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_b42 = 1.f;
519 /* > \brief \b SGSVJ0 pre-processor for the routine sgesvj. */
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download SGSVJ0 + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgsvj0.
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgsvj0.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgsvj0.
542 /* SUBROUTINE SGSVJ0( 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 /* REAL EPS, SFMIN, TOL */
547 /* CHARACTER*1 JOBV */
548 /* REAL A( LDA, * ), SVA( N ), D( N ), V( LDV, * ), */
549 /* $ WORK( LWORK ) */
552 /* > \par Purpose: */
557 /* > SGSVJ0 is called from SGESVJ as a pre-processor and that is its main */
558 /* > purpose. It applies Jacobi rotations in the same way as SGESVJ 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 REAL 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 REAL 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 REAL 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 REAL 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 */
663 /* > EPS = SLAMCH('Epsilon') */
666 /* > \param[in] SFMIN */
668 /* > SFMIN is REAL */
669 /* > SFMIN = SLAMCH('Safe Minimum') */
672 /* > \param[in] TOL */
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 ABS(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 REAL 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 realOTHERcomputational */
717 /* > \par Further Details: */
718 /* ===================== */
720 /* > SGSVJ0 is used just to enable SGESVJ 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 sgsvj0_(char *jobv, integer *m, integer *n, real *a,
736 integer *lda, real *d__, real *sva, integer *mv, real *v, integer *
737 ldv, real *eps, real *sfmin, real *tol, integer *nsweep, real *work,
738 integer *lwork, integer *info)
740 /* System generated locals */
741 integer a_dim1, a_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4, i__5,
745 /* Local variables */
746 real aapp, aapq, aaqq;
749 extern real sdot_(integer *, real *, integer *, real *, integer *);
752 extern real snrm2_(integer *, real *, integer *);
754 real t, apoaq, aqoap;
755 extern logical lsame_(char *, char *);
756 real theta, small, fastr[5];
757 logical applv, rsvec;
758 extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
761 extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *,
762 integer *), saxpy_(integer *, real *, real *, integer *, real *,
763 integer *), srotm_(integer *, real *, integer *, real *, integer *
765 real rootsfmin, cs, sn;
766 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
767 integer ijblsk, swband;
768 extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
769 real *, integer *, integer *, real *, integer *, integer *);
