14 typedef long long BLASLONG;
15 typedef unsigned long long BLASULONG;
17 typedef long BLASLONG;
18 typedef unsigned long BLASULONG;
22 typedef BLASLONG blasint;
24 #define blasabs(x) llabs(x)
26 #define blasabs(x) labs(x)
30 #define blasabs(x) abs(x)
33 typedef blasint integer;
35 typedef unsigned int uinteger;
36 typedef char *address;
37 typedef short int shortint;
39 typedef double doublereal;
40 typedef struct { real r, i; } complex;
41 typedef struct { doublereal r, i; } doublecomplex;
43 static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
44 static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
45 static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
46 static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
48 static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
49 static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
50 static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
51 static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
53 #define pCf(z) (*_pCf(z))
54 #define pCd(z) (*_pCd(z))
56 typedef short int shortlogical;
57 typedef char logical1;
58 typedef char integer1;
63 /* Extern is for use with -E */
74 /*external read, write*/
83 /*internal read, write*/
113 /*rewind, backspace, endfile*/
125 ftnint *inex; /*parameters in standard's order*/
151 union Multitype { /* for multiple entry points */
162 typedef union Multitype Multitype;
164 struct Vardesc { /* for Namelist */
170 typedef struct Vardesc Vardesc;
177 typedef struct Namelist Namelist;
179 #define abs(x) ((x) >= 0 ? (x) : -(x))
180 #define dabs(x) (fabs(x))
181 #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
182 #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
183 #define dmin(a,b) (f2cmin(a,b))
184 #define dmax(a,b) (f2cmax(a,b))
185 #define bit_test(a,b) ((a) >> (b) & 1)
186 #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
187 #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
189 #define abort_() { sig_die("Fortran abort routine called", 1); }
190 #define c_abs(z) (cabsf(Cf(z)))
191 #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
193 #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
194 #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
196 #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
197 #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
199 #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
200 #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
201 #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
202 //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
203 #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
204 #define d_abs(x) (fabs(*(x)))
205 #define d_acos(x) (acos(*(x)))
206 #define d_asin(x) (asin(*(x)))
207 #define d_atan(x) (atan(*(x)))
208 #define d_atn2(x, y) (atan2(*(x),*(y)))
209 #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
210 #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
211 #define d_cos(x) (cos(*(x)))
212 #define d_cosh(x) (cosh(*(x)))
213 #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
214 #define d_exp(x) (exp(*(x)))
215 #define d_imag(z) (cimag(Cd(z)))
216 #define r_imag(z) (cimagf(Cf(z)))
217 #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
218 #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
219 #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
220 #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
221 #define d_log(x) (log(*(x)))
222 #define d_mod(x, y) (fmod(*(x), *(y)))
223 #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
224 #define d_nint(x) u_nint(*(x))
225 #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
226 #define d_sign(a,b) u_sign(*(a),*(b))
227 #define r_sign(a,b) u_sign(*(a),*(b))
228 #define d_sin(x) (sin(*(x)))
229 #define d_sinh(x) (sinh(*(x)))
230 #define d_sqrt(x) (sqrt(*(x)))
231 #define d_tan(x) (tan(*(x)))
232 #define d_tanh(x) (tanh(*(x)))
233 #define i_abs(x) abs(*(x))
234 #define i_dnnt(x) ((integer)u_nint(*(x)))
235 #define i_len(s, n) (n)
236 #define i_nint(x) ((integer)u_nint(*(x)))
237 #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
238 #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
239 #define pow_si(B,E) spow_ui(*(B),*(E))
240 #define pow_ri(B,E) spow_ui(*(B),*(E))
241 #define pow_di(B,E) dpow_ui(*(B),*(E))
242 #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
243 #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
244 #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
245 #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
246 #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
247 #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
248 #define sig_die(s, kill) { exit(1); }
249 #define s_stop(s, n) {exit(0);}
250 static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
251 #define z_abs(z) (cabs(Cd(z)))
252 #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
253 #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
254 #define myexit_() break;
255 #define mycycle() continue;
256 #define myceiling(w) {ceil(w)}
257 #define myhuge(w) {HUGE_VAL}
258 //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
259 #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
261 /* procedure parameter types for -A and -C++ */
