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 doublereal c_b42 = 1.;
519 /* > \brief \b DGSVJ0 pre-processor for the routine dgesvj. */
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download DGSVJ0 + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgsvj0.
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgsvj0.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgsvj0.
542 /* SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, */
543 /* SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) */
545 /* INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP */
546 /* DOUBLE PRECISION EPS, SFMIN, TOL */
547 /* CHARACTER*1 JOBV */
548 /* DOUBLE PRECISION A( LDA, * ), SVA( N ), D( N ), V( LDV, * ), */
549 /* $ WORK( LWORK ) */
552 /* > \par Purpose: */
557 /* > DGSVJ0 is called from DGESVJ as a pre-processor and that is its main */
558 /* > purpose. It applies Jacobi rotations in the same way as DGESVJ does, but */
559 /* > it does not check convergence (stopping criterion). Few tuning */
560 /* > parameters (marked by [TP]) are available for the implementer. */
566 /* > \param[in] JOBV */
568 /* > JOBV is CHARACTER*1 */
569 /* > Specifies whether the output from this procedure is used */
570 /* > to compute the matrix V: */
571 /* > = 'V': the product of the Jacobi rotations is accumulated */
572 /* > by postmulyiplying the N-by-N array V. */
573 /* > (See the description of V.) */
574 /* > = 'A': the product of the Jacobi rotations is accumulated */
575 /* > by postmulyiplying the MV-by-N array V. */
576 /* > (See the descriptions of MV and V.) */
577 /* > = 'N': the Jacobi rotations are not accumulated. */
583 /* > The number of rows of the input matrix A. M >= 0. */
589 /* > The number of columns of the input matrix A. */
593 /* > \param[in,out] A */
595 /* > A is DOUBLE PRECISION array, dimension (LDA,N) */
596 /* > On entry, M-by-N matrix A, such that A*diag(D) represents */
597 /* > the input matrix. */
599 /* > A_onexit * D_onexit represents the input matrix A*diag(D) */
600 /* > post-multiplied by a sequence of Jacobi rotations, where the */
601 /* > rotation threshold and the total number of sweeps are given in */
602 /* > TOL and NSWEEP, respectively. */
603 /* > (See the descriptions of D, TOL and NSWEEP.) */
606 /* > \param[in] LDA */
608 /* > LDA is INTEGER */
609 /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
612 /* > \param[in,out] D */
614 /* > D is DOUBLE PRECISION array, dimension (N) */
615 /* > The array D accumulates the scaling factors from the fast scaled */
616 /* > Jacobi rotations. */
617 /* > On entry, A*diag(D) represents the input matrix. */
618 /* > On exit, A_onexit*diag(D_onexit) represents the input matrix */
619 /* > post-multiplied by a sequence of Jacobi rotations, where the */
620 /* > rotation threshold and the total number of sweeps are given in */
621 /* > TOL and NSWEEP, respectively. */
622 /* > (See the descriptions of A, TOL and NSWEEP.) */
625 /* > \param[in,out] SVA */
627 /* > SVA is DOUBLE PRECISION array, dimension (N) */
