1356 lines
42 KiB
C
1356 lines
42 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
static real c_b18 = .003f;
|
|
|
|
/* > \brief \b CSTEMR */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CSTEMR + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cstemr.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cstemr.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cstemr.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, */
|
|
/* M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK, */
|
|
/* IWORK, LIWORK, INFO ) */
|
|
|
|
/* CHARACTER JOBZ, RANGE */
|
|
/* LOGICAL TRYRAC */
|
|
/* INTEGER IL, INFO, IU, LDZ, NZC, LIWORK, LWORK, M, N */
|
|
/* REAL VL, VU */
|
|
/* INTEGER ISUPPZ( * ), IWORK( * ) */
|
|
/* REAL D( * ), E( * ), W( * ), WORK( * ) */
|
|
/* COMPLEX Z( LDZ, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CSTEMR computes selected eigenvalues and, optionally, eigenvectors */
|
|
/* > of a real symmetric tridiagonal matrix T. Any such unreduced matrix has */
|
|
/* > a well defined set of pairwise different real eigenvalues, the corresponding */
|
|
/* > real eigenvectors are pairwise orthogonal. */
|
|
/* > */
|
|
/* > The spectrum may be computed either completely or partially by specifying */
|
|
/* > either an interval (VL,VU] or a range of indices IL:IU for the desired */
|
|
/* > eigenvalues. */
|
|
/* > */
|
|
/* > Depending on the number of desired eigenvalues, these are computed either */
|
|
/* > by bisection or the dqds algorithm. Numerically orthogonal eigenvectors are */
|
|
/* > computed by the use of various suitable L D L^T factorizations near clusters */
|
|
/* > of close eigenvalues (referred to as RRRs, Relatively Robust */
|
|
/* > Representations). An informal sketch of the algorithm follows. */
|
|
/* > */
|
|
/* > For each unreduced block (submatrix) of T, */
|
|
/* > (a) Compute T - sigma I = L D L^T, so that L and D */
|
|
/* > define all the wanted eigenvalues to high relative accuracy. */
|
|
/* > This means that small relative changes in the entries of D and L */
|
|
/* > cause only small relative changes in the eigenvalues and */
|
|
/* > eigenvectors. The standard (unfactored) representation of the */
|
|
/* > tridiagonal matrix T does not have this property in general. */
|
|
/* > (b) Compute the eigenvalues to suitable accuracy. */
|
|
/* > If the eigenvectors are desired, the algorithm attains full */
|
|
/* > accuracy of the computed eigenvalues only right before */
|
|
/* > the corresponding vectors have to be computed, see steps c) and d). */
|
|
/* > (c) For each cluster of close eigenvalues, select a new */
|
|
/* > shift close to the cluster, find a new factorization, and refine */
|
|
/* > the shifted eigenvalues to suitable accuracy. */
|
|
/* > (d) For each eigenvalue with a large enough relative separation compute */
|
|
/* > the corresponding eigenvector by forming a rank revealing twisted */
|
|
/* > factorization. Go back to (c) for any clusters that remain. */
|
|
/* > */
|
|
/* > For more details, see: */
|
|
/* > - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations */
|
|
/* > to compute orthogonal eigenvectors of symmetric tridiagonal matrices," */
|
|
/* > Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004. */
|
|
/* > - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and */
|
|
/* > Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25, */
|
|
/* > 2004. Also LAPACK Working Note 154. */
|
|
/* > - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric */
|
|
/* > tridiagonal eigenvalue/eigenvector problem", */
|
|
/* > Computer Science Division Technical Report No. UCB/CSD-97-971, */
|
|
/* > UC Berkeley, May 1997. */
|
|
/* > */
|
|
/* > Further Details */
|
|
/* > 1.CSTEMR works only on machines which follow IEEE-754 */
|
|
/* > floating-point standard in their handling of infinities and NaNs. */
|
|
/* > This permits the use of efficient inner loops avoiding a check for */
|
|
/* > zero divisors. */
|
|
/* > */
|
|
/* > 2. LAPACK routines can be used to reduce a complex Hermitean matrix to */
|
|
/* > real symmetric tridiagonal form. */
|
|
/* > */
|
|
/* > (Any complex Hermitean tridiagonal matrix has real values on its diagonal */
|
|
/* > and potentially complex numbers on its off-diagonals. By applying a */
|
|
/* > similarity transform with an appropriate diagonal matrix */
|
|
/* > diag(1,e^{i \phy_1}, ... , e^{i \phy_{n-1}}), the complex Hermitean */
|
|
/* > matrix can be transformed into a real symmetric matrix and complex */
|
|
/* > arithmetic can be entirely avoided.) */
|
|
/* > */
|
|
/* > While the eigenvectors of the real symmetric tridiagonal matrix are real, */
|
|
/* > the eigenvectors of original complex Hermitean matrix have complex entries */
|
|
/* > in general. */
|
|
/* > Since LAPACK drivers overwrite the matrix data with the eigenvectors, */
|
|
/* > CSTEMR accepts complex workspace to facilitate interoperability */
|
|
/* > with CUNMTR or CUPMTR. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOBZ */
|
|
/* > \verbatim */
|
|
/* > JOBZ is CHARACTER*1 */
|
|
/* > = 'N': Compute eigenvalues only; */
|
|
/* > = 'V': Compute eigenvalues and eigenvectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RANGE */
|
|
/* > \verbatim */
|
|
/* > RANGE is CHARACTER*1 */
|
|
/* > = 'A': all eigenvalues will be found. */
|
|
/* > = 'V': all eigenvalues in the half-open interval (VL,VU] */
|
|
/* > will be found. */
|
|
