14 typedef long long BLASLONG;
15 typedef unsigned long long BLASULONG;
17 typedef long BLASLONG;
18 typedef unsigned long BLASULONG;
22 typedef BLASLONG blasint;
24 #define blasabs(x) llabs(x)
26 #define blasabs(x) labs(x)
30 #define blasabs(x) abs(x)
33 typedef blasint integer;
35 typedef unsigned int uinteger;
36 typedef char *address;
37 typedef short int shortint;
39 typedef double doublereal;
40 typedef struct { real r, i; } complex;
41 typedef struct { doublereal r, i; } doublecomplex;
43 static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
44 static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
45 static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
46 static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
48 static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
49 static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
50 static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
51 static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
53 #define pCf(z) (*_pCf(z))
54 #define pCd(z) (*_pCd(z))
56 typedef short int shortlogical;
57 typedef char logical1;
58 typedef char integer1;
63 /* Extern is for use with -E */
74 /*external read, write*/
83 /*internal read, write*/
113 /*rewind, backspace, endfile*/
125 ftnint *inex; /*parameters in standard's order*/
151 union Multitype { /* for multiple entry points */
162 typedef union Multitype Multitype;
164 struct Vardesc { /* for Namelist */
170 typedef struct Vardesc Vardesc;
177 typedef struct Namelist Namelist;
179 #define abs(x) ((x) >= 0 ? (x) : -(x))
180 #define dabs(x) (fabs(x))
181 #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
182 #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
183 #define dmin(a,b) (f2cmin(a,b))
184 #define dmax(a,b) (f2cmax(a,b))
185 #define bit_test(a,b) ((a) >> (b) & 1)
186 #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
187 #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
189 #define abort_() { sig_die("Fortran abort routine called", 1); }
190 #define c_abs(z) (cabsf(Cf(z)))
191 #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
193 #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
194 #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
196 #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
197 #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
199 #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
200 #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
201 #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
202 //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
203 #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
204 #define d_abs(x) (fabs(*(x)))
205 #define d_acos(x) (acos(*(x)))
206 #define d_asin(x) (asin(*(x)))
207 #define d_atan(x) (atan(*(x)))
208 #define d_atn2(x, y) (atan2(*(x),*(y)))
209 #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
210 #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
211 #define d_cos(x) (cos(*(x)))
212 #define d_cosh(x) (cosh(*(x)))
213 #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
214 #define d_exp(x) (exp(*(x)))
215 #define d_imag(z) (cimag(Cd(z)))
216 #define r_imag(z) (cimagf(Cf(z)))
217 #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
218 #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
219 #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
220 #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
221 #define d_log(x) (log(*(x)))
222 #define d_mod(x, y) (fmod(*(x), *(y)))
223 #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
224 #define d_nint(x) u_nint(*(x))
225 #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
226 #define d_sign(a,b) u_sign(*(a),*(b))
227 #define r_sign(a,b) u_sign(*(a),*(b))
228 #define d_sin(x) (sin(*(x)))
229 #define d_sinh(x) (sinh(*(x)))
230 #define d_sqrt(x) (sqrt(*(x)))
231 #define d_tan(x) (tan(*(x)))
232 #define d_tanh(x) (tanh(*(x)))
233 #define i_abs(x) abs(*(x))
234 #define i_dnnt(x) ((integer)u_nint(*(x)))
235 #define i_len(s, n) (n)
236 #define i_nint(x) ((integer)u_nint(*(x)))
237 #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
238 #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
239 #define pow_si(B,E) spow_ui(*(B),*(E))
240 #define pow_ri(B,E) spow_ui(*(B),*(E))
241 #define pow_di(B,E) dpow_ui(*(B),*(E))
242 #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
243 #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
244 #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
245 #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
246 #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
247 #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
248 #define sig_die(s, kill) { exit(1); }
249 #define s_stop(s, n) {exit(0);}
250 static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
251 #define z_abs(z) (cabs(Cd(z)))
252 #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
253 #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
254 #define myexit_() break;
255 #define mycycle() continue;
256 #define myceiling(w) {ceil(w)}
257 #define myhuge(w) {HUGE_VAL}
258 //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
259 #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
261 /* procedure parameter types for -A and -C++ */
263 #define F2C_proc_par_types 1
265 typedef logical (*L_fp)(...);
267 typedef logical (*L_fp)();
270 static float spow_ui(float x, integer n) {
271 float pow=1.0; unsigned long int u;
273 if(n < 0) n = -n, x = 1/x;
282 static double dpow_ui(double x, integer n) {
283 double pow=1.0; unsigned long int u;
285 if(n < 0) n = -n, x = 1/x;
295 static _Fcomplex cpow_ui(complex x, integer n) {
