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 SLAED8 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 SLAED8 + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slaed8.
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slaed8.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slaed8.
542 /* SUBROUTINE SLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, */
543 /* CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, */
544 /* GIVCOL, GIVNUM, INDXP, INDX, INFO ) */
546 /* INTEGER CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, */
549 /* INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), */
550 /* $ INDXQ( * ), PERM( * ) */
551 /* REAL D( * ), DLAMDA( * ), GIVNUM( 2, * ), */
552 /* $ Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * ) */
555 /* > \par Purpose: */
560 /* > SLAED8 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[in] ICOMPQ */
573 /* > ICOMPQ is INTEGER */
574 /* > = 0: Compute eigenvalues only. */
575 /* > = 1: Compute eigenvectors of original dense symmetric matrix */
576 /* > also. On entry, Q contains the orthogonal matrix used */
577 /* > to reduce the original matrix to tridiagonal form. */
580 /* > \param[out] K */
583 /* > The number of non-deflated eigenvalues, and the order of the */
584 /* > related secular equation. */
590 /* > The dimension of the symmetric tridiagonal matrix. N >= 0. */
593 /* > \param[in] QSIZ */
595 /* > QSIZ is INTEGER */
596 /* > The dimension of the orthogonal matrix used to reduce */
597 /* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */
600 /* > \param[in,out] D */
602 /* > D is REAL array, dimension (N) */
603 /* > On entry, the eigenvalues of the two submatrices to be */
604 /* > combined. On exit, the trailing (N-K) updated eigenvalues */
605 /* > (those which were deflated) sorted into increasing order. */
608 /* > \param[in,out] Q */
610 /* > Q is REAL array, dimension (LDQ,N) */
611 /* > If ICOMPQ = 0, Q is not referenced. Otherwise, */
612 /* > on entry, Q contains the eigenvectors of the partially solved */
613 /* > system which has been previously updated in matrix */
614 /* > multiplies with other partially solved eigensystems. */
615 /* > On exit, Q contains the trailing (N-K) updated eigenvectors */
616 /* > (those which were deflated) in its last N-K columns. */
619 /* > \param[in] LDQ */
621 /* > LDQ is INTEGER */
622 /* > The leading dimension of the array Q. LDQ >= f2cmax(1,N). */
625 /* > \param[in] INDXQ */
627 /* > INDXQ is INTEGER array, dimension (N) */
628 /* > The permutation which separately sorts the two sub-problems */
629 /* > in D into ascending order. Note that elements in the second */
630 /* > half of this permutation must first have CUTPNT added to */
631 /* > their values in order to be accurate. */
634 /* > \param[in,out] RHO */
637 /* > On entry, the off-diagonal element associated with the rank-1 */
638 /* > cut which originally split the two submatrices which are now */
639 /* > being recombined. */
640 /* > On exit, RHO has been modified to the value required by */
644 /* > \param[in] CUTPNT */
646 /* > CUTPNT is INTEGER */
647 /* > The location of the last eigenvalue in the leading */
648 /* > sub-matrix. f2cmin(1,N) <= CUTPNT <= N. */
653 /* > Z is REAL array, dimension (N) */
654 /* > On entry, Z contains the updating vector (the last row of */
655 /* > the first sub-eigenvector matrix and the first row of the */
656 /* > second sub-eigenvector matrix). */
657 /* > On exit, the contents of Z are destroyed by the updating */
661 /* > \param[out] DLAMDA */
663 /* > DLAMDA is REAL array, dimension (N) */
664 /* > A copy of the first K eigenvalues which will be used by */
665 /* > SLAED3 to form the secular equation. */
668 /* > \param[out] Q2 */
670 /* > Q2 is REAL array, dimension (LDQ2,N) */
671 /* > If ICOMPQ = 0, Q2 is not referenced. Otherwise, */
672 /* > a copy of the first K eigenvectors which will be used by */
673 /* > SLAED7 in a matrix multiply (SGEMM) to update the new */
