1422 lines
43 KiB
C
1422 lines
43 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)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
static integer c_n1 = -1;
|
|
static integer c__3 = 3;
|
|
static integer c__2 = 2;
|
|
static integer c__0 = 0;
|
|
|
|
/* > \brief \b DLARRD computes the eigenvalues of a symmetric tridiagonal matrix to suitable accuracy. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLARRD + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrd.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarrd.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarrd.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLARRD( RANGE, ORDER, N, VL, VU, IL, IU, GERS, */
|
|
/* RELTOL, D, E, E2, PIVMIN, NSPLIT, ISPLIT, */
|
|
/* M, W, WERR, WL, WU, IBLOCK, INDEXW, */
|
|
/* WORK, IWORK, INFO ) */
|
|
|
|
/* CHARACTER ORDER, RANGE */
|
|
/* INTEGER IL, INFO, IU, M, N, NSPLIT */
|
|
/* DOUBLE PRECISION PIVMIN, RELTOL, VL, VU, WL, WU */
|
|
/* INTEGER IBLOCK( * ), INDEXW( * ), */
|
|
/* $ ISPLIT( * ), IWORK( * ) */
|
|
/* DOUBLE PRECISION D( * ), E( * ), E2( * ), */
|
|
/* $ GERS( * ), W( * ), WERR( * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLARRD computes the eigenvalues of a symmetric tridiagonal */
|
|
/* > matrix T to suitable accuracy. This is an auxiliary code to be */
|
|
/* > called from DSTEMR. */
|
|
/* > The user may ask for all eigenvalues, all eigenvalues */
|
|
/* > in the half-open interval (VL, VU], or the IL-th through IU-th */
|
|
/* > eigenvalues. */
|
|
/* > */
|
|
/* > To avoid overflow, the matrix must be scaled so that its */
|
|
/* > largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
|
|
*/
|
|
/* > accuracy, it should not be much smaller than that. */
|
|
/* > */
|
|
/* > See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal */
|
|
/* > Matrix", Report CS41, Computer Science Dept., Stanford */
|
|
/* > University, July 21, 1966. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] RANGE */
|
|
/* > \verbatim */
|
|
/* > RANGE is CHARACTER*1 */
|
|
/* > = 'A': ("All") all eigenvalues will be found. */
|
|
/* > = 'V': ("Value") all eigenvalues in the half-open interval */
|
|
/* > (VL, VU] will be found. */
|
|
/* > = 'I': ("Index") the IL-th through IU-th eigenvalues (of the */
|
|
/* > entire matrix) will be found. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ORDER */
|
|
/* > \verbatim */
|
|
/* > ORDER is CHARACTER*1 */
|
|
/* > = 'B': ("By Block") the eigenvalues will be grouped by */
|
|
/* > split-off block (see IBLOCK, ISPLIT) and */
|
|
/* > ordered from smallest to largest within */
|
|
/* > the block. */
|
|
/* > = 'E': ("Entire matrix") */
|
|
/* > the eigenvalues for the entire matrix */
|
|
/* > will be ordered from smallest to */
|
|
/* > largest. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the tridiagonal matrix T. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VL */
|
|
/* > \verbatim */
|
|
/* > VL is DOUBLE PRECISION */
|
|
/* > If RANGE='V', the lower bound of the interval to */
|
|
/* > be searched for eigenvalues. Eigenvalues less than or equal */
|
|
/* > to VL, or greater than VU, will not be returned. VL < VU. */
|
|
/* > Not referenced if RANGE = 'A' or 'I'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VU */
|
|
/* > \verbatim */
|
