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_n1 = -1;
516 static integer c_n2 = -2;
517 static doublereal c_b23 = 0.;
518 static integer c__0 = 0;
520 /* > \brief \b DGETSLS */
525 /* SUBROUTINE DGETSLS( TRANS, M, N, NRHS, A, LDA, B, LDB, */
526 /* $ WORK, LWORK, INFO ) */
528 /* CHARACTER TRANS */
529 /* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS */
530 /* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ) */
533 /* > \par Purpose: */
538 /* > DGETSLS solves overdetermined or underdetermined real linear systems */
539 /* > involving an M-by-N matrix A, using a tall skinny QR or short wide LQ */
540 /* > factorization of A. It is assumed that A has full rank. */
544 /* > The following options are provided: */
546 /* > 1. If TRANS = 'N' and m >= n: find the least squares solution of */
547 /* > an overdetermined system, i.e., solve the least squares problem */
548 /* > minimize || B - A*X ||. */
550 /* > 2. If TRANS = 'N' and m < n: find the minimum norm solution of */
551 /* > an underdetermined system A * X = B. */
553 /* > 3. If TRANS = 'T' and m >= n: find the minimum norm solution of */
554 /* > an undetermined system A**T * X = B. */
556 /* > 4. If TRANS = 'T' and m < n: find the least squares solution of */
557 /* > an overdetermined system, i.e., solve the least squares problem */
558 /* > minimize || B - A**T * X ||. */
560 /* > Several right hand side vectors b and solution vectors x can be */
561 /* > handled in a single call; they are stored as the columns of the */
562 /* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
569 /* > \param[in] TRANS */
571 /* > TRANS is CHARACTER*1 */
572 /* > = 'N': the linear system involves A; */
573 /* > = 'T': the linear system involves A**T. */
579 /* > The number of rows of the matrix A. M >= 0. */
585 /* > The number of columns of the matrix A. N >= 0. */
588 /* > \param[in] NRHS */
590 /* > NRHS is INTEGER */
591 /* > The number of right hand sides, i.e., the number of */
592 /* > columns of the matrices B and X. NRHS >=0. */
595 /* > \param[in,out] A */
597 /* > A is DOUBLE PRECISION array, dimension (LDA,N) */
598 /* > On entry, the M-by-N matrix A. */
600 /* > A is overwritten by details of its QR or LQ */
601 /* > factorization as returned by DGEQR or DGELQ. */
604 /* > \param[in] LDA */
606 /* > LDA is INTEGER */
607 /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
610 /* > \param[in,out] B */
612 /* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */
613 /* > On entry, the matrix B of right hand side vectors, stored */
614 /* > columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS */
615 /* > if TRANS = 'T'. */
616 /* > On exit, if INFO = 0, B is overwritten by the solution */
617 /* > vectors, stored columnwise: */
618 /* > if TRANS = 'N' and m >= n, rows 1 to n of B contain the least */
619 /* > squares solution vectors. */
620 /* > if TRANS = 'N' and m < n, rows 1 to N of B contain the */
621 /* > minimum norm solution vectors; */
622 /* > if TRANS = 'T' and m >= n, rows 1 to M of B contain the */
623 /* > minimum norm solution vectors; */
624 /* > if TRANS = 'T' and m < n, rows 1 to M of B contain the */
