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 doublereal c_b9 = 0.;
516 static doublereal c_b10 = 1.;
517 static integer c__1 = 1;
519 /* > \brief \b DSBTRD */
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download DSBTRD + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsbtrd.
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbtrd.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbtrd.
542 /* SUBROUTINE DSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, */
545 /* CHARACTER UPLO, VECT */
546 /* INTEGER INFO, KD, LDAB, LDQ, N */
547 /* DOUBLE PRECISION AB( LDAB, * ), D( * ), E( * ), Q( LDQ, * ), */
551 /* > \par Purpose: */
556 /* > DSBTRD reduces a real symmetric band matrix A to symmetric */
557 /* > tridiagonal form T by an orthogonal similarity transformation: */
558 /* > Q**T * A * Q = T. */
564 /* > \param[in] VECT */
566 /* > VECT is CHARACTER*1 */
567 /* > = 'N': do not form Q; */
568 /* > = 'V': form Q; */
569 /* > = 'U': update a matrix X, by forming X*Q. */
572 /* > \param[in] UPLO */
574 /* > UPLO is CHARACTER*1 */
575 /* > = 'U': Upper triangle of A is stored; */
576 /* > = 'L': Lower triangle of A is stored. */
582 /* > The order of the matrix A. N >= 0. */
585 /* > \param[in] KD */
587 /* > KD is INTEGER */
588 /* > The number of superdiagonals of the matrix A if UPLO = 'U', */
589 /* > or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
592 /* > \param[in,out] AB */
594 /* > AB is DOUBLE PRECISION array, dimension (LDAB,N) */
595 /* > On entry, the upper or lower triangle of the symmetric band */
596 /* > matrix A, stored in the first KD+1 rows of the array. The */
597 /* > j-th column of A is stored in the j-th column of the array AB */
599 /* > if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */
600 /* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+kd). */
601 /* > On exit, the diagonal elements of AB are overwritten by the */
602 /* > diagonal elements of the tridiagonal matrix T; if KD > 0, the */
603 /* > elements on the first superdiagonal (if UPLO = 'U') or the */
604 /* > first subdiagonal (if UPLO = 'L') are overwritten by the */
605 /* > off-diagonal elements of T; the rest of AB is overwritten by */
606 /* > values generated during the reduction. */
609 /* > \param[in] LDAB */
611 /* > LDAB is INTEGER */
612 /* > The leading dimension of the array AB. LDAB >= KD+1. */
615 /* > \param[out] D */
617 /* > D is DOUBLE PRECISION array, dimension (N) */
618 /* > The diagonal elements of the tridiagonal matrix T. */
621 /* > \param[out] E */
623 /* > E is DOUBLE PRECISION array, dimension (N-1) */
624 /* > The off-diagonal elements of the tridiagonal matrix T: */
625 /* > E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. */
628 /* > \param[in,out] Q */
630 /* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
631 /* > On entry, if VECT = 'U', then Q must contain an N-by-N */
632 /* > matrix X; if VECT = 'N' or 'V', then Q need not be set. */
635 /* > if VECT = 'V', Q contains the N-by-N orthogonal matrix Q; */
636 /* > if VECT = 'U', Q contains the product X*Q; */
637 /* > if VECT = 'N', the array Q is not referenced. */
640 /* > \param[in] LDQ */
642 /* > LDQ is INTEGER */
643 /* > The leading dimension of the array Q. */
644 /* > LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. */
647 /* > \param[out] WORK */
649 /* > WORK is DOUBLE PRECISION array, dimension (N) */
652 /* > \param[out] INFO */
654 /* > INFO is INTEGER */
655 /* > = 0: successful exit */
656 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