|
/* > VU is DOUBLE PRECISION */
|
|
/* > If RANGE='V', the upper bound of the interval to */
|
|
/* > be searched for eigenvalues. Eigenvalues less than or equal */
|
|
/* > to VL, or greater than VU, will not be returned. VL < VU. */
|
|
/* > Not referenced if RANGE = 'A' or 'I'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IL */
|
|
/* > \verbatim */
|
|
/* > IL is INTEGER */
|
|
/* > If RANGE='I', the index of the */
|
|
/* > smallest eigenvalue to be returned. */
|
|
/* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
|
|
/* > Not referenced if RANGE = 'A' or 'V'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IU */
|
|
/* > \verbatim */
|
|
/* > IU is INTEGER */
|
|
/* > If RANGE='I', the index of the */
|
|
/* > largest eigenvalue to be returned. */
|
|
/* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
|
|
/* > Not referenced if RANGE = 'A' or 'V'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] GERS */
|
|
/* > \verbatim */
|
|
/* > GERS is DOUBLE PRECISION array, dimension (2*N) */
|
|
/* > The N Gerschgorin intervals (the i-th Gerschgorin interval */
|
|
/* > is (GERS(2*i-1), GERS(2*i)). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RELTOL */
|
|
/* > \verbatim */
|
|
/* > RELTOL is DOUBLE PRECISION */
|
|
/* > The minimum relative width of an interval. When an interval */
|
|
/* > is narrower 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] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension (N) */
|
|
/* > The n diagonal elements of the tridiagonal matrix T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] E */
|
|
/* > \verbatim */
|
|
/* > E is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > The (n-1) off-diagonal elements of the tridiagonal matrix T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] E2 */
|
|
/* > \verbatim */
|
|
/* > E2 is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > The (n-1) squared off-diagonal elements of the tridiagonal matrix T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] PIVMIN */
|
|
/* > \verbatim */
|
|
/* > PIVMIN is DOUBLE PRECISION */
|
|
/* > The minimum pivot allowed in the Sturm sequence for T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NSPLIT */
|
|
/* > \verbatim */
|
|
/* > NSPLIT is INTEGER */
|
|
/* > The number of diagonal blocks in the matrix T. */
|
|
/* > 1 <= NSPLIT <= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ISPLIT */
|
|
/* > \verbatim */
|
|
/* > ISPLIT is INTEGER array, dimension (N) */
|
|
/* > The splitting points, at which T breaks up into submatrices. */
|
|
/* > The first submatrix consists of rows/columns 1 to ISPLIT(1), */
|
|
/* > the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), */
|
|
/* > etc., and the NSPLIT-th consists of rows/columns */
|
|
/* > ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. */
|
|
/* > (Only the first NSPLIT elements will actually be used, but */
|
|
/* > since the user cannot know a priori what value NSPLIT will */
|
|
/* > have, N words must be reserved for ISPLIT.) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The actual number of eigenvalues found. 0 <= M <= N. */
|
|
/* > (See also the description of INFO=2,3.) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] W */
|
|
/* > \verbatim */
|
|
/* > W is DOUBLE PRECISION array, dimension (N) */
