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;
517 /* > \brief \b CGETSQRHRT */
519 /* =========== DOCUMENTATION =========== */
521 /* Online html documentation available at */
522 /* http://www.netlib.org/lapack/explore-html/ */
525 /* > Download CGETSQRHRT + dependencies */
526 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgetsqr
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgetsqr
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgetsqr
540 /* SUBROUTINE CGETSQRHRT( M, N, MB1, NB1, NB2, A, LDA, T, LDT, WORK, */
541 /* $ LWORK, INFO ) */
544 /* INTEGER INFO, LDA, LDT, LWORK, M, N, NB1, NB2, MB1 */
545 /* COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * ) */
548 /* > \par Purpose: */
553 /* > CGETSQRHRT computes a NB2-sized column blocked QR-factorization */
554 /* > of a complex M-by-N matrix A with M >= N, */
558 /* > The routine uses internally a NB1-sized column blocked and MB1-sized */
559 /* > row blocked TSQR-factorization and perfors the reconstruction */
560 /* > of the Householder vectors from the TSQR output. The routine also */
561 /* > converts the R_tsqr factor from the TSQR-factorization output into */
562 /* > the R factor that corresponds to the Householder QR-factorization, */
564 /* > A = Q_tsqr * R_tsqr = Q * R. */
566 /* > The output Q and R factors are stored in the same format as in CGEQRT */
567 /* > (Q is in blocked compact WY-representation). See the documentation */
568 /* > of CGEQRT for more details on the format. */
577 /* > The number of rows of the matrix A. M >= 0. */
583 /* > The number of columns of the matrix A. M >= N >= 0. */
586 /* > \param[in] MB1 */
588 /* > MB1 is INTEGER */
589 /* > The row block size to be used in the blocked TSQR. */
593 /* > \param[in] NB1 */
595 /* > NB1 is INTEGER */
596 /* > The column block size to be used in the blocked TSQR. */
597 /* > N >= NB1 >= 1. */
600 /* > \param[in] NB2 */
602 /* > NB2 is INTEGER */
603 /* > The block size to be used in the blocked QR that is */
604 /* > output. NB2 >= 1. */
607 /* > \param[in,out] A */
609 /* > A is COMPLEX*16 array, dimension (LDA,N) */
611 /* > On entry: an M-by-N matrix A. */
614 /* > a) the elements on and above the diagonal */
615 /* > of the array contain the N-by-N upper-triangular */
616 /* > matrix R corresponding to the Householder QR; */
617 /* > b) the elements below the diagonal represent Q by */
618 /* > the columns of blocked V (compact WY-representation). */
621 /* > \param[in] LDA */
623 /* > LDA is INTEGER */
624 /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
627 /* > \param[out] T */
629 /* > T is COMPLEX array, dimension (LDT,N)) */
630 /* > The upper triangular block reflectors stored in compact form */
631 /* > as a sequence of upper triangular blocks. */
634 /* > \param[in] LDT */
636 /* > LDT is INTEGER */
637 /* > The leading dimension of the array T. LDT >= NB2. */
640 /* > \param[out] WORK */
642 /* > (workspace) COMPLEX array, dimension (MAX(1,LWORK)) */
643 /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
646 /* > \param[in] LWORK */
648 /* > The dimension of the array WORK. */
649 /* > LWORK >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ), */
651 /* > NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)), */
652 /* > NB1LOCAL = MIN(NB1,N). */
653 /* > LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL, */
654 /* > LW1 = NB1LOCAL * N, */
655 /* > LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ), */
656 /* > If LWORK = -1, then a workspace query is assumed. */
657 /* > The routine only calculates the optimal size of the WORK */
658 /* > array, returns this value as the first entry of the WORK */
659 /* > array, and no error message related to LWORK is issued */
663 /* > \param[out] INFO */
665 /* > INFO is INTEGER */
666 /* > = 0: successful exit */
667 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
673 /* > \author Univ. of Tennessee */
674 /* > \author Univ. of California Berkeley */
675 /* > \author Univ. of Colorado Denver */
676 /* > \author NAG Ltd. */
678 /* > \ingroup comlpexOTHERcomputational */
680 /* > \par Contributors: */
681 /* ================== */
685 /* > November 2020, Igor Kozachenko, */
686 /* > Computer Science Division, */
687 /* > University of California, Berkeley */
691 /* ===================================================================== */
692 /* Subroutine */ int cgetsqrhrt_(integer *m, integer *n, integer *mb1,
693 integer *nb1, integer *nb2, complex *a, integer *lda, complex *t,
694 integer *ldt, complex *work, integer *lwork, integer *info)
696 /* System generated locals */
697 integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3, i__4;
698 real r__1, r__2, r__3;
701 /* Local variables */
702 integer ldwt, lworkopt, i__, j;
703 extern /* Subroutine */ int cungtsqr_row_(integer *, integer *, integer *
704 , integer *, complex *, integer *, complex *, integer *, complex *
