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dtbcon.c 19 kB

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  1. /* f2c.h -- Standard Fortran to C header file */
  2. /** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed."
  3. - From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
  4. #ifndef F2C_INCLUDE
  5. #define F2C_INCLUDE
  6. #include <math.h>
  7. #include <stdlib.h>
  8. #include <string.h>
  9. #include <stdio.h>
  10. #include <complex.h>
  11. #ifdef complex
  12. #undef complex
  13. #endif
  14. #ifdef I
  15. #undef I
  16. #endif
  17. #if defined(_WIN64)
  18. typedef long long BLASLONG;
  19. typedef unsigned long long BLASULONG;
  20. #else
  21. typedef long BLASLONG;
  22. typedef unsigned long BLASULONG;
  23. #endif
  24. #ifdef LAPACK_ILP64
  25. typedef BLASLONG blasint;
  26. #if defined(_WIN64)
  27. #define blasabs(x) llabs(x)
  28. #else
  29. #define blasabs(x) labs(x)
  30. #endif
  31. #else
  32. typedef int blasint;
  33. #define blasabs(x) abs(x)
  34. #endif
  35. typedef blasint integer;
  36. typedef unsigned int uinteger;
  37. typedef char *address;
  38. typedef short int shortint;
  39. typedef float real;
  40. typedef double doublereal;
  41. typedef struct { real r, i; } complex;
  42. typedef struct { doublereal r, i; } doublecomplex;
  43. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  44. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  45. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  46. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  47. #define pCf(z) (*_pCf(z))
  48. #define pCd(z) (*_pCd(z))
  49. typedef int logical;
  50. typedef short int shortlogical;
  51. typedef char logical1;
  52. typedef char integer1;
  53. #define TRUE_ (1)
  54. #define FALSE_ (0)
  55. /* Extern is for use with -E */
  56. #ifndef Extern
  57. #define Extern extern
  58. #endif
  59. /* I/O stuff */
  60. typedef int flag;
  61. typedef int ftnlen;
  62. typedef int ftnint;
  63. /*external read, write*/
  64. typedef struct
  65. { flag cierr;
  66. ftnint ciunit;
  67. flag ciend;
  68. char *cifmt;
  69. ftnint cirec;
  70. } cilist;
  71. /*internal read, write*/
  72. typedef struct
  73. { flag icierr;
  74. char *iciunit;
  75. flag iciend;
  76. char *icifmt;
  77. ftnint icirlen;
  78. ftnint icirnum;
  79. } icilist;
  80. /*open*/
  81. typedef struct
  82. { flag oerr;
  83. ftnint ounit;
  84. char *ofnm;
  85. ftnlen ofnmlen;
  86. char *osta;
  87. char *oacc;
  88. char *ofm;
  89. ftnint orl;
  90. char *oblnk;
  91. } olist;
  92. /*close*/
  93. typedef struct
  94. { flag cerr;
  95. ftnint cunit;
  96. char *csta;
  97. } cllist;
  98. /*rewind, backspace, endfile*/
  99. typedef struct
  100. { flag aerr;
  101. ftnint aunit;
  102. } alist;
  103. /* inquire */
  104. typedef struct
  105. { flag inerr;
  106. ftnint inunit;
  107. char *infile;
  108. ftnlen infilen;
  109. ftnint *inex; /*parameters in standard's order*/
  110. ftnint *inopen;
  111. ftnint *innum;
  112. ftnint *innamed;
  113. char *inname;
  114. ftnlen innamlen;
  115. char *inacc;
  116. ftnlen inacclen;
  117. char *inseq;
  118. ftnlen inseqlen;
  119. char *indir;
  120. ftnlen indirlen;
  121. char *infmt;
  122. ftnlen infmtlen;
  123. char *inform;
  124. ftnint informlen;
  125. char *inunf;
  126. ftnlen inunflen;
  127. ftnint *inrecl;
  128. ftnint *innrec;
  129. char *inblank;
  130. ftnlen inblanklen;
  131. } inlist;
  132. #define VOID void
  133. union Multitype { /* for multiple entry points */
  134. integer1 g;
  135. shortint h;
  136. integer i;
  137. /* longint j; */
  138. real r;
  139. doublereal d;
  140. complex c;
  141. doublecomplex z;
  142. };
  143. typedef union Multitype Multitype;
  144. struct Vardesc { /* for Namelist */
  145. char *name;
  146. char *addr;
  147. ftnlen *dims;
  148. int type;
  149. };
  150. typedef struct Vardesc Vardesc;
  151. struct Namelist {
  152. char *name;
  153. Vardesc **vars;
  154. int nvars;
  155. };
  156. typedef struct Namelist Namelist;
  157. #define abs(x) ((x) >= 0 ? (x) : -(x))
  158. #define dabs(x) (fabs(x))
  159. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  160. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  161. #define dmin(a,b) (f2cmin(a,b))