625 /* > least squares solution vectors. */
628 /* > \param[in] LDB */
630 /* > LDB is INTEGER */
631 /* > The leading dimension of the array B. LDB >= MAX(1,M,N). */
634 /* > \param[out] WORK */
636 /* > (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
637 /* > On exit, if INFO = 0, WORK(1) contains optimal (or either minimal */
638 /* > or optimal, if query was assumed) LWORK. */
639 /* > See LWORK for details. */
642 /* > \param[in] LWORK */
644 /* > LWORK is INTEGER */
645 /* > The dimension of the array WORK. */
646 /* > If LWORK = -1 or -2, then a workspace query is assumed. */
647 /* > If LWORK = -1, the routine calculates optimal size of WORK for the */
648 /* > optimal performance and returns this value in WORK(1). */
649 /* > If LWORK = -2, the routine calculates minimal size of WORK and */
650 /* > returns this value in WORK(1). */
653 /* > \param[out] INFO */
655 /* > INFO is INTEGER */
656 /* > = 0: successful exit */
657 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
658 /* > > 0: if INFO = i, the i-th diagonal element of the */
659 /* > triangular factor of A is zero, so that A does not have */
660 /* > full rank; the least squares solution could not be */
667 /* > \author Univ. of Tennessee */
668 /* > \author Univ. of California Berkeley */
669 /* > \author Univ. of Colorado Denver */
670 /* > \author NAG Ltd. */
672 /* > \date June 2017 */
674 /* > \ingroup doubleGEsolve */
676 /* ===================================================================== */
677 /* Subroutine */ int dgetsls_(char *trans, integer *m, integer *n, integer *
678 nrhs, doublereal *a, integer *lda, doublereal *b, integer *ldb,
679 doublereal *work, integer *lwork, integer *info)
681 /* System generated locals */
682 integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
684 /* Local variables */
685 doublereal anrm, bnrm;
687 integer brow, tszm, tszo, info2, i__, j, iascl, ibscl;
688 extern /* Subroutine */ int dgelq_(integer *, integer *, doublereal *,
689 integer *, doublereal *, integer *, doublereal *, integer *,
691 extern logical lsame_(char *, char *);
692 extern /* Subroutine */ int dgeqr_(integer *, integer *, doublereal *,
693 integer *, doublereal *, integer *, doublereal *, integer *,
695 integer minmn, maxmn;
697 extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
698 extern doublereal dlamch_(char *), dlange_(char *, integer *,
699 integer *, doublereal *, integer *, doublereal *);
700 extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
701 doublereal *, doublereal *, integer *, integer *, doublereal *,
702 integer *, integer *);
704 extern /* Subroutine */ int dgemlq_(char *, char *, integer *, integer *,
705 integer *, doublereal *, integer *, doublereal *, integer *,
706 doublereal *, integer *, doublereal *, integer *, integer *), dlaset_(char *, integer *, integer *, doublereal
707 *, doublereal *, doublereal *, integer *), xerbla_(char *,
708 integer *, ftnlen), dgemqr_(char *, char *, integer *, integer *,
709 integer *, doublereal *, integer *, doublereal *, integer *,
710 doublereal *, integer *, doublereal *, integer *, integer *);
