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dtfsm.c 44 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 doublereal c_b23 = -1.;
  487. static doublereal c_b27 = 1.;
  488. /* > \brief \b DTFSM solves a matrix equation (one operand is a triangular matrix in RFP format). */
  489. /* =========== DOCUMENTATION =========== */
  490. /* Online html documentation available at */
  491. /* http://www.netlib.org/lapack/explore-html/ */
  492. /* > \htmlonly */
  493. /* > Download DTFSM + dependencies */
  494. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtfsm.f
  495. "> */
  496. /* > [TGZ]</a> */
  497. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtfsm.f
  498. "> */
  499. /* > [ZIP]</a> */
  500. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtfsm.f
  501. "> */
  502. /* > [TXT]</a> */
  503. /* > \endhtmlonly */
  504. /* Definition: */
  505. /* =========== */
  506. /* SUBROUTINE DTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, */
  507. /* B, LDB ) */
  508. /* CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO */
  509. /* INTEGER LDB, M, N */
  510. /* DOUBLE PRECISION ALPHA */
  511. /* DOUBLE PRECISION A( 0: * ), B( 0: LDB-1, 0: * ) */
  512. /* > \par Purpose: */
  513. /* ============= */
  514. /* > */
  515. /* > \verbatim */
  516. /* > */
  517. /* > Level 3 BLAS like routine for A in RFP Format. */
  518. /* > */
  519. /* > DTFSM solves the matrix equation */
  520. /* > */
  521. /* > op( A )*X = alpha*B or X*op( A ) = alpha*B */
  522. /* > */
  523. /* > where alpha is a scalar, X and B are m by n matrices, A is a unit, or */
  524. /* > non-unit, upper or lower triangular matrix and op( A ) is one of */
  525. /* > */
  526. /* > op( A ) = A or op( A ) = A**T. */
  527. /* > */
  528. /* > A is in Rectangular Full Packed (RFP) Format. */
  529. /* > */
  530. /* > The matrix X is overwritten on B. */
  531. /* > \endverbatim */
  532. /* Arguments: */
  533. /* ========== */
  534. /* > \param[in] TRANSR */
  535. /* > \verbatim */
  536. /* > TRANSR is CHARACTER*1 */
  537. /* > = 'N': The Normal Form of RFP A is stored; */
  538. /* > = 'T': The Transpose Form of RFP A is stored. */
  539. /* > \endverbatim */
  540. /* > */
  541. /* > \param[in] SIDE */
  542. /* > \verbatim */
  543. /* > SIDE is CHARACTER*1 */
  544. /* > On entry, SIDE specifies whether op( A ) appears on the left */
  545. /* > or right of X as follows: */
  546. /* > */
  547. /* > SIDE = 'L' or 'l' op( A )*X = alpha*B. */
  548. /* > */
  549. /* > SIDE = 'R' or 'r' X*op( A ) = alpha*B. */
  550. /* > */
  551. /* > Unchanged on exit. */
  552. /* > \endverbatim */
  553. /* > */
  554. /* > \param[in] UPLO */
  555. /* > \verbatim */
  556. /* > UPLO is CHARACTER*1 */
  557. /* > On entry, UPLO specifies whether the RFP matrix A came from */
  558. /* > an upper or lower triangular matrix as follows: */
  559. /* > UPLO = 'U' or 'u' RFP A came from an upper triangular matrix */
  560. /* > UPLO = 'L' or 'l' RFP A came from a lower triangular matrix */
  561. /* > */
  562. /* > Unchanged on exit. */
  563. /* > \endverbatim */
  564. /* > */
  565. /* > \param[in] TRANS */
  566. /* > \verbatim */
  567. /* > TRANS is CHARACTER*1 */
  568. /* > On entry, TRANS specifies the form of op( A ) to be used */
  569. /* > in the matrix multiplication as follows: */
  570. /* > */
  571. /* > TRANS = 'N' or 'n' op( A ) = A. */
  572. /* > */
  573. /* > TRANS = 'T' or 't' op( A ) = A'. */
  574. /* > */
  575. /* > Unchanged on exit. */
  576. /* > \endverbatim */
  577. /* > */
  578. /* > \param[in] DIAG */
  579. /* > \verbatim */
  580. /* > DIAG is CHARACTER*1 */
  581. /* > On entry, DIAG specifies whether or not RFP A is unit */
  582. /* > triangular as follows: */
  583. /* > */