263 #define F2C_proc_par_types 1
265 typedef logical (*L_fp)(...);
267 typedef logical (*L_fp)();
270 static float spow_ui(float x, integer n) {
271 float pow=1.0; unsigned long int u;
273 if(n < 0) n = -n, x = 1/x;
282 static double dpow_ui(double x, integer n) {
283 double pow=1.0; unsigned long int u;
285 if(n < 0) n = -n, x = 1/x;
295 static _Fcomplex cpow_ui(complex x, integer n) {
296 complex pow={1.0,0.0}; unsigned long int u;
298 if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
300 if(u & 01) pow.r *= x.r, pow.i *= x.i;
301 if(u >>= 1) x.r *= x.r, x.i *= x.i;
305 _Fcomplex p={pow.r, pow.i};
309 static _Complex float cpow_ui(_Complex float x, integer n) {
310 _Complex float pow=1.0; unsigned long int u;
312 if(n < 0) n = -n, x = 1/x;
323 static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
324 _Dcomplex pow={1.0,0.0}; unsigned long int u;
326 if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
328 if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
329 if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
333 _Dcomplex p = {pow._Val[0], pow._Val[1]};
337 static _Complex double zpow_ui(_Complex double x, integer n) {
338 _Complex double pow=1.0; unsigned long int u;
340 if(n < 0) n = -n, x = 1/x;
350 static integer pow_ii(integer x, integer n) {
351 integer pow; unsigned long int u;
353 if (n == 0 || x == 1) pow = 1;
354 else if (x != -1) pow = x == 0 ? 1/x : 0;
357 if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
367 static integer dmaxloc_(double *w, integer s, integer e, integer *n)
369 double m; integer i, mi;
370 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
371 if (w[i-1]>m) mi=i ,m=w[i-1];
374 static integer smaxloc_(float *w, integer s, integer e, integer *n)
376 float m; integer i, mi;
377 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
378 if (w[i-1]>m) mi=i ,m=w[i-1];
381 static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
382 integer n = *n_, incx = *incx_, incy = *incy_, i;
384 _Fcomplex zdotc = {0.0, 0.0};
385 if (incx == 1 && incy == 1) {
386 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
387 zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
388 zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
391 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
392 zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
393 zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
399 _Complex float zdotc = 0.0;
400 if (incx == 1 && incy == 1) {
401 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
402 zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
405 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
406 zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
412 static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
413 integer n = *n_, incx = *incx_, incy = *incy_, i;
415 _Dcomplex zdotc = {0.0, 0.0};
416 if (incx == 1 && incy == 1) {
417 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
418 zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
419 zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
422 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
423 zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
424 zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
430 _Complex double zdotc = 0.0;
431 if (incx == 1 && incy == 1) {
432 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
433 zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
436 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
437 zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
443 static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
444 integer n = *n_, incx = *incx_, incy = *incy_, i;
446 _Fcomplex zdotc = {0.0, 0.0};
447 if (incx == 1 && incy == 1) {
448 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
449 zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
450 zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
453 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
454 zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
455 zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
461 _Complex float zdotc = 0.0;
462 if (incx == 1 && incy == 1) {
463 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
464 zdotc += Cf(&x[i]) * Cf(&y[i]);
467 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
468 zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
474 static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
475 integer n = *n_, incx = *incx_, incy = *incy_, i;
477 _Dcomplex zdotc = {0.0, 0.0};
478 if (incx == 1 && incy == 1) {
479 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
480 zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
481 zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
484 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
485 zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
486 zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
492 _Complex double zdotc = 0.0;
493 if (incx == 1 && incy == 1) {
494 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
495 zdotc += Cd(&x[i]) * Cd(&y[i]);
498 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
499 zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
505 /* -- translated by f2c (version 20000121).
