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;
516 static integer c_n1 = -1;
518 /* > \brief <b> SSYEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY mat
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download SSYEVX + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssyevx.
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssyevx.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssyevx.
542 /* SUBROUTINE SSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, */
543 /* ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, */
546 /* CHARACTER JOBZ, RANGE, UPLO */
547 /* INTEGER IL, INFO, IU, LDA, LDZ, LWORK, M, N */
548 /* REAL ABSTOL, VL, VU */
549 /* INTEGER IFAIL( * ), IWORK( * ) */
550 /* REAL A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * ) */
553 /* > \par Purpose: */
558 /* > SSYEVX computes selected eigenvalues and, optionally, eigenvectors */
559 /* > of a real symmetric matrix A. Eigenvalues and eigenvectors can be */
560 /* > selected by specifying either a range of values or a range of indices */
561 /* > for the desired eigenvalues. */
567 /* > \param[in] JOBZ */
569 /* > JOBZ is CHARACTER*1 */
570 /* > = 'N': Compute eigenvalues only; */
571 /* > = 'V': Compute eigenvalues and eigenvectors. */
574 /* > \param[in] RANGE */
576 /* > RANGE is CHARACTER*1 */
577 /* > = 'A': all eigenvalues will be found. */
578 /* > = 'V': all eigenvalues in the half-open interval (VL,VU] */
579 /* > will be found. */
580 /* > = 'I': the IL-th through IU-th eigenvalues will be found. */
583 /* > \param[in] UPLO */
585 /* > UPLO is CHARACTER*1 */
586 /* > = 'U': Upper triangle of A is stored; */
587 /* > = 'L': Lower triangle of A is stored. */
593 /* > The order of the matrix A. N >= 0. */
596 /* > \param[in,out] A */
598 /* > A is REAL array, dimension (LDA, N) */
599 /* > On entry, the symmetric matrix A. If UPLO = 'U', the */
600 /* > leading N-by-N upper triangular part of A contains the */
601 /* > upper triangular part of the matrix A. If UPLO = 'L', */
602 /* > the leading N-by-N lower triangular part of A contains */
603 /* > the lower triangular part of the matrix A. */
604 /* > On exit, the lower triangle (if UPLO='L') or the upper */
605 /* > triangle (if UPLO='U') of A, including the diagonal, is */
609 /* > \param[in] LDA */
611 /* > LDA is INTEGER */
612 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
615 /* > \param[in] VL */
618 /* > If RANGE='V', the lower bound of the interval to */
619 /* > be searched for eigenvalues. VL < VU. */
620 /* > Not referenced if RANGE = 'A' or 'I'. */
623 /* > \param[in] VU */
626 /* > If RANGE='V', the upper bound of the interval to */
627 /* > be searched for eigenvalues. VL < VU. */
628 /* > Not referenced if RANGE = 'A' or 'I'. */
631 /* > \param[in] IL */
633 /* > IL is INTEGER */
634 /* > If RANGE='I', the index of the */
635 /* > smallest eigenvalue to be returned. */
636 /* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
637 /* > Not referenced if RANGE = 'A' or 'V'. */
640 /* > \param[in] IU */
642 /* > IU is INTEGER */
643 /* > If RANGE='I', the index of the */
644 /* > largest eigenvalue to be returned. */
645 /* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
646 /* > Not referenced if RANGE = 'A' or 'V'. */
649 /* > \param[in] ABSTOL */
651 /* > ABSTOL is REAL */
652 /* > The absolute error tolerance for the eigenvalues. */
653 /* > An approximate eigenvalue is accepted as converged */
654 /* > when it is determined to lie in an interval [a,b] */