674 /* > eigenvectors. */
677 /* > \param[in] LDQ2 */
679 /* > LDQ2 is INTEGER */
680 /* > The leading dimension of the array Q2. LDQ2 >= f2cmax(1,N). */
683 /* > \param[out] W */
685 /* > W is REAL array, dimension (N) */
686 /* > The first k values of the final deflation-altered z-vector and */
687 /* > will be passed to SLAED3. */
690 /* > \param[out] PERM */
692 /* > PERM is INTEGER array, dimension (N) */
693 /* > The permutations (from deflation and sorting) to be applied */
694 /* > to each eigenblock. */
697 /* > \param[out] GIVPTR */
699 /* > GIVPTR is INTEGER */
700 /* > The number of Givens rotations which took place in this */
704 /* > \param[out] GIVCOL */
706 /* > GIVCOL is INTEGER array, dimension (2, N) */
707 /* > Each pair of numbers indicates a pair of columns to take place */
708 /* > in a Givens rotation. */
711 /* > \param[out] GIVNUM */
713 /* > GIVNUM is REAL array, dimension (2, N) */
714 /* > Each number indicates the S value to be used in the */
715 /* > corresponding Givens rotation. */
718 /* > \param[out] INDXP */
720 /* > INDXP is INTEGER array, dimension (N) */
721 /* > The permutation used to place deflated values of D at the end */
722 /* > of the array. INDXP(1:K) points to the nondeflated D-values */
723 /* > and INDXP(K+1:N) points to the deflated eigenvalues. */
726 /* > \param[out] INDX */
728 /* > INDX is INTEGER array, dimension (N) */
729 /* > The permutation used to sort the contents of D into ascending */
733 /* > \param[out] INFO */
735 /* > INFO is INTEGER */
736 /* > = 0: successful exit. */
737 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
743 /* > \author Univ. of Tennessee */
744 /* > \author Univ. of California Berkeley */
745 /* > \author Univ. of Colorado Denver */
746 /* > \author NAG Ltd. */
748 /* > \date December 2016 */
750 /* > \ingroup auxOTHERcomputational */
752 /* > \par Contributors: */
753 /* ================== */
755 /* > Jeff Rutter, Computer Science Division, University of California */
756 /* > at Berkeley, USA */
758 /* ===================================================================== */
759 /* Subroutine */ int slaed8_(integer *icompq, integer *k, integer *n, integer
760 *qsiz, real *d__, real *q, integer *ldq, integer *indxq, real *rho,
761 integer *cutpnt, real *z__, real *dlamda, real *q2, integer *ldq2,
762 real *w, integer *perm, integer *givptr, integer *givcol, real *
763 givnum, integer *indxp, integer *indx, integer *info)
765 /* System generated locals */
766 integer q_dim1, q_offset, q2_dim1, q2_offset, i__1;
769 /* Local variables */
770 integer jlam, imax, jmax;
771 extern /* Subroutine */ int srot_(integer *, real *, integer *, real *,
772 integer *, real *, real *);
776 extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
778 extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
781 extern real slapy2_(real *, real *);
783 extern real slamch_(char *);
784 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
785 extern integer isamax_(integer *, real *, integer *);
786 extern /* Subroutine */ int slamrg_(integer *, integer *, real *, integer
787 *, integer *, integer *), slacpy_(char *, integer *, integer *,
788 real *, integer *, real *, integer *);
793 /* -- LAPACK computational routine (version 3.7.0) -- */
794 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
795 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
799 /* ===================================================================== */
803 /* Test the input parameters. */
805 /* Parameter adjustments */
808 q_offset = 1 + q_dim1 * 1;
814 q2_offset = 1 + q2_dim1 * 1;
826 if (*icompq < 0 || *icompq > 1) {
830 } else if (*icompq == 1 && *qsiz < *n) {
832 } else if (*ldq < f2cmax(1,*n)) {
834 } else if (*cutpnt < f2cmin(1,*n) || *cutpnt > *n) {
836 } else if (*ldq2 < f2cmax(1,*n)) {
841 xerbla_("SLAED8", &i__1, (ftnlen)6);
845 /* Need to initialize GIVPTR to O here in case of quick exit */
846 /* to prevent an unspecified code behavior (usually sigfault) */
