14 typedef long long BLASLONG;
15 typedef unsigned long long BLASULONG;
17 typedef long BLASLONG;
18 typedef unsigned long BLASULONG;
22 typedef BLASLONG blasint;
24 #define blasabs(x) llabs(x)
26 #define blasabs(x) labs(x)
30 #define blasabs(x) abs(x)
33 typedef blasint integer;
35 typedef unsigned int uinteger;
36 typedef char *address;
37 typedef short int shortint;
39 typedef double doublereal;
40 typedef struct { real r, i; } complex;
41 typedef struct { doublereal r, i; } doublecomplex;
43 static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
44 static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
45 static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
46 static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
48 static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
49 static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
50 static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
51 static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
53 #define pCf(z) (*_pCf(z))
54 #define pCd(z) (*_pCd(z))
56 typedef short int shortlogical;
57 typedef char logical1;
58 typedef char integer1;
63 /* Extern is for use with -E */
74 /*external read, write*/
83 /*internal read, write*/
113 /*rewind, backspace, endfile*/
125 ftnint *inex; /*parameters in standard's order*/
151 union Multitype { /* for multiple entry points */
162 typedef union Multitype Multitype;
164 struct Vardesc { /* for Namelist */
170 typedef struct Vardesc Vardesc;
177 typedef struct Namelist Namelist;
179 #define abs(x) ((x) >= 0 ? (x) : -(x))
180 #define dabs(x) (fabs(x))
181 #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
182 #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
183 #define dmin(a,b) (f2cmin(a,b))
184 #define dmax(a,b) (f2cmax(a,b))
185 #define bit_test(a,b) ((a) >> (b) & 1)
186 #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
187 #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
189 #define abort_() { sig_die("Fortran abort routine called", 1); }
190 #define c_abs(z) (cabsf(Cf(z)))
191 #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
193 #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]);}
194 #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]);}
196 #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
197 #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
199 #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
200 #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
201 #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
202 //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
203 #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
204 #define d_abs(x) (fabs(*(x)))
205 #define d_acos(x) (acos(*(x)))
206 #define d_asin(x) (asin(*(x)))
207 #define d_atan(x) (atan(*(x)))
208 #define d_atn2(x, y) (atan2(*(x),*(y)))
209 #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
210 #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
211 #define d_cos(x) (cos(*(x)))
212 #define d_cosh(x) (cosh(*(x)))
213 #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
214 #define d_exp(x) (exp(*(x)))
215 #define d_imag(z) (cimag(Cd(z)))
216 #define r_imag(z) (cimagf(Cf(z)))
217 #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
218 #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
219 #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
220 #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
221 #define d_log(x) (log(*(x)))
222 #define d_mod(x, y) (fmod(*(x), *(y)))
223 #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
224 #define d_nint(x) u_nint(*(x))
225 #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
226 #define d_sign(a,b) u_sign(*(a),*(b))
227 #define r_sign(a,b) u_sign(*(a),*(b))
228 #define d_sin(x) (sin(*(x)))
229 #define d_sinh(x) (sinh(*(x)))
230 #define d_sqrt(x) (sqrt(*(x)))
231 #define d_tan(x) (tan(*(x)))
232 #define d_tanh(x) (tanh(*(x)))
233 #define i_abs(x) abs(*(x))
234 #define i_dnnt(x) ((integer)u_nint(*(x)))
235 #define i_len(s, n) (n)
236 #define i_nint(x) ((integer)u_nint(*(x)))
237 #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
238 #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
239 #define pow_si(B,E) spow_ui(*(B),*(E))
240 #define pow_ri(B,E) spow_ui(*(B),*(E))
241 #define pow_di(B,E) dpow_ui(*(B),*(E))
242 #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
243 #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
244 #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
245 #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++ = ' '; }
246 #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
247 #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]; }
248 #define sig_die(s, kill) { exit(1); }
249 #define s_stop(s, n) {exit(0);}
250 static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
251 #define z_abs(z) (cabs(Cd(z)))
252 #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
253 #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
254 #define myexit_() break;
255 #define mycycle() continue;
256 #define myceiling(w) {ceil(w)}
257 #define myhuge(w) {HUGE_VAL}
258 //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
259 #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