770 extern integer isamax_(integer *, real *, integer *);
773 extern /* Subroutine */ int slassq_(integer *, real *, integer *, real *,
776 integer ir1, emptsw, notrot, iswrot, jbc;
778 integer kbl, lkahead, igl, ibr, jgl, nbl, mvl;
779 real rootbig, rooteps;
784 /* -- LAPACK computational routine (version 3.8.0) -- */
785 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
786 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
790 /* ===================================================================== */
793 /* Test the input parameters. */
795 /* Parameter adjustments */
799 a_offset = 1 + a_dim1 * 1;
802 v_offset = 1 + v_dim1 * 1;
807 applv = lsame_(jobv, "A");
808 rsvec = lsame_(jobv, "V");
809 if (! (rsvec || applv || lsame_(jobv, "N"))) {
813 } else if (*n < 0 || *n > *m) {
815 } else if (*lda < *m) {
817 } else if ((rsvec || applv) && *mv < 0) {
819 } else if (rsvec && *ldv < *n || applv && *ldv < *mv) {
821 } else if (*tol <= *eps) {
823 } else if (*nsweep < 0) {
825 } else if (*lwork < *m) {
834 xerbla_("SGSVJ0", &i__1, (ftnlen)6);
843 rsvec = rsvec || applv;
844 rooteps = sqrt(*eps);
845 rootsfmin = sqrt(*sfmin);
846 small = *sfmin / *eps;
848 rootbig = 1.f / rootsfmin;
849 bigtheta = 1.f / rooteps;
850 roottol = sqrt(*tol);
853 emptsw = *n * (*n - 1) / 2;
859 /* [TP] SWBAND is a tuning parameter. It is meaningful and effective */
860 /* if SGESVJ is used as a computational routine in the preconditioned */
861 /* Jacobi SVD algorithm SGESVJ. For sweeps i=1:SWBAND the procedure */
864 /* [TP] KBL is a tuning parameter that defines the tile size in the */
865 /* tiling of the p-q loops of pivot pairs. In general, an optimal */
866 /* value of KBL depends on the matrix dimensions and on the */
867 /* parameters of the computer's memory. */
870 if (nbl * kbl != *n) {
873 /* Computing 2nd power */
875 blskip = i__1 * i__1 + 1;
876 /* [TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. */
877 rowskip = f2cmin(5,kbl);
878 /* [TP] ROWSKIP is a tuning parameter. */
880 /* [TP] LKAHEAD is a tuning parameter. */
885 for (i__ = 1; i__ <= i__1; ++i__) {
895 for (ibr = 1; ibr <= i__2; ++ibr) {
896 igl = (ibr - 1) * kbl + 1;
899 i__4 = lkahead, i__5 = nbl - ibr;
900 i__3 = f2cmin(i__4,i__5);
901 for (ir1 = 0; ir1 <= i__3; ++ir1) {
906 i__5 = igl + kbl - 1, i__6 = *n - 1;
907 i__4 = f2cmin(i__5,i__6);
908 for (p = igl; p <= i__4; ++p) {
910 q = isamax_(&i__5, &sva[p], &c__1) + p - 1;
912 sswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 +
915 sswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
928 /* Column norms are periodically updated by explicit */
929 /* norm computation. */
931 /* Some BLAS implementations compute SNRM2(M,A(1,p),1) */
932 /* as SQRT(SDOT(M,A(1,p),1,A(1,p),1)), which may result in */
