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 real c_b3 = -1.f;
516 static integer c__1 = 1;
518 /* > \brief \b CLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download CLAED8 + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/claed8.
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/claed8.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/claed8.
542 /* SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, */
543 /* Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, */
544 /* GIVCOL, GIVNUM, INFO ) */
546 /* INTEGER CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ */
548 /* INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), */
549 /* $ INDXQ( * ), PERM( * ) */
550 /* REAL D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ), */
552 /* COMPLEX Q( LDQ, * ), Q2( LDQ2, * ) */
555 /* > \par Purpose: */
560 /* > CLAED8 merges the two sets of eigenvalues together into a single */
561 /* > sorted set. Then it tries to deflate the size of the problem. */
562 /* > There are two ways in which deflation can occur: when two or more */
563 /* > eigenvalues are close together or if there is a tiny element in the */
564 /* > Z vector. For each such occurrence the order of the related secular */
565 /* > equation problem is reduced by one. */
571 /* > \param[out] K */
574 /* > Contains the number of non-deflated eigenvalues. */
575 /* > This is the order of the related secular equation. */
581 /* > The dimension of the symmetric tridiagonal matrix. N >= 0. */
584 /* > \param[in] QSIZ */
586 /* > QSIZ is INTEGER */
587 /* > The dimension of the unitary matrix used to reduce */
588 /* > the dense or band matrix to tridiagonal form. */
589 /* > QSIZ >= N if ICOMPQ = 1. */
592 /* > \param[in,out] Q */
594 /* > Q is COMPLEX array, dimension (LDQ,N) */
595 /* > On entry, Q contains the eigenvectors of the partially solved */
596 /* > system which has been previously updated in matrix */
597 /* > multiplies with other partially solved eigensystems. */
598 /* > On exit, Q contains the trailing (N-K) updated eigenvectors */
599 /* > (those which were deflated) in its last N-K columns. */
602 /* > \param[in] LDQ */
604 /* > LDQ is INTEGER */
605 /* > The leading dimension of the array Q. LDQ >= f2cmax( 1, N ). */
608 /* > \param[in,out] D */
610 /* > D is REAL array, dimension (N) */
611 /* > On entry, D contains the eigenvalues of the two submatrices to */
612 /* > be combined. On exit, D contains the trailing (N-K) updated */
613 /* > eigenvalues (those which were deflated) sorted into increasing */
617 /* > \param[in,out] RHO */
620 /* > Contains the off diagonal element associated with the rank-1 */
621 /* > cut which originally split the two submatrices which are now */
622 /* > being recombined. RHO is modified during the computation to */
623 /* > the value required by SLAED3. */
626 /* > \param[in] CUTPNT */
628 /* > CUTPNT is INTEGER */
629 /* > Contains the location of the last eigenvalue in the leading */
630 /* > sub-matrix. MIN(1,N) <= CUTPNT <= N. */
635 /* > Z is REAL array, dimension (N) */
636 /* > On input this vector contains the updating vector (the last */
637 /* > row of the first sub-eigenvector matrix and the first row of */
638 /* > the second sub-eigenvector matrix). The contents of Z are */
639 /* > destroyed during the updating process. */
642 /* > \param[out] DLAMDA */
644 /* > DLAMDA is REAL array, dimension (N) */
645 /* > Contains a copy of the first K eigenvalues which will be used */
646 /* > by SLAED3 to form the secular equation. */
649 /* > \param[out] Q2 */
651 /* > Q2 is COMPLEX array, dimension (LDQ2,N) */
652 /* > If ICOMPQ = 0, Q2 is not referenced. Otherwise, */
653 /* > Contains a copy of the first K eigenvectors which will be used */
654 /* > by SLAED7 in a matrix multiply (SGEMM) to update the new */
655 /* > eigenvectors. */
658 /* > \param[in] LDQ2 */
660 /* > LDQ2 is INTEGER */