/* > = 'I': the IL-th through IU-th eigenvalues will be found. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] D */
|
|
/* > \verbatim */
|
|
/* > D is REAL array, dimension (N) */
|
|
/* > On entry, the N diagonal elements of the tridiagonal matrix */
|
|
/* > T. On exit, D is overwritten. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] E */
|
|
/* > \verbatim */
|
|
/* > E is REAL array, dimension (N) */
|
|
/* > On entry, the (N-1) subdiagonal elements of the tridiagonal */
|
|
/* > matrix T in elements 1 to N-1 of E. E(N) need not be set on */
|
|
/* > input, but is used internally as workspace. */
|
|
/* > On exit, E is overwritten. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VL */
|
|
/* > \verbatim */
|
|
/* > VL is REAL */
|
|
/* > */
|
|
/* > If RANGE='V', the lower bound of the interval to */
|
|
/* > be searched for eigenvalues. VL < VU. */
|
|
/* > Not referenced if RANGE = 'A' or 'I'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VU */
|
|
/* > \verbatim */
|
|
/* > VU is REAL */
|
|
/* > */
|
|
/* > If RANGE='V', the upper bound of the interval to */
|
|
/* > be searched for eigenvalues. 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. */
|
|
/* > 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. */
|
|
/* > Not referenced if RANGE = 'A' or 'V'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The total number of eigenvalues found. 0 <= M <= N. */
|
|
/* > If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] W */
|
|
/* > \verbatim */
|
|
/* > W is REAL array, dimension (N) */
|
|
/* > The first M elements contain the selected eigenvalues in */
|
|
/* > ascending order. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] Z */
|
|
/* > \verbatim */
|
|
/* > Z is COMPLEX array, dimension (LDZ, f2cmax(1,M) ) */
|
|
/* > If JOBZ = 'V', and if INFO = 0, then the first M columns of Z */
|
|
/* > contain the orthonormal eigenvectors of the matrix T */
|
|
/* > corresponding to the selected eigenvalues, with the i-th */
|
|
/* > column of Z holding the eigenvector associated with W(i). */
|
|
/* > If JOBZ = 'N', then Z is not referenced. */
|
|
/* > Note: the user must ensure that at least f2cmax(1,M) columns are */
|
|
/* > supplied in the array Z; if RANGE = 'V', the exact value of M */
|
|
/* > is not known in advance and can be computed with a workspace */
|
|
/* > query by setting NZC = -1, see below. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDZ */
|
|
/* > \verbatim */
|
|
/* > LDZ is INTEGER */
|
|
/* > The leading dimension of the array Z. LDZ >= 1, and if */
|
|
/* > JOBZ = 'V', then LDZ >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NZC */
|
|
/* > \verbatim */
|
|
/* > NZC is INTEGER */
|
|
/* > The number of eigenvectors to be held in the array Z. */
|
|
/* > If RANGE = 'A', then NZC >= f2cmax(1,N). */
|
|
/* > If RANGE = 'V', then NZC >= the number of eigenvalues in (VL,VU]. */
|
|
/* > If RANGE = 'I', then NZC >= IU-IL+1. */
|
|
/* > If NZC = -1, then a workspace query is assumed; the */
|
|
/* > routine calculates the number of columns of the array Z that */
|
|
/* > are needed to hold the eigenvectors. */
|
|
/* > This value is returned as the first entry of the Z array, and */
|
|
/* > no error message related to NZC is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ISUPPZ */
|
|
/* > \verbatim */
|
|
/* > ISUPPZ is INTEGER array, dimension ( 2*f2cmax(1,M) ) */
|
|
/* > The support of the eigenvectors in Z, i.e., the indices */
|
|
/* > indicating the nonzero elements in Z. The i-th computed eigenvector */
|
|
/* > is nonzero only in elements ISUPPZ( 2*i-1 ) through */
|
|
/* > ISUPPZ( 2*i ). This is relevant in the case when the matrix */
|
|
/* > is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] TRYRAC */
|
|
/* > \verbatim */
|
|
/* > TRYRAC is LOGICAL */
|
|
/* > If TRYRAC = .TRUE., indicates that the code should check whether */
|
|
/* > the tridiagonal matrix defines its eigenvalues to high relative */
|
|
/* > accuracy. If so, the code uses relative-accuracy preserving */
|
|
/* > algorithms that might be (a bit) slower depending on the matrix. */
|
|
/* > If the matrix does not define its eigenvalues to high relative */
|
|
/* > accuracy, the code can uses possibly faster algorithms. */
|
|
/* > If TRYRAC = .FALSE., the code is not required to guarantee */
|
|
/* > relatively accurate eigenvalues and can use the fastest possible */
|
|
/* > techniques. */
|
|
/* > On exit, a .TRUE. TRYRAC will be set to .FALSE. if the matrix */
|
|
/* > does not define its eigenvalues to high relative accuracy. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is REAL array, dimension (LWORK) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal */
|
|
/* > (and minimal) LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK >= f2cmax(1,18*N) */
|
|
/* > if JOBZ = 'V', and LWORK >= f2cmax(1,12*N) if JOBZ = 'N'. */
|
|
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal size of the WORK array, returns */
|
|
/* > this value as the first entry of the WORK array, and no error */
|
|
/* > message related to LWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (LIWORK) */
|
|
/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LIWORK */
|
|
/* > \verbatim */
|
|
/* > LIWORK is INTEGER */
|
|
/* > The dimension of the array IWORK. LIWORK >= f2cmax(1,10*N) */
|
|
/* > if the eigenvectors are desired, and LIWORK >= f2cmax(1,8*N) */
|
|
/* > if only the eigenvalues are to be computed. */
|
|
/* > If LIWORK = -1, then a workspace query is assumed; the */
|
|
