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__2 = 2;
516 static integer c__1 = 1;
517 static integer c_n1 = -1;
519 /* > \brief \b DSTEIN */
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download DSTEIN + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstein.
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstein.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstein.
542 /* SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, */
543 /* IWORK, IFAIL, INFO ) */
545 /* INTEGER INFO, LDZ, M, N */
546 /* INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), */
548 /* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) */
551 /* > \par Purpose: */
556 /* > DSTEIN computes the eigenvectors of a real symmetric tridiagonal */
557 /* > matrix T corresponding to specified eigenvalues, using inverse */
560 /* > The maximum number of iterations allowed for each eigenvector is */
561 /* > specified by an internal parameter MAXITS (currently set to 5). */
570 /* > The order of the matrix. N >= 0. */
575 /* > D is DOUBLE PRECISION array, dimension (N) */
576 /* > The n diagonal elements of the tridiagonal matrix T. */
581 /* > E is DOUBLE PRECISION array, dimension (N-1) */
582 /* > The (n-1) subdiagonal elements of the tridiagonal matrix */
583 /* > T, in elements 1 to N-1. */
589 /* > The number of eigenvectors to be found. 0 <= M <= N. */
594 /* > W is DOUBLE PRECISION array, dimension (N) */
595 /* > The first M elements of W contain the eigenvalues for */
596 /* > which eigenvectors are to be computed. The eigenvalues */
597 /* > should be grouped by split-off block and ordered from */
598 /* > smallest to largest within the block. ( The output array */
599 /* > W from DSTEBZ with ORDER = 'B' is expected here. ) */
602 /* > \param[in] IBLOCK */
604 /* > IBLOCK is INTEGER array, dimension (N) */
605 /* > The submatrix indices associated with the corresponding */
606 /* > eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to */
607 /* > the first submatrix from the top, =2 if W(i) belongs to */
608 /* > the second submatrix, etc. ( The output array IBLOCK */
609 /* > from DSTEBZ is expected here. ) */
612 /* > \param[in] ISPLIT */
614 /* > ISPLIT is INTEGER array, dimension (N) */
615 /* > The splitting points, at which T breaks up into submatrices. */
616 /* > The first submatrix consists of rows/columns 1 to */
617 /* > ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 */
618 /* > through ISPLIT( 2 ), etc. */
619 /* > ( The output array ISPLIT from DSTEBZ is expected here. ) */
622 /* > \param[out] Z */
624 /* > Z is DOUBLE PRECISION array, dimension (LDZ, M) */
625 /* > The computed eigenvectors. The eigenvector associated */
626 /* > with the eigenvalue W(i) is stored in the i-th column of */
627 /* > Z. Any vector which fails to converge is set to its current */
628 /* > iterate after MAXITS iterations. */
631 /* > \param[in] LDZ */
633 /* > LDZ is INTEGER */
634 /* > The leading dimension of the array Z. LDZ >= f2cmax(1,N). */
637 /* > \param[out] WORK */
639 /* > WORK is DOUBLE PRECISION array, dimension (5*N) */
642 /* > \param[out] IWORK */
644 /* > IWORK is INTEGER array, dimension (N) */
647 /* > \param[out] IFAIL */
649 /* > IFAIL is INTEGER array, dimension (M) */
650 /* > On normal exit, all elements of IFAIL are zero. */
651 /* > If one or more eigenvectors fail to converge after */
652 /* > MAXITS iterations, then their indices are stored in */
