942 lines
26 KiB
C
942 lines
26 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 int logical;
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typedef short int shortlogical;
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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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#define F2C_proc_par_types 1
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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 {
|
|
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 DLARRB provides limited bisection to locate eigenvalues for more accuracy. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLARRB + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrb.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarrb.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarrb.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLARRB( N, D, LLD, IFIRST, ILAST, RTOL1, */
|
|
/* RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, */
|
|
/* PIVMIN, SPDIAM, TWIST, INFO ) */
|
|
|
|
/* INTEGER IFIRST, ILAST, INFO, N, OFFSET, TWIST */
|
|
/* DOUBLE PRECISION PIVMIN, RTOL1, RTOL2, SPDIAM */
|
|
/* INTEGER IWORK( * ) */
|
|
/* DOUBLE PRECISION D( * ), LLD( * ), W( * ), */
|
|
/* $ WERR( * ), WGAP( * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > Given the relatively robust representation(RRR) L D L^T, DLARRB */
|
|
/* > does "limited" bisection to refine the eigenvalues of L D L^T, */
|
|
/* > W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial */
|
|
/* > guesses for these eigenvalues are input in W, the corresponding estimate */
|
|
/* > of the error in these guesses and their gaps are input in WERR */
|
|
/* > and WGAP, respectively. During bisection, intervals */
|
|
/* > [left, right] are maintained by storing their mid-points and */
|
|
/* > semi-widths in the arrays W and WERR respectively. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension (N) */
|
|
/* > The N diagonal elements of the diagonal matrix D. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LLD */
|
|
/* > \verbatim */
|
|
/* > LLD is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > The (N-1) elements L(i)*L(i)*D(i). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IFIRST */
|
|
/* > \verbatim */
|
|
/* > IFIRST is INTEGER */
|
|
/* > The index of the first eigenvalue to be computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ILAST */
|
|
/* > \verbatim */
|
|
/* > ILAST is INTEGER */
|
|
/* > The index of the last eigenvalue to be computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RTOL1 */
|
|
/* > \verbatim */
|
|
/* > RTOL1 is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RTOL2 */
|
|
/* > \verbatim */
|
|
/* > RTOL2 is DOUBLE PRECISION */
|
|
/* > Tolerance for the convergence of the bisection intervals. */
|
|
/* > An interval [LEFT,RIGHT] has converged if */
|
|
/* > RIGHT-LEFT < MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) */
|
|
/* > where GAP is the (estimated) distance to the nearest */
|
|
/* > eigenvalue. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] OFFSET */
|
|
/* > \verbatim */
|
|
/* > OFFSET is INTEGER */
|
|
/* > Offset for the arrays W, WGAP and WERR, i.e., the IFIRST-OFFSET */
|
|
/* > through ILAST-OFFSET elements of these arrays are to be used. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] W */
|
|
/* > \verbatim */
|
|
/* > W is DOUBLE PRECISION array, dimension (N) */
|
|
/* > On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are */
|
|
/* > estimates of the eigenvalues of L D L^T indexed IFIRST through */
|
|
/* > ILAST. */
|
|
/* > On output, these estimates are refined. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] WGAP */
|
|
/* > \verbatim */
|
|
/* > WGAP is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > On input, the (estimated) gaps between consecutive */
|
|
/* > eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between */
|
|
/* > eigenvalues I and I+1. Note that if IFIRST = ILAST */
|
|
/* > then WGAP(IFIRST-OFFSET) must be set to ZERO. */