|
|
/* > On exit, the first M elements of W will contain the */
|
|
/* > eigenvalue approximations. DLARRD computes an interval */
|
|
/* > I_j = (a_j, b_j] that includes eigenvalue j. The eigenvalue */
|
|
/* > approximation is given as the interval midpoint */
|
|
/* > W(j)= ( a_j + b_j)/2. The corresponding error is bounded by */
|
|
/* > WERR(j) = abs( a_j - b_j)/2 */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WERR */
|
|
/* > \verbatim */
|
|
/* > WERR is DOUBLE PRECISION array, dimension (N) */
|
|
/* > The error bound on the corresponding eigenvalue approximation */
|
|
/* > in W. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WL */
|
|
/* > \verbatim */
|
|
/* > WL is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WU */
|
|
/* > \verbatim */
|
|
/* > WU is DOUBLE PRECISION */
|
|
/* > The interval (WL, WU] contains all the wanted eigenvalues. */
|
|
/* > If RANGE='V', then WL=VL and WU=VU. */
|
|
/* > If RANGE='A', then WL and WU are the global Gerschgorin bounds */
|
|
/* > on the spectrum. */
|
|
/* > If RANGE='I', then WL and WU are computed by DLAEBZ from the */
|
|
/* > index range specified. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IBLOCK */
|
|
/* > \verbatim */
|
|
/* > IBLOCK is INTEGER array, dimension (N) */
|
|
/* > At each row/column j where E(j) is zero or small, the */
|
|
/* > matrix T is considered to split into a block diagonal */
|
|
/* > matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which */
|
|
/* > block (from 1 to the number of blocks) the eigenvalue W(i) */
|
|
/* > belongs. (DLARRD may use the remaining N-M elements as */
|
|
/* > workspace.) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INDEXW */
|
|
/* > \verbatim */
|
|
/* > INDEXW is INTEGER array, dimension (N) */
|
|
/* > The indices of the eigenvalues within each block (submatrix); */
|
|
/* > for example, INDEXW(i)= j and IBLOCK(i)=k imply that the */
|
|
/* > i-th eigenvalue W(i) is the j-th eigenvalue in block k. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (4*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (3*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > > 0: some or all of the eigenvalues failed to converge or */
|
|
/* > were not computed: */
|
|
/* > =1 or 3: Bisection failed to converge for some */
|
|
/* > eigenvalues; these eigenvalues are flagged by a */
|
|
/* > negative block number. The effect is that the */
|
|
/* > eigenvalues may not be as accurate as the */
|
|
/* > absolute and relative tolerances. This is */
|
|
/* > generally caused by unexpectedly inaccurate */
|
|
/* > arithmetic. */
|
|
/* > =2 or 3: RANGE='I' only: Not all of the eigenvalues */
|
|
/* > IL:IU were found. */
|
|
/* > Effect: M < IU+1-IL */
|
|
/* > Cause: non-monotonic arithmetic, causing the */
|
|
/* > Sturm sequence to be non-monotonic. */
|
|
/* > Cure: recalculate, using RANGE='A', and pick */
|
|
/* > out eigenvalues IL:IU. In some cases, */
|
|
/* > increasing the PARAMETER "FUDGE" may */
|
|
/* > make things work. */
|
|
/* > = 4: RANGE='I', and the Gershgorin interval */
|
|
/* > initially used was too small. No eigenvalues */
|
|
/* > were computed. */
|
|
/* > Probable cause: your machine has sloppy */
|
|
/* > floating-point arithmetic. */
|
|
/* > Cure: Increase the PARAMETER "FUDGE", */
