1178 lines
29 KiB
C
1178 lines
29 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]/Cd(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 doublecomplex c_b1 = {0.,0.};
|
|
static doublecomplex c_b2 = {1.,0.};
|
|
static integer c__0 = 0;
|
|
static integer c__1 = 1;
|
|
static integer c__2 = 2;
|
|
static doublereal c_b41 = 1.;
|
|
|
|
/* > \brief \b ZSTEQR */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZSTEQR + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsteqr.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsteqr.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsteqr.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) */
|
|
|
|
/* CHARACTER COMPZ */
|
|
/* INTEGER INFO, LDZ, N */
|
|
/* DOUBLE PRECISION D( * ), E( * ), WORK( * ) */
|
|
/* COMPLEX*16 Z( LDZ, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a */
|
|
/* > symmetric tridiagonal matrix using the implicit QL or QR method. */
|
|
/* > The eigenvectors of a full or band complex Hermitian matrix can also */
|
|
/* > be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this */
|
|
/* > matrix to tridiagonal form. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] COMPZ */
|
|
/* > \verbatim */
|
|
/* > COMPZ is CHARACTER*1 */
|
|
/* > = 'N': Compute eigenvalues only. */
|
|
/* > = 'V': Compute eigenvalues and eigenvectors of the original */
|
|
/* > Hermitian matrix. On entry, Z must contain the */
|
|
/* > unitary matrix used to reduce the original matrix */
|
|
/* > to tridiagonal form. */
|
|
/* > = 'I': Compute eigenvalues and eigenvectors of the */
|
|
/* > tridiagonal matrix. Z is initialized to the identity */
|
|
/* > matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension (N) */
|
|
/* > On entry, the diagonal elements of the tridiagonal matrix. */
|
|
/* > On exit, if INFO = 0, the eigenvalues in ascending order. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] E */
|
|
/* > \verbatim */
|
|
/* > E is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > On entry, the (n-1) subdiagonal elements of the tridiagonal */
|
|
/* > matrix. */
|
|
/* > On exit, E has been destroyed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Z */
|
|
/* > \verbatim */
|
|
/* > Z is COMPLEX*16 array, dimension (LDZ, N) */
|
|
/* > On entry, if COMPZ = 'V', then Z contains the unitary */
|
|
/* > matrix used in the reduction to tridiagonal form. */
|
|
/* > On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */
|
|
/* > orthonormal eigenvectors of the original Hermitian matrix, */
|
|
/* > and if COMPZ = 'I', Z contains the orthonormal eigenvectors */
|
|
/* > of the symmetric tridiagonal matrix. */
|
|
/* > If COMPZ = 'N', then Z is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDZ */
|
|
/* > \verbatim */
|
|
/* > LDZ is INTEGER */
|
|
/* > The leading dimension of the array Z. LDZ >= 1, and if */
|
|
/* > eigenvectors are desired, then LDZ >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (f2cmax(1,2*N-2)) */
|
|
/* > If COMPZ = 'N', then WORK 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: the algorithm has failed to find all the eigenvalues in */
|
|
/* > a total of 30*N iterations; if INFO = i, then i */
|
|
/* > elements of E have not converged to zero; on exit, D */
|
|
/* > and E contain the elements of a symmetric tridiagonal */
|
|
/* > matrix which is unitarily similar to the original */
|
|
/* > matrix. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complex16OTHERcomputational */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zsteqr_(char *compz, integer *n, doublereal *d__,
|
|
doublereal *e, doublecomplex *z__, integer *ldz, doublereal *work,
