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 ZGEBAL */
519 /* =========== DOCUMENTATION =========== */
521 /* Online html documentation available at */
522 /* http://www.netlib.org/lapack/explore-html/ */
525 /* > Download ZGEBAL + dependencies */
526 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgebal.
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgebal.
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgebal.
540 /* SUBROUTINE ZGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO ) */
543 /* INTEGER IHI, ILO, INFO, LDA, N */
544 /* DOUBLE PRECISION SCALE( * ) */
545 /* COMPLEX*16 A( LDA, * ) */
548 /* > \par Purpose: */
553 /* > ZGEBAL balances a general complex matrix A. This involves, first, */
554 /* > permuting A by a similarity transformation to isolate eigenvalues */
555 /* > in the first 1 to ILO-1 and last IHI+1 to N elements on the */
556 /* > diagonal; and second, applying a diagonal similarity transformation */
557 /* > to rows and columns ILO to IHI to make the rows and columns as */
558 /* > close in norm as possible. Both steps are optional. */
560 /* > Balancing may reduce the 1-norm of the matrix, and improve the */
561 /* > accuracy of the computed eigenvalues and/or eigenvectors. */
567 /* > \param[in] JOB */
569 /* > JOB is CHARACTER*1 */
570 /* > Specifies the operations to be performed on A: */
571 /* > = 'N': none: simply set ILO = 1, IHI = N, SCALE(I) = 1.0 */
572 /* > for i = 1,...,N; */
573 /* > = 'P': permute only; */
574 /* > = 'S': scale only; */
575 /* > = 'B': both permute and scale. */
581 /* > The order of the matrix A. N >= 0. */
584 /* > \param[in,out] A */
586 /* > A is COMPLEX*16 array, dimension (LDA,N) */
587 /* > On entry, the input matrix A. */
588 /* > On exit, A is overwritten by the balanced matrix. */
589 /* > If JOB = 'N', A is not referenced. */
590 /* > See Further Details. */
593 /* > \param[in] LDA */
595 /* > LDA is INTEGER */
596 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
599 /* > \param[out] ILO */
601 /* > ILO is INTEGER */
604 /* > \param[out] IHI */
606 /* > IHI is INTEGER */
607 /* > ILO and IHI are set to INTEGER such that on exit */
608 /* > A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N. */
609 /* > If JOB = 'N' or 'S', ILO = 1 and IHI = N. */
612 /* > \param[out] SCALE */
614 /* > SCALE is DOUBLE PRECISION array, dimension (N) */
615 /* > Details of the permutations and scaling factors applied to */
616 /* > A. If P(j) is the index of the row and column interchanged */
617 /* > with row and column j and D(j) is the scaling factor */
618 /* > applied to row and column j, then */
619 /* > SCALE(j) = P(j) for j = 1,...,ILO-1 */
620 /* > = D(j) for j = ILO,...,IHI */
621 /* > = P(j) for j = IHI+1,...,N. */
622 /* > The order in which the interchanges are made is N to IHI+1, */
623 /* > then 1 to ILO-1. */
626 /* > \param[out] INFO */
628 /* > INFO is INTEGER */
629 /* > = 0: successful exit. */
630 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
636 /* > \author Univ. of Tennessee */
637 /* > \author Univ. of California Berkeley */
638 /* > \author Univ. of Colorado Denver */
639 /* > \author NAG Ltd. */
641 /* > \date June 2017 */
643 /* > \ingroup complex16GEcomputational */
645 /* > \par Further Details: */
646 /* ===================== */
650 /* > The permutations consist of row and column interchanges which put */
651 /* > the matrix in the form */
654 /* > P A P = ( 0 B Z ) */
657 /* > where T1 and T2 are upper triangular matrices whose eigenvalues lie */
658 /* > along the diagonal. The column indices ILO and IHI mark the starting */
659 /* > and ending columns of the submatrix B. Balancing consists of applying */
660 /* > a diagonal similarity transformation inv(D) * B * D to make the */
661 /* > 1-norms of each row of B and its corresponding column nearly equal. */
662 /* > The output matrix is */
665 /* > ( 0 inv(D)*B*D inv(D)*Z ). */
668 /* > Information about the permutations P and the diagonal matrix D is */