628 /* > On entry, SVA contains the Euclidean norms of the columns of */
629 /* > the matrix A*diag(D). */
630 /* > On exit, SVA contains the Euclidean norms of the columns of */
631 /* > the matrix onexit*diag(D_onexit). */
634 /* > \param[in] MV */
636 /* > MV is INTEGER */
637 /* > If JOBV = 'A', then MV rows of V are post-multipled by a */
638 /* > sequence of Jacobi rotations. */
639 /* > If JOBV = 'N', then MV is not referenced. */
642 /* > \param[in,out] V */
644 /* > V is DOUBLE PRECISION array, dimension (LDV,N) */
645 /* > If JOBV = 'V' then N rows of V are post-multipled by a */
646 /* > sequence of Jacobi rotations. */
647 /* > If JOBV = 'A' then MV rows of V are post-multipled by a */
648 /* > sequence of Jacobi rotations. */
649 /* > If JOBV = 'N', then V is not referenced. */
652 /* > \param[in] LDV */
654 /* > LDV is INTEGER */
655 /* > The leading dimension of the array V, LDV >= 1. */
656 /* > If JOBV = 'V', LDV >= N. */
657 /* > If JOBV = 'A', LDV >= MV. */
660 /* > \param[in] EPS */
662 /* > EPS is DOUBLE PRECISION */
663 /* > EPS = DLAMCH('Epsilon') */
666 /* > \param[in] SFMIN */
668 /* > SFMIN is DOUBLE PRECISION */
669 /* > SFMIN = DLAMCH('Safe Minimum') */
672 /* > \param[in] TOL */
674 /* > TOL is DOUBLE PRECISION */
675 /* > TOL is the threshold for Jacobi rotations. For a pair */
676 /* > A(:,p), A(:,q) of pivot columns, the Jacobi rotation is */
677 /* > applied only if DABS(COS(angle(A(:,p),A(:,q)))) > TOL. */
680 /* > \param[in] NSWEEP */
682 /* > NSWEEP is INTEGER */
683 /* > NSWEEP is the number of sweeps of Jacobi rotations to be */
687 /* > \param[out] WORK */
689 /* > WORK is DOUBLE PRECISION array, dimension (LWORK) */
692 /* > \param[in] LWORK */
694 /* > LWORK is INTEGER */
695 /* > LWORK is the dimension of WORK. LWORK >= M. */
698 /* > \param[out] INFO */
700 /* > INFO is INTEGER */
701 /* > = 0: successful exit. */
702 /* > < 0: if INFO = -i, then the i-th argument had an illegal value */
708 /* > \author Univ. of Tennessee */
709 /* > \author Univ. of California Berkeley */
710 /* > \author Univ. of Colorado Denver */
711 /* > \author NAG Ltd. */
713 /* > \date November 2017 */
715 /* > \ingroup doubleOTHERcomputational */
717 /* > \par Further Details: */
718 /* ===================== */
720 /* > DGSVJ0 is used just to enable DGESVJ to call a simplified version of */
721 /* > itself to work on a submatrix of the original matrix. */
723 /* > \par Contributors: */
724 /* ================== */
726 /* > Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) */
728 /* > \par Bugs, Examples and Comments: */
729 /* ================================= */
731 /* > Please report all bugs and send interesting test examples and comments to */
732 /* > drmac@math.hr. Thank you. */
734 /* ===================================================================== */
735 /* Subroutine */ int dgsvj0_(char *jobv, integer *m, integer *n, doublereal *
736 a, integer *lda, doublereal *d__, doublereal *sva, integer *mv,
737 doublereal *v, integer *ldv, doublereal *eps, doublereal *sfmin,