|
|
/* > recompile, and try again. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Internal Parameters: */
|
|
/* ========================= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > FUDGE DOUBLE PRECISION, default = 2 */
|
|
/* > A "fudge factor" to widen the Gershgorin intervals. Ideally, */
|
|
/* > a value of 1 should work, but on machines with sloppy */
|
|
/* > arithmetic, this needs to be larger. The default for */
|
|
/* > publicly released versions should be large enough to handle */
|
|
/* > the worst machine around. Note that this has no effect */
|
|
/* > on accuracy of the solution. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > W. Kahan, University of California, Berkeley, USA \n */
|
|
/* > 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 \n */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup OTHERauxiliary */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlarrd_(char *range, char *order, integer *n, doublereal
|
|
*vl, doublereal *vu, integer *il, integer *iu, doublereal *gers,
|
|
doublereal *reltol, doublereal *d__, doublereal *e, doublereal *e2,
|
|
doublereal *pivmin, integer *nsplit, integer *isplit, integer *m,
|
|
doublereal *w, doublereal *werr, doublereal *wl, doublereal *wu,
|
|
integer *iblock, integer *indexw, doublereal *work, integer *iwork,
|
|
integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer i__1, i__2, i__3;
|
|
doublereal d__1, d__2;
|
|
|
|
/* Local variables */
|
|
integer iend, jblk, ioff, iout, itmp1, itmp2, i__, j, jdisc;
|
|
extern logical lsame_(char *, char *);
|
|
integer iinfo;
|
|
doublereal atoli;
|
|
integer iwoff, itmax;
|
|
doublereal wkill, rtoli, uflow, tnorm;
|
|
integer ib, ie, je, nb;
|
|
doublereal gl;
|
|
integer im, in;
|
|
extern doublereal dlamch_(char *);
|
|
doublereal gu;
|
|
integer ibegin, iw;
|
|
extern /* Subroutine */ void dlaebz_(integer *, integer *, integer *,
|
|
integer *, integer *, integer *, doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *, integer *,
|
|
doublereal *, doublereal *, integer *, integer *, doublereal *,
|
|
integer *, integer *);
|
|
integer irange, idiscl, idumma[1];
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
integer idiscu;
|
|
logical ncnvrg, toofew;
|
|
integer jee;
|
|
doublereal eps;
|
|
integer nwl;
|
|
doublereal wlu, wul;
|
|
integer nwu;
|
|
doublereal tmp1, tmp2;
|
|
|
|
|
|
/* -- 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 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Parameter adjustments */
|
|
--iwork;
|
|
--work;
|
|
--indexw;
|
|
--iblock;
|
|
--werr;
|
|
--w;
|
|
--isplit;
|
|
--e2;
|
|
--e;
|
|
--d__;
|
|
--gers;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n <= 0) {
|
|
return;
|
|
}
|
|
|
|
/* Decode RANGE */
|
|
|
|
if (lsame_(range, "A")) {
|
|
irange = 1;
|
|
} else if (lsame_(range, "V")) {
|
|
irange = 2;
|
|
} else if (lsame_(range, "I")) {
|
|
irange = 3;
|
|
} else {
|
|
irange = 0;
|
|
}
|
|
|
|
/* Check for Errors */
|
|
|
|
if (irange <= 0) {
|
|
*info = -1;
|
|
} else if (! (lsame_(order, "B") || lsame_(order,
|
|
"E"))) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -3;
|
|
} else if (irange == 2) {
|
|
if (*vl >= *vu) {
|
|
*info = -5;
|
|
}
|
|
} else if (irange == 3 && (*il < 1 || *il > f2cmax(1,*n))) {
|
|
