /* > */
  522. /* > SLAQTR solves the real quasi-triangular system */
  523. /* > */
  524. /* > op(T)*p = scale*c, if LREAL = .TRUE. */
  525. /* > */
  526. /* > or the complex quasi-triangular systems */
  527. /* > */
  528. /* > op(T + iB)*(p+iq) = scale*(c+id), if LREAL = .FALSE. */
  529. /* > */
  530. /* > in real arithmetic, where T is upper quasi-triangular. */
  531. /* > If LREAL = .FALSE., then the first diagonal block of T must be */
  532. /* > 1 by 1, B is the specially structured matrix */
  533. /* > */
  534. /* > B = [ b(1) b(2) ... b(n) ] */
  535. /* > [ w ] */
  536. /* > [ w ] */
  537. /* > [ . ] */
  538. /* > [ w ] */
  539. /* > */
  540. /* > op(A) = A or A**T, A**T denotes the transpose of */
  541. /* > matrix A. */
  542. /* > */
  543. /* > On input, X = [ c ]. On output, X = [ p ]. */
  544. /* > [ d ] [ q ] */
  545. /* > */
  546. /* > This subroutine is designed for the condition number estimation */
  547. /* > in routine STRSNA. */
  548. /* > \endverbatim */
  549. /* Arguments: */
  550. /* ========== */
  551. /* > \param[in] LTRAN */
  552. /* > \verbatim */
  553. /* > LTRAN is LOGICAL */
  554. /* > On entry, LTRAN specifies the option of conjugate transpose: */
  555. /* > = .FALSE., op(T+i*B) = T+i*B, */
  556. /* > = .TRUE., op(T+i*B) = (T+i*B)**T. */
  557. /* > \endverbatim */
  558. /* > */
  559. /* > \param[in] LREAL */
  560. /* > \verbatim */
  561. /* > LREAL is LOGICAL */
  562. /* > On entry, LREAL specifies the input matrix structure: */
  563. /* > = .FALSE., the input is complex */
  564. /* > = .TRUE., the input is real */
  565. /* > \endverbatim */
  566. /* > */
  567. /* > \param[in] N */
  568. /* > \verbatim */
  569. /* > N is INTEGER */
  570. /* > On entry, N specifies the order of T+i*B. N >= 0. */
  571. /* > \endverbatim */
  572. /* > */
  573. /* > \param[in] T */
  574. /* > \verbatim */
  575. /* > T is REAL array, dimension (LDT,N) */
  576. /* > On entry, T contains a matrix in Schur canonical form. */
  577. /* > If LREAL = .FALSE., then the first diagonal block of T must */
  578. /* > be 1 by 1. */
  579. /* > \endverbatim */
  580. /* > */
  581. /* > \param[in] LDT */
  582. /* > \verbatim */
  583. /* > LDT is INTEGER */
  584. /* > The leading dimension of the matrix T. LDT >= f2cmax(1,N). */
  585. /* > \endverbatim */
  586. /* > */
  587. /* > \param[in] B */
  588. /* > \verbatim */
  589. /* > B is REAL array, dimension (N) */
  590. /* > On entry, B contains the elements to form the matrix */
  591. /* > B as described above. */
  592. /* > If LREAL = .TRUE., B is not referenced. */
  593. /* > \endverbatim */
  594. /* > */
  595. /* > \param[in] W */
  596. /* > \verbatim */
  597. /* > W is REAL */
  598. /* > On entry, W is the diagonal element of the matrix B. */
