14 typedef long long BLASLONG;
15 typedef unsigned long long BLASULONG;
17 typedef long BLASLONG;
18 typedef unsigned long BLASULONG;
22 typedef BLASLONG blasint;
24 #define blasabs(x) llabs(x)
26 #define blasabs(x) labs(x)
30 #define blasabs(x) abs(x)
33 typedef blasint integer;
35 typedef unsigned int uinteger;
36 typedef char *address;
37 typedef short int shortint;
39 typedef double doublereal;
40 typedef struct { real r, i; } complex;
41 typedef struct { doublereal r, i; } doublecomplex;
43 static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
44 static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
45 static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
46 static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
48 static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
49 static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
50 static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
51 static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
53 #define pCf(z) (*_pCf(z))
54 #define pCd(z) (*_pCd(z))
56 typedef short int shortlogical;
57 typedef char logical1;
58 typedef char integer1;
63 /* Extern is for use with -E */
74 /*external read, write*/
83 /*internal read, write*/
113 /*rewind, backspace, endfile*/
125 ftnint *inex; /*parameters in standard's order*/
151 union Multitype { /* for multiple entry points */
162 typedef union Multitype Multitype;
164 struct Vardesc { /* for Namelist */
170 typedef struct Vardesc Vardesc;
177 typedef struct Namelist Namelist;
179 #define abs(x) ((x) >= 0 ? (x) : -(x))
180 #define dabs(x) (fabs(x))
181 #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
182 #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
183 #define dmin(a,b) (f2cmin(a,b))
184 #define dmax(a,b) (f2cmax(a,b))
185 #define bit_test(a,b) ((a) >> (b) & 1)
186 #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
187 #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
189 #define abort_() { sig_die("Fortran abort routine called", 1); }
190 #define c_abs(z) (cabsf(Cf(z)))
191 #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
193 #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
194 #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
196 #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
197 #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
199 #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
200 #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
201 #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
202 //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
203 #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
204 #define d_abs(x) (fabs(*(x)))
205 #define d_acos(x) (acos(*(x)))
206 #define d_asin(x) (asin(*(x)))
207 #define d_atan(x) (atan(*(x)))
208 #define d_atn2(x, y) (atan2(*(x),*(y)))
209 #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
210 #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
211 #define d_cos(x) (cos(*(x)))
212 #define d_cosh(x) (cosh(*(x)))
213 #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
214 #define d_exp(x) (exp(*(x)))
215 #define d_imag(z) (cimag(Cd(z)))
216 #define r_imag(z) (cimagf(Cf(z)))
217 #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
218 #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
219 #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
220 #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
221 #define d_log(x) (log(*(x)))
222 #define d_mod(x, y) (fmod(*(x), *(y)))
223 #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
224 #define d_nint(x) u_nint(*(x))
225 #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
226 #define d_sign(a,b) u_sign(*(a),*(b))
227 #define r_sign(a,b) u_sign(*(a),*(b))
228 #define d_sin(x) (sin(*(x)))
229 #define d_sinh(x) (sinh(*(x)))
230 #define d_sqrt(x) (sqrt(*(x)))
231 #define d_tan(x) (tan(*(x)))
232 #define d_tanh(x) (tanh(*(x)))
233 #define i_abs(x) abs(*(x))
234 #define i_dnnt(x) ((integer)u_nint(*(x)))
235 #define i_len(s, n) (n)
236 #define i_nint(x) ((integer)u_nint(*(x)))
237 #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
238 #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
239 #define pow_si(B,E) spow_ui(*(B),*(E))
240 #define pow_ri(B,E) spow_ui(*(B),*(E))
241 #define pow_di(B,E) dpow_ui(*(B),*(E))
242 #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
243 #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
244 #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
245 #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
246 #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
247 #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
248 #define sig_die(s, kill) { exit(1); }
249 #define s_stop(s, n) {exit(0);}
250 static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
251 #define z_abs(z) (cabs(Cd(z)))
252 #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
253 #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
254 #define myexit_() break;
255 #define mycycle() continue;
256 #define myceiling(w) {ceil(w)}
257 #define myhuge(w) {HUGE_VAL}
258 //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
259 #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
261 /* procedure parameter types for -A and -C++ */