261 /* procedure parameter types for -A and -C++ */
263 #define F2C_proc_par_types 1
265 typedef logical (*L_fp)(...);
267 typedef logical (*L_fp)();
270 static float spow_ui(float x, integer n) {
271 float pow=1.0; unsigned long int u;
273 if(n < 0) n = -n, x = 1/x;
282 static double dpow_ui(double x, integer n) {
283 double pow=1.0; unsigned long int u;
285 if(n < 0) n = -n, x = 1/x;
295 static _Fcomplex cpow_ui(complex x, integer n) {
296 complex pow={1.0,0.0}; unsigned long int u;
298 if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
300 if(u & 01) pow.r *= x.r, pow.i *= x.i;
301 if(u >>= 1) x.r *= x.r, x.i *= x.i;
305 _Fcomplex p={pow.r, pow.i};
309 static _Complex float cpow_ui(_Complex float x, integer n) {
310 _Complex float pow=1.0; unsigned long int u;
312 if(n < 0) n = -n, x = 1/x;
323 static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
324 _Dcomplex pow={1.0,0.0}; unsigned long int u;
326 if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
328 if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
329 if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
333 _Dcomplex p = {pow._Val[0], pow._Val[1]};
337 static _Complex double zpow_ui(_Complex double x, integer n) {
338 _Complex double pow=1.0; unsigned long int u;
340 if(n < 0) n = -n, x = 1/x;
350 static integer pow_ii(integer x, integer n) {
351 integer pow; unsigned long int u;
353 if (n == 0 || x == 1) pow = 1;
354 else if (x != -1) pow = x == 0 ? 1/x : 0;
357 if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
367 static integer dmaxloc_(double *w, integer s, integer e, integer *n)
369 double m; integer i, mi;
370 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
371 if (w[i-1]>m) mi=i ,m=w[i-1];
374 static integer smaxloc_(float *w, integer s, integer e, integer *n)
376 float m; integer i, mi;
377 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
378 if (w[i-1]>m) mi=i ,m=w[i-1];
381 static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
382 integer n = *n_, incx = *incx_, incy = *incy_, i;
384 _Fcomplex zdotc = {0.0, 0.0};
385 if (incx == 1 && incy == 1) {
386 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
387 zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
388 zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
391 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
392 zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
393 zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
399 _Complex float zdotc = 0.0;
400 if (incx == 1 && incy == 1) {
401 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
402 zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
405 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
406 zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
412 static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
413 integer n = *n_, incx = *incx_, incy = *incy_, i;
415 _Dcomplex zdotc = {0.0, 0.0};
416 if (incx == 1 && incy == 1) {
417 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
418 zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
419 zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
422 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
423 zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
424 zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
430 _Complex double zdotc = 0.0;
431 if (incx == 1 && incy == 1) {
432 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
433 zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
436 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
437 zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
443 static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
444 integer n = *n_, incx = *incx_, incy = *incy_, i;
446 _Fcomplex zdotc = {0.0, 0.0};
447 if (incx == 1 && incy == 1) {
448 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
449 zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
450 zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
453 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
454 zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
455 zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
461 _Complex float zdotc = 0.0;
462 if (incx == 1 && incy == 1) {
463 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
464 zdotc += Cf(&x[i]) * Cf(&y[i]);
467 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
468 zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
474 static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
475 integer n = *n_, incx = *incx_, incy = *incy_, i;
477 _Dcomplex zdotc = {0.0, 0.0};
478 if (incx == 1 && incy == 1) {
479 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
480 zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
481 zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
484 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
485 zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
486 zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
492 _Complex double zdotc = 0.0;
493 if (incx == 1 && incy == 1) {
494 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
495 zdotc += Cd(&x[i]) * Cd(&y[i]);
498 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
499 zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
505 /* -- translated by f2c (version 20000121).
