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 real c_b8 = 0.f;
516 static real c_b9 = 1.f;
517 static integer c__1 = 1;
519 /* > \brief \b SGBBRD */
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download SGBBRD + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgbbrd.
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgbbrd.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgbbrd.
542 /* SUBROUTINE SGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, */
543 /* LDQ, PT, LDPT, C, LDC, WORK, INFO ) */
546 /* INTEGER INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC */
547 /* REAL AB( LDAB, * ), C( LDC, * ), D( * ), E( * ), */
548 /* $ PT( LDPT, * ), Q( LDQ, * ), WORK( * ) */
551 /* > \par Purpose: */
556 /* > SGBBRD reduces a real general m-by-n band matrix A to upper */
557 /* > bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. */
559 /* > The routine computes B, and optionally forms Q or P**T, or computes */
560 /* > Q**T*C for a given matrix C. */
566 /* > \param[in] VECT */
568 /* > VECT is CHARACTER*1 */
569 /* > Specifies whether or not the matrices Q and P**T are to be */
571 /* > = 'N': do not form Q or P**T; */
572 /* > = 'Q': form Q only; */
573 /* > = 'P': form P**T only; */
574 /* > = 'B': form both. */
580 /* > The number of rows of the matrix A. M >= 0. */
586 /* > The number of columns of the matrix A. N >= 0. */
589 /* > \param[in] NCC */
591 /* > NCC is INTEGER */
592 /* > The number of columns of the matrix C. NCC >= 0. */
595 /* > \param[in] KL */
597 /* > KL is INTEGER */
598 /* > The number of subdiagonals of the matrix A. KL >= 0. */
601 /* > \param[in] KU */
603 /* > KU is INTEGER */
604 /* > The number of superdiagonals of the matrix A. KU >= 0. */
607 /* > \param[in,out] AB */
609 /* > AB is REAL array, dimension (LDAB,N) */
610 /* > On entry, the m-by-n band matrix A, stored in rows 1 to */
611 /* > KL+KU+1. The j-th column of A is stored in the j-th column of */
612 /* > the array AB as follows: */
613 /* > AB(ku+1+i-j,j) = A(i,j) for f2cmax(1,j-ku)<=i<=f2cmin(m,j+kl). */
614 /* > On exit, A is overwritten by values generated during the */
618 /* > \param[in] LDAB */
620 /* > LDAB is INTEGER */
621 /* > The leading dimension of the array A. LDAB >= KL+KU+1. */
624 /* > \param[out] D */
626 /* > D is REAL array, dimension (f2cmin(M,N)) */
627 /* > The diagonal elements of the bidiagonal matrix B. */
630 /* > \param[out] E */
632 /* > E is REAL array, dimension (f2cmin(M,N)-1) */
633 /* > The superdiagonal elements of the bidiagonal matrix B. */
636 /* > \param[out] Q */
638 /* > Q is REAL array, dimension (LDQ,M) */
639 /* > If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q. */
640 /* > If VECT = 'N' or 'P', the array Q is not referenced. */
643 /* > \param[in] LDQ */
645 /* > LDQ is INTEGER */
646 /* > The leading dimension of the array Q. */
647 /* > LDQ >= f2cmax(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise. */
650 /* > \param[out] PT */
652 /* > PT is REAL array, dimension (LDPT,N) */
653 /* > If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'. */
654 /* > If VECT = 'N' or 'Q', the array PT is not referenced. */