662 /* > \author Univ. of Tennessee */
663 /* > \author Univ. of California Berkeley */
664 /* > \author Univ. of Colorado Denver */
665 /* > \author NAG Ltd. */
667 /* > \date December 2016 */
669 /* > \ingroup doubleOTHERcomputational */
671 /* > \par Further Details: */
672 /* ===================== */
676 /* > Modified by Linda Kaufman, Bell Labs. */
679 /* ===================================================================== */
680 /* Subroutine */ int dsbtrd_(char *vect, char *uplo, integer *n, integer *kd,
681 doublereal *ab, integer *ldab, doublereal *d__, doublereal *e,
682 doublereal *q, integer *ldq, doublereal *work, integer *info)
684 /* System generated locals */
685 integer ab_dim1, ab_offset, q_dim1, q_offset, i__1, i__2, i__3, i__4,
688 /* Local variables */
689 integer inca, jend, lend, jinc, incx, last;
691 extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
692 doublereal *, integer *, doublereal *, doublereal *);
693 integer j1end, j1inc, i__, j, k, l, iqend;
694 extern logical lsame_(char *, char *);
695 logical initq, wantq, upper;
697 extern /* Subroutine */ int dlar2v_(integer *, doublereal *, doublereal *,
698 doublereal *, integer *, doublereal *, doublereal *, integer *);
699 integer nq, nr, iqaend;
700 extern /* Subroutine */ int dlaset_(char *, integer *, integer *,
701 doublereal *, doublereal *, doublereal *, integer *),
702 dlartg_(doublereal *, doublereal *, doublereal *, doublereal *,
703 doublereal *), xerbla_(char *, integer *, ftnlen), dlargv_(
704 integer *, doublereal *, integer *, doublereal *, integer *,
705 doublereal *, integer *), dlartv_(integer *, doublereal *,
706 integer *, doublereal *, integer *, doublereal *, doublereal *,
708 integer kd1, ibl, iqb, kdn, jin, nrt, kdm1;
711 /* -- LAPACK computational routine (version 3.7.0) -- */
712 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
713 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
717 /* ===================================================================== */
720 /* Test the input parameters */
722 /* Parameter adjustments */
724 ab_offset = 1 + ab_dim1 * 1;
729 q_offset = 1 + q_dim1 * 1;
734 initq = lsame_(vect, "V");
735 wantq = initq || lsame_(vect, "U");
736 upper = lsame_(uplo, "U");
743 if (! wantq && ! lsame_(vect, "N")) {
745 } else if (! upper && ! lsame_(uplo, "L")) {
749 } else if (*kd < 0) {
751 } else if (*ldab < kd1) {
753 } else if (*ldq < f2cmax(1,*n) && wantq) {
758 xerbla_("DSBTRD", &i__1, (ftnlen)6);
762 /* Quick return if possible */
768 /* Initialize Q to the unit matrix, if needed */
771 dlaset_("Full", n, n, &c_b9, &c_b10, &q[q_offset], ldq);
774 /* Wherever possible, plane rotations are generated and applied in */
775 /* vector operations of length NR over the index set J1:J2:KD1. */
777 /* The cosines and sines of the plane rotations are stored in the */
778 /* arrays D and WORK. */
783 kdn = f2cmin(i__1,*kd);
788 /* Reduce to tridiagonal form, working with upper triangle */
795 for (i__ = 1; i__ <= i__1; ++i__) {
797 /* Reduce i-th row of matrix to tridiagonal form */
799 for (k = kdn + 1; k >= 2; --k) {
805 /* generate plane rotations to annihilate nonzero */
806 /* elements which have been created outside the band */
808 dlargv_(&nr, &ab[(j1 - 1) * ab_dim1 + 1], &inca, &
809 work[j1], &kd1, &d__[j1], &kd1);
811 /* apply rotations from the right */
814 /* Dependent on the the number of diagonals either */
815 /* DLARTV or DROT is used */
817 if (nr >= (*kd << 1) - 1) {
819 for (l = 1; l <= i__2; ++l) {
820 dlartv_(&nr, &ab[l + 1 + (j1 - 1) * ab_dim1],
