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__1 = 1;
516 static integer c_n1 = -1;
517 static doublereal c_b32 = -1.;
518 static doublereal c_b34 = 1.;
520 /* > \brief \b DGGGLM */
522 /* =========== DOCUMENTATION =========== */
524 /* Online html documentation available at */
525 /* http://www.netlib.org/lapack/explore-html/ */
528 /* > Download DGGGLM + dependencies */
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dggglm.
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dggglm.
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dggglm.
543 /* SUBROUTINE DGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK, */
546 /* INTEGER INFO, LDA, LDB, LWORK, M, N, P */
547 /* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), D( * ), WORK( * ), */
548 /* $ X( * ), Y( * ) */
551 /* > \par Purpose: */
556 /* > DGGGLM solves a general Gauss-Markov linear model (GLM) problem: */
558 /* > minimize || y ||_2 subject to d = A*x + B*y */
561 /* > where A is an N-by-M matrix, B is an N-by-P matrix, and d is a */
562 /* > given N-vector. It is assumed that M <= N <= M+P, and */
564 /* > rank(A) = M and rank( A B ) = N. */
566 /* > Under these assumptions, the constrained equation is always */
567 /* > consistent, and there is a unique solution x and a minimal 2-norm */
568 /* > solution y, which is obtained using a generalized QR factorization */
569 /* > of the matrices (A, B) given by */
571 /* > A = Q*(R), B = Q*T*Z. */
574 /* > In particular, if matrix B is square nonsingular, then the problem */
575 /* > GLM is equivalent to the following weighted linear least squares */
578 /* > minimize || inv(B)*(d-A*x) ||_2 */
581 /* > where inv(B) denotes the inverse of B. */
590 /* > The number of rows of the matrices A and B. N >= 0. */
596 /* > The number of columns of the matrix A. 0 <= M <= N. */
602 /* > The number of columns of the matrix B. P >= N-M. */
605 /* > \param[in,out] A */
607 /* > A is DOUBLE PRECISION array, dimension (LDA,M) */
608 /* > On entry, the N-by-M matrix A. */
609 /* > On exit, the upper triangular part of the array A contains */
610 /* > the M-by-M upper triangular matrix R. */
613 /* > \param[in] LDA */
615 /* > LDA is INTEGER */
616 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
619 /* > \param[in,out] B */
621 /* > B is DOUBLE PRECISION array, dimension (LDB,P) */
622 /* > On entry, the N-by-P matrix B. */
623 /* > On exit, if N <= P, the upper triangle of the subarray */
624 /* > B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T; */
625 /* > if N > P, the elements on and above the (N-P)th subdiagonal */
626 /* > contain the N-by-P upper trapezoidal matrix T. */
629 /* > \param[in] LDB */
631 /* > LDB is INTEGER */
632 /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
635 /* > \param[in,out] D */
637 /* > D is DOUBLE PRECISION array, dimension (N) */
638 /* > On entry, D is the left hand side of the GLM equation. */
639 /* > On exit, D is destroyed. */
642 /* > \param[out] X */
644 /* > X is DOUBLE PRECISION array, dimension (M) */
647 /* > \param[out] Y */
649 /* > Y is DOUBLE PRECISION array, dimension (P) */
651 /* > On exit, X and Y are the solutions of the GLM problem. */
654 /* > \param[out] WORK */
656 /* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
657 /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
660 /* > \param[in] LWORK */
662 /* > LWORK is INTEGER */
663 /* > The dimension of the array WORK. LWORK >= f2cmax(1,N+M+P). */
664 /* > For optimum performance, LWORK >= M+f2cmin(N,P)+f2cmax(N,P)*NB, */
665 /* > where NB is an upper bound for the optimal blocksizes for */
666 /* > DGEQRF, SGERQF, DORMQR and SORMRQ. */
668 /* > If LWORK = -1, then a workspace query is assumed; the routine */
669 /* > only calculates the optimal size of the WORK array, returns */
670 /* > this value as the first entry of the WORK array, and no error */
671 /* > message related to LWORK is issued by XERBLA. */
674 /* > \param[out] INFO */
676 /* > INFO is INTEGER */
677 /* > = 0: successful exit. */
678 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
679 /* > = 1: the upper triangular factor R associated with A in the */
680 /* > generalized QR factorization of the pair (A, B) is */
681 /* > singular, so that rank(A) < M; the least squares */
682 /* > solution could not be computed. */
683 /* > = 2: the bottom (N-M) by (N-M) part of the upper trapezoidal */
684 /* > factor T associated with B in the generalized QR */
685 /* > factorization of the pair (A, B) is singular, so that */
686 /* > rank( A B ) < N; the least squares solution could not */