|
|
integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer z_dim1, z_offset, i__1, i__2;
|
|
doublereal d__1, d__2;
|
|
|
|
/* Local variables */
|
|
integer lend, jtot;
|
|
extern /* Subroutine */ void dlae2_(doublereal *, doublereal *, doublereal
|
|
*, doublereal *, doublereal *);
|
|
doublereal b, c__, f, g;
|
|
integer i__, j, k, l, m;
|
|
doublereal p, r__, s;
|
|
extern logical lsame_(char *, char *);
|
|
doublereal anorm;
|
|
extern /* Subroutine */ void zlasr_(char *, char *, char *, integer *,
|
|
integer *, doublereal *, doublereal *, doublecomplex *, integer *);
|
|
integer l1;
|
|
extern /* Subroutine */ void zswap_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *), dlaev2_(doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *);
|
|
integer lendm1, lendp1;
|
|
extern doublereal dlapy2_(doublereal *, doublereal *);
|
|
integer ii;
|
|
extern doublereal dlamch_(char *);
|
|
integer mm, iscale;
|
|
extern /* Subroutine */ void dlascl_(char *, integer *, integer *,
|
|
doublereal *, doublereal *, integer *, integer *, doublereal *,
|
|
integer *, integer *);
|
|
doublereal safmin;
|
|
extern /* Subroutine */ void dlartg_(doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *);
|
|
doublereal safmax;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
|
|
extern /* Subroutine */ void dlasrt_(char *, integer *, doublereal *,
|
|
integer *);
|
|
integer lendsv;
|
|
doublereal ssfmin;
|
|
integer nmaxit, icompz;
|
|
doublereal ssfmax;
|
|
extern /* Subroutine */ void zlaset_(char *, integer *, integer *,
|
|
doublecomplex *, doublecomplex *, doublecomplex *, integer *);
|
|
integer lm1, mm1, nm1;
|
|
doublereal rt1, rt2, eps;
|
|
integer lsv;
|
|
doublereal tst, eps2;
|
|
|
|
|
|
/* -- LAPACK computational 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..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
--d__;
|
|
--e;
|
|
z_dim1 = *ldz;
|
|
z_offset = 1 + z_dim1 * 1;
|
|
z__ -= z_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
if (lsame_(compz, "N")) {
|
|
icompz = 0;
|
|
} else if (lsame_(compz, "V")) {
|
|
icompz = 1;
|
|
} else if (lsame_(compz, "I")) {
|
|
icompz = 2;
|
|
} else {
|
|
icompz = -1;
|
|
}
|
|
if (icompz < 0) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*ldz < 1 || icompz > 0 && *ldz < f2cmax(1,*n)) {
|
|
*info = -6;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZSTEQR", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
if (*n == 1) {
|
|
if (icompz == 2) {
|
|
i__1 = z_dim1 + 1;
|
|
z__[i__1].r = 1., z__[i__1].i = 0.;
|
|
}
|
|
return;
|
|
}
|
|
|
|
/* Determine the unit roundoff and over/underflow thresholds. */
|
|
|
|
eps = dlamch_("E");
|
|
/* Computing 2nd power */
|
|
d__1 = eps;
|
|
eps2 = d__1 * d__1;
|
|
safmin = dlamch_("S");
|
|
safmax = 1. / safmin;
|
|
ssfmax = sqrt(safmax) / 3.;
|
|
ssfmin = sqrt(safmin) / eps2;
|
|
|
|
/* Compute the eigenvalues and eigenvectors of the tridiagonal */
|
|
/* matrix. */
|
|
|
|
if (icompz == 2) {
|
|
zlaset_("Full", n, n, &c_b1, &c_b2, &z__[z_offset], ldz);
|
|
}
|
|
|
|
nmaxit = *n * 30;
|
|
jtot = 0;
|
|
|
|
/* Determine where the matrix splits and choose QL or QR iteration */
|
|
/* for each block, according to whether top or bottom diagonal */
|
|
/* element is smaller. */
|
|
|
|
l1 = 1;
|
|
nm1 = *n - 1;
|
|
|
|
L10:
|
|
if (l1 > *n) {
|
|
goto L160;
|
|
}
|
|
if (l1 > 1) {
|
|
e[l1 - 1] = 0.;
|
|
}
|
|
if (l1 <= nm1) {
|
|
i__1 = nm1;
|
|
for (m = l1; m <= i__1; ++m) {
|
|
tst = (d__1 = e[m], abs(d__1));
|
|
if (tst == 0.) {
|
|
goto L30;
|
|
}
|
|
if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m
|
|
+ 1], abs(d__2))) * eps) {
