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_b7 = 1.;
517 static integer c__1 = 1;
518 static integer c_n1 = -1;
520 /* > \brief \b DLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller o
521 nes by appending a row. Used by sbdsdc. */
523 /* =========== DOCUMENTATION =========== */
525 /* Online html documentation available at */
526 /* http://www.netlib.org/lapack/explore-html/ */
529 /* > Download DLASD6 + dependencies */
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd6.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasd6.
536 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasd6.
544 /* SUBROUTINE DLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA, */
545 /* IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, */
546 /* LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, */
549 /* INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, */
551 /* DOUBLE PRECISION ALPHA, BETA, C, S */
552 /* INTEGER GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ), */
554 /* DOUBLE PRECISION D( * ), DIFL( * ), DIFR( * ), */
555 /* $ GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ), */
556 /* $ VF( * ), VL( * ), WORK( * ), Z( * ) */
559 /* > \par Purpose: */
564 /* > DLASD6 computes the SVD of an updated upper bidiagonal matrix B */
565 /* > obtained by merging two smaller ones by appending a row. This */
566 /* > routine is used only for the problem which requires all singular */
567 /* > values and optionally singular vector matrices in factored form. */
568 /* > B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */
569 /* > A related subroutine, DLASD1, handles the case in which all singular */
570 /* > values and singular vectors of the bidiagonal matrix are desired. */
572 /* > DLASD6 computes the SVD as follows: */
574 /* > ( D1(in) 0 0 0 ) */
575 /* > B = U(in) * ( Z1**T a Z2**T b ) * VT(in) */
576 /* > ( 0 0 D2(in) 0 ) */
578 /* > = U(out) * ( D(out) 0) * VT(out) */
580 /* > where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M */
581 /* > with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */
582 /* > elsewhere; and the entry b is empty if SQRE = 0. */
584 /* > The singular values of B can be computed using D1, D2, the first */
585 /* > components of all the right singular vectors of the lower block, and */
586 /* > the last components of all the right singular vectors of the upper */
587 /* > block. These components are stored and updated in VF and VL, */
588 /* > respectively, in DLASD6. Hence U and VT are not explicitly */
591 /* > The singular values are stored in D. The algorithm consists of two */
594 /* > The first stage consists of deflating the size of the problem */
595 /* > when there are multiple singular values or if there is a zero */
596 /* > in the Z vector. For each such occurrence the dimension of the */
597 /* > secular equation problem is reduced by one. This stage is */
598 /* > performed by the routine DLASD7. */
600 /* > The second stage consists of calculating the updated */
601 /* > singular values. This is done by finding the roots of the */
602 /* > secular equation via the routine DLASD4 (as called by DLASD8). */
603 /* > This routine also updates VF and VL and computes the distances */
604 /* > between the updated singular values and the old singular */
607 /* > DLASD6 is called from DLASDA. */
613 /* > \param[in] ICOMPQ */
615 /* > ICOMPQ is INTEGER */
616 /* > Specifies whether singular vectors are to be computed in */
617 /* > factored form: */
618 /* > = 0: Compute singular values only. */
619 /* > = 1: Compute singular vectors in factored form as well. */
622 /* > \param[in] NL */
624 /* > NL is INTEGER */
625 /* > The row dimension of the upper block. NL >= 1. */
628 /* > \param[in] NR */
630 /* > NR is INTEGER */
631 /* > The row dimension of the lower block. NR >= 1. */
634 /* > \param[in] SQRE */
636 /* > SQRE is INTEGER */
637 /* > = 0: the lower block is an NR-by-NR square matrix. */
638 /* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */
640 /* > The bidiagonal matrix has row dimension N = NL + NR + 1, */
641 /* > and column dimension M = N + SQRE. */
644 /* > \param[in,out] D */
646 /* > D is DOUBLE PRECISION array, dimension ( NL+NR+1 ). */
647 /* > On entry D(1:NL,1:NL) contains the singular values of the */
648 /* > upper block, and D(NL+2:N) contains the singular values */
649 /* > of the lower block. On exit D(1:N) contains the singular */
650 /* > values of the modified matrix. */
653 /* > \param[in,out] VF */
655 /* > VF is DOUBLE PRECISION array, dimension ( M ) */