*info = -6;
|
|
} else if (irange == 3 && (*iu < f2cmin(*n,*il) || *iu > *n)) {
|
|
*info = -7;
|
|
}
|
|
|
|
if (*info != 0) {
|
|
return;
|
|
}
|
|
/* Initialize error flags */
|
|
*info = 0;
|
|
ncnvrg = FALSE_;
|
|
toofew = FALSE_;
|
|
/* Quick return if possible */
|
|
*m = 0;
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
/* Simplification: */
|
|
if (irange == 3 && *il == 1 && *iu == *n) {
|
|
irange = 1;
|
|
}
|
|
/* Get machine constants */
|
|
eps = dlamch_("P");
|
|
uflow = dlamch_("U");
|
|
/* Special Case when N=1 */
|
|
/* Treat case of 1x1 matrix for quick return */
|
|
if (*n == 1) {
|
|
if (irange == 1 || irange == 2 && d__[1] > *vl && d__[1] <= *vu ||
|
|
irange == 3 && *il == 1 && *iu == 1) {
|
|
*m = 1;
|
|
w[1] = d__[1];
|
|
/* The computation error of the eigenvalue is zero */
|
|
werr[1] = 0.;
|
|
iblock[1] = 1;
|
|
indexw[1] = 1;
|
|
}
|
|
return;
|
|
}
|
|
/* NB is the minimum vector length for vector bisection, or 0 */
|
|
/* if only scalar is to be done. */
|
|
nb = ilaenv_(&c__1, "DSTEBZ", " ", n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
|
|
ftnlen)1);
|
|
if (nb <= 1) {
|
|
nb = 0;
|
|
}
|
|
/* Find global spectral radius */
|
|
gl = d__[1];
|
|
gu = d__[1];
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
/* Computing MIN */
|
|
d__1 = gl, d__2 = gers[(i__ << 1) - 1];
|
|
gl = f2cmin(d__1,d__2);
|
|
/* Computing MAX */
|
|
d__1 = gu, d__2 = gers[i__ * 2];
|
|
gu = f2cmax(d__1,d__2);
|
|
/* L5: */
|
|
}
|
|
/* Compute global Gerschgorin bounds and spectral diameter */
|
|
/* Computing MAX */
|
|
d__1 = abs(gl), d__2 = abs(gu);
|
|
tnorm = f2cmax(d__1,d__2);
|
|
gl = gl - tnorm * 2. * eps * *n - *pivmin * 4.;
|
|
gu = gu + tnorm * 2. * eps * *n + *pivmin * 4.;
|
|
/* [JAN/28/2009] remove the line below since SPDIAM variable not use */
|
|
/* SPDIAM = GU - GL */
|
|
/* Input arguments for DLAEBZ: */
|
|
/* The relative tolerance. An interval (a,b] lies within */
|
|
/* "relative tolerance" if b-a < RELTOL*f2cmax(|a|,|b|), */
|
|
rtoli = *reltol;
|
|
/* Set the absolute tolerance for interval convergence to zero to force */
|
|
/* interval convergence based on relative size of the interval. */
|
|
/* This is dangerous because intervals might not converge when RELTOL is */
|
|
/* small. But at least a very small number should be selected so that for */
|
|
/* strongly graded matrices, the code can get relatively accurate */
|
|
/* eigenvalues. */
|
|
atoli = uflow * 4. + *pivmin * 4.;
|
|
if (irange == 3) {
|
|
/* RANGE='I': Compute an interval containing eigenvalues */
|
|
/* IL through IU. The initial interval [GL,GU] from the global */
|
|
/* Gerschgorin bounds GL and GU is refined by DLAEBZ. */
|
|
itmax = (integer) ((log(tnorm + *pivmin) - log(*pivmin)) / log(2.)) +
|
|
2;
|
|
work[*n + 1] = gl;
|
|
work[*n + 2] = gl;
|
|
work[*n + 3] = gu;
|
|
work[*n + 4] = gu;
|
|
work[*n + 5] = gl;
|
|
work[*n + 6] = gu;
|
|
iwork[1] = -1;
|
|
iwork[2] = -1;
|
|
iwork[3] = *n + 1;
|
|
iwork[4] = *n + 1;
|
|
iwork[5] = *il - 1;
|
|
iwork[6] = *iu;
|
|
|
|
dlaebz_(&c__3, &itmax, n, &c__2, &c__2, &nb, &atoli, &rtoli, pivmin, &
|
|
d__[1], &e[1], &e2[1], &iwork[5], &work[*n + 1], &work[*n + 5]
|
|
, &iout, &iwork[1], &w[1], &iblock[1], &iinfo);
|
|
if (iinfo != 0) {
|
|
*info = iinfo;
|
|
return;
|
|
}
|
|
