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 complex c_b1 = {0.f,0.f};
516 static integer c__2 = 2;
517 static integer c_n1 = -1;
518 static integer c__5 = 5;
519 static integer c__1 = 1;
520 static complex c_b44 = {-1.f,0.f};
521 static complex c_b45 = {1.f,0.f};
523 /* > \brief \b CTGSYL */
525 /* =========== DOCUMENTATION =========== */
527 /* Online html documentation available at */
528 /* http://www.netlib.org/lapack/explore-html/ */
531 /* > Download CTGSYL + dependencies */
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctgsyl.
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctgsyl.
538 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctgsyl.
546 /* SUBROUTINE CTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, */
547 /* LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK, */
550 /* CHARACTER TRANS */
551 /* INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF, */
553 /* REAL DIF, SCALE */
554 /* INTEGER IWORK( * ) */
555 /* COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * ), */
556 /* $ D( LDD, * ), E( LDE, * ), F( LDF, * ), */
560 /* > \par Purpose: */
565 /* > CTGSYL solves the generalized Sylvester equation: */
567 /* > A * R - L * B = scale * C (1) */
568 /* > D * R - L * E = scale * F */
570 /* > where R and L are unknown m-by-n matrices, (A, D), (B, E) and */
571 /* > (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n, */
572 /* > respectively, with complex entries. A, B, D and E are upper */
573 /* > triangular (i.e., (A,D) and (B,E) in generalized Schur form). */
575 /* > The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 */
576 /* > is an output scaling factor chosen to avoid overflow. */
578 /* > In matrix notation (1) is equivalent to solve Zx = scale*b, where Z */
579 /* > is defined as */
581 /* > Z = [ kron(In, A) -kron(B**H, Im) ] (2) */
582 /* > [ kron(In, D) -kron(E**H, Im) ], */
584 /* > Here Ix is the identity matrix of size x and X**H is the conjugate */
585 /* > transpose of X. Kron(X, Y) is the Kronecker product between the */
586 /* > matrices X and Y. */
588 /* > If TRANS = 'C', y in the conjugate transposed system Z**H *y = scale*b */
589 /* > is solved for, which is equivalent to solve for R and L in */
591 /* > A**H * R + D**H * L = scale * C (3) */
592 /* > R * B**H + L * E**H = scale * -F */
594 /* > This case (TRANS = 'C') is used to compute an one-norm-based estimate */
595 /* > of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D) */
596 /* > and (B,E), using CLACON. */
598 /* > If IJOB >= 1, CTGSYL computes a Frobenius norm-based estimate of */
599 /* > Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the */
600 /* > reciprocal of the smallest singular value of Z. */
602 /* > This is a level-3 BLAS algorithm. */
608 /* > \param[in] TRANS */
610 /* > TRANS is CHARACTER*1 */
611 /* > = 'N': solve the generalized sylvester equation (1). */
612 /* > = 'C': solve the "conjugate transposed" system (3). */
615 /* > \param[in] IJOB */
617 /* > IJOB is INTEGER */
618 /* > Specifies what kind of functionality to be performed. */
619 /* > =0: solve (1) only. */
620 /* > =1: The functionality of 0 and 3. */
621 /* > =2: The functionality of 0 and 4. */
622 /* > =3: Only an estimate of Dif[(A,D), (B,E)] is computed. */
623 /* > (look ahead strategy is used). */
624 /* > =4: Only an estimate of Dif[(A,D), (B,E)] is computed. */
625 /* > (CGECON on sub-systems is used). */
626 /* > Not referenced if TRANS = 'C'. */
632 /* > The order of the matrices A and D, and the row dimension of */
633 /* > the matrices C, F, R and L. */
639 /* > The order of the matrices B and E, and the column dimension */