738 doublereal *tol, integer *nsweep, doublereal *work, integer *lwork,
741 /* System generated locals */
742 integer a_dim1, a_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4, i__5,
744 doublereal d__1, d__2;
746 /* Local variables */
747 doublereal aapp, aapq, aaqq;
748 extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
754 extern doublereal dnrm2_(integer *, doublereal *, integer *);
757 doublereal t, apoaq, aqoap;
758 extern logical lsame_(char *, char *);
759 doublereal theta, small;
760 extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
761 doublereal *, integer *);
763 extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
764 doublereal *, integer *);
765 logical applv, rsvec;
766 extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *,
767 integer *, doublereal *, integer *), drotm_(integer *, doublereal
768 *, integer *, doublereal *, integer *, doublereal *);
770 doublereal rootsfmin, cs, sn;
771 extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
772 doublereal *, doublereal *, integer *, integer *, doublereal *,
773 integer *, integer *);
774 extern integer idamax_(integer *, doublereal *, integer *);
775 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
776 integer ijblsk, swband, blskip;
778 extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *,
779 doublereal *, doublereal *);
780 doublereal thsign, mxsinj;
781 integer ir1, emptsw, notrot, iswrot, jbc;
783 integer kbl, lkahead, igl, ibr, jgl, nbl, mvl;
784 doublereal rootbig, rooteps;
789 /* -- LAPACK computational routine (version 3.8.0) -- */
790 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
791 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
795 /* ===================================================================== */
798 /* Test the input parameters. */
800 /* Parameter adjustments */
804 a_offset = 1 + a_dim1 * 1;
807 v_offset = 1 + v_dim1 * 1;
812 applv = lsame_(jobv, "A");
813 rsvec = lsame_(jobv, "V");
814 if (! (rsvec || applv || lsame_(jobv, "N"))) {
818 } else if (*n < 0 || *n > *m) {
820 } else if (*lda < *m) {
822 } else if ((rsvec || applv) && *mv < 0) {
824 } else if (rsvec && *ldv < *n || applv && *ldv < *mv) {
826 } else if (*tol <= *eps) {
828 } else if (*nsweep < 0) {
830 } else if (*lwork < *m) {
839 xerbla_("DGSVJ0", &i__1, (ftnlen)6);
848 rsvec = rsvec || applv;
849 rooteps = sqrt(*eps);
850 rootsfmin = sqrt(*sfmin);
851 small = *sfmin / *eps;
853 rootbig = 1. / rootsfmin;
854 bigtheta = 1. / rooteps;
855 roottol = sqrt(*tol);
857 /* -#- Row-cyclic Jacobi SVD algorithm with column pivoting -#- */
859 emptsw = *n * (*n - 1) / 2;
863 /* -#- Row-cyclic pivot strategy with de Rijk's pivoting -#- */
866 /* [TP] SWBAND is a tuning parameter. It is meaningful and effective */
867 /* if SGESVJ is used as a computational routine in the preconditioned */
868 /* Jacobi SVD algorithm SGESVJ. For sweeps i=1:SWBAND the procedure */
871 /* [TP] KBL is a tuning parameter that defines the tile size in the */
872 /* tiling of the p-q loops of pivot pairs. In general, an optimal */