296 complex pow={1.0,0.0}; unsigned long int u;
298 if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
300 if(u & 01) pow.r *= x.r, pow.i *= x.i;
301 if(u >>= 1) x.r *= x.r, x.i *= x.i;
305 _Fcomplex p={pow.r, pow.i};
309 static _Complex float cpow_ui(_Complex float x, integer n) {
310 _Complex float pow=1.0; unsigned long int u;
312 if(n < 0) n = -n, x = 1/x;
323 static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
324 _Dcomplex pow={1.0,0.0}; unsigned long int u;
326 if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
328 if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
329 if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
333 _Dcomplex p = {pow._Val[0], pow._Val[1]};
337 static _Complex double zpow_ui(_Complex double x, integer n) {
338 _Complex double pow=1.0; unsigned long int u;
340 if(n < 0) n = -n, x = 1/x;
350 static integer pow_ii(integer x, integer n) {
351 integer pow; unsigned long int u;
353 if (n == 0 || x == 1) pow = 1;
354 else if (x != -1) pow = x == 0 ? 1/x : 0;
357 if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
367 static integer dmaxloc_(double *w, integer s, integer e, integer *n)
369 double m; integer i, mi;
370 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
371 if (w[i-1]>m) mi=i ,m=w[i-1];
374 static integer smaxloc_(float *w, integer s, integer e, integer *n)
376 float m; integer i, mi;
377 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
378 if (w[i-1]>m) mi=i ,m=w[i-1];
381 static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
382 integer n = *n_, incx = *incx_, incy = *incy_, i;
384 _Fcomplex zdotc = {0.0, 0.0};
385 if (incx == 1 && incy == 1) {
386 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
387 zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
388 zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
391 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
392 zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
393 zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
399 _Complex float zdotc = 0.0;
400 if (incx == 1 && incy == 1) {
401 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
402 zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
405 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
406 zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
412 static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
413 integer n = *n_, incx = *incx_, incy = *incy_, i;
415 _Dcomplex zdotc = {0.0, 0.0};
416 if (incx == 1 && incy == 1) {
417 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
418 zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
419 zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
422 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
423 zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
424 zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
430 _Complex double zdotc = 0.0;
431 if (incx == 1 && incy == 1) {
432 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
433 zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
436 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
437 zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
443 static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
444 integer n = *n_, incx = *incx_, incy = *incy_, i;
446 _Fcomplex zdotc = {0.0, 0.0};
447 if (incx == 1 && incy == 1) {
448 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
449 zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
450 zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
453 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
454 zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
455 zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
461 _Complex float zdotc = 0.0;
462 if (incx == 1 && incy == 1) {
463 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
464 zdotc += Cf(&x[i]) * Cf(&y[i]);
467 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
468 zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
474 static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
475 integer n = *n_, incx = *incx_, incy = *incy_, i;
477 _Dcomplex zdotc = {0.0, 0.0};
478 if (incx == 1 && incy == 1) {
479 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
480 zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
481 zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
484 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
485 zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
486 zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
492 _Complex double zdotc = 0.0;
493 if (incx == 1 && incy == 1) {
494 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
495 zdotc += Cd(&x[i]) * Cd(&y[i]);
498 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
499 zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
505 /* -- translated by f2c (version 20000121).
506 You must link the resulting object file with the libraries:
507 -lf2c -lm (in that order)
513 /* Table of constant values */
515 static integer c__1 = 1;
516 static integer c__0 = 0;
517 static real c_b8 = 1.f;
519 /* > \brief \b SLASD8 finds the square roots of the roots of the secular equation, and stores, for each elemen
520 t in D, the distance to its two nearest poles. Used by sbdsdc. */
522 /* =========== DOCUMENTATION =========== */
524 /* Online html documentation available at */
525 /* http://www.netlib.org/lapack/explore-html/ */
528 /* > Download SLASD8 + dependencies */
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasd8.
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasd8.
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasd8.
