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 doublecomplex c_b1 = {-1.,0.};
516 static integer c__1 = 1;
518 /* > \brief \b ZUNBDB2 */
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download ZUNBDB2 + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunbdb2
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zunbdb2
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunbdb2
541 /* SUBROUTINE ZUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, */
542 /* TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO ) */
544 /* INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21 */
545 /* DOUBLE PRECISION PHI(*), THETA(*) */
546 /* COMPLEX*16 TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), */
547 /* $ X11(LDX11,*), X21(LDX21,*) */
550 /* > \par Purpose: */
555 /* > ZUNBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny */
556 /* > matrix X with orthonomal columns: */
559 /* > [ X11 ] [ P1 | ] [ 0 ] */
560 /* > [-----] = [---------] [-----] Q1**T . */
561 /* > [ X21 ] [ | P2 ] [ B21 ] */
564 /* > X11 is P-by-Q, and X21 is (M-P)-by-Q. P must be no larger than M-P, */
565 /* > Q, or M-Q. Routines ZUNBDB1, ZUNBDB3, and ZUNBDB4 handle cases in */
566 /* > which P is not the minimum dimension. */
568 /* > The unitary matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P), */
569 /* > and (M-Q)-by-(M-Q), respectively. They are represented implicitly by */
570 /* > Householder vectors. */
572 /* > B11 and B12 are P-by-P bidiagonal matrices represented implicitly by */
573 /* > angles THETA, PHI. */
583 /* > The number of rows X11 plus the number of rows in X21. */
589 /* > The number of rows in X11. 0 <= P <= f2cmin(M-P,Q,M-Q). */
595 /* > The number of columns in X11 and X21. 0 <= Q <= M. */
598 /* > \param[in,out] X11 */
600 /* > X11 is COMPLEX*16 array, dimension (LDX11,Q) */
601 /* > On entry, the top block of the matrix X to be reduced. On */
602 /* > exit, the columns of tril(X11) specify reflectors for P1 and */
603 /* > the rows of triu(X11,1) specify reflectors for Q1. */
606 /* > \param[in] LDX11 */
608 /* > LDX11 is INTEGER */
609 /* > The leading dimension of X11. LDX11 >= P. */
612 /* > \param[in,out] X21 */
614 /* > X21 is COMPLEX*16 array, dimension (LDX21,Q) */
615 /* > On entry, the bottom block of the matrix X to be reduced. On */
616 /* > exit, the columns of tril(X21) specify reflectors for P2. */
619 /* > \param[in] LDX21 */
621 /* > LDX21 is INTEGER */
622 /* > The leading dimension of X21. LDX21 >= M-P. */
625 /* > \param[out] THETA */
627 /* > THETA is DOUBLE PRECISION array, dimension (Q) */
628 /* > The entries of the bidiagonal blocks B11, B21 are defined by */
629 /* > THETA and PHI. See Further Details. */
632 /* > \param[out] PHI */
634 /* > PHI is DOUBLE PRECISION array, dimension (Q-1) */
635 /* > The entries of the bidiagonal blocks B11, B21 are defined by */
636 /* > THETA and PHI. See Further Details. */
639 /* > \param[out] TAUP1 */
641 /* > TAUP1 is COMPLEX*16 array, dimension (P) */
642 /* > The scalar factors of the elementary reflectors that define */
646 /* > \param[out] TAUP2 */
648 /* > TAUP2 is COMPLEX*16 array, dimension (M-P) */
649 /* > The scalar factors of the elementary reflectors that define */
653 /* > \param[out] TAUQ1 */
655 /* > TAUQ1 is COMPLEX*16 array, dimension (Q) */
656 /* > The scalar factors of the elementary reflectors that define */
660 /* > \param[out] WORK */
