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__0 = 0;
516 static doublereal c_b11 = 0.;
517 static doublereal c_b12 = 1.;
518 static integer c__1 = 1;
519 static integer c__2 = 2;
521 /* > \brief \b DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with d
522 iagonal d and off-diagonal e. Used by sbdsdc. */
524 /* =========== DOCUMENTATION =========== */
526 /* Online html documentation available at */
527 /* http://www.netlib.org/lapack/explore-html/ */
530 /* > Download DLASDA + dependencies */
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasda.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasda.
537 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasda.
545 /* SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, */
546 /* DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, */
547 /* PERM, GIVNUM, C, S, WORK, IWORK, INFO ) */
549 /* INTEGER ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE */
550 /* INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), */
551 /* $ K( * ), PERM( LDGCOL, * ) */
552 /* DOUBLE PRECISION C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ), */
553 /* $ E( * ), GIVNUM( LDU, * ), POLES( LDU, * ), */
554 /* $ S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ), */
558 /* > \par Purpose: */
563 /* > Using a divide and conquer approach, DLASDA computes the singular */
564 /* > value decomposition (SVD) of a real upper bidiagonal N-by-M matrix */
565 /* > B with diagonal D and offdiagonal E, where M = N + SQRE. The */
566 /* > algorithm computes the singular values in the SVD B = U * S * VT. */
567 /* > The orthogonal matrices U and VT are optionally computed in */
568 /* > compact form. */
570 /* > A related subroutine, DLASD0, computes the singular values and */
571 /* > the singular vectors in explicit form. */
577 /* > \param[in] ICOMPQ */
579 /* > ICOMPQ is INTEGER */
580 /* > Specifies whether singular vectors are to be computed */
581 /* > in compact form, as follows */
582 /* > = 0: Compute singular values only. */
583 /* > = 1: Compute singular vectors of upper bidiagonal */
584 /* > matrix in compact form. */
587 /* > \param[in] SMLSIZ */
589 /* > SMLSIZ is INTEGER */
590 /* > The maximum size of the subproblems at the bottom of the */
591 /* > computation tree. */
597 /* > The row dimension of the upper bidiagonal matrix. This is */
598 /* > also the dimension of the main diagonal array D. */
601 /* > \param[in] SQRE */
603 /* > SQRE is INTEGER */
604 /* > Specifies the column dimension of the bidiagonal matrix. */
605 /* > = 0: The bidiagonal matrix has column dimension M = N; */
606 /* > = 1: The bidiagonal matrix has column dimension M = N + 1. */
609 /* > \param[in,out] D */
611 /* > D is DOUBLE PRECISION array, dimension ( N ) */
612 /* > On entry D contains the main diagonal of the bidiagonal */
613 /* > matrix. On exit D, if INFO = 0, contains its singular values. */
618 /* > E is DOUBLE PRECISION array, dimension ( M-1 ) */
619 /* > Contains the subdiagonal entries of the bidiagonal matrix. */
620 /* > On exit, E has been destroyed. */
623 /* > \param[out] U */
625 /* > U is DOUBLE PRECISION array, */
626 /* > dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced */
627 /* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left */
628 /* > singular vector matrices of all subproblems at the bottom */
632 /* > \param[in] LDU */
634 /* > LDU is INTEGER, LDU = > N. */
635 /* > The leading dimension of arrays U, VT, DIFL, DIFR, POLES, */
636 /* > GIVNUM, and Z. */
639 /* > \param[out] VT */
641 /* > VT is DOUBLE PRECISION array, */
642 /* > dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced */
643 /* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right */
644 /* > singular vector matrices of all subproblems at the bottom */
648 /* > \param[out] K */
650 /* > K is INTEGER array, */
