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)
514 /* Table of constant values */
516 static integer c__9 = 9;
517 static integer c__0 = 0;
518 static doublereal c_b15 = 1.;
519 static integer c__1 = 1;
520 static doublereal c_b29 = 0.;
522 /* > \brief \b DBDSDC */
524 /* =========== DOCUMENTATION =========== */
526 /* Online html documentation available at */
527 /* http://www.netlib.org/lapack/explore-html/ */
530 /* > Download DBDSDC + dependencies */
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dbdsdc.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dbdsdc.
537 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dbdsdc.
545 /* SUBROUTINE DBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, */
546 /* WORK, IWORK, INFO ) */
548 /* CHARACTER COMPQ, UPLO */
549 /* INTEGER INFO, LDU, LDVT, N */
550 /* INTEGER IQ( * ), IWORK( * ) */
551 /* DOUBLE PRECISION D( * ), E( * ), Q( * ), U( LDU, * ), */
552 /* $ VT( LDVT, * ), WORK( * ) */
555 /* > \par Purpose: */
560 /* > DBDSDC computes the singular value decomposition (SVD) of a real */
561 /* > N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT, */
562 /* > using a divide and conquer method, where S is a diagonal matrix */
563 /* > with non-negative diagonal elements (the singular values of B), and */
564 /* > U and VT are orthogonal matrices of left and right singular vectors, */
565 /* > respectively. DBDSDC can be used to compute all singular values, */
566 /* > and optionally, singular vectors or singular vectors in compact form. */
568 /* > This code makes very mild assumptions about floating point */
569 /* > arithmetic. It will work on machines with a guard digit in */
570 /* > add/subtract, or on those binary machines without guard digits */
571 /* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */
572 /* > It could conceivably fail on hexadecimal or decimal machines */
573 /* > without guard digits, but we know of none. See DLASD3 for details. */
575 /* > The code currently calls DLASDQ if singular values only are desired. */
576 /* > However, it can be slightly modified to compute singular values */
577 /* > using the divide and conquer method. */
583 /* > \param[in] UPLO */
585 /* > UPLO is CHARACTER*1 */
586 /* > = 'U': B is upper bidiagonal. */
587 /* > = 'L': B is lower bidiagonal. */
590 /* > \param[in] COMPQ */
592 /* > COMPQ is CHARACTER*1 */
593 /* > Specifies whether singular vectors are to be computed */
595 /* > = 'N': Compute singular values only; */
596 /* > = 'P': Compute singular values and compute singular */
597 /* > vectors in compact form; */
598 /* > = 'I': Compute singular values and singular vectors. */
604 /* > The order of the matrix B. N >= 0. */
607 /* > \param[in,out] D */
609 /* > D is DOUBLE PRECISION array, dimension (N) */
610 /* > On entry, the n diagonal elements of the bidiagonal matrix B. */
611 /* > On exit, if INFO=0, the singular values of B. */
614 /* > \param[in,out] E */
616 /* > E is DOUBLE PRECISION array, dimension (N-1) */
617 /* > On entry, the elements of E contain the offdiagonal */
618 /* > elements of the bidiagonal matrix whose SVD is desired. */
619 /* > On exit, E has been destroyed. */
622 /* > \param[out] U */
624 /* > U is DOUBLE PRECISION array, dimension (LDU,N) */
625 /* > If COMPQ = 'I', then: */
626 /* > On exit, if INFO = 0, U contains the left singular vectors */
627 /* > of the bidiagonal matrix. */
628 /* > For other values of COMPQ, U is not referenced. */
631 /* > \param[in] LDU */
633 /* > LDU is INTEGER */
634 /* > The leading dimension of the array U. LDU >= 1. */
635 /* > If singular vectors are desired, then LDU >= f2cmax( 1, N ). */
638 /* > \param[out] VT */
