#include #include #include #include #include #ifdef complex #undef complex #endif #ifdef I #undef I #endif #if defined(_WIN64) typedef long long BLASLONG; typedef unsigned long long BLASULONG; #else typedef long BLASLONG; typedef unsigned long BLASULONG; #endif #ifdef LAPACK_ILP64 typedef BLASLONG blasint; #if defined(_WIN64) #define blasabs(x) llabs(x) #else #define blasabs(x) labs(x) #endif #else typedef int blasint; #define blasabs(x) abs(x) #endif typedef blasint integer; typedef unsigned int uinteger; typedef char *address; typedef short int shortint; typedef float real; typedef double doublereal; typedef struct { real r, i; } complex; typedef struct { doublereal r, i; } doublecomplex; #ifdef _MSC_VER static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;} static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;} static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;} static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;} #else static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;} static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;} static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;} static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;} #endif #define pCf(z) (*_pCf(z)) #define pCd(z) (*_pCd(z)) typedef int logical; typedef short int shortlogical; typedef char logical1; typedef char integer1; #define TRUE_ (1) #define FALSE_ (0) /* Extern is for use with -E */ #ifndef Extern #define Extern extern #endif /* I/O stuff */ typedef int flag; typedef int ftnlen; typedef int ftnint; /*external read, write*/ typedef struct { flag cierr; ftnint ciunit; flag ciend; char *cifmt; ftnint cirec; } cilist; /*internal read, write*/ typedef struct { flag icierr; char *iciunit; flag iciend; char *icifmt; ftnint icirlen; ftnint icirnum; } icilist; /*open*/ typedef struct { flag oerr; ftnint ounit; char *ofnm; ftnlen ofnmlen; char *osta; char *oacc; char *ofm; ftnint orl; char *oblnk; } olist; /*close*/ typedef struct { flag cerr; ftnint cunit; char *csta; } cllist; /*rewind, backspace, endfile*/ typedef struct { flag aerr; ftnint aunit; } alist; /* inquire */ typedef struct { flag inerr; ftnint inunit; char *infile; ftnlen infilen; ftnint *inex; /*parameters in standard's order*/ ftnint *inopen; ftnint *innum; ftnint *innamed; char *inname; ftnlen innamlen; char *inacc; ftnlen inacclen; char *inseq; ftnlen inseqlen; char *indir; ftnlen indirlen; char *infmt; ftnlen infmtlen; char *inform; ftnint informlen; char *inunf; ftnlen inunflen; ftnint *inrecl; ftnint *innrec; char *inblank; ftnlen inblanklen; } inlist; #define VOID void union Multitype { /* for multiple entry points */ integer1 g; shortint h; integer i; /* longint j; */ real r; doublereal d; complex c; doublecomplex z; }; typedef union Multitype Multitype; struct Vardesc { /* for Namelist */ char *name; char *addr; ftnlen *dims; int type; }; typedef struct Vardesc Vardesc; struct Namelist { char *name; Vardesc **vars; int nvars; }; typedef struct Namelist Namelist; #define abs(x) ((x) >= 0 ? (x) : -(x)) #define dabs(x) (fabs(x)) #define f2cmin(a,b) ((a) <= (b) ? (a) : (b)) #define f2cmax(a,b) ((a) >= (b) ? (a) : (b)) #define dmin(a,b) (f2cmin(a,b)) #define dmax(a,b) (f2cmax(a,b)) #define bit_test(a,b) ((a) >> (b) & 1) #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) #define bit_set(a,b) ((a) | ((uinteger)1 << (b))) #define abort_() { sig_die("Fortran