1225 lines
36 KiB
C
1225 lines
36 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#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]);}
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#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]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#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++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#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]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* > \brief \b DLAEBZ 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 DLAEBZ + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaebz.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaebz.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaebz.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLAEBZ( 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 */
|
|
/* DOUBLE PRECISION ABSTOL, PIVMIN, RELTOL */
|
|
/* INTEGER IWORK( * ), NAB( MMAX, * ), NVAL( * ) */
|
|
/* DOUBLE PRECISION AB( MMAX, * ), C( * ), D( * ), E( * ), E2( * ), */
|
|
/* $ WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLAEBZ 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 DLAEBZ 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 DLAEBZ 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 DOUBLE PRECISION */
|
|
/* > 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 DOUBLE PRECISION */
|
|
/* > 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 DOUBLE PRECISION */
|
|
/* > 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 DOUBLE PRECISION array, dimension (N) */
|
|
/* > The diagonal elements of the tridiagonal matrix T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] E */
|
|
/* > \verbatim */
|
|
/* > E is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DLAEBZ 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 DLAEBZ is called. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION 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, DLAEBZ should have one or */
|
|
/* > more initial intervals set up in AB, and DLAEBZ 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. DLAEBZ 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). DLAEBZ 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 */ void dlaebz_(integer *ijob, integer *nitmax, integer *n,
|
|
integer *mmax, integer *minp, integer *nbmin, doublereal *abstol,
|
|
doublereal *reltol, doublereal *pivmin, doublereal *d__, doublereal *
|
|
e, doublereal *e2, integer *nval, doublereal *ab, doublereal *c__,
|
|
integer *mout, integer *nab, doublereal *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;
|
|
doublereal d__1, d__2, d__3, d__4;
|
|
|
|
/* Local variables */
|
|
integer itmp1, itmp2, j, kfnew, klnew, kf, ji, kl, jp, jit;
|
|
doublereal 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;
|
|
}
|
|
|
|
/* 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.) {
|
|
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.) {
|
|
++nab[ji + jp * nab_dim1];
|
|
}
|
|
/* L10: */
|
|
}
|
|
/* L20: */
|
|
}
|
|
*mout = *mout + nab[ji + (nab_dim1 << 1)] - nab[ji + nab_dim1];
|
|
/* L30: */
|
|
}
|
|
return;
|
|
}
|
|
|
|
/* 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)]) * .5;
|
|
/* 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 */
|
|
d__1 = work[ji], d__2 = -(*pivmin);
|
|
work[ji] = f2cmin(d__1,d__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 */
|
|
d__1 = work[ji], d__2 = -(*pivmin);
|
|
work[ji] = f2cmin(d__1,d__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;
|
|
}
|
|
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 */
|
|
d__1 = tmp2, d__2 = -(*pivmin);
|
|
tmp2 = f2cmin(d__1,d__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 */
|
|
d__1 = tmp2, d__2 = -(*pivmin);
|
|
tmp2 = f2cmin(d__1,d__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;
|
|
}
|
|
} 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 = (d__1 = ab[ji + (ab_dim1 << 1)] - ab[ji + ab_dim1], abs(
|
|
d__1));
|
|
/* Computing MAX */
|
|
d__3 = (d__1 = ab[ji + (ab_dim1 << 1)], abs(d__1)), d__4 = (d__2 =
|
|
ab[ji + ab_dim1], abs(d__2));
|
|
tmp2 = f2cmax(d__3,d__4);
|
|
/* Computing MAX */
|
|
d__1 = f2cmax(*abstol,*pivmin), d__2 = *reltol * tmp2;
|
|
if (tmp1 < f2cmax(d__1,d__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)]) * .5;
|
|
/* 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;
|
|
|
|
/* End of DLAEBZ */
|
|
|
|
} /* dlaebz_ */
|
|
|