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 /* > \brief \b SLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form. */
515 /* =========== DOCUMENTATION =========== */
517 /* Online html documentation available at */
518 /* http://www.netlib.org/lapack/explore-html/ */
521 /* > Download SLALN2 + dependencies */
522 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slaln2.
525 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slaln2.
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slaln2.
536 /* SUBROUTINE SLALN2( LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2, B, */
537 /* LDB, WR, WI, X, LDX, SCALE, XNORM, INFO ) */
540 /* INTEGER INFO, LDA, LDB, LDX, NA, NW */
541 /* REAL CA, D1, D2, SCALE, SMIN, WI, WR, XNORM */
542 /* REAL A( LDA, * ), B( LDB, * ), X( LDX, * ) */
545 /* > \par Purpose: */
550 /* > SLALN2 solves a system of the form (ca A - w D ) X = s B */
551 /* > or (ca A**T - w D) X = s B with possible scaling ("s") and */
552 /* > perturbation of A. (A**T means A-transpose.) */
554 /* > A is an NA x NA real matrix, ca is a real scalar, D is an NA x NA */
555 /* > real diagonal matrix, w is a real or complex value, and X and B are */
556 /* > NA x 1 matrices -- real if w is real, complex if w is complex. NA */
557 /* > may be 1 or 2. */
559 /* > If w is complex, X and B are represented as NA x 2 matrices, */
560 /* > the first column of each being the real part and the second */
561 /* > being the imaginary part. */
563 /* > "s" is a scaling factor (<= 1), computed by SLALN2, which is */
564 /* > so chosen that X can be computed without overflow. X is further */
565 /* > scaled if necessary to assure that norm(ca A - w D)*norm(X) is less */
566 /* > than overflow. */
568 /* > If both singular values of (ca A - w D) are less than SMIN, */
569 /* > SMIN*identity will be used instead of (ca A - w D). If only one */
570 /* > singular value is less than SMIN, one element of (ca A - w D) will be */
571 /* > perturbed enough to make the smallest singular value roughly SMIN. */
572 /* > If both singular values are at least SMIN, (ca A - w D) will not be */
573 /* > perturbed. In any case, the perturbation will be at most some small */
574 /* > multiple of f2cmax( SMIN, ulp*norm(ca A - w D) ). The singular values */
575 /* > are computed by infinity-norm approximations, and thus will only be */
576 /* > correct to a factor of 2 or so. */
578 /* > Note: all input quantities are assumed to be smaller than overflow */
579 /* > by a reasonable factor. (See BIGNUM.) */
585 /* > \param[in] LTRANS */
587 /* > LTRANS is LOGICAL */
588 /* > =.TRUE.: A-transpose will be used. */
589 /* > =.FALSE.: A will be used (not transposed.) */
592 /* > \param[in] NA */
594 /* > NA is INTEGER */
595 /* > The size of the matrix A. It may (only) be 1 or 2. */
598 /* > \param[in] NW */
600 /* > NW is INTEGER */
