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__2 = 2;
517 static integer c__10 = 10;
518 static integer c__3 = 3;
519 static integer c__4 = 4;
520 static integer c__11 = 11;
522 /* > \brief \b DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix assoc
523 iated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr. */
525 /* =========== DOCUMENTATION =========== */
527 /* Online html documentation available at */
528 /* http://www.netlib.org/lapack/explore-html/ */
531 /* > Download DLASQ2 + dependencies */
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq2.
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq2.
538 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq2.
546 /* SUBROUTINE DLASQ2( N, Z, INFO ) */
548 /* INTEGER INFO, N */
549 /* DOUBLE PRECISION Z( * ) */
552 /* > \par Purpose: */
557 /* > DLASQ2 computes all the eigenvalues of the symmetric positive */
558 /* > definite tridiagonal matrix associated with the qd array Z to high */
559 /* > relative accuracy are computed to high relative accuracy, in the */
560 /* > absence of denormalization, underflow and overflow. */
562 /* > To see the relation of Z to the tridiagonal matrix, let L be a */
563 /* > unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and */
564 /* > let U be an upper bidiagonal matrix with 1's above and diagonal */
565 /* > Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the */
566 /* > symmetric tridiagonal to which it is similar. */
568 /* > Note : DLASQ2 defines a logical variable, IEEE, which is true */
569 /* > on machines which follow ieee-754 floating-point standard in their */
570 /* > handling of infinities and NaNs, and false otherwise. This variable */
571 /* > is passed to DLASQ3. */
580 /* > The number of rows and columns in the matrix. N >= 0. */
583 /* > \param[in,out] Z */
585 /* > Z is DOUBLE PRECISION array, dimension ( 4*N ) */
586 /* > On entry Z holds the qd array. On exit, entries 1 to N hold */
587 /* > the eigenvalues in decreasing order, Z( 2*N+1 ) holds the */
588 /* > trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If */
589 /* > N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 ) */
590 /* > holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of */
591 /* > shifts that failed. */
594 /* > \param[out] INFO */
596 /* > INFO is INTEGER */
597 /* > = 0: successful exit */
598 /* > < 0: if the i-th argument is a scalar and had an illegal */
599 /* > value, then INFO = -i, if the i-th argument is an */
600 /* > array and the j-entry had an illegal value, then */
601 /* > INFO = -(i*100+j) */
602 /* > > 0: the algorithm failed */
603 /* > = 1, a split was marked by a positive value in E */
604 /* > = 2, current block of Z not diagonalized after 100*N */
605 /* > iterations (in inner while loop). On exit Z holds */
606 /* > a qd array with the same eigenvalues as the given Z. */
607 /* > = 3, termination criterion of outer while loop not met */
608 /* > (program created more than N unreduced blocks) */
614 /* > \author Univ. of Tennessee */
615 /* > \author Univ. of California Berkeley */
616 /* > \author Univ. of Colorado Denver */
617 /* > \author NAG Ltd. */
619 /* > \date December 2016 */
621 /* > \ingroup auxOTHERcomputational */
623 /* > \par Further Details: */
624 /* ===================== */