  584. /* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */
  585. /* > */
  586. /* > DIAG = 'N' or 'n' A is not assumed to be unit */
  587. /* > triangular. */
  588. /* > */
  589. /* > Unchanged on exit. */
  590. /* > \endverbatim */
  591. /* > */
  592. /* > \param[in] M */
  593. /* > \verbatim */
  594. /* > M is INTEGER */
  595. /* > On entry, M specifies the number of rows of B. M must be at */
  596. /* > least zero. */
  597. /* > Unchanged on exit. */
  598. /* > \endverbatim */
  599. /* > */
  600. /* > \param[in] N */
  601. /* > \verbatim */
  602. /* > N is INTEGER */
  603. /* > On entry, N specifies the number of columns of B. N must be */
  604. /* > at least zero. */
  605. /* > Unchanged on exit. */
  606. /* > \endverbatim */
  607. /* > */
  608. /* > \param[in] ALPHA */
  609. /* > \verbatim */
  610. /* > ALPHA is DOUBLE PRECISION */
  611. /* > On entry, ALPHA specifies the scalar alpha. When alpha is */
  612. /* > zero then A is not referenced and B need not be set before */
  613. /* > entry. */
  614. /* > Unchanged on exit. */
  615. /* > \endverbatim */
  616. /* > */
  617. /* > \param[in] A */
  618. /* > \verbatim */
  619. /* > A is DOUBLE PRECISION array, dimension (NT) */
  620. /* > NT = N*(N+1)/2. On entry, the matrix A in RFP Format. */
  621. /* > RFP Format is described by TRANSR, UPLO and N as follows: */
  622. /* > If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; */
  623. /* > K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If */
  624. /* > TRANSR = 'T' then RFP is the transpose of RFP A as */
  625. /* > defined when TRANSR = 'N'. The contents of RFP A are defined */
  626. /* > by UPLO as follows: If UPLO = 'U' the RFP A contains the NT */
  627. /* > elements of upper packed A either in normal or */
  628. /* > transpose Format. If UPLO = 'L' the RFP A contains */
  629. /* > the NT elements of lower packed A either in normal or */
  630. /* > transpose Format. The LDA of RFP A is (N+1)/2 when */
  631. /* > TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is */
  632. /* > even and is N when is odd. */
  633. /* > See the Note below for more details. Unchanged on exit. */
  634. /* > \endverbatim */
  635. /* > */
  636. /* > \param[in,out] B */
  637. /* > \verbatim */
  638. /* > B is DOUBLE PRECISION array, dimension (LDB,N) */
  639. /* > Before entry, the leading m by n part of the array B must */
  640. /* > contain the right-hand side matrix B, and on exit is */
  641. /* > overwritten by the solution matrix X. */
  642. /* > \endverbatim */
  643. /* > */
  644. /* > \param[in] LDB */
  645. /* > \verbatim */
  646. /* > LDB is INTEGER */
  647. /* > On entry, LDB specifies the first dimension of B as declared */
  648. /* > in the calling (sub) program. LDB must be at least */
  649. /* > f2cmax( 1, m ). */
  650. /* > Unchanged on exit. */
  651. /* > \endverbatim */
  652. /* Authors: */
  653. /* ======== */
  654. /* > \author Univ. of Tennessee */
  655. /* > \author Univ. of California Berkeley */
  656. /* > \author Univ. of Colorado Denver */
  657. /* > \author NAG Ltd. */
  658. /* > \date December 2016 */
  659. /* > \ingroup doubleOTHERcomputational */
  660. /* > \par Further Details: */
  661. /* ===================== */
  662. /* > */
  663. /* > \verbatim */
  664. /* > */
  665. /* > We first consider Rectangular Full Packed (RFP) Format when N is */
  666. /* > even. We give an example where N = 6. */
  667. /* > */
  668. /* > AP is Upper AP is Lower */
  669. /* > */
  670. /* > 00 01 02 03 04 05 00 */
  671. /* > 11 12 13 14 15 10 11 */
  672. /* > 22 23 24 25 20 21 22 */
  673. /* > 33 34 35 30 31 32 33 */
  674. /* > 44 45 40 41 42 43 44 */
  675. /* > 55 50 51 52 53 54 55 */
  676. /* > */
  677. /* > */