601 /* > 1 if "w" is real, 2 if "w" is complex. It may only be 1 */
605 /* > \param[in] SMIN */
608 /* > The desired lower bound on the singular values of A. This */
609 /* > should be a safe distance away from underflow or overflow, */
610 /* > say, between (underflow/machine precision) and (machine */
611 /* > precision * overflow ). (See BIGNUM and ULP.) */
614 /* > \param[in] CA */
617 /* > The coefficient c, which A is multiplied by. */
622 /* > A is REAL array, dimension (LDA,NA) */
623 /* > The NA x NA matrix A. */
626 /* > \param[in] LDA */
628 /* > LDA is INTEGER */
629 /* > The leading dimension of A. It must be at least NA. */
632 /* > \param[in] D1 */
635 /* > The 1,1 element in the diagonal matrix D. */
638 /* > \param[in] D2 */
641 /* > The 2,2 element in the diagonal matrix D. Not used if NA=1. */
646 /* > B is REAL array, dimension (LDB,NW) */
647 /* > The NA x NW matrix B (right-hand side). If NW=2 ("w" is */
648 /* > complex), column 1 contains the real part of B and column 2 */
649 /* > contains the imaginary part. */
652 /* > \param[in] LDB */
654 /* > LDB is INTEGER */
655 /* > The leading dimension of B. It must be at least NA. */
658 /* > \param[in] WR */
661 /* > The real part of the scalar "w". */
664 /* > \param[in] WI */
667 /* > The imaginary part of the scalar "w". Not used if NW=1. */
670 /* > \param[out] X */
672 /* > X is REAL array, dimension (LDX,NW) */
673 /* > The NA x NW matrix X (unknowns), as computed by SLALN2. */
674 /* > If NW=2 ("w" is complex), on exit, column 1 will contain */
675 /* > the real part of X and column 2 will contain the imaginary */
679 /* > \param[in] LDX */
681 /* > LDX is INTEGER */
682 /* > The leading dimension of X. It must be at least NA. */
685 /* > \param[out] SCALE */
687 /* > SCALE is REAL */
688 /* > The scale factor that B must be multiplied by to insure */
689 /* > that overflow does not occur when computing X. Thus, */
690 /* > (ca A - w D) X will be SCALE*B, not B (ignoring */
691 /* > perturbations of A.) It will be at most 1. */
694 /* > \param[out] XNORM */
696 /* > XNORM is REAL */
697 /* > The infinity-norm of X, when X is regarded as an NA x NW */
701 /* > \param[out] INFO */
703 /* > INFO is INTEGER */
704 /* > An error flag. It will be set to zero if no error occurs, */
705 /* > a negative number if an argument is in error, or a positive */
706 /* > number if ca A - w D had to be perturbed. */
707 /* > The possible values are: */
708 /* > = 0: No error occurred, and (ca A - w D) did not have to be */
710 /* > = 1: (ca A - w D) had to be perturbed to make its smallest */
711 /* > (or only) singular value greater than SMIN. */
712 /* > NOTE: In the interests of speed, this routine does not */
713 /* > check the inputs for errors. */
719 /* > \author Univ. of Tennessee */
720 /* > \author Univ. of California Berkeley */