873 /* value of KBL depends on the matrix dimensions and on the */
874 /* parameters of the computer's memory. */
877 if (nbl * kbl != *n) {
880 /* Computing 2nd power */
882 blskip = i__1 * i__1 + 1;
883 /* [TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. */
884 rowskip = f2cmin(5,kbl);
885 /* [TP] ROWSKIP is a tuning parameter. */
887 /* [TP] LKAHEAD is a tuning parameter. */
892 for (i__ = 1; i__ <= i__1; ++i__) {
902 for (ibr = 1; ibr <= i__2; ++ibr) {
903 igl = (ibr - 1) * kbl + 1;
906 i__4 = lkahead, i__5 = nbl - ibr;
907 i__3 = f2cmin(i__4,i__5);
908 for (ir1 = 0; ir1 <= i__3; ++ir1) {
913 i__5 = igl + kbl - 1, i__6 = *n - 1;
914 i__4 = f2cmin(i__5,i__6);
915 for (p = igl; p <= i__4; ++p) {
917 q = idamax_(&i__5, &sva[p], &c__1) + p - 1;
919 dswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 +
922 dswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
935 /* Column norms are periodically updated by explicit */
936 /* norm computation. */
938 /* Some BLAS implementations compute DNRM2(M,A(1,p),1) */
939 /* as DSQRT(DDOT(M,A(1,p),1,A(1,p),1)), which may result in */
940 /* overflow for ||A(:,p)||_2 > DSQRT(overflow_threshold), and */
941 /* undeflow for ||A(:,p)||_2 < DSQRT(underflow_threshold). */
942 /* Hence, DNRM2 cannot be trusted, not even in the case when */
943 /* the true norm is far from the under(over)flow boundaries. */
944 /* If properly implemented DNRM2 is available, the IF-THEN-ELSE */
945 /* below should read "AAPP = DNRM2( M, A(1,p), 1 ) * D(p)". */
947 if (sva[p] < rootbig && sva[p] > rootsfmin) {
948 sva[p] = dnrm2_(m, &a[p * a_dim1 + 1], &c__1) *
953 dlassq_(m, &a[p * a_dim1 + 1], &c__1, &temp1, &
955 sva[p] = temp1 * sqrt(aapp) * d__[p];
967 i__6 = igl + kbl - 1;
968 i__5 = f2cmin(i__6,*n);
969 for (q = p + 1; q <= i__5; ++q) {
976 rotok = small * aapp <= aaqq;
977 if (aapp < big / aaqq) {
978 aapq = ddot_(m, &a[p * a_dim1 + 1], &
979 c__1, &a[q * a_dim1 + 1], &
980 c__1) * d__[p] * d__[q] /
983 dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
985 dlascl_("G", &c__0, &c__0, &aapp, &
986 d__[p], m, &c__1, &work[1],
988 aapq = ddot_(m, &work[1], &c__1, &a[q
989 * a_dim1 + 1], &c__1) * d__[q]
993 rotok = aapp <= aaqq / small;
994 if (aapp > small / aaqq) {
995 aapq = ddot_(m, &a[p * a_dim1 + 1], &
996 c__1, &a[q * a_dim1 + 1], &
997 c__1) * d__[p] * d__[q] /
1000 dcopy_(m, &a[q * a_dim1 + 1], &c__1, &
1002 dlascl_("G", &c__0, &c__0, &aaqq, &
1003 d__[q], m, &c__1, &work[1],
1005 aapq = ddot_(m, &work[1], &c__1, &a[p
1006 * a_dim1 + 1], &c__1) * d__[p]
1012 d__1 = mxaapq, d__2 = abs(aapq);
1013 mxaapq = f2cmax(d__1,d__2);
1015 /* TO rotate or NOT to rotate, THAT is the question ... */
1017 if (abs(aapq) > *tol) {
1019 /* ROTATED = ROTATED + ONE */
1029 aqoap = aaqq / aapp;
1030 apoaq = aapp / aaqq;
1031 theta = (d__1 = aqoap - apoaq, abs(
1032 d__1)) * -.5 / aapq;
1034 if (abs(theta) > bigtheta) {
1037 fastr[2] = t * d__[p] / d__[q];
1038 fastr[3] = -t * d__[q] / d__[p];
1039 drotm_(m, &a[p * a_dim1 + 1], &
1040 c__1, &a[q * a_dim1 + 1],
1043 drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