263 #define F2C_proc_par_types 1
265 typedef logical (*L_fp)(...);
267 typedef logical (*L_fp)();
270 static float spow_ui(float x, integer n) {
271 float pow=1.0; unsigned long int u;
273 if(n < 0) n = -n, x = 1/x;
282 static double dpow_ui(double x, integer n) {
283 double pow=1.0; unsigned long int u;
285 if(n < 0) n = -n, x = 1/x;
295 static _Fcomplex cpow_ui(complex x, integer n) {
296 complex pow={1.0,0.0}; unsigned long int u;
298 if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
300 if(u & 01) pow.r *= x.r, pow.i *= x.i;
301 if(u >>= 1) x.r *= x.r, x.i *= x.i;
305 _Fcomplex p={pow.r, pow.i};
309 static _Complex float cpow_ui(_Complex float x, integer n) {
310 _Complex float pow=1.0; unsigned long int u;
312 if(n < 0) n = -n, x = 1/x;
323 static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
324 _Dcomplex pow={1.0,0.0}; unsigned long int u;
326 if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
328 if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
329 if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
333 _Dcomplex p = {pow._Val[0], pow._Val[1]};
337 static _Complex double zpow_ui(_Complex double x, integer n) {
338 _Complex double pow=1.0; unsigned long int u;
340 if(n < 0) n = -n, x = 1/x;
350 static integer pow_ii(integer x, integer n) {
351 integer pow; unsigned long int u;
353 if (n == 0 || x == 1) pow = 1;
354 else if (x != -1) pow = x == 0 ? 1/x : 0;
357 if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
367 static integer dmaxloc_(double *w, integer s, integer e, integer *n)
369 double m; integer i, mi;
370 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
371 if (w[i-1]>m) mi=i ,m=w[i-1];
374 static integer smaxloc_(float *w, integer s, integer e, integer *n)
376 float m; integer i, mi;
377 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
378 if (w[i-1]>m) mi=i ,m=w[i-1];
381 static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
382 integer n = *n_, incx = *incx_, incy = *incy_, i;
384 _Fcomplex zdotc = {0.0, 0.0};
385 if (incx == 1 && incy == 1) {
386 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
387 zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
388 zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
391 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
392 zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
393 zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
399 _Complex float zdotc = 0.0;
400 if (incx == 1 && incy == 1) {
401 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
402 zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
405 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
406 zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
412 static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
413 integer n = *n_, incx = *incx_, incy = *incy_, i;
415 _Dcomplex zdotc = {0.0, 0.0};
416 if (incx == 1 && incy == 1) {
417 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
418 zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
419 zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
422 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
423 zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
424 zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
430 _Complex double zdotc = 0.0;
431 if (incx == 1 && incy == 1) {
432 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
433 zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
436 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
437 zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
443 static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
444 integer n = *n_, incx = *incx_, incy = *incy_, i;
446 _Fcomplex zdotc = {0.0, 0.0};
447 if (incx == 1 && incy == 1) {
448 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
449 zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
450 zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
453 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
454 zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
455 zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
461 _Complex float zdotc = 0.0;
462 if (incx == 1 && incy == 1) {
463 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
464 zdotc += Cf(&x[i]) * Cf(&y[i]);
467 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
468 zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
474 static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
475 integer n = *n_, incx = *incx_, incy = *incy_, i;
477 _Dcomplex zdotc = {0.0, 0.0};
478 if (incx == 1 && incy == 1) {
479 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
480 zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
481 zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
484 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
485 zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
486 zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
492 _Complex double zdotc = 0.0;
493 if (incx == 1 && incy == 1) {
494 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
495 zdotc += Cd(&x[i]) * Cd(&y[i]);
498 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
499 zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
505 /* -- translated by f2c (version 20000121).