  162. #define dmax(a,b) (f2cmax(a,b))
  163. #define bit_test(a,b) ((a) >> (b) & 1)
  164. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  165. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  166. #define abort_() { sig_die("Fortran abort routine called", 1); }
  167. #define c_abs(z) (cabsf(Cf(z)))
  168. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  169. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  170. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  171. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  172. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  173. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  174. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  175. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  176. #define d_abs(x) (fabs(*(x)))
  177. #define d_acos(x) (acos(*(x)))
  178. #define d_asin(x) (asin(*(x)))
  179. #define d_atan(x) (atan(*(x)))
  180. #define d_atn2(x, y) (atan2(*(x),*(y)))
  181. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  182. #define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
  183. #define d_cos(x) (cos(*(x)))
  184. #define d_cosh(x) (cosh(*(x)))
  185. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  186. #define d_exp(x) (exp(*(x)))
  187. #define d_imag(z) (cimag(Cd(z)))
  188. #define r_imag(z) (cimag(Cf(z)))
  189. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  190. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  191. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  192. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  193. #define d_log(x) (log(*(x)))
  194. #define d_mod(x, y) (fmod(*(x), *(y)))
  195. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  196. #define d_nint(x) u_nint(*(x))
  197. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  198. #define d_sign(a,b) u_sign(*(a),*(b))
  199. #define r_sign(a,b) u_sign(*(a),*(b))
  200. #define d_sin(x) (sin(*(x)))
  201. #define d_sinh(x) (sinh(*(x)))
  202. #define d_sqrt(x) (sqrt(*(x)))
  203. #define d_tan(x) (tan(*(x)))
  204. #define d_tanh(x) (tanh(*(x)))
  205. #define i_abs(x) abs(*(x))
  206. #define i_dnnt(x) ((integer)u_nint(*(x)))
  207. #define i_len(s, n) (n)
  208. #define i_nint(x) ((integer)u_nint(*(x)))
  209. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  210. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  211. #define pow_si(B,E) spow_ui(*(B),*(E))
  212. #define pow_ri(B,E) spow_ui(*(B),*(E))
  213. #define pow_di(B,E) dpow_ui(*(B),*(E))
  214. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  215. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  216. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  217. #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
  218. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  219. #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
  220. #define sig_die(s, kill) { exit(1); }
  221. #define s_stop(s, n) {exit(0);}
  222. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  223. #define z_abs(z) (cabs(Cd(z)))
  224. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  225. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  226. #define myexit_() break;
  227. #define mycycle() continue;
  228. #define myceiling(w) {ceil(w)}
  229. #define myhuge(w) {HUGE_VAL}
  230. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  231. #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  232. /* procedure parameter types for -A and -C++ */
  233. #define F2C_proc_par_types 1
  234. #ifdef __cplusplus
  235. typedef logical (*L_fp)(...);
  236. #else
  237. typedef logical (*L_fp)();
  238. #endif
  239. static float spow_ui(float x, integer n) {
  240. float pow=1.0; unsigned long int u;
  241. if(n != 0) {
  242. if(n < 0) n = -n, x = 1/x;
  243. for(u = n; ; ) {
  244. if(u & 01) pow *= x;
  245. if(u >>= 1) x *= x;
  246. else break;
  247. }
  248. }
  249. return pow;
  250. }
  251. static double dpow_ui(double x, integer n) {
  252. double pow=1.0; unsigned long int u;
  253. if(n != 0) {
  254. if(n < 0) n = -n, x = 1/x;
  255. for(u = n; ; ) {
  256. if(u & 01) pow *= x;
  257. if(u >>= 1) x *= x;
  258. else break;
  259. }
  260. }
  261. return pow;
  262. }