1044 v_dim1 + 1], &c__1, fastr);
1047 d__1 = 0., d__2 = t * apoaq *
1049 sva[q] = aaqq * sqrt((f2cmax(d__1,
1052 d__1 = 0., d__2 = 1. - t * aqoap *
1054 aapp *= sqrt((f2cmax(d__1,d__2)));
1056 d__1 = mxsinj, d__2 = abs(t);
1057 mxsinj = f2cmax(d__1,d__2);
1062 thsign = -d_sign(&c_b42, &aapq);
1063 t = 1. / (theta + thsign * sqrt(
1064 theta * theta + 1.));
1065 cs = sqrt(1. / (t * t + 1.));
1069 d__1 = mxsinj, d__2 = abs(sn);
1070 mxsinj = f2cmax(d__1,d__2);
1072 d__1 = 0., d__2 = t * apoaq *
1074 sva[q] = aaqq * sqrt((f2cmax(d__1,
1077 d__1 = 0., d__2 = 1. - t * aqoap *
1079 aapp *= sqrt((f2cmax(d__1,d__2)));
1081 apoaq = d__[p] / d__[q];
1082 aqoap = d__[q] / d__[p];
1085 fastr[2] = t * apoaq;
1086 fastr[3] = -t * aqoap;
1089 drotm_(m, &a[p * a_dim1 + 1], &c__1, &a[q *
1090 a_dim1 + 1], &c__1, fastr);
1092 drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[
1093 q * v_dim1 + 1], &c__1, fastr);
1097 daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
1098 p * a_dim1 + 1], &c__1);
1099 d__1 = cs * sn * apoaq;
1100 daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
1101 q * a_dim1 + 1], &c__1);
1106 daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
1107 c__1, &v[p * v_dim1 + 1], &c__1);
1108 d__1 = cs * sn * apoaq;
1109 daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
1110 c__1, &v[q * v_dim1 + 1], &c__1);
1116 daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
1117 q * a_dim1 + 1], &c__1);
1118 d__1 = -cs * sn * aqoap;
1119 daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
1120 p * a_dim1 + 1], &c__1);
1125 daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
1126 c__1, &v[q * v_dim1 + 1], &c__1);
1127 d__1 = -cs * sn * aqoap;
1128 daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
1129 c__1, &v[p * v_dim1 + 1], &c__1);
1132 if (d__[p] >= d__[q]) {
1134 daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1,
1135 &a[p * a_dim1 + 1], &c__1);
1136 d__1 = cs * sn * apoaq;
1137 daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1,
1138 &a[q * a_dim1 + 1], &c__1);
1143 daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1],
1144 &c__1, &v[p * v_dim1 + 1], &
1146 d__1 = cs * sn * apoaq;
1147 daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1],
1148 &c__1, &v[q * v_dim1 + 1], &
1153 daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1,
1154 &a[q * a_dim1 + 1], &c__1);
1155 d__1 = -cs * sn * aqoap;
1156 daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1,
1157 &a[p * a_dim1 + 1], &c__1);
1162 daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1],
1163 &c__1, &v[q * v_dim1 + 1], &
1165 d__1 = -cs * sn * aqoap;
1166 daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1],
1167 &c__1, &v[p * v_dim1 + 1], &
1176 dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
1178 dlascl_("G", &c__0, &c__0, &aapp, &
1179 c_b42, m, &c__1, &work[1],
1181 dlascl_("G", &c__0, &c__0, &aaqq, &
1182 c_b42, m, &c__1, &a[q *
1183 a_dim1 + 1], lda, &ierr);
1184 temp1 = -aapq * d__[p] / d__[q];
1185 daxpy_(m, &temp1, &work[1], &c__1, &a[