506 You must link the resulting object file with the libraries:
507 -lf2c -lm (in that order)
513 /* Table of constant values */
515 static integer c__1 = 1;
517 /* > \brief <b> ZGGSVD computes the singular value decomposition (SVD) for OTHER matrices</b> */
519 /* =========== DOCUMENTATION =========== */
521 /* Online html documentation available at */
522 /* http://www.netlib.org/lapack/explore-html/ */
525 /* > Download ZGGSVD + dependencies */
526 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zggsvd.
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zggsvd.
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zggsvd.
540 /* SUBROUTINE ZGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B, */
541 /* LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK, */
542 /* RWORK, IWORK, INFO ) */
544 /* CHARACTER JOBQ, JOBU, JOBV */
545 /* INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P */
546 /* INTEGER IWORK( * ) */
547 /* DOUBLE PRECISION ALPHA( * ), BETA( * ), RWORK( * ) */
548 /* COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ), */
549 /* $ U( LDU, * ), V( LDV, * ), WORK( * ) */
552 /* > \par Purpose: */
557 /* > This routine is deprecated and has been replaced by routine ZGGSVD3. */
559 /* > ZGGSVD computes the generalized singular value decomposition (GSVD) */
560 /* > of an M-by-N complex matrix A and P-by-N complex matrix B: */
562 /* > U**H*A*Q = D1*( 0 R ), V**H*B*Q = D2*( 0 R ) */
564 /* > where U, V and Q are unitary matrices. */
565 /* > Let K+L = the effective numerical rank of the */
566 /* > matrix (A**H,B**H)**H, then R is a (K+L)-by-(K+L) nonsingular upper */
567 /* > triangular matrix, D1 and D2 are M-by-(K+L) and P-by-(K+L) "diagonal" */
568 /* > matrices and of the following structures, respectively: */
570 /* > If M-K-L >= 0, */
573 /* > D1 = K ( I 0 ) */
575 /* > M-K-L ( 0 0 ) */
578 /* > D2 = L ( 0 S ) */
582 /* > ( 0 R ) = K ( 0 R11 R12 ) */
583 /* > L ( 0 0 R22 ) */
586 /* > C = diag( ALPHA(K+1), ... , ALPHA(K+L) ), */
587 /* > S = diag( BETA(K+1), ... , BETA(K+L) ), */
588 /* > C**2 + S**2 = I. */
590 /* > R is stored in A(1:K+L,N-K-L+1:N) on exit. */
592 /* > If M-K-L < 0, */
595 /* > D1 = K ( I 0 0 ) */
596 /* > M-K ( 0 C 0 ) */
599 /* > D2 = M-K ( 0 S 0 ) */
600 /* > K+L-M ( 0 0 I ) */
601 /* > P-L ( 0 0 0 ) */
603 /* > N-K-L K M-K K+L-M */
604 /* > ( 0 R ) = K ( 0 R11 R12 R13 ) */
605 /* > M-K ( 0 0 R22 R23 ) */
606 /* > K+L-M ( 0 0 0 R33 ) */
610 /* > C = diag( ALPHA(K+1), ... , ALPHA(M) ), */
611 /* > S = diag( BETA(K+1), ... , BETA(M) ), */
612 /* > C**2 + S**2 = I. */
614 /* > (R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N), and R33 is stored */
615 /* > ( 0 R22 R23 ) */
616 /* > in B(M-K+1:L,N+M-K-L+1:N) on exit. */
618 /* > The routine computes C, S, R, and optionally the unitary */
619 /* > transformation matrices U, V and Q. */
621 /* > In particular, if B is an N-by-N nonsingular matrix, then the GSVD of */
622 /* > A and B implicitly gives the SVD of A*inv(B): */
623 /* > A*inv(B) = U*(D1*inv(D2))*V**H. */
624 /* > If ( A**H,B**H)**H has orthnormal columns, then the GSVD of A and B is also */
625 /* > equal to the CS decomposition of A and B. Furthermore, the GSVD can */
626 /* > be used to derive the solution of the eigenvalue problem: */
