1140 lines
33 KiB
C
1140 lines
33 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static doublecomplex c_b1 = {0.,0.};
|
|
static doublecomplex c_b2 = {1.,0.};
|
|
static doublereal c_b16 = 1.;
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief <b> ZHBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER
|
|
matrices</b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZHBEVX + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbevx.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbevx.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbevx.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZHBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL, */
|
|
/* VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, */
|
|
/* IWORK, IFAIL, INFO ) */
|
|
|
|
/* CHARACTER JOBZ, RANGE, UPLO */
|
|
/* INTEGER IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N */
|
|
/* DOUBLE PRECISION ABSTOL, VL, VU */
|
|
/* INTEGER IFAIL( * ), IWORK( * ) */
|
|
/* DOUBLE PRECISION RWORK( * ), W( * ) */
|
|
/* COMPLEX*16 AB( LDAB, * ), Q( LDQ, * ), WORK( * ), */
|
|
/* $ Z( LDZ, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZHBEVX computes selected eigenvalues and, optionally, eigenvectors */
|
|
/* > of a complex Hermitian band matrix A. Eigenvalues and eigenvectors */
|
|
/* > can be selected by specifying either a range of values or a range of */
|
|
/* > indices for the desired eigenvalues. */
|
|
/* > \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] 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] KD */
|
|
/* > \verbatim */
|
|
/* > KD is INTEGER */
|
|
/* > The number of superdiagonals of the matrix A if UPLO = 'U', */
|
|
/* > or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] AB */
|
|
/* > \verbatim */
|
|
/* > AB is COMPLEX*16 array, dimension (LDAB, N) */
|
|
/* > On entry, the upper or lower triangle of the Hermitian band */
|
|
/* > matrix A, stored in the first KD+1 rows of the array. The */
|
|
/* > j-th column of A is stored in the j-th column of the array AB */
|
|
/* > as follows: */
|
|
/* > if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */
|
|
/* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+kd). */
|
|
/* > */
|
|
/* > On exit, AB is overwritten by values generated during the */
|
|
/* > reduction to tridiagonal form. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDAB */
|
|
/* > \verbatim */
|
|
/* > LDAB is INTEGER */
|
|
/* > The leading dimension of the array AB. LDAB >= KD + 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is COMPLEX*16 array, dimension (LDQ, N) */
|
|
/* > If JOBZ = 'V', the N-by-N unitary matrix used in the */
|
|
/* > reduction to tridiagonal form. */
|
|
/* > If JOBZ = 'N', the array Q is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQ */
|
|
/* > \verbatim */
|
|
/* > LDQ is INTEGER */
|
|
/* > The leading dimension of the array Q. If JOBZ = 'V', then */
|
|
/* > LDQ >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VL */
|
|
/* > \verbatim */
|
|
/* > VL is DOUBLE PRECISION */
|
|
/* > 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 DOUBLE PRECISION */
|
|
/* > 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 DOUBLE PRECISION */
|
|
/* > 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 AB to tridiagonal form. */
|
|
/* > */
|
|
/* > Eigenvalues will be computed most accurately when ABSTOL is */
|
|
/* > set to twice the underflow threshold 2*DLAMCH('S'), not zero. */
|
|
/* > If this routine returns with INFO>0, indicating that some */
|
|
/* > eigenvectors did not converge, try setting ABSTOL to */
|
|
/* > 2*DLAMCH('S'). */
|
|
/* > */
|
|
/* > See "Computing Small Singular Values of Bidiagonal Matrices */
|
|
/* > with Guaranteed High Relative Accuracy," by Demmel and */
|
|
/* > Kahan, LAPACK Working Note #3. */
|
|
/* > \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 DOUBLE PRECISION array, dimension (N) */
|
|
/* > The first M elements contain the selected eigenvalues in */
|
|
/* > ascending order. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] Z */
|
|
/* > \verbatim */
|
|
/* > Z is COMPLEX*16 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 an eigenvector fails to converge, then that column of Z */
|
|
/* > contains the latest approximation to the eigenvector, and the */
|
|
/* > index of the eigenvector is returned in IFAIL. */
|
|
/* > 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] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is DOUBLE PRECISION array, dimension (7*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (5*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IFAIL */
|
|
/* > \verbatim */
|
|
/* > IFAIL is INTEGER array, dimension (N) */
|
|
/* > If JOBZ = 'V', then if INFO = 0, the first M elements of */
|
|
/* > IFAIL are zero. If INFO > 0, then IFAIL contains the */
|
|
/* > indices of the eigenvectors that failed to converge. */
|
|
/* > If JOBZ = 'N', then IFAIL is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > > 0: if INFO = i, then i eigenvectors failed to converge. */
|
|
/* > Their indices are stored in array IFAIL. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup complex16OTHEReigen */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zhbevx_(char *jobz, char *range, char *uplo, integer *n,
|
|
integer *kd, doublecomplex *ab, integer *ldab, doublecomplex *q,
|
|
integer *ldq, doublereal *vl, doublereal *vu, integer *il, integer *
|
|
iu, doublereal *abstol, integer *m, doublereal *w, doublecomplex *z__,
|
|
integer *ldz, doublecomplex *work, doublereal *rwork, integer *iwork,
|
|
integer *ifail, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer ab_dim1, ab_offset, q_dim1, q_offset, z_dim1, z_offset, i__1,
|
|
i__2;
|
|
doublereal d__1, d__2;
|
|
|
|
/* Local variables */
|
|
integer indd, inde;
|
|
doublereal anrm;
|
|
integer imax;
|
|
doublereal rmin, rmax;
|
|
logical test;
|
|
doublecomplex ctmp1;
|
|
integer itmp1, i__, j, indee;
|
|
extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
|
|
integer *);
|
|
doublereal sigma;
|
|
extern logical lsame_(char *, char *);
|
|
integer iinfo;
|
|
char order[1];
|
|
extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *);
|
|
logical lower;
|
|
extern /* Subroutine */ void zgemv_(char *, integer *, integer *,
|
|
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *);
|
|
logical wantz;
|
|