1186 q * a_dim1 + 1], &c__1);
1187 dlascl_("G", &c__0, &c__0, &c_b42, &
1188 aaqq, m, &c__1, &a[q * a_dim1
1191 d__1 = 0., d__2 = 1. - aapq * aapq;
1192 sva[q] = aaqq * sqrt((f2cmax(d__1,d__2)))
1194 mxsinj = f2cmax(mxsinj,*sfmin);
1196 /* END IF ROTOK THEN ... ELSE */
1198 /* In the case of cancellation in updating SVA(q), SVA(p) */
1199 /* recompute SVA(q), SVA(p). */
1200 /* Computing 2nd power */
1201 d__1 = sva[q] / aaqq;
1202 if (d__1 * d__1 <= rooteps) {
1203 if (aaqq < rootbig && aaqq >
1205 sva[q] = dnrm2_(m, &a[q * a_dim1
1206 + 1], &c__1) * d__[q];
1210 dlassq_(m, &a[q * a_dim1 + 1], &
1212 sva[q] = t * sqrt(aaqq) * d__[q];
1215 if (aapp / aapp0 <= rooteps) {
1216 if (aapp < rootbig && aapp >
1218 aapp = dnrm2_(m, &a[p * a_dim1 +
1219 1], &c__1) * d__[p];
1223 dlassq_(m, &a[p * a_dim1 + 1], &
1225 aapp = t * sqrt(aapp) * d__[p];
1231 /* A(:,p) and A(:,q) already numerically orthogonal */
1238 /* A(:,q) is zero column */
1245 if (i__ <= swband && pskipped > rowskip) {
1258 /* bailed out of q-loop */
1262 if (ir1 == 0 && aapp == 0.) {
1264 i__5 = igl + kbl - 1;
1265 notrot = notrot + f2cmin(i__5,*n) - p;
1271 /* end of the p-loop */
1272 /* end of doing the block ( ibr, ibr ) */
1275 /* end of ir1-loop */
1277 /* ........................................................ */
1278 /* ... go to the off diagonal blocks */
1280 igl = (ibr - 1) * kbl + 1;
1283 for (jbc = ibr + 1; jbc <= i__3; ++jbc) {
1285 jgl = (jbc - 1) * kbl + 1;
1287 /* doing the block at ( ibr, jbc ) */
1291 i__5 = igl + kbl - 1;
1292 i__4 = f2cmin(i__5,*n);
1293 for (p = igl; p <= i__4; ++p) {
1302 i__6 = jgl + kbl - 1;
1303 i__5 = f2cmin(i__6,*n);
1304 for (q = jgl; q <= i__5; ++q) {
1311 /* -#- M x 2 Jacobi SVD -#- */
1313 /* -#- Safe Gram matrix computation -#- */
1317 rotok = small * aapp <= aaqq;
1319 rotok = small * aaqq <= aapp;
1321 if (aapp < big / aaqq) {
1322 aapq = ddot_(m, &a[p * a_dim1 + 1], &
1323 c__1, &a[q * a_dim1 + 1], &
1324 c__1) * d__[p] * d__[q] /
1327 dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
1329 dlascl_("G", &c__0, &c__0, &aapp, &
1330 d__[p], m, &c__1, &work[1],
1332 aapq = ddot_(m, &work[1], &c__1, &a[q
1333 * a_dim1 + 1], &c__1) * d__[q]
1338 rotok = aapp <= aaqq / small;
1340 rotok = aaqq <= aapp / small;
1342 if (aapp > small / aaqq) {
1343 aapq = ddot_(m, &a[p * a_dim1 + 1], &
1344 c__1, &a[q * a_dim1 + 1], &
1345 c__1) * d__[p] * d__[q] /
1348 dcopy_(m, &a[q * a_dim1 + 1], &c__1, &
1350 dlascl_("G", &c__0, &c__0, &aaqq, &
1351 d__[q], m, &c__1, &work[1],
1353 aapq = ddot_(m, &work[1], &c__1, &a[p
1354 * a_dim1 + 1], &c__1) * d__[p]
1360 d__1 = mxaapq, d__2 = abs(aapq);
1361 mxaapq = f2cmax(d__1,d__2);
1363 /* TO rotate or NOT to rotate, THAT is the question ... */
1365 if (abs(aapq) > *tol) {
1367 /* ROTATED = ROTATED + 1 */
1373 aqoap = aaqq / aapp;
1374 apoaq = aapp / aaqq;
1375 theta = (d__1 = aqoap - apoaq, abs(
1376 d__1)) * -.5 / aapq;
1381 if (abs(theta) > bigtheta) {
1383 fastr[2] = t * d__[p] / d__[q];
1384 fastr[3] = -t * d__[q] / d__[p];
1385 drotm_(m, &a[p * a_dim1 + 1], &