627 /* > A**H*A x = lambda* B**H*B x. */
628 /* > In some literature, the GSVD of A and B is presented in the form */
629 /* > U**H*A*X = ( 0 D1 ), V**H*B*X = ( 0 D2 ) */
630 /* > where U and V are orthogonal and X is nonsingular, and D1 and D2 are */
631 /* > ``diagonal''. The former GSVD form can be converted to the latter */
632 /* > form by taking the nonsingular matrix X as */
634 /* > X = Q*( I 0 ) */
641 /* > \param[in] JOBU */
643 /* > JOBU is CHARACTER*1 */
644 /* > = 'U': Unitary matrix U is computed; */
645 /* > = 'N': U is not computed. */
648 /* > \param[in] JOBV */
650 /* > JOBV is CHARACTER*1 */
651 /* > = 'V': Unitary matrix V is computed; */
652 /* > = 'N': V is not computed. */
655 /* > \param[in] JOBQ */
657 /* > JOBQ is CHARACTER*1 */
658 /* > = 'Q': Unitary matrix Q is computed; */
659 /* > = 'N': Q is not computed. */
665 /* > The number of rows of the matrix A. M >= 0. */
671 /* > The number of columns of the matrices A and B. N >= 0. */
677 /* > The number of rows of the matrix B. P >= 0. */
680 /* > \param[out] K */
685 /* > \param[out] L */
689 /* > On exit, K and L specify the dimension of the subblocks */
690 /* > described in Purpose. */
691 /* > K + L = effective numerical rank of (A**H,B**H)**H. */
694 /* > \param[in,out] A */
696 /* > A is COMPLEX*16 array, dimension (LDA,N) */
697 /* > On entry, the M-by-N matrix A. */
698 /* > On exit, A contains the triangular matrix R, or part of R. */
699 /* > See Purpose for details. */
702 /* > \param[in] LDA */
704 /* > LDA is INTEGER */
705 /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
708 /* > \param[in,out] B */
710 /* > B is COMPLEX*16 array, dimension (LDB,N) */
711 /* > On entry, the P-by-N matrix B. */
712 /* > On exit, B contains part of the triangular matrix R if */
713 /* > M-K-L < 0. See Purpose for details. */
716 /* > \param[in] LDB */
718 /* > LDB is INTEGER */
719 /* > The leading dimension of the array B. LDB >= f2cmax(1,P). */
722 /* > \param[out] ALPHA */
724 /* > ALPHA is DOUBLE PRECISION array, dimension (N) */
727 /* > \param[out] BETA */
729 /* > BETA is DOUBLE PRECISION array, dimension (N) */
731 /* > On exit, ALPHA and BETA contain the generalized singular */
732 /* > value pairs of A and B; */
733 /* > ALPHA(1:K) = 1, */
734 /* > BETA(1:K) = 0, */
735 /* > and if M-K-L >= 0, */
736 /* > ALPHA(K+1:K+L) = C, */
737 /* > BETA(K+1:K+L) = S, */
738 /* > or if M-K-L < 0, */
739 /* > ALPHA(K+1:M)=C, ALPHA(M+1:K+L)=0 */
740 /* > BETA(K+1:M) =S, BETA(M+1:K+L) =1 */
742 /* > ALPHA(K+L+1:N) = 0 */
743 /* > BETA(K+L+1:N) = 0 */
746 /* > \param[out] U */
748 /* > U is COMPLEX*16 array, dimension (LDU,M) */
749 /* > If JOBU = 'U', U contains the M-by-M unitary matrix U. */
750 /* > If JOBU = 'N', U is not referenced. */
753 /* > \param[in] LDU */
755 /* > LDU is INTEGER */
756 /* > The leading dimension of the array U. LDU >= f2cmax(1,M) if */
757 /* > JOBU = 'U'; LDU >= 1 otherwise. */
760 /* > \param[out] V */
762 /* > V is COMPLEX*16 array, dimension (LDV,P) */
763 /* > If JOBV = 'V', V contains the P-by-P unitary matrix V. */
764 /* > If JOBV = 'N', V is not referenced. */
767 /* > \param[in] LDV */
769 /* > LDV is INTEGER */
