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]/Cd(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;
517 /* > \brief \b ZLASWLQ */
522 /* SUBROUTINE ZLASWLQ( M, N, MB, NB, A, LDA, T, LDT, WORK, */
525 /* INTEGER INFO, LDA, M, N, MB, NB, LDT, LWORK */
526 /* COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * ) */
529 /* > \par Purpose: */
534 /* > ZLASWLQ computes a blocked Tall-Skinny LQ factorization of */
535 /* > a complexx M-by-N matrix A for M <= N: */
537 /* > A = ( L 0 ) * Q, */
541 /* > Q is a n-by-N orthogonal matrix, stored on exit in an implicit */
542 /* > form in the elements above the digonal of the array A and in */
543 /* > the elemenst of the array T; */
544 /* > L is an lower-triangular M-by-M matrix stored on exit in */
545 /* > the elements on and below the diagonal of the array A. */
546 /* > 0 is a M-by-(N-M) zero matrix, if M < N, and is not stored. */
556 /* > The number of rows of the matrix A. M >= 0. */
562 /* > The number of columns of the matrix A. N >= M >= 0. */
565 /* > \param[in] MB */
567 /* > MB is INTEGER */
568 /* > The row block size to be used in the blocked QR. */
571 /* > \param[in] NB */
573 /* > NB is INTEGER */
574 /* > The column block size to be used in the blocked QR. */
578 /* > \param[in,out] A */
580 /* > A is COMPLEX*16 array, dimension (LDA,N) */
581 /* > On entry, the M-by-N matrix A. */
582 /* > On exit, the elements on and below the diagonal */
583 /* > of the array contain the N-by-N lower triangular matrix L; */
584 /* > the elements above the diagonal represent Q by the rows */
585 /* > of blocked V (see Further Details). */
589 /* > \param[in] LDA */
591 /* > LDA is INTEGER */
592 /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
595 /* > \param[out] T */
597 /* > T is COMPLEX*16 array, */
598 /* > dimension (LDT, N * Number_of_row_blocks) */
599 /* > where Number_of_row_blocks = CEIL((N-M)/(NB-M)) */
600 /* > The blocked upper triangular block reflectors stored in compact form */
601 /* > as a sequence of upper triangular blocks. */
602 /* > See Further Details below. */
605 /* > \param[in] LDT */
607 /* > LDT is INTEGER */
608 /* > The leading dimension of the array T. LDT >= MB. */
612 /* > \param[out] WORK */
614 /* > (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) */
617 /* > \param[in] LWORK */
619 /* > The dimension of the array WORK. LWORK >= MB*M. */
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 /* > \par Further Details: */
642 /* ===================== */
645 /* > Short-Wide LQ (SWLQ) performs LQ by a sequence of orthogonal transformations, */
646 /* > representing Q as a product of other orthogonal matrices */
647 /* > Q = Q(1) * Q(2) * . . . * Q(k) */
648 /* > where each Q(i) zeros out upper diagonal entries of a block of NB rows of A: */
649 /* > Q(1) zeros out the upper diagonal entries of rows 1:NB of A */
650 /* > Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A */
651 /* > Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A */
654 /* > Q(1) is computed by GELQT, which represents Q(1) by Householder vectors */
655 /* > stored under the diagonal of rows 1:MB of A, and by upper triangular */
656 /* > block reflectors, stored in array T(1:LDT,1:N). */
657 /* > For more information see Further Details in GELQT. */
659 /* > Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors */
660 /* > stored in columns [(i-1)*(NB-M)+M+1:i*(NB-M)+M] of A, and by upper triangular */
661 /* > block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M). */
662 /* > The last Q(k) may use fewer rows. */
663 /* > For more information see Further Details in TPQRT. */
665 /* > For more details of the overall algorithm, see the description of */
666 /* > Sequential TSQR in Section 2.2 of [1]. */
668 /* > [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations, */
669 /* > J. Demmel, L. Grigori, M. Hoemmen, J. Langou, */
670 /* > SIAM J. Sci. Comput, vol. 34, no. 1, 2012 */
673 /* ===================================================================== */
674 /* Subroutine */ int zlaswlq_(integer *m, integer *n, integer *mb, integer *
675 nb, doublecomplex *a, integer *lda, doublecomplex *t, integer *ldt,
676 doublecomplex *work, integer *lwork, integer *info)
678 /* System generated locals */
679 integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3;
681 /* Local variables */
683 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), zgelqt_(
684 integer *, integer *, integer *, doublecomplex *, integer *,
685 doublecomplex *, integer *, doublecomplex *, integer *);
687 extern /* Subroutine */ int ztplqt_(integer *, integer *, integer *,
688 integer *, doublecomplex *, integer *, doublecomplex *, integer *,
689 doublecomplex *, integer *, doublecomplex *, integer *);
693 /* -- LAPACK computational routine (version 3.9.0) -- */
694 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
695 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. -- */
699 /* ===================================================================== */
702 /* TEST THE INPUT ARGUMENTS */
704 /* Parameter adjustments */
706 a_offset = 1 + a_dim1 * 1;
709 t_offset = 1 + t_dim1 * 1;
716 lquery = *lwork == -1;
720 } else if (*n < 0 || *n < *m) {
722 } else if (*mb < 1 || *mb > *m && *m > 0) {
724 } else if (*nb <= *m) {
726 } else if (*lda < f2cmax(1,*m)) {
728 } else if (*ldt < *mb) {
730 } else if (*lwork < *m * *mb && ! lquery) {
735 work[1].r = (doublereal) i__1, work[1].i = 0.;
740 xerbla_("ZLASWLQ", &i__1, (ftnlen)7);
746 /* Quick return if possible */
748 if (f2cmin(*m,*n) == 0) {
752 /* The LQ Decomposition */
754 if (*m >= *n || *nb <= *m || *nb >= *n) {
755 zgelqt_(m, n, mb, &a[a_offset], lda, &t[t_offset], ldt, &work[1],
760 kk = (*n - *m) % (*nb - *m);
763 /* Compute the LQ factorization of the first block A(1:M,1:NB) */
765 zgelqt_(m, nb, mb, &a[a_dim1 + 1], lda, &t[t_offset], ldt, &work[1], info)
769 i__1 = ii - *nb + *m;
771 for (i__ = *nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
773 /* Compute the QR factorization of the current block A(1:M,I:I+NB-M) */
776 ztplqt_(m, &i__3, &c__0, mb, &a[a_dim1 + 1], lda, &a[i__ * a_dim1 + 1]
777 , lda, &t[(ctr * *m + 1) * t_dim1 + 1], ldt, &work[1], info);
781 /* Compute the QR factorization of the last block A(1:M,II:N) */
784 ztplqt_(m, &kk, &c__0, mb, &a[a_dim1 + 1], lda, &a[ii * a_dim1 + 1],
785 lda, &t[(ctr * *m + 1) * t_dim1 + 1], ldt, &work[1], info);
789 work[1].r = (doublereal) i__2, work[1].i = 0.;