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 doublecomplex c_b1 = {0.,0.};
516 static doublecomplex c_b2 = {1.,0.};
517 static integer c__1 = 1;
519 /* > \brief \b ZGBBRD */
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download ZGBBRD + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgbbrd.
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgbbrd.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgbbrd.
542 /* SUBROUTINE ZGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, */
543 /* LDQ, PT, LDPT, C, LDC, WORK, RWORK, INFO ) */
546 /* INTEGER INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC */
547 /* DOUBLE PRECISION D( * ), E( * ), RWORK( * ) */
548 /* COMPLEX*16 AB( LDAB, * ), C( LDC, * ), PT( LDPT, * ), */
549 /* $ Q( LDQ, * ), WORK( * ) */
552 /* > \par Purpose: */
557 /* > ZGBBRD reduces a complex general m-by-n band matrix A to real upper */
558 /* > bidiagonal form B by a unitary transformation: Q**H * A * P = B. */
560 /* > The routine computes B, and optionally forms Q or P**H, or computes */
561 /* > Q**H*C for a given matrix C. */
567 /* > \param[in] VECT */
569 /* > VECT is CHARACTER*1 */
570 /* > Specifies whether or not the matrices Q and P**H are to be */
572 /* > = 'N': do not form Q or P**H; */
573 /* > = 'Q': form Q only; */
574 /* > = 'P': form P**H only; */
575 /* > = 'B': form both. */
581 /* > The number of rows of the matrix A. M >= 0. */
587 /* > The number of columns of the matrix A. N >= 0. */
590 /* > \param[in] NCC */
592 /* > NCC is INTEGER */
593 /* > The number of columns of the matrix C. NCC >= 0. */
596 /* > \param[in] KL */
598 /* > KL is INTEGER */
599 /* > The number of subdiagonals of the matrix A. KL >= 0. */
602 /* > \param[in] KU */
604 /* > KU is INTEGER */
605 /* > The number of superdiagonals of the matrix A. KU >= 0. */
608 /* > \param[in,out] AB */
610 /* > AB is COMPLEX*16 array, dimension (LDAB,N) */
611 /* > On entry, the m-by-n band matrix A, stored in rows 1 to */
612 /* > KL+KU+1. The j-th column of A is stored in the j-th column of */
613 /* > the array AB as follows: */
614 /* > AB(ku+1+i-j,j) = A(i,j) for f2cmax(1,j-ku)<=i<=f2cmin(m,j+kl). */
615 /* > On exit, A is overwritten by values generated during the */
619 /* > \param[in] LDAB */
621 /* > LDAB is INTEGER */
622 /* > The leading dimension of the array A. LDAB >= KL+KU+1. */
625 /* > \param[out] D */
627 /* > D is DOUBLE PRECISION array, dimension (f2cmin(M,N)) */
628 /* > The diagonal elements of the bidiagonal matrix B. */
631 /* > \param[out] E */
633 /* > E is DOUBLE PRECISION array, dimension (f2cmin(M,N)-1) */
634 /* > The superdiagonal elements of the bidiagonal matrix B. */
637 /* > \param[out] Q */
639 /* > Q is COMPLEX*16 array, dimension (LDQ,M) */
640 /* > If VECT = 'Q' or 'B', the m-by-m unitary matrix Q. */
641 /* > If VECT = 'N' or 'P', the array Q is not referenced. */
644 /* > \param[in] LDQ */
646 /* > LDQ is INTEGER */
647 /* > The leading dimension of the array Q. */