770 /* > The leading dimension of the array V. LDV >= f2cmax(1,P) if */
771 /* > JOBV = 'V'; LDV >= 1 otherwise. */
774 /* > \param[out] Q */
776 /* > Q is COMPLEX*16 array, dimension (LDQ,N) */
777 /* > If JOBQ = 'Q', Q contains the N-by-N unitary matrix Q. */
778 /* > If JOBQ = 'N', Q is not referenced. */
781 /* > \param[in] LDQ */
783 /* > LDQ is INTEGER */
784 /* > The leading dimension of the array Q. LDQ >= f2cmax(1,N) if */
785 /* > JOBQ = 'Q'; LDQ >= 1 otherwise. */
788 /* > \param[out] WORK */
790 /* > WORK is COMPLEX*16 array, dimension (f2cmax(3*N,M,P)+N) */
793 /* > \param[out] RWORK */
795 /* > RWORK is DOUBLE PRECISION array, dimension (2*N) */
798 /* > \param[out] IWORK */
800 /* > IWORK is INTEGER array, dimension (N) */
801 /* > On exit, IWORK stores the sorting information. More */
802 /* > precisely, the following loop will sort ALPHA */
803 /* > for I = K+1, f2cmin(M,K+L) */
804 /* > swap ALPHA(I) and ALPHA(IWORK(I)) */
806 /* > such that ALPHA(1) >= ALPHA(2) >= ... >= ALPHA(N). */
809 /* > \param[out] INFO */
811 /* > INFO is INTEGER */
812 /* > = 0: successful exit. */
813 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
814 /* > > 0: if INFO = 1, the Jacobi-type procedure failed to */
815 /* > converge. For further details, see subroutine ZTGSJA. */
818 /* > \par Internal Parameters: */
819 /* ========================= */
822 /* > TOLA DOUBLE PRECISION */
823 /* > TOLB DOUBLE PRECISION */
824 /* > TOLA and TOLB are the thresholds to determine the effective */
825 /* > rank of (A**H,B**H)**H. Generally, they are set to */
826 /* > TOLA = MAX(M,N)*norm(A)*MAZHEPS, */
827 /* > TOLB = MAX(P,N)*norm(B)*MAZHEPS. */
828 /* > The size of TOLA and TOLB may affect the size of backward */
829 /* > errors of the decomposition. */
835 /* > \author Univ. of Tennessee */
836 /* > \author Univ. of California Berkeley */
837 /* > \author Univ. of Colorado Denver */
838 /* > \author NAG Ltd. */
840 /* > \date December 2016 */
842 /* > \ingroup complex16OTHERsing */
844 /* > \par Contributors: */
845 /* ================== */
847 /* > Ming Gu and Huan Ren, Computer Science Division, University of */
848 /* > California at Berkeley, USA */
850 /* ===================================================================== */
851 /* Subroutine */ int zggsvd_(char *jobu, char *jobv, char *jobq, integer *m,
852 integer *n, integer *p, integer *k, integer *l, doublecomplex *a,
853 integer *lda, doublecomplex *b, integer *ldb, doublereal *alpha,
854 doublereal *beta, doublecomplex *u, integer *ldu, doublecomplex *v,
855 integer *ldv, doublecomplex *q, integer *ldq, doublecomplex *work,
856 doublereal *rwork, integer *iwork, integer *info)
858 /* System generated locals */
859 integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1,
860 u_offset, v_dim1, v_offset, i__1, i__2;
862 /* Local variables */
866 doublereal tolb, unfl, temp, smax;
867 integer ncallmycycle, i__, j;
868 extern logical lsame_(char *, char *);
869 doublereal anorm, bnorm;
870 extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
871 doublereal *, integer *);
872 logical wantq, wantu, wantv;
873 extern doublereal dlamch_(char *);
874 extern /* Subroutine */ int xerbla_(char *, integer *);
875 extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