  599. /* > If LREAL = .TRUE., W is not referenced. */
  600. /* > \endverbatim */
  601. /* > */
  602. /* > \param[out] SCALE */
  603. /* > \verbatim */
  604. /* > SCALE is REAL */
  605. /* > On exit, SCALE is the scale factor. */
  606. /* > \endverbatim */
  607. /* > */
  608. /* > \param[in,out] X */
  609. /* > \verbatim */
  610. /* > X is REAL array, dimension (2*N) */
  611. /* > On entry, X contains the right hand side of the system. */
  612. /* > On exit, X is overwritten by the solution. */
  613. /* > \endverbatim */
  614. /* > */
  615. /* > \param[out] WORK */
  616. /* > \verbatim */
  617. /* > WORK is REAL array, dimension (N) */
  618. /* > \endverbatim */
  619. /* > */
  620. /* > \param[out] INFO */
  621. /* > \verbatim */
  622. /* > INFO is INTEGER */
  623. /* > On exit, INFO is set to */
  624. /* > 0: successful exit. */
  625. /* > 1: the some diagonal 1 by 1 block has been perturbed by */
  626. /* > a small number SMIN to keep nonsingularity. */
  627. /* > 2: the some diagonal 2 by 2 block has been perturbed by */
  628. /* > a small number in SLALN2 to keep nonsingularity. */
  629. /* > NOTE: In the interests of speed, this routine does not */
  630. /* > check the inputs for errors. */
  631. /* > \endverbatim */
  632. /* Authors: */
  633. /* ======== */
  634. /* > \author Univ. of Tennessee */
  635. /* > \author Univ. of California Berkeley */
  636. /* > \author Univ. of Colorado Denver */
  637. /* > \author NAG Ltd. */
  638. /* > \date December 2016 */
  639. /* > \ingroup realOTHERauxiliary */
  640. /* ===================================================================== */
  641. /* Subroutine */ void slaqtr_(logical *ltran, logical *lreal, integer *n, real
  642. *t, integer *ldt, real *b, real *w, real *scale, real *x, real *work,
  643. integer *info)
  644. {
  645. /* System generated locals */
  646. integer t_dim1, t_offset, i__1, i__2;
  647. real r__1, r__2, r__3, r__4, r__5, r__6;
  648. /* Local variables */
  649. integer ierr;
  650. real smin;
  651. extern real sdot_(integer *, real *, integer *, real *, integer *);
  652. real xmax, d__[4] /* was [2][2] */;
  653. integer i__, j, k;
  654. real v[4] /* was [2][2] */, z__;
  655. extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
  656. integer jnext;
  657. extern real sasum_(integer *, real *, integer *);
  658. integer j1, j2;
  659. real sminw;
  660. integer n1, n2;
  661. real xnorm;
  662. extern /* Subroutine */ void saxpy_(integer *, real *, real *, integer *,
  663. real *, integer *), slaln2_(logical *, integer *, integer *, real
  664. *, real *, real *, integer *, real *, real *, real *, integer *,
  665. real *, real *, real *, integer *, real *, real *, integer *);
  666. real si, xj, scaloc, sr;