656 /* > On entry, VF(1:NL+1) contains the first components of all */
657 /* > right singular vectors of the upper block; and VF(NL+2:M) */
658 /* > contains the first components of all right singular vectors */
659 /* > of the lower block. On exit, VF contains the first components */
660 /* > of all right singular vectors of the bidiagonal matrix. */
663 /* > \param[in,out] VL */
665 /* > VL is DOUBLE PRECISION array, dimension ( M ) */
666 /* > On entry, VL(1:NL+1) contains the last components of all */
667 /* > right singular vectors of the upper block; and VL(NL+2:M) */
668 /* > contains the last components of all right singular vectors of */
669 /* > the lower block. On exit, VL contains the last components of */
670 /* > all right singular vectors of the bidiagonal matrix. */
673 /* > \param[in,out] ALPHA */
675 /* > ALPHA is DOUBLE PRECISION */
676 /* > Contains the diagonal element associated with the added row. */
679 /* > \param[in,out] BETA */
681 /* > BETA is DOUBLE PRECISION */
682 /* > Contains the off-diagonal element associated with the added */
686 /* > \param[in,out] IDXQ */
688 /* > IDXQ is INTEGER array, dimension ( N ) */
689 /* > This contains the permutation which will reintegrate the */
690 /* > subproblem just solved back into sorted order, i.e. */
691 /* > D( IDXQ( I = 1, N ) ) will be in ascending order. */
694 /* > \param[out] PERM */
696 /* > PERM is INTEGER array, dimension ( N ) */
697 /* > The permutations (from deflation and sorting) to be applied */
698 /* > to each block. Not referenced if ICOMPQ = 0. */
701 /* > \param[out] GIVPTR */
703 /* > GIVPTR is INTEGER */
704 /* > The number of Givens rotations which took place in this */
705 /* > subproblem. Not referenced if ICOMPQ = 0. */
708 /* > \param[out] GIVCOL */
710 /* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */
711 /* > Each pair of numbers indicates a pair of columns to take place */
712 /* > in a Givens rotation. Not referenced if ICOMPQ = 0. */
715 /* > \param[in] LDGCOL */
717 /* > LDGCOL is INTEGER */
718 /* > leading dimension of GIVCOL, must be at least N. */
721 /* > \param[out] GIVNUM */
723 /* > GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
724 /* > Each number indicates the C or S value to be used in the */
725 /* > corresponding Givens rotation. Not referenced if ICOMPQ = 0. */
728 /* > \param[in] LDGNUM */
730 /* > LDGNUM is INTEGER */
731 /* > The leading dimension of GIVNUM and POLES, must be at least N. */
734 /* > \param[out] POLES */
736 /* > POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
737 /* > On exit, POLES(1,*) is an array containing the new singular */
738 /* > values obtained from solving the secular equation, and */
739 /* > POLES(2,*) is an array containing the poles in the secular */
740 /* > equation. Not referenced if ICOMPQ = 0. */
743 /* > \param[out] DIFL */
745 /* > DIFL is DOUBLE PRECISION array, dimension ( N ) */
746 /* > On exit, DIFL(I) is the distance between I-th updated */
747 /* > (undeflated) singular value and the I-th (undeflated) old */
748 /* > singular value. */
751 /* > \param[out] DIFR */
753 /* > DIFR is DOUBLE PRECISION array, */
754 /* > dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and */
755 /* > dimension ( K ) if ICOMPQ = 0. */
756 /* > On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not */
757 /* > defined and will not be referenced. */
759 /* > If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */
760 /* > normalizing factors for the right singular vector matrix. */
762 /* > See DLASD8 for details on DIFL and DIFR. */
765 /* > \param[out] Z */
767 /* > Z is DOUBLE PRECISION array, dimension ( M ) */
768 /* > The first elements of this array contain the components */
769 /* > of the deflation-adjusted updating row vector. */
772 /* > \param[out] K */
775 /* > Contains the dimension of the non-deflated matrix, */
776 /* > This is the order of the related secular equation. 1 <= K <=N. */
779 /* > \param[out] C */
781 /* > C is DOUBLE PRECISION */
782 /* > C contains garbage if SQRE =0 and the C-value of a Givens */
783 /* > rotation related to the right null space if SQRE = 1. */
786 /* > \param[out] S */
788 /* > S is DOUBLE PRECISION */
789 /* > S contains garbage if SQRE =0 and the S-value of a Givens */
790 /* > rotation related to the right null space if SQRE = 1. */
793 /* > \param[out] WORK */
795 /* > WORK is DOUBLE PRECISION array, dimension ( 4 * M ) */
798 /* > \param[out] IWORK */
800 /* > IWORK is INTEGER array, dimension ( 3 * N ) */
803 /* > \param[out] INFO */