506 You must link the resulting object file with the libraries:
507 -lf2c -lm (in that order)
513 /* Table of constant values */
515 static integer c__1 = 1;
516 static integer c_n1 = -1;
517 static integer c__3 = 3;
518 static integer c__2 = 2;
519 static integer c__0 = 0;
521 /* > \brief \b DSTEBZ */
523 /* =========== DOCUMENTATION =========== */
525 /* Online html documentation available at */
526 /* http://www.netlib.org/lapack/explore-html/ */
529 /* > Download DSTEBZ + dependencies */
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstebz.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstebz.
536 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstebz.
544 /* SUBROUTINE DSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, */
545 /* M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, */
548 /* CHARACTER ORDER, RANGE */
549 /* INTEGER IL, INFO, IU, M, N, NSPLIT */
550 /* DOUBLE PRECISION ABSTOL, VL, VU */
551 /* INTEGER IBLOCK( * ), ISPLIT( * ), IWORK( * ) */
552 /* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) */
555 /* > \par Purpose: */
560 /* > DSTEBZ computes the eigenvalues of a symmetric tridiagonal */
561 /* > matrix T. The user may ask for all eigenvalues, all eigenvalues */
562 /* > in the half-open interval (VL, VU], or the IL-th through IU-th */
565 /* > To avoid overflow, the matrix must be scaled so that its */
566 /* > largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
568 /* > accuracy, it should not be much smaller than that. */
570 /* > See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal */
571 /* > Matrix", Report CS41, Computer Science Dept., Stanford */
572 /* > University, July 21, 1966. */
578 /* > \param[in] RANGE */
580 /* > RANGE is CHARACTER*1 */
581 /* > = 'A': ("All") all eigenvalues will be found. */
582 /* > = 'V': ("Value") all eigenvalues in the half-open interval */
583 /* > (VL, VU] will be found. */
584 /* > = 'I': ("Index") the IL-th through IU-th eigenvalues (of the */
585 /* > entire matrix) will be found. */
588 /* > \param[in] ORDER */
590 /* > ORDER is CHARACTER*1 */
591 /* > = 'B': ("By Block") the eigenvalues will be grouped by */
592 /* > split-off block (see IBLOCK, ISPLIT) and */
593 /* > ordered from smallest to largest within */
595 /* > = 'E': ("Entire matrix") */
596 /* > the eigenvalues for the entire matrix */
597 /* > will be ordered from smallest to */
604 /* > The order of the tridiagonal matrix T. N >= 0. */
607 /* > \param[in] VL */
609 /* > VL is DOUBLE PRECISION */
611 /* > If RANGE='V', the lower bound of the interval to */
612 /* > be searched for eigenvalues. Eigenvalues less than or equal */
613 /* > to VL, or greater than VU, will not be returned. VL < VU. */
614 /* > Not referenced if RANGE = 'A' or 'I'. */
617 /* > \param[in] VU */
619 /* > VU is DOUBLE PRECISION */
621 /* > If RANGE='V', the upper bound of the interval to */
622 /* > be searched for eigenvalues. Eigenvalues less than or equal */
623 /* > to VL, or greater than VU, will not be returned. VL < VU. */
624 /* > Not referenced if RANGE = 'A' or 'I'. */
627 /* > \param[in] IL */
629 /* > IL is INTEGER */
631 /* > If RANGE='I', the index of the */
632 /* > smallest eigenvalue to be returned. */
633 /* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
634 /* > Not referenced if RANGE = 'A' or 'V'. */
637 /* > \param[in] IU */
639 /* > IU is INTEGER */
641 /* > If RANGE='I', the index of the */
642 /* > largest eigenvalue to be returned. */
643 /* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
644 /* > Not referenced if RANGE = 'A' or 'V'. */
647 /* > \param[in] ABSTOL */
649 /* > ABSTOL is DOUBLE PRECISION */
