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 doublereal c_b7 = 1.;
516 static integer c__1 = 1;
517 static doublereal c_b10 = -1.;
519 /* > \brief \b DORHR_COL */
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download DORHR_COL + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorhr_c
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorhr_c
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorhr_c
541 /* SUBROUTINE DORHR_COL( M, N, NB, A, LDA, T, LDT, D, INFO ) */
543 /* INTEGER INFO, LDA, LDT, M, N, NB */
544 /* DOUBLE PRECISION A( LDA, * ), D( * ), T( LDT, * ) */
546 /* > \par Purpose: */
551 /* > DORHR_COL takes an M-by-N real matrix Q_in with orthonormal columns */
552 /* > as input, stored in A, and performs Householder Reconstruction (HR), */
553 /* > i.e. reconstructs Householder vectors V(i) implicitly representing */
554 /* > another M-by-N matrix Q_out, with the property that Q_in = Q_out*S, */
555 /* > where S is an N-by-N diagonal matrix with diagonal entries */
556 /* > equal to +1 or -1. The Householder vectors (columns V(i) of V) are */
557 /* > stored in A on output, and the diagonal entries of S are stored in D. */
558 /* > Block reflectors are also returned in T */
559 /* > (same output format as DGEQRT). */
568 /* > The number of rows of the matrix A. M >= 0. */
574 /* > The number of columns of the matrix A. M >= N >= 0. */
577 /* > \param[in] NB */
579 /* > NB is INTEGER */
580 /* > The column block size to be used in the reconstruction */
581 /* > of Householder column vector blocks in the array A and */
582 /* > corresponding block reflectors in the array T. NB >= 1. */
583 /* > (Note that if NB > N, then N is used instead of NB */
584 /* > as the column block size.) */
587 /* > \param[in,out] A */
589 /* > A is DOUBLE PRECISION array, dimension (LDA,N) */
593 /* > The array A contains an M-by-N orthonormal matrix Q_in, */
594 /* > i.e the columns of A are orthogonal unit vectors. */
598 /* > The elements below the diagonal of A represent the unit */
599 /* > lower-trapezoidal matrix V of Householder column vectors */
600 /* > V(i). The unit diagonal entries of V are not stored */
601 /* > (same format as the output below the diagonal in A from */
602 /* > DGEQRT). The matrix T and the matrix V stored on output */
603 /* > in A implicitly define Q_out. */
605 /* > The elements above the diagonal contain the factor U */
606 /* > of the "modified" LU-decomposition: */
607 /* > Q_in - ( S ) = V * U */
609 /* > where 0 is a (M-N)-by-(M-N) zero matrix. */
612 /* > \param[in] LDA */
614 /* > LDA is INTEGER */
615 /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
618 /* > \param[out] T */
620 /* > T is DOUBLE PRECISION array, */
621 /* > dimension (LDT, N) */
623 /* > Let NOCB = Number_of_output_col_blocks */
626 /* > On exit, T(1:NB, 1:N) contains NOCB upper-triangular */
627 /* > block reflectors used to define Q_out stored in compact */
628 /* > form as a sequence of upper-triangular NB-by-NB column */
629 /* > blocks (same format as the output T in DGEQRT). */
630 /* > The matrix T and the matrix V stored on output in A */
631 /* > implicitly define Q_out. NOTE: The lower triangles */
632 /* > below the upper-triangular blcoks will be filled with */
633 /* > zeros. See Further Details. */
636 /* > \param[in] LDT */
638 /* > LDT is INTEGER */
639 /* > The leading dimension of the array T. */
640 /* > LDT >= f2cmax(1,f2cmin(NB,N)). */
643 /* > \param[out] D */
645 /* > D is DOUBLE PRECISION array, dimension f2cmin(M,N). */
646 /* > The elements can be only plus or minus one. */
648 /* > D(i) is constructed as D(i) = -SIGN(Q_in_i(i,i)), where */
649 /* > 1 <= i <= f2cmin(M,N), and Q_in_i is Q_in after performing */
650 /* > i-1 steps of “modified” Gaussian elimination. */
651 /* > See Further Details. */
654 /* > \param[out] INFO */
656 /* > INFO is INTEGER */
657 /* > = 0: successful exit */
658 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
661 /* > \par Further Details: */
662 /* ===================== */
666 /* > The computed M-by-M orthogonal factor Q_out is defined implicitly as */
667 /* > a product of orthogonal matrices Q_out(i). Each Q_out(i) is stored in */
668 /* > the compact WY-representation format in the corresponding blocks of */
669 /* > matrices V (stored in A) and T. */
