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;
517 /* > \brief \b DSYEQUB */
519 /* =========== DOCUMENTATION =========== */
521 /* Online html documentation available at */
522 /* http://www.netlib.org/lapack/explore-html/ */
525 /* > Download DSYEQUB + dependencies */
526 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyequb
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyequb
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyequb
540 /* SUBROUTINE DSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO ) */
542 /* INTEGER INFO, LDA, N */
543 /* DOUBLE PRECISION AMAX, SCOND */
545 /* DOUBLE PRECISION A( LDA, * ), S( * ), WORK( * ) */
548 /* > \par Purpose: */
553 /* > DSYEQUB computes row and column scalings intended to equilibrate a */
554 /* > symmetric matrix A (with respect to the Euclidean norm) and reduce */
555 /* > its condition number. The scale factors S are computed by the BIN */
556 /* > algorithm (see references) so that the scaled matrix B with elements */
557 /* > B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of */
558 /* > the smallest possible condition number over all possible diagonal */
565 /* > \param[in] UPLO */
567 /* > UPLO is CHARACTER*1 */
568 /* > = 'U': Upper triangle of A is stored; */
569 /* > = 'L': Lower triangle of A is stored. */
575 /* > The order of the matrix A. N >= 0. */
580 /* > A is DOUBLE PRECISION array, dimension (LDA,N) */
581 /* > The N-by-N symmetric matrix whose scaling factors are to be */
585 /* > \param[in] LDA */
587 /* > LDA is INTEGER */
588 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
591 /* > \param[out] S */
593 /* > S is DOUBLE PRECISION array, dimension (N) */
594 /* > If INFO = 0, S contains the scale factors for A. */
597 /* > \param[out] SCOND */
599 /* > SCOND is DOUBLE PRECISION */
600 /* > If INFO = 0, S contains the ratio of the smallest S(i) to */
601 /* > the largest S(i). If SCOND >= 0.1 and AMAX is neither too */
602 /* > large nor too small, it is not worth scaling by S. */
605 /* > \param[out] AMAX */
607 /* > AMAX is DOUBLE PRECISION */
608 /* > Largest absolute value of any matrix element. If AMAX is */
609 /* > very close to overflow or very close to underflow, the */
610 /* > matrix should be scaled. */
613 /* > \param[out] WORK */
615 /* > WORK is DOUBLE PRECISION array, dimension (2*N) */
618 /* > \param[out] INFO */
620 /* > INFO is INTEGER */
621 /* > = 0: successful exit */
622 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
623 /* > > 0: if INFO = i, the i-th diagonal element is nonpositive. */
629 /* > \author Univ. of Tennessee */
630 /* > \author Univ. of California Berkeley */
631 /* > \author Univ. of Colorado Denver */
632 /* > \author NAG Ltd. */
634 /* > \date November 2017 */
636 /* > \ingroup doubleSYcomputational */
638 /* > \par References: */
639 /* ================ */
641 /* > Livne, O.E. and Golub, G.H., "Scaling by Binormalization", \n */
642 /* > Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004. \n */
643 /* > DOI 10.1023/B:NUMA.0000016606.32820.69 \n */
644 /* > Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679 */
646 /* ===================================================================== */
647 /* Subroutine */ int dsyequb_(char *uplo, integer *n, doublereal *a, integer *
648 lda, doublereal *s, doublereal *scond, doublereal *amax, doublereal *
651 /* System generated locals */
652 integer a_dim1, a_offset, i__1, i__2;
653 doublereal d__1, d__2, d__3;
655 /* Local variables */
658 doublereal smin, smax, d__;
660 doublereal t, u, scale;
661 extern logical lsame_(char *, char *);
662 doublereal c0, c1, c2, sumsq;
663 extern doublereal dlamch_(char *);
666 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
668 extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *,
