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__4 = 4;
516 static integer c__1 = 1;
517 static integer c__16 = 16;
518 static integer c__0 = 0;
520 /* > \brief \b SLASY2 solves the Sylvester matrix equation where the matrices are of order 1 or 2. */
522 /* =========== DOCUMENTATION =========== */
524 /* Online html documentation available at */
525 /* http://www.netlib.org/lapack/explore-html/ */
528 /* > Download SLASY2 + dependencies */
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasy2.
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasy2.
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasy2.
543 /* SUBROUTINE SLASY2( LTRANL, LTRANR, ISGN, N1, N2, TL, LDTL, TR, */
544 /* LDTR, B, LDB, SCALE, X, LDX, XNORM, INFO ) */
546 /* LOGICAL LTRANL, LTRANR */
547 /* INTEGER INFO, ISGN, LDB, LDTL, LDTR, LDX, N1, N2 */
548 /* REAL SCALE, XNORM */
549 /* REAL B( LDB, * ), TL( LDTL, * ), TR( LDTR, * ), */
553 /* > \par Purpose: */
558 /* > SLASY2 solves for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in */
560 /* > op(TL)*X + ISGN*X*op(TR) = SCALE*B, */
562 /* > where TL is N1 by N1, TR is N2 by N2, B is N1 by N2, and ISGN = 1 or */
563 /* > -1. op(T) = T or T**T, where T**T denotes the transpose of T. */
569 /* > \param[in] LTRANL */
571 /* > LTRANL is LOGICAL */
572 /* > On entry, LTRANL specifies the op(TL): */
573 /* > = .FALSE., op(TL) = TL, */
574 /* > = .TRUE., op(TL) = TL**T. */
577 /* > \param[in] LTRANR */
579 /* > LTRANR is LOGICAL */
580 /* > On entry, LTRANR specifies the op(TR): */
581 /* > = .FALSE., op(TR) = TR, */
582 /* > = .TRUE., op(TR) = TR**T. */
585 /* > \param[in] ISGN */
587 /* > ISGN is INTEGER */
588 /* > On entry, ISGN specifies the sign of the equation */
589 /* > as described before. ISGN may only be 1 or -1. */
592 /* > \param[in] N1 */
594 /* > N1 is INTEGER */
595 /* > On entry, N1 specifies the order of matrix TL. */
596 /* > N1 may only be 0, 1 or 2. */
599 /* > \param[in] N2 */
601 /* > N2 is INTEGER */
602 /* > On entry, N2 specifies the order of matrix TR. */
603 /* > N2 may only be 0, 1 or 2. */
606 /* > \param[in] TL */
608 /* > TL is REAL array, dimension (LDTL,2) */
609 /* > On entry, TL contains an N1 by N1 matrix. */
612 /* > \param[in] LDTL */
614 /* > LDTL is INTEGER */
615 /* > The leading dimension of the matrix TL. LDTL >= f2cmax(1,N1). */
618 /* > \param[in] TR */
620 /* > TR is REAL array, dimension (LDTR,2) */
621 /* > On entry, TR contains an N2 by N2 matrix. */
624 /* > \param[in] LDTR */
626 /* > LDTR is INTEGER */
627 /* > The leading dimension of the matrix TR. LDTR >= f2cmax(1,N2). */
632 /* > B is REAL array, dimension (LDB,2) */
633 /* > On entry, the N1 by N2 matrix B contains the right-hand */
634 /* > side of the equation. */
637 /* > \param[in] LDB */
639 /* > LDB is INTEGER */
640 /* > The leading dimension of the matrix B. LDB >= f2cmax(1,N1). */
643 /* > \param[out] SCALE */
645 /* > SCALE is REAL */
646 /* > On exit, SCALE contains the scale factor. SCALE is chosen */
647 /* > less than or equal to 1 to prevent the solution overflowing. */
650 /* > \param[out] X */
652 /* > X is REAL array, dimension (LDX,2) */
