14 typedef long long BLASLONG;
15 typedef unsigned long long BLASULONG;
17 typedef long BLASLONG;
18 typedef unsigned long BLASULONG;
22 typedef BLASLONG blasint;
24 #define blasabs(x) llabs(x)
26 #define blasabs(x) labs(x)
30 #define blasabs(x) abs(x)
33 typedef blasint integer;
35 typedef unsigned int uinteger;
36 typedef char *address;
37 typedef short int shortint;
39 typedef double doublereal;
40 typedef struct { real r, i; } complex;
41 typedef struct { doublereal r, i; } doublecomplex;
43 static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
44 static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
45 static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
46 static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
48 static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
49 static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
50 static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
51 static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
53 #define pCf(z) (*_pCf(z))
54 #define pCd(z) (*_pCd(z))
56 typedef short int shortlogical;
57 typedef char logical1;
58 typedef char integer1;
63 /* Extern is for use with -E */
74 /*external read, write*/
83 /*internal read, write*/
113 /*rewind, backspace, endfile*/
125 ftnint *inex; /*parameters in standard's order*/
151 union Multitype { /* for multiple entry points */
162 typedef union Multitype Multitype;
164 struct Vardesc { /* for Namelist */
170 typedef struct Vardesc Vardesc;
177 typedef struct Namelist Namelist;
179 #define abs(x) ((x) >= 0 ? (x) : -(x))
180 #define dabs(x) (fabs(x))
181 #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
182 #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
183 #define dmin(a,b) (f2cmin(a,b))
184 #define dmax(a,b) (f2cmax(a,b))
185 #define bit_test(a,b) ((a) >> (b) & 1)
186 #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
187 #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
189 #define abort_() { sig_die("Fortran abort routine called", 1); }
190 #define c_abs(z) (cabsf(Cf(z)))
191 #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
193 #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
194 #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
196 #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
197 #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
199 #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
200 #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
201 #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
202 //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
203 #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
204 #define d_abs(x) (fabs(*(x)))
205 #define d_acos(x) (acos(*(x)))
206 #define d_asin(x) (asin(*(x)))
207 #define d_atan(x) (atan(*(x)))
208 #define d_atn2(x, y) (atan2(*(x),*(y)))
209 #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
210 #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
211 #define d_cos(x) (cos(*(x)))
212 #define d_cosh(x) (cosh(*(x)))
213 #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
214 #define d_exp(x) (exp(*(x)))
215 #define d_imag(z) (cimag(Cd(z)))
216 #define r_imag(z) (cimagf(Cf(z)))
217 #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
218 #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
219 #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
220 #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
221 #define d_log(x) (log(*(x)))
222 #define d_mod(x, y) (fmod(*(x), *(y)))
223 #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
224 #define d_nint(x) u_nint(*(x))
225 #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
226 #define d_sign(a,b) u_sign(*(a),*(b))
227 #define r_sign(a,b) u_sign(*(a),*(b))
228 #define d_sin(x) (sin(*(x)))
229 #define d_sinh(x) (sinh(*(x)))
230 #define d_sqrt(x) (sqrt(*(x)))
231 #define d_tan(x) (tan(*(x)))
232 #define d_tanh(x) (tanh(*(x)))
233 #define i_abs(x) abs(*(x))
234 #define i_dnnt(x) ((integer)u_nint(*(x)))
235 #define i_len(s, n) (n)
236 #define i_nint(x) ((integer)u_nint(*(x)))
237 #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
238 #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
239 #define pow_si(B,E) spow_ui(*(B),*(E))
240 #define pow_ri(B,E) spow_ui(*(B),*(E))
241 #define pow_di(B,E) dpow_ui(*(B),*(E))
242 #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
243 #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
244 #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
245 #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
246 #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
247 #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
248 #define sig_die(s, kill) { exit(1); }
249 #define s_stop(s, n) {exit(0);}
250 static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
251 #define z_abs(z) (cabs(Cd(z)))
252 #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
253 #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
254 #define myexit_() break;
255 #define mycycle() continue;
256 #define myceiling(w) {ceil(w)}
257 #define myhuge(w) {HUGE_VAL}
258 //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
259 #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
261 /* procedure parameter types for -A and -C++ */
263 #define F2C_proc_par_types 1
265 typedef logical (*L_fp)(...);
267 typedef logical (*L_fp)();
270 static float spow_ui(float x, integer n) {
271 float pow=1.0; unsigned long int u;