712 doublereal bignum, smlnum;
713 integer wsizem, wsizeo;
715 extern /* Subroutine */ int dtrtrs_(char *, char *, char *, integer *,
716 integer *, doublereal *, integer *, doublereal *, integer *,
718 integer lw1, lw2, mnk, lwm, lwo;
721 /* -- LAPACK driver routine (version 3.7.1) -- */
722 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
723 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
728 /* ===================================================================== */
731 /* Test the input arguments. */
733 /* Parameter adjustments */
735 a_offset = 1 + a_dim1 * 1;
738 b_offset = 1 + b_dim1 * 1;
744 minmn = f2cmin(*m,*n);
745 maxmn = f2cmax(*m,*n);
746 mnk = f2cmax(minmn,*nrhs);
747 tran = lsame_(trans, "T");
749 lquery = *lwork == -1 || *lwork == -2;
750 if (! (lsame_(trans, "N") || lsame_(trans, "T"))) {
756 } else if (*nrhs < 0) {
758 } else if (*lda < f2cmax(1,*m)) {
760 } else /* if(complicated condition) */ {
763 if (*ldb < f2cmax(i__1,*n)) {
770 /* Determine the block size and minimum LWORK */
773 dgeqr_(m, n, &a[a_offset], lda, tq, &c_n1, workq, &c_n1, &info2);
774 tszo = (integer) tq[0];
775 lwo = (integer) workq[0];
776 dgemqr_("L", trans, m, nrhs, n, &a[a_offset], lda, tq, &tszo, &b[
777 b_offset], ldb, workq, &c_n1, &info2);
779 i__1 = lwo, i__2 = (integer) workq[0];
780 lwo = f2cmax(i__1,i__2);
781 dgeqr_(m, n, &a[a_offset], lda, tq, &c_n2, workq, &c_n2, &info2);
782 tszm = (integer) tq[0];
783 lwm = (integer) workq[0];
784 dgemqr_("L", trans, m, nrhs, n, &a[a_offset], lda, tq, &tszm, &b[
785 b_offset], ldb, workq, &c_n1, &info2);
787 i__1 = lwm, i__2 = (integer) workq[0];
788 lwm = f2cmax(i__1,i__2);
792 dgelq_(m, n, &a[a_offset], lda, tq, &c_n1, workq, &c_n1, &info2);
793 tszo = (integer) tq[0];
794 lwo = (integer) workq[0];
795 dgemlq_("L", trans, n, nrhs, m, &a[a_offset], lda, tq, &tszo, &b[
796 b_offset], ldb, workq, &c_n1, &info2);
798 i__1 = lwo, i__2 = (integer) workq[0];
799 lwo = f2cmax(i__1,i__2);
800 dgelq_(m, n, &a[a_offset], lda, tq, &c_n2, workq, &c_n2, &info2);
801 tszm = (integer) tq[0];
802 lwm = (integer) workq[0];
803 dgemlq_("L", trans, n, nrhs, m, &a[a_offset], lda, tq, &tszm, &b[
804 b_offset], ldb, workq, &c_n1, &info2);
806 i__1 = lwm, i__2 = (integer) workq[0];
807 lwm = f2cmax(i__1,i__2);
812 if (*lwork < wsizem && ! lquery) {
820 xerbla_("DGETSLS", &i__1, (ftnlen)7);
821 work[1] = (doublereal) wsizeo;
826 work[1] = (real) wsizeo;
829 work[1] = (real) wsizem;
833 if (*lwork < wsizeo) {
841 /* Quick return if possible */
844 i__1 = f2cmin(*m,*n);
845 if (f2cmin(i__1,*nrhs) == 0) {
846 i__1 = f2cmax(*m,*n);
847 dlaset_("FULL", &i__1, nrhs, &c_b23, &c_b23, &b[b_offset], ldb);
851 /* Get machine parameters */
853 smlnum = dlamch_("S") / dlamch_("P");
854 bignum = 1. / smlnum;
855 dlabad_(&smlnum, &bignum);
857 /* Scale A, B if f2cmax element outside range [SMLNUM,BIGNUM] */
859 anrm = dlange_("M", m, n, &a[a_offset], lda, &work[1]);
861 if (anrm > 0. && anrm < smlnum) {
863 /* Scale matrix norm up to SMLNUM */
865 dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
868 } else if (anrm > bignum) {
870 /* Scale matrix norm down to BIGNUM */