/* > routine only calculates the optimal size of the IWORK array, */
|
|
/* > returns this value as the first entry of the IWORK array, and */
|
|
/* > no error message related to LIWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > On exit, INFO */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > > 0: if INFO = 1X, internal error in SLARRE, */
|
|
/* > if INFO = 2X, internal error in CLARRV. */
|
|
/* > Here, the digit X = ABS( IINFO ) < 10, where IINFO is */
|
|
/* > the nonzero error code returned by SLARRE or */
|
|
/* > CLARRV, respectively. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \date June 2016 */
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/* > \ingroup complexOTHERcomputational */
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/* > \par Contributors: */
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/* ================== */
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/* > */
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/* > Beresford Parlett, University of California, Berkeley, USA \n */
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/* > Jim Demmel, University of California, Berkeley, USA \n */
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/* > Inderjit Dhillon, University of Texas, Austin, USA \n */
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/* > Osni Marques, LBNL/NERSC, USA \n */
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/* > Christof Voemel, University of California, Berkeley, USA */
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/* ===================================================================== */
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/* Subroutine */ void cstemr_(char *jobz, char *range, integer *n, real *d__,
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real *e, real *vl, real *vu, integer *il, integer *iu, integer *m,
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real *w, complex *z__, integer *ldz, integer *nzc, integer *isuppz,
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logical *tryrac, real *work, integer *lwork, integer *iwork, integer *
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liwork, integer *info)
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{
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/* System generated locals */
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integer z_dim1, z_offset, i__1, i__2;
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real r__1, r__2;
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/* Local variables */
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integer indd, iend, jblk, wend;
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real rmin, rmax;
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integer itmp;
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real tnrm;
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integer inde2;
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extern /* Subroutine */ void slae2_(real *, real *, real *, real *, real *)
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;
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integer itmp2;
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real rtol1, rtol2;
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integer i__, j;
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real scale;
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integer indgp;
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extern logical lsame_(char *, char *);
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integer iinfo;
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extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
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integer iindw, ilast;
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extern /* Subroutine */ void cswap_(integer *, complex *, integer *,
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complex *, integer *);
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integer lwmin;
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extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
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integer *);
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logical wantz;
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real r1, r2;
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extern /* Subroutine */ void slaev2_(real *, real *, real *, real *, real *
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, real *, real *);
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integer jj;
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real cs;
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integer in;
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logical alleig, indeig;
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integer ibegin, iindbl;
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real sn, wl;
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logical valeig;
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extern real slamch_(char *);
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integer wbegin;
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real safmin, wu;
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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real bignum;
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integer inderr, iindwk, indgrs, offset;