650 /* > The absolute tolerance for the eigenvalues. An eigenvalue */
651 /* > (or cluster) is considered to be located if it has been */
652 /* > determined to lie in an interval whose width is ABSTOL or */
653 /* > less. If ABSTOL is less than or equal to zero, then ULP*|T| */
654 /* > will be used, where |T| means the 1-norm of T. */
656 /* > Eigenvalues will be computed most accurately when ABSTOL is */
657 /* > set to twice the underflow threshold 2*DLAMCH('S'), not zero. */
662 /* > D is DOUBLE PRECISION array, dimension (N) */
663 /* > The n diagonal elements of the tridiagonal matrix T. */
668 /* > E is DOUBLE PRECISION array, dimension (N-1) */
669 /* > The (n-1) off-diagonal elements of the tridiagonal matrix T. */
672 /* > \param[out] M */
675 /* > The actual number of eigenvalues found. 0 <= M <= N. */
676 /* > (See also the description of INFO=2,3.) */
679 /* > \param[out] NSPLIT */
681 /* > NSPLIT is INTEGER */
682 /* > The number of diagonal blocks in the matrix T. */
683 /* > 1 <= NSPLIT <= N. */
686 /* > \param[out] W */
688 /* > W is DOUBLE PRECISION array, dimension (N) */
689 /* > On exit, the first M elements of W will contain the */
690 /* > eigenvalues. (DSTEBZ may use the remaining N-M elements as */
694 /* > \param[out] IBLOCK */
696 /* > IBLOCK is INTEGER array, dimension (N) */
697 /* > At each row/column j where E(j) is zero or small, the */
698 /* > matrix T is considered to split into a block diagonal */
699 /* > matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which */
700 /* > block (from 1 to the number of blocks) the eigenvalue W(i) */
701 /* > belongs. (DSTEBZ may use the remaining N-M elements as */
705 /* > \param[out] ISPLIT */
707 /* > ISPLIT is INTEGER array, dimension (N) */
708 /* > The splitting points, at which T breaks up into submatrices. */
709 /* > The first submatrix consists of rows/columns 1 to ISPLIT(1), */
710 /* > the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), */
711 /* > etc., and the NSPLIT-th consists of rows/columns */
712 /* > ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. */
713 /* > (Only the first NSPLIT elements will actually be used, but */
714 /* > since the user cannot know a priori what value NSPLIT will */
715 /* > have, N words must be reserved for ISPLIT.) */
718 /* > \param[out] WORK */
720 /* > WORK is DOUBLE PRECISION array, dimension (4*N) */
723 /* > \param[out] IWORK */
725 /* > IWORK is INTEGER array, dimension (3*N) */
728 /* > \param[out] INFO */
730 /* > INFO is INTEGER */
731 /* > = 0: successful exit */
732 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
733 /* > > 0: some or all of the eigenvalues failed to converge or */
734 /* > were not computed: */
735 /* > =1 or 3: Bisection failed to converge for some */
736 /* > eigenvalues; these eigenvalues are flagged by a */
737 /* > negative block number. The effect is that the */
738 /* > eigenvalues may not be as accurate as the */
739 /* > absolute and relative tolerances. This is */
740 /* > generally caused by unexpectedly inaccurate */
742 /* > =2 or 3: RANGE='I' only: Not all of the eigenvalues */
743 /* > IL:IU were found. */
744 /* > Effect: M < IU+1-IL */
745 /* > Cause: non-monotonic arithmetic, causing the */
746 /* > Sturm sequence to be non-monotonic. */
747 /* > Cure: recalculate, using RANGE='A', and pick */
748 /* > out eigenvalues IL:IU. In some cases, */
749 /* > increasing the PARAMETER "FUDGE" may */
750 /* > make things work. */
751 /* > = 4: RANGE='I', and the Gershgorin interval */
752 /* > initially used was too small. No eigenvalues */
753 /* > were computed. */
754 /* > Probable cause: your machine has sloppy */
755 /* > floating-point arithmetic. */