648 /* > LDQ >= f2cmax(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise. */
651 /* > \param[out] PT */
653 /* > PT is COMPLEX*16 array, dimension (LDPT,N) */
654 /* > If VECT = 'P' or 'B', the n-by-n unitary matrix P'. */
655 /* > If VECT = 'N' or 'Q', the array PT is not referenced. */
658 /* > \param[in] LDPT */
660 /* > LDPT is INTEGER */
661 /* > The leading dimension of the array PT. */
662 /* > LDPT >= f2cmax(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise. */
665 /* > \param[in,out] C */
667 /* > C is COMPLEX*16 array, dimension (LDC,NCC) */
668 /* > On entry, an m-by-ncc matrix C. */
669 /* > On exit, C is overwritten by Q**H*C. */
670 /* > C is not referenced if NCC = 0. */
673 /* > \param[in] LDC */
675 /* > LDC is INTEGER */
676 /* > The leading dimension of the array C. */
677 /* > LDC >= f2cmax(1,M) if NCC > 0; LDC >= 1 if NCC = 0. */
680 /* > \param[out] WORK */
682 /* > WORK is COMPLEX*16 array, dimension (f2cmax(M,N)) */
685 /* > \param[out] RWORK */
687 /* > RWORK is DOUBLE PRECISION array, dimension (f2cmax(M,N)) */
690 /* > \param[out] INFO */
692 /* > INFO is INTEGER */
693 /* > = 0: successful exit. */
694 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
700 /* > \author Univ. of Tennessee */
701 /* > \author Univ. of California Berkeley */
702 /* > \author Univ. of Colorado Denver */
703 /* > \author NAG Ltd. */
705 /* > \date December 2016 */
707 /* > \ingroup complex16GBcomputational */
709 /* ===================================================================== */
710 /* Subroutine */ int zgbbrd_(char *vect, integer *m, integer *n, integer *ncc,
711 integer *kl, integer *ku, doublecomplex *ab, integer *ldab,
712 doublereal *d__, doublereal *e, doublecomplex *q, integer *ldq,
713 doublecomplex *pt, integer *ldpt, doublecomplex *c__, integer *ldc,
714 doublecomplex *work, doublereal *rwork, integer *info)
716 /* System generated locals */
717 integer ab_dim1, ab_offset, c_dim1, c_offset, pt_dim1, pt_offset, q_dim1,
718 q_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;
719 doublecomplex z__1, z__2, z__3;
721 /* Local variables */
724 extern /* Subroutine */ int zrot_(integer *, doublecomplex *, integer *,
725 doublecomplex *, integer *, doublereal *, doublecomplex *);
728 extern logical lsame_(char *, char *);
729 logical wantb, wantc;
730 extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
731 doublecomplex *, integer *);
735 doublecomplex ra, rb;
737 integer kk, ml, nr, mu;
739 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
741 extern /* Subroutine */ int zlaset_(char *, integer *, integer *,
742 doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlartg_(doublecomplex *, doublecomplex *, doublereal *,
743 doublecomplex *, doublecomplex *), zlargv_(integer *,
744 doublecomplex *, integer *, doublecomplex *, integer *,
745 doublereal *, integer *);
749 extern /* Subroutine */ int zlartv_(integer *, doublecomplex *, integer *,
750 doublecomplex *, integer *, doublereal *, doublecomplex *,
752 integer klm, kun, nrt, klu1;