  263. static _Complex float cpow_ui(_Complex float x, integer n) {
  264. _Complex float pow=1.0; unsigned long int u;
  265. if(n != 0) {
  266. if(n < 0) n = -n, x = 1/x;
  267. for(u = n; ; ) {
  268. if(u & 01) pow *= x;
  269. if(u >>= 1) x *= x;
  270. else break;
  271. }
  272. }
  273. return pow;
  274. }
  275. static _Complex double zpow_ui(_Complex double x, integer n) {
  276. _Complex double pow=1.0; unsigned long int u;
  277. if(n != 0) {
  278. if(n < 0) n = -n, x = 1/x;
  279. for(u = n; ; ) {
  280. if(u & 01) pow *= x;
  281. if(u >>= 1) x *= x;
  282. else break;
  283. }
  284. }
  285. return pow;
  286. }
  287. static integer pow_ii(integer x, integer n) {
  288. integer pow; unsigned long int u;
  289. if (n <= 0) {
  290. if (n == 0 || x == 1) pow = 1;
  291. else if (x != -1) pow = x == 0 ? 1/x : 0;
  292. else n = -n;
  293. }
  294. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  295. u = n;
  296. for(pow = 1; ; ) {
  297. if(u & 01) pow *= x;
  298. if(u >>= 1) x *= x;
  299. else break;
  300. }
  301. }
  302. return pow;
  303. }
  304. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  305. {
  306. double m; integer i, mi;
  307. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  308. if (w[i-1]>m) mi=i ,m=w[i-1];
  309. return mi-s+1;
  310. }
  311. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  312. {
  313. float m; integer i, mi;
  314. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  315. if (w[i-1]>m) mi=i ,m=w[i-1];
  316. return mi-s+1;
  317. }
  318. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  319. integer n = *n_, incx = *incx_, incy = *incy_, i;
  320. _Complex float zdotc = 0.0;
  321. if (incx == 1 && incy == 1) {
  322. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  323. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  324. }
  325. } else {
  326. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  327. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  328. }
  329. }
  330. pCf(z) = zdotc;
  331. }
  332. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  333. integer n = *n_, incx = *incx_, incy = *incy_, i;
  334. _Complex double zdotc = 0.0;
  335. if (incx == 1 && incy == 1) {
  336. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  337. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  338. }
  339. } else {
  340. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  341. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  342. }
  343. }
  344. pCd(z) = zdotc;
  345. }
  346. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  347. integer n = *n_, incx = *incx_, incy = *incy_, i;
  348. _Complex float zdotc = 0.0;
  349. if (incx == 1 && incy == 1) {
  350. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  351. zdotc += Cf(&x[i]) * Cf(&y[i]);
  352. }
  353. } else {
  354. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  355. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  356. }
  357. }
  358. pCf(z) = zdotc;
  359. }
  360. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  361. integer n = *n_, incx = *incx_, incy = *incy_, i;
  362. _Complex double zdotc = 0.0;
  363. if (incx == 1 && incy == 1) {
  364. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  365. zdotc += Cd(&x[i]) * Cd(&y[i]);
  366. }
  367. } else {
  368. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  369. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  370. }
  371. }
  372. pCd(z) = zdotc;
  373. }
  374. #endif
  375. /* -- translated by f2c (version 20000121).
  376. You must link the resulting object file with the libraries:
  377. -lf2c -lm (in that order)
  378. */
  379. /* Table of constant values */
  380. static integer c__1 = 1;
  381. /* > \brief \b DTBCON */
  382. /* =========== DOCUMENTATION =========== */
  383. /* Online html documentation available at */
  384. /* http://www.netlib.org/lapack/explore-html/ */
  385. /* > \htmlonly */
  386. /* > Download DTBCON + dependencies */
  387. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtbcon.
  388. f"> */
  389. /* > [TGZ]</a> */
  390. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtbcon.
  391. f"> */
  392. /* > [ZIP]</a> */
  393. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtbcon.