671 /* > The M-by-N unit lower-trapezoidal matrix V stored in the M-by-N */
672 /* > matrix A contains the column vectors V(i) in NB-size column */
673 /* > blocks VB(j). For example, VB(1) contains the columns */
674 /* > V(1), V(2), ... V(NB). NOTE: The unit entries on */
675 /* > the diagonal of Y are not stored in A. */
677 /* > The number of column blocks is */
679 /* > NOCB = Number_of_output_col_blocks = CEIL(N/NB) */
681 /* > where each block is of order NB except for the last block, which */
682 /* > is of order LAST_NB = N - (NOCB-1)*NB. */
684 /* > For example, if M=6, N=5 and NB=2, the matrix V is */
687 /* > V = ( VB(1), VB(2), VB(3) ) = */
691 /* > ( v31 v32 1 ) */
692 /* > ( v41 v42 v43 1 ) */
693 /* > ( v51 v52 v53 v54 1 ) */
694 /* > ( v61 v62 v63 v54 v65 ) */
697 /* > For each of the column blocks VB(i), an upper-triangular block */
698 /* > reflector TB(i) is computed. These blocks are stored as */
699 /* > a sequence of upper-triangular column blocks in the NB-by-N */
700 /* > matrix T. The size of each TB(i) block is NB-by-NB, except */
701 /* > for the last block, whose size is LAST_NB-by-LAST_NB. */
703 /* > For example, if M=6, N=5 and NB=2, the matrix T is */
705 /* > T = ( TB(1), TB(2), TB(3) ) = */
707 /* > = ( t11 t12 t13 t14 t15 ) */
711 /* > The M-by-M factor Q_out is given as a product of NOCB */
712 /* > orthogonal M-by-M matrices Q_out(i). */
714 /* > Q_out = Q_out(1) * Q_out(2) * ... * Q_out(NOCB), */
716 /* > where each matrix Q_out(i) is given by the WY-representation */
717 /* > using corresponding blocks from the matrices V and T: */
719 /* > Q_out(i) = I - VB(i) * TB(i) * (VB(i))**T, */
721 /* > where I is the identity matrix. Here is the formula with matrix */
724 /* > Q(i){M-by-M} = I{M-by-M} - */
725 /* > VB(i){M-by-INB} * TB(i){INB-by-INB} * (VB(i))**T {INB-by-M}, */
727 /* > where INB = NB, except for the last block NOCB */
728 /* > for which INB=LAST_NB. */
734 /* > If Q_in is the result of doing a QR factorization */
735 /* > B = Q_in * R_in, then: */
737 /* > B = (Q_out*S) * R_in = Q_out * (S * R_in) = O_out * R_out. */
739 /* > So if one wants to interpret Q_out as the result */
740 /* > of the QR factorization of B, then corresponding R_out */
741 /* > should be obtained by R_out = S * R_in, i.e. some rows of R_in */
742 /* > should be multiplied by -1. */
744 /* > For the details of the algorithm, see [1]. */
746 /* > [1] "Reconstructing Householder vectors from tall-skinny QR", */
747 /* > G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen, */
748 /* > E. Solomonik, J. Parallel Distrib. Comput., */
749 /* > vol. 85, pp. 3-31, 2015. */
755 /* > \author Univ. of Tennessee */
756 /* > \author Univ. of California Berkeley */
757 /* > \author Univ. of Colorado Denver */
758 /* > \author NAG Ltd. */
760 /* > \date November 2019 */
762 /* > \ingroup doubleOTHERcomputational */
764 /* > \par Contributors: */
765 /* ================== */
769 /* > November 2019, Igor Kozachenko, */
770 /* > Computer Science Division, */
771 /* > University of California, Berkeley */
775 /* ===================================================================== */
776 /* Subroutine */ int dorhr_col_(integer *m, integer *n, integer *nb,
777 doublereal *a, integer *lda, doublereal *t, integer *ldt, doublereal *
780 /* System generated locals */
781 integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3, i__4;
783 /* Local variables */
784 extern /* Subroutine */ int dlaorhr_col_getrfnp_(integer *, integer *,
785 doublereal *, integer *, doublereal *, integer *);
786 integer nplusone, i__, j;
787 extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
790 extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
791 doublereal *, integer *), dtrsm_(char *, char *, char *, char *,
792 integer *, integer *, doublereal *, doublereal *, integer *,
793 doublereal *, integer *);
795 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
796 integer jbtemp1, jbtemp2, jnb;
799 /* -- LAPACK computational routine (version 3.9.0) -- */
800 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
801 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
805 /* ===================================================================== */
808 /* Test the input parameters */
810 /* Parameter adjustments */
812 a_offset = 1 + a_dim1 * 1;