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extern /* Subroutine */ void slarrc_(char *, integer *, real *, real *,
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real *, real *, real *, integer *, integer *, integer *, integer *
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), clarrv_(integer *, real *, real *, real *, real *,
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real *, integer *, integer *, integer *, integer *, real *, real *
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, real *, real *, real *, real *, integer *, integer *, real *,
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complex *, integer *, integer *, real *, integer *, integer *),
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slarre_(char *, integer *, real *, real *, integer *, integer *,
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real *, real *, real *, real *, real *, real *, integer *,
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integer *, integer *, real *, real *, real *, integer *, integer *
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, real *, real *, real *, integer *, integer *);
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integer iinspl, indwrk, ifirst, liwmin, nzcmin;
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real pivmin, thresh;
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extern real slanst_(char *, integer *, real *, real *);
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extern /* Subroutine */ void slarrj_(integer *, real *, real *, integer *,
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integer *, real *, integer *, real *, real *, real *, integer *,
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real *, real *, integer *);
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integer nsplit;
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extern /* Subroutine */ void slarrr_(integer *, real *, real *, integer *);
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real smlnum;
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extern /* Subroutine */ void slasrt_(char *, integer *, real *, integer *);
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logical lquery, zquery;
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integer iil, iiu;
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real eps, tmp;
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/* -- LAPACK computational routine (version 3.7.1) -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* June 2016 */
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/* ===================================================================== */
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/* Test the input parameters. */
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/* Parameter adjustments */
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--d__;
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--e;
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--w;
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z_dim1 = *ldz;
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z_offset = 1 + z_dim1 * 1;
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z__ -= z_offset;
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--isuppz;
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--work;
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--iwork;
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/* Function Body */
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wantz = lsame_(jobz, "V");
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alleig = lsame_(range, "A");
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valeig = lsame_(range, "V");
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indeig = lsame_(range, "I");
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lquery = *lwork == -1 || *liwork == -1;
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zquery = *nzc == -1;
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/* SSTEMR needs WORK of size 6*N, IWORK of size 3*N. */
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/* In addition, SLARRE needs WORK of size 6*N, IWORK of size 5*N. */
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/* Furthermore, CLARRV needs WORK of size 12*N, IWORK of size 7*N. */
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if (wantz) {
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lwmin = *n * 18;
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liwmin = *n * 10;
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} else {
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/* need less workspace if only the eigenvalues are wanted */
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lwmin = *n * 12;
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liwmin = *n << 3;
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}
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wl = 0.f;
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wu = 0.f;
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iil = 0;
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iiu = 0;
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nsplit = 0;
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if (valeig) {
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/* We do not reference VL, VU in the cases RANGE = 'I','A' */
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/* The interval (WL, WU] contains all the wanted eigenvalues. */
