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;
516 static integer c__0 = 0;
517 static real c_b18 = 1.f;
519 /* > \brief \b CGSVJ1 pre-processor for the routine cgesvj, applies Jacobi rotations targeting only particular
522 /* =========== DOCUMENTATION =========== */
524 /* Online html documentation available at */
525 /* http://www.netlib.org/lapack/explore-html/ */
528 /* > Download CGSVJ1 + dependencies */
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgsvj1.
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgsvj1.
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgsvj1.
543 /* SUBROUTINE CGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, */
544 /* EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) */
546 /* REAL EPS, SFMIN, TOL */
547 /* INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP */
548 /* CHARACTER*1 JOBV */
549 /* COMPLEX A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK ) */
553 /* > \par Purpose: */
558 /* > CGSVJ1 is called from CGESVJ as a pre-processor and that is its main */
559 /* > purpose. It applies Jacobi rotations in the same way as CGESVJ does, but */
560 /* > it targets only particular pivots and it does not check convergence */
561 /* > (stopping criterion). Few tunning parameters (marked by [TP]) are */
562 /* > available for the implementer. */
564 /* > Further Details */
565 /* > ~~~~~~~~~~~~~~~ */
566 /* > CGSVJ1 applies few sweeps of Jacobi rotations in the column space of */
567 /* > the input M-by-N matrix A. The pivot pairs are taken from the (1,2) */
568 /* > off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The */
569 /* > block-entries (tiles) of the (1,2) off-diagonal block are marked by the */
570 /* > [x]'s in the following scheme: */
572 /* > | * * * [x] [x] [x]| */
573 /* > | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks. */
574 /* > | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block. */
575 /* > |[x] [x] [x] * * * | */
576 /* > |[x] [x] [x] * * * | */
577 /* > |[x] [x] [x] * * * | */
579 /* > In terms of the columns of A, the first N1 columns are rotated 'against' */
580 /* > the remaining N-N1 columns, trying to increase the angle between the */
581 /* > corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is */
582 /* > tiled using quadratic tiles of side KBL. Here, KBL is a tunning parameter. */
583 /* > The number of sweeps is given in NSWEEP and the orthogonality threshold */
584 /* > is given in TOL. */
590 /* > \param[in] JOBV */
592 /* > JOBV is CHARACTER*1 */
593 /* > Specifies whether the output from this procedure is used */
594 /* > to compute the matrix V: */
595 /* > = 'V': the product of the Jacobi rotations is accumulated */
596 /* > by postmulyiplying the N-by-N array V. */
597 /* > (See the description of V.) */
598 /* > = 'A': the product of the Jacobi rotations is accumulated */
599 /* > by postmulyiplying the MV-by-N array V. */
600 /* > (See the descriptions of MV and V.) */
601 /* > = 'N': the Jacobi rotations are not accumulated. */
607 /* > The number of rows of the input matrix A. M >= 0. */
613 /* > The number of columns of the input matrix A. */
617 /* > \param[in] N1 */
619 /* > N1 is INTEGER */
620 /* > N1 specifies the 2 x 2 block partition, the first N1 columns are */
621 /* > rotated 'against' the remaining N-N1 columns of A. */
624 /* > \param[in,out] A */
626 /* > A is COMPLEX array, dimension (LDA,N) */
627 /* > On entry, M-by-N matrix A, such that A*diag(D) represents */
628 /* > the input matrix. */