669 /* > returned in the vector SCALE. */
671 /* > This subroutine is based on the EISPACK routine CBAL. */
673 /* > Modified by Tzu-Yi Chen, Computer Science Division, University of */
674 /* > California at Berkeley, USA */
677 /* ===================================================================== */
678 /* Subroutine */ int zgebal_(char *job, integer *n, doublecomplex *a, integer
679 *lda, integer *ilo, integer *ihi, doublereal *scale, integer *info)
681 /* System generated locals */
682 integer a_dim1, a_offset, i__1, i__2, i__3;
683 doublereal d__1, d__2;
685 /* Local variables */
687 doublereal c__, f, g;
688 integer i__, j, k, l, m;
690 extern logical lsame_(char *, char *);
691 extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *,
692 doublecomplex *, integer *);
693 doublereal sfmin1, sfmin2, sfmax1, sfmax2, ca;
694 extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
696 extern doublereal dlamch_(char *);
697 extern logical disnan_(doublereal *);
698 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), zdscal_(
699 integer *, doublereal *, doublecomplex *, integer *);
700 extern integer izamax_(integer *, doublecomplex *, integer *);
705 /* -- LAPACK computational routine (version 3.7.1) -- */
706 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
707 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
711 /* ===================================================================== */
714 /* Test the input parameters */
716 /* Parameter adjustments */
718 a_offset = 1 + a_dim1 * 1;
724 if (! lsame_(job, "N") && ! lsame_(job, "P") && ! lsame_(job, "S")
725 && ! lsame_(job, "B")) {
729 } else if (*lda < f2cmax(1,*n)) {
734 xerbla_("ZGEBAL", &i__1, (ftnlen)6);
745 if (lsame_(job, "N")) {
747 for (i__ = 1; i__ <= i__1; ++i__) {
754 if (lsame_(job, "S")) {
758 /* Permutation to isolate eigenvalues if possible */
762 /* Row and column exchange. */
765 scale[m] = (doublereal) j;
770 zswap_(&l, &a[j * a_dim1 + 1], &c__1, &a[m * a_dim1 + 1], &c__1);
772 zswap_(&i__1, &a[j + k * a_dim1], lda, &a[m + k * a_dim1], lda);
780 /* Search for rows isolating an eigenvalue and push them down. */
789 for (j = l; j >= 1; --j) {
792 for (i__ = 1; i__ <= i__1; ++i__) {
796 i__2 = j + i__ * a_dim1;
797 if (a[i__2].r != 0. || d_imag(&a[j + i__ * a_dim1]) != 0.) {
813 /* Search for columns isolating an eigenvalue and push them left. */
820 for (j = k; j <= i__1; ++j) {
823 for (i__ = k; i__ <= i__2; ++i__) {
827 i__3 = i__ + j * a_dim1;
828 if (a[i__3].r != 0. || d_imag(&a[i__ + j * a_dim1]) != 0.) {
844 for (i__ = k; i__ <= i__1; ++i__) {
849 if (lsame_(job, "P")) {
853 /* Balance the submatrix in rows K to L. */
855 /* Iterative loop for norm reduction */
857 sfmin1 = dlamch_("S") / dlamch_("P");
858 sfmax1 = 1. / sfmin1;
859 sfmin2 = sfmin1 * 2.;
860 sfmax2 = 1. / sfmin2;
865 for (i__ = k; i__ <= i__1; ++i__) {
868 c__ = dznrm2_(&i__2, &a[k + i__ * a_dim1], &c__1);
870 r__ = dznrm2_(&i__2, &a[i__ + k * a_dim1], lda);
871 ica = izamax_(&l, &a[i__ * a_dim1 + 1], &c__1);
872 ca = z_abs(&a[ica + i__ * a_dim1]);
874 ira = izamax_(&i__2, &a[i__ + k * a_dim1], lda);
875 ra = z_abs(&a[i__ + (ira + k - 1) * a_dim1]);
877 /* Guard against zero C or R due to underflow. */
879 if (c__ == 0. || r__ == 0.) {
887 d__1 = f2cmax(f,c__);
889 d__2 = f2cmin(r__,g);
890 if (c__ >= g || f2cmax(d__1,ca) >= sfmax2 || f2cmin(d__2,ra) <= sfmin2) {
893 d__1 = c__ + f + ca + r__ + g + ra;
894 if (disnan_(&d__1)) {
896 /* Exit if NaN to avoid infinite loop */
900 xerbla_("ZGEBAL", &i__2, (ftnlen)6);
915 d__1 = f2cmin(f,c__), d__1 = f2cmin(d__1,g);
916 if (g < r__ || f2cmax(r__,ra) >= sfmax2 || f2cmin(d__1,ca) <= sfmin2) {
930 if (c__ + r__ >= s * .95) {
933 if (f < 1. && scale[i__] < 1.) {
934 if (f * scale[i__] <= sfmin1) {
938 if (f > 1. && scale[i__] > 1.) {
939 if (scale[i__] >= sfmax1 / f) {
948 zdscal_(&i__2, &g, &a[i__ + k * a_dim1], lda);
949 zdscal_(&l, &f, &a[i__ * a_dim1 + 1], &c__1);