651 /* > dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. */
652 /* > If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th */
653 /* > secular equation on the computation tree. */
656 /* > \param[out] DIFL */
658 /* > DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ), */
659 /* > where NLVL = floor(log_2 (N/SMLSIZ))). */
662 /* > \param[out] DIFR */
664 /* > DIFR is DOUBLE PRECISION array, */
665 /* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and */
666 /* > dimension ( N ) if ICOMPQ = 0. */
667 /* > If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) */
668 /* > record distances between singular values on the I-th */
669 /* > level and singular values on the (I -1)-th level, and */
670 /* > DIFR(1:N, 2 * I ) contains the normalizing factors for */
671 /* > the right singular vector matrix. See DLASD8 for details. */
674 /* > \param[out] Z */
676 /* > Z is DOUBLE PRECISION array, */
677 /* > dimension ( LDU, NLVL ) if ICOMPQ = 1 and */
678 /* > dimension ( N ) if ICOMPQ = 0. */
679 /* > The first K elements of Z(1, I) contain the components of */
680 /* > the deflation-adjusted updating row vector for subproblems */
681 /* > on the I-th level. */
684 /* > \param[out] POLES */
686 /* > POLES is DOUBLE PRECISION array, */
687 /* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced */
688 /* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and */
689 /* > POLES(1, 2*I) contain the new and old singular values */
690 /* > involved in the secular equations on the I-th level. */
693 /* > \param[out] GIVPTR */
695 /* > GIVPTR is INTEGER array, */
696 /* > dimension ( N ) if ICOMPQ = 1, and not referenced if */
697 /* > ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records */
698 /* > the number of Givens rotations performed on the I-th */
699 /* > problem on the computation tree. */
702 /* > \param[out] GIVCOL */
704 /* > GIVCOL is INTEGER array, */
705 /* > dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not */
706 /* > referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */
707 /* > GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations */
708 /* > of Givens rotations performed on the I-th level on the */
709 /* > computation tree. */
712 /* > \param[in] LDGCOL */
714 /* > LDGCOL is INTEGER, LDGCOL = > N. */
715 /* > The leading dimension of arrays GIVCOL and PERM. */
718 /* > \param[out] PERM */
720 /* > PERM is INTEGER array, */
721 /* > dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced */
722 /* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records */
723 /* > permutations done on the I-th level of the computation tree. */
726 /* > \param[out] GIVNUM */
728 /* > GIVNUM is DOUBLE PRECISION array, */
729 /* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not */
730 /* > referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */
731 /* > GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- */
732 /* > values of Givens rotations performed on the I-th level on */
733 /* > the computation tree. */
736 /* > \param[out] C */
738 /* > C is DOUBLE PRECISION array, */
739 /* > dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. */
740 /* > If ICOMPQ = 1 and the I-th subproblem is not square, on exit, */
741 /* > C( I ) contains the C-value of a Givens rotation related to */
742 /* > the right null space of the I-th subproblem. */
745 /* > \param[out] S */
747 /* > S is DOUBLE PRECISION array, dimension ( N ) if */
748 /* > ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 */
749 /* > and the I-th subproblem is not square, on exit, S( I ) */
750 /* > contains the S-value of a Givens rotation related to */
751 /* > the right null space of the I-th subproblem. */
754 /* > \param[out] WORK */
756 /* > WORK is DOUBLE PRECISION array, dimension */
757 /* > (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). */