|
|
e[m] = 0.;
|
|
goto L30;
|
|
}
|
|
/* L20: */
|
|
}
|
|
}
|
|
m = *n;
|
|
|
|
L30:
|
|
l = l1;
|
|
lsv = l;
|
|
lend = m;
|
|
lendsv = lend;
|
|
l1 = m + 1;
|
|
if (lend == l) {
|
|
goto L10;
|
|
}
|
|
|
|
/* Scale submatrix in rows and columns L to LEND */
|
|
|
|
i__1 = lend - l + 1;
|
|
anorm = dlanst_("I", &i__1, &d__[l], &e[l]);
|
|
iscale = 0;
|
|
if (anorm == 0.) {
|
|
goto L10;
|
|
}
|
|
if (anorm > ssfmax) {
|
|
iscale = 1;
|
|
i__1 = lend - l + 1;
|
|
dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n,
|
|
info);
|
|
i__1 = lend - l;
|
|
dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n,
|
|
info);
|
|
} else if (anorm < ssfmin) {
|
|
iscale = 2;
|
|
i__1 = lend - l + 1;
|
|
dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n,
|
|
info);
|
|
i__1 = lend - l;
|
|
dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n,
|
|
info);
|
|
}
|
|
|
|
/* Choose between QL and QR iteration */
|
|
|
|
if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) {
|
|
lend = lsv;
|
|
l = lendsv;
|
|
}
|
|
|
|
if (lend > l) {
|
|
|
|
/* QL Iteration */
|
|
|
|
/* Look for small subdiagonal element. */
|
|
|
|
L40:
|
|
if (l != lend) {
|
|
lendm1 = lend - 1;
|
|
i__1 = lendm1;
|
|
for (m = l; m <= i__1; ++m) {
|
|
/* Computing 2nd power */
|
|
d__2 = (d__1 = e[m], abs(d__1));
|
|
tst = d__2 * d__2;
|
|
if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m
|
|
+ 1], abs(d__2)) + safmin) {
|
|
goto L60;
|
|
}
|
|
/* L50: */
|
|
}
|
|
}
|
|
|
|
m = lend;
|
|
|
|
L60:
|
|
if (m < lend) {
|
|
e[m] = 0.;
|
|
}
|
|
p = d__[l];
|
|
if (m == l) {
|
|
goto L80;
|
|
}
|
|
|
|
/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */
|
|
/* to compute its eigensystem. */
|
|
|
|
if (m == l + 1) {
|
|
if (icompz > 0) {
|
|
dlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s);
|
|
work[l] = c__;
|
|
work[*n - 1 + l] = s;
|
|
zlasr_("R", "V", "B", n, &c__2, &work[l], &work[*n - 1 + l], &
|
|
z__[l * z_dim1 + 1], ldz);
|
|
} else {
|
|
dlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2);
|
|
}
|
|
d__[l] = rt1;
|
|
d__[l + 1] = rt2;
|
|
e[l] = 0.;
|
|
l += 2;
|
|
if (l <= lend) {
|
|
goto L40;
|
|
}
|
|
goto L140;
|
|
}
|
|
|
|
if (jtot == nmaxit) {
|
|
goto L140;
|
|
}
|
|
++jtot;
|
|
|
|
/* Form shift. */
|
|
|
|
g = (d__[l + 1] - p) / (e[l] * 2.);
|
|
r__ = dlapy2_(&g, &c_b41);
|
|
g = d__[m] - p + e[l] / (g + d_sign(&r__, &g));
|
|
|
|
s = 1.;
|
|
c__ = 1.;
|
|
p = 0.;
|
|
|
|
/* Inner loop */
|
|
|
|
mm1 = m - 1;
|
|
i__1 = l;
|
|
for (i__ = mm1; i__ >= i__1; --i__) {
|
|
f = s * e[i__];
|
|
b = c__ * e[i__];
|
|
dlartg_(&g, &f, &c__, &s, &r__);
|
|
if (i__ != m - 1) {
|
|
e[i__ + 1] = r__;
|
|
}
|
|
g = d__[i__ + 1] - p;
|
|
r__ = (d__[i__] - g) * s + c__ * 2. * b;
|
|
p = s * r__;
|
|
d__[i__ + 1] = g + p;
|
|
g = c__ * r__ - b;
|
|
|
|
/* If eigenvectors are desired, then save rotations. */
|
|
|
|
if (icompz > 0) {
|
|
work[i__] = c__;
|
|
work[*n - 1 + i__] = -s;
|
|
}
|
|
|
|
/* L70: */
|
|
}
|
|
|
|
/* If eigenvectors are desired, then apply saved rotations. */
|
|
|
|
if (icompz > 0) {
|
|
mm = m - l + 1;
|
|
zlasr_("R", "V", "B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l
|
|
* z_dim1 + 1], ldz);
|
|
}
|
|
|
|
d__[l] -= p;
|
|
e[l] = g;
|
|
goto L40;
|
|
|
|
/* Eigenvalue found. */
|
|
|
|
L80:
|
|
d__[l] = p;
|
|
|
|
++l;
|
|
if (l <= lend) {
|
|
goto L40;
|
|
}
|
|
goto L140;
|
|
|
|
} else {
|
|
|
|
/* QR Iteration */
|
|
|
|
/* Look for small superdiagonal element. */
|
|
|
|
L90:
|
|
if (l != lend) {
|
|
lendp1 = lend + 1;
|
|
i__1 = lendp1;
|
|
for (m = l; m >= i__1; --m) {
|
|
/* Computing 2nd power */
|
|