  667. extern real slamch_(char *), slange_(char *, integer *, integer *,
  668. real *, integer *, real *);
  669. real bignum;
  670. extern integer isamax_(integer *, real *, integer *);
  671. extern /* Subroutine */ void sladiv_(real *, real *, real *, real *, real *
  672. , real *);
  673. logical notran;
  674. real smlnum, rec, eps, tjj, tmp;
  675. /* -- LAPACK auxiliary routine (version 3.7.0) -- */
  676. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  677. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  678. /* December 2016 */
  679. /* ===================================================================== */
  680. /* Do not test the input parameters for errors */
  681. /* Parameter adjustments */
  682. t_dim1 = *ldt;
  683. t_offset = 1 + t_dim1 * 1;
  684. t -= t_offset;
  685. --b;
  686. --x;
  687. --work;
  688. /* Function Body */
  689. notran = ! (*ltran);
  690. *info = 0;
  691. /* Quick return if possible */
  692. if (*n == 0) {
  693. return;
  694. }
  695. /* Set constants to control overflow */
  696. eps = slamch_("P");
  697. smlnum = slamch_("S") / eps;
  698. bignum = 1.f / smlnum;
  699. xnorm = slange_("M", n, n, &t[t_offset], ldt, d__);
  700. if (! (*lreal)) {
  701. /* Computing MAX */
  702. r__1 = xnorm, r__2 = abs(*w), r__1 = f2cmax(r__1,r__2), r__2 = slange_(
  703. "M", n, &c__1, &b[1], n, d__);
  704. xnorm = f2cmax(r__1,r__2);
  705. }
  706. /* Computing MAX */
  707. r__1 = smlnum, r__2 = eps * xnorm;
  708. smin = f2cmax(r__1,r__2);
  709. /* Compute 1-norm of each column of strictly upper triangular */
  710. /* part of T to control overflow in triangular solver. */
  711. work[1] = 0.f;
  712. i__1 = *n;
  713. for (j = 2; j <= i__1; ++j) {
  714. i__2 = j - 1;
  715. work[j] = sasum_(&i__2, &t[j * t_dim1 + 1], &c__1);
  716. /* L10: */
  717. }
  718. if (! (*lreal)) {
  719. i__1 = *n;
  720. for (i__ = 2; i__ <= i__1; ++i__) {
  721. work[i__] += (r__1 = b[i__], abs(r__1));
  722. /* L20: */
  723. }
  724. }
  725. n2 = *n << 1;
  726. n1 = *n;
  727. if (! (*lreal)) {
  728. n1 = n2;
  729. }
  730. k = isamax_(&n1, &x[1], &c__1);
  731. xmax = (r__1 = x[k], abs(r__1));
  732. *scale = 1.f;
  733. if (xmax > bignum) {
  734. *scale = bignum / xmax;
  735. sscal_(&n1, scale, &x[1], &c__1);
  736. xmax = bignum;
  737. }
  738. if (*lreal) {
  739. if (notran) {
  740. /* Solve T*p = scale*c */
  741. jnext = *n;
  742. for (j = *n; j >= 1; --j) {
  743. if (j > jnext) {
  744. goto L30;
  745. }
  746. j1 = j;
  747. j2 = j;
  748. jnext = j - 1;
  749. if (j > 1) {
  750. if (t[j + (j - 1) * t_dim1] != 0.f) {
  751. j1 = j - 1;
  752. jnext = j - 2;
  753. }
  754. }
  755. if (j1 == j2) {
  756. /* Meet 1 by 1 diagonal block */
  757. /* Scale to avoid overflow when computing */
  758. /* x(j) = b(j)/T(j,j) */