506 You must link the resulting object file with the libraries:
507 -lf2c -lm (in that order)
513 /* Table of constant values */
515 static integer c__2 = 2;
516 static integer c__1 = 1;
517 static real c_b10 = 1.f;
518 static real c_b11 = 0.f;
519 static integer c_n1 = -1;
521 /* > \brief \b SLAED7 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification
522 by a rank-one symmetric matrix. Used when the original matrix is dense. */
524 /* =========== DOCUMENTATION =========== */
526 /* Online html documentation available at */
527 /* http://www.netlib.org/lapack/explore-html/ */
530 /* > Download SLAED7 + dependencies */
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slaed7.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slaed7.
537 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slaed7.
545 /* SUBROUTINE SLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, */
546 /* LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, */
547 /* PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, */
550 /* INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, */
553 /* INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), */
554 /* $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) */
555 /* REAL D( * ), GIVNUM( 2, * ), Q( LDQ, * ), */
556 /* $ QSTORE( * ), WORK( * ) */
559 /* > \par Purpose: */
564 /* > SLAED7 computes the updated eigensystem of a diagonal */
565 /* > matrix after modification by a rank-one symmetric matrix. This */
566 /* > routine is used only for the eigenproblem which requires all */
567 /* > eigenvalues and optionally eigenvectors of a dense symmetric matrix */
568 /* > that has been reduced to tridiagonal form. SLAED1 handles */
569 /* > the case in which all eigenvalues and eigenvectors of a symmetric */
570 /* > tridiagonal matrix are desired. */
572 /* > T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) */
574 /* > where Z = Q**Tu, u is a vector of length N with ones in the */
575 /* > CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */
577 /* > The eigenvectors of the original matrix are stored in Q, and the */
578 /* > eigenvalues are in D. The algorithm consists of three stages: */
580 /* > The first stage consists of deflating the size of the problem */
581 /* > when there are multiple eigenvalues or if there is a zero in */
582 /* > the Z vector. For each such occurrence the dimension of the */
583 /* > secular equation problem is reduced by one. This stage is */
584 /* > performed by the routine SLAED8. */
586 /* > The second stage consists of calculating the updated */
587 /* > eigenvalues. This is done by finding the roots of the secular */
588 /* > equation via the routine SLAED4 (as called by SLAED9). */
589 /* > This routine also calculates the eigenvectors of the current */
592 /* > The final stage consists of computing the updated eigenvectors */
593 /* > directly using the updated eigenvalues. The eigenvectors for */
594 /* > the current problem are multiplied with the eigenvectors from */
595 /* > the overall problem. */
601 /* > \param[in] ICOMPQ */
603 /* > ICOMPQ is INTEGER */
604 /* > = 0: Compute eigenvalues only. */
605 /* > = 1: Compute eigenvectors of original dense symmetric matrix */
606 /* > also. On entry, Q contains the orthogonal matrix used */
607 /* > to reduce the original matrix to tridiagonal form. */
613 /* > The dimension of the symmetric tridiagonal matrix. N >= 0. */
616 /* > \param[in] QSIZ */
618 /* > QSIZ is INTEGER */
619 /* > The dimension of the orthogonal matrix used to reduce */
620 /* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */
623 /* > \param[in] TLVLS */
625 /* > TLVLS is INTEGER */
626 /* > The total number of merging levels in the overall divide and */
627 /* > conquer tree. */
630 /* > \param[in] CURLVL */
632 /* > CURLVL is INTEGER */
633 /* > The current level in the overall merge routine, */