abort routine called", 1); } #define c_abs(z) (cabsf(Cf(z))) #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); } #ifdef _MSC_VER #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]);} #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]);} #else #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);} #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);} #endif #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));} #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));} #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));} //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));} #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));} #define d_abs(x) (fabs(*(x))) #define d_acos(x) (acos(*(x))) #define d_asin(x) (asin(*(x))) #define d_atan(x) (atan(*(x))) #define d_atn2(x, y) (atan2(*(x),*(y))) #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); } #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); } #define d_cos(x) (cos(*(x))) #define d_cosh(x) (cosh(*(x))) #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 ) #define d_exp(x) (exp(*(x))) #define d_imag(z) (cimag(Cd(z))) #define r_imag(z) (cimagf(Cf(z))) #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define d_log(x) (log(*(x))) #define d_mod(x, y) (fmod(*(x), *(y))) #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x))) #define d_nint(x) u_nint(*(x)) #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a))) #define d_sign(a,b) u_sign(*(a),*(b)) #define r_sign(a,b) u_sign(*(a),*(b)) #define d_sin(x) (sin(*(x))) #define d_sinh(x) (sinh(*(x))) #define d_sqrt(x) (sqrt(*(x))) #define d_tan(x) (tan(*(x))) #define d_tanh(x) (tanh(*(x))) #define i_abs(x) abs(*(x)) #define i_dnnt(x) ((integer)u_nint(*(x))) #define i_len(s, n) (n) #define i_nint(x) ((integer)u_nint(*(x))) #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b))) #define pow_dd(ap, bp) ( pow(*(ap), *(bp))) #define pow_si(B,E) spow_ui(*(B),*(E)) #define pow_ri(B,E) spow_ui(*(B),*(E)) #define pow_di(B,E) dpow_ui(*(B),*(E)) #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));} #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));} #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));} #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++ = ' '; } #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d)))) #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]; } #define sig_die(s, kill) { exit(1); } #define s_stop(s, n) {exit(0);} static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n"; #define z_abs(z) (cabs(Cd(z))) #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));} #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));} #define myexit_() break; #define mycycle() continue; #define myceiling(w) {ceil(w)} #define myhuge(w) {HUGE_VAL} //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);} #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)} /* procedure parameter types for -A and -C++ */ #define F2C_proc_par_types 1 #ifdef __cplusplus typedef logical (*L_fp)(...); #else typedef logical (*L_fp)(); #endif static float spow_ui(float x, integer n) { float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static double dpow_ui(double x, integer n) { double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #ifdef _MSC_VER static _Fcomplex cpow_ui(complex x, integer n) { complex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i; for(u = n; ; ) { if(u & 01) pow.r *= x.r, pow.i *= x.i; if(u >>= 1) x.r *= x.r, x.i *= x.i; else break; } } _Fcomplex p={pow.r, pow.i}; return p; } #else static _Complex float cpow_ui(_Complex float x, integer n) { _Complex float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif #ifdef _MSC_VER static _Dcomplex zpow_ui(_Dcomplex x, integer n) { _Dcomplex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1]; for(u = n; ; ) { if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1]; if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1]; else break; } } _Dcomplex p = {pow._Val[0], pow._Val[1]}; return p; } #else static _Complex double zpow_ui(_Complex double x, integer n) { _Complex double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif static integer pow_ii(integer x, integer n) { integer pow; unsigned long int u; if (n <= 0) { if (n == 0 || x == 1) pow = 1; else if (x != -1) pow = x == 0 ? 1/x : 0; else n = -n; } if ((n > 0) || !(n == 0 || x == 1 || x != -1)) { u = n; for(pow = 1; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static integer dmaxloc_(double *w, integer s, integer e, integer *n) { double m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static integer smaxloc_(float *w, integer s, integer e, integer *n) { float m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) { integer n = *n_, incx = *incx_, incy = *incy_, i; #ifdef _MSC_VER _Fcomplex zdotc = {0.0, 0.0}; if (incx == 1 && incy == 1) { for (i=0;i \brief \b SLAEBZ computes the number of eigenvalues of a real symmetric tridiagonal matrix which are less than or equal to a given value, and performs other tasks required by the routine sstebz. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SLAEBZ + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SLAEBZ( IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL, */ /* RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT, */ /* NAB, WORK, IWORK, INFO ) */ /* INTEGER IJOB, INFO, MINP, MMAX, MOUT, N, NBMIN, NITMAX */ /* REAL ABSTOL, PIVMIN, RELTOL */ /* INTEGER IWORK( * ), NAB( MMAX, * ), NVAL( * ) */ /* REAL AB( MMAX, * ), C( * ), D( * ), E( * ), E2( * ), */ /* $ WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SLAEBZ contains the iteration loops which compute and use the */ /* > function N(w), which is the count of eigenvalues of a symmetric */ /* > tridiagonal matrix T less than or equal to its argument w. It */ /* > performs a choice of two types of loops: */ /* > */ /* > IJOB=1, followed by */ /* > IJOB=2: It takes as input a list of intervals and returns a list of */ /* > sufficiently small intervals whose union contains the same */ /* > eigenvalues as the union of the original intervals. */ /* > The input intervals are (AB(j,1),AB(j,2)], j=1,...,MINP. */ /* > The output interval (AB(j,1),AB(j,2)] will contain */ /* > eigenvalues NAB(j,1)+1,...,NAB(j,2), where 1 <= j <= MOUT. */ /* > */ /* > IJOB=3: It performs a binary search in each input interval */ /* > (AB(j,1),AB(j,2)] for a point w(j) such that */ /* > N(w(j))=NVAL(j), and uses C(j) as the starting point of */ /* > the search. If such a w(j) is found, then on output */ /* > AB(j,1)=AB(j,2)=w. If no such w(j) is found, then on output */ /* > (AB(j,1),AB(j,2)] will be a small interval containing the */ /* > point where N(w) jumps through NVAL(j), unless that point */ /* > lies outside the initial interval. */ /* > */ /* > Note