/* On exit, output intervals may not be ordered by ascending negcount */
|
|
if (iwork[6] == *iu) {
|
|
*wl = work[*n + 1];
|
|
wlu = work[*n + 3];
|
|
nwl = iwork[1];
|
|
*wu = work[*n + 4];
|
|
wul = work[*n + 2];
|
|
nwu = iwork[4];
|
|
} else {
|
|
*wl = work[*n + 2];
|
|
wlu = work[*n + 4];
|
|
nwl = iwork[2];
|
|
*wu = work[*n + 3];
|
|
wul = work[*n + 1];
|
|
nwu = iwork[3];
|
|
}
|
|
/* On exit, the interval [WL, WLU] contains a value with negcount NWL, */
|
|
/* and [WUL, WU] contains a value with negcount NWU. */
|
|
if (nwl < 0 || nwl >= *n || nwu < 1 || nwu > *n) {
|
|
*info = 4;
|
|
return;
|
|
}
|
|
} else if (irange == 2) {
|
|
*wl = *vl;
|
|
*wu = *vu;
|
|
} else if (irange == 1) {
|
|
*wl = gl;
|
|
*wu = gu;
|
|
}
|
|
/* Find Eigenvalues -- Loop Over blocks and recompute NWL and NWU. */
|
|
/* NWL accumulates the number of eigenvalues .le. WL, */
|
|
/* NWU accumulates the number of eigenvalues .le. WU */
|
|
*m = 0;
|
|
iend = 0;
|
|
*info = 0;
|
|
nwl = 0;
|
|
nwu = 0;
|
|
|
|
i__1 = *nsplit;
|
|
for (jblk = 1; jblk <= i__1; ++jblk) {
|
|
ioff = iend;
|
|
ibegin = ioff + 1;
|
|
iend = isplit[jblk];
|
|
in = iend - ioff;
|
|
|
|
if (in == 1) {
|
|
/* 1x1 block */
|
|
if (*wl >= d__[ibegin] - *pivmin) {
|
|
++nwl;
|
|
}
|
|
if (*wu >= d__[ibegin] - *pivmin) {
|
|
++nwu;
|
|
}
|
|
if (irange == 1 || *wl < d__[ibegin] - *pivmin && *wu >= d__[
|
|
ibegin] - *pivmin) {
|
|
++(*m);
|
|
w[*m] = d__[ibegin];
|
|
werr[*m] = 0.;
|
|
/* The gap for a single block doesn't matter for the later */
|
|
/* algorithm and is assigned an arbitrary large value */
|
|
iblock[*m] = jblk;
|
|
indexw[*m] = 1;
|
|
}
|
|
/* Disabled 2x2 case because of a failure on the following matrix */
|
|
/* RANGE = 'I', IL = IU = 4 */
|
|
/* Original Tridiagonal, d = [ */
|
|
/* -0.150102010615740E+00 */
|
|
/* -0.849897989384260E+00 */
|
|
/* -0.128208148052635E-15 */
|
|
/* 0.128257718286320E-15 */
|
|
/* ]; */
|
|
/* e = [ */
|
|
/* -0.357171383266986E+00 */
|
|
/* -0.180411241501588E-15 */
|
|
/* -0.175152352710251E-15 */
|
|
/* ]; */
|
|
|
|
/* ELSE IF( IN.EQ.2 ) THEN */
|
|
/* * 2x2 block */
|
|
/* DISC = SQRT( (HALF*(D(IBEGIN)-D(IEND)))**2 + E(IBEGIN)**2 ) */
|
|
/* TMP1 = HALF*(D(IBEGIN)+D(IEND)) */
|
|
/* L1 = TMP1 - DISC */
|
|
/* IF( WL.GE. L1-PIVMIN ) */
|
|
/* $ NWL = NWL + 1 */
|
|
/* IF( WU.GE. L1-PIVMIN ) */
|
|
/* $ NWU = NWU + 1 */
|
|
/* IF( IRANGE.EQ.ALLRNG .OR. ( WL.LT.L1-PIVMIN .AND. WU.GE. */
|
|
/* $ L1-PIVMIN ) ) THEN */
|
|
/* M = M + 1 */
|
|
/* W( M ) = L1 */
|
|
/* * The uncertainty of eigenvalues of a 2x2 matrix is very small */
|
|
/* WERR( M ) = EPS * ABS( W( M ) ) * TWO */
|
|
/* IBLOCK( M ) = JBLK */
|
|
/* INDEXW( M ) = 1 */
|
|
/* ENDIF */
|
|
/* L2 = TMP1 + DISC */
|
|
/* IF( WL.GE. L2-PIVMIN ) */
|
|
/* $ NWL = NWL + 1 */
|
|
/* IF( WU.GE. L2-PIVMIN ) */
|
|
/* $ NWU = NWU + 1 */
|
|
/* IF( IRANGE.EQ.ALLRNG .OR. ( WL.LT.L2-PIVMIN .AND. WU.GE. */
|
|
/* $ L2-PIVMIN ) ) THEN */
|
|
/* M = M + 1 */
|
|
/* W( M ) = L2 */
|
|
/* * The uncertainty of eigenvalues of a 2x2 matrix is very small */
|
|
/* WERR( M ) = EPS * ABS( W( M ) ) * TWO */
|
|
/* IBLOCK( M ) = JBLK */
|
|
/* INDEXW( M ) = 2 */
|
|
/* ENDIF */
|
|
} else {
|
|
/* General Case - block of size IN >= 2 */
|
|
/* Compute local Gerschgorin interval and use it as the initial */