640 /* > of the matrices C, F, R and L. */
645 /* > A is COMPLEX array, dimension (LDA, M) */
646 /* > The upper triangular matrix A. */
649 /* > \param[in] LDA */
651 /* > LDA is INTEGER */
652 /* > The leading dimension of the array A. LDA >= f2cmax(1, M). */
657 /* > B is COMPLEX array, dimension (LDB, N) */
658 /* > The upper triangular matrix B. */
661 /* > \param[in] LDB */
663 /* > LDB is INTEGER */
664 /* > The leading dimension of the array B. LDB >= f2cmax(1, N). */
667 /* > \param[in,out] C */
669 /* > C is COMPLEX array, dimension (LDC, N) */
670 /* > On entry, C contains the right-hand-side of the first matrix */
671 /* > equation in (1) or (3). */
672 /* > On exit, if IJOB = 0, 1 or 2, C has been overwritten by */
673 /* > the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R, */
674 /* > the solution achieved during the computation of the */
675 /* > Dif-estimate. */
678 /* > \param[in] LDC */
680 /* > LDC is INTEGER */
681 /* > The leading dimension of the array C. LDC >= f2cmax(1, M). */
686 /* > D is COMPLEX array, dimension (LDD, M) */
687 /* > The upper triangular matrix D. */
690 /* > \param[in] LDD */
692 /* > LDD is INTEGER */
693 /* > The leading dimension of the array D. LDD >= f2cmax(1, M). */
698 /* > E is COMPLEX array, dimension (LDE, N) */
699 /* > The upper triangular matrix E. */
702 /* > \param[in] LDE */
704 /* > LDE is INTEGER */
705 /* > The leading dimension of the array E. LDE >= f2cmax(1, N). */
708 /* > \param[in,out] F */
710 /* > F is COMPLEX array, dimension (LDF, N) */
711 /* > On entry, F contains the right-hand-side of the second matrix */
712 /* > equation in (1) or (3). */
713 /* > On exit, if IJOB = 0, 1 or 2, F has been overwritten by */
714 /* > the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L, */
715 /* > the solution achieved during the computation of the */
716 /* > Dif-estimate. */
719 /* > \param[in] LDF */
721 /* > LDF is INTEGER */
722 /* > The leading dimension of the array F. LDF >= f2cmax(1, M). */
725 /* > \param[out] DIF */
728 /* > On exit DIF is the reciprocal of a lower bound of the */
729 /* > reciprocal of the Dif-function, i.e. DIF is an upper bound of */
730 /* > Dif[(A,D), (B,E)] = sigma-f2cmin(Z), where Z as in (2). */
731 /* > IF IJOB = 0 or TRANS = 'C', DIF is not referenced. */
734 /* > \param[out] SCALE */
736 /* > SCALE is REAL */
737 /* > On exit SCALE is the scaling factor in (1) or (3). */
738 /* > If 0 < SCALE < 1, C and F hold the solutions R and L, resp., */
739 /* > to a slightly perturbed system but the input matrices A, B, */
740 /* > D and E have not been changed. If SCALE = 0, R and L will */
741 /* > hold the solutions to the homogenious system with C = F = 0. */
744 /* > \param[out] WORK */
746 /* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
747 /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
750 /* > \param[in] LWORK */
752 /* > LWORK is INTEGER */
753 /* > The dimension of the array WORK. LWORK > = 1. */
754 /* > If IJOB = 1 or 2 and TRANS = 'N', LWORK >= f2cmax(1,2*M*N). */
756 /* > If LWORK = -1, then a workspace query is assumed; the routine */
757 /* > only calculates the optimal size of the WORK array, returns */
758 /* > this value as the first entry of the WORK array, and no error */
759 /* > message related to LWORK is issued by XERBLA. */
762 /* > \param[out] IWORK */
764 /* > IWORK is INTEGER array, dimension (M+N+2) */
767 /* > \param[out] INFO */
769 /* > INFO is INTEGER */
770 /* > =0: successful exit */
771 /* > <0: If INFO = -i, the i-th argument had an illegal value. */