847 /* when IWORK array on entry to *stedc is not zeroed */
848 /* (or at least some IWORK entries which used in *laed7 for GIVPTR). */
852 /* Quick return if possible */
863 sscal_(&n2, &c_b3, &z__[n1p1], &c__1);
866 /* Normalize z so that norm(z) = 1 */
870 for (j = 1; j <= i__1; ++j) {
874 sscal_(n, &t, &z__[1], &c__1);
875 *rho = (r__1 = *rho * 2.f, abs(r__1));
877 /* Sort the eigenvalues into increasing order */
880 for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) {
881 indxq[i__] += *cutpnt;
885 for (i__ = 1; i__ <= i__1; ++i__) {
886 dlamda[i__] = d__[indxq[i__]];
887 w[i__] = z__[indxq[i__]];
892 slamrg_(&n1, &n2, &dlamda[1], &c__1, &c__1, &indx[1]);
894 for (i__ = 1; i__ <= i__1; ++i__) {
895 d__[i__] = dlamda[indx[i__]];
896 z__[i__] = w[indx[i__]];
900 /* Calculate the allowable deflation tolerance */
902 imax = isamax_(n, &z__[1], &c__1);
903 jmax = isamax_(n, &d__[1], &c__1);
904 eps = slamch_("Epsilon");
905 tol = eps * 8.f * (r__1 = d__[jmax], abs(r__1));
907 /* If the rank-1 modifier is small enough, no more needs to be done */
908 /* except to reorganize Q so that its columns correspond with the */
911 if (*rho * (r__1 = z__[imax], abs(r__1)) <= tol) {
915 for (j = 1; j <= i__1; ++j) {
916 perm[j] = indxq[indx[j]];
921 for (j = 1; j <= i__1; ++j) {
922 perm[j] = indxq[indx[j]];
923 scopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1
927 slacpy_("A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq);
932 /* If there are multiple eigenvalues then the problem deflates. Here */
933 /* the number of equal eigenvalues are found. As each equal */
934 /* eigenvalue is found, an elementary reflector is computed to rotate */
935 /* the corresponding eigensubspace so that the corresponding */
936 /* components of Z are zero in this new basis. */
941 for (j = 1; j <= i__1; ++j) {
942 if (*rho * (r__1 = z__[j], abs(r__1)) <= tol) {
944 /* Deflate due to small z component. */
962 if (*rho * (r__1 = z__[j], abs(r__1)) <= tol) {
964 /* Deflate due to small z component. */
970 /* Check if eigenvalues are close enough to allow deflation. */
975 /* Find sqrt(a**2+b**2) without overflow or */
976 /* destructive underflow. */
978 tau = slapy2_(&c__, &s);
979 t = d__[j] - d__[jlam];
982 if ((r__1 = t * c__ * s, abs(r__1)) <= tol) {
984 /* Deflation is possible. */
989 /* Record the appropriate Givens rotation */
992 givcol[(*givptr << 1) + 1] = indxq[indx[jlam]];
993 givcol[(*givptr << 1) + 2] = indxq[indx[j]];
994 givnum[(*givptr << 1) + 1] = c__;
995 givnum[(*givptr << 1) + 2] = s;
997 srot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[
998 indxq[indx[j]] * q_dim1 + 1], &c__1, &c__, &s);
1000 t = d__[jlam] * c__ * c__ + d__[j] * s * s;
1001 d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__;
1006 if (k2 + i__ <= *n) {
1007 if (d__[jlam] < d__[indxp[k2 + i__]]) {
1008 indxp[k2 + i__ - 1] = indxp[k2 + i__];
1009 indxp[k2 + i__] = jlam;
1013 indxp[k2 + i__ - 1] = jlam;
1016 indxp[k2 + i__ - 1] = jlam;
1022 dlamda[*k] = d__[jlam];
1030 /* Record the last eigenvalue. */
1034 dlamda[*k] = d__[jlam];
1039 /* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */
1040 /* and Q2 respectively. The eigenvalues/vectors which were not */
1041 /* deflated go into the first K slots of DLAMDA and Q2 respectively, */
1042 /* while those which were deflated go into the last N - K slots. */
1046 for (j = 1; j <= i__1; ++j) {
1048 dlamda[j] = d__[jp];
1049 perm[j] = indxq[indx[jp]];
1054 for (j = 1; j <= i__1; ++j) {
1056 dlamda[j] = d__[jp];
1057 perm[j] = indxq[indx[jp]];
1058 scopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1]
1064 /* The deflated eigenvalues and their corresponding vectors go back */
1065 /* into the last N - K slots of D and Q respectively. */
1070 scopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1);
1073 scopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1);
1075 slacpy_("A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*
1076 k + 1) * q_dim1 + 1], ldq);