640 /* > VT is DOUBLE PRECISION array, dimension (LDVT,N) */
641 /* > If COMPQ = 'I', then: */
642 /* > On exit, if INFO = 0, VT**T contains the right singular */
643 /* > vectors of the bidiagonal matrix. */
644 /* > For other values of COMPQ, VT is not referenced. */
647 /* > \param[in] LDVT */
649 /* > LDVT is INTEGER */
650 /* > The leading dimension of the array VT. LDVT >= 1. */
651 /* > If singular vectors are desired, then LDVT >= f2cmax( 1, N ). */
654 /* > \param[out] Q */
656 /* > Q is DOUBLE PRECISION array, dimension (LDQ) */
657 /* > If COMPQ = 'P', then: */
658 /* > On exit, if INFO = 0, Q and IQ contain the left */
659 /* > and right singular vectors in a compact form, */
660 /* > requiring O(N log N) space instead of 2*N**2. */
661 /* > In particular, Q contains all the DOUBLE PRECISION data in */
662 /* > LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1)))) */
663 /* > words of memory, where SMLSIZ is returned by ILAENV and */
664 /* > is equal to the maximum size of the subproblems at the */
665 /* > bottom of the computation tree (usually about 25). */
666 /* > For other values of COMPQ, Q is not referenced. */
669 /* > \param[out] IQ */
671 /* > IQ is INTEGER array, dimension (LDIQ) */
672 /* > If COMPQ = 'P', then: */
673 /* > On exit, if INFO = 0, Q and IQ contain the left */
674 /* > and right singular vectors in a compact form, */
675 /* > requiring O(N log N) space instead of 2*N**2. */
676 /* > In particular, IQ contains all INTEGER data in */
677 /* > LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1)))) */
678 /* > words of memory, where SMLSIZ is returned by ILAENV and */
679 /* > is equal to the maximum size of the subproblems at the */
680 /* > bottom of the computation tree (usually about 25). */
681 /* > For other values of COMPQ, IQ is not referenced. */
684 /* > \param[out] WORK */
686 /* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
687 /* > If COMPQ = 'N' then LWORK >= (4 * N). */
688 /* > If COMPQ = 'P' then LWORK >= (6 * N). */
689 /* > If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N). */
692 /* > \param[out] IWORK */
694 /* > IWORK is INTEGER array, dimension (8*N) */
697 /* > \param[out] INFO */
699 /* > INFO is INTEGER */
700 /* > = 0: successful exit. */
701 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
702 /* > > 0: The algorithm failed to compute a singular value. */
703 /* > The update process of divide and conquer failed. */
709 /* > \author Univ. of Tennessee */
710 /* > \author Univ. of California Berkeley */
711 /* > \author Univ. of Colorado Denver */
712 /* > \author NAG Ltd. */
714 /* > \date June 2016 */
716 /* > \ingroup auxOTHERcomputational */
718 /* > \par Contributors: */
719 /* ================== */
721 /* > Ming Gu and Huan Ren, Computer Science Division, University of */
722 /* > California at Berkeley, USA */
724 /* ===================================================================== */
725 /* Subroutine */ int dbdsdc_(char *uplo, char *compq, integer *n, doublereal *
726 d__, doublereal *e, doublereal *u, integer *ldu, doublereal *vt,
727 integer *ldvt, doublereal *q, integer *iq, doublereal *work, integer *
728 iwork, integer *info)
730 /* System generated locals */
731 integer u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2;
734 /* Local variables */
735 integer difl, difr, ierr, perm, mlvl, sqre, i__, j, k;
738 extern logical lsame_(char *, char *);
739 extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *,
740 integer *, doublereal *, doublereal *, doublereal *, integer *), dcopy_(integer *, doublereal *, integer *
741 , doublereal *, integer *), dswap_(integer *, doublereal *,