|
|
/* interval for DLAEBZ */
|
|
gu = d__[ibegin];
|
|
gl = d__[ibegin];
|
|
tmp1 = 0.;
|
|
i__2 = iend;
|
|
for (j = ibegin; j <= i__2; ++j) {
|
|
/* Computing MIN */
|
|
d__1 = gl, d__2 = gers[(j << 1) - 1];
|
|
gl = f2cmin(d__1,d__2);
|
|
/* Computing MAX */
|
|
d__1 = gu, d__2 = gers[j * 2];
|
|
gu = f2cmax(d__1,d__2);
|
|
/* L40: */
|
|
}
|
|
/* [JAN/28/2009] */
|
|
/* change SPDIAM by TNORM in lines 2 and 3 thereafter */
|
|
/* line 1: remove computation of SPDIAM (not useful anymore) */
|
|
/* SPDIAM = GU - GL */
|
|
/* GL = GL - FUDGE*SPDIAM*EPS*IN - FUDGE*PIVMIN */
|
|
/* GU = GU + FUDGE*SPDIAM*EPS*IN + FUDGE*PIVMIN */
|
|
gl = gl - tnorm * 2. * eps * in - *pivmin * 2.;
|
|
gu = gu + tnorm * 2. * eps * in + *pivmin * 2.;
|
|
|
|
if (irange > 1) {
|
|
if (gu < *wl) {
|
|
/* the local block contains none of the wanted eigenvalues */
|
|
nwl += in;
|
|
nwu += in;
|
|
goto L70;
|
|
}
|
|
/* refine search interval if possible, only range (WL,WU] matters */
|
|
gl = f2cmax(gl,*wl);
|
|
gu = f2cmin(gu,*wu);
|
|
if (gl >= gu) {
|
|
goto L70;
|
|
}
|
|
}
|
|
/* Find negcount of initial interval boundaries GL and GU */
|
|
work[*n + 1] = gl;
|
|
work[*n + in + 1] = gu;
|
|
dlaebz_(&c__1, &c__0, &in, &in, &c__1, &nb, &atoli, &rtoli,
|
|
pivmin, &d__[ibegin], &e[ibegin], &e2[ibegin], idumma, &
|
|
work[*n + 1], &work[*n + (in << 1) + 1], &im, &iwork[1], &
|
|
w[*m + 1], &iblock[*m + 1], &iinfo);
|
|
if (iinfo != 0) {
|
|
*info = iinfo;
|
|
return;
|
|
}
|
|
|
|
nwl += iwork[1];
|
|
nwu += iwork[in + 1];
|
|
iwoff = *m - iwork[1];
|
|
/* Compute Eigenvalues */
|
|
itmax = (integer) ((log(gu - gl + *pivmin) - log(*pivmin)) / log(
|
|
2.)) + 2;
|
|
dlaebz_(&c__2, &itmax, &in, &in, &c__1, &nb, &atoli, &rtoli,
|
|
pivmin, &d__[ibegin], &e[ibegin], &e2[ibegin], idumma, &
|
|
work[*n + 1], &work[*n + (in << 1) + 1], &iout, &iwork[1],
|
|
&w[*m + 1], &iblock[*m + 1], &iinfo);
|
|
if (iinfo != 0) {
|
|
*info = iinfo;
|
|
return;
|
|
}
|
|
|
|
/* Copy eigenvalues into W and IBLOCK */
|
|
/* Use -JBLK for block number for unconverged eigenvalues. */
|
|
/* Loop over the number of output intervals from DLAEBZ */
|
|
i__2 = iout;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
/* eigenvalue approximation is middle point of interval */
|
|
tmp1 = (work[j + *n] + work[j + in + *n]) * .5;
|
|
/* semi length of error interval */
|
|
tmp2 = (d__1 = work[j + *n] - work[j + in + *n], abs(d__1)) *
|
|
.5;
|
|
if (j > iout - iinfo) {
|
|
/* Flag non-convergence. */
|
|
ncnvrg = TRUE_;
|
|
ib = -jblk;
|
|
} else {
|
|
ib = jblk;
|
|
}
|
|
i__3 = iwork[j + in] + iwoff;
|
|
for (je = iwork[j] + 1 + iwoff; je <= i__3; ++je) {
|
|
w[je] = tmp1;
|
|
werr[je] = tmp2;
|
|
indexw[je] = je - iwoff;
|
|
iblock[je] = ib;
|
|
/* L50: */
|
|
}
|
|
/* L60: */
|
|
}
|
|
|
|
*m += im;
|
|
}
|
|
L70:
|
|
;
|
|
}
|
|
/* If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU */
|
|
/* If NWL+1 < IL or NWU > IU, discard extra eigenvalues. */
|
|
if (irange == 3) {
|
|
idiscl = *il - 1 - nwl;
|
|
idiscu = nwu - *iu;
|
|
|
|
if (idiscl > 0) {
|
|
im = 0;
|
|
i__1 = *m;
|
|
for (je = 1; je <= i__1; ++je) {
|
|
/* Remove some of the smallest eigenvalues from the left so that */
|
|
/* at the end IDISCL =0. Move all eigenvalues up to the left. */
|
|
if (w[je] <= wlu && idiscl > 0) {
|
|