630 /* > A_onexit * D_onexit represents the input matrix A*diag(D) */
631 /* > post-multiplied by a sequence of Jacobi rotations, where the */
632 /* > rotation threshold and the total number of sweeps are given in */
633 /* > TOL and NSWEEP, respectively. */
634 /* > (See the descriptions of N1, D, TOL and NSWEEP.) */
637 /* > \param[in] LDA */
639 /* > LDA is INTEGER */
640 /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
643 /* > \param[in,out] D */
645 /* > D is COMPLEX array, dimension (N) */
646 /* > The array D accumulates the scaling factors from the fast scaled */
647 /* > Jacobi rotations. */
648 /* > On entry, A*diag(D) represents the input matrix. */
649 /* > On exit, A_onexit*diag(D_onexit) represents the input matrix */
650 /* > post-multiplied by a sequence of Jacobi rotations, where the */
651 /* > rotation threshold and the total number of sweeps are given in */
652 /* > TOL and NSWEEP, respectively. */
653 /* > (See the descriptions of N1, A, TOL and NSWEEP.) */
656 /* > \param[in,out] SVA */
658 /* > SVA is REAL array, dimension (N) */
659 /* > On entry, SVA contains the Euclidean norms of the columns of */
660 /* > the matrix A*diag(D). */
661 /* > On exit, SVA contains the Euclidean norms of the columns of */
662 /* > the matrix onexit*diag(D_onexit). */
665 /* > \param[in] MV */
667 /* > MV is INTEGER */
668 /* > If JOBV = 'A', then MV rows of V are post-multipled by a */
669 /* > sequence of Jacobi rotations. */
670 /* > If JOBV = 'N', then MV is not referenced. */
673 /* > \param[in,out] V */
675 /* > V is COMPLEX array, dimension (LDV,N) */
676 /* > If JOBV = 'V' then N rows of V are post-multipled by a */
677 /* > sequence of Jacobi rotations. */
678 /* > If JOBV = 'A' then MV rows of V are post-multipled by a */
679 /* > sequence of Jacobi rotations. */
680 /* > If JOBV = 'N', then V is not referenced. */
683 /* > \param[in] LDV */
685 /* > LDV is INTEGER */
686 /* > The leading dimension of the array V, LDV >= 1. */
687 /* > If JOBV = 'V', LDV >= N. */
688 /* > If JOBV = 'A', LDV >= MV. */
691 /* > \param[in] EPS */
694 /* > EPS = SLAMCH('Epsilon') */
697 /* > \param[in] SFMIN */
699 /* > SFMIN is REAL */
700 /* > SFMIN = SLAMCH('Safe Minimum') */
703 /* > \param[in] TOL */
706 /* > TOL is the threshold for Jacobi rotations. For a pair */
707 /* > A(:,p), A(:,q) of pivot columns, the Jacobi rotation is */
708 /* > applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL. */
711 /* > \param[in] NSWEEP */
713 /* > NSWEEP is INTEGER */
714 /* > NSWEEP is the number of sweeps of Jacobi rotations to be */
718 /* > \param[out] WORK */
720 /* > WORK is COMPLEX array, dimension (LWORK) */
723 /* > \param[in] LWORK */
725 /* > LWORK is INTEGER */
726 /* > LWORK is the dimension of WORK. LWORK >= M. */
729 /* > \param[out] INFO */
731 /* > INFO is INTEGER */
732 /* > = 0: successful exit. */
733 /* > < 0: if INFO = -i, then the i-th argument had an illegal value */
739 /* > \author Univ. of Tennessee */
740 /* > \author Univ. of California Berkeley */
741 /* > \author Univ. of Colorado Denver */
742 /* > \author NAG Ltd. */
744 /* > \date June 2016 */
746 /* > \ingroup complexOTHERcomputational */
748 /* > \par Contributor: */
749 /* ================== */
751 /* > Zlatko Drmac (Zagreb, Croatia) */
753 /* ===================================================================== */
754 /* Subroutine */ int cgsvj1_(char *jobv, integer *m, integer *n, integer *n1,
755 complex *a, integer *lda, complex *d__, real *sva, integer *mv,