  759. xj = (r__1 = x[j1], abs(r__1));
  760. tjj = (r__1 = t[j1 + j1 * t_dim1], abs(r__1));
  761. tmp = t[j1 + j1 * t_dim1];
  762. if (tjj < smin) {
  763. tmp = smin;
  764. tjj = smin;
  765. *info = 1;
  766. }
  767. if (xj == 0.f) {
  768. goto L30;
  769. }
  770. if (tjj < 1.f) {
  771. if (xj > bignum * tjj) {
  772. rec = 1.f / xj;
  773. sscal_(n, &rec, &x[1], &c__1);
  774. *scale *= rec;
  775. xmax *= rec;
  776. }
  777. }
  778. x[j1] /= tmp;
  779. xj = (r__1 = x[j1], abs(r__1));
  780. /* Scale x if necessary to avoid overflow when adding a */
  781. /* multiple of column j1 of T. */
  782. if (xj > 1.f) {
  783. rec = 1.f / xj;
  784. if (work[j1] > (bignum - xmax) * rec) {
  785. sscal_(n, &rec, &x[1], &c__1);
  786. *scale *= rec;
  787. }
  788. }
  789. if (j1 > 1) {
  790. i__1 = j1 - 1;
  791. r__1 = -x[j1];
  792. saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
  793. , &c__1);
  794. i__1 = j1 - 1;
  795. k = isamax_(&i__1, &x[1], &c__1);
  796. xmax = (r__1 = x[k], abs(r__1));
  797. }
  798. } else {
  799. /* Meet 2 by 2 diagonal block */
  800. /* Call 2 by 2 linear system solve, to take */
  801. /* care of possible overflow by scaling factor. */
  802. d__[0] = x[j1];
  803. d__[1] = x[j2];
  804. slaln2_(&c_false, &c__2, &c__1, &smin, &c_b21, &t[j1 + j1
  805. * t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, &
  806. c_b25, &c_b25, v, &c__2, &scaloc, &xnorm, &ierr);
  807. if (ierr != 0) {
  808. *info = 2;
  809. }
  810. if (scaloc != 1.f) {
  811. sscal_(n, &scaloc, &x[1], &c__1);
  812. *scale *= scaloc;
  813. }
  814. x[j1] = v[0];
  815. x[j2] = v[1];
  816. /* Scale V(1,1) (= X(J1)) and/or V(2,1) (=X(J2)) */
  817. /* to avoid overflow in updating right-hand side. */
  818. /* Computing MAX */
  819. r__1 = abs(v[0]), r__2 = abs(v[1]);
  820. xj = f2cmax(r__1,r__2);
  821. if (xj > 1.f) {
  822. rec = 1.f / xj;
  823. /* Computing MAX */
  824. r__1 = work[j1], r__2 = work[j2];
  825. if (f2cmax(r__1,r__2) > (bignum - xmax) * rec) {
  826. sscal_(n, &rec, &x[1], &c__1);
  827. *scale *= rec;
  828. }
  829. }
  830. /* Update right-hand side */
  831. if (j1 > 1) {
  832. i__1 = j1 - 1;
  833. r__1 = -x[j1];
  834. saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
  835. , &c__1);
  836. i__1 = j1 - 1;
  837. r__1 = -x[j2];
  838. saxpy_(&i__1, &r__1, &t[j2 * t_dim1 + 1], &c__1, &x[1]
  839. , &c__1);
  840. i__1 = j1 - 1;
  841. k = isamax_(&i__1, &x[1], &c__1);
  842. xmax = (r__1 = x[k], abs(r__1));
  843. }
  844. }
  845. L30:
  846. ;
  847. }
  848. } else {
  849. /* Solve T**T*p = scale*c */
  850. jnext = 1;
  851. i__1 = *n;
  852. for (j = 1; j <= i__1; ++j) {
  853. if (j < jnext) {
  854. goto L40;
  855. }
  856. j1 = j;
  857. j2 = j;
  858. jnext = j + 1;