772 /* > >0: (A, D) and (B, E) have common or very close */
779 /* > \author Univ. of Tennessee */
780 /* > \author Univ. of California Berkeley */
781 /* > \author Univ. of Colorado Denver */
782 /* > \author NAG Ltd. */
784 /* > \date December 2016 */
786 /* > \ingroup complexSYcomputational */
788 /* > \par Contributors: */
789 /* ================== */
791 /* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
792 /* > Umea University, S-901 87 Umea, Sweden. */
794 /* > \par References: */
795 /* ================ */
797 /* > [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */
798 /* > for Solving the Generalized Sylvester Equation and Estimating the */
799 /* > Separation between Regular Matrix Pairs, Report UMINF - 93.23, */
800 /* > Department of Computing Science, Umea University, S-901 87 Umea, */
801 /* > Sweden, December 1993, Revised April 1994, Also as LAPACK Working */
802 /* > Note 75. To appear in ACM Trans. on Math. Software, Vol 22, */
805 /* > [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester */
806 /* > Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal. */
807 /* > Appl., 15(4):1045-1060, 1994. */
809 /* > [3] B. Kagstrom and L. Westin, Generalized Schur Methods with */
810 /* > Condition Estimators for Solving the Generalized Sylvester */
811 /* > Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, */
812 /* > July 1989, pp 745-751. */
814 /* ===================================================================== */
815 /* Subroutine */ int ctgsyl_(char *trans, integer *ijob, integer *m, integer *
816 n, complex *a, integer *lda, complex *b, integer *ldb, complex *c__,
817 integer *ldc, complex *d__, integer *ldd, complex *e, integer *lde,
818 complex *f, integer *ldf, real *scale, real *dif, complex *work,
819 integer *lwork, integer *iwork, integer *info)
821 /* System generated locals */
822 integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, d_dim1,
823 d_offset, e_dim1, e_offset, f_dim1, f_offset, i__1, i__2, i__3,
827 /* Local variables */
829 integer i__, j, k, p, q;
830 extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
831 integer *), cgemm_(char *, char *, integer *, integer *, integer *
832 , complex *, complex *, integer *, complex *, integer *, complex *
833 , complex *, integer *);
834 extern logical lsame_(char *, char *);
835 integer ifunc, linfo, lwmin;
837 extern /* Subroutine */ int ctgsy2_(char *, integer *, integer *, integer
838 *, complex *, integer *, complex *, integer *, complex *, integer
839 *, complex *, integer *, complex *, integer *, complex *, integer
840 *, real *, real *, real *, integer *);
841 integer ie, je, mb, nb;
845 extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
846 *, integer *, complex *, integer *), claset_(char *,
847 integer *, integer *, complex *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen);
848 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
849 integer *, integer *, ftnlen, ftnlen);
856 /* -- LAPACK computational routine (version 3.7.0) -- */
857 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
858 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
862 /* ===================================================================== */
863 /* Replaced various illegal calls to CCOPY by calls to CLASET. */
864 /* Sven Hammarling, 1/5/02. */
867 /* Decode and test input parameters */
869 /* Parameter adjustments */
871 a_offset = 1 + a_dim1 * 1;
874 b_offset = 1 + b_dim1 * 1;
877 c_offset = 1 + c_dim1 * 1;
880 d_offset = 1 + d_dim1 * 1;
883 e_offset = 1 + e_dim1 * 1;
886 f_offset = 1 + f_dim1 * 1;
893 notran = lsame_(trans, "N");
894 lquery = *lwork == -1;
