1760 lines
53 KiB
C
1760 lines
53 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]/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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#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 integer c__1 = 1;
|
|
static integer c__2 = 2;
|
|
|
|
/* > \brief \b ZHGEQZ */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZHGEQZ + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhgeqz.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhgeqz.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhgeqz.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, */
|
|
/* ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, */
|
|
/* RWORK, INFO ) */
|
|
|
|
/* CHARACTER COMPQ, COMPZ, JOB */
|
|
/* INTEGER IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N */
|
|
/* DOUBLE PRECISION RWORK( * ) */
|
|
/* COMPLEX*16 ALPHA( * ), BETA( * ), H( LDH, * ), */
|
|
/* $ Q( LDQ, * ), T( LDT, * ), WORK( * ), */
|
|
/* $ Z( LDZ, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZHGEQZ computes the eigenvalues of a complex matrix pair (H,T), */
|
|
/* > where H is an upper Hessenberg matrix and T is upper triangular, */
|
|
/* > using the single-shift QZ method. */
|
|
/* > Matrix pairs of this type are produced by the reduction to */
|
|
/* > generalized upper Hessenberg form of a complex matrix pair (A,B): */
|
|
/* > */
|
|
/* > A = Q1*H*Z1**H, B = Q1*T*Z1**H, */
|
|
/* > */
|
|
/* > as computed by ZGGHRD. */
|
|
/* > */
|
|
/* > If JOB='S', then the Hessenberg-triangular pair (H,T) is */
|
|
/* > also reduced to generalized Schur form, */
|
|
/* > */
|
|
/* > H = Q*S*Z**H, T = Q*P*Z**H, */
|
|
/* > */
|
|
/* > where Q and Z are unitary matrices and S and P are upper triangular. */
|
|
/* > */
|
|
/* > Optionally, the unitary matrix Q from the generalized Schur */
|
|
/* > factorization may be postmultiplied into an input matrix Q1, and the */
|
|
/* > unitary matrix Z may be postmultiplied into an input matrix Z1. */
|
|
/* > If Q1 and Z1 are the unitary matrices from ZGGHRD that reduced */
|
|
/* > the matrix pair (A,B) to generalized Hessenberg form, then the output */
|
|
/* > matrices Q1*Q and Z1*Z are the unitary factors from the generalized */
|
|
/* > Schur factorization of (A,B): */
|
|
/* > */
|
|
/* > A = (Q1*Q)*S*(Z1*Z)**H, B = (Q1*Q)*P*(Z1*Z)**H. */
|
|
/* > */
|
|
/* > To avoid overflow, eigenvalues of the matrix pair (H,T) */
|
|
/* > (equivalently, of (A,B)) are computed as a pair of complex values */
|
|
/* > (alpha,beta). If beta is nonzero, lambda = alpha / beta is an */
|
|
/* > eigenvalue of the generalized nonsymmetric eigenvalue problem (GNEP) */
|
|
/* > A*x = lambda*B*x */
|
|
/* > and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the */
|
|
/* > alternate form of the GNEP */
|
|
/* > mu*A*y = B*y. */
|
|
/* > The values of alpha and beta for the i-th eigenvalue can be read */
|
|
/* > directly from the generalized Schur form: alpha = S(i,i), */
|
|
/* > beta = P(i,i). */
|
|
/* > */
|
|
/* > Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix */
|
|
/* > Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973), */
|
|
/* > pp. 241--256. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOB */
|
|
/* > \verbatim */
|
|
/* > JOB is CHARACTER*1 */
|
|
/* > = 'E': Compute eigenvalues only; */
|
|
/* > = 'S': Computer eigenvalues and the Schur form. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] COMPQ */
|
|
/* > \verbatim */
|
|
/* > COMPQ is CHARACTER*1 */
|
|
/* > = 'N': Left Schur vectors (Q) are not computed; */
|
|
/* > = 'I': Q is initialized to the unit matrix and the matrix Q */
|
|
/* > of left Schur vectors of (H,T) is returned; */
|
|
/* > = 'V': Q must contain a unitary matrix Q1 on entry and */
|
|
/* > the product Q1*Q is returned. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] COMPZ */
|
|
/* > \verbatim */
|
|
/* > COMPZ is CHARACTER*1 */
|
|
/* > = 'N': Right Schur vectors (Z) are not computed; */
|
|
