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__0 = 0;
516 static real c_b13 = 0.f;
517 static integer c__2 = 2;
518 static integer c__1 = 1;
519 static real c_b36 = 1.f;
521 /* > \brief <b> SGELSX 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 SGELSX + dependencies */
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgelsx.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgelsx.
536 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgelsx.
544 /* SUBROUTINE SGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, */
547 /* INTEGER INFO, LDA, LDB, M, N, NRHS, RANK */
549 /* INTEGER JPVT( * ) */
550 /* REAL A( LDA, * ), B( LDB, * ), WORK( * ) */
553 /* > \par Purpose: */
558 /* > This routine is deprecated and has been replaced by routine SGELSY. */
560 /* > SGELSX computes the minimum-norm solution to a real linear least */
561 /* > squares problem: */
562 /* > minimize || A * X - B || */
563 /* > using a complete orthogonal factorization of A. A is an M-by-N */
564 /* > matrix which may be rank-deficient. */
566 /* > Several right hand side vectors b and solution vectors x can be */
567 /* > handled in a single call; they are stored as the columns of the */
568 /* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
571 /* > The routine first computes a QR factorization with column pivoting: */
572 /* > A * P = Q * [ R11 R12 ] */
574 /* > with R11 defined as the largest leading submatrix whose estimated */
575 /* > condition number is less than 1/RCOND. The order of R11, RANK, */
576 /* > is the effective rank of A. */
578 /* > Then, R22 is considered to be negligible, and R12 is annihilated */
579 /* > by orthogonal transformations from the right, arriving at the */
580 /* > complete orthogonal factorization: */
581 /* > A * P = Q * [ T11 0 ] * Z */
583 /* > The minimum-norm solution is then */
584 /* > X = P * Z**T [ inv(T11)*Q1**T*B ] */
586 /* > where Q1 consists of the first RANK columns of Q. */
595 /* > The number of rows of the matrix A. M >= 0. */
601 /* > The number of columns of the matrix A. N >= 0. */
604 /* > \param[in] NRHS */
606 /* > NRHS is INTEGER */
607 /* > The number of right hand sides, i.e., the number of */
608 /* > columns of matrices B and X. NRHS >= 0. */
611 /* > \param[in,out] A */
613 /* > A is REAL array, dimension (LDA,N) */
614 /* > On entry, the M-by-N matrix A. */
615 /* > On exit, A has been overwritten by details of its */
616 /* > complete orthogonal factorization. */
619 /* > \param[in] LDA */
621 /* > LDA is INTEGER */
622 /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
625 /* > \param[in,out] B */
627 /* > B is REAL array, dimension (LDB,NRHS) */
628 /* > On entry, the M-by-NRHS right hand side matrix B. */
629 /* > On exit, the N-by-NRHS solution matrix X. */
630 /* > If m >= n and RANK = n, the residual sum-of-squares for */
631 /* > the solution in the i-th column is given by the sum of */
632 /* > squares of elements N+1:M in that column. */
635 /* > \param[in] LDB */
637 /* > LDB is INTEGER */
638 /* > The leading dimension of the array B. LDB >= f2cmax(1,M,N). */
641 /* > \param[in,out] JPVT */
643 /* > JPVT is INTEGER array, dimension (N) */
644 /* > On entry, if JPVT(i) .ne. 0, the i-th column of A is an */
645 /* > initial column, otherwise it is a free column. Before */
646 /* > the QR factorization of A, all initial columns are */
647 /* > permuted to the leading positions; only the remaining */
648 /* > free columns are moved as a result of column pivoting */
649 /* > during the factorization. */
650 /* > On exit, if JPVT(i) = k, then the i-th column of A*P */
651 /* > was the k-th column of A. */
654 /* > \param[in] RCOND */
