1309 lines
41 KiB
C
1309 lines
41 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__10 = 10;
|
|
static integer c__1 = 1;
|
|
static integer c__2 = 2;
|
|
static integer c__3 = 3;
|
|
static integer c__4 = 4;
|
|
static integer c_n1 = -1;
|
|
|
|
/* > \brief <b> CHEEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE mat
|
|
rices</b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CHEEVR + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cheevr.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cheevr.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cheevr.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, */
|
|
/* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, */
|
|
/* RWORK, LRWORK, IWORK, LIWORK, INFO ) */
|
|
|
|
/* CHARACTER JOBZ, RANGE, UPLO */
|
|
/* INTEGER IL, INFO, IU, LDA, LDZ, LIWORK, LRWORK, LWORK, */
|
|
/* $ M, N */
|
|
/* REAL ABSTOL, VL, VU */
|
|
/* INTEGER ISUPPZ( * ), IWORK( * ) */
|
|
/* REAL RWORK( * ), W( * ) */
|
|
/* COMPLEX A( LDA, * ), WORK( * ), Z( LDZ, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CHEEVR computes selected eigenvalues and, optionally, eigenvectors */
|
|
/* > of a complex Hermitian matrix A. Eigenvalues and eigenvectors can */
|
|
/* > be selected by specifying either a range of values or a range of */
|
|
/* > indices for the desired eigenvalues. */
|
|
/* > */
|
|
/* > CHEEVR first reduces the matrix A to tridiagonal form T with a call */
|
|
/* > to CHETRD. Then, whenever possible, CHEEVR calls CSTEMR to compute */
|
|
/* > the eigenspectrum using Relatively Robust Representations. CSTEMR */
|
|
/* > computes eigenvalues by the dqds algorithm, while orthogonal */
|
|
/* > eigenvectors are computed from various "good" L D L^T representations */
|
|
/* > (also known as Relatively Robust Representations). Gram-Schmidt */
|
|
/* > orthogonalization is avoided as far as possible. More specifically, */
|
|
/* > the various steps of the algorithm are as 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. */
|
|
/* > */
|
|
/* > The desired accuracy of the output can be specified by the input */
|
|
/* > parameter ABSTOL. */
|
|
/* > */
|
|
/* > For more details, see DSTEMR's documentation and: */
|
|
/* > - 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. */
|
|
/* > */
|
|
/* > */
|
|
/* > Note 1 : CHEEVR calls CSTEMR when the full spectrum is requested */
|
|
/* > on machines which conform to the ieee-754 floating point standard. */
|
|
/* > CHEEVR calls SSTEBZ and CSTEIN on non-ieee machines and */
|
|
/* > when partial spectrum requests are made. */
|
|
/* > */
|
|
/* > Normal execution of CSTEMR may create NaNs and infinities and */
|
|
/* > hence may abort due to a floating point exception in environments */
|
|
/* > which do not handle NaNs and infinities in the ieee standard default */
|
|
/* > manner. */
|
|
/* > \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. */
|
|
/* > For RANGE = 'V' or 'I' and IU - IL < N - 1, SSTEBZ and */
|
|
/* > CSTEIN are called */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > = 'U': Upper triangle of A is stored; */
|
|
/* > = 'L': Lower triangle of A is stored. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX array, dimension (LDA, N) */
|
|
/* > On entry, the Hermitian matrix A. If UPLO = 'U', the */
|
|
/* > leading N-by-N upper triangular part of A contains the */
|
|
/* > upper triangular part of the matrix A. If UPLO = 'L', */