  678. /* > Let TRANSR = 'N'. RFP holds AP as follows: */
  679. /* > For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last */
  680. /* > three columns of AP upper. The lower triangle A(4:6,0:2) consists of */
  681. /* > the transpose of the first three columns of AP upper. */
  682. /* > For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first */
  683. /* > three columns of AP lower. The upper triangle A(0:2,0:2) consists of */
  684. /* > the transpose of the last three columns of AP lower. */
  685. /* > This covers the case N even and TRANSR = 'N'. */
  686. /* > */
  687. /* > RFP A RFP A */
  688. /* > */
  689. /* > 03 04 05 33 43 53 */
  690. /* > 13 14 15 00 44 54 */
  691. /* > 23 24 25 10 11 55 */
  692. /* > 33 34 35 20 21 22 */
  693. /* > 00 44 45 30 31 32 */
  694. /* > 01 11 55 40 41 42 */
  695. /* > 02 12 22 50 51 52 */
  696. /* > */
  697. /* > Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */
  698. /* > transpose of RFP A above. One therefore gets: */
  699. /* > */
  700. /* > */
  701. /* > RFP A RFP A */
  702. /* > */
  703. /* > 03 13 23 33 00 01 02 33 00 10 20 30 40 50 */
  704. /* > 04 14 24 34 44 11 12 43 44 11 21 31 41 51 */
  705. /* > 05 15 25 35 45 55 22 53 54 55 22 32 42 52 */
  706. /* > */
  707. /* > */
  708. /* > We then consider Rectangular Full Packed (RFP) Format when N is */
  709. /* > odd. We give an example where N = 5. */
  710. /* > */
  711. /* > AP is Upper AP is Lower */
  712. /* > */
  713. /* > 00 01 02 03 04 00 */
  714. /* > 11 12 13 14 10 11 */
  715. /* > 22 23 24 20 21 22 */
  716. /* > 33 34 30 31 32 33 */
  717. /* > 44 40 41 42 43 44 */
  718. /* > */
  719. /* > */
  720. /* > Let TRANSR = 'N'. RFP holds AP as follows: */
  721. /* > For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last */
  722. /* > three columns of AP upper. The lower triangle A(3:4,0:1) consists of */
  723. /* > the transpose of the first two columns of AP upper. */
  724. /* > For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first */
  725. /* > three columns of AP lower. The upper triangle A(0:1,1:2) consists of */
  726. /* > the transpose of the last two columns of AP lower. */
  727. /* > This covers the case N odd and TRANSR = 'N'. */
  728. /* > */
  729. /* > RFP A RFP A */
  730. /* > */
  731. /* > 02 03 04 00 33 43 */
  732. /* > 12 13 14 10 11 44 */
  733. /* > 22 23 24 20 21 22 */
  734. /* > 00 33 34 30 31 32 */
  735. /* > 01 11 44 40 41 42 */
  736. /* > */
  737. /* > Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */
  738. /* > transpose of RFP A above. One therefore gets: */
  739. /* > */
  740. /* > RFP A RFP A */
  741. /* > */
  742. /* > 02 12 22 00 01 00 10 20 30 40 50 */
  743. /* > 03 13 23 33 11 33 11 21 31 41 51 */
  744. /* > 04 14 24 34 44 43 44 22 32 42 52 */
  745. /* > \endverbatim */
  746. /* ===================================================================== */
  747. /* Subroutine */ int dtfsm_(char *transr, char *side, char *uplo, char *trans,
  748. char *diag, integer *m, integer *n, doublereal *alpha, doublereal *a,
  749. doublereal *b, integer *ldb)
  750. {
  751. /* System generated locals */
  752. integer b_dim1, b_offset, i__1, i__2;
  753. /* Local variables */
  754. integer info, i__, j, k;
  755. logical normaltransr;
  756. extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
  757. integer *, doublereal *, doublereal *, integer *, doublereal *,
  758. integer *, doublereal *, doublereal *, integer *);
  759. logical lside;
  760. extern logical lsame_(char *, char *);
  761. logical lower;
  762. extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *,
  763. integer *, integer *, doublereal *, doublereal *, integer *,
  764. doublereal *, integer *);
  765. integer m1, m2, n1, n2;