760 /* > \param[out] IWORK */
762 /* > IWORK is INTEGER array, dimension (7*N) */
765 /* > \param[out] INFO */
767 /* > INFO is INTEGER */
768 /* > = 0: successful exit. */
769 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
770 /* > > 0: if INFO = 1, a singular value did not converge */
776 /* > \author Univ. of Tennessee */
777 /* > \author Univ. of California Berkeley */
778 /* > \author Univ. of Colorado Denver */
779 /* > \author NAG Ltd. */
781 /* > \date June 2017 */
783 /* > \ingroup OTHERauxiliary */
785 /* > \par Contributors: */
786 /* ================== */
788 /* > Ming Gu and Huan Ren, Computer Science Division, University of */
789 /* > California at Berkeley, USA */
791 /* ===================================================================== */
792 /* Subroutine */ int dlasda_(integer *icompq, integer *smlsiz, integer *n,
793 integer *sqre, doublereal *d__, doublereal *e, doublereal *u, integer
794 *ldu, doublereal *vt, integer *k, doublereal *difl, doublereal *difr,
795 doublereal *z__, doublereal *poles, integer *givptr, integer *givcol,
796 integer *ldgcol, integer *perm, doublereal *givnum, doublereal *c__,
797 doublereal *s, doublereal *work, integer *iwork, integer *info)
799 /* System generated locals */
800 integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1,
801 difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset,
802 poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset,
803 z_dim1, z_offset, i__1, i__2;
805 /* Local variables */
807 integer idxq, nlvl, i__, j, m;
809 integer inode, ndiml, ndimr, idxqi, itemp;
810 extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
811 doublereal *, integer *);
813 extern /* Subroutine */ int dlasd6_(integer *, integer *, integer *,
814 integer *, doublereal *, doublereal *, doublereal *, doublereal *,
815 doublereal *, integer *, integer *, integer *, integer *,
816 integer *, doublereal *, integer *, doublereal *, doublereal *,
817 doublereal *, doublereal *, integer *, doublereal *, doublereal *,
818 doublereal *, integer *, integer *);
819 integer ic, nwork1, lf, nd, nwork2, ll, nl, vf, nr, vl;
820 extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer
821 *, integer *, integer *, doublereal *, doublereal *, doublereal *,
822 integer *, doublereal *, integer *, doublereal *, integer *,
823 doublereal *, integer *), dlasdt_(integer *, integer *,
824 integer *, integer *, integer *, integer *, integer *), dlaset_(
825 char *, integer *, integer *, doublereal *, doublereal *,
826 doublereal *, integer *), xerbla_(char *, integer *, ftnlen);
827 integer im1, smlszp, ncc, nlf, nrf, vfi, iwk, vli, lvl, nru, ndb1, nlp1,
831 /* -- LAPACK auxiliary routine (version 3.7.1) -- */
832 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
833 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
837 /* ===================================================================== */
840 /* Test the input parameters. */
842 /* Parameter adjustments */
846 givnum_offset = 1 + givnum_dim1 * 1;
847 givnum -= givnum_offset;
849 poles_offset = 1 + poles_dim1 * 1;
850 poles -= poles_offset;
852 z_offset = 1 + z_dim1 * 1;
855 difr_offset = 1 + difr_dim1 * 1;
858 difl_offset = 1 + difl_dim1 * 1;
861 vt_offset = 1 + vt_dim1 * 1;
864 u_offset = 1 + u_dim1 * 1;
869 perm_offset = 1 + perm_dim1 * 1;
871 givcol_dim1 = *ldgcol;
872 givcol_offset = 1 + givcol_dim1 * 1;
873 givcol -= givcol_offset;
882 if (*icompq < 0 || *icompq > 1) {
884 } else if (*smlsiz < 3) {
888 } else if (*sqre < 0 || *sqre > 1) {
890 } else if (*ldu < *n + *sqre) {
892 } else if (*ldgcol < *n) {
897 xerbla_("DLASDA", &i__1, (ftnlen)6);
903 /* If the input matrix is too small, call DLASDQ to find the SVD. */
907 dlasdq_("U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[
908 vt_offset], ldu, &u[u_offset], ldu, &u[u_offset], ldu, &
