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_b12 = 1.f;
516 static real c_b13 = 0.f;
518 /* > \brief \b SSBGVD */
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download SSBGVD + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssbgvd.
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssbgvd.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssbgvd.
541 /* SUBROUTINE SSBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, */
542 /* Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO ) */
544 /* CHARACTER JOBZ, UPLO */
545 /* INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LWORK, N */
546 /* INTEGER IWORK( * ) */
547 /* REAL AB( LDAB, * ), BB( LDBB, * ), W( * ), */
548 /* $ WORK( * ), Z( LDZ, * ) */
551 /* > \par Purpose: */
556 /* > SSBGVD computes all the eigenvalues, and optionally, the eigenvectors */
557 /* > of a real generalized symmetric-definite banded eigenproblem, of the */
558 /* > form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and */
559 /* > banded, and B is also positive definite. If eigenvectors are */
560 /* > desired, it uses a divide and conquer algorithm. */
562 /* > The divide and conquer algorithm makes very mild assumptions about */
563 /* > floating point arithmetic. It will work on machines with a guard */
564 /* > digit in add/subtract, or on those binary machines without guard */
565 /* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
566 /* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */
567 /* > without guard digits, but we know of none. */
573 /* > \param[in] JOBZ */
575 /* > JOBZ is CHARACTER*1 */
576 /* > = 'N': Compute eigenvalues only; */
577 /* > = 'V': Compute eigenvalues and eigenvectors. */
580 /* > \param[in] UPLO */
582 /* > UPLO is CHARACTER*1 */
583 /* > = 'U': Upper triangles of A and B are stored; */
584 /* > = 'L': Lower triangles of A and B are stored. */
590 /* > The order of the matrices A and B. N >= 0. */
593 /* > \param[in] KA */
595 /* > KA is INTEGER */
596 /* > The number of superdiagonals of the matrix A if UPLO = 'U', */
597 /* > or the number of subdiagonals if UPLO = 'L'. KA >= 0. */
600 /* > \param[in] KB */
602 /* > KB is INTEGER */
603 /* > The number of superdiagonals of the matrix B if UPLO = 'U', */
604 /* > or the number of subdiagonals if UPLO = 'L'. KB >= 0. */
607 /* > \param[in,out] AB */
609 /* > AB is REAL array, dimension (LDAB, N) */
610 /* > On entry, the upper or lower triangle of the symmetric band */
611 /* > matrix A, stored in the first ka+1 rows of the array. The */
612 /* > j-th column of A is stored in the j-th column of the array AB */
614 /* > if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for f2cmax(1,j-ka)<=i<=j; */
615 /* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+ka). */
617 /* > On exit, the contents of AB are destroyed. */
620 /* > \param[in] LDAB */
622 /* > LDAB is INTEGER */
623 /* > The leading dimension of the array AB. LDAB >= KA+1. */
626 /* > \param[in,out] BB */
628 /* > BB is REAL array, dimension (LDBB, N) */
629 /* > On entry, the upper or lower triangle of the symmetric band */
630 /* > matrix B, stored in the first kb+1 rows of the array. The */
631 /* > j-th column of B is stored in the j-th column of the array BB */
633 /* > if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for f2cmax(1,j-kb)<=i<=j; */
634 /* > if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=f2cmin(n,j+kb). */
636 /* > On exit, the factor S from the split Cholesky factorization */
637 /* > B = S**T*S, as returned by SPBSTF. */
640 /* > \param[in] LDBB */
642 /* > LDBB is INTEGER */
643 /* > The leading dimension of the array BB. LDBB >= KB+1. */
646 /* > \param[out] W */
648 /* > W is REAL array, dimension (N) */
649 /* > If INFO = 0, the eigenvalues in ascending order. */
652 /* > \param[out] Z */
654 /* > Z is REAL array, dimension (LDZ, N) */
655 /* > If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */
656 /* > eigenvectors, with the i-th column of Z holding the */
657 /* > eigenvector associated with W(i). The eigenvectors are */
658 /* > normalized so Z**T*B*Z = I. */
659 /* > If JOBZ = 'N', then Z is not referenced. */
662 /* > \param[in] LDZ */
664 /* > LDZ is INTEGER */
665 /* > The leading dimension of the array Z. LDZ >= 1, and if */
666 /* > JOBZ = 'V', LDZ >= f2cmax(1,N). */
669 /* > \param[out] WORK */
671 /* > WORK is REAL array, dimension (MAX(1,LWORK)) */
672 /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
675 /* > \param[in] LWORK */
677 /* > LWORK is INTEGER */
678 /* > The dimension of the array WORK. */
679 /* > If N <= 1, LWORK >= 1. */
680 /* > If JOBZ = 'N' and N > 1, LWORK >= 3*N. */
681 /* > If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2. */
683 /* > If LWORK = -1, then a workspace query is assumed; the routine */
684 /* > only calculates the optimal sizes of the WORK and IWORK */
685 /* > arrays, returns these values as the first entries of the WORK */
686 /* > and IWORK arrays, and no error message related to LWORK or */
687 /* > LIWORK is issued by XERBLA. */
690 /* > \param[out] IWORK */