655 /* > of width less than or equal to */
657 /* > ABSTOL + EPS * f2cmax( |a|,|b| ) , */
659 /* > where EPS is the machine precision. If ABSTOL is less than */
660 /* > or equal to zero, then EPS*|T| will be used in its place, */
661 /* > where |T| is the 1-norm of the tridiagonal matrix obtained */
662 /* > by reducing A to tridiagonal form. */
664 /* > Eigenvalues will be computed most accurately when ABSTOL is */
665 /* > set to twice the underflow threshold 2*SLAMCH('S'), not zero. */
666 /* > If this routine returns with INFO>0, indicating that some */
667 /* > eigenvectors did not converge, try setting ABSTOL to */
668 /* > 2*SLAMCH('S'). */
670 /* > See "Computing Small Singular Values of Bidiagonal Matrices */
671 /* > with Guaranteed High Relative Accuracy," by Demmel and */
672 /* > Kahan, LAPACK Working Note #3. */
675 /* > \param[out] M */
678 /* > The total number of eigenvalues found. 0 <= M <= N. */
679 /* > If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */
682 /* > \param[out] W */
684 /* > W is REAL array, dimension (N) */
685 /* > On normal exit, the first M elements contain the selected */
686 /* > eigenvalues in ascending order. */
689 /* > \param[out] Z */
691 /* > Z is REAL array, dimension (LDZ, f2cmax(1,M)) */
692 /* > If JOBZ = 'V', then if INFO = 0, the first M columns of Z */
693 /* > contain the orthonormal eigenvectors of the matrix A */
694 /* > corresponding to the selected eigenvalues, with the i-th */
695 /* > column of Z holding the eigenvector associated with W(i). */
696 /* > If an eigenvector fails to converge, then that column of Z */
697 /* > contains the latest approximation to the eigenvector, and the */
698 /* > index of the eigenvector is returned in IFAIL. */
699 /* > If JOBZ = 'N', then Z is not referenced. */
700 /* > Note: the user must ensure that at least f2cmax(1,M) columns are */
701 /* > supplied in the array Z; if RANGE = 'V', the exact value of M */
702 /* > is not known in advance and an upper bound must be used. */
705 /* > \param[in] LDZ */
707 /* > LDZ is INTEGER */
708 /* > The leading dimension of the array Z. LDZ >= 1, and if */
709 /* > JOBZ = 'V', LDZ >= f2cmax(1,N). */
712 /* > \param[out] WORK */
714 /* > WORK is REAL array, dimension (MAX(1,LWORK)) */
715 /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
718 /* > \param[in] LWORK */
720 /* > LWORK is INTEGER */
721 /* > The length of the array WORK. LWORK >= 1, when N <= 1; */
722 /* > otherwise 8*N. */
723 /* > For optimal efficiency, LWORK >= (NB+3)*N, */
724 /* > where NB is the f2cmax of the blocksize for SSYTRD and SORMTR */
725 /* > returned by ILAENV. */
727 /* > If LWORK = -1, then a workspace query is assumed; the routine */
728 /* > only calculates the optimal size of the WORK array, returns */
729 /* > this value as the first entry of the WORK array, and no error */
730 /* > message related to LWORK is issued by XERBLA. */
733 /* > \param[out] IWORK */
735 /* > IWORK is INTEGER array, dimension (5*N) */
738 /* > \param[out] IFAIL */
740 /* > IFAIL is INTEGER array, dimension (N) */
741 /* > If JOBZ = 'V', then if INFO = 0, the first M elements of */
742 /* > IFAIL are zero. If INFO > 0, then IFAIL contains the */
743 /* > indices of the eigenvectors that failed to converge. */
744 /* > If JOBZ = 'N', then IFAIL is not referenced. */
747 /* > \param[out] INFO */
749 /* > INFO is INTEGER */
750 /* > = 0: successful exit */
751 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
752 /* > > 0: if INFO = i, then i eigenvectors failed to converge. */