756 complex *v, integer *ldv, real *eps, real *sfmin, real *tol, integer *
757 nsweep, complex *work, integer *lwork, integer *info)
759 /* System generated locals */
760 integer a_dim1, a_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4, i__5,
763 complex q__1, q__2, q__3;
765 /* Local variables */
772 extern /* Subroutine */ int crot_(integer *, complex *, integer *,
773 complex *, integer *, real *, complex *);
776 real aapp0, aapq1, temp1;
779 extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
780 *, complex *, integer *);
782 extern logical lsame_(char *, char *);
784 extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
785 complex *, integer *), cswap_(integer *, complex *, integer *,
786 complex *, integer *);
787 logical applv, rsvec;
788 extern /* Subroutine */ int caxpy_(integer *, complex *, complex *,
789 integer *, complex *, integer *);
792 extern real scnrm2_(integer *, complex *, integer *);
794 extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *,
795 real *, integer *, integer *, complex *, integer *, integer *), xerbla_(char *, integer *, ftnlen);
796 integer ijblsk, swband;
797 extern integer isamax_(integer *, real *, integer *);
799 extern /* Subroutine */ int classq_(integer *, complex *, integer *, real
801 real mxaapq, thsign, mxsinj;
802 integer emptsw, notrot, iswrot, jbc;
804 integer kbl, igl, ibr, jgl, mvl;
805 real rootbig, rooteps;
810 /* -- LAPACK computational routine (version 3.8.0) -- */
811 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
812 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
816 /* ===================================================================== */
819 /* Test the input parameters. */
821 /* Parameter adjustments */
825 a_offset = 1 + a_dim1 * 1;
828 v_offset = 1 + v_dim1 * 1;
833 applv = lsame_(jobv, "A");
834 rsvec = lsame_(jobv, "V");
835 if (! (rsvec || applv || lsame_(jobv, "N"))) {
839 } else if (*n < 0 || *n > *m) {
841 } else if (*n1 < 0) {
843 } else if (*lda < *m) {
845 } else if ((rsvec || applv) && *mv < 0) {
847 } else if (rsvec && *ldv < *n || applv && *ldv < *mv) {
849 } else if (*tol <= *eps) {
851 } else if (*nsweep < 0) {
853 } else if (*lwork < *m) {
862 xerbla_("CGSVJ1", &i__1, (ftnlen)6);
871 rsvec = rsvec || applv;
872 rooteps = sqrt(*eps);
873 rootsfmin = sqrt(*sfmin);
874 small = *sfmin / *eps;
876 rootbig = 1.f / rootsfmin;
877 /* LARGE = BIG / SQRT( REAL( M*N ) ) */
878 bigtheta = 1.f / rooteps;
879 roottol = sqrt(*tol);
882 /* RSVEC = LSAME( JOBV, 'Y' ) */
884 emptsw = *n1 * (*n - *n1);
890 if (nblr * kbl != *n1) {
893 nblc = (*n - *n1) / kbl;
894 if (nblc * kbl != *n - *n1) {
897 /* Computing 2nd power */
899 blskip = i__1 * i__1 + 1;
900 /* [TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. */
901 rowskip = f2cmin(5,kbl);
902 /* [TP] ROWSKIP is a tuning parameter. */
904 /* [TP] SWBAND is a tuning parameter. It is meaningful and effective */
905 /* if CGESVJ is used as a computational routine in the preconditioned */
906 /* Jacobi SVD algorithm CGEJSV. */
909 /* | * * * [x] [x] [x]| */
910 /* | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks. */
911 /* | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block. */
912 /* |[x] [x] [x] * * * | */
913 /* |[x] [x] [x] * * * | */
914 /* |[x] [x] [x] * * * | */
918 for (i__ = 1; i__ <= i__1; ++i__) {
928 /* Each sweep is unrolled using KBL-by-KBL tiles over the pivot pairs */
929 /* 1 <= p < q <= N. This is the first step toward a blocked implementation */
930 /* of the rotations. New implementation, based on block transformations, */