543 /* SUBROUTINE SLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, */
544 /* DSIGMA, WORK, INFO ) */
546 /* INTEGER ICOMPQ, INFO, K, LDDIFR */
547 /* REAL D( * ), DIFL( * ), DIFR( LDDIFR, * ), */
548 /* $ DSIGMA( * ), VF( * ), VL( * ), WORK( * ), */
552 /* > \par Purpose: */
557 /* > SLASD8 finds the square roots of the roots of the secular equation, */
558 /* > as defined by the values in DSIGMA and Z. It makes the appropriate */
559 /* > calls to SLASD4, and stores, for each element in D, the distance */
560 /* > to its two nearest poles (elements in DSIGMA). It also updates */
561 /* > the arrays VF and VL, the first and last components of all the */
562 /* > right singular vectors of the original bidiagonal matrix. */
564 /* > SLASD8 is called from SLASD6. */
570 /* > \param[in] ICOMPQ */
572 /* > ICOMPQ is INTEGER */
573 /* > Specifies whether singular vectors are to be computed in */
574 /* > factored form in the calling routine: */
575 /* > = 0: Compute singular values only. */
576 /* > = 1: Compute singular vectors in factored form as well. */
582 /* > The number of terms in the rational function to be solved */
583 /* > by SLASD4. K >= 1. */
586 /* > \param[out] D */
588 /* > D is REAL array, dimension ( K ) */
589 /* > On output, D contains the updated singular values. */
592 /* > \param[in,out] Z */
594 /* > Z is REAL array, dimension ( K ) */
595 /* > On entry, the first K elements of this array contain the */
596 /* > components of the deflation-adjusted updating row vector. */
597 /* > On exit, Z is updated. */
600 /* > \param[in,out] VF */
602 /* > VF is REAL array, dimension ( K ) */
603 /* > On entry, VF contains information passed through DBEDE8. */
604 /* > On exit, VF contains the first K components of the first */
605 /* > components of all right singular vectors of the bidiagonal */
609 /* > \param[in,out] VL */
611 /* > VL is REAL array, dimension ( K ) */
612 /* > On entry, VL contains information passed through DBEDE8. */
613 /* > On exit, VL contains the first K components of the last */
614 /* > components of all right singular vectors of the bidiagonal */
618 /* > \param[out] DIFL */
620 /* > DIFL is REAL array, dimension ( K ) */
621 /* > On exit, DIFL(I) = D(I) - DSIGMA(I). */
624 /* > \param[out] DIFR */
626 /* > DIFR is REAL array, */
627 /* > dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and */
628 /* > dimension ( K ) if ICOMPQ = 0. */
629 /* > On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not */
630 /* > defined and will not be referenced. */
632 /* > If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */
633 /* > normalizing factors for the right singular vector matrix. */
636 /* > \param[in] LDDIFR */
638 /* > LDDIFR is INTEGER */
639 /* > The leading dimension of DIFR, must be at least K. */
642 /* > \param[in,out] DSIGMA */
644 /* > DSIGMA is REAL array, dimension ( K ) */
645 /* > On entry, the first K elements of this array contain the old */
646 /* > roots of the deflated updating problem. These are the poles */
647 /* > of the secular equation. */
648 /* > On exit, the elements of DSIGMA may be very slightly altered */
652 /* > \param[out] WORK */
654 /* > WORK is REAL array, dimension (3*K) */
657 /* > \param[out] INFO */
659 /* > INFO is INTEGER */
660 /* > = 0: successful exit. */
661 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
662 /* > > 0: if INFO = 1, a singular value did not converge */
668 /* > \author Univ. of Tennessee */
669 /* > \author Univ. of California Berkeley */
670 /* > \author Univ. of Colorado Denver */
671 /* > \author NAG Ltd. */
673 /* > \date June 2017 */
675 /* > \ingroup OTHERauxiliary */
677 /* > \par Contributors: */
678 /* ================== */
680 /* > Ming Gu and Huan Ren, Computer Science Division, University of */
681 /* > California at Berkeley, USA */
683 /* ===================================================================== */
684 /* Subroutine */ int slasd8_(integer *icompq, integer *k, real *d__, real *
685 z__, real *vf, real *vl, real *difl, real *difr, integer *lddifr,
686 real *dsigma, real *work, integer *info)
688 /* System generated locals */
689 integer difr_dim1, difr_offset, i__1, i__2;
692 /* Local variables */