  766. extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
  767. logical misodd, nisodd, notrans;
  768. /* -- LAPACK computational routine (version 3.7.0) -- */
  769. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  770. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  771. /* December 2016 */
  772. /* ===================================================================== */
  773. /* Test the input parameters. */
  774. /* Parameter adjustments */
  775. b_dim1 = *ldb - 1 - 0 + 1;
  776. b_offset = 0 + b_dim1 * 0;
  777. b -= b_offset;
  778. /* Function Body */
  779. info = 0;
  780. normaltransr = lsame_(transr, "N");
  781. lside = lsame_(side, "L");
  782. lower = lsame_(uplo, "L");
  783. notrans = lsame_(trans, "N");
  784. if (! normaltransr && ! lsame_(transr, "T")) {
  785. info = -1;
  786. } else if (! lside && ! lsame_(side, "R")) {
  787. info = -2;
  788. } else if (! lower && ! lsame_(uplo, "U")) {
  789. info = -3;
  790. } else if (! notrans && ! lsame_(trans, "T")) {
  791. info = -4;
  792. } else if (! lsame_(diag, "N") && ! lsame_(diag,
  793. "U")) {
  794. info = -5;
  795. } else if (*m < 0) {
  796. info = -6;
  797. } else if (*n < 0) {
  798. info = -7;
  799. } else if (*ldb < f2cmax(1,*m)) {
  800. info = -11;
  801. }
  802. if (info != 0) {
  803. i__1 = -info;
  804. xerbla_("DTFSM ", &i__1, (ftnlen)6);
  805. return 0;
  806. }
  807. /* Quick return when ( (N.EQ.0).OR.(M.EQ.0) ) */
  808. if (*m == 0 || *n == 0) {
  809. return 0;
  810. }
  811. /* Quick return when ALPHA.EQ.(0D+0) */
  812. if (*alpha == 0.) {
  813. i__1 = *n - 1;
  814. for (j = 0; j <= i__1; ++j) {
  815. i__2 = *m - 1;
  816. for (i__ = 0; i__ <= i__2; ++i__) {
  817. b[i__ + j * b_dim1] = 0.;
  818. /* L10: */
  819. }
  820. /* L20: */
  821. }
  822. return 0;
  823. }
  824. if (lside) {
  825. /* SIDE = 'L' */
  826. /* A is M-by-M. */
  827. /* If M is odd, set NISODD = .TRUE., and M1 and M2. */
  828. /* If M is even, NISODD = .FALSE., and M. */
  829. if (*m % 2 == 0) {
  830. misodd = FALSE_;
  831. k = *m / 2;
  832. } else {
  833. misodd = TRUE_;
  834. if (lower) {
  835. m2 = *m / 2;
  836. m1 = *m - m2;
  837. } else {
  838. m1 = *m / 2;
  839. m2 = *m - m1;
  840. }
  841. }
  842. if (misodd) {
  843. /* SIDE = 'L' and N is odd */
  844. if (normaltransr) {
  845. /* SIDE = 'L', N is odd, and TRANSR = 'N' */
  846. if (lower) {
  847. /* SIDE ='L', N is odd, TRANSR = 'N', and UPLO = 'L' */
  848. if (notrans) {
  849. /* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and */
  850. /* TRANS = 'N' */
  851. if (*m == 1) {
  852. dtrsm_("L", "L", "N", diag, &m1, n, alpha, a, m, &
  853. b[b_offset], ldb);
  854. } else {
  855. dtrsm_("L", "L", "N", diag, &m1, n, alpha, a, m, &
  856. b[b_offset], ldb);
  857. dgemm_("N", "N", &m2, n, &m1, &c_b23, &a[m1], m, &
  858. b[b_offset], ldb, alpha, &b[m1], ldb);
  859. dtrsm_("L", "U", "T", diag, &m2, n, &c_b27, &a[*m]
  860. , m, &b[m1], ldb);
  861. }
  862. } else {
  863. /* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and */
  864. /* TRANS = 'T' */
  865. if (*m == 1) {
  866. dtrsm_("L", "L", "T", diag, &m1, n, alpha, a, m, &
  867. b[b_offset], ldb);
  868. } else {
  869. dtrsm_("L", "U", "N", diag, &m2, n, alpha, &a[*m],
  870. m, &b[m1], ldb);
  871. dgemm_("T", "N", &m1, n, &m2, &c_b23, &a[m1], m, &
  872. b[m1], ldb, alpha, &b[b_offset], ldb);
  873. dtrsm_("L", "L", "T", diag, &m1, n, &c_b27, a, m,
  874. &b[b_offset], ldb);
  875. }
  876. }
  877. } else {
  878. /* SIDE ='L', N is odd, TRANSR = 'N', and UPLO = 'U' */
  879. if (! notrans) {
  880. /* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'U', and */
  881. /* TRANS = 'N' */
  882. dtrsm_("L", "L", "N", diag, &m1, n, alpha, &a[m2], m,