1386 c__1, &a[q * a_dim1 + 1],
1389 drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
1390 v_dim1 + 1], &c__1, fastr);
1393 d__1 = 0., d__2 = t * apoaq *
1395 sva[q] = aaqq * sqrt((f2cmax(d__1,
1398 d__1 = 0., d__2 = 1. - t * aqoap *
1400 aapp *= sqrt((f2cmax(d__1,d__2)));
1402 d__1 = mxsinj, d__2 = abs(t);
1403 mxsinj = f2cmax(d__1,d__2);
1407 thsign = -d_sign(&c_b42, &aapq);
1411 t = 1. / (theta + thsign * sqrt(
1412 theta * theta + 1.));
1413 cs = sqrt(1. / (t * t + 1.));
1416 d__1 = mxsinj, d__2 = abs(sn);
1417 mxsinj = f2cmax(d__1,d__2);
1419 d__1 = 0., d__2 = t * apoaq *
1421 sva[q] = aaqq * sqrt((f2cmax(d__1,
1424 d__1 = 0., d__2 = 1. - t * aqoap *
1426 aapp *= sqrt((f2cmax(d__1,d__2)));
1428 apoaq = d__[p] / d__[q];
1429 aqoap = d__[q] / d__[p];
1433 fastr[2] = t * apoaq;
1434 fastr[3] = -t * aqoap;
1437 drotm_(m, &a[p * a_dim1 + 1], &c__1, &a[q *
1438 a_dim1 + 1], &c__1, fastr);
1440 drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[
1441 q * v_dim1 + 1], &c__1, fastr);
1445 daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
1446 p * a_dim1 + 1], &c__1);
1447 d__1 = cs * sn * apoaq;
1448 daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
1449 q * a_dim1 + 1], &c__1);
1452 daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
1453 c__1, &v[p * v_dim1 + 1], &c__1);
1454 d__1 = cs * sn * apoaq;
1455 daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
1456 c__1, &v[q * v_dim1 + 1], &c__1);
1464 daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
1465 q * a_dim1 + 1], &c__1);
1466 d__1 = -cs * sn * aqoap;
1467 daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
1468 p * a_dim1 + 1], &c__1);
1471 daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
1472 c__1, &v[q * v_dim1 + 1], &c__1);
1473 d__1 = -cs * sn * aqoap;
1474 daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
1475 c__1, &v[p * v_dim1 + 1], &c__1);
1480 if (d__[p] >= d__[q]) {
1482 daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1,
1483 &a[p * a_dim1 + 1], &c__1);
1484 d__1 = cs * sn * apoaq;
1485 daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1,
1486 &a[q * a_dim1 + 1], &c__1);
1491 daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1],
1492 &c__1, &v[p * v_dim1 + 1], &
1494 d__1 = cs * sn * apoaq;
1495 daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1],
1496 &c__1, &v[q * v_dim1 + 1], &
1501 daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1,
1502 &a[q * a_dim1 + 1], &c__1);
1503 d__1 = -cs * sn * aqoap;
1504 daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1,
1505 &a[p * a_dim1 + 1], &c__1);
1510 daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1],
1511 &c__1, &v[q * v_dim1 + 1], &
1513 d__1 = -cs * sn * aqoap;
1514 daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1],
1515 &c__1, &v[p * v_dim1 + 1], &
1525 dcopy_(m, &a[p * a_dim1 + 1], &
1526 c__1, &work[1], &c__1);
1527 dlascl_("G", &c__0, &c__0, &aapp,
1528 &c_b42, m, &c__1, &work[1]
1530 dlascl_("G", &c__0, &c__0, &aaqq,
1531 &c_b42, m, &c__1, &a[q *
1532 a_dim1 + 1], lda, &ierr);
1533 temp1 = -aapq * d__[p] / d__[q];