876 integer *, doublereal *);
877 extern /* Subroutine */ int ztgsja_(char *, char *, char *, integer *,
878 integer *, integer *, integer *, integer *, doublecomplex *,
879 integer *, doublecomplex *, integer *, doublereal *, doublereal *,
880 doublereal *, doublereal *, doublecomplex *, integer *,
881 doublecomplex *, integer *, doublecomplex *, integer *,
882 doublecomplex *, integer *, integer *),
883 zggsvp_(char *, char *, char *, integer *, integer *, integer *,
884 doublecomplex *, integer *, doublecomplex *, integer *,
885 doublereal *, doublereal *, integer *, integer *, doublecomplex *,
886 integer *, doublecomplex *, integer *, doublecomplex *, integer *
887 , integer *, doublereal *, doublecomplex *, doublecomplex *,
892 /* -- LAPACK driver routine (version 3.7.0) -- */
893 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
894 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
898 /* ===================================================================== */
901 /* Decode and test the input parameters */
903 /* Parameter adjustments */
905 a_offset = 1 + a_dim1 * 1;
908 b_offset = 1 + b_dim1 * 1;
913 u_offset = 1 + u_dim1 * 1;
916 v_offset = 1 + v_dim1 * 1;
919 q_offset = 1 + q_dim1 * 1;
926 wantu = lsame_(jobu, "U");
927 wantv = lsame_(jobv, "V");
928 wantq = lsame_(jobq, "Q");
931 if (! (wantu || lsame_(jobu, "N"))) {
933 } else if (! (wantv || lsame_(jobv, "N"))) {
935 } else if (! (wantq || lsame_(jobq, "N"))) {
943 } else if (*lda < f2cmax(1,*m)) {
945 } else if (*ldb < f2cmax(1,*p)) {
947 } else if (*ldu < 1 || wantu && *ldu < *m) {
949 } else if (*ldv < 1 || wantv && *ldv < *p) {
951 } else if (*ldq < 1 || wantq && *ldq < *n) {
956 xerbla_("ZGGSVD", &i__1);
960 /* Compute the Frobenius norm of matrices A and B */
962 anorm = zlange_("1", m, n, &a[a_offset], lda, &rwork[1]);
963 bnorm = zlange_("1", p, n, &b[b_offset], ldb, &rwork[1]);
965 /* Get machine precision and set up threshold for determining */
966 /* the effective numerical rank of the matrices A and B. */
968 ulp = dlamch_("Precision");
969 unfl = dlamch_("Safe Minimum");
970 tola = f2cmax(*m,*n) * f2cmax(anorm,unfl) * ulp;
971 tolb = f2cmax(*p,*n) * f2cmax(bnorm,unfl) * ulp;
973 zggsvp_(jobu, jobv, jobq, m, p, n, &a[a_offset], lda, &b[b_offset], ldb, &
974 tola, &tolb, k, l, &u[u_offset], ldu, &v[v_offset], ldv, &q[
975 q_offset], ldq, &iwork[1], &rwork[1], &work[1], &work[*n + 1],
978 /* Compute the GSVD of two upper "triangular" matrices */
980 ztgsja_(jobu, jobv, jobq, m, p, n, k, l, &a[a_offset], lda, &b[b_offset],
981 ldb, &tola, &tolb, &alpha[1], &beta[1], &u[u_offset], ldu, &v[
982 v_offset], ldv, &q[q_offset], ldq, &work[1], &ncallmycycle, info);
984 /* Sort the singular values and store the pivot indices in IWORK */
985 /* Copy ALPHA to RWORK, then sort ALPHA in RWORK */
987 dcopy_(n, &alpha[1], &c__1, &rwork[1], &c__1);
989 i__1 = *l, i__2 = *m - *k;
990 ibnd = f2cmin(i__1,i__2);
992 for (i__ = 1; i__ <= i__1; ++i__) {
994 /* Scan for largest ALPHA(K+I) */
997 smax = rwork[*k + i__];
999 for (j = i__ + 1; j <= i__2; ++j) {
1000 temp = rwork[*k + j];
1008 rwork[*k + isub] = rwork[*k + i__];
1009 rwork[*k + i__] = smax;
1010 iwork[*k + i__] = *k + isub;
1012 iwork[*k + i__] = *k + i__;