653 /* > On exit, X contains the N1 by N2 solution. */
656 /* > \param[in] LDX */
658 /* > LDX is INTEGER */
659 /* > The leading dimension of the matrix X. LDX >= f2cmax(1,N1). */
662 /* > \param[out] XNORM */
664 /* > XNORM is REAL */
665 /* > On exit, XNORM is the infinity-norm of the solution. */
668 /* > \param[out] INFO */
670 /* > INFO is INTEGER */
671 /* > On exit, INFO is set to */
672 /* > 0: successful exit. */
673 /* > 1: TL and TR have too close eigenvalues, so TL or */
674 /* > TR is perturbed to get a nonsingular equation. */
675 /* > NOTE: In the interests of speed, this routine does not */
676 /* > check the inputs for errors. */
682 /* > \author Univ. of Tennessee */
683 /* > \author Univ. of California Berkeley */
684 /* > \author Univ. of Colorado Denver */
685 /* > \author NAG Ltd. */
687 /* > \date June 2016 */
689 /* > \ingroup realSYauxiliary */
691 /* ===================================================================== */
692 /* Subroutine */ int slasy2_(logical *ltranl, logical *ltranr, integer *isgn,
693 integer *n1, integer *n2, real *tl, integer *ldtl, real *tr, integer *
694 ldtr, real *b, integer *ldb, real *scale, real *x, integer *ldx, real
695 *xnorm, integer *info)
697 /* Initialized data */
699 static integer locu12[4] = { 3,4,1,2 };
700 static integer locl21[4] = { 2,1,4,3 };
701 static integer locu22[4] = { 4,3,2,1 };
702 static logical xswpiv[4] = { FALSE_,FALSE_,TRUE_,TRUE_ };
703 static logical bswpiv[4] = { FALSE_,TRUE_,FALSE_,TRUE_ };
705 /* System generated locals */
706 integer b_dim1, b_offset, tl_dim1, tl_offset, tr_dim1, tr_offset, x_dim1,
708 real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8;
710 /* Local variables */
716 integer ipsv, jpsv, i__, j, k;
718 extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
719 integer *), sswap_(integer *, real *, integer *, real *, integer *
722 real x2[2], l21, u11, u12;
724 real u22, t16[16] /* was [4][4] */;
725 extern real slamch_(char *);
726 extern integer isamax_(integer *, real *, integer *);
727 real smlnum, gam, bet, eps, sgn, tmp[4], tau1;
730 /* -- LAPACK auxiliary routine (version 3.7.0) -- */
731 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
732 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
736 /* ===================================================================== */
738 /* Parameter adjustments */
740 tl_offset = 1 + tl_dim1 * 1;
743 tr_offset = 1 + tr_dim1 * 1;
746 b_offset = 1 + b_dim1 * 1;
749 x_offset = 1 + x_dim1 * 1;
754 /* Do not check the input parameters for errors */
758 /* Quick return if possible */
760 if (*n1 == 0 || *n2 == 0) {
764 /* Set constants to control overflow */
767 smlnum = slamch_("S") / eps;
768 sgn = (real) (*isgn);
770 k = *n1 + *n1 + *n2 - 2;
778 /* 1 by 1: TL11*X + SGN*X*TR11 = B11 */
781 tau1 = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
790 gam = (r__1 = b[b_dim1 + 1], abs(r__1));
791 if (smlnum * gam > bet) {
795 x[x_dim1 + 1] = b[b_dim1 + 1] * *scale / tau1;
796 *xnorm = (r__1 = x[x_dim1 + 1], abs(r__1));
800 /* TL11*[X11 X12] + ISGN*[X11 X12]*op[TR11 TR12] = [B11 B12] */
807 r__7 = (r__1 = tl[tl_dim1 + 1], abs(r__1)), r__8 = (r__2 = tr[tr_dim1 + 1]