742 integer *, doublereal *, integer *);
743 integer poles, iuplo, nsize, start;
744 extern /* Subroutine */ int dlasd0_(integer *, integer *, doublereal *,
745 doublereal *, doublereal *, integer *, doublereal *, integer *,
746 integer *, integer *, doublereal *, integer *);
749 extern doublereal dlamch_(char *);
750 extern /* Subroutine */ int dlasda_(integer *, integer *, integer *,
751 integer *, doublereal *, doublereal *, doublereal *, integer *,
752 doublereal *, integer *, doublereal *, doublereal *, doublereal *,
753 doublereal *, integer *, integer *, integer *, integer *,
754 doublereal *, doublereal *, doublereal *, doublereal *, integer *,
758 extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
759 doublereal *, doublereal *, integer *, integer *, doublereal *,
760 integer *, integer *), dlasdq_(char *, integer *, integer
761 *, integer *, integer *, integer *, doublereal *, doublereal *,
762 doublereal *, integer *, doublereal *, integer *, doublereal *,
763 integer *, doublereal *, integer *), dlaset_(char *,
764 integer *, integer *, doublereal *, doublereal *, doublereal *,
765 integer *), dlartg_(doublereal *, doublereal *,
766 doublereal *, doublereal *, doublereal *);
767 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
768 integer *, integer *, ftnlen, ftnlen);
769 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
771 extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
774 integer givnum, givptr, nm1, qstart, smlsiz, wstart, smlszp;
779 /* -- LAPACK computational routine (version 3.7.1) -- */
780 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
781 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
785 /* ===================================================================== */
786 /* Changed dimension statement in comment describing E from (N) to */
787 /* (N-1). Sven, 17 Feb 05. */
788 /* ===================================================================== */
791 /* Test the input parameters. */
793 /* Parameter adjustments */
797 u_offset = 1 + u_dim1 * 1;
800 vt_offset = 1 + vt_dim1 * 1;
811 if (lsame_(uplo, "U")) {
814 if (lsame_(uplo, "L")) {
817 if (lsame_(compq, "N")) {
819 } else if (lsame_(compq, "P")) {
821 } else if (lsame_(compq, "I")) {
828 } else if (icompq < 0) {
832 } else if (*ldu < 1 || icompq == 2 && *ldu < *n) {
834 } else if (*ldvt < 1 || icompq == 2 && *ldvt < *n) {
839 xerbla_("DBDSDC", &i__1, (ftnlen)6);
843 /* Quick return if possible */
848 smlsiz = ilaenv_(&c__9, "DBDSDC", " ", &c__0, &c__0, &c__0, &c__0, (
849 ftnlen)6, (ftnlen)1);
852 q[1] = d_sign(&c_b15, &d__[1]);
853 q[smlsiz * *n + 1] = 1.;
854 } else if (icompq == 2) {
855 u[u_dim1 + 1] = d_sign(&c_b15, &d__[1]);
856 vt[vt_dim1 + 1] = 1.;
858 d__[1] = abs(d__[1]);
863 /* If matrix lower bidiagonal, rotate to be upper bidiagonal */
864 /* by applying Givens rotations on the left */
869 dcopy_(n, &d__[1], &c__1, &q[1], &c__1);
871 dcopy_(&i__1, &e[1], &c__1, &q[*n + 1], &c__1);
876 wstart = (*n << 1) - 1;
879 for (i__ = 1; i__ <= i__1; ++i__) {
880 dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
882 e[i__] = sn * d__[i__ + 1];
883 d__[i__ + 1] = cs * d__[i__ + 1];
885 q[i__ + (*n << 1)] = cs;
886 q[i__ + *n * 3] = sn;
887 } else if (icompq == 2) {
889 work[nm1 + i__] = -sn;
895 /* If ICOMPQ = 0, use DLASDQ to compute the singular values. */
898 /* Ignore WSTART, instead using WORK( 1 ), since the two vectors */
899 /* for CS and -SN above are added only if ICOMPQ == 2, */
900 /* and adding them exceeds documented WORK size of 4*n. */
901 dlasdq_("U", &c__0, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[
902 vt_offset], ldvt, &u[u_offset], ldu, &u[u_offset], ldu, &work[