933 /* overflow for ||A(:,p)||_2 > SQRT(overflow_threshold), and */
934 /* undeflow for ||A(:,p)||_2 < SQRT(underflow_threshold). */
935 /* Hence, SNRM2 cannot be trusted, not even in the case when */
936 /* the true norm is far from the under(over)flow boundaries. */
937 /* If properly implemented SNRM2 is available, the IF-THEN-ELSE */
938 /* below should read "AAPP = SNRM2( M, A(1,p), 1 ) * D(p)". */
940 if (sva[p] < rootbig && sva[p] > rootsfmin) {
941 sva[p] = snrm2_(m, &a[p * a_dim1 + 1], &c__1) *
946 slassq_(m, &a[p * a_dim1 + 1], &c__1, &temp1, &
948 sva[p] = temp1 * sqrt(aapp) * d__[p];
960 i__6 = igl + kbl - 1;
961 i__5 = f2cmin(i__6,*n);
962 for (q = p + 1; q <= i__5; ++q) {
969 rotok = small * aapp <= aaqq;
970 if (aapp < big / aaqq) {
971 aapq = sdot_(m, &a[p * a_dim1 + 1], &
972 c__1, &a[q * a_dim1 + 1], &
973 c__1) * d__[p] * d__[q] /
976 scopy_(m, &a[p * a_dim1 + 1], &c__1, &
978 slascl_("G", &c__0, &c__0, &aapp, &
979 d__[p], m, &c__1, &work[1],
981 aapq = sdot_(m, &work[1], &c__1, &a[q
982 * a_dim1 + 1], &c__1) * d__[q]
986 rotok = aapp <= aaqq / small;
987 if (aapp > small / aaqq) {
988 aapq = sdot_(m, &a[p * a_dim1 + 1], &
989 c__1, &a[q * a_dim1 + 1], &
990 c__1) * d__[p] * d__[q] /
993 scopy_(m, &a[q * a_dim1 + 1], &c__1, &
995 slascl_("G", &c__0, &c__0, &aaqq, &
996 d__[q], m, &c__1, &work[1],
998 aapq = sdot_(m, &work[1], &c__1, &a[p
999 * a_dim1 + 1], &c__1) * d__[p]
1005 r__1 = mxaapq, r__2 = abs(aapq);
1006 mxaapq = f2cmax(r__1,r__2);
1008 /* TO rotate or NOT to rotate, THAT is the question ... */
1010 if (abs(aapq) > *tol) {
1012 /* ROTATED = ROTATED + ONE */
1022 aqoap = aaqq / aapp;
1023 apoaq = aapp / aaqq;
1024 theta = (r__1 = aqoap - apoaq, abs(
1025 r__1)) * -.5f / aapq;
1027 if (abs(theta) > bigtheta) {
1030 fastr[2] = t * d__[p] / d__[q];
1031 fastr[3] = -t * d__[q] / d__[p];
1032 srotm_(m, &a[p * a_dim1 + 1], &
1033 c__1, &a[q * a_dim1 + 1],
1036 srotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
1037 v_dim1 + 1], &c__1, fastr);
1040 r__1 = 0.f, r__2 = t * apoaq *
1042 sva[q] = aaqq * sqrt((f2cmax(r__1,
1045 r__1 = 0.f, r__2 = 1.f - t *
1047 aapp *= sqrt((f2cmax(r__1,r__2)));
1049 r__1 = mxsinj, r__2 = abs(t);
1050 mxsinj = f2cmax(r__1,r__2);
1055 thsign = -r_sign(&c_b42, &aapq);
1056 t = 1.f / (theta + thsign * sqrt(
1057 theta * theta + 1.f));
1058 cs = sqrt(1.f / (t * t + 1.f));
1062 r__1 = mxsinj, r__2 = abs(sn);
1063 mxsinj = f2cmax(r__1,r__2);
1065 r__1 = 0.f, r__2 = t * apoaq *
1067 sva[q] = aaqq * sqrt((f2cmax(r__1,
1070 r__1 = 0.f, r__2 = 1.f - t *
1072 aapp *= sqrt((f2cmax(r__1,r__2)));
1074 apoaq = d__[p] / d__[q];
1075 aqoap = d__[q] / d__[p];
1076 if (d__[p] >= 1.f) {
1077 if (d__[q] >= 1.f) {
1078 fastr[2] = t * apoaq;
1079 fastr[3] = -t * aqoap;