815 t_offset = 1 + t_dim1 * 1;
823 } else if (*n < 0 || *n > *m) {
825 } else if (*nb < 1) {
827 } else if (*lda < f2cmax(1,*m)) {
829 } else /* if(complicated condition) */ {
831 i__1 = 1, i__2 = f2cmin(*nb,*n);
832 if (*ldt < f2cmax(i__1,i__2)) {
837 /* Handle error in the input parameters. */
841 xerbla_("DORHR_COL", &i__1, (ftnlen)9);
845 /* Quick return if possible */
847 if (f2cmin(*m,*n) == 0) {
851 /* On input, the M-by-N matrix A contains the orthogonal */
852 /* M-by-N matrix Q_in. */
854 /* (1) Compute the unit lower-trapezoidal V (ones on the diagonal */
855 /* are not stored) by performing the "modified" LU-decomposition. */
857 /* Q_in - ( S ) = V * U = ( V1 ) * U, */
860 /* where 0 is an (M-N)-by-N zero matrix. */
862 /* (1-1) Factor V1 and U. */
863 dlaorhr_col_getrfnp_(n, n, &a[a_offset], lda, &d__[1], &iinfo);
865 /* (1-2) Solve for V2. */
869 dtrsm_("R", "U", "N", "N", &i__1, n, &c_b7, &a[a_offset], lda, &a[*n
873 /* (2) Reconstruct the block reflector T stored in T(1:NB, 1:N) */
874 /* as a sequence of upper-triangular blocks with NB-size column */
877 /* Loop over the column blocks of size NB of the array A(1:M,1:N) */
878 /* and the array T(1:NB,1:N), JB is the column index of a column */
879 /* block, JNB is the column block size at each step JB. */
884 for (jb = 1; i__2 < 0 ? jb >= i__1 : jb <= i__1; jb += i__2) {
886 /* (2-0) Determine the column block size JNB. */
889 i__3 = nplusone - jb;
890 jnb = f2cmin(i__3,*nb);
892 /* (2-1) Copy the upper-triangular part of the current JNB-by-JNB */
893 /* diagonal block U(JB) (of the N-by-N matrix U) stored */
894 /* in A(JB:JB+JNB-1,JB:JB+JNB-1) into the upper-triangular part */
895 /* of the current JNB-by-JNB block T(1:JNB,JB:JB+JNB-1) */
896 /* column-by-column, total JNB*(JNB+1)/2 elements. */
900 for (j = jb; j <= i__3; ++j) {
902 dcopy_(&i__4, &a[jb + j * a_dim1], &c__1, &t[j * t_dim1 + 1], &
906 /* (2-2) Perform on the upper-triangular part of the current */
907 /* JNB-by-JNB diagonal block U(JB) (of the N-by-N matrix U) stored */
908 /* in T(1:JNB,JB:JB+JNB-1) the following operation in place: */
909 /* (-1)*U(JB)*S(JB), i.e the result will be stored in the upper- */
910 /* triangular part of T(1:JNB,JB:JB+JNB-1). This multiplication */
911 /* of the JNB-by-JNB diagonal block U(JB) by the JNB-by-JNB */
912 /* diagonal block S(JB) of the N-by-N sign matrix S from the */
913 /* right means changing the sign of each J-th column of the block */
914 /* U(JB) according to the sign of the diagonal element of the block */
915 /* S(JB), i.e. S(J,J) that is stored in the array element D(J). */
918 for (j = jb; j <= i__3; ++j) {
921 dscal_(&i__4, &c_b10, &t[j * t_dim1 + 1], &c__1);
925 /* (2-3) Perform the triangular solve for the current block */
928 /* X(JB) * (A(JB)**T) = B(JB), where: */
930 /* A(JB)**T is a JNB-by-JNB unit upper-triangular */
931 /* coefficient block, and A(JB)=V1(JB), which */
932 /* is a JNB-by-JNB unit lower-triangular block */
933 /* stored in A(JB:JB+JNB-1,JB:JB+JNB-1). */
934 /* The N-by-N matrix V1 is the upper part */
935 /* of the M-by-N lower-trapezoidal matrix V */
936 /* stored in A(1:M,1:N); */
938 /* B(JB) is a JNB-by-JNB upper-triangular right-hand */
939 /* side block, B(JB) = (-1)*U(JB)*S(JB), and */
940 /* B(JB) is stored in T(1:JNB,JB:JB+JNB-1); */
942 /* X(JB) is a JNB-by-JNB upper-triangular solution */
943 /* block, X(JB) is the upper-triangular block */
944 /* reflector T(JB), and X(JB) is stored */
945 /* in T(1:JNB,JB:JB+JNB-1). */
947 /* In other words, we perform the triangular solve for the */
948 /* upper-triangular block T(JB): */
950 /* T(JB) * (V1(JB)**T) = (-1)*U(JB)*S(JB). */
952 /* Even though the blocks X(JB) and B(JB) are upper- */
953 /* triangular, the routine DTRSM will access all JNB**2 */
954 /* elements of the square T(1:JNB,JB:JB+JNB-1). Therefore, */
955 /* we need to set to zero the elements of the block */
956 /* T(1:JNB,JB:JB+JNB-1) below the diagonal before the call */
959 /* (2-3a) Set the elements to zero. */
963 for (j = jb; j <= i__3; ++j) {
965 for (i__ = j - jbtemp2; i__ <= i__4; ++i__) {
966 t[i__ + j * t_dim1] = 0.;
970 /* (2-3b) Perform the triangular solve. */
972 dtrsm_("R", "L", "T", "U", &jnb, &jnb, &c_b7, &a[jb + jb * a_dim1],
973 lda, &t[jb * t_dim1 + 1], ldt);
979 /* End of DORHR_COL */