907 /* If N is smaller than the minimum divide size SMLSIZ, then solve */
908 /* the problem with another solver. */
912 dlaset_("A", n, n, &c_b29, &c_b15, &u[u_offset], ldu);
913 dlaset_("A", n, n, &c_b29, &c_b15, &vt[vt_offset], ldvt);
914 dlasdq_("U", &c__0, n, n, n, &c__0, &d__[1], &e[1], &vt[vt_offset]
915 , ldvt, &u[u_offset], ldu, &u[u_offset], ldu, &work[
917 } else if (icompq == 1) {
920 dlaset_("A", n, n, &c_b29, &c_b15, &q[iu + (qstart - 1) * *n], n);
921 dlaset_("A", n, n, &c_b29, &c_b15, &q[ivt + (qstart - 1) * *n], n);
922 dlasdq_("U", &c__0, n, n, n, &c__0, &d__[1], &e[1], &q[ivt + (
923 qstart - 1) * *n], n, &q[iu + (qstart - 1) * *n], n, &q[
924 iu + (qstart - 1) * *n], n, &work[wstart], info);
930 dlaset_("A", n, n, &c_b29, &c_b15, &u[u_offset], ldu);
931 dlaset_("A", n, n, &c_b29, &c_b15, &vt[vt_offset], ldvt);
936 orgnrm = dlanst_("M", n, &d__[1], &e[1]);
940 dlascl_("G", &c__0, &c__0, &orgnrm, &c_b15, n, &c__1, &d__[1], n, &ierr);
941 dlascl_("G", &c__0, &c__0, &orgnrm, &c_b15, &nm1, &c__1, &e[1], &nm1, &
944 eps = dlamch_("Epsilon") * .9;
946 mlvl = (integer) (log((doublereal) (*n) / (doublereal) (smlsiz + 1)) /
955 z__ = difr + (mlvl << 1);
959 givnum = poles + (mlvl << 1);
964 givcol = perm + mlvl;
968 for (i__ = 1; i__ <= i__1; ++i__) {
969 if ((d__1 = d__[i__], abs(d__1)) < eps) {
970 d__[i__] = d_sign(&eps, &d__[i__]);
979 for (i__ = 1; i__ <= i__1; ++i__) {
980 if ((d__1 = e[i__], abs(d__1)) < eps || i__ == nm1) {
982 /* Subproblem found. First determine its size and then */
983 /* apply divide and conquer on it. */
987 /* A subproblem with E(I) small for I < NM1. */
989 nsize = i__ - start + 1;
990 } else if ((d__1 = e[i__], abs(d__1)) >= eps) {
992 /* A subproblem with E(NM1) not too small but I = NM1. */
994 nsize = *n - start + 1;
997 /* A subproblem with E(NM1) small. This implies an */
998 /* 1-by-1 subproblem at D(N). Solve this 1-by-1 problem */
1001 nsize = i__ - start + 1;
1003 u[*n + *n * u_dim1] = d_sign(&c_b15, &d__[*n]);
1004 vt[*n + *n * vt_dim1] = 1.;
1005 } else if (icompq == 1) {
1006 q[*n + (qstart - 1) * *n] = d_sign(&c_b15, &d__[*n]);
1007 q[*n + (smlsiz + qstart - 1) * *n] = 1.;
1009 d__[*n] = (d__1 = d__[*n], abs(d__1));
1012 dlasd0_(&nsize, &sqre, &d__[start], &e[start], &u[start +
1013 start * u_dim1], ldu, &vt[start + start * vt_dim1],
1014 ldvt, &smlsiz, &iwork[1], &work[wstart], info);
1016 dlasda_(&icompq, &smlsiz, &nsize, &sqre, &d__[start], &e[
1017 start], &q[start + (iu + qstart - 2) * *n], n, &q[
1018 start + (ivt + qstart - 2) * *n], &iq[start + k * *n],
1019 &q[start + (difl + qstart - 2) * *n], &q[start + (
1020 difr + qstart - 2) * *n], &q[start + (z__ + qstart -
1021 2) * *n], &q[start + (poles + qstart - 2) * *n], &iq[
1022 start + givptr * *n], &iq[start + givcol * *n], n, &
1023 iq[start + perm * *n], &q[start + (givnum + qstart -
1024 2) * *n], &q[start + (ic + qstart - 2) * *n], &q[
1025 start + (is + qstart - 2) * *n], &work[wstart], &
1038 dlascl_("G", &c__0, &c__0, &c_b15, &orgnrm, n, &c__1, &d__[1], n, &ierr);
1041 /* Use Selection Sort to minimize swaps of singular vectors */
1044 for (ii = 2; ii <= i__1; ++ii) {
1049 for (j = ii; j <= i__2; ++j) {
1061 } else if (icompq == 2) {
1062 dswap_(n, &u[i__ * u_dim1 + 1], &c__1, &u[kk * u_dim1 + 1], &
1064 dswap_(n, &vt[i__ + vt_dim1], ldvt, &vt[kk + vt_dim1], ldvt);
1066 } else if (icompq == 1) {
1072 /* If ICOMPQ = 1, use IQ(N,1) as the indicator for UPLO */
1082 /* If B is lower bidiagonal, update U by those Givens rotations */
1083 /* which rotated B to be upper bidiagonal */
1085 if (iuplo == 2 && icompq == 2) {
1086 dlasr_("L", "V", "B", n, n, &work[1], &work[*n], &u[u_offset], ldu);