657 /* > \param[in] LDPT */
659 /* > LDPT is INTEGER */
660 /* > The leading dimension of the array PT. */
661 /* > LDPT >= f2cmax(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise. */
664 /* > \param[in,out] C */
666 /* > C is REAL array, dimension (LDC,NCC) */
667 /* > On entry, an m-by-ncc matrix C. */
668 /* > On exit, C is overwritten by Q**T*C. */
669 /* > C is not referenced if NCC = 0. */
672 /* > \param[in] LDC */
674 /* > LDC is INTEGER */
675 /* > The leading dimension of the array C. */
676 /* > LDC >= f2cmax(1,M) if NCC > 0; LDC >= 1 if NCC = 0. */
679 /* > \param[out] WORK */
681 /* > WORK is REAL array, dimension (2*f2cmax(M,N)) */
684 /* > \param[out] INFO */
686 /* > INFO is INTEGER */
687 /* > = 0: successful exit. */
688 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
694 /* > \author Univ. of Tennessee */
695 /* > \author Univ. of California Berkeley */
696 /* > \author Univ. of Colorado Denver */
697 /* > \author NAG Ltd. */
699 /* > \date December 2016 */
701 /* > \ingroup realGBcomputational */
703 /* ===================================================================== */
704 /* Subroutine */ int sgbbrd_(char *vect, integer *m, integer *n, integer *ncc,
705 integer *kl, integer *ku, real *ab, integer *ldab, real *d__, real *
706 e, real *q, integer *ldq, real *pt, integer *ldpt, real *c__, integer
707 *ldc, real *work, integer *info)
709 /* System generated locals */
710 integer ab_dim1, ab_offset, c_dim1, c_offset, pt_dim1, pt_offset, q_dim1,
711 q_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;
713 /* Local variables */
715 extern /* Subroutine */ int srot_(integer *, real *, integer *, real *,
716 integer *, real *, real *);
718 extern logical lsame_(char *, char *);
719 logical wantb, wantc;
724 integer kk, ml, mn, nr, mu;
726 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), slaset_(
727 char *, integer *, integer *, real *, real *, real *, integer *), slartg_(real *, real *, real *, real *, real *);
729 extern /* Subroutine */ int slargv_(integer *, real *, integer *, real *,
730 integer *, real *, integer *);
732 extern /* Subroutine */ int slartv_(integer *, real *, integer *, real *,
733 integer *, real *, real *, integer *);
735 integer mu0, klm, kun, nrt, klu1;
738 /* -- LAPACK computational routine (version 3.7.0) -- */
739 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
740 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
744 /* ===================================================================== */
747 /* Test the input parameters */
749 /* Parameter adjustments */
751 ab_offset = 1 + ab_dim1 * 1;
756 q_offset = 1 + q_dim1 * 1;
759 pt_offset = 1 + pt_dim1 * 1;
762 c_offset = 1 + c_dim1 * 1;
767 wantb = lsame_(vect, "B");
768 wantq = lsame_(vect, "Q") || wantb;
769 wantpt = lsame_(vect, "P") || wantb;
771 klu1 = *kl + *ku + 1;
773 if (! wantq && ! wantpt && ! lsame_(vect, "N")) {
779 } else if (*ncc < 0) {
781 } else if (*kl < 0) {
783 } else if (*ku < 0) {
785 } else if (*ldab < klu1) {
787 } else if (*ldq < 1 || wantq && *ldq < f2cmax(1,*m)) {
789 } else if (*ldpt < 1 || wantpt && *ldpt < f2cmax(1,*n)) {