628 /* > Local Variables: I0:N0 defines a current unreduced segment of Z. */
629 /* > The shifts are accumulated in SIGMA. Iteration count is in ITER. */
630 /* > Ping-pong is controlled by PP (alternates between 0 and 1). */
633 /* ===================================================================== */
634 /* Subroutine */ int dlasq2_(integer *n, doublereal *z__, integer *info)
636 /* System generated locals */
637 integer i__1, i__2, i__3;
638 doublereal d__1, d__2;
640 /* Local variables */
643 doublereal dmin__, emin, emax;
644 integer kmin, ndiv, iter;
645 doublereal qmin, temp, qmax, zmax;
647 doublereal dmin1, dmin2, d__, e, g;
651 doublereal desig, trace, sigma;
653 doublereal tempe, tempq;
654 integer i0, i1, i4, n0, n1, ttype;
655 extern /* Subroutine */ int dlasq3_(integer *, integer *, doublereal *,
656 integer *, doublereal *, doublereal *, doublereal *, doublereal *,
657 integer *, integer *, integer *, logical *, integer *,
658 doublereal *, doublereal *, doublereal *, doublereal *,
659 doublereal *, doublereal *, doublereal *);
661 extern doublereal dlamch_(char *);
664 integer iwhila, iwhilb;
665 doublereal oldemn, safmin;
666 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
667 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
668 integer *, integer *, ftnlen, ftnlen);
669 extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *,
671 doublereal dn1, dn2, dee, eps, tau, tol;
676 /* -- LAPACK computational routine (version 3.7.0) -- */
677 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
678 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
682 /* ===================================================================== */
685 /* Test the input arguments. */
686 /* (in case DLASQ2 is not called by DLASQ1) */
688 /* Parameter adjustments */
693 eps = dlamch_("Precision");
694 safmin = dlamch_("Safe minimum");
696 /* Computing 2nd power */
702 xerbla_("DLASQ2", &c__1, (ftnlen)6);
704 } else if (*n == 0) {
706 } else if (*n == 1) {
712 xerbla_("DLASQ2", &c__2, (ftnlen)6);
715 } else if (*n == 2) {
721 xerbla_("DLASQ2", &c__2, (ftnlen)6);
723 } else if (z__[2] < 0.) {
725 xerbla_("DLASQ2", &c__2, (ftnlen)6);
727 } else if (z__[3] < 0.) {
729 xerbla_("DLASQ2", &c__2, (ftnlen)6);
731 } else if (z__[3] > z__[1]) {
736 z__[5] = z__[1] + z__[2] + z__[3];
737 if (z__[2] > z__[3] * tol2) {
738 t = (z__[1] - z__[3] + z__[2]) * .5;
739 s = z__[3] * (z__[2] / t);
741 s = z__[3] * (z__[2] / (t * (sqrt(s / t + 1.) + 1.)));
743 s = z__[3] * (z__[2] / (t + sqrt(t) * sqrt(t + s)));
745 t = z__[1] + (s + z__[2]);
746 z__[3] *= z__[1] / t;
750 z__[6] = z__[2] + z__[1];
754 /* Check for negative data and compute sums of q's and e's. */
764 for (k = 1; k <= i__1; k += 2) {
767 xerbla_("DLASQ2", &c__2, (ftnlen)6);
769 } else if (z__[k + 1] < 0.) {
771 xerbla_("DLASQ2", &c__2, (ftnlen)6);
777 d__1 = qmax, d__2 = z__[k];
778 qmax = f2cmax(d__1,d__2);
780 d__1 = emin, d__2 = z__[k + 1];
781 emin = f2cmin(d__1,d__2);
783 d__1 = f2cmax(qmax,zmax), d__2 = z__[k + 1];
784 zmax = f2cmax(d__1,d__2);
787 if (z__[(*n << 1) - 1] < 0.) {
788 *info = -((*n << 1) + 199);
789 xerbla_("DLASQ2", &c__2, (ftnlen)6);
792 d__ += z__[(*n << 1) - 1];
794 d__1 = qmax, d__2 = z__[(*n << 1) - 1];
795 qmax = f2cmax(d__1,d__2);
796 zmax = f2cmax(qmax,zmax);
798 /* Check for diagonality. */
802 for (k = 2; k <= i__1; ++k) {