that the intervals are in all cases half-open intervals, */ /* > i.e., of the form (a,b] , which includes b but not a . */ /* > */ /* > To avoid underflow, the matrix should be scaled so that its largest */ /* > element is no greater than overflow**(1/2) * underflow**(1/4) */ /* > in absolute value. To assure the most accurate computation */ /* > of small eigenvalues, the matrix should be scaled to be */ /* > not much smaller than that, either. */ /* > */ /* > See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal */ /* > Matrix", Report CS41, Computer Science Dept., Stanford */ /* > University, July 21, 1966 */ /* > */ /* > Note: the arguments are, in general, *not* checked for unreasonable */ /* > values. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] IJOB */ /* > \verbatim */ /* > IJOB is INTEGER */ /* > Specifies what is to be done: */ /* > = 1: Compute NAB for the initial intervals. */ /* > = 2: Perform bisection iteration to find eigenvalues of T. */ /* > = 3: Perform bisection iteration to invert N(w), i.e., */ /* > to find a point which has a specified number of */ /* > eigenvalues of T to its left. */ /* > Other values will cause SLAEBZ to return with INFO=-1. */ /* > \endverbatim */ /* > */ /* > \param[in] NITMAX */ /* > \verbatim */ /* > NITMAX is INTEGER */ /* > The maximum number of "levels" of bisection to be */ /* > performed, i.e., an interval of width W will not be made */ /* > smaller than 2^(-NITMAX) * W. If not all intervals */ /* > have converged after NITMAX iterations, then INFO is set */ /* > to the number of non-converged intervals. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The dimension n of the tridiagonal matrix T. It must be at */ /* > least 1. */ /* > \endverbatim */ /* > */ /* > \param[in] MMAX */ /* > \verbatim */ /* > MMAX is INTEGER */ /* > The maximum number of intervals. If more than MMAX intervals */ /* > are generated, then SLAEBZ will quit with INFO=MMAX+1. */ /* > \endverbatim */ /* > */ /* > \param[in] MINP */ /* > \verbatim */ /* > MINP is INTEGER */ /* > The initial number of intervals. It may not be greater than */ /* > MMAX. */ /* > \endverbatim */ /* > */ /* > \param[in] NBMIN */ /* > \verbatim */ /* > NBMIN is INTEGER */ /* > The smallest number of intervals that should be processed */ /* > using a vector loop. If zero, then only the scalar loop */ /* > will be used. */ /* > \endverbatim */ /* > */ /* > \param[in] ABSTOL */ /* > \verbatim */ /* > ABSTOL is REAL */ /* > The minimum (absolute) width of an interval. When an */ /* > interval is narrower than ABSTOL, or than RELTOL times the */ /* > larger (in magnitude) endpoint, then it is considered to be */ /* > sufficiently small, i.e., converged. This must be at least */ /* > zero. */ /* > \endverbatim */ /* > */ /* > \param[in] RELTOL */ /* > \verbatim */ /* > RELTOL is REAL */ /* > The minimum relative width of an interval. When an interval */ /* > is narrower than ABSTOL, or than RELTOL times the larger (in */ /* > magnitude) endpoint, then it is considered to be */ /* > sufficiently small, i.e., converged. Note: this should */ /* > always be at least radix*machine epsilon. */ /* > \endverbatim */ /* > */ /* > \param[in] PIVMIN */ /* > \verbatim */ /* > PIVMIN is REAL */ /* > The minimum absolute value of a "pivot" in the Sturm */ /* > sequence loop. */ /* > This must be at least f2cmax |e(j)**2|*safe_min and at */ /* > least