896 if (! notran && ! lsame_(trans, "C")) {
899 if (*ijob < 0 || *ijob > 4) {
906 } else if (*n <= 0) {
908 } else if (*lda < f2cmax(1,*m)) {
910 } else if (*ldb < f2cmax(1,*n)) {
912 } else if (*ldc < f2cmax(1,*m)) {
914 } else if (*ldd < f2cmax(1,*m)) {
916 } else if (*lde < f2cmax(1,*n)) {
918 } else if (*ldf < f2cmax(1,*m)) {
925 if (*ijob == 1 || *ijob == 2) {
927 i__1 = 1, i__2 = (*m << 1) * *n;
928 lwmin = f2cmax(i__1,i__2);
935 work[1].r = (real) lwmin, work[1].i = 0.f;
937 if (*lwork < lwmin && ! lquery) {
944 xerbla_("CTGSYL", &i__1, (ftnlen)6);
950 /* Quick return if possible */
952 if (*m == 0 || *n == 0) {
962 /* Determine optimal block sizes MB and NB */
964 mb = ilaenv_(&c__2, "CTGSYL", trans, m, n, &c_n1, &c_n1, (ftnlen)6, (
966 nb = ilaenv_(&c__5, "CTGSYL", trans, m, n, &c_n1, &c_n1, (ftnlen)6, (
974 claset_("F", m, n, &c_b1, &c_b1, &c__[c_offset], ldc);
975 claset_("F", m, n, &c_b1, &c_b1, &f[f_offset], ldf);
976 } else if (*ijob >= 1 && notran) {
981 if (mb <= 1 && nb <= 1 || mb >= *m && nb >= *n) {
983 /* Use unblocked Level 2 solver */
986 for (iround = 1; iround <= i__1; ++iround) {
992 ctgsy2_(trans, &ifunc, m, n, &a[a_offset], lda, &b[b_offset], ldb,
993 &c__[c_offset], ldc, &d__[d_offset], ldd, &e[e_offset],
994 lde, &f[f_offset], ldf, scale, &dsum, &dscale, info);
996 if (*ijob == 1 || *ijob == 3) {
997 *dif = sqrt((real) ((*m << 1) * *n)) / (dscale * sqrt(
1000 *dif = sqrt((real) pq) / (dscale * sqrt(dsum));
1003 if (isolve == 2 && iround == 1) {
1008 clacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m);
1009 clacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m);
1010 claset_("F", m, n, &c_b1, &c_b1, &c__[c_offset], ldc);
1011 claset_("F", m, n, &c_b1, &c_b1, &f[f_offset], ldf)
1013 } else if (isolve == 2 && iround == 2) {
1014 clacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc);
1015 clacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf);
1025 /* Determine block structure of A */
1041 iwork[p + 1] = *m + 1;
1042 if (iwork[p] == iwork[p + 1]) {
1046 /* Determine block structure of B */
1064 iwork[q + 1] = *n + 1;
1065 if (iwork[q] == iwork[q + 1]) {
1071 for (iround = 1; iround <= i__1; ++iround) {
1073 /* Solve (I, J) - subsystem */
1074 /* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J) */
1075 /* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J) */
1076 /* for I = P, P - 1, ..., 1; J = 1, 2, ..., Q */
1083 for (j = p + 2; j <= i__2; ++j) {
1085 je = iwork[j + 1] - 1;
1087 for (i__ = p; i__ >= 1; --i__) {
1089 ie = iwork[i__ + 1] - 1;
1091 ctgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1],
1092 lda, &b[js + js * b_dim1], ldb, &c__[is + js *
1093 c_dim1], ldc, &d__[is + is * d_dim1], ldd, &e[js
1094 + js * e_dim1], lde, &f[is + js * f_dim1], ldf, &
1095 scaloc, &dsum, &dscale, &linfo);
1100 if (scaloc != 1.f) {
1102 for (k = 1; k <= i__3; ++k) {
1103 q__1.r = scaloc, q__1.i = 0.f;
1104 cscal_(m, &q__1, &c__[k * c_dim1 + 1], &c__1);
1105 q__1.r = scaloc, q__1.i = 0.f;
1106 cscal_(m, &q__1, &f[k * f_dim1 + 1], &c__1);
1110 for (k = js; k <= i__3; ++k) {
1112 q__1.r = scaloc, q__1.i = 0.f;
1113 cscal_(&i__4, &q__1, &c__[k * c_dim1 + 1], &c__1);
1115 q__1.r = scaloc, q__1.i = 0.f;
1116 cscal_(&i__4, &q__1, &f[k * f_dim1 + 1], &c__1);
1120 for (k = js; k <= i__3; ++k) {
1122 q__1.r = scaloc, q__1.i = 0.f;
1123 cscal_(&i__4, &q__1, &c__[ie + 1 + k * c_dim1], &
1126 q__1.r = scaloc, q__1.i = 0.f;
1127 cscal_(&i__4, &q__1, &f[ie + 1 + k * f_dim1], &
1132 for (k = je + 1; k <= i__3; ++k) {
1133 q__1.r = scaloc, q__1.i = 0.f;
1134 cscal_(m, &q__1, &c__[k * c_dim1 + 1], &c__1);