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/* It is either given by the user or computed in SLARRE. */
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wl = *vl;
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wu = *vu;
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} else if (indeig) {
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/* We do not reference IL, IU in the cases RANGE = 'V','A' */
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iil = *il;
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iiu = *iu;
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}
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*info = 0;
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if (! (wantz || lsame_(jobz, "N"))) {
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*info = -1;
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} else if (! (alleig || valeig || indeig)) {
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*info = -2;
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} else if (*n < 0) {
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*info = -3;
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} else if (valeig && *n > 0 && wu <= wl) {
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*info = -7;
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} else if (indeig && (iil < 1 || iil > *n)) {
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*info = -8;
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} else if (indeig && (iiu < iil || iiu > *n)) {
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*info = -9;
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} else if (*ldz < 1 || wantz && *ldz < *n) {
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*info = -13;
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} else if (*lwork < lwmin && ! lquery) {
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*info = -17;
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} else if (*liwork < liwmin && ! lquery) {
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*info = -19;
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}
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/* Get machine constants. */
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safmin = slamch_("Safe minimum");
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eps = slamch_("Precision");
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smlnum = safmin / eps;
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bignum = 1.f / smlnum;
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rmin = sqrt(smlnum);
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/* Computing MIN */
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r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin));
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rmax = f2cmin(r__1,r__2);
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if (*info == 0) {
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work[1] = (real) lwmin;
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iwork[1] = liwmin;
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if (wantz && alleig) {
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nzcmin = *n;
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} else if (wantz && valeig) {
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slarrc_("T", n, vl, vu, &d__[1], &e[1], &safmin, &nzcmin, &itmp, &
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itmp2, info);
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} else if (wantz && indeig) {
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nzcmin = iiu - iil + 1;
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} else {
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/* WANTZ .EQ. FALSE. */
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nzcmin = 0;
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}
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if (zquery && *info == 0) {
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i__1 = z_dim1 + 1;
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z__[i__1].r = (real) nzcmin, z__[i__1].i = 0.f;
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} else if (*nzc < nzcmin && ! zquery) {
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*info = -14;
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}
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("CSTEMR", &i__1, (ftnlen)6);
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return;
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} else if (lquery || zquery) {
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return;
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}
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/* Handle N = 0, 1, and 2 cases immediately */
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*m = 0;
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if (*n == 0) {
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return;
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}
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if (*n == 1) {
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if (alleig || indeig) {
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*m = 1;
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w[1] = d__[1];
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} else {
