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 integer c__3 = 3;
518 static integer c__2 = 2;
520 /* > \brief \b DGEQP3 */
522 /* =========== DOCUMENTATION =========== */
524 /* Online html documentation available at */
525 /* http://www.netlib.org/lapack/explore-html/ */
528 /* > Download DGEQP3 + dependencies */
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqp3.
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqp3.
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqp3.
543 /* SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO ) */
545 /* INTEGER INFO, LDA, LWORK, M, N */
546 /* INTEGER JPVT( * ) */
547 /* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */
550 /* > \par Purpose: */
555 /* > DGEQP3 computes a QR factorization with column pivoting of a */
556 /* > matrix A: A*P = Q*R using Level 3 BLAS. */
565 /* > The number of rows of the matrix A. M >= 0. */
571 /* > The number of columns of the matrix A. N >= 0. */
574 /* > \param[in,out] A */
576 /* > A is DOUBLE PRECISION array, dimension (LDA,N) */
577 /* > On entry, the M-by-N matrix A. */
578 /* > On exit, the upper triangle of the array contains the */
579 /* > f2cmin(M,N)-by-N upper trapezoidal matrix R; the elements below */
580 /* > the diagonal, together with the array TAU, represent the */
581 /* > orthogonal matrix Q as a product of f2cmin(M,N) elementary */
585 /* > \param[in] LDA */
587 /* > LDA is INTEGER */
588 /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
591 /* > \param[in,out] JPVT */
593 /* > JPVT is INTEGER array, dimension (N) */
594 /* > On entry, if JPVT(J).ne.0, the J-th column of A is permuted */
595 /* > to the front of A*P (a leading column); if JPVT(J)=0, */
596 /* > the J-th column of A is a free column. */
597 /* > On exit, if JPVT(J)=K, then the J-th column of A*P was the */
598 /* > the K-th column of A. */
601 /* > \param[out] TAU */
603 /* > TAU is DOUBLE PRECISION array, dimension (f2cmin(M,N)) */
604 /* > The scalar factors of the elementary reflectors. */
607 /* > \param[out] WORK */
609 /* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
610 /* > On exit, if INFO=0, WORK(1) returns the optimal LWORK. */
613 /* > \param[in] LWORK */
615 /* > LWORK is INTEGER */
616 /* > The dimension of the array WORK. LWORK >= 3*N+1. */
617 /* > For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB */
618 /* > is the optimal blocksize. */
620 /* > If LWORK = -1, then a workspace query is assumed; the routine */
621 /* > only calculates the optimal size of the WORK array, returns */
622 /* > this value as the first entry of the WORK array, and no error */
623 /* > message related to LWORK is issued by XERBLA. */
626 /* > \param[out] INFO */
628 /* > INFO is INTEGER */
629 /* > = 0: successful exit. */
630 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
636 /* > \author Univ. of Tennessee */
637 /* > \author Univ. of California Berkeley */
638 /* > \author Univ. of Colorado Denver */
639 /* > \author NAG Ltd. */
641 /* > \date December 2016 */
643 /* > \ingroup doubleGEcomputational */
645 /* > \par Further Details: */
646 /* ===================== */
650 /* > The matrix Q is represented as a product of elementary reflectors */
652 /* > Q = H(1) H(2) . . . H(k), where k = f2cmin(m,n). */
654 /* > Each H(i) has the form */
656 /* > H(i) = I - tau * v * v**T */
658 /* > where tau is a real scalar, and v is a real/complex vector */
659 /* > with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in */
660 /* > A(i+1:m,i), and tau in TAU(i). */
663 /* > \par Contributors: */
664 /* ================== */
666 /* > G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain */
667 /* > X. Sun, Computer Science Dept., Duke University, USA */
669 /* ===================================================================== */
670 /* Subroutine */ int dgeqp3_(integer *m, integer *n, doublereal *a, integer *
671 lda, integer *jpvt, doublereal *tau, doublereal *work, integer *lwork,
674 /* System generated locals */
675 integer a_dim1, a_offset, i__1, i__2, i__3;
677 /* Local variables */
679 extern doublereal dnrm2_(integer *, doublereal *, integer *);
680 integer j, nbmin, minmn;
681 extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
682 doublereal *, integer *);