1082 srotm_(m, &a[p * a_dim1 + 1], &c__1, &a[q *
1083 a_dim1 + 1], &c__1, fastr);
1085 srotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[
1086 q * v_dim1 + 1], &c__1, fastr);
1090 saxpy_(m, &r__1, &a[q * a_dim1 + 1], &c__1, &a[
1091 p * a_dim1 + 1], &c__1);
1092 r__1 = cs * sn * apoaq;
1093 saxpy_(m, &r__1, &a[p * a_dim1 + 1], &c__1, &a[
1094 q * a_dim1 + 1], &c__1);
1099 saxpy_(&mvl, &r__1, &v[q * v_dim1 + 1], &
1100 c__1, &v[p * v_dim1 + 1], &c__1);
1101 r__1 = cs * sn * apoaq;
1102 saxpy_(&mvl, &r__1, &v[p * v_dim1 + 1], &
1103 c__1, &v[q * v_dim1 + 1], &c__1);
1107 if (d__[q] >= 1.f) {
1109 saxpy_(m, &r__1, &a[p * a_dim1 + 1], &c__1, &a[
1110 q * a_dim1 + 1], &c__1);
1111 r__1 = -cs * sn * aqoap;
1112 saxpy_(m, &r__1, &a[q * a_dim1 + 1], &c__1, &a[
1113 p * a_dim1 + 1], &c__1);
1118 saxpy_(&mvl, &r__1, &v[p * v_dim1 + 1], &
1119 c__1, &v[q * v_dim1 + 1], &c__1);
1120 r__1 = -cs * sn * aqoap;
1121 saxpy_(&mvl, &r__1, &v[q * v_dim1 + 1], &
1122 c__1, &v[p * v_dim1 + 1], &c__1);
1125 if (d__[p] >= d__[q]) {
1127 saxpy_(m, &r__1, &a[q * a_dim1 + 1], &c__1,
1128 &a[p * a_dim1 + 1], &c__1);
1129 r__1 = cs * sn * apoaq;
1130 saxpy_(m, &r__1, &a[p * a_dim1 + 1], &c__1,
1131 &a[q * a_dim1 + 1], &c__1);
1136 saxpy_(&mvl, &r__1, &v[q * v_dim1 + 1],
1137 &c__1, &v[p * v_dim1 + 1], &
1139 r__1 = cs * sn * apoaq;
1140 saxpy_(&mvl, &r__1, &v[p * v_dim1 + 1],
1141 &c__1, &v[q * v_dim1 + 1], &
1146 saxpy_(m, &r__1, &a[p * a_dim1 + 1], &c__1,
1147 &a[q * a_dim1 + 1], &c__1);
1148 r__1 = -cs * sn * aqoap;
1149 saxpy_(m, &r__1, &a[q * a_dim1 + 1], &c__1,
1150 &a[p * a_dim1 + 1], &c__1);
1155 saxpy_(&mvl, &r__1, &v[p * v_dim1 + 1],
1156 &c__1, &v[q * v_dim1 + 1], &
1158 r__1 = -cs * sn * aqoap;
1159 saxpy_(&mvl, &r__1, &v[q * v_dim1 + 1],
1160 &c__1, &v[p * v_dim1 + 1], &
1169 scopy_(m, &a[p * a_dim1 + 1], &c__1, &
1171 slascl_("G", &c__0, &c__0, &aapp, &
1172 c_b42, m, &c__1, &work[1],
1174 slascl_("G", &c__0, &c__0, &aaqq, &
1175 c_b42, m, &c__1, &a[q *
1176 a_dim1 + 1], lda, &ierr);
1177 temp1 = -aapq * d__[p] / d__[q];
1178 saxpy_(m, &temp1, &work[1], &c__1, &a[
1179 q * a_dim1 + 1], &c__1);
1180 slascl_("G", &c__0, &c__0, &c_b42, &
1181 aaqq, m, &c__1, &a[q * a_dim1
1184 r__1 = 0.f, r__2 = 1.f - aapq * aapq;
1185 sva[q] = aaqq * sqrt((f2cmax(r__1,r__2)))
1187 mxsinj = f2cmax(mxsinj,*sfmin);
1189 /* END IF ROTOK THEN ... ELSE */
1191 /* In the case of cancellation in updating SVA(q), SVA(p) */
1192 /* recompute SVA(q), SVA(p). */
1193 /* Computing 2nd power */
1194 r__1 = sva[q] / aaqq;
1195 if (r__1 * r__1 <= rooteps) {
1196 if (aaqq < rootbig && aaqq >
1198 sva[q] = snrm2_(m, &a[q * a_dim1
1199 + 1], &c__1) * d__[q];
1203 slassq_(m, &a[q * a_dim1 + 1], &
1205 sva[q] = t * sqrt(aaqq) * d__[q];
1208 if (aapp / aapp0 <= rooteps) {