  859. if (j < *n) {
  860. if (t[j + 1 + j * t_dim1] != 0.f) {
  861. j2 = j + 1;
  862. jnext = j + 2;
  863. }
  864. }
  865. if (j1 == j2) {
  866. /* 1 by 1 diagonal block */
  867. /* Scale if necessary to avoid overflow in forming the */
  868. /* right-hand side element by inner product. */
  869. xj = (r__1 = x[j1], abs(r__1));
  870. if (xmax > 1.f) {
  871. rec = 1.f / xmax;
  872. if (work[j1] > (bignum - xj) * rec) {
  873. sscal_(n, &rec, &x[1], &c__1);
  874. *scale *= rec;
  875. xmax *= rec;
  876. }
  877. }
  878. i__2 = j1 - 1;
  879. x[j1] -= sdot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[1], &
  880. c__1);
  881. xj = (r__1 = x[j1], abs(r__1));
  882. tjj = (r__1 = t[j1 + j1 * t_dim1], abs(r__1));
  883. tmp = t[j1 + j1 * t_dim1];
  884. if (tjj < smin) {
  885. tmp = smin;
  886. tjj = smin;
  887. *info = 1;
  888. }
  889. if (tjj < 1.f) {
  890. if (xj > bignum * tjj) {
  891. rec = 1.f / xj;
  892. sscal_(n, &rec, &x[1], &c__1);
  893. *scale *= rec;
  894. xmax *= rec;
  895. }
  896. }
  897. x[j1] /= tmp;
  898. /* Computing MAX */
  899. r__2 = xmax, r__3 = (r__1 = x[j1], abs(r__1));
  900. xmax = f2cmax(r__2,r__3);
  901. } else {
  902. /* 2 by 2 diagonal block */
  903. /* Scale if necessary to avoid overflow in forming the */
  904. /* right-hand side elements by inner product. */
  905. /* Computing MAX */
  906. r__3 = (r__1 = x[j1], abs(r__1)), r__4 = (r__2 = x[j2],
  907. abs(r__2));
  908. xj = f2cmax(r__3,r__4);
  909. if (xmax > 1.f) {
  910. rec = 1.f / xmax;
  911. /* Computing MAX */
  912. r__1 = work[j2], r__2 = work[j1];
  913. if (f2cmax(r__1,r__2) > (bignum - xj) * rec) {
  914. sscal_(n, &rec, &x[1], &c__1);
  915. *scale *= rec;
  916. xmax *= rec;
  917. }
  918. }
  919. i__2 = j1 - 1;
  920. d__[0] = x[j1] - sdot_(&i__2, &t[j1 * t_dim1 + 1], &c__1,
  921. &x[1], &c__1);
  922. i__2 = j1 - 1;
  923. d__[1] = x[j2] - sdot_(&i__2, &t[j2 * t_dim1 + 1], &c__1,
  924. &x[1], &c__1);
  925. slaln2_(&c_true, &c__2, &c__1, &smin, &c_b21, &t[j1 + j1 *
  926. t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, &c_b25,
  927. &c_b25, v, &c__2, &scaloc, &xnorm, &ierr);
  928. if (ierr != 0) {
  929. *info = 2;
  930. }
  931. if (scaloc != 1.f) {
  932. sscal_(n, &scaloc, &x[1], &c__1);
  933. *scale *= scaloc;
  934. }
  935. x[j1] = v[0];
  936. x[j2] = v[1];
  937. /* Computing MAX */
  938. r__3 = (r__1 = x[j1], abs(r__1)), r__4 = (r__2 = x[j2],
  939. abs(r__2)), r__3 = f2cmax(r__3,r__4);
  940. xmax = f2cmax(r__3,xmax);
  941. }
  942. L40:
  943. ;
  944. }
  945. }
  946. } else {
  947. /* Computing MAX */
  948. r__1 = eps * abs(*w);
  949. sminw = f2cmax(r__1,smin);
  950. if (notran) {
  951. /* Solve (T + iB)*(p+iq) = c+id */
  952. jnext = *n;
  953. for (j = *n; j >= 1; --j) {
  954. if (j > jnext) {