661 /* > The leading dimension of the array Q2. LDQ2 >= f2cmax( 1, N ). */
664 /* > \param[out] W */
666 /* > W is REAL array, dimension (N) */
667 /* > This will hold the first k values of the final */
668 /* > deflation-altered z-vector and will be passed to SLAED3. */
671 /* > \param[out] INDXP */
673 /* > INDXP is INTEGER array, dimension (N) */
674 /* > This will contain the permutation used to place deflated */
675 /* > values of D at the end of the array. On output INDXP(1:K) */
676 /* > points to the nondeflated D-values and INDXP(K+1:N) */
677 /* > points to the deflated eigenvalues. */
680 /* > \param[out] INDX */
682 /* > INDX is INTEGER array, dimension (N) */
683 /* > This will contain the permutation used to sort the contents of */
684 /* > D into ascending order. */
687 /* > \param[in] INDXQ */
689 /* > INDXQ is INTEGER array, dimension (N) */
690 /* > This contains the permutation which separately sorts the two */
691 /* > sub-problems in D into ascending order. Note that elements in */
692 /* > the second half of this permutation must first have CUTPNT */
693 /* > added to their values in order to be accurate. */
696 /* > \param[out] PERM */
698 /* > PERM is INTEGER array, dimension (N) */
699 /* > Contains the permutations (from deflation and sorting) to be */
700 /* > applied to each eigenblock. */
703 /* > \param[out] GIVPTR */
705 /* > GIVPTR is INTEGER */
706 /* > Contains the number of Givens rotations which took place in */
707 /* > this subproblem. */
710 /* > \param[out] GIVCOL */
712 /* > GIVCOL is INTEGER array, dimension (2, N) */
713 /* > Each pair of numbers indicates a pair of columns to take place */
714 /* > in a Givens rotation. */
717 /* > \param[out] GIVNUM */
719 /* > GIVNUM is REAL array, dimension (2, N) */
720 /* > Each number indicates the S value to be used in the */
721 /* > corresponding Givens rotation. */
724 /* > \param[out] INFO */
726 /* > INFO is INTEGER */
727 /* > = 0: successful exit. */
728 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
734 /* > \author Univ. of Tennessee */
735 /* > \author Univ. of California Berkeley */
736 /* > \author Univ. of Colorado Denver */
737 /* > \author NAG Ltd. */
739 /* > \date December 2016 */
741 /* > \ingroup complexOTHERcomputational */
743 /* ===================================================================== */
744 /* Subroutine */ int claed8_(integer *k, integer *n, integer *qsiz, complex *
745 q, integer *ldq, real *d__, real *rho, integer *cutpnt, real *z__,
746 real *dlamda, complex *q2, integer *ldq2, real *w, integer *indxp,
747 integer *indx, integer *indxq, integer *perm, integer *givptr,
748 integer *givcol, real *givnum, integer *info)
750 /* System generated locals */
751 integer q_dim1, q_offset, q2_dim1, q2_offset, i__1;
754 /* Local variables */
755 integer jlam, imax, jmax;
759 extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *),
760 ccopy_(integer *, complex *, integer *, complex *, integer *),
761 csrot_(integer *, complex *, integer *, complex *, integer *,
764 extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
767 extern real slapy2_(real *, real *);
769 extern real slamch_(char *);
770 extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
771 *, integer *, complex *, integer *), xerbla_(char *,
773 extern integer isamax_(integer *, real *, integer *);
774 extern /* Subroutine */ int slamrg_(integer *, integer *, real *, integer
775 *, integer *, integer *);
780 /* -- LAPACK computational routine (version 3.7.0) -- */
781 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
782 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
786 /* ===================================================================== */
789 /* Test the input parameters. */
791 /* Parameter adjustments */
793 q_offset = 1 + q_dim1 * 1;
799 q2_offset = 1 + q2_dim1 * 1;
814 } else if (*qsiz < *n) {
816 } else if (*ldq < f2cmax(1,*n)) {
818 } else if (*cutpnt < f2cmin(1,*n) || *cutpnt > *n) {
820 } else if (*ldq2 < f2cmax(1,*n)) {