1209 if (aapp < rootbig && aapp >
1211 aapp = snrm2_(m, &a[p * a_dim1 +
1212 1], &c__1) * d__[p];
1216 slassq_(m, &a[p * a_dim1 + 1], &
1218 aapp = t * sqrt(aapp) * d__[p];
1224 /* A(:,p) and A(:,q) already numerically orthogonal */
1231 /* A(:,q) is zero column */
1238 if (i__ <= swband && pskipped > rowskip) {
1251 /* bailed out of q-loop */
1255 if (ir1 == 0 && aapp == 0.f) {
1257 i__5 = igl + kbl - 1;
1258 notrot = notrot + f2cmin(i__5,*n) - p;
1264 /* end of the p-loop */
1265 /* end of doing the block ( ibr, ibr ) */
1268 /* end of ir1-loop */
1270 /* ........................................................ */
1271 /* ... go to the off diagonal blocks */
1273 igl = (ibr - 1) * kbl + 1;
1276 for (jbc = ibr + 1; jbc <= i__3; ++jbc) {
1278 jgl = (jbc - 1) * kbl + 1;
1280 /* doing the block at ( ibr, jbc ) */
1284 i__5 = igl + kbl - 1;
1285 i__4 = f2cmin(i__5,*n);
1286 for (p = igl; p <= i__4; ++p) {
1295 i__6 = jgl + kbl - 1;
1296 i__5 = f2cmin(i__6,*n);
1297 for (q = jgl; q <= i__5; ++q) {
1308 rotok = small * aapp <= aaqq;
1310 rotok = small * aaqq <= aapp;
1312 if (aapp < big / aaqq) {
1313 aapq = sdot_(m, &a[p * a_dim1 + 1], &
1314 c__1, &a[q * a_dim1 + 1], &
1315 c__1) * d__[p] * d__[q] /
1318 scopy_(m, &a[p * a_dim1 + 1], &c__1, &
1320 slascl_("G", &c__0, &c__0, &aapp, &
1321 d__[p], m, &c__1, &work[1],
1323 aapq = sdot_(m, &work[1], &c__1, &a[q
1324 * a_dim1 + 1], &c__1) * d__[q]
1329 rotok = aapp <= aaqq / small;
1331 rotok = aaqq <= aapp / small;
1333 if (aapp > small / aaqq) {
1334 aapq = sdot_(m, &a[p * a_dim1 + 1], &
1335 c__1, &a[q * a_dim1 + 1], &
1336 c__1) * d__[p] * d__[q] /
1339 scopy_(m, &a[q * a_dim1 + 1], &c__1, &
1341 slascl_("G", &c__0, &c__0, &aaqq, &
1342 d__[q], m, &c__1, &work[1],
1344 aapq = sdot_(m, &work[1], &c__1, &a[p
1345 * a_dim1 + 1], &c__1) * d__[p]
1351 r__1 = mxaapq, r__2 = abs(aapq);
1352 mxaapq = f2cmax(r__1,r__2);
1354 /* TO rotate or NOT to rotate, THAT is the question ... */
1356 if (abs(aapq) > *tol) {
1358 /* ROTATED = ROTATED + 1 */
1364 aqoap = aaqq / aapp;
1365 apoaq = aapp / aaqq;
1366 theta = (r__1 = aqoap - apoaq, abs(
1367 r__1)) * -.5f / aapq;
1372 if (abs(theta) > bigtheta) {
1374 fastr[2] = t * d__[p] / d__[q];
1375 fastr[3] = -t * d__[q] / d__[p];
1376 srotm_(m, &a[p * a_dim1 + 1], &
1377 c__1, &a[q * a_dim1 + 1],
1380 srotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
1381 v_dim1 + 1], &c__1, fastr);
1384 r__1 = 0.f, r__2 = t * apoaq *
1386 sva[q] = aaqq * sqrt((f2cmax(r__1,
1389 r__1 = 0.f, r__2 = 1.f - t *
1391 aapp *= sqrt((f2cmax(r__1,r__2)));
1393 r__1 = mxsinj, r__2 = abs(t);
1394 mxsinj = f2cmax(r__1,r__2);
1398 thsign = -r_sign(&c_b42, &aapq);
1402 t = 1.f / (theta + thsign * sqrt(
1403 theta * theta + 1.f));