684 extern /* Subroutine */ int dlaqp2_(integer *, integer *, integer *,
685 doublereal *, integer *, integer *, doublereal *, doublereal *,
686 doublereal *, doublereal *);
687 integer jb, na, nb, sm, sn, nx;
688 extern /* Subroutine */ int dgeqrf_(integer *, integer *, doublereal *,
689 integer *, doublereal *, doublereal *, integer *, integer *),
690 xerbla_(char *, integer *, ftnlen);
691 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
692 integer *, integer *, ftnlen, ftnlen);
693 extern /* Subroutine */ int dlaqps_(integer *, integer *, integer *,
694 integer *, integer *, doublereal *, integer *, integer *,
695 doublereal *, doublereal *, doublereal *, doublereal *,
696 doublereal *, integer *);
697 integer topbmn, sminmn;
698 extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *,
699 integer *, doublereal *, integer *, doublereal *, doublereal *,
700 integer *, doublereal *, integer *, integer *);
706 /* -- LAPACK computational routine (version 3.7.0) -- */
707 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
708 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
712 /* ===================================================================== */
715 /* Test input arguments */
716 /* ==================== */
718 /* Parameter adjustments */
720 a_offset = 1 + a_dim1 * 1;
728 lquery = *lwork == -1;
733 } else if (*lda < f2cmax(1,*m)) {
738 minmn = f2cmin(*m,*n);
744 nb = ilaenv_(&c__1, "DGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6,
746 lwkopt = (*n << 1) + (*n + 1) * nb;
748 work[1] = (doublereal) lwkopt;
750 if (*lwork < iws && ! lquery) {
757 xerbla_("DGEQP3", &i__1, (ftnlen)6);
763 /* Move initial columns up front. */
767 for (j = 1; j <= i__1; ++j) {
770 dswap_(m, &a[j * a_dim1 + 1], &c__1, &a[nfxd * a_dim1 + 1], &
772 jpvt[j] = jpvt[nfxd];
785 /* Factorize fixed columns */
786 /* ======================= */
788 /* Compute the QR factorization of fixed columns and update */
789 /* remaining columns. */
792 na = f2cmin(*m,nfxd);
793 /* CC CALL DGEQR2( M, NA, A, LDA, TAU, WORK, INFO ) */
794 dgeqrf_(m, &na, &a[a_offset], lda, &tau[1], &work[1], lwork, info);
796 i__1 = iws, i__2 = (integer) work[1];
797 iws = f2cmax(i__1,i__2);
799 /* CC CALL DORM2R( 'Left', 'Transpose', M, N-NA, NA, A, LDA, */
800 /* CC $ TAU, A( 1, NA+1 ), LDA, WORK, INFO ) */
802 dormqr_("Left", "Transpose", m, &i__1, &na, &a[a_offset], lda, &
803 tau[1], &a[(na + 1) * a_dim1 + 1], lda, &work[1], lwork,
806 i__1 = iws, i__2 = (integer) work[1];
807 iws = f2cmax(i__1,i__2);
811 /* Factorize free columns */
812 /* ====================== */
818 sminmn = minmn - nfxd;
820 /* Determine the block size. */
822 nb = ilaenv_(&c__1, "DGEQRF", " ", &sm, &sn, &c_n1, &c_n1, (ftnlen)6,
827 if (nb > 1 && nb < sminmn) {
829 /* Determine when to cross over from blocked to unblocked code. */
832 i__1 = 0, i__2 = ilaenv_(&c__3, "DGEQRF", " ", &sm, &sn, &c_n1, &
833 c_n1, (ftnlen)6, (ftnlen)1);
834 nx = f2cmax(i__1,i__2);
839 /* Determine if workspace is large enough for blocked code. */
841 minws = (sn << 1) + (sn + 1) * nb;
842 iws = f2cmax(iws,minws);
843 if (*lwork < minws) {
845 /* Not enough workspace to use optimal NB: Reduce NB and */
846 /* determine the minimum value of NB. */
848 nb = (*lwork - (sn << 1)) / (sn + 1);
850 i__1 = 2, i__2 = ilaenv_(&c__2, "DGEQRF", " ", &sm, &sn, &
851 c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
852 nbmin = f2cmax(i__1,i__2);
859 /* Initialize partial column norms. The first N elements of work */
860 /* store the exact column norms. */
863 for (j = nfxd + 1; j <= i__1; ++j) {
864 work[j] = dnrm2_(&sm, &a[nfxd + 1 + j * a_dim1], &c__1);
865 work[*n + j] = work[j];
869 if (nb >= nbmin && nb < sminmn && nx < sminmn) {
871 /* Use blocked code initially. */
875 /* Compute factorization: while loop. */
882 i__1 = nb, i__2 = topbmn - j + 1;
883 jb = f2cmin(i__1,i__2);
885 /* Factorize JB columns among columns J:N. */
890 dlaqps_(m, &i__1, &i__2, &jb, &fjb, &a[j * a_dim1 + 1], lda, &
891 jpvt[j], &tau[j], &work[j], &work[*n + j], &work[(*n
892 << 1) + 1], &work[(*n << 1) + jb + 1], &i__3);
901 /* Use unblocked code to factor the last or only block. */
907 dlaqp2_(m, &i__1, &i__2, &a[j * a_dim1 + 1], lda, &jpvt[j], &tau[
908 j], &work[j], &work[*n + j], &work[(*n << 1) + 1]);
913 work[1] = (doublereal) iws;