669 doublereal *, doublereal *);
670 doublereal smlnum, avg, std, tol;
673 /* -- LAPACK computational routine (version 3.8.0) -- */
674 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
675 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
679 /* ===================================================================== */
682 /* Test the input parameters. */
684 /* Parameter adjustments */
686 a_offset = 1 + a_dim1 * 1;
693 if (! (lsame_(uplo, "U") || lsame_(uplo, "L"))) {
697 } else if (*lda < f2cmax(1,*n)) {
702 xerbla_("DSYEQUB", &i__1, (ftnlen)7);
705 up = lsame_(uplo, "U");
708 /* Quick return if possible. */
715 for (i__ = 1; i__ <= i__1; ++i__) {
721 for (j = 1; j <= i__1; ++j) {
723 for (i__ = 1; i__ <= i__2; ++i__) {
725 d__2 = s[i__], d__3 = (d__1 = a[i__ + j * a_dim1], abs(d__1));
726 s[i__] = f2cmax(d__2,d__3);
728 d__2 = s[j], d__3 = (d__1 = a[i__ + j * a_dim1], abs(d__1));
729 s[j] = f2cmax(d__2,d__3);
731 d__2 = *amax, d__3 = (d__1 = a[i__ + j * a_dim1], abs(d__1));
732 *amax = f2cmax(d__2,d__3);
735 d__2 = s[j], d__3 = (d__1 = a[j + j * a_dim1], abs(d__1));
736 s[j] = f2cmax(d__2,d__3);
738 d__2 = *amax, d__3 = (d__1 = a[j + j * a_dim1], abs(d__1));
739 *amax = f2cmax(d__2,d__3);
743 for (j = 1; j <= i__1; ++j) {
745 d__2 = s[j], d__3 = (d__1 = a[j + j * a_dim1], abs(d__1));
746 s[j] = f2cmax(d__2,d__3);
748 d__2 = *amax, d__3 = (d__1 = a[j + j * a_dim1], abs(d__1));
749 *amax = f2cmax(d__2,d__3);
751 for (i__ = j + 1; i__ <= i__2; ++i__) {
753 d__2 = s[i__], d__3 = (d__1 = a[i__ + j * a_dim1], abs(d__1));
754 s[i__] = f2cmax(d__2,d__3);
756 d__2 = s[j], d__3 = (d__1 = a[i__ + j * a_dim1], abs(d__1));
757 s[j] = f2cmax(d__2,d__3);
759 d__2 = *amax, d__3 = (d__1 = a[i__ + j * a_dim1], abs(d__1));
760 *amax = f2cmax(d__2,d__3);
765 for (j = 1; j <= i__1; ++j) {
768 tol = 1. / sqrt(*n * 2.);
769 for (iter = 1; iter <= 100; ++iter) {
774 for (i__ = 1; i__ <= i__1; ++i__) {
779 for (j = 1; j <= i__1; ++j) {
781 for (i__ = 1; i__ <= i__2; ++i__) {
782 work[i__] += (d__1 = a[i__ + j * a_dim1], abs(d__1)) * s[
784 work[j] += (d__1 = a[i__ + j * a_dim1], abs(d__1)) * s[
787 work[j] += (d__1 = a[j + j * a_dim1], abs(d__1)) * s[j];
791 for (j = 1; j <= i__1; ++j) {
792 work[j] += (d__1 = a[j + j * a_dim1], abs(d__1)) * s[j];
794 for (i__ = j + 1; i__ <= i__2; ++i__) {
795 work[i__] += (d__1 = a[i__ + j * a_dim1], abs(d__1)) * s[
797 work[j] += (d__1 = a[i__ + j * a_dim1], abs(d__1)) * s[
802 /* avg = s^T beta / n */
805 for (i__ = 1; i__ <= i__1; ++i__) {
806 avg += s[i__] * work[i__];
811 for (i__ = *n + 1; i__ <= i__1; ++i__) {
812 work[i__] = s[i__ - *n] * work[i__ - *n] - avg;
814 dlassq_(n, &work[*n + 1], &c__1, &scale, &sumsq);
815 std = scale * sqrt(sumsq / *n);
816 if (std < tol * avg) {
820 for (i__ = 1; i__ <= i__1; ++i__) {
821 t = (d__1 = a[i__ + i__ * a_dim1], abs(d__1));
824 c1 = (*n - 2) * (work[i__] - t * si);
825 c0 = -(t * si) * si + work[i__] * 2 * si - *n * avg;
826 d__ = c1 * c1 - c0 * 4 * c2;
831 si = c0 * -2 / (c1 + sqrt(d__));
836 for (j = 1; j <= i__2; ++j) {
837 t = (d__1 = a[j + i__ * a_dim1], abs(d__1));
842 for (j = i__ + 1; j <= i__2; ++j) {
843 t = (d__1 = a[i__ + j * a_dim1], abs(d__1));
849 for (j = 1; j <= i__2; ++j) {
850 t = (d__1 = a[i__ + j * a_dim1], abs(d__1));
855 for (j = i__ + 1; j <= i__2; ++j) {
856 t = (d__1 = a[j + i__ * a_dim1], abs(d__1));
861 avg += (u + work[i__]) * d__ / *n;
866 smlnum = dlamch_("SAFEMIN");
867 bignum = 1. / smlnum;
874 for (i__ = 1; i__ <= i__1; ++i__) {
875 i__2 = (integer) (u * log(s[i__] * t));
876 s[i__] = pow_di(&base, &i__2);
878 d__1 = smin, d__2 = s[i__];
879 smin = f2cmin(d__1,d__2);
881 d__1 = smax, d__2 = s[i__];
882 smax = f2cmax(d__1,d__2);
884 *scond = f2cmax(smin,smlnum) / f2cmin(smax,bignum);