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 doublereal c_b22 = 1.;
517 static doublereal c_b23 = 0.;
519 /* > \brief \b DLAED3 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Us
520 ed when the original matrix is tridiagonal. */
522 /* =========== DOCUMENTATION =========== */
524 /* Online html documentation available at */
525 /* http://www.netlib.org/lapack/explore-html/ */
528 /* > Download DLAED3 + dependencies */
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed3.
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed3.
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed3.
543 /* SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, */
544 /* CTOT, W, S, INFO ) */
546 /* INTEGER INFO, K, LDQ, N, N1 */
547 /* DOUBLE PRECISION RHO */
548 /* INTEGER CTOT( * ), INDX( * ) */
549 /* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), */
550 /* $ S( * ), W( * ) */
553 /* > \par Purpose: */
558 /* > DLAED3 finds the roots of the secular equation, as defined by the */
559 /* > values in D, W, and RHO, between 1 and K. It makes the */
560 /* > appropriate calls to DLAED4 and then updates the eigenvectors by */
561 /* > multiplying the matrix of eigenvectors of the pair of eigensystems */
562 /* > being combined by the matrix of eigenvectors of the K-by-K system */
563 /* > which is solved here. */
565 /* > This code makes very mild assumptions about floating point */
566 /* > arithmetic. It will work on machines with a guard digit in */
567 /* > add/subtract, or on those binary machines without guard digits */
568 /* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */
569 /* > It could conceivably fail on hexadecimal or decimal machines */
570 /* > without guard digits, but we know of none. */
579 /* > The number of terms in the rational function to be solved by */
580 /* > DLAED4. K >= 0. */
586 /* > The number of rows and columns in the Q matrix. */
587 /* > N >= K (deflation may result in N>K). */
590 /* > \param[in] N1 */
592 /* > N1 is INTEGER */
593 /* > The location of the last eigenvalue in the leading submatrix. */
594 /* > f2cmin(1,N) <= N1 <= N/2. */
597 /* > \param[out] D */
599 /* > D is DOUBLE PRECISION array, dimension (N) */
600 /* > D(I) contains the updated eigenvalues for */
604 /* > \param[out] Q */
606 /* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
607 /* > Initially the first K columns are used as workspace. */
608 /* > On output the columns 1 to K contain */
609 /* > the updated eigenvectors. */
612 /* > \param[in] LDQ */
614 /* > LDQ is INTEGER */
615 /* > The leading dimension of the array Q. LDQ >= f2cmax(1,N). */
618 /* > \param[in] RHO */
620 /* > RHO is DOUBLE PRECISION */
621 /* > The value of the parameter in the rank one update equation. */
622 /* > RHO >= 0 required. */
625 /* > \param[in,out] DLAMDA */
627 /* > DLAMDA is DOUBLE PRECISION array, dimension (K) */
628 /* > The first K elements of this array contain the old roots */
629 /* > of the deflated updating problem. These are the poles */
630 /* > of the secular equation. May be changed on output by */
631 /* > having lowest order bit set to zero on Cray X-MP, Cray Y-MP, */
632 /* > Cray-2, or Cray C-90, as described above. */
635 /* > \param[in] Q2 */
637 /* > Q2 is DOUBLE PRECISION array, dimension (LDQ2*N) */
638 /* > The first K columns of this matrix contain the non-deflated */
639 /* > eigenvectors for the split problem. */
642 /* > \param[in] INDX */
644 /* > INDX is INTEGER array, dimension (N) */
645 /* > The permutation used to arrange the columns of the deflated */
646 /* > Q matrix into three groups (see DLAED2). */
647 /* > The rows of the eigenvectors found by DLAED4 must be likewise */
648 /* > permuted before the matrix multiply can take place. */
651 /* > \param[in] CTOT */
653 /* > CTOT is INTEGER array, dimension (4) */
654 /* > A count of the total number of the various types of columns */
655 /* > in Q, as described in INDX. The fourth column type is any */
656 /* > column which has been deflated. */
659 /* > \param[in,out] W */
661 /* > W is DOUBLE PRECISION array, dimension (K) */
662 /* > The first K elements of this array contain the components */
663 /* > of the deflation-adjusted updating vector. Destroyed on */
667 /* > \param[out] S */
669 /* > S is DOUBLE PRECISION array, dimension (N1 + 1)*K */
670 /* > Will contain the eigenvectors of the repaired matrix which */
671 /* > will be multiplied by the previously accumulated eigenvectors */
672 /* > to update the system. */
675 /* > \param[out] INFO */
677 /* > INFO is INTEGER */
678 /* > = 0: successful exit. */
679 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
680 /* > > 0: if INFO = 1, an eigenvalue did not converge */
686 /* > \author Univ. of Tennessee */
687 /* > \author Univ. of California Berkeley */
688 /* > \author Univ. of Colorado Denver */