753 /* > Their indices are stored in array IFAIL. */
759 /* > \author Univ. of Tennessee */
760 /* > \author Univ. of California Berkeley */
761 /* > \author Univ. of Colorado Denver */
762 /* > \author NAG Ltd. */
764 /* > \date June 2016 */
766 /* > \ingroup realSYeigen */
768 /* ===================================================================== */
769 /* Subroutine */ int ssyevx_(char *jobz, char *range, char *uplo, integer *n,
770 real *a, integer *lda, real *vl, real *vu, integer *il, integer *iu,
771 real *abstol, integer *m, real *w, real *z__, integer *ldz, real *
772 work, integer *lwork, integer *iwork, integer *ifail, integer *info)
774 /* System generated locals */
775 integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2;
778 /* Local variables */
784 integer itmp1, i__, j, indee;
786 extern logical lsame_(char *, char *);
788 extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
791 extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
792 integer *), sswap_(integer *, real *, integer *, real *, integer *
796 logical alleig, indeig;
797 integer iscale, indibl;
799 extern real slamch_(char *);
801 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
802 integer *, integer *, ftnlen, ftnlen);
803 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
805 integer indtau, indisp, indiwo, indwkn;
806 extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
807 integer *, real *, integer *);
808 integer indwrk, lwkmin;
809 extern /* Subroutine */ int sstein_(integer *, real *, real *, integer *,
810 real *, integer *, integer *, real *, integer *, real *, integer *
811 , integer *, integer *), ssterf_(integer *, real *, real *,
813 integer llwrkn, llwork, nsplit;
815 extern real slansy_(char *, char *, integer *, real *, integer *, real *);
816 extern /* Subroutine */ int sstebz_(char *, char *, integer *, real *,
817 real *, integer *, integer *, real *, real *, real *, integer *,
818 integer *, real *, integer *, integer *, real *, integer *,
822 extern /* Subroutine */ int sorgtr_(char *, integer *, real *, integer *,
823 real *, real *, integer *, integer *), ssteqr_(char *,
824 integer *, real *, real *, real *, integer *, real *, integer *), sormtr_(char *, char *, char *, integer *, integer *,
825 real *, integer *, real *, real *, integer *, real *, integer *,
826 integer *), ssytrd_(char *, integer *,
827 real *, integer *, real *, real *, real *, real *, integer *,
829 real eps, vll, vuu, tmp1;
832 /* -- LAPACK driver routine (version 3.7.0) -- */
833 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
834 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
838 /* ===================================================================== */
841 /* Test the input parameters. */
843 /* Parameter adjustments */
845 a_offset = 1 + a_dim1 * 1;
849 z_offset = 1 + z_dim1 * 1;
856 lower = lsame_(uplo, "L");
857 wantz = lsame_(jobz, "V");
858 alleig = lsame_(range, "A");
859 valeig = lsame_(range, "V");
860 indeig = lsame_(range, "I");
861 lquery = *lwork == -1;
864 if (! (wantz || lsame_(jobz, "N"))) {
866 } else if (! (alleig || valeig || indeig)) {
868 } else if (! (lower || lsame_(uplo, "U"))) {
872 } else if (*lda < f2cmax(1,*n)) {
876 if (*n > 0 && *vu <= *vl) {
880 if (*il < 1 || *il > f2cmax(1,*n)) {
882 } else if (*iu < f2cmin(*n,*il) || *iu > *n) {
888 if (*ldz < 1 || wantz && *ldz < *n) {
896 work[1] = (real) lwkmin;
899 nb = ilaenv_(&c__1, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (
900 ftnlen)6, (ftnlen)1);