extern /* Subroutine */ void zcopy_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *), zswap_(integer *, doublecomplex *,
|
|
integer *, doublecomplex *, integer *);
|
|
integer jj;
|
|
extern doublereal dlamch_(char *);
|
|
logical alleig, indeig;
|
|
integer iscale, indibl;
|
|
logical valeig;
|
|
doublereal safmin;
|
|
extern doublereal zlanhb_(char *, char *, integer *, integer *,
|
|
doublecomplex *, integer *, doublereal *);
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
doublereal abstll, bignum;
|
|
integer indiwk, indisp;
|
|
extern /* Subroutine */ void dsterf_(integer *, doublereal *, doublereal *,
|
|
integer *), zlascl_(char *, integer *, integer *, doublereal *,
|
|
doublereal *, integer *, integer *, doublecomplex *, integer *,
|
|
integer *), dstebz_(char *, char *, integer *, doublereal
|
|
*, doublereal *, integer *, integer *, doublereal *, doublereal *,
|
|
doublereal *, integer *, integer *, doublereal *, integer *,
|
|
integer *, doublereal *, integer *, integer *),
|
|
zhbtrd_(char *, char *, integer *, integer *, doublecomplex *,
|
|
integer *, doublereal *, doublereal *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *);
|
|
integer indrwk, indwrk;
|
|
extern /* Subroutine */ void zlacpy_(char *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *);
|
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integer nsplit;
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doublereal smlnum;
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extern /* Subroutine */ void zstein_(integer *, doublereal *, doublereal *,
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integer *, doublereal *, integer *, integer *, doublecomplex *,
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integer *, doublereal *, integer *, integer *, integer *),
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zsteqr_(char *, integer *, doublereal *, doublereal *,
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doublecomplex *, integer *, doublereal *, integer *);
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doublereal eps, vll, vuu, tmp1;
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/* -- LAPACK driver routine (version 3.7.0) -- */
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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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ab_dim1 = *ldab;
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ab_offset = 1 + ab_dim1 * 1;
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ab -= ab_offset;
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q_dim1 = *ldq;
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q_offset = 1 + q_dim1 * 1;
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q -= q_offset;
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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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--work;
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--rwork;
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--iwork;
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--ifail;
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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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lower = lsame_(uplo, "L");
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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 (! (lower || lsame_(uplo, "U"))) {
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*info = -3;
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} else if (*n < 0) {
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*info = -4;
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} else if (*kd < 0) {
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*info = -5;
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} else if (*ldab < *kd + 1) {
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*info = -7;
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} else if (wantz && *ldq < f2cmax(1,*n)) {
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*info = -9;
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} else {
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if (valeig) {
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if (*n > 0 && *vu <= *vl) {
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*info = -11;
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}
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} else if (indeig) {
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if (*il < 1 || *il > f2cmax(1,*n)) {
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*info = -12;
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} else if (*iu < f2cmin(*n,*il) || *iu > *n) {
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*info = -13;
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}
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}
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}
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if (*info == 0) {
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if (*ldz < 1 || wantz && *ldz < *n) {
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*info = -18;
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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_("ZHBEVX", &i__1, (ftnlen)6);
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return;
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}
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/* Quick return if possible */
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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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*m = 1;
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if (lower) {
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i__1 = ab_dim1 + 1;
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ctmp1.r = ab[i__1].r, ctmp1.i = ab[i__1].i;
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} else {
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i__1 = *kd + 1 + ab_dim1;
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ctmp1.r = ab[i__1].r, ctmp1.i = ab[i__1].i;
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}
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tmp1 = ctmp1.r;
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if (valeig) {
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if (! (*vl < tmp1 && *vu >= tmp1)) {
