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 doublecomplex c_b1 = {0.,0.};
516 static doublecomplex c_b2 = {1.,0.};
517 static integer c__0 = 0;
518 static integer c__2 = 2;
519 static integer c__1 = 1;
521 /* > \brief <b> ZGELSX solves overdetermined or underdetermined systems for GE matrices</b> */
523 /* =========== DOCUMENTATION =========== */
525 /* Online html documentation available at */
526 /* http://www.netlib.org/lapack/explore-html/ */
529 /* > Download ZGELSX + dependencies */
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgelsx.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgelsx.
536 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgelsx.
544 /* SUBROUTINE ZGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, */
545 /* WORK, RWORK, INFO ) */
547 /* INTEGER INFO, LDA, LDB, M, N, NRHS, RANK */
548 /* DOUBLE PRECISION RCOND */
549 /* INTEGER JPVT( * ) */
550 /* DOUBLE PRECISION RWORK( * ) */
551 /* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) */
554 /* > \par Purpose: */
559 /* > This routine is deprecated and has been replaced by routine ZGELSY. */
561 /* > ZGELSX computes the minimum-norm solution to a complex linear least */
562 /* > squares problem: */
563 /* > minimize || A * X - B || */
564 /* > using a complete orthogonal factorization of A. A is an M-by-N */
565 /* > matrix which may be rank-deficient. */
567 /* > Several right hand side vectors b and solution vectors x can be */
568 /* > handled in a single call; they are stored as the columns of the */
569 /* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
572 /* > The routine first computes a QR factorization with column pivoting: */
573 /* > A * P = Q * [ R11 R12 ] */
575 /* > with R11 defined as the largest leading submatrix whose estimated */
576 /* > condition number is less than 1/RCOND. The order of R11, RANK, */
577 /* > is the effective rank of A. */
579 /* > Then, R22 is considered to be negligible, and R12 is annihilated */
580 /* > by unitary transformations from the right, arriving at the */
581 /* > complete orthogonal factorization: */
582 /* > A * P = Q * [ T11 0 ] * Z */
584 /* > The minimum-norm solution is then */
585 /* > X = P * Z**H [ inv(T11)*Q1**H*B ] */
587 /* > where Q1 consists of the first RANK columns of Q. */
596 /* > The number of rows of the matrix A. M >= 0. */
602 /* > The number of columns of the matrix A. N >= 0. */
605 /* > \param[in] NRHS */
607 /* > NRHS is INTEGER */
608 /* > The number of right hand sides, i.e., the number of */
609 /* > columns of matrices B and X. NRHS >= 0. */
612 /* > \param[in,out] A */
614 /* > A is COMPLEX*16 array, dimension (LDA,N) */
615 /* > On entry, the M-by-N matrix A. */
616 /* > On exit, A has been overwritten by details of its */
617 /* > complete orthogonal factorization. */
620 /* > \param[in] LDA */
622 /* > LDA is INTEGER */
623 /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
626 /* > \param[in,out] B */
628 /* > B is COMPLEX*16 array, dimension (LDB,NRHS) */
629 /* > On entry, the M-by-NRHS right hand side matrix B. */
630 /* > On exit, the N-by-NRHS solution matrix X. */
631 /* > If m >= n and RANK = n, the residual sum-of-squares for */
632 /* > the solution in the i-th column is given by the sum of */
633 /* > squares of elements N+1:M in that column. */
636 /* > \param[in] LDB */
638 /* > LDB is INTEGER */
639 /* > The leading dimension of the array B. LDB >= f2cmax(1,M,N). */
642 /* > \param[in,out] JPVT */
644 /* > JPVT is INTEGER array, dimension (N) */
645 /* > On entry, if JPVT(i) .ne. 0, the i-th column of A is an */
646 /* > initial column, otherwise it is a free column. Before */
647 /* > the QR factorization of A, all initial columns are */
648 /* > permuted to the leading positions; only the remaining */
649 /* > free columns are moved as a result of column pivoting */
650 /* > during the factorization. */
651 /* > On exit, if JPVT(i) = k, then the i-th column of A*P */
652 /* > was the k-th column of A. */
655 /* > \param[in] RCOND */
657 /* > RCOND is DOUBLE PRECISION */
658 /* > RCOND is used to determine the effective rank of A, which */
659 /* > is defined as the order of the largest leading triangular */
660 /* > submatrix R11 in the QR factorization with pivoting of A, */