|
|
/* > On output, these gaps are refined. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] WERR */
|
|
/* > \verbatim */
|
|
/* > WERR is DOUBLE PRECISION array, dimension (N) */
|
|
/* > On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are */
|
|
/* > the errors in the estimates of the corresponding elements in W. */
|
|
/* > On output, these errors are refined. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (2*N) */
|
|
/* > Workspace. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (2*N) */
|
|
/* > Workspace. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] PIVMIN */
|
|
/* > \verbatim */
|
|
/* > PIVMIN is DOUBLE PRECISION */
|
|
/* > The minimum pivot in the Sturm sequence. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SPDIAM */
|
|
/* > \verbatim */
|
|
/* > SPDIAM is DOUBLE PRECISION */
|
|
/* > The spectral diameter of the matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TWIST */
|
|
/* > \verbatim */
|
|
/* > TWIST is INTEGER */
|
|
/* > The twist index for the twisted factorization that is used */
|
|
/* > for the negcount. */
|
|
/* > TWIST = N: Compute negcount from L D L^T - LAMBDA I = L+ D+ L+^T */
|
|
/* > TWIST = 1: Compute negcount from L D L^T - LAMBDA I = U- D- U-^T */
|
|
/* > TWIST = R: Compute negcount from L D L^T - LAMBDA I = N(r) D(r) N(r) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > Error flag. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2017 */
|
|
|
|
/* > \ingroup OTHERauxiliary */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Beresford Parlett, University of California, Berkeley, USA \n */
|
|
/* > Jim Demmel, University of California, Berkeley, USA \n */
|
|
/* > Inderjit Dhillon, University of Texas, Austin, USA \n */
|
|
/* > Osni Marques, LBNL/NERSC, USA \n */
|
|
/* > Christof Voemel, University of California, Berkeley, USA */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ int dlarrb_(integer *n, doublereal *d__, doublereal *lld,
|
|
integer *ifirst, integer *ilast, doublereal *rtol1, doublereal *rtol2,
|
|
integer *offset, doublereal *w, doublereal *wgap, doublereal *werr,
|
|
doublereal *work, integer *iwork, doublereal *pivmin, doublereal *
|
|
spdiam, integer *twist, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer i__1;
|
|
doublereal d__1, d__2;
|
|
|
|
/* Local variables */
|
|
doublereal back, lgap, rgap, left;
|
|
integer iter, nint, prev, next, i__, k, r__;
|
|
doublereal cvrgd, right, width;
|
|
integer i1, ii, ip;
|
|
extern integer dlaneg_(integer *, doublereal *, doublereal *, doublereal *
|
|
, doublereal *, integer *);
|
|
integer negcnt;
|
|
doublereal mnwdth;
|
|
integer olnint, maxitr;
|
|
doublereal gap, mid, tmp;
|
|
|
|
|
|
/* -- LAPACK auxiliary routine (version 3.7.1) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 2017 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
|
|
/* Parameter adjustments */
|
|
--iwork;
|
|
--work;
|
|
--werr;
|
|
--wgap;
|
|
--w;
|
|
--lld;
|
|
--d__;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n <= 0) {
|
|
return 0;
|
|
}
|
|
|
|
maxitr = (integer) ((log(*spdiam + *pivmin) - log(*pivmin)) / log(2.)) +
|
|
2;
|
|
mnwdth = *pivmin * 2.;
|
|
|
|
r__ = *twist;
|
|
if (r__ < 1 || r__ > *n) {
|
|
r__ = *n;
|
|
}
|
|
|
|
/* Initialize unconverged intervals in [ WORK(2*I-1), WORK(2*I) ]. */
|
|
/* The Sturm Count, Count( WORK(2*I-1) ) is arranged to be I-1, while */
|
|
/* Count( WORK(2*I) ) is stored in IWORK( 2*I ). The integer IWORK( 2*I-1 ) */
|
|
/* for an unconverged interval is set to the index of the next unconverged */
|
|
/* interval, and is -1 or 0 for a converged interval. Thus a linked */
|
|
/* list of unconverged intervals is set up. */
|
|
|
|
i1 = *ifirst;
|
|
/* The number of unconverged intervals */
|
|
nint = 0;
|
|
/* The last unconverged interval found */
|
|
prev = 0;
|
|
rgap = wgap[i1 - *offset];
|
|
i__1 = *ilast;
|
|
for (i__ = i1; i__ <= i__1; ++i__) {
|
|
k = i__ << 1;
|
|
ii = i__ - *offset;
|
|
left = w[ii] - werr[ii];
|
|
right = w[ii] + werr[ii];
|
|
lgap = rgap;