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 doubleOTHEReigen */
702 /* ===================================================================== */
703 /* Subroutine */ int dggglm_(integer *n, integer *m, integer *p, doublereal *
704 a, integer *lda, doublereal *b, integer *ldb, doublereal *d__,
705 doublereal *x, doublereal *y, doublereal *work, integer *lwork,
708 /* System generated locals */
709 integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
711 /* Local variables */
713 extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
714 doublereal *, doublereal *, integer *, doublereal *, integer *,
715 doublereal *, doublereal *, integer *), dcopy_(integer *,
716 doublereal *, integer *, doublereal *, integer *);
718 extern /* Subroutine */ int dggqrf_(integer *, integer *, integer *,
719 doublereal *, integer *, doublereal *, doublereal *, integer *,
720 doublereal *, doublereal *, integer *, integer *), xerbla_(char *,
722 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
723 integer *, integer *, ftnlen, ftnlen);
724 integer lwkmin, nb1, nb2, nb3, nb4;
725 extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *,
726 integer *, doublereal *, integer *, doublereal *, doublereal *,
727 integer *, doublereal *, integer *, integer *),
728 dormrq_(char *, char *, integer *, integer *, integer *,
729 doublereal *, integer *, doublereal *, doublereal *, integer *,
730 doublereal *, integer *, integer *);
733 extern /* Subroutine */ int dtrtrs_(char *, char *, char *, integer *,
734 integer *, doublereal *, integer *, doublereal *, integer *,
738 /* -- LAPACK driver routine (version 3.7.0) -- */
739 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
740 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
744 /* =================================================================== */
747 /* Test the input parameters */
749 /* Parameter adjustments */
751 a_offset = 1 + a_dim1 * 1;
754 b_offset = 1 + b_dim1 * 1;
764 lquery = *lwork == -1;
767 } else if (*m < 0 || *m > *n) {
769 } else if (*p < 0 || *p < *n - *m) {
771 } else if (*lda < f2cmax(1,*n)) {
773 } else if (*ldb < f2cmax(1,*n)) {
777 /* Calculate workspace */
784 nb1 = ilaenv_(&c__1, "DGEQRF", " ", n, m, &c_n1, &c_n1, (ftnlen)6,
786 nb2 = ilaenv_(&c__1, "DGERQF", " ", n, m, &c_n1, &c_n1, (ftnlen)6,
788 nb3 = ilaenv_(&c__1, "DORMQR", " ", n, m, p, &c_n1, (ftnlen)6, (
790 nb4 = ilaenv_(&c__1, "DORMRQ", " ", n, m, p, &c_n1, (ftnlen)6, (
793 i__1 = f2cmax(nb1,nb2), i__1 = f2cmax(i__1,nb3);
794 nb = f2cmax(i__1,nb4);
795 lwkmin = *m + *n + *p;
796 lwkopt = *m + np + f2cmax(*n,*p) * nb;
798 work[1] = (doublereal) lwkopt;
800 if (*lwork < lwkmin && ! lquery) {
807 xerbla_("DGGGLM", &i__1, (ftnlen)6);
813 /* Quick return if possible */
817 for (i__ = 1; i__ <= i__1; ++i__) {
821 for (i__ = 1; i__ <= i__1; ++i__) {
827 /* Compute the GQR factorization of matrices A and B: */
829 /* Q**T*A = ( R11 ) M, Q**T*B*Z**T = ( T11 T12 ) M */
830 /* ( 0 ) N-M ( 0 T22 ) N-M */
833 /* where R11 and T22 are upper triangular, and Q and Z are */
836 i__1 = *lwork - *m - np;
837 dggqrf_(n, m, p, &a[a_offset], lda, &work[1], &b[b_offset], ldb, &work[*m
838 + 1], &work[*m + np + 1], &i__1, info);
839 lopt = (integer) work[*m + np + 1];
841 /* Update left-hand-side vector d = Q**T*d = ( d1 ) M */
845 i__2 = *lwork - *m - np;
846 dormqr_("Left", "Transpose", n, &c__1, m, &a[a_offset], lda, &work[1], &
847 d__[1], &i__1, &work[*m + np + 1], &i__2, info);
849 i__1 = lopt, i__2 = (integer) work[*m + np + 1];
850 lopt = f2cmax(i__1,i__2);
852 /* Solve T22*y2 = d2 for y2 */
857 dtrtrs_("Upper", "No transpose", "Non unit", &i__1, &c__1, &b[*m + 1
858 + (*m + *p - *n + 1) * b_dim1], ldb, &d__[*m + 1], &i__2,
867 dcopy_(&i__1, &d__[*m + 1], &c__1, &y[*m + *p - *n + 1], &c__1);
873 for (i__ = 1; i__ <= i__1; ++i__) {
878 /* Update d1 = d1 - T12*y2 */
881 dgemv_("No transpose", m, &i__1, &c_b32, &b[(*m + *p - *n + 1) * b_dim1 +
882 1], ldb, &y[*m + *p - *n + 1], &c__1, &c_b34, &d__[1], &c__1);
884 /* Solve triangular system: R11*x = d1 */
887 dtrtrs_("Upper", "No Transpose", "Non unit", m, &c__1, &a[a_offset],
888 lda, &d__[1], m, info);
897 dcopy_(m, &d__[1], &c__1, &x[1], &c__1);
900 /* Backward transformation y = Z**T *y */
903 i__1 = 1, i__2 = *n - *p + 1;
905 i__4 = *lwork - *m - np;
906 dormrq_("Left", "Transpose", p, &c__1, &np, &b[f2cmax(i__1,i__2) + b_dim1],
907 ldb, &work[*m + 1], &y[1], &i__3, &work[*m + np + 1], &i__4, info);
909 i__1 = lopt, i__2 = (integer) work[*m + np + 1];
910 work[1] = (doublereal) (*m + np + f2cmax(i__1,i__2));