791 } else if (*ldc < 1 || wantc && *ldc < f2cmax(1,*m)) {
796 xerbla_("SGBBRD", &i__1, (ftnlen)6);
800 /* Initialize Q and P**T to the unit matrix, if needed */
803 slaset_("Full", m, m, &c_b8, &c_b9, &q[q_offset], ldq);
806 slaset_("Full", n, n, &c_b8, &c_b9, &pt[pt_offset], ldpt);
809 /* Quick return if possible. */
811 if (*m == 0 || *n == 0) {
815 minmn = f2cmin(*m,*n);
819 /* Reduce to upper bidiagonal form if KU > 0; if KU = 0, reduce */
820 /* first to lower bidiagonal form and then transform to upper */
831 /* Wherever possible, plane rotations are generated and applied in */
832 /* vector operations of length NR over the index set J1:J2:KLU1. */
834 /* The sines of the plane rotations are stored in WORK(1:f2cmax(m,n)) */
835 /* and the cosines in WORK(f2cmax(m,n)+1:2*f2cmax(m,n)). */
840 klm = f2cmin(i__1,*kl);
843 kun = f2cmin(i__1,*ku);
852 for (i__ = 1; i__ <= i__1; ++i__) {
854 /* Reduce i-th column and i-th row of matrix to bidiagonal form */
859 for (kk = 1; kk <= i__2; ++kk) {
863 /* generate plane rotations to annihilate nonzero elements */
864 /* which have been created below the band */
867 slargv_(&nr, &ab[klu1 + (j1 - klm - 1) * ab_dim1], &inca,
868 &work[j1], &kb1, &work[mn + j1], &kb1);
871 /* apply plane rotations from the left */
874 for (l = 1; l <= i__3; ++l) {
875 if (j2 - klm + l - 1 > *n) {
881 slartv_(&nrt, &ab[klu1 - l + (j1 - klm + l - 1) *
882 ab_dim1], &inca, &ab[klu1 - l + 1 + (j1 - klm
883 + l - 1) * ab_dim1], &inca, &work[mn + j1], &
890 if (ml <= *m - i__ + 1) {
892 /* generate plane rotation to annihilate a(i+ml-1,i) */
893 /* within the band, and apply rotation from the left */
895 slartg_(&ab[*ku + ml - 1 + i__ * ab_dim1], &ab[*ku +
896 ml + i__ * ab_dim1], &work[mn + i__ + ml - 1],
897 &work[i__ + ml - 1], &ra);
898 ab[*ku + ml - 1 + i__ * ab_dim1] = ra;
901 i__4 = *ku + ml - 2, i__5 = *n - i__;
902 i__3 = f2cmin(i__4,i__5);
905 srot_(&i__3, &ab[*ku + ml - 2 + (i__ + 1) *
906 ab_dim1], &i__6, &ab[*ku + ml - 1 + (i__
907 + 1) * ab_dim1], &i__7, &work[mn + i__ +
908 ml - 1], &work[i__ + ml - 1]);
917 /* accumulate product of plane rotations in Q */
921 for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4)
923 srot_(m, &q[(j - 1) * q_dim1 + 1], &c__1, &q[j *
924 q_dim1 + 1], &c__1, &work[mn + j], &work[j]);
931 /* apply plane rotations to C */
935 for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3)
937 srot_(ncc, &c__[j - 1 + c_dim1], ldc, &c__[j + c_dim1]
938 , ldc, &work[mn + j], &work[j]);
945 /* adjust J2 to keep within the bounds of the matrix */
953 for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
955 /* create nonzero element a(j-1,j+ku) above the band */
956 /* and store it in WORK(n+1:2*n) */
958 work[j + kun] = work[j] * ab[(j + kun) * ab_dim1 + 1];
959 ab[(j + kun) * ab_dim1 + 1] = work[mn + j] * ab[(j + kun)
964 /* generate plane rotations to annihilate nonzero elements */
965 /* which have been generated above the band */
968 slargv_(&nr, &ab[(j1 + kun - 1) * ab_dim1 + 1], &inca, &
969 work[j1 + kun], &kb1, &work[mn + j1 + kun], &kb1);
972 /* apply plane rotations from the right */
975 for (l = 1; l <= i__4; ++l) {