  883. &b[b_offset], ldb);
  884. dgemm_("T", "N", &m2, n, &m1, &c_b23, a, m, &b[
  885. b_offset], ldb, alpha, &b[m1], ldb);
  886. dtrsm_("L", "U", "T", diag, &m2, n, &c_b27, &a[m1], m,
  887. &b[m1], ldb);
  888. } else {
  889. /* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'U', and */
  890. /* TRANS = 'T' */
  891. dtrsm_("L", "U", "N", diag, &m2, n, alpha, &a[m1], m,
  892. &b[m1], ldb);
  893. dgemm_("N", "N", &m1, n, &m2, &c_b23, a, m, &b[m1],
  894. ldb, alpha, &b[b_offset], ldb);
  895. dtrsm_("L", "L", "T", diag, &m1, n, &c_b27, &a[m2], m,
  896. &b[b_offset], ldb);
  897. }
  898. }
  899. } else {
  900. /* SIDE = 'L', N is odd, and TRANSR = 'T' */
  901. if (lower) {
  902. /* SIDE ='L', N is odd, TRANSR = 'T', and UPLO = 'L' */
  903. if (notrans) {
  904. /* SIDE ='L', N is odd, TRANSR = 'T', UPLO = 'L', and */
  905. /* TRANS = 'N' */
  906. if (*m == 1) {
  907. dtrsm_("L", "U", "T", diag, &m1, n, alpha, a, &m1,
  908. &b[b_offset], ldb);
  909. } else {
  910. dtrsm_("L", "U", "T", diag, &m1, n, alpha, a, &m1,
  911. &b[b_offset], ldb);
  912. dgemm_("T", "N", &m2, n, &m1, &c_b23, &a[m1 * m1],
  913. &m1, &b[b_offset], ldb, alpha, &b[m1],
  914. ldb);
  915. dtrsm_("L", "L", "N", diag, &m2, n, &c_b27, &a[1],
  916. &m1, &b[m1], ldb);
  917. }
  918. } else {
  919. /* SIDE ='L', N is odd, TRANSR = 'T', UPLO = 'L', and */
  920. /* TRANS = 'T' */
  921. if (*m == 1) {
  922. dtrsm_("L", "U", "N", diag, &m1, n, alpha, a, &m1,
  923. &b[b_offset], ldb);
  924. } else {
  925. dtrsm_("L", "L", "T", diag, &m2, n, alpha, &a[1],
  926. &m1, &b[m1], ldb);
  927. dgemm_("N", "N", &m1, n, &m2, &c_b23, &a[m1 * m1],
  928. &m1, &b[m1], ldb, alpha, &b[b_offset],
  929. ldb);
  930. dtrsm_("L", "U", "N", diag, &m1, n, &c_b27, a, &
  931. m1, &b[b_offset], ldb);
  932. }
  933. }
  934. } else {
  935. /* SIDE ='L', N is odd, TRANSR = 'T', and UPLO = 'U' */
  936. if (! notrans) {
  937. /* SIDE ='L', N is odd, TRANSR = 'T', UPLO = 'U', and */
  938. /* TRANS = 'N' */
  939. dtrsm_("L", "U", "T", diag, &m1, n, alpha, &a[m2 * m2]
  940. , &m2, &b[b_offset], ldb);
  941. dgemm_("N", "N", &m2, n, &m1, &c_b23, a, &m2, &b[
  942. b_offset], ldb, alpha, &b[m1], ldb);
  943. dtrsm_("L", "L", "N", diag, &m2, n, &c_b27, &a[m1 *
  944. m2], &m2, &b[m1], ldb);
  945. } else {
  946. /* SIDE ='L', N is odd, TRANSR = 'T', UPLO = 'U', and */
  947. /* TRANS = 'T' */
  948. dtrsm_("L", "L", "T", diag, &m2, n, alpha, &a[m1 * m2]
  949. , &m2, &b[m1], ldb);
  950. dgemm_("T", "N", &m1, n, &m2, &c_b23, a, &m2, &b[m1],
  951. ldb, alpha, &b[b_offset], ldb);
  952. dtrsm_("L", "U", "N", diag, &m1, n, &c_b27, &a[m2 *
  953. m2], &m2, &b[b_offset], ldb);
  954. }
  955. }
  956. }
  957. } else {
  958. /* SIDE = 'L' and N is even */
  959. if (normaltransr) {
  960. /* SIDE = 'L', N is even, and TRANSR = 'N' */
  961. if (lower) {
  962. /* SIDE ='L', N is even, TRANSR = 'N', and UPLO = 'L' */
  963. if (notrans) {
  964. /* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'L', */
  965. /* and TRANS = 'N' */
  966. i__1 = *m + 1;
  967. dtrsm_("L", "L", "N", diag, &k, n, alpha, &a[1], &
  968. i__1, &b[b_offset], ldb);
  969. i__1 = *m + 1;
  970. dgemm_("N", "N", &k, n, &k, &c_b23, &a[k + 1], &i__1,
  971. &b[b_offset], ldb, alpha, &b[k], ldb);
  972. i__1 = *m + 1;
  973. dtrsm_("L", "U", "T", diag, &k, n, &c_b27, a, &i__1, &
  974. b[k], ldb);
  975. } else {
  976. /* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'L', */
  977. /* and TRANS = 'T' */
  978. i__1 = *m + 1;
  979. dtrsm_("L", "U", "N", diag, &k, n, alpha, a, &i__1, &
  980. b[k], ldb);
  981. i__1 = *m + 1;
  982. dgemm_("T", "N", &k, n, &k, &c_b23, &a[k + 1], &i__1,
  983. &b[k], ldb, alpha, &b[b_offset], ldb);
  984. i__1 = *m + 1;