/* > = 'I': Q is initialized to the unit matrix and the matrix Z */
|
|
/* > of right Schur vectors of (H,T) is returned; */
|
|
/* > = 'V': Z must contain a unitary matrix Z1 on entry and */
|
|
/* > the product Z1*Z is returned. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrices H, T, Q, and Z. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ILO */
|
|
/* > \verbatim */
|
|
/* > ILO is INTEGER */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IHI */
|
|
/* > \verbatim */
|
|
/* > IHI is INTEGER */
|
|
/* > ILO and IHI mark the rows and columns of H which are in */
|
|
/* > Hessenberg form. It is assumed that A is already upper */
|
|
/* > triangular in rows and columns 1:ILO-1 and IHI+1:N. */
|
|
/* > If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] H */
|
|
/* > \verbatim */
|
|
/* > H is COMPLEX*16 array, dimension (LDH, N) */
|
|
/* > On entry, the N-by-N upper Hessenberg matrix H. */
|
|
/* > On exit, if JOB = 'S', H contains the upper triangular */
|
|
/* > matrix S from the generalized Schur factorization. */
|
|
/* > If JOB = 'E', the diagonal of H matches that of S, but */
|
|
/* > the rest of H is unspecified. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDH */
|
|
/* > \verbatim */
|
|
/* > LDH is INTEGER */
|
|
/* > The leading dimension of the array H. LDH >= f2cmax( 1, N ). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] T */
|
|
/* > \verbatim */
|
|
/* > T is COMPLEX*16 array, dimension (LDT, N) */
|
|
/* > On entry, the N-by-N upper triangular matrix T. */
|
|
/* > On exit, if JOB = 'S', T contains the upper triangular */
|
|
/* > matrix P from the generalized Schur factorization. */
|
|
/* > If JOB = 'E', the diagonal of T matches that of P, but */
|
|
/* > the rest of T is unspecified. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDT */
|
|
/* > \verbatim */
|
|
/* > LDT is INTEGER */
|
|
/* > The leading dimension of the array T. LDT >= f2cmax( 1, N ). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ALPHA */
|
|
/* > \verbatim */
|
|
/* > ALPHA is COMPLEX*16 array, dimension (N) */
|
|
/* > The complex scalars alpha that define the eigenvalues of */
|
|
/* > GNEP. ALPHA(i) = S(i,i) in the generalized Schur */
|
|
/* > factorization. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] BETA */
|
|
/* > \verbatim */
|
|
/* > BETA is COMPLEX*16 array, dimension (N) */
|
|
/* > The real non-negative scalars beta that define the */
|
|
/* > eigenvalues of GNEP. BETA(i) = P(i,i) in the generalized */
|
|
/* > Schur factorization. */
|
|
/* > */
|
|
/* > Together, the quantities alpha = ALPHA(j) and beta = BETA(j) */
|
|
/* > represent the j-th eigenvalue of the matrix pair (A,B), in */
|
|
/* > one of the forms lambda = alpha/beta or mu = beta/alpha. */
|
|
/* > Since either lambda or mu may overflow, they should not, */
|
|
/* > in general, be computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is COMPLEX*16 array, dimension (LDQ, N) */
|
|
/* > On entry, if COMPQ = 'V', the unitary matrix Q1 used in the */
|
|
/* > reduction of (A,B) to generalized Hessenberg form. */
|
|
/* > On exit, if COMPQ = 'I', the unitary matrix of left Schur */
|
|
/* > vectors of (H,T), and if COMPQ = 'V', the unitary matrix of */
|
|
/* > left Schur vectors of (A,B). */
|
|
/* > Not referenced if COMPQ = 'N'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQ */
|
|
/* > \verbatim */
|
|
/* > LDQ is INTEGER */
|
|
/* > The leading dimension of the array Q. LDQ >= 1. */
|
|
/* > If COMPQ='V' or 'I', then LDQ >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Z */
|
|
/* > \verbatim */
|
|
/* > Z is COMPLEX*16 array, dimension (LDZ, N) */
|
|
/* > On entry, if COMPZ = 'V', the unitary matrix Z1 used in the */
|
|
/* > reduction of (A,B) to generalized Hessenberg form. */
|
|
/* > On exit, if COMPZ = 'I', the unitary matrix of right Schur */
|
|
/* > vectors of (H,T), and if COMPZ = 'V', the unitary matrix of */
|
|
/* > right Schur vectors of (A,B). */
|
|