1404 cs = sqrt(1.f / (t * t + 1.f));
1407 r__1 = mxsinj, r__2 = abs(sn);
1408 mxsinj = f2cmax(r__1,r__2);
1410 r__1 = 0.f, r__2 = t * apoaq *
1412 sva[q] = aaqq * sqrt((f2cmax(r__1,
1415 r__1 = 0.f, r__2 = 1.f - t *
1417 aapp *= sqrt((f2cmax(r__1,r__2)));
1419 apoaq = d__[p] / d__[q];
1420 aqoap = d__[q] / d__[p];
1421 if (d__[p] >= 1.f) {
1423 if (d__[q] >= 1.f) {
1424 fastr[2] = t * apoaq;
1425 fastr[3] = -t * aqoap;
1428 srotm_(m, &a[p * a_dim1 + 1], &c__1, &a[q *
1429 a_dim1 + 1], &c__1, fastr);
1431 srotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[
1432 q * v_dim1 + 1], &c__1, fastr);
1436 saxpy_(m, &r__1, &a[q * a_dim1 + 1], &c__1, &a[
1437 p * a_dim1 + 1], &c__1);
1438 r__1 = cs * sn * apoaq;
1439 saxpy_(m, &r__1, &a[p * a_dim1 + 1], &c__1, &a[
1440 q * a_dim1 + 1], &c__1);
1443 saxpy_(&mvl, &r__1, &v[q * v_dim1 + 1], &
1444 c__1, &v[p * v_dim1 + 1], &c__1);
1445 r__1 = cs * sn * apoaq;
1446 saxpy_(&mvl, &r__1, &v[p * v_dim1 + 1], &
1447 c__1, &v[q * v_dim1 + 1], &c__1);
1453 if (d__[q] >= 1.f) {
1455 saxpy_(m, &r__1, &a[p * a_dim1 + 1], &c__1, &a[
1456 q * a_dim1 + 1], &c__1);
1457 r__1 = -cs * sn * aqoap;
1458 saxpy_(m, &r__1, &a[q * a_dim1 + 1], &c__1, &a[
1459 p * a_dim1 + 1], &c__1);
1462 saxpy_(&mvl, &r__1, &v[p * v_dim1 + 1], &
1463 c__1, &v[q * v_dim1 + 1], &c__1);
1464 r__1 = -cs * sn * aqoap;
1465 saxpy_(&mvl, &r__1, &v[q * v_dim1 + 1], &
1466 c__1, &v[p * v_dim1 + 1], &c__1);
1471 if (d__[p] >= d__[q]) {
1473 saxpy_(m, &r__1, &a[q * a_dim1 + 1], &c__1,
1474 &a[p * a_dim1 + 1], &c__1);
1475 r__1 = cs * sn * apoaq;
1476 saxpy_(m, &r__1, &a[p * a_dim1 + 1], &c__1,
1477 &a[q * a_dim1 + 1], &c__1);
1482 saxpy_(&mvl, &r__1, &v[q * v_dim1 + 1],
1483 &c__1, &v[p * v_dim1 + 1], &
1485 r__1 = cs * sn * apoaq;
1486 saxpy_(&mvl, &r__1, &v[p * v_dim1 + 1],
1487 &c__1, &v[q * v_dim1 + 1], &
1492 saxpy_(m, &r__1, &a[p * a_dim1 + 1], &c__1,
1493 &a[q * a_dim1 + 1], &c__1);
1494 r__1 = -cs * sn * aqoap;
1495 saxpy_(m, &r__1, &a[q * a_dim1 + 1], &c__1,
1496 &a[p * a_dim1 + 1], &c__1);
1501 saxpy_(&mvl, &r__1, &v[p * v_dim1 + 1],
1502 &c__1, &v[q * v_dim1 + 1], &
1504 r__1 = -cs * sn * aqoap;
1505 saxpy_(&mvl, &r__1, &v[q * v_dim1 + 1],
1506 &c__1, &v[p * v_dim1 + 1], &
1516 scopy_(m, &a[p * a_dim1 + 1], &
1517 c__1, &work[1], &c__1);
1518 slascl_("G", &c__0, &c__0, &aapp,
1519 &c_b42, m, &c__1, &work[1]
1521 slascl_("G", &c__0, &c__0, &aaqq,
1522 &c_b42, m, &c__1, &a[q *
1523 a_dim1 + 1], lda, &ierr);
1524 temp1 = -aapq * d__[p] / d__[q];
1525 saxpy_(m, &temp1, &work[1], &c__1,
1526 &a[q * a_dim1 + 1], &
1528 slascl_("G", &c__0, &c__0, &c_b42,
1529 &aaqq, m, &c__1, &a[q *
1530 a_dim1 + 1], lda, &ierr);
1532 r__1 = 0.f, r__2 = 1.f - aapq *
1534 sva[q] = aaqq * sqrt((f2cmax(r__1,
1536 mxsinj = f2cmax(mxsinj,*sfmin);