694 extern real sdot_(integer *, real *, integer *, real *, integer *);
695 integer iwk2i, iwk3i;
696 extern real snrm2_(integer *, real *, integer *);
698 real diflj, difrj, dsigj;
699 extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
701 extern real slamc3_(real *, real *);
702 extern /* Subroutine */ int slasd4_(integer *, integer *, real *, real *,
703 real *, real *, real *, real *, integer *);
705 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
707 extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
708 real *, integer *, integer *, real *, integer *, integer *), slaset_(char *, integer *, integer *, real *, real *,
711 integer iwk1, iwk2, iwk3;
714 /* -- LAPACK auxiliary routine (version 3.7.1) -- */
715 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
716 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
720 /* ===================================================================== */
723 /* Test the input parameters. */
725 /* Parameter adjustments */
732 difr_offset = 1 + difr_dim1 * 1;
740 if (*icompq < 0 || *icompq > 1) {
744 } else if (*lddifr < *k) {
749 xerbla_("SLASD8", &i__1, (ftnlen)6);
753 /* Quick return if possible */
756 d__[1] = abs(z__[1]);
760 difr[(difr_dim1 << 1) + 1] = 1.f;
765 /* Modify values DSIGMA(i) to make sure all DSIGMA(i)-DSIGMA(j) can */
766 /* be computed with high relative accuracy (barring over/underflow). */
767 /* This is a problem on machines without a guard digit in */
768 /* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */
769 /* The following code replaces DSIGMA(I) by 2*DSIGMA(I)-DSIGMA(I), */
770 /* which on any of these machines zeros out the bottommost */
771 /* bit of DSIGMA(I) if it is 1; this makes the subsequent */
772 /* subtractions DSIGMA(I)-DSIGMA(J) unproblematic when cancellation */
773 /* occurs. On binary machines with a guard digit (almost all */
774 /* machines) it does not change DSIGMA(I) at all. On hexadecimal */
775 /* and decimal machines with a guard digit, it slightly */
776 /* changes the bottommost bits of DSIGMA(I). It does not account */
777 /* for hexadecimal or decimal machines without guard digits */
778 /* (we know of none). We use a subroutine call to compute */
779 /* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */
783 for (i__ = 1; i__ <= i__1; ++i__) {
784 dsigma[i__] = slamc3_(&dsigma[i__], &dsigma[i__]) - dsigma[i__];
798 rho = snrm2_(k, &z__[1], &c__1);
799 slascl_("G", &c__0, &c__0, &rho, &c_b8, k, &c__1, &z__[1], k, info);
802 /* Initialize WORK(IWK3). */
804 slaset_("A", k, &c__1, &c_b8, &c_b8, &work[iwk3], k);
806 /* Compute the updated singular values, the arrays DIFL, DIFR, */
807 /* and the updated Z. */
810 for (j = 1; j <= i__1; ++j) {
811 slasd4_(k, &j, &dsigma[1], &z__[1], &work[iwk1], &rho, &d__[j], &work[
814 /* If the root finder fails, report the convergence failure. */
819 work[iwk3i + j] = work[iwk3i + j] * work[j] * work[iwk2i + j];
821 difr[j + difr_dim1] = -work[j + 1];
823 for (i__ = 1; i__ <= i__2; ++i__) {
824 work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i +
825 i__] / (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[
830 for (i__ = j + 1; i__ <= i__2; ++i__) {
831 work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i +
832 i__] / (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[
839 /* Compute updated Z. */
842 for (i__ = 1; i__ <= i__1; ++i__) {
843 r__2 = sqrt((r__1 = work[iwk3i + i__], abs(r__1)));
844 z__[i__] = r_sign(&r__2, &z__[i__]);
848 /* Update VF and VL. */
851 for (j = 1; j <= i__1; ++j) {
856 difrj = -difr[j + difr_dim1];
857 dsigjp = -dsigma[j + 1];
859 work[j] = -z__[j] / diflj / (dsigma[j] + dj);
861 for (i__ = 1; i__ <= i__2; ++i__) {
862 work[i__] = z__[i__] / (slamc3_(&dsigma[i__], &dsigj) - diflj) / (
867 for (i__ = j + 1; i__ <= i__2; ++i__) {
868 work[i__] = z__[i__] / (slamc3_(&dsigma[i__], &dsigjp) + difrj) /
872 temp = snrm2_(k, &work[1], &c__1);
873 work[iwk2i + j] = sdot_(k, &work[1], &c__1, &vf[1], &c__1) / temp;
874 work[iwk3i + j] = sdot_(k, &work[1], &c__1, &vl[1], &c__1) / temp;
876 difr[j + (difr_dim1 << 1)] = temp;
881 scopy_(k, &work[iwk2], &c__1, &vf[1], &c__1);
882 scopy_(k, &work[iwk3], &c__1, &vl[1], &c__1);