656 /* > RCOND is REAL */
657 /* > RCOND is used to determine the effective rank of A, which */
658 /* > is defined as the order of the largest leading triangular */
659 /* > submatrix R11 in the QR factorization with pivoting of A, */
660 /* > whose estimated condition number < 1/RCOND. */
663 /* > \param[out] RANK */
665 /* > RANK is INTEGER */
666 /* > The effective rank of A, i.e., the order of the submatrix */
667 /* > R11. This is the same as the order of the submatrix T11 */
668 /* > in the complete orthogonal factorization of A. */
671 /* > \param[out] WORK */
673 /* > WORK is REAL array, dimension */
674 /* > (f2cmax( f2cmin(M,N)+3*N, 2*f2cmin(M,N)+NRHS )), */
677 /* > \param[out] INFO */
679 /* > INFO is INTEGER */
680 /* > = 0: successful exit */
681 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
687 /* > \author Univ. of Tennessee */
688 /* > \author Univ. of California Berkeley */
689 /* > \author Univ. of Colorado Denver */
690 /* > \author NAG Ltd. */
692 /* > \date December 2016 */
694 /* > \ingroup realGEsolve */
696 /* ===================================================================== */
697 /* Subroutine */ int sgelsx_(integer *m, integer *n, integer *nrhs, real *a,
698 integer *lda, real *b, integer *ldb, integer *jpvt, real *rcond,
699 integer *rank, real *work, integer *info)
701 /* System generated locals */
702 integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
705 /* Local variables */
706 real anrm, bnrm, smin, smax;
707 integer i__, j, k, iascl, ibscl, ismin, ismax;
708 real c1, c2, s1, s2, t1, t2;
709 extern /* Subroutine */ int strsm_(char *, char *, char *, char *,
710 integer *, integer *, real *, real *, integer *, real *, integer *
711 ), slaic1_(integer *, integer *,
712 real *, real *, real *, real *, real *, real *, real *), sorm2r_(
713 char *, char *, integer *, integer *, integer *, real *, integer *
714 , real *, real *, integer *, real *, integer *),
715 slabad_(real *, real *);
717 extern real slamch_(char *), slange_(char *, integer *, integer *,
718 real *, integer *, real *);
719 extern /* Subroutine */ int xerbla_(char *, integer *);
721 extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
722 real *, integer *, integer *, real *, integer *, integer *), sgeqpf_(integer *, integer *, real *, integer *, integer
723 *, real *, real *, integer *), slaset_(char *, integer *, integer
724 *, real *, real *, real *, integer *);
725 real sminpr, smaxpr, smlnum;
726 extern /* Subroutine */ int slatzm_(char *, integer *, integer *, real *,
727 integer *, real *, real *, real *, integer *, real *),
728 stzrqf_(integer *, integer *, real *, integer *, real *, integer *
732 /* -- LAPACK driver routine (version 3.7.0) -- */
733 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
734 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
738 /* ===================================================================== */
741 /* Parameter adjustments */
743 a_offset = 1 + a_dim1 * 1;
746 b_offset = 1 + b_dim1 * 1;
754 ismax = (mn << 1) + 1;
756 /* Test the input arguments. */
763 } else if (*nrhs < 0) {
765 } else if (*lda < f2cmax(1,*m)) {
767 } else /* if(complicated condition) */ {
770 if (*ldb < f2cmax(i__1,*n)) {
777 xerbla_("SGELSX", &i__1);
781 /* Quick return if possible */
784 i__1 = f2cmin(*m,*n);
785 if (f2cmin(i__1,*nrhs) == 0) {
790 /* Get machine parameters */
792 smlnum = slamch_("S") / slamch_("P");
793 bignum = 1.f / smlnum;
794 slabad_(&smlnum, &bignum);
796 /* Scale A, B if f2cmax elements outside range [SMLNUM,BIGNUM] */
798 anrm = slange_("M", m, n, &a[a_offset], lda, &work[1]);
800 if (anrm > 0.f && anrm < smlnum) {