803 z__[k] = z__[(k << 1) - 1];
806 dlasrt_("D", n, &z__[1], &iinfo);
807 z__[(*n << 1) - 1] = d__;
813 /* Check for zero data. */
816 z__[(*n << 1) - 1] = 0.;
820 /* Check whether the machine is IEEE conformable. */
822 ieee = ilaenv_(&c__10, "DLASQ2", "N", &c__1, &c__2, &c__3, &c__4, (ftnlen)
823 6, (ftnlen)1) == 1 && ilaenv_(&c__11, "DLASQ2", "N", &c__1, &c__2,
824 &c__3, &c__4, (ftnlen)6, (ftnlen)1) == 1;
826 /* Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...). */
828 for (k = *n << 1; k >= 2; k += -2) {
830 z__[(k << 1) - 1] = z__[k];
831 z__[(k << 1) - 2] = 0.;
832 z__[(k << 1) - 3] = z__[k - 1];
839 /* Reverse the qd-array, if warranted. */
841 if (z__[(i0 << 2) - 3] * 1.5 < z__[(n0 << 2) - 3]) {
843 i__1 = i0 + n0 - 1 << 1;
844 for (i4 = i0 << 2; i4 <= i__1; i4 += 4) {
846 z__[i4 - 3] = z__[ipn4 - i4 - 3];
847 z__[ipn4 - i4 - 3] = temp;
849 z__[i4 - 1] = z__[ipn4 - i4 - 5];
850 z__[ipn4 - i4 - 5] = temp;
855 /* Initial split checking via dqd and Li's test. */
859 for (k = 1; k <= 2; ++k) {
861 d__ = z__[(n0 << 2) + pp - 3];
862 i__1 = (i0 << 2) + pp;
863 for (i4 = (n0 - 1 << 2) + pp; i4 >= i__1; i4 += -4) {
864 if (z__[i4 - 1] <= tol2 * d__) {
868 d__ = z__[i4 - 3] * (d__ / (d__ + z__[i4 - 1]));
873 /* dqd maps Z to ZZ plus Li's test. */
875 emin = z__[(i0 << 2) + pp + 1];
876 d__ = z__[(i0 << 2) + pp - 3];
877 i__1 = (n0 - 1 << 2) + pp;
878 for (i4 = (i0 << 2) + pp; i4 <= i__1; i4 += 4) {
879 z__[i4 - (pp << 1) - 2] = d__ + z__[i4 - 1];
880 if (z__[i4 - 1] <= tol2 * d__) {
882 z__[i4 - (pp << 1) - 2] = d__;
883 z__[i4 - (pp << 1)] = 0.;
885 } else if (safmin * z__[i4 + 1] < z__[i4 - (pp << 1) - 2] &&
886 safmin * z__[i4 - (pp << 1) - 2] < z__[i4 + 1]) {
887 temp = z__[i4 + 1] / z__[i4 - (pp << 1) - 2];
888 z__[i4 - (pp << 1)] = z__[i4 - 1] * temp;
891 z__[i4 - (pp << 1)] = z__[i4 + 1] * (z__[i4 - 1] / z__[i4 - (
893 d__ = z__[i4 + 1] * (d__ / z__[i4 - (pp << 1) - 2]);
896 d__1 = emin, d__2 = z__[i4 - (pp << 1)];
897 emin = f2cmin(d__1,d__2);
900 z__[(n0 << 2) - pp - 2] = d__;
904 qmax = z__[(i0 << 2) - pp - 2];
905 i__1 = (n0 << 2) - pp - 2;
906 for (i4 = (i0 << 2) - pp + 2; i4 <= i__1; i4 += 4) {
908 d__1 = qmax, d__2 = z__[i4];
909 qmax = f2cmax(d__1,d__2);
913 /* Prepare for the next iteration on K. */
919 /* Initialise variables to pass to DLASQ3. */
935 for (iwhila = 1; iwhila <= i__1; ++iwhila) {
940 /* While array unfinished do */
942 /* E(N0) holds the value of SIGMA when submatrix in I0:N0 */
943 /* splits from the rest of the array, but is negated. */
949 sigma = -z__[(n0 << 2) - 1];
956 /* Find last unreduced submatrix's top index I0, find QMAX and */
957 /* EMIN. Find Gershgorin-type bound if Q's much greater than E's. */
961 emin = (d__1 = z__[(n0 << 2) - 5], abs(d__1));
965 qmin = z__[(n0 << 2) - 3];
967 for (i4 = n0 << 2; i4 >= 8; i4 += -4) {
968 if (z__[i4 - 5] <= 0.) {
971 if (qmin >= emax * 4.) {
973 d__1 = qmin, d__2 = z__[i4 - 3];
974 qmin = f2cmin(d__1,d__2);
976 d__1 = emax, d__2 = z__[i4 - 5];
977 emax = f2cmax(d__1,d__2);
980 d__1 = qmax, d__2 = z__[i4 - 7] + z__[i4 - 5];
981 qmax = f2cmax(d__1,d__2);
983 d__1 = emin, d__2 = z__[i4 - 5];
984 emin = f2cmin(d__1,d__2);
994 dee = z__[(i0 << 2) - 3];
997 i__2 = (n0 << 2) - 3;
998 for (i4 = (i0 << 2) + 1; i4 <= i__2; i4 += 4) {
999 dee = z__[i4] * (dee / (dee + z__[i4 - 2]));
1000 if (dee <= deemin) {