821 &inca, &ab[l + j1 * ab_dim1], &inca, &
822 d__[j1], &work[j1], &kd1);
827 jend = j1 + (nr - 1) * kd1;
830 for (jinc = j1; i__3 < 0 ? jinc >= i__2 : jinc <=
831 i__2; jinc += i__3) {
832 drot_(&kdm1, &ab[(jinc - 1) * ab_dim1 + 2], &
833 c__1, &ab[jinc * ab_dim1 + 1], &c__1,
834 &d__[jinc], &work[jinc]);
842 if (k <= *n - i__ + 1) {
844 /* generate plane rotation to annihilate a(i,i+k-1) */
845 /* within the band */
847 dlartg_(&ab[*kd - k + 3 + (i__ + k - 2) * ab_dim1]
848 , &ab[*kd - k + 2 + (i__ + k - 1) *
849 ab_dim1], &d__[i__ + k - 1], &work[i__ +
851 ab[*kd - k + 3 + (i__ + k - 2) * ab_dim1] = temp;
853 /* apply rotation from the right */
856 drot_(&i__3, &ab[*kd - k + 4 + (i__ + k - 2) *
857 ab_dim1], &c__1, &ab[*kd - k + 3 + (i__ +
858 k - 1) * ab_dim1], &c__1, &d__[i__ + k -
859 1], &work[i__ + k - 1]);
865 /* apply plane rotations from both sides to diagonal */
869 dlar2v_(&nr, &ab[kd1 + (j1 - 1) * ab_dim1], &ab[kd1 +
870 j1 * ab_dim1], &ab[*kd + j1 * ab_dim1], &inca,
871 &d__[j1], &work[j1], &kd1);
874 /* apply plane rotations from the left */
877 if ((*kd << 1) - 1 < nr) {
879 /* Dependent on the the number of diagonals either */
880 /* DLARTV or DROT is used */
883 for (l = 1; l <= i__3; ++l) {
890 dlartv_(&nrt, &ab[*kd - l + (j1 + l) *
891 ab_dim1], &inca, &ab[*kd - l + 1
892 + (j1 + l) * ab_dim1], &inca, &
893 d__[j1], &work[j1], &kd1);
898 j1end = j1 + kd1 * (nr - 2);
902 for (jin = j1; i__2 < 0 ? jin >= i__3 : jin <=
905 drot_(&i__4, &ab[*kd - 1 + (jin + 1) *
906 ab_dim1], &incx, &ab[*kd + (jin +
907 1) * ab_dim1], &incx, &d__[jin], &
913 i__2 = kdm1, i__3 = *n - j2;
914 lend = f2cmin(i__2,i__3);
917 drot_(&lend, &ab[*kd - 1 + (last + 1) *
918 ab_dim1], &incx, &ab[*kd + (last + 1)
919 * ab_dim1], &incx, &d__[last], &work[
927 /* accumulate product of plane rotations in Q */
931 /* take advantage of the fact that Q was */
932 /* initially the Identity matrix */
934 iqend = f2cmax(iqend,j2);
936 i__2 = 0, i__3 = k - 3;
937 i2 = f2cmax(i__2,i__3);
938 iqaend = i__ * *kd + 1;
942 iqaend = f2cmin(iqaend,iqend);
945 for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j
947 ibl = i__ - i2 / kdm1;
950 i__4 = 1, i__5 = j - ibl;
951 iqb = f2cmax(i__4,i__5);
952 nq = iqaend + 1 - iqb;
955 iqaend = f2cmin(i__4,iqend);
956 drot_(&nq, &q[iqb + (j - 1) * q_dim1], &c__1,
957 &q[iqb + j * q_dim1], &c__1, &d__[j],
965 for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j
967 drot_(n, &q[(j - 1) * q_dim1 + 1], &c__1, &q[
968 j * q_dim1 + 1], &c__1, &d__[j], &
978 /* adjust J2 to keep within the bounds of the matrix */
986 for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j += i__3)
989 /* create nonzero element a(j-1,j+kd) outside the band */
990 /* and store it in WORK */
992 work[j + *kd] = work[j] * ab[(j + *kd) * ab_dim1 + 1];
993 ab[(j + *kd) * ab_dim1 + 1] = d__[j] * ab[(j + *kd) *
1005 /* copy off-diagonal elements to E */
1008 for (i__ = 1; i__ <= i__1; ++i__) {
1009 e[i__] = ab[*kd + (i__ + 1) * ab_dim1];
1014 /* set E to zero if original matrix was diagonal */
1017 for (i__ = 1; i__ <= i__1; ++i__) {
1023 /* copy diagonal elements to D */
1026 for (i__ = 1; i__ <= i__1; ++i__) {
1027 d__[i__] = ab[kd1 + i__ * ab_dim1];
1035 /* Reduce to tridiagonal form, working with lower triangle */
1042 for (i__ = 1; i__ <= i__1; ++i__) {
1044 /* Reduce i-th column of matrix to tridiagonal form */
1046 for (k = kdn + 1; k >= 2; --k) {
1052 /* generate plane rotations to annihilate nonzero */
1053 /* elements which have been created outside the band */
1055 dlargv_(&nr, &ab[kd1 + (j1 - kd1) * ab_dim1], &inca, &