692 /* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */
693 /* > On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK. */
696 /* > \param[in] LIWORK */
698 /* > LIWORK is INTEGER */
699 /* > The dimension of the array IWORK. */
700 /* > If JOBZ = 'N' or N <= 1, LIWORK >= 1. */
701 /* > If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. */
703 /* > If LIWORK = -1, then a workspace query is assumed; the */
704 /* > routine only calculates the optimal sizes of the WORK and */
705 /* > IWORK arrays, returns these values as the first entries of */
706 /* > the WORK and IWORK arrays, and no error message related to */
707 /* > LWORK or LIWORK is issued by XERBLA. */
710 /* > \param[out] INFO */
712 /* > INFO is INTEGER */
713 /* > = 0: successful exit */
714 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
715 /* > > 0: if INFO = i, and i is: */
716 /* > <= N: the algorithm failed to converge: */
717 /* > i off-diagonal elements of an intermediate */
718 /* > tridiagonal form did not converge to zero; */
719 /* > > N: if INFO = N + i, for 1 <= i <= N, then SPBSTF */
720 /* > returned INFO = i: B is not positive definite. */
721 /* > The factorization of B could not be completed and */
722 /* > no eigenvalues or eigenvectors were computed. */
728 /* > \author Univ. of Tennessee */
729 /* > \author Univ. of California Berkeley */
730 /* > \author Univ. of Colorado Denver */
731 /* > \author NAG Ltd. */
733 /* > \date June 2016 */
735 /* > \ingroup realOTHEReigen */
737 /* > \par Contributors: */
738 /* ================== */
740 /* > Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */
742 /* ===================================================================== */
743 /* Subroutine */ int ssbgvd_(char *jobz, char *uplo, integer *n, integer *ka,
744 integer *kb, real *ab, integer *ldab, real *bb, integer *ldbb, real *
745 w, real *z__, integer *ldz, real *work, integer *lwork, integer *
746 iwork, integer *liwork, integer *info)
748 /* System generated locals */
749 integer ab_dim1, ab_offset, bb_dim1, bb_offset, z_dim1, z_offset, i__1;
751 /* Local variables */
754 extern logical lsame_(char *, char *);
756 extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
757 integer *, real *, real *, integer *, real *, integer *, real *,
760 logical upper, wantz;
761 integer indwk2, llwrk2;
762 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), sstedc_(
763 char *, integer *, real *, real *, real *, integer *, real *,
764 integer *, integer *, integer *, integer *), slacpy_(char
765 *, integer *, integer *, real *, integer *, real *, integer *);
766 integer indwrk, liwmin;
767 extern /* Subroutine */ int spbstf_(char *, integer *, integer *, real *,
768 integer *, integer *), ssbtrd_(char *, char *, integer *,
769 integer *, real *, integer *, real *, real *, real *, integer *,
770 real *, integer *), ssbgst_(char *, char *,
771 integer *, integer *, integer *, real *, integer *, real *,
772 integer *, real *, integer *, real *, integer *),
773 ssterf_(integer *, real *, real *, integer *);
777 /* -- LAPACK driver routine (version 3.7.0) -- */
778 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
779 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
783 /* ===================================================================== */
786 /* Test the input parameters. */
788 /* Parameter adjustments */
790 ab_offset = 1 + ab_dim1 * 1;
793 bb_offset = 1 + bb_dim1 * 1;
797 z_offset = 1 + z_dim1 * 1;
803 wantz = lsame_(jobz, "V");
804 upper = lsame_(uplo, "U");
805 lquery = *lwork == -1 || *liwork == -1;
813 /* Computing 2nd power */
815 lwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
821 if (! (wantz || lsame_(jobz, "N"))) {
823 } else if (! (upper || lsame_(uplo, "L"))) {
827 } else if (*ka < 0) {
829 } else if (*kb < 0 || *kb > *ka) {
831 } else if (*ldab < *ka + 1) {
833 } else if (*ldbb < *kb + 1) {
835 } else if (*ldz < 1 || wantz && *ldz < *n) {
840 work[1] = (real) lwmin;
843 if (*lwork < lwmin && ! lquery) {
845 } else if (*liwork < liwmin && ! lquery) {
852 xerbla_("SSBGVD", &i__1, (ftnlen)6);
858 /* Quick return if possible */
864 /* Form a split Cholesky factorization of B. */
866 spbstf_(uplo, n, kb, &bb[bb_offset], ldbb, info);
872 /* Transform problem to standard eigenvalue problem. */
876 indwk2 = indwrk + *n * *n;
877 llwrk2 = *lwork - indwk2 + 1;
878 ssbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb,
879 &z__[z_offset], ldz, &work[1], &iinfo);
881 /* Reduce to tridiagonal form. */
884 *(unsigned char *)vect = 'U';
886 *(unsigned char *)vect = 'N';
888 ssbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &w[1], &work[inde], &z__[
889 z_offset], ldz, &work[indwrk], &iinfo);
891 /* For eigenvalues only, call SSTERF. For eigenvectors, call SSTEDC. */
894 ssterf_(n, &w[1], &work[inde], info);
896 sstedc_("I", n, &w[1], &work[inde], &work[indwrk], n, &work[indwk2], &
897 llwrk2, &iwork[1], liwork, info);
898 sgemm_("N", "N", n, n, n, &c_b12, &z__[z_offset], ldz, &work[indwrk],
899 n, &c_b13, &work[indwk2], n);
900 slacpy_("A", n, n, &work[indwk2], n, &z__[z_offset], ldz);
903 work[1] = (real) lwmin;