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)
512 /* Table of constant values */
514 static doublereal c_b5 = -1.;
515 static integer c__1 = 1;
516 static doublereal c_b11 = 1.;
517 static doublereal c_b13 = 0.;
518 static integer c__0 = 0;
520 /* > \brief \b DLALS0 applies back multiplying factors in solving the least squares problem using divide and c
521 onquer SVD approach. Used by sgelsd. */
523 /* =========== DOCUMENTATION =========== */
525 /* Online html documentation available at */
526 /* http://www.netlib.org/lapack/explore-html/ */
529 /* > Download DLALS0 + dependencies */
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlals0.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlals0.
536 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlals0.
544 /* SUBROUTINE DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, */
545 /* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, */
546 /* POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO ) */
548 /* INTEGER GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, */
549 /* $ LDGNUM, NL, NR, NRHS, SQRE */
550 /* DOUBLE PRECISION C, S */
551 /* INTEGER GIVCOL( LDGCOL, * ), PERM( * ) */
552 /* DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), DIFL( * ), */
553 /* $ DIFR( LDGNUM, * ), GIVNUM( LDGNUM, * ), */
554 /* $ POLES( LDGNUM, * ), WORK( * ), Z( * ) */
557 /* > \par Purpose: */
562 /* > DLALS0 applies back the multiplying factors of either the left or the */
563 /* > right singular vector matrix of a diagonal matrix appended by a row */
564 /* > to the right hand side matrix B in solving the least squares problem */
565 /* > using the divide-and-conquer SVD approach. */
567 /* > For the left singular vector matrix, three types of orthogonal */
568 /* > matrices are involved: */
570 /* > (1L) Givens rotations: the number of such rotations is GIVPTR; the */
571 /* > pairs of columns/rows they were applied to are stored in GIVCOL; */
572 /* > and the C- and S-values of these rotations are stored in GIVNUM. */
574 /* > (2L) Permutation. The (NL+1)-st row of B is to be moved to the first */
575 /* > row, and for J=2:N, PERM(J)-th row of B is to be moved to the */
578 /* > (3L) The left singular vector matrix of the remaining matrix. */
580 /* > For the right singular vector matrix, four types of orthogonal */
581 /* > matrices are involved: */
583 /* > (1R) The right singular vector matrix of the remaining matrix. */
585 /* > (2R) If SQRE = 1, one extra Givens rotation to generate the right */
588 /* > (3R) The inverse transformation of (2L). */
590 /* > (4R) The inverse transformation of (1L). */
596 /* > \param[in] ICOMPQ */
598 /* > ICOMPQ is INTEGER */
599 /* > Specifies whether singular vectors are to be computed in */
600 /* > factored form: */
601 /* > = 0: Left singular vector matrix. */
602 /* > = 1: Right singular vector matrix. */
605 /* > \param[in] NL */
607 /* > NL is INTEGER */
608 /* > The row dimension of the upper block. NL >= 1. */
611 /* > \param[in] NR */
613 /* > NR is INTEGER */
614 /* > The row dimension of the lower block. NR >= 1. */
617 /* > \param[in] SQRE */
619 /* > SQRE is INTEGER */
620 /* > = 0: the lower block is an NR-by-NR square matrix. */
621 /* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */
623 /* > The bidiagonal matrix has row dimension N = NL + NR + 1, */
624 /* > and column dimension M = N + SQRE. */
627 /* > \param[in] NRHS */
629 /* > NRHS is INTEGER */
630 /* > The number of columns of B and BX. NRHS must be at least 1. */
633 /* > \param[in,out] B */
635 /* > B is DOUBLE PRECISION array, dimension ( LDB, NRHS ) */
636 /* > On input, B contains the right hand sides of the least */
637 /* > squares problem in rows 1 through M. On output, B contains */
638 /* > the solution X in rows 1 through N. */
641 /* > \param[in] LDB */
643 /* > LDB is INTEGER */
644 /* > The leading dimension of B. LDB must be at least */
645 /* > f2cmax(1,MAX( M, N ) ). */
648 /* > \param[out] BX */
650 /* > BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ) */
653 /* > \param[in] LDBX */
655 /* > LDBX is INTEGER */
656 /* > The leading dimension of BX. */
659 /* > \param[in] PERM */
661 /* > PERM is INTEGER array, dimension ( N ) */
662 /* > The permutations (from deflation and sorting) applied */
663 /* > to the two blocks. */
666 /* > \param[in] GIVPTR */
668 /* > GIVPTR is INTEGER */
669 /* > The number of Givens rotations which took place in this */
673 /* > \param[in] GIVCOL */
675 /* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */
676 /* > Each pair of numbers indicates a pair of rows/columns */
677 /* > involved in a Givens rotation. */
680 /* > \param[in] LDGCOL */