1056 work[j1], &kd1, &d__[j1], &kd1);
1058 /* apply plane rotations from one side */
1061 /* Dependent on the the number of diagonals either */
1062 /* DLARTV or DROT is used */
1064 if (nr > (*kd << 1) - 1) {
1066 for (l = 1; l <= i__3; ++l) {
1067 dlartv_(&nr, &ab[kd1 - l + (j1 - kd1 + l) *
1068 ab_dim1], &inca, &ab[kd1 - l + 1 + (
1069 j1 - kd1 + l) * ab_dim1], &inca, &d__[
1070 j1], &work[j1], &kd1);
1074 jend = j1 + kd1 * (nr - 1);
1077 for (jinc = j1; i__2 < 0 ? jinc >= i__3 : jinc <=
1078 i__3; jinc += i__2) {
1079 drot_(&kdm1, &ab[*kd + (jinc - *kd) * ab_dim1]
1080 , &incx, &ab[kd1 + (jinc - *kd) *
1081 ab_dim1], &incx, &d__[jinc], &work[
1090 if (k <= *n - i__ + 1) {
1092 /* generate plane rotation to annihilate a(i+k-1,i) */
1093 /* within the band */
1095 dlartg_(&ab[k - 1 + i__ * ab_dim1], &ab[k + i__ *
1096 ab_dim1], &d__[i__ + k - 1], &work[i__ +
1098 ab[k - 1 + i__ * ab_dim1] = temp;
1100 /* apply rotation from the left */
1105 drot_(&i__2, &ab[k - 2 + (i__ + 1) * ab_dim1], &
1106 i__3, &ab[k - 1 + (i__ + 1) * ab_dim1], &
1107 i__4, &d__[i__ + k - 1], &work[i__ + k -
1114 /* apply plane rotations from both sides to diagonal */
1118 dlar2v_(&nr, &ab[(j1 - 1) * ab_dim1 + 1], &ab[j1 *
1119 ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 + 2], &
1120 inca, &d__[j1], &work[j1], &kd1);
1123 /* apply plane rotations from the right */
1126 /* Dependent on the the number of diagonals either */
1127 /* DLARTV or DROT is used */
1130 if (nr > (*kd << 1) - 1) {
1132 for (l = 1; l <= i__2; ++l) {
1139 dlartv_(&nrt, &ab[l + 2 + (j1 - 1) *
1140 ab_dim1], &inca, &ab[l + 1 + j1 *
1141 ab_dim1], &inca, &d__[j1], &work[
1147 j1end = j1 + kd1 * (nr - 2);
1151 for (j1inc = j1; i__3 < 0 ? j1inc >= i__2 :
1152 j1inc <= i__2; j1inc += i__3) {
1153 drot_(&kdm1, &ab[(j1inc - 1) * ab_dim1 +
1154 3], &c__1, &ab[j1inc * ab_dim1 +
1155 2], &c__1, &d__[j1inc], &work[
1161 i__3 = kdm1, i__2 = *n - j2;
1162 lend = f2cmin(i__3,i__2);
1165 drot_(&lend, &ab[(last - 1) * ab_dim1 + 3], &
1166 c__1, &ab[last * ab_dim1 + 2], &c__1,
1167 &d__[last], &work[last]);
1176 /* accumulate product of plane rotations in Q */
1180 /* take advantage of the fact that Q was */
1181 /* initially the Identity matrix */
1183 iqend = f2cmax(iqend,j2);
1185 i__3 = 0, i__2 = k - 3;
1186 i2 = f2cmax(i__3,i__2);
1187 iqaend = i__ * *kd + 1;
1191 iqaend = f2cmin(iqaend,iqend);
1194 for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j
1196 ibl = i__ - i2 / kdm1;
1199 i__4 = 1, i__5 = j - ibl;
1200 iqb = f2cmax(i__4,i__5);
1201 nq = iqaend + 1 - iqb;
1203 i__4 = iqaend + *kd;
1204 iqaend = f2cmin(i__4,iqend);
1205 drot_(&nq, &q[iqb + (j - 1) * q_dim1], &c__1,
1206 &q[iqb + j * q_dim1], &c__1, &d__[j],
1214 for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j
1216 drot_(n, &q[(j - 1) * q_dim1 + 1], &c__1, &q[
1217 j * q_dim1 + 1], &c__1, &d__[j], &
1224 if (j2 + kdn > *n) {
1226 /* adjust J2 to keep within the bounds of the matrix */
1234 for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2)
1237 /* create nonzero element a(j+kd,j-1) outside the */
1238 /* band and store it in WORK */
1240 work[j + *kd] = work[j] * ab[kd1 + j * ab_dim1];
1241 ab[kd1 + j * ab_dim1] = d__[j] * ab[kd1 + j * ab_dim1]
1253 /* copy off-diagonal elements to E */
1256 for (i__ = 1; i__ <= i__1; ++i__) {
1257 e[i__] = ab[i__ * ab_dim1 + 2];
1262 /* set E to zero if original matrix was diagonal */
1265 for (i__ = 1; i__ <= i__1; ++i__) {
1271 /* copy diagonal elements to D */
1274 for (i__ = 1; i__ <= i__1; ++i__) {
1275 d__[i__] = ab[i__ * ab_dim1 + 1];