  955. goto L70;
  956. }
  957. j1 = j;
  958. j2 = j;
  959. jnext = j - 1;
  960. if (j > 1) {
  961. if (t[j + (j - 1) * t_dim1] != 0.f) {
  962. j1 = j - 1;
  963. jnext = j - 2;
  964. }
  965. }
  966. if (j1 == j2) {
  967. /* 1 by 1 diagonal block */
  968. /* Scale if necessary to avoid overflow in division */
  969. z__ = *w;
  970. if (j1 == 1) {
  971. z__ = b[1];
  972. }
  973. xj = (r__1 = x[j1], abs(r__1)) + (r__2 = x[*n + j1], abs(
  974. r__2));
  975. tjj = (r__1 = t[j1 + j1 * t_dim1], abs(r__1)) + abs(z__);
  976. tmp = t[j1 + j1 * t_dim1];
  977. if (tjj < sminw) {
  978. tmp = sminw;
  979. tjj = sminw;
  980. *info = 1;
  981. }
  982. if (xj == 0.f) {
  983. goto L70;
  984. }
  985. if (tjj < 1.f) {
  986. if (xj > bignum * tjj) {
  987. rec = 1.f / xj;
  988. sscal_(&n2, &rec, &x[1], &c__1);
  989. *scale *= rec;
  990. xmax *= rec;
  991. }
  992. }
  993. sladiv_(&x[j1], &x[*n + j1], &tmp, &z__, &sr, &si);
  994. x[j1] = sr;
  995. x[*n + j1] = si;
  996. xj = (r__1 = x[j1], abs(r__1)) + (r__2 = x[*n + j1], abs(
  997. r__2));
  998. /* Scale x if necessary to avoid overflow when adding a */
  999. /* multiple of column j1 of T. */
  1000. if (xj > 1.f) {
  1001. rec = 1.f / xj;
  1002. if (work[j1] > (bignum - xmax) * rec) {
  1003. sscal_(&n2, &rec, &x[1], &c__1);
  1004. *scale *= rec;
  1005. }
  1006. }
  1007. if (j1 > 1) {
  1008. i__1 = j1 - 1;
  1009. r__1 = -x[j1];
  1010. saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
  1011. , &c__1);
  1012. i__1 = j1 - 1;
  1013. r__1 = -x[*n + j1];
  1014. saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[*
  1015. n + 1], &c__1);
  1016. x[1] += b[j1] * x[*n + j1];
  1017. x[*n + 1] -= b[j1] * x[j1];
  1018. xmax = 0.f;
  1019. i__1 = j1 - 1;
  1020. for (k = 1; k <= i__1; ++k) {
  1021. /* Computing MAX */
  1022. r__3 = xmax, r__4 = (r__1 = x[k], abs(r__1)) + (
  1023. r__2 = x[k + *n], abs(r__2));
  1024. xmax = f2cmax(r__3,r__4);
  1025. /* L50: */
  1026. }
  1027. }
  1028. } else {
  1029. /* Meet 2 by 2 diagonal block */
  1030. d__[0] = x[j1];
  1031. d__[1] = x[j2];
  1032. d__[2] = x[*n + j1];
  1033. d__[3] = x[*n + j2];
  1034. r__1 = -(*w);
  1035. slaln2_(&c_false, &c__2, &c__2, &sminw, &c_b21, &t[j1 +
  1036. j1 * t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, &
  1037. c_b25, &r__1, v, &c__2, &scaloc, &xnorm, &ierr);
  1038. if (ierr != 0) {
  1039. *info = 2;
  1040. }
  1041. if (scaloc != 1.f) {
  1042. i__1 = *n << 1;
  1043. sscal_(&i__1, &scaloc, &x[1], &c__1);
  1044. *scale = scaloc * *scale;
  1045. }
  1046. x[j1] = v[0];
  1047. x[j2] = v[1];
  1048. x[*n + j1] = v[2];
  1049. x[*n + j2] = v[3];
  1050. /* Scale X(J1), .... to avoid overflow in */
  1051. /* updating right hand side. */
  1052. /* Computing MAX */