802 /* Scale matrix norm up to SMLNUM */
804 slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
807 } else if (anrm > bignum) {
809 /* Scale matrix norm down to BIGNUM */
811 slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
814 } else if (anrm == 0.f) {
816 /* Matrix all zero. Return zero solution. */
818 i__1 = f2cmax(*m,*n);
819 slaset_("F", &i__1, nrhs, &c_b13, &c_b13, &b[b_offset], ldb);
824 bnrm = slange_("M", m, nrhs, &b[b_offset], ldb, &work[1]);
826 if (bnrm > 0.f && bnrm < smlnum) {
828 /* Scale matrix norm up to SMLNUM */
830 slascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
833 } else if (bnrm > bignum) {
835 /* Scale matrix norm down to BIGNUM */
837 slascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
842 /* Compute QR factorization with column pivoting of A: */
845 sgeqpf_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn + 1], info);
847 /* workspace 3*N. Details of Householder rotations stored */
850 /* Determine RANK using incremental condition estimation */
854 smax = (r__1 = a[a_dim1 + 1], abs(r__1));
856 if ((r__1 = a[a_dim1 + 1], abs(r__1)) == 0.f) {
858 i__1 = f2cmax(*m,*n);
859 slaset_("F", &i__1, nrhs, &c_b13, &c_b13, &b[b_offset], ldb);
868 slaic1_(&c__2, rank, &work[ismin], &smin, &a[i__ * a_dim1 + 1], &a[
869 i__ + i__ * a_dim1], &sminpr, &s1, &c1);
870 slaic1_(&c__1, rank, &work[ismax], &smax, &a[i__ * a_dim1 + 1], &a[
871 i__ + i__ * a_dim1], &smaxpr, &s2, &c2);
873 if (smaxpr * *rcond <= sminpr) {
875 for (i__ = 1; i__ <= i__1; ++i__) {
876 work[ismin + i__ - 1] = s1 * work[ismin + i__ - 1];
877 work[ismax + i__ - 1] = s2 * work[ismax + i__ - 1];
880 work[ismin + *rank] = c1;
881 work[ismax + *rank] = c2;
889 /* Logically partition R = [ R11 R12 ] */
891 /* where R11 = R(1:RANK,1:RANK) */
893 /* [R11,R12] = [ T11, 0 ] * Y */
896 stzrqf_(rank, n, &a[a_offset], lda, &work[mn + 1], info);
899 /* Details of Householder rotations stored in WORK(MN+1:2*MN) */
901 /* B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS) */
903 sorm2r_("Left", "Transpose", m, nrhs, &mn, &a[a_offset], lda, &work[1], &
904 b[b_offset], ldb, &work[(mn << 1) + 1], info);
908 /* B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */
910 strsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b36, &
911 a[a_offset], lda, &b[b_offset], ldb);
914 for (i__ = *rank + 1; i__ <= i__1; ++i__) {
916 for (j = 1; j <= i__2; ++j) {
917 b[i__ + j * b_dim1] = 0.f;
923 /* B(1:N,1:NRHS) := Y**T * B(1:N,1:NRHS) */
927 for (i__ = 1; i__ <= i__1; ++i__) {
928 i__2 = *n - *rank + 1;
929 slatzm_("Left", &i__2, nrhs, &a[i__ + (*rank + 1) * a_dim1], lda,
930 &work[mn + i__], &b[i__ + b_dim1], &b[*rank + 1 + b_dim1],
931 ldb, &work[(mn << 1) + 1]);
938 /* B(1:N,1:NRHS) := P * B(1:N,1:NRHS) */
941 for (j = 1; j <= i__1; ++j) {
943 for (i__ = 1; i__ <= i__2; ++i__) {
944 work[(mn << 1) + i__] = 1.f;
948 for (i__ = 1; i__ <= i__2; ++i__) {
949 if (work[(mn << 1) + i__] == 1.f) {
950 if (jpvt[i__] != i__) {
952 t1 = b[k + j * b_dim1];
953 t2 = b[jpvt[k] + j * b_dim1];
955 b[jpvt[k] + j * b_dim1] = t1;
956 work[(mn << 1) + k] = 0.f;
959 t2 = b[jpvt[k] + j * b_dim1];
960 if (jpvt[k] != i__) {
963 b[i__ + j * b_dim1] = t1;
964 work[(mn << 1) + k] = 0.f;
975 slascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
977 slascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset],
979 } else if (iascl == 2) {
980 slascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
982 slascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset],
986 slascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
988 } else if (ibscl == 2) {
989 slascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,