808 , abs(r__2)), r__7 = f2cmax(r__7,r__8), r__8 = (r__3 = tr[(tr_dim1 <<
809 1) + 1], abs(r__3)), r__7 = f2cmax(r__7,r__8), r__8 = (r__4 = tr[
810 tr_dim1 + 2], abs(r__4)), r__7 = f2cmax(r__7,r__8), r__8 = (r__5 =
811 tr[(tr_dim1 << 1) + 2], abs(r__5));
812 r__6 = eps * f2cmax(r__7,r__8);
813 smin = f2cmax(r__6,smlnum);
814 tmp[0] = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
815 tmp[3] = tl[tl_dim1 + 1] + sgn * tr[(tr_dim1 << 1) + 2];
817 tmp[1] = sgn * tr[tr_dim1 + 2];
818 tmp[2] = sgn * tr[(tr_dim1 << 1) + 1];
820 tmp[1] = sgn * tr[(tr_dim1 << 1) + 1];
821 tmp[2] = sgn * tr[tr_dim1 + 2];
823 btmp[0] = b[b_dim1 + 1];
824 btmp[1] = b[(b_dim1 << 1) + 1];
828 /* op[TL11 TL12]*[X11] + ISGN* [X11]*TR11 = [B11] */
829 /* [TL21 TL22] [X21] [X21] [B21] */
834 r__7 = (r__1 = tr[tr_dim1 + 1], abs(r__1)), r__8 = (r__2 = tl[tl_dim1 + 1]
835 , abs(r__2)), r__7 = f2cmax(r__7,r__8), r__8 = (r__3 = tl[(tl_dim1 <<
836 1) + 1], abs(r__3)), r__7 = f2cmax(r__7,r__8), r__8 = (r__4 = tl[
837 tl_dim1 + 2], abs(r__4)), r__7 = f2cmax(r__7,r__8), r__8 = (r__5 =
838 tl[(tl_dim1 << 1) + 2], abs(r__5));
839 r__6 = eps * f2cmax(r__7,r__8);
840 smin = f2cmax(r__6,smlnum);
841 tmp[0] = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
842 tmp[3] = tl[(tl_dim1 << 1) + 2] + sgn * tr[tr_dim1 + 1];
844 tmp[1] = tl[(tl_dim1 << 1) + 1];
845 tmp[2] = tl[tl_dim1 + 2];
847 tmp[1] = tl[tl_dim1 + 2];
848 tmp[2] = tl[(tl_dim1 << 1) + 1];
850 btmp[0] = b[b_dim1 + 1];
851 btmp[1] = b[b_dim1 + 2];
854 /* Solve 2 by 2 system using complete pivoting. */
855 /* Set pivots less than SMIN to SMIN. */
857 ipiv = isamax_(&c__4, tmp, &c__1);
859 if (abs(u11) <= smin) {
863 u12 = tmp[locu12[ipiv - 1] - 1];
864 l21 = tmp[locl21[ipiv - 1] - 1] / u11;
865 u22 = tmp[locu22[ipiv - 1] - 1] - u12 * l21;
866 xswap = xswpiv[ipiv - 1];
867 bswap = bswpiv[ipiv - 1];
868 if (abs(u22) <= smin) {
874 btmp[1] = btmp[0] - l21 * temp;
877 btmp[1] -= l21 * btmp[0];
880 if (smlnum * 2.f * abs(btmp[1]) > abs(u22) || smlnum * 2.f * abs(btmp[0])
883 r__1 = abs(btmp[0]), r__2 = abs(btmp[1]);
884 *scale = .5f / f2cmax(r__1,r__2);
888 x2[1] = btmp[1] / u22;
889 x2[0] = btmp[0] / u11 - u12 / u11 * x2[1];
895 x[x_dim1 + 1] = x2[0];
897 x[(x_dim1 << 1) + 1] = x2[1];
898 *xnorm = (r__1 = x[x_dim1 + 1], abs(r__1)) + (r__2 = x[(x_dim1 << 1)
901 x[x_dim1 + 2] = x2[1];
903 r__3 = (r__1 = x[x_dim1 + 1], abs(r__1)), r__4 = (r__2 = x[x_dim1 + 2]
905 *xnorm = f2cmax(r__3,r__4);
910 /* op[TL11 TL12]*[X11 X12] +ISGN* [X11 X12]*op[TR11 TR12] = [B11 B12] */
911 /* [TL21 TL22] [X21 X22] [X21 X22] [TR21 TR22] [B21 B22] */
913 /* Solve equivalent 4 by 4 system using complete pivoting. */
914 /* Set pivots less than SMIN to SMIN. */
918 r__5 = (r__1 = tr[tr_dim1 + 1], abs(r__1)), r__6 = (r__2 = tr[(tr_dim1 <<
919 1) + 1], abs(r__2)), r__5 = f2cmax(r__5,r__6), r__6 = (r__3 = tr[
920 tr_dim1 + 2], abs(r__3)), r__5 = f2cmax(r__5,r__6), r__6 = (r__4 =
921 tr[(tr_dim1 << 1) + 2], abs(r__4));
922 smin = f2cmax(r__5,r__6);
924 r__5 = smin, r__6 = (r__1 = tl[tl_dim1 + 1], abs(r__1)), r__5 = f2cmax(r__5,
925 r__6), r__6 = (r__2 = tl[(tl_dim1 << 1) + 1], abs(r__2)), r__5 =