662 /* > WORK is COMPLEX*16 array, dimension (LWORK) */
665 /* > \param[in] LWORK */
667 /* > LWORK is INTEGER */
668 /* > The dimension of the array WORK. LWORK >= M-Q. */
670 /* > If LWORK = -1, then a workspace query is assumed; the routine */
671 /* > only calculates the optimal size of the WORK array, returns */
672 /* > this value as the first entry of the WORK array, and no error */
673 /* > message related to LWORK is issued by XERBLA. */
676 /* > \param[out] INFO */
678 /* > INFO is INTEGER */
679 /* > = 0: successful exit. */
680 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
686 /* > \author Univ. of Tennessee */
687 /* > \author Univ. of California Berkeley */
688 /* > \author Univ. of Colorado Denver */
689 /* > \author NAG Ltd. */
691 /* > \date July 2012 */
693 /* > \ingroup complex16OTHERcomputational */
695 /* > \par Further Details: */
696 /* ===================== */
700 /* > The upper-bidiagonal blocks B11, B21 are represented implicitly by */
701 /* > angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry */
702 /* > in each bidiagonal band is a product of a sine or cosine of a THETA */
703 /* > with a sine or cosine of a PHI. See [1] or ZUNCSD for details. */
705 /* > P1, P2, and Q1 are represented as products of elementary reflectors. */
706 /* > See ZUNCSD2BY1 for details on generating P1, P2, and Q1 using ZUNGQR */
710 /* > \par References: */
711 /* ================ */
713 /* > [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. */
714 /* > Algorithms, 50(1):33-65, 2009. */
716 /* ===================================================================== */
717 /* Subroutine */ int zunbdb2_(integer *m, integer *p, integer *q,
718 doublecomplex *x11, integer *ldx11, doublecomplex *x21, integer *
719 ldx21, doublereal *theta, doublereal *phi, doublecomplex *taup1,
720 doublecomplex *taup2, doublecomplex *tauq1, doublecomplex *work,
721 integer *lwork, integer *info)
723 /* System generated locals */
724 integer x11_dim1, x11_offset, x21_dim1, x21_offset, i__1, i__2, i__3,
726 doublereal d__1, d__2;
729 /* Local variables */
730 integer lworkmin, lworkopt;
734 integer ilarf, llarf;
735 extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
736 doublecomplex *, integer *);
738 extern /* Subroutine */ int zlarf_(char *, integer *, integer *,
739 doublecomplex *, integer *, doublecomplex *, doublecomplex *,
740 integer *, doublecomplex *), zdrot_(integer *,
741 doublecomplex *, integer *, doublecomplex *, integer *,
742 doublereal *, doublereal *);
743 extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
744 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), zlacgv_(
745 integer *, doublecomplex *, integer *);
747 integer iorbdb5, lorbdb5;
748 extern /* Subroutine */ int zunbdb5_(integer *, integer *, integer *,
749 doublecomplex *, integer *, doublecomplex *, integer *,
750 doublecomplex *, integer *, doublecomplex *, integer *,
751 doublecomplex *, integer *, integer *), zlarfgp_(integer *,
752 doublecomplex *, doublecomplex *, integer *, doublecomplex *);
755 /* -- LAPACK computational routine (version 3.8.0) -- */
756 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
757 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
761 /* ==================================================================== */
764 /* Test input arguments */
766 /* Parameter adjustments */
768 x11_offset = 1 + x11_dim1 * 1;
771 x21_offset = 1 + x21_dim1 * 1;
782 lquery = *lwork == -1;