656 /* > \param[out] INFO */
658 /* > INFO is INTEGER */
659 /* > = 0: successful exit. */
660 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
661 /* > > 0: if INFO = i, then i eigenvectors failed to converge */
662 /* > in MAXITS iterations. Their indices are stored in */
666 /* > \par Internal Parameters: */
667 /* ========================= */
670 /* > MAXITS INTEGER, default = 5 */
671 /* > The maximum number of iterations performed. */
673 /* > EXTRA INTEGER, default = 2 */
674 /* > The number of iterations performed after norm growth */
675 /* > criterion is satisfied, should be at least 1. */
681 /* > \author Univ. of Tennessee */
682 /* > \author Univ. of California Berkeley */
683 /* > \author Univ. of Colorado Denver */
684 /* > \author NAG Ltd. */
686 /* > \date December 2016 */
688 /* > \ingroup doubleOTHERcomputational */
690 /* ===================================================================== */
691 /* Subroutine */ int dstein_(integer *n, doublereal *d__, doublereal *e,
692 integer *m, doublereal *w, integer *iblock, integer *isplit,
693 doublereal *z__, integer *ldz, doublereal *work, integer *iwork,
694 integer *ifail, integer *info)
696 /* System generated locals */
697 integer z_dim1, z_offset, i__1, i__2, i__3;
698 doublereal d__1, d__2, d__3, d__4, d__5;
700 /* Local variables */
702 extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
705 extern doublereal dnrm2_(integer *, doublereal *, integer *);
707 extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
709 integer iseed[4], gpind, iinfo;
710 extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
711 doublereal *, integer *);
713 extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *,
714 integer *, doublereal *, integer *);
717 integer indrv1, indrv2, indrv3, indrv4, indrv5, bn;
718 extern doublereal dlamch_(char *);
719 extern /* Subroutine */ int dlagtf_(integer *, doublereal *, doublereal *,
720 doublereal *, doublereal *, doublereal *, doublereal *, integer *
723 extern integer idamax_(integer *, doublereal *, integer *);
724 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dlagts_(
725 integer *, integer *, doublereal *, doublereal *, doublereal *,
726 doublereal *, integer *, doublereal *, doublereal *, integer *);
728 extern /* Subroutine */ int dlarnv_(integer *, integer *, integer *,
731 doublereal onenrm, dtpcrt, pertol, scl, eps, sep, nrm, tol;
733 doublereal xjm, ztr, eps1;
736 /* -- LAPACK computational routine (version 3.7.0) -- */
737 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
738 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
742 /* ===================================================================== */
745 /* Test the input parameters. */
747 /* Parameter adjustments */
754 z_offset = 1 + z_dim1 * 1;
763 for (i__ = 1; i__ <= i__1; ++i__) {
770 } else if (*m < 0 || *m > *n) {
772 } else if (*ldz < f2cmax(1,*n)) {
776 for (j = 2; j <= i__1; ++j) {
777 if (iblock[j] < iblock[j - 1]) {
781 if (iblock[j] == iblock[j - 1] && w[j] < w[j - 1]) {
793 xerbla_("DSTEIN", &i__1, (ftnlen)6);
797 /* Quick return if possible */
799 if (*n == 0 || *m == 0) {
801 } else if (*n == 1) {
802 z__[z_dim1 + 1] = 1.;
806 /* Get machine constants. */
808 eps = dlamch_("Precision");
810 /* Initialize seed for random number generator DLARNV. */
812 for (i__ = 1; i__ <= 4; ++i__) {
817 /* Initialize pointers. */
820 indrv2 = indrv1 + *n;