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*m = 0;
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}
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}
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if (*m == 1) {
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w[1] = ctmp1.r;
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if (wantz) {
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i__1 = z_dim1 + 1;
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z__[i__1].r = 1., z__[i__1].i = 0.;
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}
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}
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return;
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}
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/* Get machine constants. */
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safmin = dlamch_("Safe minimum");
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eps = dlamch_("Precision");
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smlnum = safmin / eps;
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bignum = 1. / smlnum;
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rmin = sqrt(smlnum);
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/* Computing MIN */
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d__1 = sqrt(bignum), d__2 = 1. / sqrt(sqrt(safmin));
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rmax = f2cmin(d__1,d__2);
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/* Scale matrix to allowable range, if necessary. */
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iscale = 0;
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abstll = *abstol;
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if (valeig) {
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vll = *vl;
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vuu = *vu;
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} else {
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vll = 0.;
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vuu = 0.;
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}
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anrm = zlanhb_("M", uplo, n, kd, &ab[ab_offset], ldab, &rwork[1]);
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if (anrm > 0. && anrm < rmin) {
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iscale = 1;
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sigma = rmin / anrm;
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} else if (anrm > rmax) {
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iscale = 1;
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sigma = rmax / anrm;
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}
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if (iscale == 1) {
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if (lower) {
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zlascl_("B", kd, kd, &c_b16, &sigma, n, n, &ab[ab_offset], ldab,
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info);
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} else {
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zlascl_("Q", kd, kd, &c_b16, &sigma, n, n, &ab[ab_offset], ldab,
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info);
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}
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if (*abstol > 0.) {
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abstll = *abstol * sigma;
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}
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if (valeig) {
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vll = *vl * sigma;
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vuu = *vu * sigma;
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}
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}
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/* Call ZHBTRD to reduce Hermitian band matrix to tridiagonal form. */
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indd = 1;
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inde = indd + *n;
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indrwk = inde + *n;
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indwrk = 1;
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zhbtrd_(jobz, uplo, n, kd, &ab[ab_offset], ldab, &rwork[indd], &rwork[
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inde], &q[q_offset], ldq, &work[indwrk], &iinfo);
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/* If all eigenvalues are desired and ABSTOL is less than or equal */
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/* to zero, then call DSTERF or ZSTEQR. If this fails for some */
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/* eigenvalue, then try DSTEBZ. */
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test = FALSE_;
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if (indeig) {
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if (*il == 1 && *iu == *n) {
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test = TRUE_;
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}
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}
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if ((alleig || test) && *abstol <= 0.) {
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dcopy_(n, &rwork[indd], &c__1, &w[1], &c__1);
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indee = indrwk + (*n << 1);
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if (! wantz) {
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i__1 = *n - 1;
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dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1);
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dsterf_(n, &w[1], &rwork[indee], info);
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} else {
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zlacpy_("A", n, n, &q[q_offset], ldq, &z__[z_offset], ldz);
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i__1 = *n - 1;
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dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1);
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zsteqr_(jobz, n, &w[1], &rwork[indee], &z__[z_offset], ldz, &