682 /* > LDGCOL is INTEGER */
683 /* > The leading dimension of GIVCOL, must be at least N. */
686 /* > \param[in] GIVNUM */
688 /* > GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
689 /* > Each number indicates the C or S value used in the */
690 /* > corresponding Givens rotation. */
693 /* > \param[in] LDGNUM */
695 /* > LDGNUM is INTEGER */
696 /* > The leading dimension of arrays DIFR, POLES and */
697 /* > GIVNUM, must be at least K. */
700 /* > \param[in] POLES */
702 /* > POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
703 /* > On entry, POLES(1:K, 1) contains the new singular */
704 /* > values obtained from solving the secular equation, and */
705 /* > POLES(1:K, 2) is an array containing the poles in the secular */
709 /* > \param[in] DIFL */
711 /* > DIFL is DOUBLE PRECISION array, dimension ( K ). */
712 /* > On entry, DIFL(I) is the distance between I-th updated */
713 /* > (undeflated) singular value and the I-th (undeflated) old */
714 /* > singular value. */
717 /* > \param[in] DIFR */
719 /* > DIFR is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). */
720 /* > On entry, DIFR(I, 1) contains the distances between I-th */
721 /* > updated (undeflated) singular value and the I+1-th */
722 /* > (undeflated) old singular value. And DIFR(I, 2) is the */
723 /* > normalizing factor for the I-th right singular vector. */
728 /* > Z is DOUBLE PRECISION array, dimension ( K ) */
729 /* > Contain the components of the deflation-adjusted updating row */
736 /* > Contains the dimension of the non-deflated matrix, */
737 /* > This is the order of the related secular equation. 1 <= K <=N. */
742 /* > C is DOUBLE PRECISION */
743 /* > C contains garbage if SQRE =0 and the C-value of a Givens */
744 /* > rotation related to the right null space if SQRE = 1. */
749 /* > S is DOUBLE PRECISION */
750 /* > S contains garbage if SQRE =0 and the S-value of a Givens */
751 /* > rotation related to the right null space if SQRE = 1. */
754 /* > \param[out] WORK */
756 /* > WORK is DOUBLE PRECISION array, dimension ( K ) */
759 /* > \param[out] INFO */
761 /* > INFO is INTEGER */
762 /* > = 0: successful exit. */
763 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
769 /* > \author Univ. of Tennessee */
770 /* > \author Univ. of California Berkeley */
771 /* > \author Univ. of Colorado Denver */
772 /* > \author NAG Ltd. */
774 /* > \date December 2016 */
776 /* > \ingroup doubleOTHERcomputational */
778 /* > \par Contributors: */
779 /* ================== */
781 /* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */
782 /* > California at Berkeley, USA \n */
783 /* > Osni Marques, LBNL/NERSC, USA \n */
785 /* ===================================================================== */
786 /* Subroutine */ int dlals0_(integer *icompq, integer *nl, integer *nr,
787 integer *sqre, integer *nrhs, doublereal *b, integer *ldb, doublereal
788 *bx, integer *ldbx, integer *perm, integer *givptr, integer *givcol,
789 integer *ldgcol, doublereal *givnum, integer *ldgnum, doublereal *
790 poles, doublereal *difl, doublereal *difr, doublereal *z__, integer *
791 k, doublereal *c__, doublereal *s, doublereal *work, integer *info)
793 /* System generated locals */
794 integer givcol_dim1, givcol_offset, b_dim1, b_offset, bx_dim1, bx_offset,
795 difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1,
796 poles_offset, i__1, i__2;
799 /* Local variables */
801 extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
802 doublereal *, integer *, doublereal *, doublereal *);
803 extern doublereal dnrm2_(integer *, doublereal *, integer *);
804 integer i__, j, m, n;
805 extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
807 doublereal diflj, difrj, dsigj;
808 extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
809 doublereal *, doublereal *, integer *, doublereal *, integer *,
810 doublereal *, doublereal *, integer *), dcopy_(integer *,
811 doublereal *, integer *, doublereal *, integer *);
812 extern doublereal dlamc3_(doublereal *, doublereal *);
814 extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
815 doublereal *, doublereal *, integer *, integer *, doublereal *,
816 integer *, integer *), dlacpy_(char *, integer *, integer
817 *, doublereal *, integer *, doublereal *, integer *),
818 xerbla_(char *, integer *, ftnlen);
823 /* -- LAPACK computational routine (version 3.7.0) -- */
824 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
825 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
829 /* ===================================================================== */
832 /* Test the input parameters. */
834 /* Parameter adjustments */
836 b_offset = 1 + b_dim1 * 1;