902 i__1 = nb, i__2 = ilaenv_(&c__1, "SORMTR", uplo, n, &c_n1, &c_n1,
903 &c_n1, (ftnlen)6, (ftnlen)1);
904 nb = f2cmax(i__1,i__2);
906 i__1 = lwkmin, i__2 = (nb + 3) * *n;
907 lwkopt = f2cmax(i__1,i__2);
908 work[1] = (real) lwkopt;
911 if (*lwork < lwkmin && ! lquery) {
918 xerbla_("SSYEVX", &i__1, (ftnlen)6);
924 /* Quick return if possible */
932 if (alleig || indeig) {
934 w[1] = a[a_dim1 + 1];
936 if (*vl < a[a_dim1 + 1] && *vu >= a[a_dim1 + 1]) {
938 w[1] = a[a_dim1 + 1];
942 z__[z_dim1 + 1] = 1.f;
947 /* Get machine constants. */
949 safmin = slamch_("Safe minimum");
950 eps = slamch_("Precision");
951 smlnum = safmin / eps;
952 bignum = 1.f / smlnum;
955 r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin));
956 rmax = f2cmin(r__1,r__2);
958 /* Scale matrix to allowable range, if necessary. */
966 anrm = slansy_("M", uplo, n, &a[a_offset], lda, &work[1]);
967 if (anrm > 0.f && anrm < rmin) {
970 } else if (anrm > rmax) {
977 for (j = 1; j <= i__1; ++j) {
979 sscal_(&i__2, &sigma, &a[j + j * a_dim1], &c__1);
984 for (j = 1; j <= i__1; ++j) {
985 sscal_(&j, &sigma, &a[j * a_dim1 + 1], &c__1);
990 abstll = *abstol * sigma;
998 /* Call SSYTRD to reduce symmetric matrix to tridiagonal form. */
1004 llwork = *lwork - indwrk + 1;
1005 ssytrd_(uplo, n, &a[a_offset], lda, &work[indd], &work[inde], &work[
1006 indtau], &work[indwrk], &llwork, &iinfo);
1008 /* If all eigenvalues are desired and ABSTOL is less than or equal to */
1009 /* zero, then call SSTERF or SORGTR and SSTEQR. If this fails for */
1010 /* some eigenvalue, then try SSTEBZ. */
1014 if (*il == 1 && *iu == *n) {
1018 if ((alleig || test) && *abstol <= 0.f) {
1019 scopy_(n, &work[indd], &c__1, &w[1], &c__1);
1020 indee = indwrk + (*n << 1);
1023 scopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1);
1024 ssterf_(n, &w[1], &work[indee], info);
1026 slacpy_("A", n, n, &a[a_offset], lda, &z__[z_offset], ldz);
1027 sorgtr_(uplo, n, &z__[z_offset], ldz, &work[indtau], &work[indwrk]
1030 scopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1);
1031 ssteqr_(jobz, n, &w[1], &work[indee], &z__[z_offset], ldz, &work[
1035 for (i__ = 1; i__ <= i__1; ++i__) {
1048 /* Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN. */
1051 *(unsigned char *)order = 'B';
1053 *(unsigned char *)order = 'E';
1056 indisp = indibl + *n;
1057 indiwo = indisp + *n;
1058 sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &work[indd], &work[
1059 inde], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &work[
1060 indwrk], &iwork[indiwo], info);
1063 sstein_(n, &work[indd], &work[inde], m, &w[1], &iwork[indibl], &iwork[
1064 indisp], &z__[z_offset], ldz, &work[indwrk], &iwork[indiwo], &
1067 /* Apply orthogonal matrix used in reduction to tridiagonal */
1068 /* form to eigenvectors returned by SSTEIN. */
1071 llwrkn = *lwork - indwkn + 1;
1072 sormtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau], &z__[
1073 z_offset], ldz, &work[indwkn], &llwrkn, &iinfo);
1076 /* If matrix was scaled, then rescale eigenvalues appropriately. */
1086 sscal_(&imax, &r__1, &w[1], &c__1);
1089 /* If eigenvalues are not in order, then sort them, along with */
1094 for (j = 1; j <= i__1; ++j) {
1098 for (jj = j + 1; jj <= i__2; ++jj) {
1107 itmp1 = iwork[indibl + i__ - 1];
1109 iwork[indibl + i__ - 1] = iwork[indibl + j - 1];
1111 iwork[indibl + j - 1] = itmp1;
1112 sswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1],
1116 ifail[i__] = ifail[j];
1124 /* Set WORK(1) to optimal workspace size. */
1126 work[1] = (real) lwkopt;