661 /* > whose estimated condition number < 1/RCOND. */
664 /* > \param[out] RANK */
666 /* > RANK is INTEGER */
667 /* > The effective rank of A, i.e., the order of the submatrix */
668 /* > R11. This is the same as the order of the submatrix T11 */
669 /* > in the complete orthogonal factorization of A. */
672 /* > \param[out] WORK */
674 /* > WORK is COMPLEX*16 array, dimension */
675 /* > (f2cmin(M,N) + f2cmax( N, 2*f2cmin(M,N)+NRHS )), */
678 /* > \param[out] RWORK */
680 /* > RWORK is DOUBLE PRECISION array, dimension (2*N) */
683 /* > \param[out] INFO */
685 /* > INFO is INTEGER */
686 /* > = 0: successful exit */
687 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
693 /* > \author Univ. of Tennessee */
694 /* > \author Univ. of California Berkeley */
695 /* > \author Univ. of Colorado Denver */
696 /* > \author NAG Ltd. */
698 /* > \date December 2016 */
700 /* > \ingroup complex16GEsolve */
702 /* ===================================================================== */
703 /* Subroutine */ int zgelsx_(integer *m, integer *n, integer *nrhs,
704 doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb,
705 integer *jpvt, doublereal *rcond, integer *rank, doublecomplex *work,
706 doublereal *rwork, integer *info)
708 /* System generated locals */
709 integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
712 /* Local variables */
713 doublereal anrm, bnrm, smin, smax;
714 integer i__, j, k, iascl, ibscl, ismin, ismax;
715 doublecomplex c1, c2, s1, s2, t1, t2;
716 extern /* Subroutine */ int ztrsm_(char *, char *, char *, char *,
717 integer *, integer *, doublecomplex *, doublecomplex *, integer *,
718 doublecomplex *, integer *),
719 zlaic1_(integer *, integer *, doublecomplex *, doublereal *,
720 doublecomplex *, doublecomplex *, doublereal *, doublecomplex *,
721 doublecomplex *), dlabad_(doublereal *, doublereal *);
722 extern doublereal dlamch_(char *);
724 extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *,
725 integer *, doublecomplex *, integer *, doublecomplex *,
726 doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(char *, integer *);
727 extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
728 integer *, doublereal *);
730 extern /* Subroutine */ int zlascl_(char *, integer *, integer *,
731 doublereal *, doublereal *, integer *, integer *, doublecomplex *,
732 integer *, integer *), zgeqpf_(integer *, integer *,
733 doublecomplex *, integer *, integer *, doublecomplex *,
734 doublecomplex *, doublereal *, integer *), zlaset_(char *,
735 integer *, integer *, doublecomplex *, doublecomplex *,
736 doublecomplex *, integer *);
737 doublereal sminpr, smaxpr, smlnum;
738 extern /* Subroutine */ int zlatzm_(char *, integer *, integer *,
739 doublecomplex *, integer *, doublecomplex *, doublecomplex *,
740 doublecomplex *, integer *, doublecomplex *), ztzrqf_(
741 integer *, integer *, doublecomplex *, integer *, doublecomplex *,
745 /* -- LAPACK driver routine (version 3.7.0) -- */
746 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
747 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
751 /* ===================================================================== */
754 /* Parameter adjustments */
756 a_offset = 1 + a_dim1 * 1;
759 b_offset = 1 + b_dim1 * 1;
768 ismax = (mn << 1) + 1;
770 /* Test the input arguments. */
777 } else if (*nrhs < 0) {
779 } else if (*lda < f2cmax(1,*m)) {
781 } else /* if(complicated condition) */ {
784 if (*ldb < f2cmax(i__1,*n)) {
791 xerbla_("ZGELSX", &i__1);
795 /* Quick return if possible */
798 i__1 = f2cmin(*m,*n);
799 if (f2cmin(i__1,*nrhs) == 0) {
804 /* Get machine parameters */
806 smlnum = dlamch_("S") / dlamch_("P");
807 bignum = 1. / smlnum;
808 dlabad_(&smlnum, &bignum);
810 /* Scale A, B if f2cmax elements outside range [SMLNUM,BIGNUM] */
812 anrm = zlange_("M", m, n, &a[a_offset], lda, &rwork[1]);
814 if (anrm > 0. && anrm < smlnum) {
816 /* Scale matrix norm up to SMLNUM */
818 zlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
821 } else if (anrm > bignum) {
823 /* Scale matrix norm down to BIGNUM */
825 zlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
828 } else if (anrm == 0.) {
830 /* Matrix all zero. Return zero solution. */
832 i__1 = f2cmax(*m,*n);