755 /* -- LAPACK computational routine (version 3.7.0) -- */
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 the input parameters */
766 /* Parameter adjustments */
768 ab_offset = 1 + ab_dim1 * 1;
773 q_offset = 1 + q_dim1 * 1;
776 pt_offset = 1 + pt_dim1 * 1;
779 c_offset = 1 + c_dim1 * 1;
785 wantb = lsame_(vect, "B");
786 wantq = lsame_(vect, "Q") || wantb;
787 wantpt = lsame_(vect, "P") || wantb;
789 klu1 = *kl + *ku + 1;
791 if (! wantq && ! wantpt && ! lsame_(vect, "N")) {
797 } else if (*ncc < 0) {
799 } else if (*kl < 0) {
801 } else if (*ku < 0) {
803 } else if (*ldab < klu1) {
805 } else if (*ldq < 1 || wantq && *ldq < f2cmax(1,*m)) {
807 } else if (*ldpt < 1 || wantpt && *ldpt < f2cmax(1,*n)) {
809 } else if (*ldc < 1 || wantc && *ldc < f2cmax(1,*m)) {
814 xerbla_("ZGBBRD", &i__1, (ftnlen)6);
818 /* Initialize Q and P**H to the unit matrix, if needed */
821 zlaset_("Full", m, m, &c_b1, &c_b2, &q[q_offset], ldq);
824 zlaset_("Full", n, n, &c_b1, &c_b2, &pt[pt_offset], ldpt);
827 /* Quick return if possible. */
829 if (*m == 0 || *n == 0) {
833 minmn = f2cmin(*m,*n);
837 /* Reduce to upper bidiagonal form if KU > 0; if KU = 0, reduce */
838 /* first to lower bidiagonal form and then transform to upper */
849 /* Wherever possible, plane rotations are generated and applied in */
850 /* vector operations of length NR over the index set J1:J2:KLU1. */
852 /* The complex sines of the plane rotations are stored in WORK, */
853 /* and the real cosines in RWORK. */
857 klm = f2cmin(i__1,*kl);
860 kun = f2cmin(i__1,*ku);
869 for (i__ = 1; i__ <= i__1; ++i__) {
871 /* Reduce i-th column and i-th row of matrix to bidiagonal form */
876 for (kk = 1; kk <= i__2; ++kk) {
880 /* generate plane rotations to annihilate nonzero elements */
881 /* which have been created below the band */
884 zlargv_(&nr, &ab[klu1 + (j1 - klm - 1) * ab_dim1], &inca,
885 &work[j1], &kb1, &rwork[j1], &kb1);
888 /* apply plane rotations from the left */
891 for (l = 1; l <= i__3; ++l) {
892 if (j2 - klm + l - 1 > *n) {
898 zlartv_(&nrt, &ab[klu1 - l + (j1 - klm + l - 1) *
899 ab_dim1], &inca, &ab[klu1 - l + 1 + (j1 - klm
900 + l - 1) * ab_dim1], &inca, &rwork[j1], &work[
907 if (ml <= *m - i__ + 1) {
909 /* generate plane rotation to annihilate a(i+ml-1,i) */
910 /* within the band, and apply rotation from the left */
912 zlartg_(&ab[*ku + ml - 1 + i__ * ab_dim1], &ab[*ku +
913 ml + i__ * ab_dim1], &rwork[i__ + ml - 1], &
914 work[i__ + ml - 1], &ra);
915 i__3 = *ku + ml - 1 + i__ * ab_dim1;
916 ab[i__3].r = ra.r, ab[i__3].i = ra.i;
919 i__4 = *ku + ml - 2, i__5 = *n - i__;
920 i__3 = f2cmin(i__4,i__5);
923 zrot_(&i__3, &ab[*ku + ml - 2 + (i__ + 1) *
924 ab_dim1], &i__6, &ab[*ku + ml - 1 + (i__
925 + 1) * ab_dim1], &i__7, &rwork[i__ + ml -
926 1], &work[i__ + ml - 1]);
935 /* accumulate product of plane rotations in Q */
939 for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4)
941 d_cnjg(&z__1, &work[j]);
942 zrot_(m, &q[(j - 1) * q_dim1 + 1], &c__1, &q[j *
943 q_dim1 + 1], &c__1, &rwork[j], &z__1);