  985. dtrsm_("L", "L", "T", diag, &k, n, &c_b27, &a[1], &
  986. i__1, &b[b_offset], ldb);
  987. }
  988. } else {
  989. /* SIDE ='L', N is even, TRANSR = 'N', and UPLO = 'U' */
  990. if (! notrans) {
  991. /* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'U', */
  992. /* and TRANS = 'N' */
  993. i__1 = *m + 1;
  994. dtrsm_("L", "L", "N", diag, &k, n, alpha, &a[k + 1], &
  995. i__1, &b[b_offset], ldb);
  996. i__1 = *m + 1;
  997. dgemm_("T", "N", &k, n, &k, &c_b23, a, &i__1, &b[
  998. b_offset], ldb, alpha, &b[k], ldb);
  999. i__1 = *m + 1;
  1000. dtrsm_("L", "U", "T", diag, &k, n, &c_b27, &a[k], &
  1001. i__1, &b[k], ldb);
  1002. } else {
  1003. /* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'U', */
  1004. /* and TRANS = 'T' */
  1005. i__1 = *m + 1;
  1006. dtrsm_("L", "U", "N", diag, &k, n, alpha, &a[k], &
  1007. i__1, &b[k], ldb);
  1008. i__1 = *m + 1;
  1009. dgemm_("N", "N", &k, n, &k, &c_b23, a, &i__1, &b[k],
  1010. ldb, alpha, &b[b_offset], ldb);
  1011. i__1 = *m + 1;
  1012. dtrsm_("L", "L", "T", diag, &k, n, &c_b27, &a[k + 1],
  1013. &i__1, &b[b_offset], ldb);
  1014. }
  1015. }
  1016. } else {
  1017. /* SIDE = 'L', N is even, and TRANSR = 'T' */
  1018. if (lower) {
  1019. /* SIDE ='L', N is even, TRANSR = 'T', and UPLO = 'L' */
  1020. if (notrans) {
  1021. /* SIDE ='L', N is even, TRANSR = 'T', UPLO = 'L', */
  1022. /* and TRANS = 'N' */
  1023. dtrsm_("L", "U", "T", diag, &k, n, alpha, &a[k], &k, &
  1024. b[b_offset], ldb);
  1025. dgemm_("T", "N", &k, n, &k, &c_b23, &a[k * (k + 1)], &
  1026. k, &b[b_offset], ldb, alpha, &b[k], ldb);
  1027. dtrsm_("L", "L", "N", diag, &k, n, &c_b27, a, &k, &b[
  1028. k], ldb);
  1029. } else {
  1030. /* SIDE ='L', N is even, TRANSR = 'T', UPLO = 'L', */
  1031. /* and TRANS = 'T' */
  1032. dtrsm_("L", "L", "T", diag, &k, n, alpha, a, &k, &b[k]
  1033. , ldb);
  1034. dgemm_("N", "N", &k, n, &k, &c_b23, &a[k * (k + 1)], &
  1035. k, &b[k], ldb, alpha, &b[b_offset], ldb);
  1036. dtrsm_("L", "U", "N", diag, &k, n, &c_b27, &a[k], &k,
  1037. &b[b_offset], ldb);
  1038. }
  1039. } else {
  1040. /* SIDE ='L', N is even, TRANSR = 'T', and UPLO = 'U' */
  1041. if (! notrans) {
  1042. /* SIDE ='L', N is even, TRANSR = 'T', UPLO = 'U', */
  1043. /* and TRANS = 'N' */
  1044. dtrsm_("L", "U", "T", diag, &k, n, alpha, &a[k * (k +
  1045. 1)], &k, &b[b_offset], ldb);
  1046. dgemm_("N", "N", &k, n, &k, &c_b23, a, &k, &b[
  1047. b_offset], ldb, alpha, &b[k], ldb);
  1048. dtrsm_("L", "L", "N", diag, &k, n, &c_b27, &a[k * k],
  1049. &k, &b[k], ldb);
  1050. } else {
  1051. /* SIDE ='L', N is even, TRANSR = 'T', UPLO = 'U', */
  1052. /* and TRANS = 'T' */
  1053. dtrsm_("L", "L", "T", diag, &k, n, alpha, &a[k * k], &
  1054. k, &b[k], ldb);
  1055. dgemm_("T", "N", &k, n, &k, &c_b23, a, &k, &b[k], ldb,
  1056. alpha, &b[b_offset], ldb);
  1057. dtrsm_("L", "U", "N", diag, &k, n, &c_b27, &a[k * (k
  1058. + 1)], &k, &b[b_offset], ldb);
  1059. }
  1060. }
  1061. }
  1062. }
  1063. } else {
  1064. /* SIDE = 'R' */
  1065. /* A is N-by-N. */
  1066. /* If N is odd, set NISODD = .TRUE., and N1 and N2. */
  1067. /* If N is even, NISODD = .FALSE., and K. */
  1068. if (*n % 2 == 0) {
  1069. nisodd = FALSE_;
  1070. k = *n / 2;
  1071. } else {
  1072. nisodd = TRUE_;
  1073. if (lower) {
  1074. n2 = *n / 2;
  1075. n1 = *n - n2;
  1076. } else {
  1077. n1 = *n / 2;
  1078. n2 = *n - n1;
  1079. }
  1080. }
  1081. if (nisodd) {
  1082. /* SIDE = 'R' and N is odd */
  1083. if (normaltransr) {
  1084. /* SIDE = 'R', N is odd, and TRANSR = 'N' */
  1085. if (lower) {
  1086. /* SIDE ='R', N is odd, TRANSR = 'N', and UPLO = 'L' */
  1087. if (notrans) {
  1088. /* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'L', and */
  1089. /* TRANS = 'N' */