  1053. r__1 = abs(v[0]) + abs(v[2]), r__2 = abs(v[1]) + abs(v[3])
  1054. ;
  1055. xj = f2cmax(r__1,r__2);
  1056. if (xj > 1.f) {
  1057. rec = 1.f / xj;
  1058. /* Computing MAX */
  1059. r__1 = work[j1], r__2 = work[j2];
  1060. if (f2cmax(r__1,r__2) > (bignum - xmax) * rec) {
  1061. sscal_(&n2, &rec, &x[1], &c__1);
  1062. *scale *= rec;
  1063. }
  1064. }
  1065. /* Update the right-hand side. */
  1066. if (j1 > 1) {
  1067. i__1 = j1 - 1;
  1068. r__1 = -x[j1];
  1069. saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
  1070. , &c__1);
  1071. i__1 = j1 - 1;
  1072. r__1 = -x[j2];
  1073. saxpy_(&i__1, &r__1, &t[j2 * t_dim1 + 1], &c__1, &x[1]
  1074. , &c__1);
  1075. i__1 = j1 - 1;
  1076. r__1 = -x[*n + j1];
  1077. saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[*
  1078. n + 1], &c__1);
  1079. i__1 = j1 - 1;
  1080. r__1 = -x[*n + j2];
  1081. saxpy_(&i__1, &r__1, &t[j2 * t_dim1 + 1], &c__1, &x[*
  1082. n + 1], &c__1);
  1083. x[1] = x[1] + b[j1] * x[*n + j1] + b[j2] * x[*n + j2];
  1084. x[*n + 1] = x[*n + 1] - b[j1] * x[j1] - b[j2] * x[j2];
  1085. xmax = 0.f;
  1086. i__1 = j1 - 1;
  1087. for (k = 1; k <= i__1; ++k) {
  1088. /* Computing MAX */
  1089. r__3 = (r__1 = x[k], abs(r__1)) + (r__2 = x[k + *
  1090. n], abs(r__2));
  1091. xmax = f2cmax(r__3,xmax);
  1092. /* L60: */
  1093. }
  1094. }
  1095. }
  1096. L70:
  1097. ;
  1098. }
  1099. } else {
  1100. /* Solve (T + iB)**T*(p+iq) = c+id */
  1101. jnext = 1;
  1102. i__1 = *n;
  1103. for (j = 1; j <= i__1; ++j) {
  1104. if (j < jnext) {
  1105. goto L80;
  1106. }
  1107. j1 = j;
  1108. j2 = j;
  1109. jnext = j + 1;
  1110. if (j < *n) {
  1111. if (t[j + 1 + j * t_dim1] != 0.f) {
  1112. j2 = j + 1;
  1113. jnext = j + 2;
  1114. }
  1115. }
  1116. if (j1 == j2) {
  1117. /* 1 by 1 diagonal block */
  1118. /* Scale if necessary to avoid overflow in forming the */
  1119. /* right-hand side element by inner product. */
  1120. xj = (r__1 = x[j1], abs(r__1)) + (r__2 = x[j1 + *n], abs(
  1121. r__2));
  1122. if (xmax > 1.f) {
  1123. rec = 1.f / xmax;
  1124. if (work[j1] > (bignum - xj) * rec) {
  1125. sscal_(&n2, &rec, &x[1], &c__1);
  1126. *scale *= rec;
  1127. xmax *= rec;
  1128. }
  1129. }
  1130. i__2 = j1 - 1;
  1131. x[j1] -= sdot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[1], &
  1132. c__1);
  1133. i__2 = j1 - 1;
  1134. x[*n + j1] -= sdot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[
  1135. *n + 1], &c__1);
  1136. if (j1 > 1) {
  1137. x[j1] -= b[j1] * x[*n + 1];
  1138. x[*n + j1] += b[j1] * x[1];
  1139. }
  1140. xj = (r__1 = x[j1], abs(r__1)) + (r__2 = x[j1 + *n], abs(
  1141. r__2));
  1142. z__ = *w;
  1143. if (j1 == 1) {
  1144. z__ = b[1];
  1145. }
  1146. /* Scale if necessary to avoid overflow in */