273 if(n < 0) n = -n, x = 1/x;
282 static double dpow_ui(double x, integer n) {
283 double pow=1.0; unsigned long int u;
285 if(n < 0) n = -n, x = 1/x;
295 static _Fcomplex cpow_ui(complex x, integer n) {
296 complex pow={1.0,0.0}; unsigned long int u;
298 if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
300 if(u & 01) pow.r *= x.r, pow.i *= x.i;
301 if(u >>= 1) x.r *= x.r, x.i *= x.i;
305 _Fcomplex p={pow.r, pow.i};
309 static _Complex float cpow_ui(_Complex float x, integer n) {
310 _Complex float pow=1.0; unsigned long int u;
312 if(n < 0) n = -n, x = 1/x;
323 static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
324 _Dcomplex pow={1.0,0.0}; unsigned long int u;
326 if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
328 if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
329 if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
333 _Dcomplex p = {pow._Val[0], pow._Val[1]};
337 static _Complex double zpow_ui(_Complex double x, integer n) {
338 _Complex double pow=1.0; unsigned long int u;
340 if(n < 0) n = -n, x = 1/x;
350 static integer pow_ii(integer x, integer n) {
351 integer pow; unsigned long int u;
353 if (n == 0 || x == 1) pow = 1;
354 else if (x != -1) pow = x == 0 ? 1/x : 0;
357 if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
367 static integer dmaxloc_(double *w, integer s, integer e, integer *n)
369 double m; integer i, mi;
370 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
371 if (w[i-1]>m) mi=i ,m=w[i-1];
374 static integer smaxloc_(float *w, integer s, integer e, integer *n)
376 float m; integer i, mi;
377 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
378 if (w[i-1]>m) mi=i ,m=w[i-1];
381 static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
382 integer n = *n_, incx = *incx_, incy = *incy_, i;
384 _Fcomplex zdotc = {0.0, 0.0};
385 if (incx == 1 && incy == 1) {
386 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
387 zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
388 zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
391 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
392 zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
393 zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
399 _Complex float zdotc = 0.0;
400 if (incx == 1 && incy == 1) {
401 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
402 zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
405 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
406 zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
412 static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
413 integer n = *n_, incx = *incx_, incy = *incy_, i;
415 _Dcomplex zdotc = {0.0, 0.0};
416 if (incx == 1 && incy == 1) {
417 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
418 zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
419 zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
422 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
423 zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
424 zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
430 _Complex double zdotc = 0.0;
431 if (incx == 1 && incy == 1) {
432 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
433 zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
436 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
437 zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
443 static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
444 integer n = *n_, incx = *incx_, incy = *incy_, i;
446 _Fcomplex zdotc = {0.0, 0.0};
447 if (incx == 1 && incy == 1) {
448 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
449 zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
450 zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
453 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
454 zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
455 zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
461 _Complex float zdotc = 0.0;
462 if (incx == 1 && incy == 1) {
463 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
464 zdotc += Cf(&x[i]) * Cf(&y[i]);
467 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
468 zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
474 static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
475 integer n = *n_, incx = *incx_, incy = *incy_, i;
477 _Dcomplex zdotc = {0.0, 0.0};
478 if (incx == 1 && incy == 1) {
479 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
480 zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
481 zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
484 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
485 zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
486 zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
492 _Complex double zdotc = 0.0;
493 if (incx == 1 && incy == 1) {
494 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
495 zdotc += Cd(&x[i]) * Cd(&y[i]);
498 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
499 zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
505 /* -- translated by f2c (version 20000121).
506 You must link the resulting object file with the libraries:
507 -lf2c -lm (in that order)
513 /* Table of constant values */
515 static integer c__1 = 1;
517 /* > \brief \b DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download DLASDQ + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasdq.
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasdq.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasdq.