634 /* > 0 <= CURLVL <= TLVLS. */
637 /* > \param[in] CURPBM */
639 /* > CURPBM is INTEGER */
640 /* > The current problem in the current level in the overall */
641 /* > merge routine (counting from upper left to lower right). */
644 /* > \param[in,out] D */
646 /* > D is REAL array, dimension (N) */
647 /* > On entry, the eigenvalues of the rank-1-perturbed matrix. */
648 /* > On exit, the eigenvalues of the repaired matrix. */
651 /* > \param[in,out] Q */
653 /* > Q is REAL array, dimension (LDQ, N) */
654 /* > On entry, the eigenvectors of the rank-1-perturbed matrix. */
655 /* > On exit, the eigenvectors of the repaired tridiagonal matrix. */
658 /* > \param[in] LDQ */
660 /* > LDQ is INTEGER */
661 /* > The leading dimension of the array Q. LDQ >= f2cmax(1,N). */
664 /* > \param[out] INDXQ */
666 /* > INDXQ is INTEGER array, dimension (N) */
667 /* > The permutation which will reintegrate the subproblem just */
668 /* > solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) */
669 /* > will be in ascending order. */
672 /* > \param[in] RHO */
675 /* > The subdiagonal element used to create the rank-1 */
676 /* > modification. */
679 /* > \param[in] CUTPNT */
681 /* > CUTPNT is INTEGER */
682 /* > Contains the location of the last eigenvalue in the leading */
683 /* > sub-matrix. f2cmin(1,N) <= CUTPNT <= N. */
686 /* > \param[in,out] QSTORE */
688 /* > QSTORE is REAL array, dimension (N**2+1) */
689 /* > Stores eigenvectors of submatrices encountered during */
690 /* > divide and conquer, packed together. QPTR points to */
691 /* > beginning of the submatrices. */
694 /* > \param[in,out] QPTR */
696 /* > QPTR is INTEGER array, dimension (N+2) */
697 /* > List of indices pointing to beginning of submatrices stored */
698 /* > in QSTORE. The submatrices are numbered starting at the */
699 /* > bottom left of the divide and conquer tree, from left to */
700 /* > right and bottom to top. */
703 /* > \param[in] PRMPTR */
705 /* > PRMPTR is INTEGER array, dimension (N lg N) */
706 /* > Contains a list of pointers which indicate where in PERM a */
707 /* > level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */
708 /* > indicates the size of the permutation and also the size of */
709 /* > the full, non-deflated problem. */
712 /* > \param[in] PERM */
714 /* > PERM is INTEGER array, dimension (N lg N) */
715 /* > Contains the permutations (from deflation and sorting) to be */
716 /* > applied to each eigenblock. */
719 /* > \param[in] GIVPTR */
721 /* > GIVPTR is INTEGER array, dimension (N lg N) */
722 /* > Contains a list of pointers which indicate where in GIVCOL a */
723 /* > level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */
724 /* > indicates the number of Givens rotations. */
727 /* > \param[in] GIVCOL */
729 /* > GIVCOL is INTEGER array, dimension (2, N lg N) */
730 /* > Each pair of numbers indicates a pair of columns to take place */
731 /* > in a Givens rotation. */
734 /* > \param[in] GIVNUM */
736 /* > GIVNUM is REAL array, dimension (2, N lg N) */
737 /* > Each number indicates the S value to be used in the */
738 /* > corresponding Givens rotation. */
741 /* > \param[out] WORK */
743 /* > WORK is REAL array, dimension (3*N+2*QSIZ*N) */
746 /* > \param[out] IWORK */
748 /* > IWORK is INTEGER array, dimension (4*N) */
751 /* > \param[out] INFO */
753 /* > INFO is INTEGER */
754 /* > = 0: successful exit. */
755 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
756 /* > > 0: if INFO = 1, an eigenvalue did not converge */
762 /* > \author Univ. of Tennessee */
763 /* > \author Univ. of California Berkeley */
764 /* > \author Univ. of Colorado Denver */
765 /* > \author NAG Ltd. */
767 /* > \date June 2016 */
769 /* > \ingroup auxOTHERcomputational */
771 /* > \par Contributors: */
772 /* ================== */
774 /* > Jeff Rutter, Computer Science Division, University of California */
775 /* > at Berkeley, USA */