950 /* apply plane rotations to C */
954 for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3)
956 zrot_(ncc, &c__[j - 1 + c_dim1], ldc, &c__[j + c_dim1]
957 , ldc, &rwork[j], &work[j]);
964 /* adjust J2 to keep within the bounds of the matrix */
972 for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
974 /* create nonzero element a(j-1,j+ku) above the band */
975 /* and store it in WORK(n+1:2*n) */
979 i__7 = (j + kun) * ab_dim1 + 1;
980 z__1.r = work[i__6].r * ab[i__7].r - work[i__6].i * ab[
981 i__7].i, z__1.i = work[i__6].r * ab[i__7].i +
982 work[i__6].i * ab[i__7].r;
983 work[i__5].r = z__1.r, work[i__5].i = z__1.i;
984 i__5 = (j + kun) * ab_dim1 + 1;
986 i__7 = (j + kun) * ab_dim1 + 1;
987 z__1.r = rwork[i__6] * ab[i__7].r, z__1.i = rwork[i__6] *
989 ab[i__5].r = z__1.r, ab[i__5].i = z__1.i;
993 /* generate plane rotations to annihilate nonzero elements */
994 /* which have been generated above the band */
997 zlargv_(&nr, &ab[(j1 + kun - 1) * ab_dim1 + 1], &inca, &
998 work[j1 + kun], &kb1, &rwork[j1 + kun], &kb1);
1001 /* apply plane rotations from the right */
1004 for (l = 1; l <= i__4; ++l) {
1005 if (j2 + l - 1 > *m) {
1011 zlartv_(&nrt, &ab[l + 1 + (j1 + kun - 1) * ab_dim1], &
1012 inca, &ab[l + (j1 + kun) * ab_dim1], &inca, &
1013 rwork[j1 + kun], &work[j1 + kun], &kb1);
1018 if (ml == ml0 && mu > mu0) {
1019 if (mu <= *n - i__ + 1) {
1021 /* generate plane rotation to annihilate a(i,i+mu-1) */
1022 /* within the band, and apply rotation from the right */
1024 zlartg_(&ab[*ku - mu + 3 + (i__ + mu - 2) * ab_dim1],
1025 &ab[*ku - mu + 2 + (i__ + mu - 1) * ab_dim1],
1026 &rwork[i__ + mu - 1], &work[i__ + mu - 1], &
1028 i__4 = *ku - mu + 3 + (i__ + mu - 2) * ab_dim1;
1029 ab[i__4].r = ra.r, ab[i__4].i = ra.i;
1031 i__3 = *kl + mu - 2, i__5 = *m - i__;
1032 i__4 = f2cmin(i__3,i__5);
1033 zrot_(&i__4, &ab[*ku - mu + 4 + (i__ + mu - 2) *
1034 ab_dim1], &c__1, &ab[*ku - mu + 3 + (i__ + mu
1035 - 1) * ab_dim1], &c__1, &rwork[i__ + mu - 1],
1036 &work[i__ + mu - 1]);
1044 /* accumulate product of plane rotations in P**H */
1048 for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3)
1050 d_cnjg(&z__1, &work[j + kun]);
1051 zrot_(n, &pt[j + kun - 1 + pt_dim1], ldpt, &pt[j +
1052 kun + pt_dim1], ldpt, &rwork[j + kun], &z__1);
1059 /* adjust J2 to keep within the bounds of the matrix */
1067 for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
1069 /* create nonzero element a(j+kl+ku,j+ku-1) below the */
1070 /* band and store it in WORK(1:n) */
1074 i__7 = klu1 + (j + kun) * ab_dim1;
1075 z__1.r = work[i__6].r * ab[i__7].r - work[i__6].i * ab[
1076 i__7].i, z__1.i = work[i__6].r * ab[i__7].i +
1077 work[i__6].i * ab[i__7].r;
1078 work[i__5].r = z__1.r, work[i__5].i = z__1.i;
1079 i__5 = klu1 + (j + kun) * ab_dim1;
1081 i__7 = klu1 + (j + kun) * ab_dim1;
1082 z__1.r = rwork[i__6] * ab[i__7].r, z__1.i = rwork[i__6] *
1084 ab[i__5].r = z__1.r, ab[i__5].i = z__1.i;
1099 if (*ku == 0 && *kl > 0) {
1101 /* A has been reduced to complex lower bidiagonal form */