|
|
/* > the leading N-by-N lower triangular part of A contains */
|
|
/* > the lower triangular part of the matrix A. */
|
|
/* > On exit, the lower triangle (if UPLO='L') or the upper */
|
|
/* > triangle (if UPLO='U') of A, including the diagonal, is */
|
|
/* > destroyed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \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; 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] ABSTOL */
|
|
/* > \verbatim */
|
|
/* > ABSTOL is REAL */
|
|
/* > The absolute error tolerance for the eigenvalues. */
|
|
/* > An approximate eigenvalue is accepted as converged */
|
|
/* > when it is determined to lie in an interval [a,b] */
|
|
/* > of width less than or equal to */
|
|
/* > */
|
|
/* > ABSTOL + EPS * f2cmax( |a|,|b| ) , */
|
|
/* > */
|
|
/* > where EPS is the machine precision. If ABSTOL is less than */
|
|
/* > or equal to zero, then EPS*|T| will be used in its place, */
|
|
/* > where |T| is the 1-norm of the tridiagonal matrix obtained */
|
|
/* > by reducing A to tridiagonal form. */
|
|
/* > */
|
|
/* > See "Computing Small Singular Values of Bidiagonal Matrices */
|
|
/* > with Guaranteed High Relative Accuracy," by Demmel and */
|
|
/* > Kahan, LAPACK Working Note #3. */
|
|
/* > */
|
|
/* > If high relative accuracy is important, set ABSTOL to */
|
|
/* > SLAMCH( 'Safe minimum' ). Doing so will guarantee that */
|
|
/* > eigenvalues are computed to high relative accuracy when */
|
|
/* > possible in future releases. The current code does not */
|
|
/* > make any guarantees about high relative accuracy, but */
|
|
/* > future releases will. See J. Barlow and J. Demmel, */
|
|
/* > "Computing Accurate Eigensystems of Scaled Diagonally */
|
|
/* > Dominant Matrices", LAPACK Working Note #7, for a discussion */
|
|
/* > of which matrices define their eigenvalues to high relative */
|
|
/* > accuracy. */
|
|
/* > \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', then if INFO = 0, the first M columns of Z */
|
|
/* > contain the orthonormal eigenvectors of the matrix A */
|
|
/* > 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 an upper bound must be used. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDZ */
|
|
/* > \verbatim */
|
|
/* > LDZ is INTEGER */
|
|
/* > The leading dimension of the array Z. LDZ >= 1, and if */
|
|
/* > JOBZ = 'V', LDZ >= f2cmax(1,N). */
|
|
/* > \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 eigenvector */
|
|
/* > is nonzero only in elements ISUPPZ( 2*i-1 ) through */
|
|
/* > ISUPPZ( 2*i ). This is an output of CSTEMR (tridiagonal */
|
|
/* > matrix). The support of the eigenvectors of A is typically */
|
|
/* > 1:N because of the unitary transformations applied by CUNMTR. */
|
|
/* > Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The length of the array WORK. LWORK >= f2cmax(1,2*N). */
|
|
/* > For optimal efficiency, LWORK >= (NB+1)*N, */
|
|
/* > where NB is the f2cmax of the blocksize for CHETRD and for */
|
|
/* > CUNMTR as returned by ILAENV. */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal sizes of the WORK, RWORK and */
|
|
/* > IWORK arrays, returns these values as the first entries of */
|
|
/* > the WORK, RWORK and IWORK arrays, and no error message */
|
|
/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is REAL array, dimension (MAX(1,LRWORK)) */
|
|
/* > On exit, if INFO = 0, RWORK(1) returns the optimal */
|
|