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if (wl < d__[1] && wu >= d__[1]) {
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*m = 1;
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w[1] = d__[1];
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}
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}
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if (wantz && ! zquery) {
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i__1 = z_dim1 + 1;
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z__[i__1].r = 1.f, z__[i__1].i = 0.f;
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isuppz[1] = 1;
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isuppz[2] = 1;
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}
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return;
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}
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if (*n == 2) {
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if (! wantz) {
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slae2_(&d__[1], &e[1], &d__[2], &r1, &r2);
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} else if (wantz && ! zquery) {
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slaev2_(&d__[1], &e[1], &d__[2], &r1, &r2, &cs, &sn);
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}
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if (alleig || valeig && r2 > wl && r2 <= wu || indeig && iil == 1) {
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++(*m);
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w[*m] = r2;
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if (wantz && ! zquery) {
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i__1 = *m * z_dim1 + 1;
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r__1 = -sn;
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z__[i__1].r = r__1, z__[i__1].i = 0.f;
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i__1 = *m * z_dim1 + 2;
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z__[i__1].r = cs, z__[i__1].i = 0.f;
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/* Note: At most one of SN and CS can be zero. */
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if (sn != 0.f) {
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if (cs != 0.f) {
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isuppz[(*m << 1) - 1] = 1;
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isuppz[*m * 2] = 2;
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} else {
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isuppz[(*m << 1) - 1] = 1;
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isuppz[*m * 2] = 1;
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}
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} else {
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isuppz[(*m << 1) - 1] = 2;
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isuppz[*m * 2] = 2;
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}
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}
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}
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if (alleig || valeig && r1 > wl && r1 <= wu || indeig && iiu == 2) {
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++(*m);
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w[*m] = r1;
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if (wantz && ! zquery) {
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i__1 = *m * z_dim1 + 1;
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z__[i__1].r = cs, z__[i__1].i = 0.f;
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i__1 = *m * z_dim1 + 2;
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z__[i__1].r = sn, z__[i__1].i = 0.f;
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/* Note: At most one of SN and CS can be zero. */
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if (sn != 0.f) {
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if (cs != 0.f) {
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isuppz[(*m << 1) - 1] = 1;
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isuppz[*m * 2] = 2;
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} else {
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isuppz[(*m << 1) - 1] = 1;
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isuppz[*m * 2] = 1;
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}
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} else {
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isuppz[(*m << 1) - 1] = 2;
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isuppz[*m * 2] = 2;
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}
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}
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}
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} else {
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/* Continue with general N */
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indgrs = 1;
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inderr = (*n << 1) + 1;
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indgp = *n * 3 + 1;
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indd = (*n << 2) + 1;
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inde2 = *n * 5 + 1;
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indwrk = *n * 6 + 1;
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iinspl = 1;
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iindbl = *n + 1;