777 /* ===================================================================== */
778 /* Subroutine */ int slaed7_(integer *icompq, integer *n, integer *qsiz,
779 integer *tlvls, integer *curlvl, integer *curpbm, real *d__, real *q,
780 integer *ldq, integer *indxq, real *rho, integer *cutpnt, real *
781 qstore, integer *qptr, integer *prmptr, integer *perm, integer *
782 givptr, integer *givcol, real *givnum, real *work, integer *iwork,
785 /* System generated locals */
786 integer q_dim1, q_offset, i__1, i__2;
788 /* Local variables */
789 integer indx, curr, i__, k, indxc;
790 extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
791 integer *, real *, real *, integer *, real *, integer *, real *,
793 integer indxp, n1, n2;
794 extern /* Subroutine */ int slaed8_(integer *, integer *, integer *,
795 integer *, real *, real *, integer *, integer *, real *, integer *
796 , real *, real *, real *, integer *, real *, integer *, integer *,
797 integer *, real *, integer *, integer *, integer *), slaed9_(
798 integer *, integer *, integer *, integer *, real *, real *,
799 integer *, real *, real *, real *, real *, integer *, integer *),
800 slaeda_(integer *, integer *, integer *, integer *, integer *,
801 integer *, integer *, integer *, real *, real *, integer *, real *
802 , real *, integer *);
803 integer idlmda, is, iw, iz;
804 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), slamrg_(
805 integer *, integer *, real *, integer *, integer *, integer *);
806 integer coltyp, iq2, ptr, ldq2;
809 /* -- LAPACK computational routine (version 3.7.0) -- */
810 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
811 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
815 /* ===================================================================== */
818 /* Test the input parameters. */
820 /* Parameter adjustments */
823 q_offset = 1 + q_dim1 * 1;
839 if (*icompq < 0 || *icompq > 1) {
843 } else if (*icompq == 1 && *qsiz < *n) {
845 } else if (*ldq < f2cmax(1,*n)) {
847 } else if (f2cmin(1,*n) > *cutpnt || *n < *cutpnt) {
852 xerbla_("SLAED7", &i__1, (ftnlen)6);
856 /* Quick return if possible */
862 /* The following values are for bookkeeping purposes only. They are */
863 /* integer pointers which indicate the portion of the workspace */
864 /* used by a particular array in SLAED8 and SLAED9. */
876 is = iq2 + *n * ldq2;
883 /* Form the z-vector which consists of the last row of Q_1 and the */
884 /* first row of Q_2. */
886 ptr = pow_ii(&c__2, tlvls) + 1;
888 for (i__ = 1; i__ <= i__1; ++i__) {
890 ptr += pow_ii(&c__2, &i__2);
893 curr = ptr + *curpbm;
894 slaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], &
895 givcol[3], &givnum[3], &qstore[1], &qptr[1], &work[iz], &work[iz
898 /* When solving the final problem, we no longer need the stored data, */
899 /* so we will overwrite the data from this level onto the previously */
900 /* used storage space. */
902 if (*curlvl == *tlvls) {
908 /* Sort and Deflate eigenvalues. */
910 slaed8_(icompq, &k, n, qsiz, &d__[1], &q[q_offset], ldq, &indxq[1], rho,
911 cutpnt, &work[iz], &work[idlmda], &work[iq2], &ldq2, &work[iw], &
912 perm[prmptr[curr]], &givptr[curr + 1], &givcol[(givptr[curr] << 1)
913 + 1], &givnum[(givptr[curr] << 1) + 1], &iwork[indxp], &iwork[
915 prmptr[curr + 1] = prmptr[curr] + *n;
916 givptr[curr + 1] += givptr[curr];
918 /* Solve Secular Equation. */
921 slaed9_(&k, &c__1, &k, n, &d__[1], &work[is], &k, rho, &work[idlmda],
922 &work[iw], &qstore[qptr[curr]], &k, info);
927 sgemm_("N", "N", qsiz, &k, &k, &c_b10, &work[iq2], &ldq2, &qstore[
928 qptr[curr]], &k, &c_b11, &q[q_offset], ldq);
930 /* Computing 2nd power */
932 qptr[curr + 1] = qptr[curr] + i__1 * i__1;
934 /* Prepare the INDXQ sorting permutation. */
938 slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]);
940 qptr[curr + 1] = qptr[curr];
942 for (i__ = 1; i__ <= i__1; ++i__) {