/* > (and minimal) LRWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LRWORK */
|
|
/* > \verbatim */
|
|
/* > LRWORK is INTEGER */
|
|
/* > The length of the array RWORK. LRWORK >= f2cmax(1,24*N). */
|
|
/* > */
|
|
/* > If LRWORK = -1, then a workspace query is assumed; the */
|
|
/* > routine only calculates the optimal sizes of the WORK, RWORK */
|
|
/* > and IWORK arrays, returns these values as the first entries */
|
|
/* > of the WORK, RWORK and IWORK arrays, and no error message */
|
|
/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */
|
|
/* > On exit, if INFO = 0, IWORK(1) returns the optimal */
|
|
/* > (and minimal) LIWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LIWORK */
|
|
/* > \verbatim */
|
|
/* > LIWORK is INTEGER */
|
|
/* > The dimension of the array IWORK. LIWORK >= f2cmax(1,10*N). */
|
|
/* > */
|
|
/* > If LIWORK = -1, then a workspace query is assumed; the */
|
|
/* > routine only calculates the optimal sizes of the WORK, RWORK */
|
|
/* > and IWORK arrays, returns these values as the first entries */
|
|
/* > of the WORK, RWORK and IWORK arrays, and no error message */
|
|
/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > > 0: Internal error */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup complexHEeigen */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Inderjit Dhillon, IBM Almaden, USA \n */
|
|
/* > Osni Marques, LBNL/NERSC, USA \n */
|
|
/* > Ken Stanley, Computer Science Division, University of */
|
|
/* > California at Berkeley, USA \n */
|
|
/* > Jason Riedy, Computer Science Division, University of */
|
|
/* > California at Berkeley, USA \n */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void cheevr_(char *jobz, char *range, char *uplo, integer *n,
|
|
complex *a, integer *lda, real *vl, real *vu, integer *il, integer *
|
|
iu, real *abstol, integer *m, real *w, complex *z__, integer *ldz,
|
|
integer *isuppz, complex *work, integer *lwork, real *rwork, integer *
|
|
lrwork, integer *iwork, integer *liwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2;
|
|
real r__1, r__2;
|
|
|
|
/* Local variables */
|
|
real anrm;
|
|
integer imax;
|
|
real rmin, rmax;
|
|
logical test;
|
|
integer itmp1, i__, j, indrd, indre;
|
|
real sigma;
|
|
extern logical lsame_(char *, char *);
|
|
integer iinfo;
|
|
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
|
|
char order[1];
|
|
integer indwk;
|
|
extern /* Subroutine */ void cswap_(integer *, complex *, integer *,
|
|
complex *, integer *);
|
|
integer lwmin;
|
|
logical lower;
|
|
extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
|
|
integer *);
|
|
logical wantz;
|
|
integer nb, jj;
|
|
logical alleig, indeig;
|
|
integer iscale, ieeeok, indibl, indrdd, indifl, indree;
|
|
logical valeig;
|
|
extern real slamch_(char *);
|
|
extern /* Subroutine */ void chetrd_(char *, integer *, complex *, integer
|
|
*, real *, real *, complex *, complex *, integer *, integer *), csscal_(integer *, real *, complex *, integer *);
|
|
real safmin;
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
real abstll, bignum;
|
|
integer indtau, indisp;
|
|
extern /* Subroutine */ void cstein_(integer *, real *, real *, integer *,
|
|
real *, integer *, integer *, complex *, integer *, real *,
|
|
integer *, integer *, integer *);
|
|
integer indiwo, indwkn;
|
|
extern real clansy_(char *, char *, integer *, complex *, integer *, real
|
|
*);
|
|
extern /* Subroutine */ void cstemr_(char *, char *, integer *, real *,