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iindw = (*n << 1) + 1;
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iindwk = *n * 3 + 1;
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/* Scale matrix to allowable range, if necessary. */
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/* The allowable range is related to the PIVMIN parameter; see the */
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/* comments in SLARRD. The preference for scaling small values */
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/* up is heuristic; we expect users' matrices not to be close to the */
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/* RMAX threshold. */
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scale = 1.f;
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tnrm = slanst_("M", n, &d__[1], &e[1]);
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if (tnrm > 0.f && tnrm < rmin) {
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scale = rmin / tnrm;
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} else if (tnrm > rmax) {
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scale = rmax / tnrm;
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}
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if (scale != 1.f) {
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sscal_(n, &scale, &d__[1], &c__1);
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i__1 = *n - 1;
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sscal_(&i__1, &scale, &e[1], &c__1);
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tnrm *= scale;
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if (valeig) {
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/* If eigenvalues in interval have to be found, */
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/* scale (WL, WU] accordingly */
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wl *= scale;
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wu *= scale;
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}
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}
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/* Compute the desired eigenvalues of the tridiagonal after splitting */
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/* into smaller subblocks if the corresponding off-diagonal elements */
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/* are small */
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/* THRESH is the splitting parameter for SLARRE */
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/* A negative THRESH forces the old splitting criterion based on the */
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/* size of the off-diagonal. A positive THRESH switches to splitting */
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/* which preserves relative accuracy. */
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if (*tryrac) {
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/* Test whether the matrix warrants the more expensive relative approach. */
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slarrr_(n, &d__[1], &e[1], &iinfo);
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} else {
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/* The user does not care about relative accurately eigenvalues */
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iinfo = -1;
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}
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/* Set the splitting criterion */
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if (iinfo == 0) {
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thresh = eps;
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} else {
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thresh = -eps;
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/* relative accuracy is desired but T does not guarantee it */
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*tryrac = FALSE_;
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}
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if (*tryrac) {
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/* Copy original diagonal, needed to guarantee relative accuracy */
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scopy_(n, &d__[1], &c__1, &work[indd], &c__1);
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}
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/* Store the squares of the offdiagonal values of T */
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i__1 = *n - 1;
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for (j = 1; j <= i__1; ++j) {
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/* Computing 2nd power */
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r__1 = e[j];
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work[inde2 + j - 1] = r__1 * r__1;
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/* L5: */
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}
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/* Set the tolerance parameters for bisection */
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if (! wantz) {
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/* SLARRE computes the eigenvalues to full precision. */
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rtol1 = eps * 4.f;
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rtol2 = eps * 4.f;
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} else {