safe_min, where safe_min is at least */ /* > the smallest number that can divide one without overflow. */ /* > \endverbatim */ /* > */ /* > \param[in] D */ /* > \verbatim */ /* > D is REAL array, dimension (N) */ /* > The diagonal elements of the tridiagonal matrix T. */ /* > \endverbatim */ /* > */ /* > \param[in] E */ /* > \verbatim */ /* > E is REAL array, dimension (N) */ /* > The offdiagonal elements of the tridiagonal matrix T in */ /* > positions 1 through N-1. E(N) is arbitrary. */ /* > \endverbatim */ /* > */ /* > \param[in] E2 */ /* > \verbatim */ /* > E2 is REAL array, dimension (N) */ /* > The squares of the offdiagonal elements of the tridiagonal */ /* > matrix T. E2(N) is ignored. */ /* > \endverbatim */ /* > */ /* > \param[in,out] NVAL */ /* > \verbatim */ /* > NVAL is INTEGER array, dimension (MINP) */ /* > If IJOB=1 or 2, not referenced. */ /* > If IJOB=3, the desired values of N(w). The elements of NVAL */ /* > will be reordered to correspond with the intervals in AB. */ /* > Thus, NVAL(j) on output will not, in general be the same as */ /* > NVAL(j) on input, but it will correspond with the interval */ /* > (AB(j,1),AB(j,2)] on output. */ /* > \endverbatim */ /* > */ /* > \param[in,out] AB */ /* > \verbatim */ /* > AB is REAL array, dimension (MMAX,2) */ /* > The endpoints of the intervals. AB(j,1) is a(j), the left */ /* > endpoint of the j-th interval, and AB(j,2) is b(j), the */ /* > right endpoint of the j-th interval. The input intervals */ /* > will, in general, be modified, split, and reordered by the */ /* > calculation. */ /* > \endverbatim */ /* > */ /* > \param[in,out] C */ /* > \verbatim */ /* > C is REAL array, dimension (MMAX) */ /* > If IJOB=1, ignored. */ /* > If IJOB=2, workspace. */ /* > If IJOB=3, then on input C(j) should be initialized to the */ /* > first search point in the binary search. */ /* > \endverbatim */ /* > */ /* > \param[out] MOUT */ /* > \verbatim */ /* > MOUT is INTEGER */ /* > If IJOB=1, the number of eigenvalues in the intervals. */ /* > If IJOB=2 or 3, the number of intervals output. */ /* > If IJOB=3, MOUT will equal MINP. */ /* > \endverbatim */ /* > */ /* > \param[in,out] NAB */ /* > \verbatim */ /* > NAB is INTEGER array, dimension (MMAX,2) */ /* > If IJOB=1, then on output NAB(i,j) will be set to N(AB(i,j)). */ /* > If IJOB=2, then on input, NAB(i,j) should be set. It must */ /* > satisfy the condition: */ /* > N(AB(i,1)) <= NAB(i,1) <= NAB(i,2) <= N(AB(i,2)), */ /* > which means that in interval i only eigenvalues */ /* > NAB(i,1)+1,...,NAB(i,2) will be considered. Usually, */ /* > NAB(i,j)=N(AB(i,j)), from a previous call to SLAEBZ with */ /* > IJOB=1. */ /* > On output, NAB(i,j) will contain */ /* > f2cmax(na(k),f2cmin(nb(k),N(AB(i,j)))), where k is the index of */ /* > the input interval that the output interval */ /* > (AB(j,1),AB(j,2)] came from, and na(k) and nb(k) are the */ /* > the input values of NAB(k,1) and NAB(k,2). */ /* > If IJOB=3, then on output, NAB(i,j) contains N(AB(i,j)), */ /* > unless N(w) > NVAL(i) for all search points w , in which */ /* > case NAB(i,1) will not be modified, i.e., the output */ /* > value will be the same as the input value (modulo */ /* > reorderings -- see NVAL and AB), or unless N(w) < NVAL(i) */ /* > for all search points w , in which case NAB(i,2) will */ /* > not be modified. Normally, NAB should be set to some */ /* > distinctive value(s) before SLAEBZ is called. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension (MMAX) */ /* > Workspace. */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (MMAX) */ /* > Workspace. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: All intervals converged. */ /* > = 1--MMAX: The last INFO intervals did not converge. */ /* > = MMAX+1: More than MMAX intervals were generated. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup OTHERauxiliary */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > This routine is intended to be called only by other LAPACK */ /* > routines, thus the interface is less user-friendly. It is intended */ /* > for two purposes: */ /* > */ /* > (a) finding eigenvalues. In this case, SLAEBZ should have one or */ /* > more initial intervals set up in AB, and SLAEBZ should be called */ /* > with IJOB=1. This sets up NAB, and also counts the eigenvalues. */ /* > Intervals with no eigenvalues would usually be thrown out at */ /* > this point. Also, if not all the eigenvalues in an interval i */ /* > are desired, NAB(i,1) can be increased or NAB(i,2) decreased. */ /* > For example, set NAB(i,1)=NAB(i,2)-1 to get the largest */ /* > eigenvalue. SLAEBZ is then called with IJOB=2 and MMAX */ /* > no smaller than the value of MOUT returned by the call with */ /* > IJOB=1. After this (IJOB=2) call, eigenvalues NAB(i,1)+1 */ /* > through NAB(i,2) are approximately AB(i,1) (or AB(i,2)) to the */ /* > tolerance specified by ABSTOL and RELTOL. */ /* > */ /* > (b) finding an interval (a',b'] containing eigenvalues w(f),...,w(l). */ /* > In this case, start with a Gershgorin interval (a,b). Set up */ /* > AB to contain 2 search intervals, both initially (a,b). One */ /* > NVAL element should contain f-1 and the other should contain l */ /* > , while C should contain a and b, resp. NAB(i,1) should be -1 */ /* > and NAB(i,2) should be N+1, to flag an error if the desired */ /* > interval does not lie in (a,b). SLAEBZ is then called with */ /* > IJOB=3. On exit, if w(f-1) < w(f), then one of the intervals -- */ /* > j -- will have AB(j,1)=AB(j,2) and NAB(j,1)=NAB(j,2)=f-1, while */ /* > if, to the specified tolerance, w(f-k)=...=w(f+r), k > 0 and r */ /* > >= 0, then the interval will have N(AB(j,1))=NAB(j,1)=f-k and */ /* > N(AB(j,2))=NAB(j,2)=f+r. The cases w(l) < w(l+1) and */ /* > w(l-r)=...=w(l+k) are handled similarly. */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int slaebz_(integer *ijob, integer *nitmax, integer *n, integer *mmax, integer *minp, integer *nbmin, real *abstol, real * reltol, real *pivmin, real *d__, real *e, real *e2, integer *nval, real *ab, real *c__, integer *mout, integer *nab, real *work, integer *iwork, integer *info) { /* System generated locals */ integer nab_dim1, nab_offset, ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5, i__6; real r__1, r__2, r__3, r__4; /* Local variables */ integer itmp1, itmp2, j, kfnew, klnew, kf, ji, kl, jp, jit; real tmp1, tmp2; /* -- LAPACK auxiliary routine (version 3.7.