|
|
real *, real *, real *, integer *, integer *, integer *, real *,
|
|
complex *, integer *, integer *, integer *, logical *, real *,
|
|
integer *, integer *, integer *, integer *);
|
|
integer indrwk, liwmin;
|
|
logical tryrac;
|
|
extern /* Subroutine */ void ssterf_(integer *, real *, real *, integer *);
|
|
integer lrwmin, llwrkn, llwork, nsplit;
|
|
real smlnum;
|
|
extern /* Subroutine */ void cunmtr_(char *, char *, char *, integer *,
|
|
integer *, complex *, integer *, complex *, complex *, integer *,
|
|
complex *, integer *, integer *), sstebz_(
|
|
char *, char *, integer *, real *, real *, integer *, integer *,
|
|
real *, real *, real *, integer *, integer *, real *, integer *,
|
|
integer *, real *, integer *, integer *);
|
|
logical lquery;
|
|
integer lwkopt;
|
|
real eps, vll, vuu;
|
|
integer llrwork;
|
|
real tmp1;
|
|
|
|
|
|
/* -- LAPACK driver routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--w;
|
|
z_dim1 = *ldz;
|
|
z_offset = 1 + z_dim1 * 1;
|
|
z__ -= z_offset;
|
|
--isuppz;
|
|
--work;
|
|
--rwork;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
ieeeok = ilaenv_(&c__10, "CHEEVR", "N", &c__1, &c__2, &c__3, &c__4, (
|
|
ftnlen)6, (ftnlen)1);
|
|
|
|
lower = lsame_(uplo, "L");
|
|
wantz = lsame_(jobz, "V");
|
|
alleig = lsame_(range, "A");
|
|
valeig = lsame_(range, "V");
|
|
indeig = lsame_(range, "I");
|
|
|
|
lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
|
|
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *n * 24;
|
|
lrwmin = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *n * 10;
|
|
liwmin = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *n << 1;
|
|
lwmin = f2cmax(i__1,i__2);
|
|
|
|
*info = 0;
|
|
if (! (wantz || lsame_(jobz, "N"))) {
|
|
*info = -1;
|
|
} else if (! (alleig || valeig || indeig)) {
|
|
*info = -2;
|
|
} else if (! (lower || lsame_(uplo, "U"))) {
|
|
*info = -3;
|
|
} else if (*n < 0) {
|
|
*info = -4;
|
|
} else if (*lda < f2cmax(1,*n)) {
|
|
*info = -6;
|
|
} else {
|
|
if (valeig) {
|
|
if (*n > 0 && *vu <= *vl) {
|
|
*info = -8;
|
|
}
|
|
} else if (indeig) {
|
|
if (*il < 1 || *il > f2cmax(1,*n)) {
|
|
*info = -9;
|
|
} else if (*iu < f2cmin(*n,*il) || *iu > *n) {
|
|
*info = -10;
|
|
}
|
|
}
|
|
}
|
|
if (*info == 0) {
|
|
if (*ldz < 1 || wantz && *ldz < *n) {
|
|
*info = -15;
|
|
}
|
|
}
|
|
|
|
if (*info == 0) {
|
|
nb = ilaenv_(&c__1, "CHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
|
|
(ftnlen)1);
|
|
/* Computing MAX */
|
|
i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMTR", uplo, n, &c_n1, &c_n1, &
|
|
c_n1, (ftnlen)6, (ftnlen)1);
|
|
nb = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = (nb + 1) * *n;
|
|
lwkopt = f2cmax(i__1,lwmin);
|
|
work[1].r = (real) lwkopt, work[1].i = 0.f;
|
|
rwork[1] = (real) lrwmin;
|
|
iwork[1] = liwmin;
|
|
|
|
if (*lwork < lwmin && ! lquery) {
|
|
*info = -18;
|
|
} else if (*lrwork < lrwmin && ! lquery) {
|
|
*info = -20;
|
|
} else if (*liwork < liwmin && ! lquery) {
|
|
*info = -22;
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("CHEEVR", &i__1, (ftnlen)6);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
*m = 0;
|
|
if (*n == 0) {
|
|
work[1].r = 1.f, work[1].i = 0.f;
|
|
return;
|
|
}
|
|
|
|
if (*n == 1) {
|
|
work[1].r = 2.f, work[1].i = 0.f;
|
|
if (alleig || indeig) {
|
|
*m = 1;
|
|
i__1 = a_dim1 + 1;
|
|
w[1] = a[i__1].r;
|
|
} else {
|
|
i__1 = a_dim1 + 1;
|
|
i__2 = a_dim1 + 1;