  1090. dtrsm_("R", "U", "T", diag, m, &n2, alpha, &a[*n], n,
  1091. &b[n1 * b_dim1], ldb);
  1092. dgemm_("N", "N", m, &n1, &n2, &c_b23, &b[n1 * b_dim1],
  1093. ldb, &a[n1], n, alpha, b, ldb);
  1094. dtrsm_("R", "L", "N", diag, m, &n1, &c_b27, a, n, b,
  1095. ldb);
  1096. } else {
  1097. /* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'L', and */
  1098. /* TRANS = 'T' */
  1099. dtrsm_("R", "L", "T", diag, m, &n1, alpha, a, n, b,
  1100. ldb);
  1101. dgemm_("N", "T", m, &n2, &n1, &c_b23, b, ldb, &a[n1],
  1102. n, alpha, &b[n1 * b_dim1], ldb);
  1103. dtrsm_("R", "U", "N", diag, m, &n2, &c_b27, &a[*n], n,
  1104. &b[n1 * b_dim1], ldb);
  1105. }
  1106. } else {
  1107. /* SIDE ='R', N is odd, TRANSR = 'N', and UPLO = 'U' */
  1108. if (notrans) {
  1109. /* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'U', and */
  1110. /* TRANS = 'N' */
  1111. dtrsm_("R", "L", "T", diag, m, &n1, alpha, &a[n2], n,
  1112. b, ldb);
  1113. dgemm_("N", "N", m, &n2, &n1, &c_b23, b, ldb, a, n,
  1114. alpha, &b[n1 * b_dim1], ldb);
  1115. dtrsm_("R", "U", "N", diag, m, &n2, &c_b27, &a[n1], n,
  1116. &b[n1 * b_dim1], ldb);
  1117. } else {
  1118. /* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'U', and */
  1119. /* TRANS = 'T' */
  1120. dtrsm_("R", "U", "T", diag, m, &n2, alpha, &a[n1], n,
  1121. &b[n1 * b_dim1], ldb);
  1122. dgemm_("N", "T", m, &n1, &n2, &c_b23, &b[n1 * b_dim1],
  1123. ldb, a, n, alpha, b, ldb);
  1124. dtrsm_("R", "L", "N", diag, m, &n1, &c_b27, &a[n2], n,
  1125. b, ldb);
  1126. }
  1127. }
  1128. } else {
  1129. /* SIDE = 'R', N is odd, and TRANSR = 'T' */
  1130. if (lower) {
  1131. /* SIDE ='R', N is odd, TRANSR = 'T', and UPLO = 'L' */
  1132. if (notrans) {
  1133. /* SIDE ='R', N is odd, TRANSR = 'T', UPLO = 'L', and */
  1134. /* TRANS = 'N' */
  1135. dtrsm_("R", "L", "N", diag, m, &n2, alpha, &a[1], &n1,
  1136. &b[n1 * b_dim1], ldb);
  1137. dgemm_("N", "T", m, &n1, &n2, &c_b23, &b[n1 * b_dim1],
  1138. ldb, &a[n1 * n1], &n1, alpha, b, ldb);
  1139. dtrsm_("R", "U", "T", diag, m, &n1, &c_b27, a, &n1, b,
  1140. ldb);
  1141. } else {
  1142. /* SIDE ='R', N is odd, TRANSR = 'T', UPLO = 'L', and */
  1143. /* TRANS = 'T' */
  1144. dtrsm_("R", "U", "N", diag, m, &n1, alpha, a, &n1, b,
  1145. ldb);
  1146. dgemm_("N", "N", m, &n2, &n1, &c_b23, b, ldb, &a[n1 *
  1147. n1], &n1, alpha, &b[n1 * b_dim1], ldb);
  1148. dtrsm_("R", "L", "T", diag, m, &n2, &c_b27, &a[1], &
  1149. n1, &b[n1 * b_dim1], ldb);
  1150. }
  1151. } else {
  1152. /* SIDE ='R', N is odd, TRANSR = 'T', and UPLO = 'U' */
  1153. if (notrans) {
  1154. /* SIDE ='R', N is odd, TRANSR = 'T', UPLO = 'U', and */
  1155. /* TRANS = 'N' */
  1156. dtrsm_("R", "U", "N", diag, m, &n1, alpha, &a[n2 * n2]
  1157. , &n2, b, ldb);
  1158. dgemm_("N", "T", m, &n2, &n1, &c_b23, b, ldb, a, &n2,
  1159. alpha, &b[n1 * b_dim1], ldb);
  1160. dtrsm_("R", "L", "T", diag, m, &n2, &c_b27, &a[n1 *
  1161. n2], &n2, &b[n1 * b_dim1], ldb);
  1162. } else {
  1163. /* SIDE ='R', N is odd, TRANSR = 'T', UPLO = 'U', and */
  1164. /* TRANS = 'T' */
  1165. dtrsm_("R", "L", "N", diag, m, &n2, alpha, &a[n1 * n2]
  1166. , &n2, &b[n1 * b_dim1], ldb);
  1167. dgemm_("N", "N", m, &n1, &n2, &c_b23, &b[n1 * b_dim1],
  1168. ldb, a, &n2, alpha, b, ldb);
  1169. dtrsm_("R", "U", "T", diag, m, &n1, &c_b27, &a[n2 *
  1170. n2], &n2, b, ldb);
  1171. }
  1172. }
  1173. }
  1174. } else {
  1175. /* SIDE = 'R' and N is even */
  1176. if (normaltransr) {
  1177. /* SIDE = 'R', N is even, and TRANSR = 'N' */
  1178. if (lower) {
  1179. /* SIDE ='R', N is even, TRANSR = 'N', and UPLO = 'L' */
  1180. if (notrans) {
  1181. /* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'L', */
  1182. /* and TRANS = 'N' */
  1183. i__1 = *n + 1;