872 dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
875 } else if (anrm == 0.) {
877 /* Matrix all zero. Return zero solution. */
879 dlaset_("F", &maxmn, nrhs, &c_b23, &c_b23, &b[b_offset], ldb);
887 bnrm = dlange_("M", &brow, nrhs, &b[b_offset], ldb, &work[1]);
889 if (bnrm > 0. && bnrm < smlnum) {
891 /* Scale matrix norm up to SMLNUM */
893 dlascl_("G", &c__0, &c__0, &bnrm, &smlnum, &brow, nrhs, &b[b_offset],
896 } else if (bnrm > bignum) {
898 /* Scale matrix norm down to BIGNUM */
900 dlascl_("G", &c__0, &c__0, &bnrm, &bignum, &brow, nrhs, &b[b_offset],
907 /* compute QR factorization of A */
909 dgeqr_(m, n, &a[a_offset], lda, &work[lw2 + 1], &lw1, &work[1], &lw2,
913 /* Least-Squares Problem f2cmin || A * X - B || */
915 /* B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS) */
917 dgemqr_("L", "T", m, nrhs, n, &a[a_offset], lda, &work[lw2 + 1], &
918 lw1, &b[b_offset], ldb, &work[1], &lw2, info);
920 /* B(1:N,1:NRHS) := inv(R) * B(1:N,1:NRHS) */
922 dtrtrs_("U", "N", "N", n, nrhs, &a[a_offset], lda, &b[b_offset],
930 /* Overdetermined system of equations A**T * X = B */
932 /* B(1:N,1:NRHS) := inv(R**T) * B(1:N,1:NRHS) */
934 dtrtrs_("U", "T", "N", n, nrhs, &a[a_offset], lda, &b[b_offset],
941 /* B(N+1:M,1:NRHS) = ZERO */
944 for (j = 1; j <= i__1; ++j) {
946 for (i__ = *n + 1; i__ <= i__2; ++i__) {
947 b[i__ + j * b_dim1] = 0.;
953 /* B(1:M,1:NRHS) := Q(1:N,:) * B(1:N,1:NRHS) */
955 dgemqr_("L", "N", m, nrhs, n, &a[a_offset], lda, &work[lw2 + 1], &
956 lw1, &b[b_offset], ldb, &work[1], &lw2, info);
964 /* Compute LQ factorization of A */
966 dgelq_(m, n, &a[a_offset], lda, &work[lw2 + 1], &lw1, &work[1], &lw2,
969 /* workspace at least M, optimally M*NB. */
973 /* underdetermined system of equations A * X = B */
975 /* B(1:M,1:NRHS) := inv(L) * B(1:M,1:NRHS) */
977 dtrtrs_("L", "N", "N", m, nrhs, &a[a_offset], lda, &b[b_offset],
984 /* B(M+1:N,1:NRHS) = 0 */
987 for (j = 1; j <= i__1; ++j) {
989 for (i__ = *m + 1; i__ <= i__2; ++i__) {
990 b[i__ + j * b_dim1] = 0.;
996 /* B(1:N,1:NRHS) := Q(1:N,:)**T * B(1:M,1:NRHS) */
998 dgemlq_("L", "T", n, nrhs, m, &a[a_offset], lda, &work[lw2 + 1], &
999 lw1, &b[b_offset], ldb, &work[1], &lw2, info);
1001 /* workspace at least NRHS, optimally NRHS*NB */
1007 /* overdetermined system f2cmin || A**T * X - B || */
1009 /* B(1:N,1:NRHS) := Q * B(1:N,1:NRHS) */
1011 dgemlq_("L", "N", n, nrhs, m, &a[a_offset], lda, &work[lw2 + 1], &
1012 lw1, &b[b_offset], ldb, &work[1], &lw2, info);
1014 /* workspace at least NRHS, optimally NRHS*NB */
1016 /* B(1:M,1:NRHS) := inv(L**T) * B(1:M,1:NRHS) */
1018 dtrtrs_("Lower", "Transpose", "Non-unit", m, nrhs, &a[a_offset],
1019 lda, &b[b_offset], ldb, info);
1034 dlascl_("G", &c__0, &c__0, &anrm, &smlnum, &scllen, nrhs, &b[b_offset]
1036 } else if (iascl == 2) {
1037 dlascl_("G", &c__0, &c__0, &anrm, &bignum, &scllen, nrhs, &b[b_offset]
1041 dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, &scllen, nrhs, &b[b_offset]
1043 } else if (ibscl == 2) {
1044 dlascl_("G", &c__0, &c__0, &bignum, &bnrm, &scllen, nrhs, &b[b_offset]
1049 work[1] = (doublereal) (tszo + lwo);
1052 /* End of DGETSLS */