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/* SLARRE computes the eigenvalues to less than full precision. */
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/* CLARRV will refine the eigenvalue approximations, and we only */
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/* need less accurate initial bisection in SLARRE. */
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/* Note: these settings do only affect the subset case and SLARRE */
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/* Computing MAX */
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r__1 = sqrt(eps) * .05f, r__2 = eps * 4.f;
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rtol1 = f2cmax(r__1,r__2);
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/* Computing MAX */
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r__1 = sqrt(eps) * .005f, r__2 = eps * 4.f;
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rtol2 = f2cmax(r__1,r__2);
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}
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slarre_(range, n, &wl, &wu, &iil, &iiu, &d__[1], &e[1], &work[inde2],
|
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&rtol1, &rtol2, &thresh, &nsplit, &iwork[iinspl], m, &w[1], &
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work[inderr], &work[indgp], &iwork[iindbl], &iwork[iindw], &
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work[indgrs], &pivmin, &work[indwrk], &iwork[iindwk], &iinfo);
|
|
if (iinfo != 0) {
|
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*info = abs(iinfo) + 10;
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return;
|
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}
|
|
/* Note that if RANGE .NE. 'V', SLARRE computes bounds on the desired */
|
|
/* part of the spectrum. All desired eigenvalues are contained in */
|
|
/* (WL,WU] */
|
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if (wantz) {
|
|
|
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/* Compute the desired eigenvectors corresponding to the computed */
|
|
/* eigenvalues */
|
|
|
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clarrv_(n, &wl, &wu, &d__[1], &e[1], &pivmin, &iwork[iinspl], m, &
|
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c__1, m, &c_b18, &rtol1, &rtol2, &w[1], &work[inderr], &
|
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work[indgp], &iwork[iindbl], &iwork[iindw], &work[indgrs],
|
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&z__[z_offset], ldz, &isuppz[1], &work[indwrk], &iwork[
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iindwk], &iinfo);
|
|
if (iinfo != 0) {
|
|
*info = abs(iinfo) + 20;
|
|
return;
|
|
}
|
|
} else {
|
|
/* SLARRE computes eigenvalues of the (shifted) root representation */
|
|
/* CLARRV returns the eigenvalues of the unshifted matrix. */
|
|
/* However, if the eigenvectors are not desired by the user, we need */
|
|
/* to apply the corresponding shifts from SLARRE to obtain the */
|
|
/* eigenvalues of the original matrix. */
|
|
i__1 = *m;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
itmp = iwork[iindbl + j - 1];
|
|
w[j] += e[iwork[iinspl + itmp - 1]];
|
|
/* L20: */
|
|
}
|
|
}
|
|
|
|
if (*tryrac) {
|
|
/* Refine computed eigenvalues so that they are relatively accurate */
|
|
/* with respect to the original matrix T. */
|
|
ibegin = 1;
|
|
wbegin = 1;
|
|
i__1 = iwork[iindbl + *m - 1];
|
|
for (jblk = 1; jblk <= i__1; ++jblk) {
|
|
iend = iwork[iinspl + jblk - 1];
|
|
in = iend - ibegin + 1;
|
|
wend = wbegin - 1;
|
|
/* check if any eigenvalues have to be refined in this block */
|
|
L36:
|
|
if (wend < *m) {
|
|
if (iwork[iindbl + wend] == jblk) {
|
|
++wend;
|
|
goto L36;
|
|
}
|
|
}
|
|
if (wend < wbegin) {
|
|
ibegin = iend + 1;
|
|
goto L39;
|
|
}
|
|
offset = iwork[iindw + wbegin - 1] - 1;
|
|
ifirst = iwork[iindw + wbegin - 1];
|
|
ilast = iwork[iindw + wend - 1];
|
|
rtol2 = eps * 4.f;
|
|
slarrj_(&in, &work[indd + ibegin - 1], &work[inde2 + ibegin -
|
|
1], &ifirst, &ilast, &rtol2, &offset, &w[wbegin], &
|
|
work[inderr + wbegin - 1], &work[indwrk], &iwork[
|
|
iindwk], &pivmin, &tnrm, &iinfo);
|
|
ibegin = iend + 1;
|
|
wbegin = wend + 1;
|
|
L39:
|
|
;
|
|
}
|
|
}
|
|
|
|
/* If matrix was scaled, then rescale eigenvalues appropriately. */
|
|
|
|
if (scale != 1.f) {
|
|
r__1 = 1.f / scale;
|
|
sscal_(m, &r__1, &w[1], &c__1);
|
|
}
|
|
}
|
|
|
|
/* If eigenvalues are not in increasing order, then sort them, */
|
|
/* possibly along with eigenvectors. */
|
|
|
|
if (nsplit > 1 || *n == 2) {
|
|
if (! wantz) {
|
|
slasrt_("I", m, &w[1], &iinfo);
|
|
if (iinfo != 0) {
|
|
*info = 3;
|
|
return;
|
|
}
|
|
} else {
|
|
i__1 = *m - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__ = 0;
|
|
tmp = w[j];
|
|
i__2 = *m;
|
|
for (jj = j + 1; jj <= i__2; ++jj) {
|
|
if (w[jj] < tmp) {
|
|
i__ = jj;
|
|
tmp = w[jj];
|
|
}
|
|
/* L50: */
|
|
}
|
|
if (i__ != 0) {
|
|
w[i__] = w[j];
|
|
w[j] = tmp;
|
|
if (wantz) {
|
|
cswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j *
|
|
z_dim1 + 1], &c__1);
|
|
itmp = isuppz[(i__ << 1) - 1];
|
|
isuppz[(i__ << 1) - 1] = isuppz[(j << 1) - 1];
|
|
isuppz[(j << 1) - 1] = itmp;
|
|
itmp = isuppz[i__ * 2];
|
|
isuppz[i__ * 2] = isuppz[j * 2];
|
|
isuppz[j * 2] = itmp;
|
|
}
|
|
}
|
|
/* L60: */
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
work[1] = (real) lwmin;
|
|
iwork[1] = liwmin;
|
|
return;
|
|
|
|
/* End of CSTEMR */
|
|
|
|
} /* cstemr_ */
|
|
|