1534 daxpy_(m, &temp1, &work[1], &c__1,
1535 &a[q * a_dim1 + 1], &
1537 dlascl_("G", &c__0, &c__0, &c_b42,
1538 &aaqq, m, &c__1, &a[q *
1539 a_dim1 + 1], lda, &ierr);
1541 d__1 = 0., d__2 = 1. - aapq *
1543 sva[q] = aaqq * sqrt((f2cmax(d__1,
1545 mxsinj = f2cmax(mxsinj,*sfmin);
1547 dcopy_(m, &a[q * a_dim1 + 1], &
1548 c__1, &work[1], &c__1);
1549 dlascl_("G", &c__0, &c__0, &aaqq,
1550 &c_b42, m, &c__1, &work[1]
1552 dlascl_("G", &c__0, &c__0, &aapp,
1553 &c_b42, m, &c__1, &a[p *
1554 a_dim1 + 1], lda, &ierr);
1555 temp1 = -aapq * d__[q] / d__[p];
1556 daxpy_(m, &temp1, &work[1], &c__1,
1557 &a[p * a_dim1 + 1], &
1559 dlascl_("G", &c__0, &c__0, &c_b42,
1560 &aapp, m, &c__1, &a[p *
1561 a_dim1 + 1], lda, &ierr);
1563 d__1 = 0., d__2 = 1. - aapq *
1565 sva[p] = aapp * sqrt((f2cmax(d__1,
1567 mxsinj = f2cmax(mxsinj,*sfmin);
1570 /* END IF ROTOK THEN ... ELSE */
1572 /* In the case of cancellation in updating SVA(q) */
1573 /* Computing 2nd power */
1574 d__1 = sva[q] / aaqq;
1575 if (d__1 * d__1 <= rooteps) {
1576 if (aaqq < rootbig && aaqq >
1578 sva[q] = dnrm2_(m, &a[q * a_dim1
1579 + 1], &c__1) * d__[q];
1583 dlassq_(m, &a[q * a_dim1 + 1], &
1585 sva[q] = t * sqrt(aaqq) * d__[q];
1588 /* Computing 2nd power */
1589 d__1 = aapp / aapp0;
1590 if (d__1 * d__1 <= rooteps) {
1591 if (aapp < rootbig && aapp >
1593 aapp = dnrm2_(m, &a[p * a_dim1 +
1594 1], &c__1) * d__[p];
1598 dlassq_(m, &a[p * a_dim1 + 1], &
1600 aapp = t * sqrt(aapp) * d__[p];
1604 /* end of OK rotation */
1616 if (i__ <= swband && ijblsk >= blskip) {
1621 if (i__ <= swband && pskipped > rowskip) {
1629 /* end of the q-loop */
1637 i__5 = jgl + kbl - 1;
1638 notrot = notrot + f2cmin(i__5,*n) - jgl + 1;
1646 /* end of the p-loop */
1649 /* end of the jbc-loop */
1651 /* 2011 bailed out of the jbc-loop */
1653 i__4 = igl + kbl - 1;
1654 i__3 = f2cmin(i__4,*n);
1655 for (p = igl; p <= i__3; ++p) {
1656 sva[p] = (d__1 = sva[p], abs(d__1));
1662 /* 2000 :: end of the ibr-loop */
1664 if (sva[*n] < rootbig && sva[*n] > rootsfmin) {
1665 sva[*n] = dnrm2_(m, &a[*n * a_dim1 + 1], &c__1) * d__[*n];
1669 dlassq_(m, &a[*n * a_dim1 + 1], &c__1, &t, &aapp);
1670 sva[*n] = t * sqrt(aapp) * d__[*n];
1673 /* Additional steering devices */
1675 if (i__ < swband && (mxaapq <= roottol || iswrot <= *n)) {
1679 if (i__ > swband + 1 && mxaapq < (doublereal) (*n) * *tol && (
1680 doublereal) (*n) * mxaapq * mxsinj < *tol) {
1684 if (notrot >= emptsw) {
1689 /* end i=1:NSWEEP loop */
1690 /* #:) Reaching this point means that the procedure has completed the given */
1691 /* number of iterations. */
1692 *info = *nsweep - 1;
1695 /* #:) Reaching this point means that during the i-th sweep all pivots were */
1696 /* below the given tolerance, causing early exit. */
1699 /* #:) INFO = 0 confirms successful iterations. */
1702 /* Sort the vector D. */
1704 for (p = 1; p <= i__1; ++p) {
1706 q = idamax_(&i__2, &sva[p], &c__1) + p - 1;
1714 dswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1);
1716 dswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], &