1002 kmin = (i4 + 3) / 4;
1006 if (kmin - i0 << 1 < n0 - kmin && deemin <= z__[(n0 << 2) - 3] *
1008 ipn4 = i0 + n0 << 2;
1010 i__2 = i0 + n0 - 1 << 1;
1011 for (i4 = i0 << 2; i4 <= i__2; i4 += 4) {
1013 z__[i4 - 3] = z__[ipn4 - i4 - 3];
1014 z__[ipn4 - i4 - 3] = temp;
1016 z__[i4 - 2] = z__[ipn4 - i4 - 2];
1017 z__[ipn4 - i4 - 2] = temp;
1019 z__[i4 - 1] = z__[ipn4 - i4 - 5];
1020 z__[ipn4 - i4 - 5] = temp;
1022 z__[i4] = z__[ipn4 - i4 - 4];
1023 z__[ipn4 - i4 - 4] = temp;
1029 /* Put -(initial shift) into DMIN. */
1032 d__1 = 0., d__2 = qmin - sqrt(qmin) * 2. * sqrt(emax);
1033 dmin__ = -f2cmax(d__1,d__2);
1035 /* Now I0:N0 is unreduced. */
1036 /* PP = 0 for ping, PP = 1 for pong. */
1037 /* PP = 2 indicates that flipping was applied to the Z array and */
1038 /* and that the tests for deflation upon entry in DLASQ3 */
1039 /* should not be performed. */
1041 nbig = (n0 - i0 + 1) * 100;
1043 for (iwhilb = 1; iwhilb <= i__2; ++iwhilb) {
1048 /* While submatrix unfinished take a good dqds step. */
1050 dlasq3_(&i0, &n0, &z__[1], &pp, &dmin__, &sigma, &desig, &qmax, &
1051 nfail, &iter, &ndiv, &ieee, &ttype, &dmin1, &dmin2, &dn, &
1052 dn1, &dn2, &g, &tau);
1056 /* When EMIN is very small check for splits. */
1058 if (pp == 0 && n0 - i0 >= 3) {
1059 if (z__[n0 * 4] <= tol2 * qmax || z__[(n0 << 2) - 1] <= tol2 *
1062 qmax = z__[(i0 << 2) - 3];
1063 emin = z__[(i0 << 2) - 1];
1064 oldemn = z__[i0 * 4];
1066 for (i4 = i0 << 2; i4 <= i__3; i4 += 4) {
1067 if (z__[i4] <= tol2 * z__[i4 - 3] || z__[i4 - 1] <=
1069 z__[i4 - 1] = -sigma;
1073 oldemn = z__[i4 + 4];
1076 d__1 = qmax, d__2 = z__[i4 + 1];
1077 qmax = f2cmax(d__1,d__2);
1079 d__1 = emin, d__2 = z__[i4 - 1];
1080 emin = f2cmin(d__1,d__2);
1082 d__1 = oldemn, d__2 = z__[i4];
1083 oldemn = f2cmin(d__1,d__2);
1087 z__[(n0 << 2) - 1] = emin;
1088 z__[n0 * 4] = oldemn;
1098 /* Maximum number of iterations exceeded, restore the shift */
1099 /* SIGMA and place the new d's and e's in a qd array. */
1100 /* This might need to be done for several blocks */
1105 tempq = z__[(i0 << 2) - 3];
1106 z__[(i0 << 2) - 3] += sigma;
1108 for (k = i0 + 1; k <= i__2; ++k) {
1109 tempe = z__[(k << 2) - 5];
1110 z__[(k << 2) - 5] *= tempq / z__[(k << 2) - 7];
1111 tempq = z__[(k << 2) - 3];
1112 z__[(k << 2) - 3] = z__[(k << 2) - 3] + sigma + tempe - z__[(k <<
1116 /* Prepare to do this on the previous block if there is one */
1120 while(i1 >= 2 && z__[(i1 << 2) - 5] >= 0.) {
1123 sigma = -z__[(n1 << 2) - 1];
1127 for (k = 1; k <= i__2; ++k) {
1128 z__[(k << 1) - 1] = z__[(k << 2) - 3];
1130 /* Only the block 1..N0 is unfinished. The rest of the e's */
1131 /* must be essentially zero, although sometimes other data */
1132 /* has been stored in them. */
1135 z__[k * 2] = z__[(k << 2) - 1];
1157 /* Move q's to the front. */
1160 for (k = 2; k <= i__1; ++k) {
1161 z__[k] = z__[(k << 2) - 3];
1165 /* Sort and compute sum of eigenvalues. */
1167 dlasrt_("D", n, &z__[1], &iinfo);
1170 for (k = *n; k >= 1; --k) {
1175 /* Store trace, sum(eigenvalues) and information on performance. */
1177 z__[(*n << 1) + 1] = trace;
1178 z__[(*n << 1) + 2] = e;
1179 z__[(*n << 1) + 3] = (doublereal) iter;
1180 /* Computing 2nd power */
1182 z__[(*n << 1) + 4] = (doublereal) ndiv / (doublereal) (i__1 * i__1);
1183 z__[(*n << 1) + 5] = nfail * 100. / (doublereal) iter;