689 /* > \author NAG Ltd. */
691 /* > \date June 2017 */
693 /* > \ingroup auxOTHERcomputational */
695 /* > \par Contributors: */
696 /* ================== */
698 /* > Jeff Rutter, Computer Science Division, University of California */
699 /* > at Berkeley, USA \n */
700 /* > Modified by Francoise Tisseur, University of Tennessee */
702 /* ===================================================================== */
703 /* Subroutine */ int dlaed3_(integer *k, integer *n, integer *n1, doublereal *
704 d__, doublereal *q, integer *ldq, doublereal *rho, doublereal *dlamda,
705 doublereal *q2, integer *indx, integer *ctot, doublereal *w,
706 doublereal *s, integer *info)
708 /* System generated locals */
709 integer q_dim1, q_offset, i__1, i__2;
712 /* Local variables */
714 extern doublereal dnrm2_(integer *, doublereal *, integer *);
716 extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
717 integer *, doublereal *, doublereal *, integer *, doublereal *,
718 integer *, doublereal *, doublereal *, integer *),
719 dcopy_(integer *, doublereal *, integer *, doublereal *, integer
720 *), dlaed4_(integer *, integer *, doublereal *, doublereal *,
721 doublereal *, doublereal *, doublereal *, integer *);
723 extern doublereal dlamc3_(doublereal *, doublereal *);
724 integer n12, ii, n23;
725 extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
726 doublereal *, integer *, doublereal *, integer *),
727 dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
728 doublereal *, integer *), xerbla_(char *, integer *, ftnlen);
732 /* -- LAPACK computational routine (version 3.7.1) -- */
733 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
734 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
738 /* ===================================================================== */
741 /* Test the input parameters. */
743 /* Parameter adjustments */
746 q_offset = 1 + q_dim1 * 1;
760 } else if (*n < *k) {
762 } else if (*ldq < f2cmax(1,*n)) {
767 xerbla_("DLAED3", &i__1, (ftnlen)6);
771 /* Quick return if possible */
777 /* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */
778 /* be computed with high relative accuracy (barring over/underflow). */
779 /* This is a problem on machines without a guard digit in */
780 /* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */
781 /* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */
782 /* which on any of these machines zeros out the bottommost */
783 /* bit of DLAMDA(I) if it is 1; this makes the subsequent */
784 /* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */
785 /* occurs. On binary machines with a guard digit (almost all */
786 /* machines) it does not change DLAMDA(I) at all. On hexadecimal */
787 /* and decimal machines with a guard digit, it slightly */
788 /* changes the bottommost bits of DLAMDA(I). It does not account */
789 /* for hexadecimal or decimal machines without guard digits */
790 /* (we know of none). We use a subroutine call to compute */
791 /* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */
795 for (i__ = 1; i__ <= i__1; ++i__) {
796 dlamda[i__] = dlamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__];
801 for (j = 1; j <= i__1; ++j) {
802 dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j],
805 /* If the zero finder fails, the computation is terminated. */
818 for (j = 1; j <= i__1; ++j) {
819 w[1] = q[j * q_dim1 + 1];
820 w[2] = q[j * q_dim1 + 2];
822 q[j * q_dim1 + 1] = w[ii];
824 q[j * q_dim1 + 2] = w[ii];
830 /* Compute updated W. */
832 dcopy_(k, &w[1], &c__1, &s[1], &c__1);
834 /* Initialize W(I) = Q(I,I) */
837 dcopy_(k, &q[q_offset], &i__1, &w[1], &c__1);
839 for (j = 1; j <= i__1; ++j) {
841 for (i__ = 1; i__ <= i__2; ++i__) {
842 w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
846 for (i__ = j + 1; i__ <= i__2; ++i__) {
847 w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
853 for (i__ = 1; i__ <= i__1; ++i__) {
854 d__1 = sqrt(-w[i__]);
855 w[i__] = d_sign(&d__1, &s[i__]);
859 /* Compute eigenvectors of the modified rank-1 modification. */
862 for (j = 1; j <= i__1; ++j) {
864 for (i__ = 1; i__ <= i__2; ++i__) {
865 s[i__] = w[i__] / q[i__ + j * q_dim1];
868 temp = dnrm2_(k, &s[1], &c__1);
870 for (i__ = 1; i__ <= i__2; ++i__) {
872 q[i__ + j * q_dim1] = s[ii] / temp;
878 /* Compute the updated eigenvectors. */
883 n12 = ctot[1] + ctot[2];
884 n23 = ctot[2] + ctot[3];
886 dlacpy_("A", &n23, k, &q[ctot[1] + 1 + q_dim1], ldq, &s[1], &n23);
889 dgemm_("N", "N", &n2, k, &n23, &c_b22, &q2[iq2], &n2, &s[1], &n23, &
890 c_b23, &q[*n1 + 1 + q_dim1], ldq);
892 dlaset_("A", &n2, k, &c_b23, &c_b23, &q[*n1 + 1 + q_dim1], ldq);
895 dlacpy_("A", &n12, k, &q[q_offset], ldq, &s[1], &n12);
897 dgemm_("N", "N", n1, k, &n12, &c_b22, &q2[1], n1, &s[1], &n12, &c_b23,
900 dlaset_("A", n1, k, &c_b23, &c_b23, &q[q_dim1 + 1], ldq);