931 /* is under development. */
934 for (ibr = 1; ibr <= i__2; ++ibr) {
936 igl = (ibr - 1) * kbl + 1;
939 /* ... go to the off diagonal blocks */
941 igl = (ibr - 1) * kbl + 1;
943 /* DO 2010 jbc = ibr + 1, NBL */
945 for (jbc = 1; jbc <= i__3; ++jbc) {
947 jgl = (jbc - 1) * kbl + *n1 + 1;
949 /* doing the block at ( ibr, jbc ) */
953 i__5 = igl + kbl - 1;
954 i__4 = f2cmin(i__5,*n1);
955 for (p = igl; p <= i__4; ++p) {
963 i__6 = jgl + kbl - 1;
964 i__5 = f2cmin(i__6,*n);
965 for (q = jgl; q <= i__5; ++q) {
972 /* Safe Gram matrix computation */
976 rotok = small * aapp <= aaqq;
978 rotok = small * aaqq <= aapp;
980 if (aapp < big / aaqq) {
981 cdotc_(&q__3, m, &a[p * a_dim1 + 1], &
982 c__1, &a[q * a_dim1 + 1], &
984 q__2.r = q__3.r / aaqq, q__2.i =
986 q__1.r = q__2.r / aapp, q__1.i =
988 aapq.r = q__1.r, aapq.i = q__1.i;
990 ccopy_(m, &a[p * a_dim1 + 1], &c__1, &
992 clascl_("G", &c__0, &c__0, &aapp, &
993 c_b18, m, &c__1, &work[1],
995 cdotc_(&q__2, m, &work[1], &c__1, &a[
996 q * a_dim1 + 1], &c__1);
997 q__1.r = q__2.r / aaqq, q__1.i =
999 aapq.r = q__1.r, aapq.i = q__1.i;
1003 rotok = aapp <= aaqq / small;
1005 rotok = aaqq <= aapp / small;
1007 if (aapp > small / aaqq) {
1008 cdotc_(&q__3, m, &a[p * a_dim1 + 1], &
1009 c__1, &a[q * a_dim1 + 1], &
1011 r__1 = f2cmax(aaqq,aapp);
1012 q__2.r = q__3.r / r__1, q__2.i =
1014 r__2 = f2cmin(aaqq,aapp);
1015 q__1.r = q__2.r / r__2, q__1.i =
1017 aapq.r = q__1.r, aapq.i = q__1.i;
1019 ccopy_(m, &a[q * a_dim1 + 1], &c__1, &
1021 clascl_("G", &c__0, &c__0, &aaqq, &
1022 c_b18, m, &c__1, &work[1],
1024 cdotc_(&q__2, m, &a[p * a_dim1 + 1], &
1025 c__1, &work[1], &c__1);
1026 q__1.r = q__2.r / aapp, q__1.i =
1028 aapq.r = q__1.r, aapq.i = q__1.i;
1032 /* AAPQ = AAPQ * CONJG(CWORK(p))*CWORK(q) */
1033 aapq1 = -c_abs(&aapq);
1035 r__1 = mxaapq, r__2 = -aapq1;
1036 mxaapq = f2cmax(r__1,r__2);
1038 /* TO rotate or NOT to rotate, THAT is the question ... */
1040 if (abs(aapq1) > *tol) {
1041 r__1 = c_abs(&aapq);
1042 q__1.r = aapq.r / r__1, q__1.i = aapq.i /
1044 ompq.r = q__1.r, ompq.i = q__1.i;
1046 /* [RTD] ROTATED = ROTATED + 1 */
1052 aqoap = aaqq / aapp;
1053 apoaq = aapp / aaqq;
1054 theta = (r__1 = aqoap - apoaq, abs(
1055 r__1)) * -.5f / aapq1;
1060 if (abs(theta) > bigtheta) {
1063 r_cnjg(&q__2, &ompq);
1064 q__1.r = t * q__2.r, q__1.i = t *
1066 crot_(m, &a[p * a_dim1 + 1], &
1067 c__1, &a[q * a_dim1 + 1],
1070 r_cnjg(&q__2, &ompq);
1071 q__1.r = t * q__2.r, q__1.i = t * q__2.i;
1072 crot_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
1073 v_dim1 + 1], &c__1, &cs, &q__1);
1076 r__1 = 0.f, r__2 = t * apoaq *
1078 sva[q] = aaqq * sqrt((f2cmax(r__1,
1081 r__1 = 0.f, r__2 = 1.f - t *
1083 aapp *= sqrt((f2cmax(r__1,r__2)));
1085 r__1 = mxsinj, r__2 = abs(t);
1086 mxsinj = f2cmax(r__1,r__2);
1090 thsign = -r_sign(&c_b18, &aapq1);
1094 t = 1.f / (theta + thsign * sqrt(
1095 theta * theta + 1.f));
1096 cs = sqrt(1.f / (t * t + 1.f));
1099 r__1 = mxsinj, r__2 = abs(sn);
1100 mxsinj = f2cmax(r__1,r__2);
1102 r__1 = 0.f, r__2 = t * apoaq *
1104 sva[q] = aaqq * sqrt((f2cmax(r__1,
1107 r__1 = 0.f, r__2 = 1.f - t *
1109 aapp *= sqrt((f2cmax(r__1,r__2)));
1111 r_cnjg(&q__2, &ompq);
1112 q__1.r = sn * q__2.r, q__1.i = sn
1114 crot_(m, &a[p * a_dim1 + 1], &
1115 c__1, &a[q * a_dim1 + 1],
1118 r_cnjg(&q__2, &ompq);
1119 q__1.r = sn * q__2.r, q__1.i = sn * q__2.i;
1120 crot_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
1121 v_dim1 + 1], &c__1, &cs, &q__1);
1126 q__2.r = -d__[i__7].r, q__2.i = -d__[