  394. f"> */
  395. /* > [TXT]</a> */
  396. /* > \endhtmlonly */
  397. /* Definition: */
  398. /* =========== */
  399. /* SUBROUTINE DTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, */
  400. /* IWORK, INFO ) */
  401. /* CHARACTER DIAG, NORM, UPLO */
  402. /* INTEGER INFO, KD, LDAB, N */
  403. /* DOUBLE PRECISION RCOND */
  404. /* INTEGER IWORK( * ) */
  405. /* DOUBLE PRECISION AB( LDAB, * ), WORK( * ) */
  406. /* > \par Purpose: */
  407. /* ============= */
  408. /* > */
  409. /* > \verbatim */
  410. /* > */
  411. /* > DTBCON estimates the reciprocal of the condition number of a */
  412. /* > triangular band matrix A, in either the 1-norm or the infinity-norm. */
  413. /* > */
  414. /* > The norm of A is computed and an estimate is obtained for */
  415. /* > norm(inv(A)), then the reciprocal of the condition number is */
  416. /* > computed as */
  417. /* > RCOND = 1 / ( norm(A) * norm(inv(A)) ). */
  418. /* > \endverbatim */
  419. /* Arguments: */
  420. /* ========== */
  421. /* > \param[in] NORM */
  422. /* > \verbatim */
  423. /* > NORM is CHARACTER*1 */
  424. /* > Specifies whether the 1-norm condition number or the */
  425. /* > infinity-norm condition number is required: */
  426. /* > = '1' or 'O': 1-norm; */
  427. /* > = 'I': Infinity-norm. */
  428. /* > \endverbatim */
  429. /* > */
  430. /* > \param[in] UPLO */
  431. /* > \verbatim */
  432. /* > UPLO is CHARACTER*1 */
  433. /* > = 'U': A is upper triangular; */
  434. /* > = 'L': A is lower triangular. */
  435. /* > \endverbatim */
  436. /* > */
  437. /* > \param[in] DIAG */
  438. /* > \verbatim */
  439. /* > DIAG is CHARACTER*1 */
  440. /* > = 'N': A is non-unit triangular; */
  441. /* > = 'U': A is unit triangular. */
  442. /* > \endverbatim */
  443. /* > */
  444. /* > \param[in] N */
  445. /* > \verbatim */
  446. /* > N is INTEGER */
  447. /* > The order of the matrix A. N >= 0. */
  448. /* > \endverbatim */
  449. /* > */
  450. /* > \param[in] KD */
  451. /* > \verbatim */
  452. /* > KD is INTEGER */
  453. /* > The number of superdiagonals or subdiagonals of the */
  454. /* > triangular band matrix A. KD >= 0. */
  455. /* > \endverbatim */
  456. /* > */
  457. /* > \param[in] AB */
  458. /* > \verbatim */
  459. /* > AB is DOUBLE PRECISION array, dimension (LDAB,N) */
  460. /* > The upper or lower triangular band matrix A, stored in the */
  461. /* > first kd+1 rows of the array. The j-th column of A is stored */
  462. /* > in the j-th column of the array AB as follows: */
  463. /* > if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */
  464. /* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+kd). */
  465. /* > If DIAG = 'U', the diagonal elements of A are not referenced */
  466. /* > and are assumed to be 1. */
  467. /* > \endverbatim */
  468. /* > */
  469. /* > \param[in] LDAB */
  470. /* > \verbatim */
  471. /* > LDAB is INTEGER */
  472. /* > The leading dimension of the array AB. LDAB >= KD+1. */
  473. /* > \endverbatim */
  474. /* > */
  475. /* > \param[out] RCOND */
  476. /* > \verbatim */
  477. /* > RCOND is DOUBLE PRECISION */
  478. /* > The reciprocal of the condition number of the matrix A, */
  479. /* > computed as RCOND = 1/(norm(A) * norm(inv(A))). */
  480. /* > \endverbatim */
  481. /* > */
  482. /* > \param[out] WORK */
  483. /* > \verbatim */
  484. /* > WORK is DOUBLE PRECISION array, dimension (3*N) */
  485. /* > \endverbatim */
  486. /* > */
  487. /* > \param[out] IWORK */
  488. /* > \verbatim */
  489. /* > IWORK is INTEGER array, dimension (N) */
  490. /* > \endverbatim */
  491. /* > */
  492. /* > \param[out] INFO */
  493. /* > \verbatim */
  494. /* > INFO is INTEGER */
  495. /* > = 0: successful exit */
  496. /* > < 0: if INFO = -i, the i-th argument had an illegal value */
  497. /* > \endverbatim */
  498. /* Authors: */
  499. /* ======== */
  500. /* > \author Univ. of Tennessee */
  501. /* > \author Univ. of California Berkeley */
  502. /* > \author Univ. of Colorado Denver */
  503. /* > \author NAG Ltd. */
  504. /* > \date December 2016 */
  505. /* > \ingroup doubleOTHERcomputational */
  506. /* ===================================================================== */