976 if (j2 + l - 1 > *m) {
982 slartv_(&nrt, &ab[l + 1 + (j1 + kun - 1) * ab_dim1], &
983 inca, &ab[l + (j1 + kun) * ab_dim1], &inca, &
984 work[mn + j1 + kun], &work[j1 + kun], &kb1);
989 if (ml == ml0 && mu > mu0) {
990 if (mu <= *n - i__ + 1) {
992 /* generate plane rotation to annihilate a(i,i+mu-1) */
993 /* within the band, and apply rotation from the right */
995 slartg_(&ab[*ku - mu + 3 + (i__ + mu - 2) * ab_dim1],
996 &ab[*ku - mu + 2 + (i__ + mu - 1) * ab_dim1],
997 &work[mn + i__ + mu - 1], &work[i__ + mu - 1],
999 ab[*ku - mu + 3 + (i__ + mu - 2) * ab_dim1] = ra;
1001 i__3 = *kl + mu - 2, i__5 = *m - i__;
1002 i__4 = f2cmin(i__3,i__5);
1003 srot_(&i__4, &ab[*ku - mu + 4 + (i__ + mu - 2) *
1004 ab_dim1], &c__1, &ab[*ku - mu + 3 + (i__ + mu
1005 - 1) * ab_dim1], &c__1, &work[mn + i__ + mu -
1006 1], &work[i__ + mu - 1]);
1014 /* accumulate product of plane rotations in P**T */
1018 for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3)
1020 srot_(n, &pt[j + kun - 1 + pt_dim1], ldpt, &pt[j +
1021 kun + pt_dim1], ldpt, &work[mn + j + kun], &
1029 /* adjust J2 to keep within the bounds of the matrix */
1037 for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
1039 /* create nonzero element a(j+kl+ku,j+ku-1) below the */
1040 /* band and store it in WORK(1:n) */
1042 work[j + kb] = work[j + kun] * ab[klu1 + (j + kun) *
1044 ab[klu1 + (j + kun) * ab_dim1] = work[mn + j + kun] * ab[
1045 klu1 + (j + kun) * ab_dim1];
1060 if (*ku == 0 && *kl > 0) {
1062 /* A has been reduced to lower bidiagonal form */
1064 /* Transform lower bidiagonal form to upper bidiagonal by applying */
1065 /* plane rotations from the left, storing diagonal elements in D */
1066 /* and off-diagonal elements in E */
1070 i__1 = f2cmin(i__2,*n);
1071 for (i__ = 1; i__ <= i__1; ++i__) {
1072 slartg_(&ab[i__ * ab_dim1 + 1], &ab[i__ * ab_dim1 + 2], &rc, &rs,
1076 e[i__] = rs * ab[(i__ + 1) * ab_dim1 + 1];
1077 ab[(i__ + 1) * ab_dim1 + 1] = rc * ab[(i__ + 1) * ab_dim1 + 1]
1081 srot_(m, &q[i__ * q_dim1 + 1], &c__1, &q[(i__ + 1) * q_dim1 +
1082 1], &c__1, &rc, &rs);
1085 srot_(ncc, &c__[i__ + c_dim1], ldc, &c__[i__ + 1 + c_dim1],
1091 d__[*m] = ab[*m * ab_dim1 + 1];
1093 } else if (*ku > 0) {
1095 /* A has been reduced to upper bidiagonal form */
1099 /* Annihilate a(m,m+1) by applying plane rotations from the */
1100 /* right, storing diagonal elements in D and off-diagonal */
1103 rb = ab[*ku + (*m + 1) * ab_dim1];
1104 for (i__ = *m; i__ >= 1; --i__) {
1105 slartg_(&ab[*ku + 1 + i__ * ab_dim1], &rb, &rc, &rs, &ra);
1108 rb = -rs * ab[*ku + i__ * ab_dim1];
1109 e[i__ - 1] = rc * ab[*ku + i__ * ab_dim1];
1112 srot_(n, &pt[i__ + pt_dim1], ldpt, &pt[*m + 1 + pt_dim1],
1119 /* Copy off-diagonal elements to E and diagonal elements to D */
1122 for (i__ = 1; i__ <= i__1; ++i__) {
1123 e[i__] = ab[*ku + (i__ + 1) * ab_dim1];
1127 for (i__ = 1; i__ <= i__1; ++i__) {
1128 d__[i__] = ab[*ku + 1 + i__ * ab_dim1];
1134 /* A is diagonal. Set elements of E to zero and copy diagonal */
1135 /* elements to D. */
1138 for (i__ = 1; i__ <= i__1; ++i__) {
1143 for (i__ = 1; i__ <= i__1; ++i__) {
1144 d__[i__] = ab[i__ * ab_dim1 + 1];