721 /* > \author Univ. of Colorado Denver */
722 /* > \author NAG Ltd. */
724 /* > \date December 2016 */
726 /* > \ingroup realOTHERauxiliary */
728 /* ===================================================================== */
729 /* Subroutine */ int slaln2_(logical *ltrans, integer *na, integer *nw, real *
730 smin, real *ca, real *a, integer *lda, real *d1, real *d2, real *b,
731 integer *ldb, real *wr, real *wi, real *x, integer *ldx, real *scale,
732 real *xnorm, integer *info)
734 /* Initialized data */
736 static logical cswap[4] = { FALSE_,FALSE_,TRUE_,TRUE_ };
737 static logical rswap[4] = { FALSE_,TRUE_,FALSE_,TRUE_ };
738 static integer ipivot[16] /* was [4][4] */ = { 1,2,3,4,2,1,4,3,3,4,1,2,
741 /* System generated locals */
742 integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset;
743 real r__1, r__2, r__3, r__4, r__5, r__6;
744 static real equiv_0[4], equiv_1[4];
746 /* Local variables */
747 real bbnd, cmax, ui11r, ui12s, temp, ur11r, ur12s;
751 real bnorm, cnorm, smini;
754 extern real slamch_(char *);
756 extern /* Subroutine */ int sladiv_(real *, real *, real *, real *, real *
758 real bi1, bi2, br1, br2, smlnum, xi1, xi2, xr1, xr2, ci21, ci22, cr21,
759 cr22, li21, csi, ui11, lr21, ui12, ui22;
760 #define civ (equiv_0)
761 real csr, ur11, ur12, ur22;
762 #define crv (equiv_1)
765 /* -- LAPACK auxiliary routine (version 3.7.0) -- */
766 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
767 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
771 /* ===================================================================== */
773 /* Parameter adjustments */
775 a_offset = 1 + a_dim1 * 1;
778 b_offset = 1 + b_dim1 * 1;
781 x_offset = 1 + x_dim1 * 1;
788 smlnum = 2.f * slamch_("Safe minimum");
789 bignum = 1.f / smlnum;
790 smini = f2cmax(*smin,smlnum);
792 /* Don't check for input errors */
796 /* Standard Initializations */
802 /* 1 x 1 (i.e., scalar) system C X = B */
806 /* Real 1x1 system. */
810 csr = *ca * a[a_dim1 + 1] - *wr * *d1;
813 /* If | C | < SMINI, use C = SMINI */
821 /* Check scaling for X = B / C */
823 bnorm = (r__1 = b[b_dim1 + 1], abs(r__1));
824 if (cnorm < 1.f && bnorm > 1.f) {
825 if (bnorm > bignum * cnorm) {
826 *scale = 1.f / bnorm;
832 x[x_dim1 + 1] = b[b_dim1 + 1] * *scale / csr;
833 *xnorm = (r__1 = x[x_dim1 + 1], abs(r__1));
836 /* Complex 1x1 system (w is complex) */
840 csr = *ca * a[a_dim1 + 1] - *wr * *d1;
842 cnorm = abs(csr) + abs(csi);
844 /* If | C | < SMINI, use C = SMINI */
853 /* Check scaling for X = B / C */
855 bnorm = (r__1 = b[b_dim1 + 1], abs(r__1)) + (r__2 = b[(b_dim1 <<
857 if (cnorm < 1.f && bnorm > 1.f) {
858 if (bnorm > bignum * cnorm) {
859 *scale = 1.f / bnorm;
865 r__1 = *scale * b[b_dim1 + 1];
866 r__2 = *scale * b[(b_dim1 << 1) + 1];
867 sladiv_(&r__1, &r__2, &csr, &csi, &x[x_dim1 + 1], &x[(x_dim1 << 1)