825 xerbla_("CLAED8", &i__1, (ftnlen)6);
829 /* Need to initialize GIVPTR to O here in case of quick exit */
830 /* to prevent an unspecified code behavior (usually sigfault) */
831 /* when IWORK array on entry to *stedc is not zeroed */
832 /* (or at least some IWORK entries which used in *laed7 for GIVPTR). */
836 /* Quick return if possible */
847 sscal_(&n2, &c_b3, &z__[n1p1], &c__1);
850 /* Normalize z so that norm(z) = 1 */
854 for (j = 1; j <= i__1; ++j) {
858 sscal_(n, &t, &z__[1], &c__1);
859 *rho = (r__1 = *rho * 2.f, abs(r__1));
861 /* Sort the eigenvalues into increasing order */
864 for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) {
865 indxq[i__] += *cutpnt;
869 for (i__ = 1; i__ <= i__1; ++i__) {
870 dlamda[i__] = d__[indxq[i__]];
871 w[i__] = z__[indxq[i__]];
876 slamrg_(&n1, &n2, &dlamda[1], &c__1, &c__1, &indx[1]);
878 for (i__ = 1; i__ <= i__1; ++i__) {
879 d__[i__] = dlamda[indx[i__]];
880 z__[i__] = w[indx[i__]];
884 /* Calculate the allowable deflation tolerance */
886 imax = isamax_(n, &z__[1], &c__1);
887 jmax = isamax_(n, &d__[1], &c__1);
888 eps = slamch_("Epsilon");
889 tol = eps * 8.f * (r__1 = d__[jmax], abs(r__1));
891 /* If the rank-1 modifier is small enough, no more needs to be done */
892 /* -- except to reorganize Q so that its columns correspond with the */
895 if (*rho * (r__1 = z__[imax], abs(r__1)) <= tol) {
898 for (j = 1; j <= i__1; ++j) {
899 perm[j] = indxq[indx[j]];
900 ccopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1]
904 clacpy_("A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq);
908 /* If there are multiple eigenvalues then the problem deflates. Here */
909 /* the number of equal eigenvalues are found. As each equal */
910 /* eigenvalue is found, an elementary reflector is computed to rotate */
911 /* the corresponding eigensubspace so that the corresponding */
912 /* components of Z are zero in this new basis. */
917 for (j = 1; j <= i__1; ++j) {
918 if (*rho * (r__1 = z__[j], abs(r__1)) <= tol) {
920 /* Deflate due to small z component. */
938 if (*rho * (r__1 = z__[j], abs(r__1)) <= tol) {
940 /* Deflate due to small z component. */
946 /* Check if eigenvalues are close enough to allow deflation. */
951 /* Find sqrt(a**2+b**2) without overflow or */
952 /* destructive underflow. */
954 tau = slapy2_(&c__, &s);
955 t = d__[j] - d__[jlam];
958 if ((r__1 = t * c__ * s, abs(r__1)) <= tol) {
960 /* Deflation is possible. */
965 /* Record the appropriate Givens rotation */
968 givcol[(*givptr << 1) + 1] = indxq[indx[jlam]];
969 givcol[(*givptr << 1) + 2] = indxq[indx[j]];
970 givnum[(*givptr << 1) + 1] = c__;
971 givnum[(*givptr << 1) + 2] = s;
972 csrot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[indxq[
973 indx[j]] * q_dim1 + 1], &c__1, &c__, &s);
974 t = d__[jlam] * c__ * c__ + d__[j] * s * s;
975 d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__;
980 if (k2 + i__ <= *n) {
981 if (d__[jlam] < d__[indxp[k2 + i__]]) {
982 indxp[k2 + i__ - 1] = indxp[k2 + i__];
983 indxp[k2 + i__] = jlam;
987 indxp[k2 + i__ - 1] = jlam;
990 indxp[k2 + i__ - 1] = jlam;
996 dlamda[*k] = d__[jlam];
1004 /* Record the last eigenvalue. */
1008 dlamda[*k] = d__[jlam];
1013 /* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */
1014 /* and Q2 respectively. The eigenvalues/vectors which were not */
1015 /* deflated go into the first K slots of DLAMDA and Q2 respectively, */
1016 /* while those which were deflated go into the last N - K slots. */
1019 for (j = 1; j <= i__1; ++j) {
1021 dlamda[j] = d__[jp];
1022 perm[j] = indxq[indx[jp]];
1023 ccopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], &
1028 /* The deflated eigenvalues and their corresponding vectors go back */
1029 /* into the last N - K slots of D and Q respectively. */
1033 scopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1);
1035 clacpy_("A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*k +
1036 1) * q_dim1 + 1], ldq);