756 /* > Cure: Increase the PARAMETER "FUDGE", */
757 /* > recompile, and try again. */
760 /* > \par Internal Parameters: */
761 /* ========================= */
764 /* > RELFAC DOUBLE PRECISION, default = 2.0e0 */
765 /* > The relative tolerance. An interval (a,b] lies within */
766 /* > "relative tolerance" if b-a < RELFAC*ulp*f2cmax(|a|,|b|), */
767 /* > where "ulp" is the machine precision (distance from 1 to */
768 /* > the next larger floating point number.) */
770 /* > FUDGE DOUBLE PRECISION, default = 2 */
771 /* > A "fudge factor" to widen the Gershgorin intervals. Ideally, */
772 /* > a value of 1 should work, but on machines with sloppy */
773 /* > arithmetic, this needs to be larger. The default for */
774 /* > publicly released versions should be large enough to handle */
775 /* > the worst machine around. Note that this has no effect */
776 /* > on accuracy of the solution. */
782 /* > \author Univ. of Tennessee */
783 /* > \author Univ. of California Berkeley */
784 /* > \author Univ. of Colorado Denver */
785 /* > \author NAG Ltd. */
787 /* > \date June 2016 */
789 /* > \ingroup auxOTHERcomputational */
791 /* ===================================================================== */
792 /* Subroutine */ int dstebz_(char *range, char *order, integer *n, doublereal
793 *vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol,
794 doublereal *d__, doublereal *e, integer *m, integer *nsplit,
795 doublereal *w, integer *iblock, integer *isplit, doublereal *work,
796 integer *iwork, integer *info)
798 /* System generated locals */
799 integer i__1, i__2, i__3;
800 doublereal d__1, d__2, d__3, d__4, d__5;
802 /* Local variables */
803 integer iend, ioff, iout, itmp1, j, jdisc;
804 extern logical lsame_(char *, char *);
810 doublereal wkill, rtoli, tnorm;
811 integer ib, jb, ie, je, nb;
814 extern doublereal dlamch_(char *);
818 extern /* Subroutine */ int dlaebz_(integer *, integer *, integer *,
819 integer *, integer *, integer *, doublereal *, doublereal *,
820 doublereal *, doublereal *, doublereal *, doublereal *, integer *,
821 doublereal *, doublereal *, integer *, integer *, doublereal *,
822 integer *, integer *);
824 integer irange, idiscl;
825 doublereal safemn, wu;
827 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
828 integer *, integer *, ftnlen, ftnlen);
829 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
830 integer idiscu, iorder;
835 doublereal ulp, wlu, wul;
837 doublereal tmp1, tmp2;
840 /* -- LAPACK computational routine (version 3.7.0) -- */
841 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
842 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
846 /* ===================================================================== */
849 /* Parameter adjustments */
863 if (lsame_(range, "A")) {
865 } else if (lsame_(range, "V")) {
867 } else if (lsame_(range, "I")) {
875 if (lsame_(order, "B")) {
877 } else if (lsame_(order, "E")) {
883 /* Check for Errors */
887 } else if (iorder <= 0) {
891 } else if (irange == 2) {
895 } else if (irange == 3 && (*il < 1 || *il > f2cmax(1,*n))) {
897 } else if (irange == 3 && (*iu < f2cmin(*n,*il) || *iu > *n)) {
903 xerbla_("DSTEBZ", &i__1, (ftnlen)6);
907 /* Initialize error flags */
913 /* Quick return if possible */
920 /* Simplifications: */
922 if (irange == 3 && *il == 1 && *iu == *n) {
926 /* Get machine constants */
927 /* NB is the minimum vector length for vector bisection, or 0 */
928 /* if only scalar is to be done. */
930 safemn = dlamch_("S");
933 nb = ilaenv_(&c__1, "DSTEBZ", " ", n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
939 /* Special Case when N=1 */
944 if (irange == 2 && (*vl >= d__[1] || *vu < d__[1])) {