869 *xnorm = (r__1 = x[x_dim1 + 1], abs(r__1)) + (r__2 = x[(x_dim1 <<
877 /* Compute the real part of C = ca A - w D (or ca A**T - w D ) */
879 cr[0] = *ca * a[a_dim1 + 1] - *wr * *d1;
880 cr[3] = *ca * a[(a_dim1 << 1) + 2] - *wr * *d2;
882 cr[2] = *ca * a[a_dim1 + 2];
883 cr[1] = *ca * a[(a_dim1 << 1) + 1];
885 cr[1] = *ca * a[a_dim1 + 2];
886 cr[2] = *ca * a[(a_dim1 << 1) + 1];
891 /* Real 2x2 system (w is real) */
893 /* Find the largest element in C */
898 for (j = 1; j <= 4; ++j) {
899 if ((r__1 = crv[j - 1], abs(r__1)) > cmax) {
900 cmax = (r__1 = crv[j - 1], abs(r__1));
906 /* If norm(C) < SMINI, use SMINI*identity. */
910 r__3 = (r__1 = b[b_dim1 + 1], abs(r__1)), r__4 = (r__2 = b[
911 b_dim1 + 2], abs(r__2));
912 bnorm = f2cmax(r__3,r__4);
913 if (smini < 1.f && bnorm > 1.f) {
914 if (bnorm > bignum * smini) {
915 *scale = 1.f / bnorm;
918 temp = *scale / smini;
919 x[x_dim1 + 1] = temp * b[b_dim1 + 1];
920 x[x_dim1 + 2] = temp * b[b_dim1 + 2];
921 *xnorm = temp * bnorm;
926 /* Gaussian elimination with complete pivoting. */
928 ur11 = crv[icmax - 1];
929 cr21 = crv[ipivot[(icmax << 2) - 3] - 1];
930 ur12 = crv[ipivot[(icmax << 2) - 2] - 1];
931 cr22 = crv[ipivot[(icmax << 2) - 1] - 1];
934 ur22 = cr22 - ur12 * lr21;
936 /* If smaller pivot < SMINI, use SMINI */
938 if (abs(ur22) < smini) {
942 if (rswap[icmax - 1]) {
951 r__2 = (r__1 = br1 * (ur22 * ur11r), abs(r__1)), r__3 = abs(br2);
952 bbnd = f2cmax(r__2,r__3);
953 if (bbnd > 1.f && abs(ur22) < 1.f) {
954 if (bbnd >= bignum * abs(ur22)) {
959 xr2 = br2 * *scale / ur22;
960 xr1 = *scale * br1 * ur11r - xr2 * (ur11r * ur12);
961 if (cswap[icmax - 1]) {
969 r__1 = abs(xr1), r__2 = abs(xr2);
970 *xnorm = f2cmax(r__1,r__2);
972 /* Further scaling if norm(A) norm(X) > overflow */
974 if (*xnorm > 1.f && cmax > 1.f) {
975 if (*xnorm > bignum / cmax) {
976 temp = cmax / bignum;
977 x[x_dim1 + 1] = temp * x[x_dim1 + 1];
978 x[x_dim1 + 2] = temp * x[x_dim1 + 2];
979 *xnorm = temp * *xnorm;
980 *scale = temp * *scale;
985 /* Complex 2x2 system (w is complex) */
987 /* Find the largest element in C */
989 ci[0] = -(*wi) * *d1;
992 ci[3] = -(*wi) * *d2;
996 for (j = 1; j <= 4; ++j) {
997 if ((r__1 = crv[j - 1], abs(r__1)) + (r__2 = civ[j - 1], abs(
999 cmax = (r__1 = crv[j - 1], abs(r__1)) + (r__2 = civ[j - 1]
1006 /* If norm(C) < SMINI, use SMINI*identity. */
1010 r__5 = (r__1 = b[b_dim1 + 1], abs(r__1)) + (r__2 = b[(b_dim1
1011 << 1) + 1], abs(r__2)), r__6 = (r__3 = b[b_dim1 + 2],
1012 abs(r__3)) + (r__4 = b[(b_dim1 << 1) + 2], abs(r__4));
1013 bnorm = f2cmax(r__5,r__6);
1014 if (smini < 1.f && bnorm > 1.f) {
1015 if (bnorm > bignum * smini) {
1016 *scale = 1.f / bnorm;
1019 temp = *scale / smini;
1020 x[x_dim1 + 1] = temp * b[b_dim1 + 1];
1021 x[x_dim1 + 2] = temp * b[b_dim1 + 2];
1022 x[(x_dim1 << 1) + 1] = temp * b[(b_dim1 << 1) + 1];
1023 x[(x_dim1 << 1) + 2] = temp * b[(b_dim1 << 1) + 2];