  507. /* Subroutine */ int dtbcon_(char *norm, char *uplo, char *diag, integer *n,
  508. integer *kd, doublereal *ab, integer *ldab, doublereal *rcond,
  509. doublereal *work, integer *iwork, integer *info)
  510. {
  511. /* System generated locals */
  512. integer ab_dim1, ab_offset, i__1;
  513. doublereal d__1;
  514. /* Local variables */
  515. integer kase, kase1;
  516. doublereal scale;
  517. extern logical lsame_(char *, char *);
  518. integer isave[3];
  519. extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *,
  520. integer *);
  521. doublereal anorm;
  522. logical upper;
  523. doublereal xnorm;
  524. extern /* Subroutine */ int dlacn2_(integer *, doublereal *, doublereal *,
  525. integer *, doublereal *, integer *, integer *);
  526. extern doublereal dlamch_(char *);
  527. integer ix;
  528. extern integer idamax_(integer *, doublereal *, integer *);
  529. extern doublereal dlantb_(char *, char *, char *, integer *, integer *,
  530. doublereal *, integer *, doublereal *);
  531. extern /* Subroutine */ int dlatbs_(char *, char *, char *, char *,
  532. integer *, integer *, doublereal *, integer *, doublereal *,
  533. doublereal *, doublereal *, integer *), xerbla_(char *, integer *, ftnlen);
  534. doublereal ainvnm;
  535. logical onenrm;
  536. char normin[1];
  537. doublereal smlnum;
  538. logical nounit;
  539. /* -- LAPACK computational routine (version 3.7.0) -- */
  540. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  541. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  542. /* December 2016 */
  543. /* ===================================================================== */
  544. /* Test the input parameters. */
  545. /* Parameter adjustments */
  546. ab_dim1 = *ldab;
  547. ab_offset = 1 + ab_dim1 * 1;
  548. ab -= ab_offset;
  549. --work;
  550. --iwork;
  551. /* Function Body */
  552. *info = 0;
  553. upper = lsame_(uplo, "U");
  554. onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");
  555. nounit = lsame_(diag, "N");
  556. if (! onenrm && ! lsame_(norm, "I")) {
  557. *info = -1;
  558. } else if (! upper && ! lsame_(uplo, "L")) {
  559. *info = -2;
  560. } else if (! nounit && ! lsame_(diag, "U")) {
  561. *info = -3;
  562. } else if (*n < 0) {
  563. *info = -4;
  564. } else if (*kd < 0) {
  565. *info = -5;
  566. } else if (*ldab < *kd + 1) {
  567. *info = -7;
  568. }
  569. if (*info != 0) {
  570. i__1 = -(*info);
  571. xerbla_("DTBCON", &i__1, (ftnlen)6);
  572. return 0;
  573. }
  574. /* Quick return if possible */
  575. if (*n == 0) {
  576. *rcond = 1.;
  577. return 0;
  578. }
  579. *rcond = 0.;
  580. smlnum = dlamch_("Safe minimum") * (doublereal) f2cmax(1,*n);
  581. /* Compute the norm of the triangular matrix A. */
  582. anorm = dlantb_(norm, uplo, diag, n, kd, &ab[ab_offset], ldab, &work[1]);
  583. /* Continue only if ANORM > 0. */
  584. if (anorm > 0.) {
  585. /* Estimate the norm of the inverse of A. */
  586. ainvnm = 0.;
  587. *(unsigned char *)normin = 'N';
  588. if (onenrm) {
  589. kase1 = 1;
  590. } else {
  591. kase1 = 2;
  592. }
  593. kase = 0;
  594. L10:
  595. dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave);
  596. if (kase != 0) {
  597. if (kase == kase1) {
  598. /* Multiply by inv(A). */
  599. dlatbs_(uplo, "No transpose", diag, normin, n, kd, &ab[
  600. ab_offset], ldab, &work[1], &scale, &work[(*n << 1) +
  601. 1], info)
  602. ;
  603. } else {
  604. /* Multiply by inv(A**T). */
  605. dlatbs_(uplo, "Transpose", diag, normin, n, kd, &ab[ab_offset]
  606. , ldab, &work[1], &scale, &work[(*n << 1) + 1], info);
  607. }
  608. *(unsigned char *)normin = 'Y';
  609. /* Multiply by 1/SCALE if doing so will not cause overflow. */
  610. if (scale != 1.) {
  611. ix = idamax_(n, &work[1], &c__1);
  612. xnorm = (d__1 = work[ix], abs(d__1));
  613. if (scale < xnorm * smlnum || scale == 0.) {
  614. goto L20;
  615. }
  616. drscl_(n, &scale, &work[1], &c__1);
  617. }
  618. goto L10;
  619. }
  620. /* Compute the estimate of the reciprocal condition number. */
  621. if (ainvnm != 0.) {
  622. *rcond = 1. / anorm / ainvnm;
  623. }
  624. }
  625. L20:
  626. return 0;
  627. /* End of DTBCON */
  628. } /* dtbcon_ */