911 dlasdq_("U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset]
912 , ldu, &u[u_offset], ldu, &u[u_offset], ldu, &work[1],
918 /* Book-keeping and set up the computation tree. */
929 smlszp = *smlsiz + 1;
933 nwork2 = nwork1 + smlszp * smlszp;
935 dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr],
938 /* for the nodes on bottom level of the tree, solve */
939 /* their subproblems by DLASDQ. */
943 for (i__ = ndb1; i__ <= i__1; ++i__) {
945 /* IC : center row of each node */
946 /* NL : number of rows of left subproblem */
947 /* NR : number of rows of right subproblem */
948 /* NLF: starting row of the left subproblem */
949 /* NRF: starting row of the right subproblem */
952 ic = iwork[inode + i1];
953 nl = iwork[ndiml + i1];
955 nr = iwork[ndimr + i1];
958 idxqi = idxq + nlf - 2;
963 dlaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp);
964 dlasdq_("U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], &
965 work[nwork1], &smlszp, &work[nwork2], &nl, &work[nwork2],
966 &nl, &work[nwork2], info);
967 itemp = nwork1 + nl * smlszp;
968 dcopy_(&nlp1, &work[nwork1], &c__1, &work[vfi], &c__1);
969 dcopy_(&nlp1, &work[itemp], &c__1, &work[vli], &c__1);
971 dlaset_("A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu);
972 dlaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1],
974 dlasdq_("U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], &
975 vt[nlf + vt_dim1], ldu, &u[nlf + u_dim1], ldu, &u[nlf +
976 u_dim1], ldu, &work[nwork1], info);
977 dcopy_(&nlp1, &vt[nlf + vt_dim1], &c__1, &work[vfi], &c__1);
978 dcopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1)
985 for (j = 1; j <= i__2; ++j) {
986 iwork[idxqi + j] = j;
989 if (i__ == nd && *sqre == 0) {
999 dlaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp);
1000 dlasdq_("U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], &
1001 work[nwork1], &smlszp, &work[nwork2], &nr, &work[nwork2],
1002 &nr, &work[nwork2], info);
1003 itemp = nwork1 + (nrp1 - 1) * smlszp;
1004 dcopy_(&nrp1, &work[nwork1], &c__1, &work[vfi], &c__1);
1005 dcopy_(&nrp1, &work[itemp], &c__1, &work[vli], &c__1);
1007 dlaset_("A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu);
1008 dlaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1],
1010 dlasdq_("U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], &
1011 vt[nrf + vt_dim1], ldu, &u[nrf + u_dim1], ldu, &u[nrf +
1012 u_dim1], ldu, &work[nwork1], info);
1013 dcopy_(&nrp1, &vt[nrf + vt_dim1], &c__1, &work[vfi], &c__1);
1014 dcopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1)
1021 for (j = 1; j <= i__2; ++j) {
1022 iwork[idxqi + j] = j;
1028 /* Now conquer each subproblem bottom-up. */
1030 j = pow_ii(&c__2, &nlvl);
1031 for (lvl = nlvl; lvl >= 1; --lvl) {
1032 lvl2 = (lvl << 1) - 1;
1034 /* Find the first node LF and last node LL on */
1035 /* the current level LVL. */
1042 lf = pow_ii(&c__2, &i__1);
1046 for (i__ = lf; i__ <= i__1; ++i__) {
1048 ic = iwork[inode + im1];
1049 nl = iwork[ndiml + im1];
1050 nr = iwork[ndimr + im1];
1060 idxqi = idxq + nlf - 1;
1064 dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &
1065 work[vli], &alpha, &beta, &iwork[idxqi], &perm[
1066 perm_offset], &givptr[1], &givcol[givcol_offset],
1067 ldgcol, &givnum[givnum_offset], ldu, &poles[
1068 poles_offset], &difl[difl_offset], &difr[difr_offset],
1069 &z__[z_offset], &k[1], &c__[1], &s[1], &work[nwork1],
1073 dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &
1074 work[vli], &alpha, &beta, &iwork[idxqi], &perm[nlf +
1075 lvl * perm_dim1], &givptr[j], &givcol[nlf + lvl2 *
1076 givcol_dim1], ldgcol, &givnum[nlf + lvl2 *
1077 givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], &
1078 difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 *
1079 difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[j],
1080 &s[j], &work[nwork1], &iwork[iwk], info);