--idiscl;
|
|
} else {
|
|
++im;
|
|
w[im] = w[je];
|
|
werr[im] = werr[je];
|
|
indexw[im] = indexw[je];
|
|
iblock[im] = iblock[je];
|
|
}
|
|
/* L80: */
|
|
}
|
|
*m = im;
|
|
}
|
|
if (idiscu > 0) {
|
|
/* Remove some of the largest eigenvalues from the right so that */
|
|
/* at the end IDISCU =0. Move all eigenvalues up to the left. */
|
|
im = *m + 1;
|
|
for (je = *m; je >= 1; --je) {
|
|
if (w[je] >= wul && idiscu > 0) {
|
|
--idiscu;
|
|
} else {
|
|
--im;
|
|
w[im] = w[je];
|
|
werr[im] = werr[je];
|
|
indexw[im] = indexw[je];
|
|
iblock[im] = iblock[je];
|
|
}
|
|
/* L81: */
|
|
}
|
|
jee = 0;
|
|
i__1 = *m;
|
|
for (je = im; je <= i__1; ++je) {
|
|
++jee;
|
|
w[jee] = w[je];
|
|
werr[jee] = werr[je];
|
|
indexw[jee] = indexw[je];
|
|
iblock[jee] = iblock[je];
|
|
/* L82: */
|
|
}
|
|
*m = *m - im + 1;
|
|
}
|
|
if (idiscl > 0 || idiscu > 0) {
|
|
/* Code to deal with effects of bad arithmetic. (If N(w) is */
|
|
/* monotone non-decreasing, this should never happen.) */
|
|
/* Some low eigenvalues to be discarded are not in (WL,WLU], */
|
|
/* or high eigenvalues to be discarded are not in (WUL,WU] */
|
|
/* so just kill off the smallest IDISCL/largest IDISCU */
|
|
/* eigenvalues, by marking the corresponding IBLOCK = 0 */
|
|
if (idiscl > 0) {
|
|
wkill = *wu;
|
|
i__1 = idiscl;
|
|
for (jdisc = 1; jdisc <= i__1; ++jdisc) {
|
|
iw = 0;
|
|
i__2 = *m;
|
|
for (je = 1; je <= i__2; ++je) {
|
|
if (iblock[je] != 0 && (w[je] < wkill || iw == 0)) {
|
|
iw = je;
|
|
wkill = w[je];
|
|
}
|
|
/* L90: */
|
|
}
|
|
iblock[iw] = 0;
|
|
/* L100: */
|
|
}
|
|
}
|
|
if (idiscu > 0) {
|
|
wkill = *wl;
|
|
i__1 = idiscu;
|
|
for (jdisc = 1; jdisc <= i__1; ++jdisc) {
|
|
iw = 0;
|
|
i__2 = *m;
|
|
for (je = 1; je <= i__2; ++je) {
|
|
if (iblock[je] != 0 && (w[je] >= wkill || iw == 0)) {
|
|
iw = je;
|
|
wkill = w[je];
|
|
}
|
|
/* L110: */
|
|
}
|
|
iblock[iw] = 0;
|
|
/* L120: */
|
|
}
|
|
}
|
|
/* Now erase all eigenvalues with IBLOCK set to zero */
|
|
im = 0;
|
|
i__1 = *m;
|
|
for (je = 1; je <= i__1; ++je) {
|
|
if (iblock[je] != 0) {
|
|
++im;
|
|
w[im] = w[je];
|
|
werr[im] = werr[je];
|
|
indexw[im] = indexw[je];
|
|
iblock[im] = iblock[je];
|
|
}
|
|
/* L130: */
|
|
}
|
|
*m = im;
|
|
}
|
|
if (idiscl < 0 || idiscu < 0) {
|
|
toofew = TRUE_;
|
|
}
|
|
}
|
|
|
|
if (irange == 1 && *m != *n || irange == 3 && *m != *iu - *il + 1) {
|
|
toofew = TRUE_;
|
|
}
|
|
/* If ORDER='B', do nothing the eigenvalues are already sorted by */
|
|
/* block. */
|
|
/* If ORDER='E', sort the eigenvalues from smallest to largest */
|
|
if (lsame_(order, "E") && *nsplit > 1) {
|
|
i__1 = *m - 1;
|
|
for (je = 1; je <= i__1; ++je) {
|
|
ie = 0;
|
|
tmp1 = w[je];
|
|
i__2 = *m;
|
|
for (j = je + 1; j <= i__2; ++j) {
|
|
if (w[j] < tmp1) {
|
|
ie = j;
|
|
tmp1 = w[j];
|
|
}
|
|
/* L140: */
|
|
}
|
|
if (ie != 0) {
|
|
tmp2 = werr[ie];
|
|
itmp1 = iblock[ie];
|
|
itmp2 = indexw[ie];
|
|
w[ie] = w[je];
|
|
werr[ie] = werr[je];
|
|
iblock[ie] = iblock[je];
|
|
indexw[ie] = indexw[je];
|
|
w[je] = tmp1;
|
|
werr[je] = tmp2;
|
|
iblock[je] = itmp1;
|
|
indexw[je] = itmp2;
|
|
}
|
|
/* L150: */
|
|
}
|
|
}
|
|
|
|
*info = 0;
|
|
if (ncnvrg) {
|
|
++(*info);
|
|
}
|
|
if (toofew) {
|
|
*info += 2;
|
|
}
|
|
return;
|
|
|
|
/* End of DLARRD */
|
|
|
|
} /* dlarrd_ */
|
|
|