805 /* > INFO is INTEGER */
806 /* > = 0: successful exit. */
807 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
808 /* > > 0: if INFO = 1, a singular value did not converge */
814 /* > \author Univ. of Tennessee */
815 /* > \author Univ. of California Berkeley */
816 /* > \author Univ. of Colorado Denver */
817 /* > \author NAG Ltd. */
819 /* > \date June 2016 */
821 /* > \ingroup OTHERauxiliary */
823 /* > \par Contributors: */
824 /* ================== */
826 /* > Ming Gu and Huan Ren, Computer Science Division, University of */
827 /* > California at Berkeley, USA */
829 /* ===================================================================== */
830 /* Subroutine */ int dlasd6_(integer *icompq, integer *nl, integer *nr,
831 integer *sqre, doublereal *d__, doublereal *vf, doublereal *vl,
832 doublereal *alpha, doublereal *beta, integer *idxq, integer *perm,
833 integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum,
834 integer *ldgnum, doublereal *poles, doublereal *difl, doublereal *
835 difr, doublereal *z__, integer *k, doublereal *c__, doublereal *s,
836 doublereal *work, integer *iwork, integer *info)
838 /* System generated locals */
839 integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset,
840 poles_dim1, poles_offset, i__1;
841 doublereal d__1, d__2;
843 /* Local variables */
844 integer idxc, idxp, ivfw, ivlw, i__, m, n;
845 extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
846 doublereal *, integer *);
848 extern /* Subroutine */ int dlasd7_(integer *, integer *, integer *,
849 integer *, integer *, doublereal *, doublereal *, doublereal *,
850 doublereal *, doublereal *, doublereal *, doublereal *,
851 doublereal *, doublereal *, doublereal *, integer *, integer *,
852 integer *, integer *, integer *, integer *, integer *, doublereal
853 *, integer *, doublereal *, doublereal *, integer *), dlasd8_(
854 integer *, integer *, doublereal *, doublereal *, doublereal *,
855 doublereal *, doublereal *, doublereal *, integer *, doublereal *,
856 doublereal *, integer *);
858 extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
859 doublereal *, doublereal *, integer *, integer *, doublereal *,
860 integer *, integer *), dlamrg_(integer *, integer *,
861 doublereal *, integer *, integer *, integer *);
863 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
868 /* -- LAPACK auxiliary routine (version 3.7.0) -- */
869 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
870 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
874 /* ===================================================================== */
877 /* Test the input parameters. */
879 /* Parameter adjustments */
885 givcol_dim1 = *ldgcol;
886 givcol_offset = 1 + givcol_dim1 * 1;
887 givcol -= givcol_offset;
888 poles_dim1 = *ldgnum;
889 poles_offset = 1 + poles_dim1 * 1;
890 poles -= poles_offset;
891 givnum_dim1 = *ldgnum;
892 givnum_offset = 1 + givnum_dim1 * 1;
893 givnum -= givnum_offset;
905 if (*icompq < 0 || *icompq > 1) {
907 } else if (*nl < 1) {
909 } else if (*nr < 1) {
911 } else if (*sqre < 0 || *sqre > 1) {
913 } else if (*ldgcol < n) {
915 } else if (*ldgnum < n) {
920 xerbla_("DLASD6", &i__1, (ftnlen)6);
924 /* The following values are for bookkeeping purposes only. They are */
925 /* integer pointers which indicate the portion of the workspace */
926 /* used by a particular array in DLASD7 and DLASD8. */
940 d__1 = abs(*alpha), d__2 = abs(*beta);
941 orgnrm = f2cmax(d__1,d__2);
944 for (i__ = 1; i__ <= i__1; ++i__) {
945 if ((d__1 = d__[i__], abs(d__1)) > orgnrm) {
946 orgnrm = (d__1 = d__[i__], abs(d__1));
950 dlascl_("G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info);
954 /* Sort and Deflate singular values. */
956 dlasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], &
957 work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], &
958 iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[
959 givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s,
962 /* Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */
964 dlasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1],
965 ldgnum, &work[isigma], &work[iw], info);
967 /* Report the possible convergence failure. */
973 /* Save the poles if ICOMPQ = 1. */
976 dcopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1);
977 dcopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1);
982 dlascl_("G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info);
984 /* Prepare the IDXQ sorting permutation. */
988 dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]);