  1147. /* complex division */
  1148. tjj = (r__1 = t[j1 + j1 * t_dim1], abs(r__1)) + abs(z__);
  1149. tmp = t[j1 + j1 * t_dim1];
  1150. if (tjj < sminw) {
  1151. tmp = sminw;
  1152. tjj = sminw;
  1153. *info = 1;
  1154. }
  1155. if (tjj < 1.f) {
  1156. if (xj > bignum * tjj) {
  1157. rec = 1.f / xj;
  1158. sscal_(&n2, &rec, &x[1], &c__1);
  1159. *scale *= rec;
  1160. xmax *= rec;
  1161. }
  1162. }
  1163. r__1 = -z__;
  1164. sladiv_(&x[j1], &x[*n + j1], &tmp, &r__1, &sr, &si);
  1165. x[j1] = sr;
  1166. x[j1 + *n] = si;
  1167. /* Computing MAX */
  1168. r__3 = (r__1 = x[j1], abs(r__1)) + (r__2 = x[j1 + *n],
  1169. abs(r__2));
  1170. xmax = f2cmax(r__3,xmax);
  1171. } else {
  1172. /* 2 by 2 diagonal block */
  1173. /* Scale if necessary to avoid overflow in forming the */
  1174. /* right-hand side element by inner product. */
  1175. /* Computing MAX */
  1176. r__5 = (r__1 = x[j1], abs(r__1)) + (r__2 = x[*n + j1],
  1177. abs(r__2)), r__6 = (r__3 = x[j2], abs(r__3)) + (
  1178. r__4 = x[*n + j2], abs(r__4));
  1179. xj = f2cmax(r__5,r__6);
  1180. if (xmax > 1.f) {
  1181. rec = 1.f / xmax;
  1182. /* Computing MAX */
  1183. r__1 = work[j1], r__2 = work[j2];
  1184. if (f2cmax(r__1,r__2) > (bignum - xj) / xmax) {
  1185. sscal_(&n2, &rec, &x[1], &c__1);
  1186. *scale *= rec;
  1187. xmax *= rec;
  1188. }
  1189. }
  1190. i__2 = j1 - 1;
  1191. d__[0] = x[j1] - sdot_(&i__2, &t[j1 * t_dim1 + 1], &c__1,
  1192. &x[1], &c__1);
  1193. i__2 = j1 - 1;
  1194. d__[1] = x[j2] - sdot_(&i__2, &t[j2 * t_dim1 + 1], &c__1,
  1195. &x[1], &c__1);
  1196. i__2 = j1 - 1;
  1197. d__[2] = x[*n + j1] - sdot_(&i__2, &t[j1 * t_dim1 + 1], &
  1198. c__1, &x[*n + 1], &c__1);
  1199. i__2 = j1 - 1;
  1200. d__[3] = x[*n + j2] - sdot_(&i__2, &t[j2 * t_dim1 + 1], &
  1201. c__1, &x[*n + 1], &c__1);
  1202. d__[0] -= b[j1] * x[*n + 1];
  1203. d__[1] -= b[j2] * x[*n + 1];
  1204. d__[2] += b[j1] * x[1];
  1205. d__[3] += b[j2] * x[1];
  1206. slaln2_(&c_true, &c__2, &c__2, &sminw, &c_b21, &t[j1 + j1
  1207. * t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, &
  1208. c_b25, w, v, &c__2, &scaloc, &xnorm, &ierr);
  1209. if (ierr != 0) {
  1210. *info = 2;
  1211. }
  1212. if (scaloc != 1.f) {
  1213. sscal_(&n2, &scaloc, &x[1], &c__1);
  1214. *scale = scaloc * *scale;
  1215. }
  1216. x[j1] = v[0];
  1217. x[j2] = v[1];
  1218. x[*n + j1] = v[2];
  1219. x[*n + j2] = v[3];
  1220. /* Computing MAX */
  1221. r__5 = (r__1 = x[j1], abs(r__1)) + (r__2 = x[*n + j1],
  1222. abs(r__2)), r__6 = (r__3 = x[j2], abs(r__3)) + (
  1223. r__4 = x[*n + j2], abs(r__4)), r__5 = f2cmax(r__5,
  1224. r__6);
  1225. xmax = f2cmax(r__5,xmax);
  1226. }
  1227. L80:
  1228. ;
  1229. }
  1230. }
  1231. }
  1232. return;
  1233. /* End of SLAQTR */
  1234. } /* slaqtr_ */