1128 q__1.r = q__2.r * ompq.r - q__2.i *
1129 ompq.i, q__1.i = q__2.r *
1130 ompq.i + q__2.i * ompq.r;
1131 d__[i__6].r = q__1.r, d__[i__6].i =
1136 ccopy_(m, &a[p * a_dim1 + 1], &
1137 c__1, &work[1], &c__1);
1138 clascl_("G", &c__0, &c__0, &aapp,
1139 &c_b18, m, &c__1, &work[1]
1141 clascl_("G", &c__0, &c__0, &aaqq,
1142 &c_b18, m, &c__1, &a[q *
1143 a_dim1 + 1], lda, &ierr);
1144 q__1.r = -aapq.r, q__1.i =
1146 caxpy_(m, &q__1, &work[1], &c__1,
1147 &a[q * a_dim1 + 1], &c__1)
1149 clascl_("G", &c__0, &c__0, &c_b18,
1150 &aaqq, m, &c__1, &a[q *
1151 a_dim1 + 1], lda, &ierr);
1153 r__1 = 0.f, r__2 = 1.f - aapq1 *
1155 sva[q] = aaqq * sqrt((f2cmax(r__1,
1157 mxsinj = f2cmax(mxsinj,*sfmin);
1159 ccopy_(m, &a[q * a_dim1 + 1], &
1160 c__1, &work[1], &c__1);
1161 clascl_("G", &c__0, &c__0, &aaqq,
1162 &c_b18, m, &c__1, &work[1]
1164 clascl_("G", &c__0, &c__0, &aapp,
1165 &c_b18, m, &c__1, &a[p *
1166 a_dim1 + 1], lda, &ierr);
1167 r_cnjg(&q__2, &aapq);
1168 q__1.r = -q__2.r, q__1.i =
1170 caxpy_(m, &q__1, &work[1], &c__1,
1171 &a[p * a_dim1 + 1], &c__1)
1173 clascl_("G", &c__0, &c__0, &c_b18,
1174 &aapp, m, &c__1, &a[p *
1175 a_dim1 + 1], lda, &ierr);
1177 r__1 = 0.f, r__2 = 1.f - aapq1 *
1179 sva[p] = aapp * sqrt((f2cmax(r__1,
1181 mxsinj = f2cmax(mxsinj,*sfmin);
1184 /* END IF ROTOK THEN ... ELSE */
1186 /* In the case of cancellation in updating SVA(q), SVA(p) */
1187 /* Computing 2nd power */
1188 r__1 = sva[q] / aaqq;
1189 if (r__1 * r__1 <= rooteps) {
1190 if (aaqq < rootbig && aaqq >
1192 sva[q] = scnrm2_(m, &a[q * a_dim1
1197 classq_(m, &a[q * a_dim1 + 1], &
1199 sva[q] = t * sqrt(aaqq);
1202 /* Computing 2nd power */
1203 r__1 = aapp / aapp0;
1204 if (r__1 * r__1 <= rooteps) {
1205 if (aapp < rootbig && aapp >
1207 aapp = scnrm2_(m, &a[p * a_dim1 +
1212 classq_(m, &a[p * a_dim1 + 1], &
1214 aapp = t * sqrt(aapp);
1218 /* end of OK rotation */
1221 /* [RTD] SKIPPED = SKIPPED + 1 */
1231 if (i__ <= swband && ijblsk >= blskip) {
1236 if (i__ <= swband && pskipped > rowskip) {
1244 /* end of the q-loop */
1253 i__5 = jgl + kbl - 1;
1254 notrot = notrot + f2cmin(i__5,*n) - jgl + 1;
1264 /* end of the p-loop */
1267 /* end of the jbc-loop */
1269 /* 2011 bailed out of the jbc-loop */
1271 i__4 = igl + kbl - 1;
1272 i__3 = f2cmin(i__4,*n);
1273 for (p = igl; p <= i__3; ++p) {
1274 sva[p] = (r__1 = sva[p], abs(r__1));
1280 /* 2000 :: end of the ibr-loop */
1282 if (sva[*n] < rootbig && sva[*n] > rootsfmin) {
1283 sva[*n] = scnrm2_(m, &a[*n * a_dim1 + 1], &c__1);
1287 classq_(m, &a[*n * a_dim1 + 1], &c__1, &t, &aapp);
1288 sva[*n] = t * sqrt(aapp);
1291 /* Additional steering devices */
1293 if (i__ < swband && (mxaapq <= roottol || iswrot <= *n)) {
1297 if (i__ > swband + 1 && mxaapq < sqrt((real) (*n)) * *tol && (real) (*
1298 n) * mxaapq * mxsinj < *tol) {
1302 if (notrot >= emptsw) {
1308 /* end i=1:NSWEEP loop */
1310 /* #:( Reaching this point means that the procedure has not converged. */
1311 *info = *nsweep - 1;
1315 /* #:) Reaching this point means numerical convergence after the i-th */
1319 /* #:) INFO = 0 confirms successful iterations. */
1322 /* Sort the vector SVA() of column norms. */
1324 for (p = 1; p <= i__1; ++p) {
1326 q = isamax_(&i__2, &sva[p], &c__1) + p - 1;
1332 aapq.r = d__[i__2].r, aapq.i = d__[i__2].i;
1335 d__[i__2].r = d__[i__3].r, d__[i__2].i = d__[i__3].i;
1337 d__[i__2].r = aapq.r, d__[i__2].i = aapq.i;
1338 cswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1);
1340 cswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], &