|
|
if (*vl < a[i__1].r && *vu >= a[i__2].r) {
|
|
*m = 1;
|
|
i__1 = a_dim1 + 1;
|
|
w[1] = a[i__1].r;
|
|
}
|
|
}
|
|
if (wantz) {
|
|
i__1 = z_dim1 + 1;
|
|
z__[i__1].r = 1.f, z__[i__1].i = 0.f;
|
|
isuppz[1] = 1;
|
|
isuppz[2] = 1;
|
|
}
|
|
return;
|
|
}
|
|
|
|
/* Get machine constants. */
|
|
|
|
safmin = slamch_("Safe minimum");
|
|
eps = slamch_("Precision");
|
|
smlnum = safmin / eps;
|
|
bignum = 1.f / smlnum;
|
|
rmin = sqrt(smlnum);
|
|
/* Computing MIN */
|
|
r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin));
|
|
rmax = f2cmin(r__1,r__2);
|
|
|
|
/* Scale matrix to allowable range, if necessary. */
|
|
|
|
iscale = 0;
|
|
abstll = *abstol;
|
|
if (valeig) {
|
|
vll = *vl;
|
|
vuu = *vu;
|
|
}
|
|
anrm = clansy_("M", uplo, n, &a[a_offset], lda, &rwork[1]);
|
|
if (anrm > 0.f && anrm < rmin) {
|
|
iscale = 1;
|
|
sigma = rmin / anrm;
|
|
} else if (anrm > rmax) {
|
|
iscale = 1;
|
|
sigma = rmax / anrm;
|
|
}
|
|
if (iscale == 1) {
|
|
if (lower) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *n - j + 1;
|
|
csscal_(&i__2, &sigma, &a[j + j * a_dim1], &c__1);
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
csscal_(&j, &sigma, &a[j * a_dim1 + 1], &c__1);
|
|
/* L20: */
|
|
}
|
|
}
|
|
if (*abstol > 0.f) {
|
|
abstll = *abstol * sigma;
|
|
}
|
|
if (valeig) {
|
|
vll = *vl * sigma;
|
|
vuu = *vu * sigma;
|
|
}
|
|
}
|
|
/* Initialize indices into workspaces. Note: The IWORK indices are */
|
|
/* used only if SSTERF or CSTEMR fail. */
|
|
/* WORK(INDTAU:INDTAU+N-1) stores the complex scalar factors of the */
|
|
/* elementary reflectors used in CHETRD. */
|
|
indtau = 1;
|
|
/* INDWK is the starting offset of the remaining complex workspace, */
|
|
/* and LLWORK is the remaining complex workspace size. */
|
|
indwk = indtau + *n;
|
|
llwork = *lwork - indwk + 1;
|
|
/* RWORK(INDRD:INDRD+N-1) stores the real tridiagonal's diagonal */
|
|
/* entries. */
|
|
indrd = 1;
|
|
/* RWORK(INDRE:INDRE+N-1) stores the off-diagonal entries of the */
|
|
/* tridiagonal matrix from CHETRD. */
|
|
indre = indrd + *n;
|
|
/* RWORK(INDRDD:INDRDD+N-1) is a copy of the diagonal entries over */
|
|
/* -written by CSTEMR (the SSTERF path copies the diagonal to W). */
|
|
indrdd = indre + *n;
|
|
/* RWORK(INDREE:INDREE+N-1) is a copy of the off-diagonal entries over */
|
|
/* -written while computing the eigenvalues in SSTERF and CSTEMR. */
|
|
indree = indrdd + *n;
|
|
/* INDRWK is the starting offset of the left-over real workspace, and */
|
|
/* LLRWORK is the remaining workspace size. */
|
|
indrwk = indree + *n;
|
|
llrwork = *lrwork - indrwk + 1;
|
|
/* IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in SSTEBZ and */
|
|
/* stores the block indices of each of the M<=N eigenvalues. */
|
|
indibl = 1;
|
|
/* IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in SSTEBZ and */
|
|
/* stores the starting and finishing indices of each block. */
|
|
indisp = indibl + *n;
|
|
/* IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors */
|
|
/* that corresponding to eigenvectors that fail to converge in */
|
|
/* SSTEIN. This information is discarded; if any fail, the driver */
|
|
/* returns INFO > 0. */
|
|
indifl = indisp + *n;
|
|
/* INDIWO is the offset of the remaining integer workspace. */
|
|
indiwo = indifl + *n;
|
|
|
|
/* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */
|
|
|
|
chetrd_(uplo, n, &a[a_offset], lda, &rwork[indrd], &rwork[indre], &work[