821 indrv3 = indrv2 + *n;
822 indrv4 = indrv3 + *n;
823 indrv5 = indrv4 + *n;
825 /* Compute eigenvectors of matrix blocks. */
829 for (nblk = 1; nblk <= i__1; ++nblk) {
831 /* Find starting and ending indices of block nblk. */
836 b1 = isplit[nblk - 1] + 1;
839 blksiz = bn - b1 + 1;
845 /* Compute reorthogonalization criterion and stopping criterion. */
847 onenrm = (d__1 = d__[b1], abs(d__1)) + (d__2 = e[b1], abs(d__2));
849 d__3 = onenrm, d__4 = (d__1 = d__[bn], abs(d__1)) + (d__2 = e[bn - 1],
851 onenrm = f2cmax(d__3,d__4);
853 for (i__ = b1 + 1; i__ <= i__2; ++i__) {
855 d__4 = onenrm, d__5 = (d__1 = d__[i__], abs(d__1)) + (d__2 = e[
856 i__ - 1], abs(d__2)) + (d__3 = e[i__], abs(d__3));
857 onenrm = f2cmax(d__4,d__5);
860 ortol = onenrm * .001;
862 dtpcrt = sqrt(.1 / blksiz);
864 /* Loop through eigenvalues of block nblk. */
869 for (j = j1; j <= i__2; ++j) {
870 if (iblock[j] != nblk) {
877 /* Skip all the work if the block size is one. */
880 work[indrv1 + 1] = 1.;
884 /* If eigenvalues j and j-1 are too close, add a relatively */
885 /* small perturbation. */
888 eps1 = (d__1 = eps * xj, abs(d__1));
899 /* Get random starting vector. */
901 dlarnv_(&c__2, iseed, &blksiz, &work[indrv1 + 1]);
903 /* Copy the matrix T so it won't be destroyed in factorization. */
905 dcopy_(&blksiz, &d__[b1], &c__1, &work[indrv4 + 1], &c__1);
907 dcopy_(&i__3, &e[b1], &c__1, &work[indrv2 + 2], &c__1);
909 dcopy_(&i__3, &e[b1], &c__1, &work[indrv3 + 1], &c__1);
911 /* Compute LU factors with partial pivoting ( PT = LU ) */
914 dlagtf_(&blksiz, &work[indrv4 + 1], &xj, &work[indrv2 + 2], &work[
915 indrv3 + 1], &tol, &work[indrv5 + 1], &iwork[1], &iinfo);
917 /* Update iteration count. */
925 /* Normalize and scale the righthand side vector Pb. */
927 jmax = idamax_(&blksiz, &work[indrv1 + 1], &c__1);
929 d__3 = eps, d__4 = (d__1 = work[indrv4 + blksiz], abs(d__1));
930 scl = blksiz * onenrm * f2cmax(d__3,d__4) / (d__2 = work[indrv1 +
932 dscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1);
934 /* Solve the system LU = Pb. */
936 dlagts_(&c_n1, &blksiz, &work[indrv4 + 1], &work[indrv2 + 2], &
937 work[indrv3 + 1], &work[indrv5 + 1], &iwork[1], &work[
938 indrv1 + 1], &tol, &iinfo);
940 /* Reorthogonalize by modified Gram-Schmidt if eigenvalues are */
946 if ((d__1 = xj - xjm, abs(d__1)) > ortol) {
951 for (i__ = gpind; i__ <= i__3; ++i__) {
952 ztr = -ddot_(&blksiz, &work[indrv1 + 1], &c__1, &z__[b1 +
953 i__ * z_dim1], &c__1);
954 daxpy_(&blksiz, &ztr, &z__[b1 + i__ * z_dim1], &c__1, &
955 work[indrv1 + 1], &c__1);
960 /* Check the infinity norm of the iterate. */
963 jmax = idamax_(&blksiz, &work[indrv1 + 1], &c__1);
964 nrm = (d__1 = work[indrv1 + jmax], abs(d__1));
966 /* Continue for additional iterations after norm reaches */
967 /* stopping criterion. */
979 /* If stopping criterion was not satisfied, update info and */
980 /* store eigenvector number in array ifail. */
986 /* Accept iterate as jth eigenvector. */
989 scl = 1. / dnrm2_(&blksiz, &work[indrv1 + 1], &c__1);
990 jmax = idamax_(&blksiz, &work[indrv1 + 1], &c__1);
991 if (work[indrv1 + jmax] < 0.) {
994 dscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1);
997 for (i__ = 1; i__ <= i__3; ++i__) {
998 z__[i__ + j * z_dim1] = 0.;
1002 for (i__ = 1; i__ <= i__3; ++i__) {
1003 z__[b1 + i__ - 1 + j * z_dim1] = work[indrv1 + i__];
1007 /* Save the shift to check eigenvalue spacing at next */