d__2 = (d__1 = e[m - 1], abs(d__1));
|
|
tst = d__2 * d__2;
|
|
if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m
|
|
- 1], abs(d__2)) + safmin) {
|
|
goto L110;
|
|
}
|
|
/* L100: */
|
|
}
|
|
}
|
|
|
|
m = lend;
|
|
|
|
L110:
|
|
if (m > lend) {
|
|
e[m - 1] = 0.;
|
|
}
|
|
p = d__[l];
|
|
if (m == l) {
|
|
goto L130;
|
|
}
|
|
|
|
/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */
|
|
/* to compute its eigensystem. */
|
|
|
|
if (m == l - 1) {
|
|
if (icompz > 0) {
|
|
dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s)
|
|
;
|
|
work[m] = c__;
|
|
work[*n - 1 + m] = s;
|
|
zlasr_("R", "V", "F", n, &c__2, &work[m], &work[*n - 1 + m], &
|
|
z__[(l - 1) * z_dim1 + 1], ldz);
|
|
} else {
|
|
dlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2);
|
|
}
|
|
d__[l - 1] = rt1;
|
|
d__[l] = rt2;
|
|
e[l - 1] = 0.;
|
|
l += -2;
|
|
if (l >= lend) {
|
|
goto L90;
|
|
}
|
|
goto L140;
|
|
}
|
|
|
|
if (jtot == nmaxit) {
|
|
goto L140;
|
|
}
|
|
++jtot;
|
|
|
|
/* Form shift. */
|
|
|
|
g = (d__[l - 1] - p) / (e[l - 1] * 2.);
|
|
r__ = dlapy2_(&g, &c_b41);
|
|
g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g));
|
|
|
|
s = 1.;
|
|
c__ = 1.;
|
|
p = 0.;
|
|
|
|
/* Inner loop */
|
|
|
|
lm1 = l - 1;
|
|
i__1 = lm1;
|
|
for (i__ = m; i__ <= i__1; ++i__) {
|
|
f = s * e[i__];
|
|
b = c__ * e[i__];
|
|
dlartg_(&g, &f, &c__, &s, &r__);
|
|
if (i__ != m) {
|
|
e[i__ - 1] = r__;
|
|
}
|
|
g = d__[i__] - p;
|
|
r__ = (d__[i__ + 1] - g) * s + c__ * 2. * b;
|
|
p = s * r__;
|
|
d__[i__] = g + p;
|
|
g = c__ * r__ - b;
|
|
|
|
/* If eigenvectors are desired, then save rotations. */
|
|
|
|
if (icompz > 0) {
|
|
work[i__] = c__;
|
|
work[*n - 1 + i__] = s;
|
|
}
|
|
|
|
/* L120: */
|
|
}
|
|
|
|
/* If eigenvectors are desired, then apply saved rotations. */
|
|
|
|
if (icompz > 0) {
|
|
mm = l - m + 1;
|
|
zlasr_("R", "V", "F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m
|
|
* z_dim1 + 1], ldz);
|
|
}
|
|
|
|
d__[l] -= p;
|
|
e[lm1] = g;
|
|
goto L90;
|
|
|
|
/* Eigenvalue found. */
|
|
|
|
L130:
|
|
d__[l] = p;
|
|
|
|
--l;
|
|
if (l >= lend) {
|
|
goto L90;
|
|
}
|
|
goto L140;
|
|
|
|
}
|
|
|
|
/* Undo scaling if necessary */
|
|
|
|
L140:
|
|
if (iscale == 1) {
|
|
i__1 = lendsv - lsv + 1;
|
|
dlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv],
|
|
n, info);
|
|
i__1 = lendsv - lsv;
|
|
dlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n,
|
|
info);
|
|
} else if (iscale == 2) {
|
|
i__1 = lendsv - lsv + 1;
|
|
dlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv],
|
|
n, info);
|
|
i__1 = lendsv - lsv;
|
|
dlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n,
|
|
info);
|
|
}
|
|
|
|
/* Check for no convergence to an eigenvalue after a total */
|
|
/* of N*MAXIT iterations. */
|
|
|
|
if (jtot == nmaxit) {
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if (e[i__] != 0.) {
|
|
++(*info);
|
|
}
|
|
/* L150: */
|
|
}
|
|
return;
|
|
}
|
|
goto L10;
|
|
|
|
/* Order eigenvalues and eigenvectors. */
|
|
|
|
L160:
|
|
if (icompz == 0) {
|
|
|
|
/* Use Quick Sort */
|
|
|
|
dlasrt_("I", n, &d__[1], info);
|
|
|
|
} else {
|
|
|
|
/* Use Selection Sort to minimize swaps of eigenvectors */
|
|
|
|
i__1 = *n;
|
|
for (ii = 2; ii <= i__1; ++ii) {
|
|
i__ = ii - 1;
|
|
k = i__;
|
|
p = d__[i__];
|
|
i__2 = *n;
|
|
for (j = ii; j <= i__2; ++j) {
|
|
if (d__[j] < p) {
|
|
k = j;
|
|
p = d__[j];
|
|
}
|
|
/* L170: */
|
|
}
|
|
if (k != i__) {
|
|
d__[k] = d__[i__];
|
|
d__[i__] = p;
|
|
zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1],
|
|
&c__1);
|
|
}
|
|
/* L180: */
|
|
}
|
|
}
|
|
return;
|
|
|
|
/* End of ZSTEQR */
|
|
|
|
} /* zsteqr_ */
|
|
|