|
|
indtau], &work[indwk], &llwork, &iinfo);
|
|
|
|
/* If all eigenvalues are desired */
|
|
/* then call SSTERF or CSTEMR and CUNMTR. */
|
|
|
|
test = FALSE_;
|
|
if (indeig) {
|
|
if (*il == 1 && *iu == *n) {
|
|
test = TRUE_;
|
|
}
|
|
}
|
|
if ((alleig || test) && ieeeok == 1) {
|
|
if (! wantz) {
|
|
scopy_(n, &rwork[indrd], &c__1, &w[1], &c__1);
|
|
i__1 = *n - 1;
|
|
scopy_(&i__1, &rwork[indre], &c__1, &rwork[indree], &c__1);
|
|
ssterf_(n, &w[1], &rwork[indree], info);
|
|
} else {
|
|
i__1 = *n - 1;
|
|
scopy_(&i__1, &rwork[indre], &c__1, &rwork[indree], &c__1);
|
|
scopy_(n, &rwork[indrd], &c__1, &rwork[indrdd], &c__1);
|
|
|
|
if (*abstol <= *n * 2.f * eps) {
|
|
tryrac = TRUE_;
|
|
} else {
|
|
tryrac = FALSE_;
|
|
}
|
|
cstemr_(jobz, "A", n, &rwork[indrdd], &rwork[indree], vl, vu, il,
|
|
iu, m, &w[1], &z__[z_offset], ldz, n, &isuppz[1], &tryrac,
|
|
&rwork[indrwk], &llrwork, &iwork[1], liwork, info);
|
|
|
|
/* Apply unitary matrix used in reduction to tridiagonal */
|
|
/* form to eigenvectors returned by CSTEMR. */
|
|
|
|
if (wantz && *info == 0) {
|
|
indwkn = indwk;
|
|
llwrkn = *lwork - indwkn + 1;
|
|
cunmtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau]
|
|
, &z__[z_offset], ldz, &work[indwkn], &llwrkn, &iinfo);
|
|
}
|
|
}
|
|
|
|
|
|
if (*info == 0) {
|
|
*m = *n;
|
|
goto L30;
|
|
}
|
|
*info = 0;
|
|
}
|
|
|
|
/* Otherwise, call SSTEBZ and, if eigenvectors are desired, CSTEIN. */
|
|
/* Also call SSTEBZ and CSTEIN if CSTEMR fails. */
|
|
|
|
if (wantz) {
|
|
*(unsigned char *)order = 'B';
|
|
} else {
|
|
*(unsigned char *)order = 'E';
|
|
}
|
|
sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &rwork[indrd], &
|
|
rwork[indre], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &
|
|
rwork[indrwk], &iwork[indiwo], info);
|
|
|
|
if (wantz) {
|
|
cstein_(n, &rwork[indrd], &rwork[indre], m, &w[1], &iwork[indibl], &
|
|
iwork[indisp], &z__[z_offset], ldz, &rwork[indrwk], &iwork[
|
|
indiwo], &iwork[indifl], info);
|
|
|
|
/* Apply unitary matrix used in reduction to tridiagonal */
|
|
/* form to eigenvectors returned by CSTEIN. */
|
|
|
|
indwkn = indwk;
|
|
llwrkn = *lwork - indwkn + 1;
|
|
cunmtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau], &z__[
|
|
z_offset], ldz, &work[indwkn], &llwrkn, &iinfo);
|
|
}
|
|
|
|
/* If matrix was scaled, then rescale eigenvalues appropriately. */
|
|
|
|
L30:
|
|
if (iscale == 1) {
|
|
if (*info == 0) {
|
|
imax = *m;
|
|
} else {
|
|
imax = *info - 1;
|
|
}
|
|
r__1 = 1.f / sigma;
|
|
sscal_(&imax, &r__1, &w[1], &c__1);
|
|
}
|
|
|
|
/* If eigenvalues are not in order, then sort them, along with */
|
|
/* eigenvectors. */
|
|
|
|
if (wantz) {
|
|
i__1 = *m - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__ = 0;
|
|
tmp1 = w[j];
|
|
i__2 = *m;
|
|
for (jj = j + 1; jj <= i__2; ++jj) {
|
|
if (w[jj] < tmp1) {
|
|
i__ = jj;
|
|
tmp1 = w[jj];
|
|
}
|
|
/* L40: */
|
|
}
|
|
|
|
if (i__ != 0) {
|
|
itmp1 = iwork[indibl + i__ - 1];
|
|
w[i__] = w[j];
|
|
iwork[indibl + i__ - 1] = iwork[indibl + j - 1];
|
|
w[j] = tmp1;
|
|
iwork[indibl + j - 1] = itmp1;
|
|
cswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1],
|
|
&c__1);
|
|
}
|
|
/* L50: */
|
|
}
|
|
}
|
|
|
|
/* Set WORK(1) to optimal workspace size. */
|
|
|
|
work[1].r = (real) lwkopt, work[1].i = 0.f;
|
|
rwork[1] = (real) lrwmin;
|
|
iwork[1] = liwmin;
|
|
|
|
return;
|
|
|
|
/* End of CHEEVR */
|
|
|
|
} /* cheevr_ */
|
|
|