833 zlaset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
838 bnrm = zlange_("M", m, nrhs, &b[b_offset], ldb, &rwork[1]);
840 if (bnrm > 0. && bnrm < smlnum) {
842 /* Scale matrix norm up to SMLNUM */
844 zlascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
847 } else if (bnrm > bignum) {
849 /* Scale matrix norm down to BIGNUM */
851 zlascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
856 /* Compute QR factorization with column pivoting of A: */
859 zgeqpf_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn + 1], &
862 /* complex workspace MN+N. Real workspace 2*N. Details of Householder */
863 /* rotations stored in WORK(1:MN). */
865 /* Determine RANK using incremental condition estimation */
868 work[i__1].r = 1., work[i__1].i = 0.;
870 work[i__1].r = 1., work[i__1].i = 0.;
871 smax = z_abs(&a[a_dim1 + 1]);
873 if (z_abs(&a[a_dim1 + 1]) == 0.) {
875 i__1 = f2cmax(*m,*n);
876 zlaset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
885 zlaic1_(&c__2, rank, &work[ismin], &smin, &a[i__ * a_dim1 + 1], &a[
886 i__ + i__ * a_dim1], &sminpr, &s1, &c1);
887 zlaic1_(&c__1, rank, &work[ismax], &smax, &a[i__ * a_dim1 + 1], &a[
888 i__ + i__ * a_dim1], &smaxpr, &s2, &c2);
890 if (smaxpr * *rcond <= sminpr) {
892 for (i__ = 1; i__ <= i__1; ++i__) {
893 i__2 = ismin + i__ - 1;
894 i__3 = ismin + i__ - 1;
895 z__1.r = s1.r * work[i__3].r - s1.i * work[i__3].i, z__1.i =
896 s1.r * work[i__3].i + s1.i * work[i__3].r;
897 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
898 i__2 = ismax + i__ - 1;
899 i__3 = ismax + i__ - 1;
900 z__1.r = s2.r * work[i__3].r - s2.i * work[i__3].i, z__1.i =
901 s2.r * work[i__3].i + s2.i * work[i__3].r;
902 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
905 i__1 = ismin + *rank;
906 work[i__1].r = c1.r, work[i__1].i = c1.i;
907 i__1 = ismax + *rank;
908 work[i__1].r = c2.r, work[i__1].i = c2.i;
916 /* Logically partition R = [ R11 R12 ] */
918 /* where R11 = R(1:RANK,1:RANK) */
920 /* [R11,R12] = [ T11, 0 ] * Y */
923 ztzrqf_(rank, n, &a[a_offset], lda, &work[mn + 1], info);
926 /* Details of Householder rotations stored in WORK(MN+1:2*MN) */
928 /* B(1:M,1:NRHS) := Q**H * B(1:M,1:NRHS) */
930 zunm2r_("Left", "Conjugate transpose", m, nrhs, &mn, &a[a_offset], lda, &
931 work[1], &b[b_offset], ldb, &work[(mn << 1) + 1], info);
935 /* B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */
937 ztrsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b2, &a[
938 a_offset], lda, &b[b_offset], ldb);
941 for (i__ = *rank + 1; i__ <= i__1; ++i__) {
943 for (j = 1; j <= i__2; ++j) {
944 i__3 = i__ + j * b_dim1;
945 b[i__3].r = 0., b[i__3].i = 0.;
951 /* B(1:N,1:NRHS) := Y**H * B(1:N,1:NRHS) */
955 for (i__ = 1; i__ <= i__1; ++i__) {
956 i__2 = *n - *rank + 1;
957 d_cnjg(&z__1, &work[mn + i__]);
958 zlatzm_("Left", &i__2, nrhs, &a[i__ + (*rank + 1) * a_dim1], lda,
959 &z__1, &b[i__ + b_dim1], &b[*rank + 1 + b_dim1], ldb, &
960 work[(mn << 1) + 1]);
967 /* B(1:N,1:NRHS) := P * B(1:N,1:NRHS) */
970 for (j = 1; j <= i__1; ++j) {
972 for (i__ = 1; i__ <= i__2; ++i__) {
973 i__3 = (mn << 1) + i__;
974 work[i__3].r = 1., work[i__3].i = 0.;
978 for (i__ = 1; i__ <= i__2; ++i__) {
979 i__3 = (mn << 1) + i__;
980 if (work[i__3].r == 1. && work[i__3].i == 0.) {
981 if (jpvt[i__] != i__) {
983 i__3 = k + j * b_dim1;
984 t1.r = b[i__3].r, t1.i = b[i__3].i;
985 i__3 = jpvt[k] + j * b_dim1;
986 t2.r = b[i__3].r, t2.i = b[i__3].i;
988 i__3 = jpvt[k] + j * b_dim1;
989 b[i__3].r = t1.r, b[i__3].i = t1.i;
990 i__3 = (mn << 1) + k;
991 work[i__3].r = 0., work[i__3].i = 0.;
992 t1.r = t2.r, t1.i = t2.i;
994 i__3 = jpvt[k] + j * b_dim1;
995 t2.r = b[i__3].r, t2.i = b[i__3].i;
996 if (jpvt[k] != i__) {
999 i__3 = i__ + j * b_dim1;
1000 b[i__3].r = t1.r, b[i__3].i = t1.i;
1001 i__3 = (mn << 1) + k;
1002 work[i__3].r = 0., work[i__3].i = 0.;
1013 zlascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
1015 zlascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset],
1017 } else if (iascl == 2) {
1018 zlascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
1020 zlascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset],
1024 zlascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
1026 } else if (ibscl == 2) {
1027 zlascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,