786 } else if (*p < 0 || *p > *m - *p) {
788 } else if (*q < 0 || *q < *p || *m - *q < *p) {
790 } else if (*ldx11 < f2cmax(1,*p)) {
792 } else /* if(complicated condition) */ {
794 i__1 = 1, i__2 = *m - *p;
795 if (*ldx21 < f2cmax(i__1,i__2)) {
800 /* Compute workspace */
805 i__1 = *p - 1, i__2 = *m - *p, i__1 = f2cmax(i__1,i__2), i__2 = *q - 1;
806 llarf = f2cmax(i__1,i__2);
810 i__1 = ilarf + llarf - 1, i__2 = iorbdb5 + lorbdb5 - 1;
811 lworkopt = f2cmax(i__1,i__2);
813 work[1].r = (doublereal) lworkopt, work[1].i = 0.;
814 if (*lwork < lworkmin && ! lquery) {
820 xerbla_("ZUNBDB2", &i__1, (ftnlen)7);
826 /* Reduce rows 1, ..., P of X11 and X21 */
829 for (i__ = 1; i__ <= i__1; ++i__) {
833 zdrot_(&i__2, &x11[i__ + i__ * x11_dim1], ldx11, &x21[i__ - 1 +
834 i__ * x21_dim1], ldx21, &c__, &s);
837 zlacgv_(&i__2, &x11[i__ + i__ * x11_dim1], ldx11);
839 zlarfgp_(&i__2, &x11[i__ + i__ * x11_dim1], &x11[i__ + (i__ + 1) *
840 x11_dim1], ldx11, &tauq1[i__]);
841 i__2 = i__ + i__ * x11_dim1;
843 i__2 = i__ + i__ * x11_dim1;
844 x11[i__2].r = 1., x11[i__2].i = 0.;
847 zlarf_("R", &i__2, &i__3, &x11[i__ + i__ * x11_dim1], ldx11, &tauq1[
848 i__], &x11[i__ + 1 + i__ * x11_dim1], ldx11, &work[ilarf]);
849 i__2 = *m - *p - i__ + 1;
851 zlarf_("R", &i__2, &i__3, &x11[i__ + i__ * x11_dim1], ldx11, &tauq1[
852 i__], &x21[i__ + i__ * x21_dim1], ldx21, &work[ilarf]);
854 zlacgv_(&i__2, &x11[i__ + i__ * x11_dim1], ldx11);
856 /* Computing 2nd power */
857 d__1 = dznrm2_(&i__2, &x11[i__ + 1 + i__ * x11_dim1], &c__1);
858 i__3 = *m - *p - i__ + 1;
859 /* Computing 2nd power */
860 d__2 = dznrm2_(&i__3, &x21[i__ + i__ * x21_dim1], &c__1);
861 s = sqrt(d__1 * d__1 + d__2 * d__2);
862 theta[i__] = atan2(s, c__);
865 i__3 = *m - *p - i__ + 1;
867 zunbdb5_(&i__2, &i__3, &i__4, &x11[i__ + 1 + i__ * x11_dim1], &c__1, &
868 x21[i__ + i__ * x21_dim1], &c__1, &x11[i__ + 1 + (i__ + 1) *
869 x11_dim1], ldx11, &x21[i__ + (i__ + 1) * x21_dim1], ldx21, &
870 work[iorbdb5], &lorbdb5, &childinfo);
872 zscal_(&i__2, &c_b1, &x11[i__ + 1 + i__ * x11_dim1], &c__1);
873 i__2 = *m - *p - i__ + 1;
874 zlarfgp_(&i__2, &x21[i__ + i__ * x21_dim1], &x21[i__ + 1 + i__ *
875 x21_dim1], &c__1, &taup2[i__]);
878 zlarfgp_(&i__2, &x11[i__ + 1 + i__ * x11_dim1], &x11[i__ + 2 +
879 i__ * x11_dim1], &c__1, &taup1[i__]);
880 phi[i__] = atan2((doublereal) x11[i__ + 1 + i__ * x11_dim1].r, (
881 doublereal) x21[i__ + i__ * x21_dim1].r);
884 i__2 = i__ + 1 + i__ * x11_dim1;
885 x11[i__2].r = 1., x11[i__2].i = 0.;
888 d_cnjg(&z__1, &taup1[i__]);
889 zlarf_("L", &i__2, &i__3, &x11[i__ + 1 + i__ * x11_dim1], &c__1, &
890 z__1, &x11[i__ + 1 + (i__ + 1) * x11_dim1], ldx11, &work[
893 i__2 = i__ + i__ * x21_dim1;
894 x21[i__2].r = 1., x21[i__2].i = 0.;
895 i__2 = *m - *p - i__ + 1;
897 d_cnjg(&z__1, &taup2[i__]);
898 zlarf_("L", &i__2, &i__3, &x21[i__ + i__ * x21_dim1], &c__1, &z__1, &
899 x21[i__ + (i__ + 1) * x21_dim1], ldx21, &work[ilarf]);
903 /* Reduce the bottom-right portion of X21 to the identity matrix */
906 for (i__ = *p + 1; i__ <= i__1; ++i__) {
907 i__2 = *m - *p - i__ + 1;
908 zlarfgp_(&i__2, &x21[i__ + i__ * x21_dim1], &x21[i__ + 1 + i__ *
909 x21_dim1], &c__1, &taup2[i__]);
910 i__2 = i__ + i__ * x21_dim1;
911 x21[i__2].r = 1., x21[i__2].i = 0.;
912 i__2 = *m - *p - i__ + 1;
914 d_cnjg(&z__1, &taup2[i__]);
915 zlarf_("L", &i__2, &i__3, &x21[i__ + i__ * x21_dim1], &c__1, &z__1, &
916 x21[i__ + (i__ + 1) * x21_dim1], ldx21, &work[ilarf]);