  1184. dtrsm_("R", "U", "T", diag, m, &k, alpha, a, &i__1, &
  1185. b[k * b_dim1], ldb);
  1186. i__1 = *n + 1;
  1187. dgemm_("N", "N", m, &k, &k, &c_b23, &b[k * b_dim1],
  1188. ldb, &a[k + 1], &i__1, alpha, b, ldb);
  1189. i__1 = *n + 1;
  1190. dtrsm_("R", "L", "N", diag, m, &k, &c_b27, &a[1], &
  1191. i__1, b, ldb);
  1192. } else {
  1193. /* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'L', */
  1194. /* and TRANS = 'T' */
  1195. i__1 = *n + 1;
  1196. dtrsm_("R", "L", "T", diag, m, &k, alpha, &a[1], &
  1197. i__1, b, ldb);
  1198. i__1 = *n + 1;
  1199. dgemm_("N", "T", m, &k, &k, &c_b23, b, ldb, &a[k + 1],
  1200. &i__1, alpha, &b[k * b_dim1], ldb);
  1201. i__1 = *n + 1;
  1202. dtrsm_("R", "U", "N", diag, m, &k, &c_b27, a, &i__1, &
  1203. b[k * b_dim1], ldb);
  1204. }
  1205. } else {
  1206. /* SIDE ='R', N is even, TRANSR = 'N', and UPLO = 'U' */
  1207. if (notrans) {
  1208. /* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'U', */
  1209. /* and TRANS = 'N' */
  1210. i__1 = *n + 1;
  1211. dtrsm_("R", "L", "T", diag, m, &k, alpha, &a[k + 1], &
  1212. i__1, b, ldb);
  1213. i__1 = *n + 1;
  1214. dgemm_("N", "N", m, &k, &k, &c_b23, b, ldb, a, &i__1,
  1215. alpha, &b[k * b_dim1], ldb);
  1216. i__1 = *n + 1;
  1217. dtrsm_("R", "U", "N", diag, m, &k, &c_b27, &a[k], &
  1218. i__1, &b[k * b_dim1], ldb);
  1219. } else {
  1220. /* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'U', */
  1221. /* and TRANS = 'T' */
  1222. i__1 = *n + 1;
  1223. dtrsm_("R", "U", "T", diag, m, &k, alpha, &a[k], &
  1224. i__1, &b[k * b_dim1], ldb);
  1225. i__1 = *n + 1;
  1226. dgemm_("N", "T", m, &k, &k, &c_b23, &b[k * b_dim1],
  1227. ldb, a, &i__1, alpha, b, ldb);
  1228. i__1 = *n + 1;
  1229. dtrsm_("R", "L", "N", diag, m, &k, &c_b27, &a[k + 1],
  1230. &i__1, b, ldb);
  1231. }
  1232. }
  1233. } else {
  1234. /* SIDE = 'R', N is even, and TRANSR = 'T' */
  1235. if (lower) {
  1236. /* SIDE ='R', N is even, TRANSR = 'T', and UPLO = 'L' */
  1237. if (notrans) {
  1238. /* SIDE ='R', N is even, TRANSR = 'T', UPLO = 'L', */
  1239. /* and TRANS = 'N' */
  1240. dtrsm_("R", "L", "N", diag, m, &k, alpha, a, &k, &b[k
  1241. * b_dim1], ldb);
  1242. dgemm_("N", "T", m, &k, &k, &c_b23, &b[k * b_dim1],
  1243. ldb, &a[(k + 1) * k], &k, alpha, b, ldb);
  1244. dtrsm_("R", "U", "T", diag, m, &k, &c_b27, &a[k], &k,
  1245. b, ldb);
  1246. } else {
  1247. /* SIDE ='R', N is even, TRANSR = 'T', UPLO = 'L', */
  1248. /* and TRANS = 'T' */
  1249. dtrsm_("R", "U", "N", diag, m, &k, alpha, &a[k], &k,
  1250. b, ldb);
  1251. dgemm_("N", "N", m, &k, &k, &c_b23, b, ldb, &a[(k + 1)
  1252. * k], &k, alpha, &b[k * b_dim1], ldb);
  1253. dtrsm_("R", "L", "T", diag, m, &k, &c_b27, a, &k, &b[
  1254. k * b_dim1], ldb);
  1255. }
  1256. } else {
  1257. /* SIDE ='R', N is even, TRANSR = 'T', and UPLO = 'U' */
  1258. if (notrans) {
  1259. /* SIDE ='R', N is even, TRANSR = 'T', UPLO = 'U', */
  1260. /* and TRANS = 'N' */
  1261. dtrsm_("R", "U", "N", diag, m, &k, alpha, &a[(k + 1) *
  1262. k], &k, b, ldb);
  1263. dgemm_("N", "T", m, &k, &k, &c_b23, b, ldb, a, &k,
  1264. alpha, &b[k * b_dim1], ldb);
  1265. dtrsm_("R", "L", "T", diag, m, &k, &c_b27, &a[k * k],
  1266. &k, &b[k * b_dim1], ldb);
  1267. } else {
  1268. /* SIDE ='R', N is even, TRANSR = 'T', UPLO = 'U', */
  1269. /* and TRANS = 'T' */
  1270. dtrsm_("R", "L", "N", diag, m, &k, alpha, &a[k * k], &
  1271. k, &b[k * b_dim1], ldb);
  1272. dgemm_("N", "N", m, &k, &k, &c_b23, &b[k * b_dim1],
  1273. ldb, a, &k, alpha, b, ldb);
  1274. dtrsm_("R", "U", "T", diag, m, &k, &c_b27, &a[(k + 1)
  1275. * k], &k, b, ldb);
  1276. }
  1277. }
  1278. }
  1279. }
  1280. }
  1281. return 0;
  1282. /* End of DTFSM */
  1283. } /* dtfsm_ */