839 bx_offset = 1 + bx_dim1 * 1;
842 givcol_dim1 = *ldgcol;
843 givcol_offset = 1 + givcol_dim1 * 1;
844 givcol -= givcol_offset;
846 difr_offset = 1 + difr_dim1 * 1;
848 poles_dim1 = *ldgnum;
849 poles_offset = 1 + poles_dim1 * 1;
850 poles -= poles_offset;
851 givnum_dim1 = *ldgnum;
852 givnum_offset = 1 + givnum_dim1 * 1;
853 givnum -= givnum_offset;
862 if (*icompq < 0 || *icompq > 1) {
864 } else if (*nl < 1) {
866 } else if (*nr < 1) {
868 } else if (*sqre < 0 || *sqre > 1) {
870 } else if (*nrhs < 1) {
872 } else if (*ldb < n) {
874 } else if (*ldbx < n) {
876 } else if (*givptr < 0) {
878 } else if (*ldgcol < n) {
880 } else if (*ldgnum < n) {
882 //} else if (*k < 1) {
888 xerbla_("DLALS0", &i__1, (ftnlen)6);
897 /* Apply back orthogonal transformations from the left. */
899 /* Step (1L): apply back the Givens rotations performed. */
902 for (i__ = 1; i__ <= i__1; ++i__) {
903 drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, &
904 b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ +
905 (givnum_dim1 << 1)], &givnum[i__ + givnum_dim1]);
909 /* Step (2L): permute rows of B. */
911 dcopy_(nrhs, &b[nlp1 + b_dim1], ldb, &bx[bx_dim1 + 1], ldbx);
913 for (i__ = 2; i__ <= i__1; ++i__) {
914 dcopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1],
919 /* Step (3L): apply the inverse of the left singular vector */
923 dcopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb);
925 dscal_(nrhs, &c_b5, &b[b_offset], ldb);
929 for (j = 1; j <= i__1; ++j) {
931 dj = poles[j + poles_dim1];
932 dsigj = -poles[j + (poles_dim1 << 1)];
934 difrj = -difr[j + difr_dim1];
935 dsigjp = -poles[j + 1 + (poles_dim1 << 1)];
937 if (z__[j] == 0. || poles[j + (poles_dim1 << 1)] == 0.) {
940 work[j] = -poles[j + (poles_dim1 << 1)] * z__[j] / diflj /
941 (poles[j + (poles_dim1 << 1)] + dj);
944 for (i__ = 1; i__ <= i__2; ++i__) {
945 if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] ==
949 work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__]
950 / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], &
951 dsigj) - diflj) / (poles[i__ + (poles_dim1 <<
957 for (i__ = j + 1; i__ <= i__2; ++i__) {
958 if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] ==
962 work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__]
963 / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], &
964 dsigjp) + difrj) / (poles[i__ + (poles_dim1 <<
970 temp = dnrm2_(k, &work[1], &c__1);
971 dgemv_("T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], &
972 c__1, &c_b13, &b[j + b_dim1], ldb);
973 dlascl_("G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b[j +
979 /* Move the deflated rows of BX to B also. */
981 if (*k < f2cmax(m,n)) {
983 dlacpy_("A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1
988 /* Apply back the right orthogonal transformations. */
990 /* Step (1R): apply back the new right singular vector matrix */
994 dcopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx);
997 for (j = 1; j <= i__1; ++j) {
998 dsigj = poles[j + (poles_dim1 << 1)];
1002 work[j] = -z__[j] / difl[j] / (dsigj + poles[j +
1003 poles_dim1]) / difr[j + (difr_dim1 << 1)];
1006 for (i__ = 1; i__ <= i__2; ++i__) {
1010 d__1 = -poles[i__ + 1 + (poles_dim1 << 1)];
1011 work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difr[
1012 i__ + difr_dim1]) / (dsigj + poles[i__ +
1013 poles_dim1]) / difr[i__ + (difr_dim1 << 1)];
1018 for (i__ = j + 1; i__ <= i__2; ++i__) {
1022 d__1 = -poles[i__ + (poles_dim1 << 1)];
1023 work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difl[
1024 i__]) / (dsigj + poles[i__ + poles_dim1]) /
1025 difr[i__ + (difr_dim1 << 1)];
1029 dgemv_("T", k, nrhs, &c_b11, &b[b_offset], ldb, &work[1], &
1030 c__1, &c_b13, &bx[j + bx_dim1], ldbx);
1035 /* Step (2R): if SQRE = 1, apply back the rotation that is */
1036 /* related to the right null space of the subproblem. */
1039 dcopy_(nrhs, &b[m + b_dim1], ldb, &bx[m + bx_dim1], ldbx);
1040 drot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__,
1043 if (*k < f2cmax(m,n)) {
1045 dlacpy_("A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 +
1049 /* Step (3R): permute rows of B. */
1051 dcopy_(nrhs, &bx[bx_dim1 + 1], ldbx, &b[nlp1 + b_dim1], ldb);
1053 dcopy_(nrhs, &bx[m + bx_dim1], ldbx, &b[m + b_dim1], ldb);
1056 for (i__ = 2; i__ <= i__1; ++i__) {
1057 dcopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1],
1062 /* Step (4R): apply back the Givens rotations performed. */
1064 for (i__ = *givptr; i__ >= 1; --i__) {
1065 d__1 = -givnum[i__ + givnum_dim1];
1066 drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, &
1067 b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ +
1068 (givnum_dim1 << 1)], &d__1);