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* December 2016 */ /* ===================================================================== */ /* Check for Errors */ /* Parameter adjustments */ nab_dim1 = *mmax; nab_offset = 1 + nab_dim1 * 1; nab -= nab_offset; ab_dim1 = *mmax; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; --d__; --e; --e2; --nval; --c__; --work; --iwork; /* Function Body */ *info = 0; if (*ijob < 1 || *ijob > 3) { *info = -1; return 0; } /* Initialize NAB */ if (*ijob == 1) { /* Compute the number of eigenvalues in the initial intervals. */ *mout = 0; i__1 = *minp; for (ji = 1; ji <= i__1; ++ji) { for (jp = 1; jp <= 2; ++jp) { tmp1 = d__[1] - ab[ji + jp * ab_dim1]; if (abs(tmp1) < *pivmin) { tmp1 = -(*pivmin); } nab[ji + jp * nab_dim1] = 0; if (tmp1 <= 0.f) { nab[ji + jp * nab_dim1] = 1; } i__2 = *n; for (j = 2; j <= i__2; ++j) { tmp1 = d__[j] - e2[j - 1] / tmp1 - ab[ji + jp * ab_dim1]; if (abs(tmp1) < *pivmin) { tmp1 = -(*pivmin); } if (tmp1 <= 0.f) { ++nab[ji + jp * nab_dim1]; } /* L10: */ } /* L20: */ } *mout = *mout + nab[ji + (nab_dim1 << 1)] - nab[ji + nab_dim1]; /* L30: */ } return 0; } /* Initialize for loop */ /* KF and KL have the following meaning: */ /* Intervals 1,...,KF-1 have converged. */ /* Intervals KF,...,KL still need to be refined. */ kf = 1; kl = *minp; /* If IJOB=2, initialize C. */ /* If IJOB=3, use the user-supplied starting point. */ if (*ijob == 2) { i__1 = *minp; for (ji = 1; ji <= i__1; ++ji) { c__[ji] = (ab[ji + ab_dim1] + ab[ji + (ab_dim1 << 1)]) * .5f; /* L40: */ } } /* Iteration loop */ i__1 = *nitmax; for (jit = 1; jit <= i__1; ++jit) { /* Loop over intervals */ if (kl - kf + 1 >= *nbmin && *nbmin > 0) { /* Begin of Parallel Version of the loop */ i__2 = kl; for (ji = kf; ji <= i__2; ++ji) { /* Compute N(c), the number of eigenvalues less than c */ work[ji] = d__[1] - c__[ji]; iwork[ji] = 0; if (work[ji] <= *pivmin) { iwork[ji] = 1; /* Computing MIN */ r__1 = work[ji], r__2 = -(*pivmin); work[ji] = f2cmin(r__1,r__2); } i__3 = *n; for (j = 2; j <= i__3; ++j) { work[ji] = d__[j] - e2[j - 1] / work[ji] - c__[ji]; if (work[ji] <= *pivmin) { ++iwork[ji]; /* Computing MIN */ r__1 = work[ji], r__2 = -(*pivmin); work[ji] = f2cmin(r__1,r__2); } /* L50: */ } /* L60: */ } if (*ijob <= 2) { /* IJOB=2: Choose all intervals containing eigenvalues. */ klnew = kl; i__2 = kl; for (ji = kf; ji <= i__2; ++ji) { /* Insure that N(w) is monotone */ /* Computing MIN */ /* Computing MAX */ i__5 = nab[ji + nab_dim1], i__6 = iwork[ji]; i__3 = nab[ji + (nab_dim1 << 1)], i__4 = f2cmax(i__5,i__6); iwork[ji] = f2cmin(i__3,i__4); /* Update the Queue -- add intervals if both halves */ /* contain eigenvalues. */ if (iwork[ji] == nab[ji + (nab_dim1 << 1)]) { /* No eigenvalue in the upper interval: */ /* just use the lower interval. */ ab[ji + (ab_dim1 << 1)] = c__[ji]; } else if (iwork[ji] == nab[ji + nab_dim1]) { /* No eigenvalue in the lower interval: */ /* just use the upper interval. */ ab[ji + ab_dim1] = c__[ji]; } else { ++klnew; if (klnew <= *mmax) { /* Eigenvalue in both intervals -- add upper to */ /* queue. */ ab[klnew + (ab_dim1 << 1)] = ab[ji + (ab_dim1 << 1)]; nab[klnew + (nab_dim1 << 1)] = nab[ji + (nab_dim1 << 1)]; ab[klnew + ab_dim1] = c__[ji]; nab[klnew + nab_dim1] = iwork[ji]; ab[ji + (ab_dim1 << 1)] = c__[ji]; nab[ji + (nab_dim1 << 1)] = iwork[ji]; } else { *info = *mmax + 1; } } /* L70: */ } if (*info != 0) { return 0; } kl = klnew; } else { /* IJOB=3: Binary search. Keep only the interval containing */ /* w s.t. N(w) = NVAL */ i__2 = kl; for (ji = kf; ji <= i__2; ++ji) { if (iwork[ji] <= nval[ji]) { ab[ji + ab_dim1] = c__[ji]; nab[ji + nab_dim1] = iwork[ji]; } if (iwork[ji] >= nval[ji]) { ab[ji + (ab_dim1 << 1)] = c__[ji]; nab[ji + (nab_dim1 << 1)] = iwork[ji]; } /* L80: */ } } } else { /* End of Parallel Version of the loop */ /* Begin of Serial Version of the loop */ klnew = kl; i__2 = kl; for (ji = kf; ji <= i__2; ++ji) { /* Compute N(w), the number of eigenvalues less than w */ tmp1 = c__[ji]; tmp2 = d__[1] - tmp1; itmp1 = 0; if (tmp2 <= *pivmin) { itmp1 = 1; /* Computing MIN */ r__1 = tmp2, r__2 = -(*pivmin); tmp2 = f2cmin(r__1,r__2); } i__3 = *n; for (j = 2; j <= i__3; ++j) { tmp2 = d__[j] - e2[j - 1] / tmp2 - tmp1; if (tmp2 <= *pivmin) { ++itmp1; /* Computing MIN */ r__1 = tmp2, r__2 = -(*pivmin); tmp2 = f2cmin(r__1,r__2); } /* L90: */ } if (*ijob <= 2) { /* IJOB=2: Choose all intervals containing eigenvalues. */ /* Insure that N(w) is monotone */ /* Computing MIN */ /* Computing MAX */ i__5 = nab[ji + nab_dim1]; i__3 = nab[ji + (nab_dim1 << 1)], i__4 = f2cmax(i__5,itmp1); itmp1 = f2cmin(i__3,i__4); /* Update the Queue -- add intervals if both halves */ /* contain eigenvalues. */ if (itmp1 == nab[ji + (nab_dim1 << 1)]) { /* No eigenvalue in the upper interval: */ /* just use the lower interval. */ ab[ji + (ab_dim1 << 1)] = tmp1; } else if (itmp1 == nab[ji + nab_dim1]) { /* No eigenvalue in the lower interval: */ /* just use the upper interval. */ ab[ji + ab_dim1] = tmp1; } else if (klnew < *mmax) { /* Eigenvalue in both intervals -- add upper to queue. */ ++klnew; ab[klnew + (ab_dim1 << 1)] = ab[ji + (ab_dim1 << 1)]; nab[klnew + (nab_dim1 << 1)] = nab[ji + (nab_dim1 << 1)]; ab[klnew + ab_dim1] = tmp1; nab[klnew + nab_dim1] = itmp1; ab[ji + (ab_dim1 << 1)] = tmp1; nab[ji + (nab_dim1 << 1)] = itmp1; } else { *info = *mmax + 1; return 0; } } else { /* IJOB=3: Binary search. Keep only the interval */ /* containing w s.t. N(w) = NVAL */ if (itmp1 <= nval[ji]) { ab[ji + ab_dim1] = tmp1; nab[ji + nab_dim1] = itmp1; } if (itmp1 >= nval[ji]) { ab[ji + (ab_dim1 << 1)] = tmp1; nab[ji + (nab_dim1 << 1)] = itmp1; } } /* L100: */ } kl = klnew; } /* Check for convergence */ kfnew = kf; i__2 = kl; for (ji = kf; ji <= i__2; ++ji) { tmp1 = (r__1 = ab[ji + (ab_dim1 << 1)] - ab[ji + ab_dim1], abs( r__1)); /* Computing MAX */ r__3 = (r__1 = ab[ji + (ab_dim1 << 1)], abs(r__1)), r__4 = (r__2 = ab[ji + ab_dim1], abs(r__2)); tmp2 = f2cmax(r__3,r__4); /* Computing MAX */ r__1 = f2cmax(*abstol,*pivmin), r__2 = *reltol * tmp2; if (tmp1 < f2cmax(r__1,r__2) || nab[ji + nab_dim1] >= nab[ji + ( nab_dim1 << 1)]) { /* Converged -- Swap with position KFNEW, */ /* then increment KFNEW */ if (ji > kfnew) { tmp1 = ab[ji + ab_dim1]; tmp2 = ab[ji + (ab_dim1 << 1)]; itmp1 = nab[ji + nab_dim1]; itmp2 = nab[ji + (nab_dim1 << 1)]; ab[ji + ab_dim1] = ab[kfnew + ab_dim1]; ab[ji + (ab_dim1 << 1)] = ab[kfnew + (ab_dim1 << 1)]; nab[ji + nab_dim1] = nab[kfnew + nab_dim1]; nab[ji + (nab_dim1 << 1)] = nab[kfnew + (nab_dim1 << 1)]; ab[kfnew + ab_dim1] = tmp1; ab[kfnew + (ab_dim1 << 1)] = tmp2; nab[kfnew + nab_dim1] = itmp1; nab[kfnew + (nab_dim1 << 1)] = itmp2; if (*ijob == 3) { itmp1 = nval[ji]; nval[ji] = nval[kfnew]; nval[kfnew] = itmp1; } } ++kfnew; } /* L110: */ } kf = kfnew; /* Choose Midpoints */ i__2 = kl; for (ji = kf; ji <= i__2; ++ji) { c__[ji] = (ab[ji + ab_dim1] + ab[ji + (ab_dim1 << 1)]) * .5f; /* L120: */ } /* If no more intervals to refine, quit. */ if (kf > kl) { goto L140; } /* L130: */ } /* Converged */ L140: /* Computing MAX */ i__1 = kl + 1 - kf; *info = f2cmax(i__1,0); *mout = kl; return 0; /* End of SLAEBZ */ } /* slaebz_ */