|
|
rgap = wgap[ii];
|
|
gap = f2cmin(lgap,rgap);
|
|
/* Make sure that [LEFT,RIGHT] contains the desired eigenvalue */
|
|
/* Compute negcount from dstqds facto L+D+L+^T = L D L^T - LEFT */
|
|
|
|
/* Do while( NEGCNT(LEFT).GT.I-1 ) */
|
|
|
|
back = werr[ii];
|
|
L20:
|
|
negcnt = dlaneg_(n, &d__[1], &lld[1], &left, pivmin, &r__);
|
|
if (negcnt > i__ - 1) {
|
|
left -= back;
|
|
back *= 2.;
|
|
goto L20;
|
|
}
|
|
|
|
/* Do while( NEGCNT(RIGHT).LT.I ) */
|
|
/* Compute negcount from dstqds facto L+D+L+^T = L D L^T - RIGHT */
|
|
|
|
back = werr[ii];
|
|
L50:
|
|
negcnt = dlaneg_(n, &d__[1], &lld[1], &right, pivmin, &r__);
|
|
if (negcnt < i__) {
|
|
right += back;
|
|
back *= 2.;
|
|
goto L50;
|
|
}
|
|
width = (d__1 = left - right, abs(d__1)) * .5;
|
|
/* Computing MAX */
|
|
d__1 = abs(left), d__2 = abs(right);
|
|
tmp = f2cmax(d__1,d__2);
|
|
/* Computing MAX */
|
|
d__1 = *rtol1 * gap, d__2 = *rtol2 * tmp;
|
|
cvrgd = f2cmax(d__1,d__2);
|
|
if (width <= cvrgd || width <= mnwdth) {
|
|
/* This interval has already converged and does not need refinement. */
|
|
/* (Note that the gaps might change through refining the */
|
|
/* eigenvalues, however, they can only get bigger.) */
|
|
/* Remove it from the list. */
|
|
iwork[k - 1] = -1;
|
|
/* Make sure that I1 always points to the first unconverged interval */
|
|
if (i__ == i1 && i__ < *ilast) {
|
|
i1 = i__ + 1;
|
|
}
|
|
if (prev >= i1 && i__ <= *ilast) {
|
|
iwork[(prev << 1) - 1] = i__ + 1;
|
|
}
|
|
} else {
|
|
/* unconverged interval found */
|
|
prev = i__;
|
|
++nint;
|
|
iwork[k - 1] = i__ + 1;
|
|
iwork[k] = negcnt;
|
|
}
|
|
work[k - 1] = left;
|
|
work[k] = right;
|
|
/* L75: */
|
|
}
|
|
|
|
/* Do while( NINT.GT.0 ), i.e. there are still unconverged intervals */
|
|
/* and while (ITER.LT.MAXITR) */
|
|
|
|
iter = 0;
|
|
L80:
|
|
prev = i1 - 1;
|
|
i__ = i1;
|
|
olnint = nint;
|
|
i__1 = olnint;
|
|
for (ip = 1; ip <= i__1; ++ip) {
|
|
k = i__ << 1;
|
|
ii = i__ - *offset;
|
|
rgap = wgap[ii];
|
|
lgap = rgap;
|
|
if (ii > 1) {
|
|
lgap = wgap[ii - 1];
|
|
}
|
|
gap = f2cmin(lgap,rgap);
|
|
next = iwork[k - 1];
|
|
left = work[k - 1];
|
|
right = work[k];
|
|
mid = (left + right) * .5;
|
|
/* semiwidth of interval */
|
|
width = right - mid;
|
|
/* Computing MAX */
|
|
d__1 = abs(left), d__2 = abs(right);
|
|
tmp = f2cmax(d__1,d__2);
|
|
/* Computing MAX */
|
|
d__1 = *rtol1 * gap, d__2 = *rtol2 * tmp;
|
|
cvrgd = f2cmax(d__1,d__2);
|
|
if (width <= cvrgd || width <= mnwdth || iter == maxitr) {
|
|
/* reduce number of unconverged intervals */
|
|
--nint;
|
|
/* Mark interval as converged. */
|
|
iwork[k - 1] = 0;
|
|
if (i1 == i__) {
|
|
i1 = next;
|
|
} else {
|
|
/* Prev holds the last unconverged interval previously examined */
|
|
if (prev >= i1) {
|
|
iwork[(prev << 1) - 1] = next;
|
|
}
|
|
}
|
|
i__ = next;
|
|
goto L100;
|
|
}
|
|
prev = i__;
|
|
|
|
/* Perform one bisection step */
|
|
|
|
negcnt = dlaneg_(n, &d__[1], &lld[1], &mid, pivmin, &r__);
|
|
if (negcnt <= i__ - 1) {
|
|
work[k - 1] = mid;
|
|
} else {
|
|
work[k] = mid;
|
|
}
|
|
i__ = next;
|
|
L100:
|
|
;
|
|
}
|
|
++iter;
|
|
/* do another loop if there are still unconverged intervals */
|
|
/* However, in the last iteration, all intervals are accepted */
|
|
/* since this is the best we can do. */
|
|
if (nint > 0 && iter <= maxitr) {
|
|
goto L80;
|
|
}
|
|
|
|
|
|
/* At this point, all the intervals have converged */
|
|
i__1 = *ilast;
|
|
for (i__ = *ifirst; i__ <= i__1; ++i__) {
|
|
k = i__ << 1;
|
|
ii = i__ - *offset;
|
|
/* All intervals marked by '0' have been refined. */
|
|
if (iwork[k - 1] == 0) {
|
|
w[ii] = (work[k - 1] + work[k]) * .5;
|
|
werr[ii] = work[k] - w[ii];
|
|
}
|
|
/* L110: */
|
|
}
|
|
|
|
i__1 = *ilast;
|
|
for (i__ = *ifirst + 1; i__ <= i__1; ++i__) {
|
|
k = i__ << 1;
|
|
ii = i__ - *offset;
|
|
/* Computing MAX */
|
|
d__1 = 0., d__2 = w[ii] - werr[ii] - w[ii - 1] - werr[ii - 1];
|
|
wgap[ii - 1] = f2cmax(d__1,d__2);
|
|
/* L111: */
|
|
}
|
|
return 0;
|
|
|
|
/* End of DLARRB */
|
|
|
|
} /* dlarrb_ */
|
|
|