954 /* Compute Splitting Points */
961 for (j = 2; j <= i__1; ++j) {
962 /* Computing 2nd power */
965 /* Computing 2nd power */
967 if ((d__1 = d__[j] * d__[j - 1], abs(d__1)) * (d__2 * d__2) + safemn
969 isplit[*nsplit] = j - 1;
974 pivmin = f2cmax(pivmin,tmp1);
978 isplit[*nsplit] = *n;
981 /* Compute Interval and ATOLI */
985 /* RANGE='I': Compute the interval containing eigenvalues */
988 /* Compute Gershgorin interval for entire (split) matrix */
989 /* and use it as the initial interval */
996 for (j = 1; j <= i__1; ++j) {
997 tmp2 = sqrt(work[j]);
999 d__1 = gu, d__2 = d__[j] + tmp1 + tmp2;
1000 gu = f2cmax(d__1,d__2);
1002 d__1 = gl, d__2 = d__[j] - tmp1 - tmp2;
1003 gl = f2cmin(d__1,d__2);
1009 d__1 = gu, d__2 = d__[*n] + tmp1;
1010 gu = f2cmax(d__1,d__2);
1012 d__1 = gl, d__2 = d__[*n] - tmp1;
1013 gl = f2cmin(d__1,d__2);
1015 d__1 = abs(gl), d__2 = abs(gu);
1016 tnorm = f2cmax(d__1,d__2);
1017 gl = gl - tnorm * 2.1 * ulp * *n - pivmin * 4.2000000000000002;
1018 gu = gu + tnorm * 2.1 * ulp * *n + pivmin * 2.1;
1020 /* Compute Iteration parameters */
1022 itmax = (integer) ((log(tnorm + pivmin) - log(pivmin)) / log(2.)) + 2;
1023 if (*abstol <= 0.) {
1024 atoli = ulp * tnorm;
1042 dlaebz_(&c__3, &itmax, n, &c__2, &c__2, &nb, &atoli, &rtoli, &pivmin,
1043 &d__[1], &e[1], &work[1], &iwork[5], &work[*n + 1], &work[*n
1044 + 5], &iout, &iwork[1], &w[1], &iblock[1], &iinfo);
1046 if (iwork[6] == *iu) {
1062 if (nwl < 0 || nwl >= *n || nwu < 1 || nwu > *n) {
1068 /* RANGE='A' or 'V' -- Set ATOLI */
1071 d__3 = abs(d__[1]) + abs(e[1]), d__4 = (d__1 = d__[*n], abs(d__1)) + (
1072 d__2 = e[*n - 1], abs(d__2));
1073 tnorm = f2cmax(d__3,d__4);
1076 for (j = 2; j <= i__1; ++j) {
1078 d__4 = tnorm, d__5 = (d__1 = d__[j], abs(d__1)) + (d__2 = e[j - 1]
1079 , abs(d__2)) + (d__3 = e[j], abs(d__3));
1080 tnorm = f2cmax(d__4,d__5);
1084 if (*abstol <= 0.) {
1085 atoli = ulp * tnorm;
1099 /* Find Eigenvalues -- Loop Over Blocks and recompute NWL and NWU. */
1100 /* NWL accumulates the number of eigenvalues .le. WL, */
1101 /* NWU accumulates the number of eigenvalues .le. WU */
1110 for (jb = 1; jb <= i__1; ++jb) {
1118 /* Special Case -- IN=1 */
1120 if (irange == 1 || wl >= d__[ibegin] - pivmin) {
1123 if (irange == 1 || wu >= d__[ibegin] - pivmin) {
1126 if (irange == 1 || wl < d__[ibegin] - pivmin && wu >= d__[ibegin]
1129 w[*m] = d__[ibegin];
1134 /* General Case -- IN > 1 */
1136 /* Compute Gershgorin Interval */
1137 /* and use it as the initial interval */
1144 for (j = ibegin; j <= i__2; ++j) {
1145 tmp2 = (d__1 = e[j], abs(d__1));
1147 d__1 = gu, d__2 = d__[j] + tmp1 + tmp2;
1148 gu = f2cmax(d__1,d__2);
1150 d__1 = gl, d__2 = d__[j] - tmp1 - tmp2;
1151 gl = f2cmin(d__1,d__2);
1157 d__1 = gu, d__2 = d__[iend] + tmp1;
1158 gu = f2cmax(d__1,d__2);
1160 d__1 = gl, d__2 = d__[iend] - tmp1;
1161 gl = f2cmin(d__1,d__2);
1163 d__1 = abs(gl), d__2 = abs(gu);
1164 bnorm = f2cmax(d__1,d__2);
1165 gl = gl - bnorm * 2.1 * ulp * in - pivmin * 2.1;
1166 gu = gu + bnorm * 2.1 * ulp * in + pivmin * 2.1;
1168 /* Compute ATOLI for the current submatrix */
1170 if (*abstol <= 0.) {
1172 d__1 = abs(gl), d__2 = abs(gu);
1173 atoli = ulp * f2cmax(d__1,d__2);
1191 /* Set Up Initial Interval */
1194 work[*n + in + 1] = gu;
1195 dlaebz_(&c__1, &c__0, &in, &in, &c__1, &nb, &atoli, &rtoli, &
1196 pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
1197 work[*n + 1], &work[*n + (in << 1) + 1], &im, &iwork[1], &
1198 w[*m + 1], &iblock[*m + 1], &iinfo);
1201 nwu += iwork[in + 1];
1202 iwoff = *m - iwork[1];
1204 /* Compute Eigenvalues */
1206 itmax = (integer) ((log(gu - gl + pivmin) - log(pivmin)) / log(2.)