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rwork[indrwk], info);
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if (*info == 0) {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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ifail[i__] = 0;
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/* L10: */
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}
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}
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}
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if (*info == 0) {
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*m = *n;
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goto L30;
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}
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*info = 0;
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}
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/* Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN. */
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if (wantz) {
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*(unsigned char *)order = 'B';
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} else {
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*(unsigned char *)order = 'E';
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}
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indibl = 1;
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indisp = indibl + *n;
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indiwk = indisp + *n;
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dstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &rwork[indd], &
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rwork[inde], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &
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rwork[indrwk], &iwork[indiwk], info);
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if (wantz) {
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zstein_(n, &rwork[indd], &rwork[inde], m, &w[1], &iwork[indibl], &
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iwork[indisp], &z__[z_offset], ldz, &rwork[indrwk], &iwork[
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indiwk], &ifail[1], info);
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/* Apply unitary matrix used in reduction to tridiagonal */
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/* form to eigenvectors returned by ZSTEIN. */
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i__1 = *m;
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for (j = 1; j <= i__1; ++j) {
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zcopy_(n, &z__[j * z_dim1 + 1], &c__1, &work[1], &c__1);
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zgemv_("N", n, n, &c_b2, &q[q_offset], ldq, &work[1], &c__1, &
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c_b1, &z__[j * z_dim1 + 1], &c__1);
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/* L20: */
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}
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}
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/* If matrix was scaled, then rescale eigenvalues appropriately. */
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L30:
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if (iscale == 1) {
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if (*info == 0) {
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imax = *m;
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} else {
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imax = *info - 1;
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}
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d__1 = 1. / sigma;
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dscal_(&imax, &d__1, &w[1], &c__1);
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}
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/* If eigenvalues are not in order, then sort them, along with */
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/* eigenvectors. */
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if (wantz) {
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i__1 = *m - 1;
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for (j = 1; j <= i__1; ++j) {
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i__ = 0;
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tmp1 = w[j];
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i__2 = *m;
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for (jj = j + 1; jj <= i__2; ++jj) {
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if (w[jj] < tmp1) {
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i__ = jj;
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tmp1 = w[jj];
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}
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/* L40: */
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}
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if (i__ != 0) {
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itmp1 = iwork[indibl + i__ - 1];
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w[i__] = w[j];
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iwork[indibl + i__ - 1] = iwork[indibl + j - 1];
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w[j] = tmp1;
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iwork[indibl + j - 1] = itmp1;
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zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1],
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&c__1);
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if (*info != 0) {
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itmp1 = ifail[i__];
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ifail[i__] = ifail[j];
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ifail[j] = itmp1;
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}
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}
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/* L50: */
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}
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}
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return;
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/* End of ZHBEVX */
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} /* zhbevx_ */
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