1103 /* Transform lower bidiagonal form to upper bidiagonal by applying */
1104 /* plane rotations from the left, overwriting superdiagonal */
1105 /* elements on subdiagonal elements */
1109 i__1 = f2cmin(i__2,*n);
1110 for (i__ = 1; i__ <= i__1; ++i__) {
1111 zlartg_(&ab[i__ * ab_dim1 + 1], &ab[i__ * ab_dim1 + 2], &rc, &rs,
1113 i__2 = i__ * ab_dim1 + 1;
1114 ab[i__2].r = ra.r, ab[i__2].i = ra.i;
1116 i__2 = i__ * ab_dim1 + 2;
1117 i__4 = (i__ + 1) * ab_dim1 + 1;
1118 z__1.r = rs.r * ab[i__4].r - rs.i * ab[i__4].i, z__1.i = rs.r
1119 * ab[i__4].i + rs.i * ab[i__4].r;
1120 ab[i__2].r = z__1.r, ab[i__2].i = z__1.i;
1121 i__2 = (i__ + 1) * ab_dim1 + 1;
1122 i__4 = (i__ + 1) * ab_dim1 + 1;
1123 z__1.r = rc * ab[i__4].r, z__1.i = rc * ab[i__4].i;
1124 ab[i__2].r = z__1.r, ab[i__2].i = z__1.i;
1128 zrot_(m, &q[i__ * q_dim1 + 1], &c__1, &q[(i__ + 1) * q_dim1 +
1129 1], &c__1, &rc, &z__1);
1132 zrot_(ncc, &c__[i__ + c_dim1], ldc, &c__[i__ + 1 + c_dim1],
1139 /* A has been reduced to complex upper bidiagonal form or is */
1142 if (*ku > 0 && *m < *n) {
1144 /* Annihilate a(m,m+1) by applying plane rotations from the */
1147 i__1 = *ku + (*m + 1) * ab_dim1;
1148 rb.r = ab[i__1].r, rb.i = ab[i__1].i;
1149 for (i__ = *m; i__ >= 1; --i__) {
1150 zlartg_(&ab[*ku + 1 + i__ * ab_dim1], &rb, &rc, &rs, &ra);
1151 i__1 = *ku + 1 + i__ * ab_dim1;
1152 ab[i__1].r = ra.r, ab[i__1].i = ra.i;
1155 z__2.r = -z__3.r, z__2.i = -z__3.i;
1156 i__1 = *ku + i__ * ab_dim1;
1157 z__1.r = z__2.r * ab[i__1].r - z__2.i * ab[i__1].i,
1158 z__1.i = z__2.r * ab[i__1].i + z__2.i * ab[i__1]
1160 rb.r = z__1.r, rb.i = z__1.i;
1161 i__1 = *ku + i__ * ab_dim1;
1162 i__2 = *ku + i__ * ab_dim1;
1163 z__1.r = rc * ab[i__2].r, z__1.i = rc * ab[i__2].i;
1164 ab[i__1].r = z__1.r, ab[i__1].i = z__1.i;
1168 zrot_(n, &pt[i__ + pt_dim1], ldpt, &pt[*m + 1 + pt_dim1],
1176 /* Make diagonal and superdiagonal elements real, storing them in D */
1179 i__1 = *ku + 1 + ab_dim1;
1180 t.r = ab[i__1].r, t.i = ab[i__1].i;
1182 for (i__ = 1; i__ <= i__1; ++i__) {
1186 z__1.r = t.r / abst, z__1.i = t.i / abst;
1187 t.r = z__1.r, t.i = z__1.i;
1192 zscal_(m, &t, &q[i__ * q_dim1 + 1], &c__1);
1196 zscal_(ncc, &z__1, &c__[i__ + c_dim1], ldc);
1199 if (*ku == 0 && *kl == 0) {
1201 i__2 = (i__ + 1) * ab_dim1 + 1;
1202 t.r = ab[i__2].r, t.i = ab[i__2].i;
1205 i__2 = i__ * ab_dim1 + 2;
1207 z__1.r = ab[i__2].r * z__2.r - ab[i__2].i * z__2.i,
1208 z__1.i = ab[i__2].r * z__2.i + ab[i__2].i *
1210 t.r = z__1.r, t.i = z__1.i;
1212 i__2 = *ku + (i__ + 1) * ab_dim1;
1214 z__1.r = ab[i__2].r * z__2.r - ab[i__2].i * z__2.i,
1215 z__1.i = ab[i__2].r * z__2.i + ab[i__2].i *
1217 t.r = z__1.r, t.i = z__1.i;
1222 z__1.r = t.r / abst, z__1.i = t.i / abst;
1223 t.r = z__1.r, t.i = z__1.i;
1228 zscal_(n, &t, &pt[i__ + 1 + pt_dim1], ldpt);
1230 i__2 = *ku + 1 + (i__ + 1) * ab_dim1;
1232 z__1.r = ab[i__2].r * z__2.r - ab[i__2].i * z__2.i, z__1.i =
1233 ab[i__2].r * z__2.i + ab[i__2].i * z__2.r;
1234 t.r = z__1.r, t.i = z__1.i;