926 f2cmax(r__5,r__6), r__6 = (r__3 = tl[tl_dim1 + 2], abs(r__3)), r__5 =
927 f2cmax(r__5,r__6), r__6 = (r__4 = tl[(tl_dim1 << 1) + 2], abs(r__4))
929 smin = f2cmax(r__5,r__6);
932 smin = f2cmax(r__1,smlnum);
934 scopy_(&c__16, btmp, &c__0, t16, &c__1);
935 t16[0] = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
936 t16[5] = tl[(tl_dim1 << 1) + 2] + sgn * tr[tr_dim1 + 1];
937 t16[10] = tl[tl_dim1 + 1] + sgn * tr[(tr_dim1 << 1) + 2];
938 t16[15] = tl[(tl_dim1 << 1) + 2] + sgn * tr[(tr_dim1 << 1) + 2];
940 t16[4] = tl[tl_dim1 + 2];
941 t16[1] = tl[(tl_dim1 << 1) + 1];
942 t16[14] = tl[tl_dim1 + 2];
943 t16[11] = tl[(tl_dim1 << 1) + 1];
945 t16[4] = tl[(tl_dim1 << 1) + 1];
946 t16[1] = tl[tl_dim1 + 2];
947 t16[14] = tl[(tl_dim1 << 1) + 1];
948 t16[11] = tl[tl_dim1 + 2];
951 t16[8] = sgn * tr[(tr_dim1 << 1) + 1];
952 t16[13] = sgn * tr[(tr_dim1 << 1) + 1];
953 t16[2] = sgn * tr[tr_dim1 + 2];
954 t16[7] = sgn * tr[tr_dim1 + 2];
956 t16[8] = sgn * tr[tr_dim1 + 2];
957 t16[13] = sgn * tr[tr_dim1 + 2];
958 t16[2] = sgn * tr[(tr_dim1 << 1) + 1];
959 t16[7] = sgn * tr[(tr_dim1 << 1) + 1];
961 btmp[0] = b[b_dim1 + 1];
962 btmp[1] = b[b_dim1 + 2];
963 btmp[2] = b[(b_dim1 << 1) + 1];
964 btmp[3] = b[(b_dim1 << 1) + 2];
966 /* Perform elimination */
968 for (i__ = 1; i__ <= 3; ++i__) {
970 for (ip = i__; ip <= 4; ++ip) {
971 for (jp = i__; jp <= 4; ++jp) {
972 if ((r__1 = t16[ip + (jp << 2) - 5], abs(r__1)) >= xmax) {
973 xmax = (r__1 = t16[ip + (jp << 2) - 5], abs(r__1));
982 sswap_(&c__4, &t16[ipsv - 1], &c__4, &t16[i__ - 1], &c__4);
983 temp = btmp[i__ - 1];
984 btmp[i__ - 1] = btmp[ipsv - 1];
985 btmp[ipsv - 1] = temp;
988 sswap_(&c__4, &t16[(jpsv << 2) - 4], &c__1, &t16[(i__ << 2) - 4],
991 jpiv[i__ - 1] = jpsv;
992 if ((r__1 = t16[i__ + (i__ << 2) - 5], abs(r__1)) < smin) {
994 t16[i__ + (i__ << 2) - 5] = smin;
996 for (j = i__ + 1; j <= 4; ++j) {
997 t16[j + (i__ << 2) - 5] /= t16[i__ + (i__ << 2) - 5];
998 btmp[j - 1] -= t16[j + (i__ << 2) - 5] * btmp[i__ - 1];
999 for (k = i__ + 1; k <= 4; ++k) {
1000 t16[j + (k << 2) - 5] -= t16[j + (i__ << 2) - 5] * t16[i__ + (
1008 if (abs(t16[15]) < smin) {
1013 if (smlnum * 8.f * abs(btmp[0]) > abs(t16[0]) || smlnum * 8.f * abs(btmp[
1014 1]) > abs(t16[5]) || smlnum * 8.f * abs(btmp[2]) > abs(t16[10]) ||
1015 smlnum * 8.f * abs(btmp[3]) > abs(t16[15])) {
1017 r__1 = abs(btmp[0]), r__2 = abs(btmp[1]), r__1 = f2cmax(r__1,r__2), r__2
1018 = abs(btmp[2]), r__1 = f2cmax(r__1,r__2), r__2 = abs(btmp[3]);
1019 *scale = .125f / f2cmax(r__1,r__2);
1025 for (i__ = 1; i__ <= 4; ++i__) {
1027 temp = 1.f / t16[k + (k << 2) - 5];
1028 tmp[k - 1] = btmp[k - 1] * temp;
1029 for (j = k + 1; j <= 4; ++j) {
1030 tmp[k - 1] -= temp * t16[k + (j << 2) - 5] * tmp[j - 1];
1035 for (i__ = 1; i__ <= 3; ++i__) {
1036 if (jpiv[4 - i__ - 1] != 4 - i__) {
1037 temp = tmp[4 - i__ - 1];
1038 tmp[4 - i__ - 1] = tmp[jpiv[4 - i__ - 1] - 1];
1039 tmp[jpiv[4 - i__ - 1] - 1] = temp;
1043 x[x_dim1 + 1] = tmp[0];
1044 x[x_dim1 + 2] = tmp[1];
1045 x[(x_dim1 << 1) + 1] = tmp[2];
1046 x[(x_dim1 << 1) + 2] = tmp[3];
1048 r__1 = abs(tmp[0]) + abs(tmp[2]), r__2 = abs(tmp[1]) + abs(tmp[3]);
1049 *xnorm = f2cmax(r__1,r__2);