705 , integer *, integer *);
707 extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
708 complex *, integer *), cunhr_col_(integer *, integer *, integer *
709 , complex *, integer *, complex *, integer *, complex *, integer *
710 ), xerbla_(char *, integer *, ftnlen);
712 integer lw1, lw2, num_all_row_blocks__, lwt;
713 extern /* Subroutine */ int clatsqr_(integer *, integer *, integer *,
714 integer *, complex *, integer *, complex *, integer *, complex *,
715 integer *, integer *);
716 integer nb1local, nb2local;
719 /* -- LAPACK computational routine -- */
720 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
721 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
724 /* ===================================================================== */
727 /* Test the input arguments */
729 /* Parameter adjustments */
731 a_offset = 1 + a_dim1 * 1;
734 t_offset = 1 + t_dim1 * 1;
740 lquery = *lwork == -1;
743 } else if (*n < 0 || *m < *n) {
745 } else if (*mb1 <= *n) {
747 } else if (*nb1 < 1) {
749 } else if (*nb2 < 1) {
751 } else if (*lda < f2cmax(1,*m)) {
753 } else /* if(complicated condition) */ {
755 i__1 = 1, i__2 = f2cmin(*nb2,*n);
756 if (*ldt < f2cmax(i__1,i__2)) {
760 /* Test the input LWORK for the dimension of the array WORK. */
761 /* This workspace is used to store array: */
762 /* a) Matrix T and WORK for CLATSQR; */
763 /* b) N-by-N upper-triangular factor R_tsqr; */
764 /* c) Matrix T and array WORK for CUNGTSQR_ROW; */
765 /* d) Diagonal D for CUNHR_COL. */
767 if (*lwork < *n * *n + 1 && ! lquery) {
771 /* Set block size for column blocks */
773 nb1local = f2cmin(*nb1,*n);
776 r__3 = (real) (*m - *n) / (real) (*mb1 - *n) + .5f;
777 r__1 = 1.f, r__2 = r_int(&r__3);
778 num_all_row_blocks__ = f2cmax(r__1,r__2);
780 /* Length and leading dimension of WORK array to place */
781 /* T array in TSQR. */
783 lwt = num_all_row_blocks__ * *n * nb1local;
786 /* Length of TSQR work array */
790 /* Length of CUNGTSQR_ROW work array. */
793 i__1 = nb1local, i__2 = *n - nb1local;
794 lw2 = nb1local * f2cmax(i__1,i__2);
798 i__3 = lwt + *n * *n + lw2, i__4 = lwt + *n * *n + *n;
799 i__1 = lwt + lw1, i__2 = f2cmax(i__3,i__4);
800 lworkopt = f2cmax(i__1,i__2);
802 if (*lwork < f2cmax(1,lworkopt) && ! lquery) {
810 /* Handle error in the input parameters and return workspace query. */
814 xerbla_("CGETSQRHRT", &i__1, (ftnlen)10);
817 q__1.r = (real) lworkopt, q__1.i = 0.f;
818 work[1].r = q__1.r, work[1].i = q__1.i;
822 /* Quick return if possible */
824 if (f2cmin(*m,*n) == 0) {
825 q__1.r = (real) lworkopt, q__1.i = 0.f;
826 work[1].r = q__1.r, work[1].i = q__1.i;
830 nb2local = f2cmin(*nb2,*n);
833 /* (1) Perform TSQR-factorization of the M-by-N matrix A. */
835 clatsqr_(m, n, mb1, &nb1local, &a[a_offset], lda, &work[1], &ldwt, &work[
836 lwt + 1], &lw1, &iinfo);
838 /* (2) Copy the factor R_tsqr stored in the upper-triangular part */
839 /* of A into the square matrix in the work array */
840 /* WORK(LWT+1:LWT+N*N) column-by-column. */
843 for (j = 1; j <= i__1; ++j) {
844 ccopy_(&j, &a[j * a_dim1 + 1], &c__1, &work[lwt + *n * (j - 1) + 1], &
848 /* (3) Generate a M-by-N matrix Q with orthonormal columns from */
849 /* the result stored below the diagonal in the array A in place. */
851 cungtsqr_row_(m, n, mb1, &nb1local, &a[a_offset], lda, &work[1], &ldwt, &
852 work[lwt + *n * *n + 1], &lw2, &iinfo);
854 /* (4) Perform the reconstruction of Householder vectors from */
855 /* the matrix Q (stored in A) in place. */
857 cunhr_col_(m, n, &nb2local, &a[a_offset], lda, &t[t_offset], ldt, &work[
858 lwt + *n * *n + 1], &iinfo);
860 /* (5) Copy the factor R_tsqr stored in the square matrix in the */
861 /* work array WORK(LWT+1:LWT+N*N) into the upper-triangular */
864 /* (6) Compute from R_tsqr the factor R_hr corresponding to */
865 /* the reconstructed Householder vectors, i.e. R_hr = S * R_tsqr. */
866 /* This multiplication by the sign matrix S on the left means */
867 /* changing the sign of I-th row of the matrix R_tsqr according */
868 /* to sign of the I-th diagonal element DIAG(I) of the matrix S. */
869 /* DIAG is stored in WORK( LWT+N*N+1 ) from the CUNHR_COL output. */
871 /* (5) and (6) can be combined in a single loop, so the rows in A */
872 /* are accessed only once. */
875 for (i__ = 1; i__ <= i__1; ++i__) {
876 i__2 = lwt + *n * *n + i__;
877 q__1.r = -1.f, q__1.i = 0.f;
878 if (work[i__2].r == q__1.r && work[i__2].i == q__1.i) {
880 for (j = i__; j <= i__2; ++j) {
881 i__3 = i__ + j * a_dim1;
882 q__2.r = -1.f, q__2.i = 0.f;
883 i__4 = lwt + *n * (j - 1) + i__;
884 q__1.r = q__2.r * work[i__4].r - q__2.i * work[i__4].i,
885 q__1.i = q__2.r * work[i__4].i + q__2.i * work[i__4]
887 a[i__3].r = q__1.r, a[i__3].i = q__1.i;
891 ccopy_(&i__2, &work[lwt + *n * (i__ - 1) + i__], n, &a[i__ + i__ *
896 q__1.r = (real) lworkopt, q__1.i = 0.f;
897 work[1].r = q__1.r, work[1].i = q__1.i;
900 /* End of CGETSQRHRT */