1538 scopy_(m, &a[q * a_dim1 + 1], &
1539 c__1, &work[1], &c__1);
1540 slascl_("G", &c__0, &c__0, &aaqq,
1541 &c_b42, m, &c__1, &work[1]
1543 slascl_("G", &c__0, &c__0, &aapp,
1544 &c_b42, m, &c__1, &a[p *
1545 a_dim1 + 1], lda, &ierr);
1546 temp1 = -aapq * d__[q] / d__[p];
1547 saxpy_(m, &temp1, &work[1], &c__1,
1548 &a[p * a_dim1 + 1], &
1550 slascl_("G", &c__0, &c__0, &c_b42,
1551 &aapp, m, &c__1, &a[p *
1552 a_dim1 + 1], lda, &ierr);
1554 r__1 = 0.f, r__2 = 1.f - aapq *
1556 sva[p] = aapp * sqrt((f2cmax(r__1,
1558 mxsinj = f2cmax(mxsinj,*sfmin);
1561 /* END IF ROTOK THEN ... ELSE */
1563 /* In the case of cancellation in updating SVA(q) */
1564 /* Computing 2nd power */
1565 r__1 = sva[q] / aaqq;
1566 if (r__1 * r__1 <= rooteps) {
1567 if (aaqq < rootbig && aaqq >
1569 sva[q] = snrm2_(m, &a[q * a_dim1
1570 + 1], &c__1) * d__[q];
1574 slassq_(m, &a[q * a_dim1 + 1], &
1576 sva[q] = t * sqrt(aaqq) * d__[q];
1579 /* Computing 2nd power */
1580 r__1 = aapp / aapp0;
1581 if (r__1 * r__1 <= rooteps) {
1582 if (aapp < rootbig && aapp >
1584 aapp = snrm2_(m, &a[p * a_dim1 +
1585 1], &c__1) * d__[p];
1589 slassq_(m, &a[p * a_dim1 + 1], &
1591 aapp = t * sqrt(aapp) * d__[p];
1595 /* end of OK rotation */
1607 if (i__ <= swband && ijblsk >= blskip) {
1612 if (i__ <= swband && pskipped > rowskip) {
1620 /* end of the q-loop */
1628 i__5 = jgl + kbl - 1;
1629 notrot = notrot + f2cmin(i__5,*n) - jgl + 1;
1637 /* end of the p-loop */
1640 /* end of the jbc-loop */
1642 /* 2011 bailed out of the jbc-loop */
1644 i__4 = igl + kbl - 1;
1645 i__3 = f2cmin(i__4,*n);
1646 for (p = igl; p <= i__3; ++p) {
1647 sva[p] = (r__1 = sva[p], abs(r__1));
1653 /* 2000 :: end of the ibr-loop */
1655 if (sva[*n] < rootbig && sva[*n] > rootsfmin) {
1656 sva[*n] = snrm2_(m, &a[*n * a_dim1 + 1], &c__1) * d__[*n];
1660 slassq_(m, &a[*n * a_dim1 + 1], &c__1, &t, &aapp);
1661 sva[*n] = t * sqrt(aapp) * d__[*n];
1664 /* Additional steering devices */
1666 if (i__ < swband && (mxaapq <= roottol || iswrot <= *n)) {
1670 if (i__ > swband + 1 && mxaapq < (real) (*n) * *tol && (real) (*n) *
1671 mxaapq * mxsinj < *tol) {
1675 if (notrot >= emptsw) {
1680 /* end i=1:NSWEEP loop */
1681 /* #:) Reaching this point means that the procedure has completed the given */
1682 /* number of iterations. */
1683 *info = *nsweep - 1;
1686 /* #:) Reaching this point means that during the i-th sweep all pivots were */
1687 /* below the given tolerance, causing early exit. */
1690 /* #:) INFO = 0 confirms successful iterations. */
1693 /* Sort the vector D. */
1695 for (p = 1; p <= i__1; ++p) {
1697 q = isamax_(&i__2, &sva[p], &c__1) + p - 1;
1705 sswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1);
1707 sswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], &