1024 *xnorm = temp * bnorm;
1029 /* Gaussian elimination with complete pivoting. */
1031 ur11 = crv[icmax - 1];
1032 ui11 = civ[icmax - 1];
1033 cr21 = crv[ipivot[(icmax << 2) - 3] - 1];
1034 ci21 = civ[ipivot[(icmax << 2) - 3] - 1];
1035 ur12 = crv[ipivot[(icmax << 2) - 2] - 1];
1036 ui12 = civ[ipivot[(icmax << 2) - 2] - 1];
1037 cr22 = crv[ipivot[(icmax << 2) - 1] - 1];
1038 ci22 = civ[ipivot[(icmax << 2) - 1] - 1];
1039 if (icmax == 1 || icmax == 4) {
1041 /* Code when off-diagonals of pivoted C are real */
1043 if (abs(ur11) > abs(ui11)) {
1045 /* Computing 2nd power */
1047 ur11r = 1.f / (ur11 * (r__1 * r__1 + 1.f));
1048 ui11r = -temp * ur11r;
1051 /* Computing 2nd power */
1053 ui11r = -1.f / (ui11 * (r__1 * r__1 + 1.f));
1054 ur11r = -temp * ui11r;
1056 lr21 = cr21 * ur11r;
1057 li21 = cr21 * ui11r;
1058 ur12s = ur12 * ur11r;
1059 ui12s = ur12 * ui11r;
1060 ur22 = cr22 - ur12 * lr21;
1061 ui22 = ci22 - ur12 * li21;
1064 /* Code when diagonals of pivoted C are real */
1068 lr21 = cr21 * ur11r;
1069 li21 = ci21 * ur11r;
1070 ur12s = ur12 * ur11r;
1071 ui12s = ui12 * ur11r;
1072 ur22 = cr22 - ur12 * lr21 + ui12 * li21;
1073 ui22 = -ur12 * li21 - ui12 * lr21;
1075 u22abs = abs(ur22) + abs(ui22);
1077 /* If smaller pivot < SMINI, use SMINI */
1079 if (u22abs < smini) {
1084 if (rswap[icmax - 1]) {
1085 br2 = b[b_dim1 + 1];
1086 br1 = b[b_dim1 + 2];
1087 bi2 = b[(b_dim1 << 1) + 1];
1088 bi1 = b[(b_dim1 << 1) + 2];
1090 br1 = b[b_dim1 + 1];
1091 br2 = b[b_dim1 + 2];
1092 bi1 = b[(b_dim1 << 1) + 1];
1093 bi2 = b[(b_dim1 << 1) + 2];
1095 br2 = br2 - lr21 * br1 + li21 * bi1;
1096 bi2 = bi2 - li21 * br1 - lr21 * bi1;
1098 r__1 = (abs(br1) + abs(bi1)) * (u22abs * (abs(ur11r) + abs(ui11r))
1099 ), r__2 = abs(br2) + abs(bi2);
1100 bbnd = f2cmax(r__1,r__2);
1101 if (bbnd > 1.f && u22abs < 1.f) {
1102 if (bbnd >= bignum * u22abs) {
1103 *scale = 1.f / bbnd;
1111 sladiv_(&br2, &bi2, &ur22, &ui22, &xr2, &xi2);
1112 xr1 = ur11r * br1 - ui11r * bi1 - ur12s * xr2 + ui12s * xi2;
1113 xi1 = ui11r * br1 + ur11r * bi1 - ui12s * xr2 - ur12s * xi2;
1114 if (cswap[icmax - 1]) {
1115 x[x_dim1 + 1] = xr2;
1116 x[x_dim1 + 2] = xr1;
1117 x[(x_dim1 << 1) + 1] = xi2;
1118 x[(x_dim1 << 1) + 2] = xi1;
1120 x[x_dim1 + 1] = xr1;
1121 x[x_dim1 + 2] = xr2;
1122 x[(x_dim1 << 1) + 1] = xi1;
1123 x[(x_dim1 << 1) + 2] = xi2;
1126 r__1 = abs(xr1) + abs(xi1), r__2 = abs(xr2) + abs(xi2);
1127 *xnorm = f2cmax(r__1,r__2);
1129 /* Further scaling if norm(A) norm(X) > overflow */
1131 if (*xnorm > 1.f && cmax > 1.f) {
1132 if (*xnorm > bignum / cmax) {
1133 temp = cmax / bignum;
1134 x[x_dim1 + 1] = temp * x[x_dim1 + 1];
1135 x[x_dim1 + 2] = temp * x[x_dim1 + 2];
1136 x[(x_dim1 << 1) + 1] = temp * x[(x_dim1 << 1) + 1];
1137 x[(x_dim1 << 1) + 2] = temp * x[(x_dim1 << 1) + 2];
1138 *xnorm = temp * *xnorm;
1139 *scale = temp * *scale;