541 /* SUBROUTINE DLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, */
542 /* U, LDU, C, LDC, WORK, INFO ) */
545 /* INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU, SQRE */
546 /* DOUBLE PRECISION C( LDC, * ), D( * ), E( * ), U( LDU, * ), */
547 /* $ VT( LDVT, * ), WORK( * ) */
550 /* > \par Purpose: */
555 /* > DLASDQ computes the singular value decomposition (SVD) of a real */
556 /* > (upper or lower) bidiagonal matrix with diagonal D and offdiagonal */
557 /* > E, accumulating the transformations if desired. Letting B denote */
558 /* > the input bidiagonal matrix, the algorithm computes orthogonal */
559 /* > matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose */
560 /* > of P). The singular values S are overwritten on D. */
562 /* > The input matrix U is changed to U * Q if desired. */
563 /* > The input matrix VT is changed to P**T * VT if desired. */
564 /* > The input matrix C is changed to Q**T * C if desired. */
566 /* > See "Computing Small Singular Values of Bidiagonal Matrices With */
567 /* > Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, */
568 /* > LAPACK Working Note #3, for a detailed description of the algorithm. */
574 /* > \param[in] UPLO */
576 /* > UPLO is CHARACTER*1 */
577 /* > On entry, UPLO specifies whether the input bidiagonal matrix */
578 /* > is upper or lower bidiagonal, and whether it is square are */
580 /* > UPLO = 'U' or 'u' B is upper bidiagonal. */
581 /* > UPLO = 'L' or 'l' B is lower bidiagonal. */
584 /* > \param[in] SQRE */
586 /* > SQRE is INTEGER */
587 /* > = 0: then the input matrix is N-by-N. */
588 /* > = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and */
589 /* > (N+1)-by-N if UPLU = 'L'. */
591 /* > The bidiagonal matrix has */
592 /* > N = NL + NR + 1 rows and */
593 /* > M = N + SQRE >= N columns. */
599 /* > On entry, N specifies the number of rows and columns */
600 /* > in the matrix. N must be at least 0. */
603 /* > \param[in] NCVT */
605 /* > NCVT is INTEGER */
606 /* > On entry, NCVT specifies the number of columns of */
607 /* > the matrix VT. NCVT must be at least 0. */
610 /* > \param[in] NRU */
612 /* > NRU is INTEGER */
613 /* > On entry, NRU specifies the number of rows of */
614 /* > the matrix U. NRU must be at least 0. */
617 /* > \param[in] NCC */
619 /* > NCC is INTEGER */
620 /* > On entry, NCC specifies the number of columns of */
621 /* > the matrix C. NCC must be at least 0. */
624 /* > \param[in,out] D */
626 /* > D is DOUBLE PRECISION array, dimension (N) */
627 /* > On entry, D contains the diagonal entries of the */
628 /* > bidiagonal matrix whose SVD is desired. On normal exit, */
629 /* > D contains the singular values in ascending order. */
632 /* > \param[in,out] E */
634 /* > E is DOUBLE PRECISION array. */
635 /* > dimension is (N-1) if SQRE = 0 and N if SQRE = 1. */
636 /* > On entry, the entries of E contain the offdiagonal entries */
637 /* > of the bidiagonal matrix whose SVD is desired. On normal */
638 /* > exit, E will contain 0. If the algorithm does not converge, */
639 /* > D and E will contain the diagonal and superdiagonal entries */
640 /* > of a bidiagonal matrix orthogonally equivalent to the one */
641 /* > given as input. */
644 /* > \param[in,out] VT */
646 /* > VT is DOUBLE PRECISION array, dimension (LDVT, NCVT) */
647 /* > On entry, contains a matrix which on exit has been */
648 /* > premultiplied by P**T, dimension N-by-NCVT if SQRE = 0 */
649 /* > and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0). */
652 /* > \param[in] LDVT */
654 /* > LDVT is INTEGER */
655 /* > On entry, LDVT specifies the leading dimension of VT as */
656 /* > declared in the calling (sub) program. LDVT must be at */
657 /* > least 1. If NCVT is nonzero LDVT must also be at least N. */
660 /* > \param[in,out] U */
662 /* > U is DOUBLE PRECISION array, dimension (LDU, N) */
663 /* > On entry, contains a matrix which on exit has been */
664 /* > postmultiplied by Q, dimension NRU-by-N if SQRE = 0 */
665 /* > and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0). */
668 /* > \param[in] LDU */
670 /* > LDU is INTEGER */
671 /* > On entry, LDU specifies the leading dimension of U as */
672 /* > declared in the calling (sub) program. LDU must be at */
673 /* > least f2cmax( 1, NRU ) . */
676 /* > \param[in,out] C */
678 /* > C is DOUBLE PRECISION array, dimension (LDC, NCC) */
679 /* > On entry, contains an N-by-NCC matrix which on exit */
680 /* > has been premultiplied by Q**T dimension N-by-NCC if SQRE = 0 */
681 /* > and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0). */
684 /* > \param[in] LDC */
686 /* > LDC is INTEGER */
687 /* > On entry, LDC specifies the leading dimension of C as */
688 /* > declared in the calling (sub) program. LDC must be at */
689 /* > least 1. If NCC is nonzero, LDC must also be at least N. */
692 /* > \param[out] WORK */
694 /* > WORK is DOUBLE PRECISION array, dimension (4*N) */