1208 dlaebz_(&c__2, &itmax, &in, &in, &c__1, &nb, &atoli, &rtoli, &
1209 pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
1210 work[*n + 1], &work[*n + (in << 1) + 1], &iout, &iwork[1],
1211 &w[*m + 1], &iblock[*m + 1], &iinfo);
1213 /* Copy Eigenvalues Into W and IBLOCK */
1214 /* Use -JB for block number for unconverged eigenvalues. */
1217 for (j = 1; j <= i__2; ++j) {
1218 tmp1 = (work[j + *n] + work[j + in + *n]) * .5;
1220 /* Flag non-convergence. */
1222 if (j > iout - iinfo) {
1228 i__3 = iwork[j + in] + iwoff;
1229 for (je = iwork[j] + 1 + iwoff; je <= i__3; ++je) {
1243 /* If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU */
1244 /* If NWL+1 < IL or NWU > IU, discard extra eigenvalues. */
1248 idiscl = *il - 1 - nwl;
1251 if (idiscl > 0 || idiscu > 0) {
1253 for (je = 1; je <= i__1; ++je) {
1254 if (w[je] <= wlu && idiscl > 0) {
1256 } else if (w[je] >= wul && idiscu > 0) {
1261 iblock[im] = iblock[je];
1267 if (idiscl > 0 || idiscu > 0) {
1269 /* Code to deal with effects of bad arithmetic: */
1270 /* Some low eigenvalues to be discarded are not in (WL,WLU], */
1271 /* or high eigenvalues to be discarded are not in (WUL,WU] */
1272 /* so just kill off the smallest IDISCL/largest IDISCU */
1273 /* eigenvalues, by simply finding the smallest/largest */
1274 /* eigenvalue(s). */
1276 /* (If N(w) is monotone non-decreasing, this should never */
1282 for (jdisc = 1; jdisc <= i__1; ++jdisc) {
1285 for (je = 1; je <= i__2; ++je) {
1286 if (iblock[je] != 0 && (w[je] < wkill || iw == 0)) {
1300 for (jdisc = 1; jdisc <= i__1; ++jdisc) {
1303 for (je = 1; je <= i__2; ++je) {
1304 if (iblock[je] != 0 && (w[je] > wkill || iw == 0)) {
1316 for (je = 1; je <= i__1; ++je) {
1317 if (iblock[je] != 0) {
1320 iblock[im] = iblock[je];
1326 if (idiscl < 0 || idiscu < 0) {
1331 /* If ORDER='B', do nothing -- the eigenvalues are already sorted */
1333 /* If ORDER='E', sort the eigenvalues from smallest to largest */
1335 if (iorder == 1 && *nsplit > 1) {
1337 for (je = 1; je <= i__1; ++je) {
1341 for (j = je + 1; j <= i__2; ++j) {
1352 iblock[ie] = iblock[je];