1135 q__1.r = scaloc, q__1.i = 0.f;
1136 cscal_(m, &q__1, &f[k * f_dim1 + 1], &c__1);
1142 /* Substitute R(I,J) and L(I,J) into remaining equation. */
1146 cgemm_("N", "N", &i__3, &nb, &mb, &c_b44, &a[is *
1147 a_dim1 + 1], lda, &c__[is + js * c_dim1], ldc,
1148 &c_b45, &c__[js * c_dim1 + 1], ldc);
1150 cgemm_("N", "N", &i__3, &nb, &mb, &c_b44, &d__[is *
1151 d_dim1 + 1], ldd, &c__[is + js * c_dim1], ldc,
1152 &c_b45, &f[js * f_dim1 + 1], ldf);
1156 cgemm_("N", "N", &mb, &i__3, &nb, &c_b45, &f[is + js *
1157 f_dim1], ldf, &b[js + (je + 1) * b_dim1],
1158 ldb, &c_b45, &c__[is + (je + 1) * c_dim1],
1161 cgemm_("N", "N", &mb, &i__3, &nb, &c_b45, &f[is + js *
1162 f_dim1], ldf, &e[js + (je + 1) * e_dim1],
1163 lde, &c_b45, &f[is + (je + 1) * f_dim1], ldf);
1169 if (dscale != 0.f) {
1170 if (*ijob == 1 || *ijob == 3) {
1171 *dif = sqrt((real) ((*m << 1) * *n)) / (dscale * sqrt(
1174 *dif = sqrt((real) pq) / (dscale * sqrt(dsum));
1177 if (isolve == 2 && iround == 1) {
1182 clacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m);
1183 clacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m);
1184 claset_("F", m, n, &c_b1, &c_b1, &c__[c_offset], ldc);
1185 claset_("F", m, n, &c_b1, &c_b1, &f[f_offset], ldf)
1187 } else if (isolve == 2 && iround == 2) {
1188 clacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc);
1189 clacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf);
1196 /* Solve transposed (I, J)-subsystem */
1197 /* A(I, I)**H * R(I, J) + D(I, I)**H * L(I, J) = C(I, J) */
1198 /* R(I, J) * B(J, J) + L(I, J) * E(J, J) = -F(I, J) */
1199 /* for I = 1,2,..., P; J = Q, Q-1,..., 1 */
1203 for (i__ = 1; i__ <= i__1; ++i__) {
1205 ie = iwork[i__ + 1] - 1;
1208 for (j = q; j >= i__2; --j) {
1210 je = iwork[j + 1] - 1;
1212 ctgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1], lda, &
1213 b[js + js * b_dim1], ldb, &c__[is + js * c_dim1], ldc,
1214 &d__[is + is * d_dim1], ldd, &e[js + js * e_dim1],
1215 lde, &f[is + js * f_dim1], ldf, &scaloc, &dsum, &
1220 if (scaloc != 1.f) {
1222 for (k = 1; k <= i__3; ++k) {
1223 q__1.r = scaloc, q__1.i = 0.f;
1224 cscal_(m, &q__1, &c__[k * c_dim1 + 1], &c__1);
1225 q__1.r = scaloc, q__1.i = 0.f;
1226 cscal_(m, &q__1, &f[k * f_dim1 + 1], &c__1);
1230 for (k = js; k <= i__3; ++k) {
1232 q__1.r = scaloc, q__1.i = 0.f;
1233 cscal_(&i__4, &q__1, &c__[k * c_dim1 + 1], &c__1);
1235 q__1.r = scaloc, q__1.i = 0.f;
1236 cscal_(&i__4, &q__1, &f[k * f_dim1 + 1], &c__1);
1240 for (k = js; k <= i__3; ++k) {
1242 q__1.r = scaloc, q__1.i = 0.f;
1243 cscal_(&i__4, &q__1, &c__[ie + 1 + k * c_dim1], &c__1)
1246 q__1.r = scaloc, q__1.i = 0.f;
1247 cscal_(&i__4, &q__1, &f[ie + 1 + k * f_dim1], &c__1);
1251 for (k = je + 1; k <= i__3; ++k) {
1252 q__1.r = scaloc, q__1.i = 0.f;
1253 cscal_(m, &q__1, &c__[k * c_dim1 + 1], &c__1);
1254 q__1.r = scaloc, q__1.i = 0.f;
1255 cscal_(m, &q__1, &f[k * f_dim1 + 1], &c__1);
1261 /* Substitute R(I,J) and L(I,J) into remaining equation. */
1265 cgemm_("N", "C", &mb, &i__3, &nb, &c_b45, &c__[is + js *
1266 c_dim1], ldc, &b[js * b_dim1 + 1], ldb, &c_b45, &
1267 f[is + f_dim1], ldf);
1269 cgemm_("N", "C", &mb, &i__3, &nb, &c_b45, &f[is + js *
1270 f_dim1], ldf, &e[js * e_dim1 + 1], lde, &c_b45, &
1271 f[is + f_dim1], ldf);
1275 cgemm_("C", "N", &i__3, &nb, &mb, &c_b44, &a[is + (ie + 1)
1276 * a_dim1], lda, &c__[is + js * c_dim1], ldc, &
1277 c_b45, &c__[ie + 1 + js * c_dim1], ldc);
1279 cgemm_("C", "N", &i__3, &nb, &mb, &c_b44, &d__[is + (ie +
1280 1) * d_dim1], ldd, &f[is + js * f_dim1], ldf, &
1281 c_b45, &c__[ie + 1 + js * c_dim1], ldc);
1289 work[1].r = (real) lwmin, work[1].i = 0.f;