695 /* > Workspace. Only referenced if one of NCVT, NRU, or NCC is */
696 /* > nonzero, and if N is at least 2. */
699 /* > \param[out] INFO */
701 /* > INFO is INTEGER */
702 /* > On exit, a value of 0 indicates a successful exit. */
703 /* > If INFO < 0, argument number -INFO is illegal. */
704 /* > If INFO > 0, the algorithm did not converge, and INFO */
705 /* > specifies how many superdiagonals did not converge. */
711 /* > \author Univ. of Tennessee */
712 /* > \author Univ. of California Berkeley */
713 /* > \author Univ. of Colorado Denver */
714 /* > \author NAG Ltd. */
716 /* > \date June 2016 */
718 /* > \ingroup OTHERauxiliary */
720 /* > \par Contributors: */
721 /* ================== */
723 /* > Ming Gu and Huan Ren, Computer Science Division, University of */
724 /* > California at Berkeley, USA */
726 /* ===================================================================== */
727 /* Subroutine */ int dlasdq_(char *uplo, integer *sqre, integer *n, integer *
728 ncvt, integer *nru, integer *ncc, doublereal *d__, doublereal *e,
729 doublereal *vt, integer *ldvt, doublereal *u, integer *ldu,
730 doublereal *c__, integer *ldc, doublereal *work, integer *info)
732 /* System generated locals */
733 integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
736 /* Local variables */
739 integer sqre1, i__, j;
741 extern logical lsame_(char *, char *);
742 extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *,
743 integer *, doublereal *, doublereal *, doublereal *, integer *), dswap_(integer *, doublereal *, integer *
744 , doublereal *, integer *);
747 extern /* Subroutine */ int dlartg_(doublereal *, doublereal *,
748 doublereal *, doublereal *, doublereal *), xerbla_(char *,
749 integer *, ftnlen), dbdsqr_(char *, integer *, integer *, integer
750 *, integer *, doublereal *, doublereal *, doublereal *, integer *,
751 doublereal *, integer *, doublereal *, integer *, doublereal *,
757 /* -- LAPACK auxiliary routine (version 3.7.0) -- */
758 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
759 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
763 /* ===================================================================== */
766 /* Test the input parameters. */
768 /* Parameter adjustments */
772 vt_offset = 1 + vt_dim1 * 1;
775 u_offset = 1 + u_dim1 * 1;
778 c_offset = 1 + c_dim1 * 1;
785 if (lsame_(uplo, "U")) {
788 if (lsame_(uplo, "L")) {
793 } else if (*sqre < 0 || *sqre > 1) {
797 } else if (*ncvt < 0) {
799 } else if (*nru < 0) {
801 } else if (*ncc < 0) {
803 } else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < f2cmax(1,*n)) {
805 } else if (*ldu < f2cmax(1,*nru)) {
807 } else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < f2cmax(1,*n)) {
812 xerbla_("DLASDQ", &i__1, (ftnlen)6);
819 /* ROTATE is true if any singular vectors desired, false otherwise */
821 rotate = *ncvt > 0 || *nru > 0 || *ncc > 0;
825 /* If matrix non-square upper bidiagonal, rotate to be lower */
826 /* bidiagonal. The rotations are on the right. */
828 if (iuplo == 1 && sqre1 == 1) {
830 for (i__ = 1; i__ <= i__1; ++i__) {
831 dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
833 e[i__] = sn * d__[i__ + 1];
834 d__[i__ + 1] = cs * d__[i__ + 1];
841 dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__);
851 /* Update singular vectors if desired. */
854 dlasr_("L", "V", "F", &np1, ncvt, &work[1], &work[np1], &vt[
859 /* If matrix lower bidiagonal, rotate to be upper bidiagonal */
860 /* by applying Givens rotations on the left. */
864 for (i__ = 1; i__ <= i__1; ++i__) {
865 dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
867 e[i__] = sn * d__[i__ + 1];
868 d__[i__ + 1] = cs * d__[i__ + 1];
876 /* If matrix (N+1)-by-N lower bidiagonal, one additional */
877 /* rotation is needed. */
880 dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__);
888 /* Update singular vectors if desired. */
892 dlasr_("R", "V", "F", nru, n, &work[1], &work[np1], &u[
895 dlasr_("R", "V", "F", nru, &np1, &work[1], &work[np1], &u[
901 dlasr_("L", "V", "F", n, ncc, &work[1], &work[np1], &c__[
904 dlasr_("L", "V", "F", &np1, ncc, &work[1], &work[np1], &c__[
910 /* Call DBDSQR to compute the SVD of the reduced real */
911 /* N-by-N upper bidiagonal matrix. */
913 dbdsqr_("U", n, ncvt, nru, ncc, &d__[1], &e[1], &vt[vt_offset], ldvt, &u[
914 u_offset], ldu, &c__[c_offset], ldc, &work[1], info);
916 /* Sort the singular values into ascending order (insertion sort on */
917 /* singular values, but only one transposition per singular vector) */
920 for (i__ = 1; i__ <= i__1; ++i__) {
922 /* Scan for smallest D(I). */
927 for (j = i__ + 1; j <= i__2; ++j) {
936 /* Swap singular values and vectors. */
938 d__[isub] = d__[i__];
941 dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[i__ + vt_dim1],
945 dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[i__ * u_dim1 + 1]
949 dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[i__ + c_dim1], ldc)