/* > Not referenced if COMPZ = 'N'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDZ */
|
|
/* > \verbatim */
|
|
/* > LDZ is INTEGER */
|
|
/* > The leading dimension of the array Z. LDZ >= 1. */
|
|
/* > If COMPZ='V' or 'I', then LDZ >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO >= 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK >= f2cmax(1,N). */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal size of the WORK array, returns */
|
|
/* > this value as the first entry of the WORK array, and no error */
|
|
/* > message related to LWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is DOUBLE PRECISION array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > = 1,...,N: the QZ iteration did not converge. (H,T) is not */
|
|
/* > in Schur form, but ALPHA(i) and BETA(i), */
|
|
/* > i=INFO+1,...,N should be correct. */
|
|
/* > = N+1,...,2*N: the shift calculation failed. (H,T) is not */
|
|
/* > in Schur form, but ALPHA(i) and BETA(i), */
|
|
/* > i=INFO-N+1,...,N should be correct. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date April 2012 */
|
|
|
|
/* > \ingroup complex16GEcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > We assume that complex ABS works as long as its value is less than */
|
|
/* > overflow. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zhgeqz_(char *job, char *compq, char *compz, integer *n,
|
|
integer *ilo, integer *ihi, doublecomplex *h__, integer *ldh,
|
|
doublecomplex *t, integer *ldt, doublecomplex *alpha, doublecomplex *
|
|
beta, doublecomplex *q, integer *ldq, doublecomplex *z__, integer *
|
|
ldz, doublecomplex *work, integer *lwork, doublereal *rwork, integer *
|
|
info)
|
|
{
|
|
/* System generated locals */
|
|
integer h_dim1, h_offset, q_dim1, q_offset, t_dim1, t_offset, z_dim1,
|
|
z_offset, i__1, i__2, i__3, i__4, i__5, i__6;
|
|
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
|
|
doublecomplex z__1, z__2, z__3, z__4, z__5, z__6, z__7;
|
|
|
|
/* Local variables */
|
|
doublereal absb, atol, btol, temp;
|
|
extern /* Subroutine */ void zrot_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublereal *, doublecomplex *);
|
|
doublereal temp2, c__;
|
|
integer j;
|
|
doublecomplex s, x, y;
|
|
extern logical lsame_(char *, char *);
|
|
doublecomplex ctemp;
|
|
integer iiter, ilast, jiter;
|
|
doublereal anorm, bnorm;
|
|
integer maxit;
|
|
doublecomplex shift;
|
|
extern /* Subroutine */ void zscal_(integer *, doublecomplex *,
|
|
doublecomplex *, integer *);
|
|
doublereal tempr;
|
|
doublecomplex ctemp2, ctemp3;
|
|
logical ilazr2;
|
|
integer jc, in;
|
|
doublereal ascale, bscale;
|
|
doublecomplex u12;
|
|
extern doublereal dlamch_(char *);
|
|
integer jr;
|
|
doublecomplex signbc;
|
|
doublereal safmin;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
doublecomplex eshift;
|
|
logical ilschr;
|
|
integer icompq, ilastm;
|
|
extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
|
|
doublecomplex *);
|
|
integer ischur;
|
|
extern doublereal zlanhs_(char *, integer *, doublecomplex *, integer *,
|
|
doublereal *);
|
|
logical ilazro;
|
|
integer icompz, ifirst;
|
|
extern /* Subroutine */ void zlartg_(doublecomplex *, doublecomplex *,
|
|
doublereal *, doublecomplex *, doublecomplex *);
|
|
integer ifrstm;
|
|
extern /* Subroutine */ void zlaset_(char *, integer *, integer *,
|
|
doublecomplex *, doublecomplex *, doublecomplex *, integer *);
|
|
integer istart;
|
|
logical lquery;
|
|
doublecomplex ad11, ad12, ad21, ad22;
|
|
integer jch;
|
|
logical ilq, ilz;
|
|
doublereal ulp;
|
|
doublecomplex abi12, abi22;
|
|
|
|
|
|
/* -- 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..-- */
|
|
/* April 2012 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Decode JOB, COMPQ, COMPZ */
|
|
|
|
/* Parameter adjustments */
|
|
h_dim1 = *ldh;
|
|
h_offset = 1 + h_dim1 * 1;
|
|
h__ -= h_offset;
|
|
t_dim1 = *ldt;
|
|
t_offset = 1 + t_dim1 * 1;
|
|
t -= t_offset;
|
|
--alpha;
|
|
--beta;
|
|
q_dim1 = *ldq;
|
|
q_offset = 1 + q_dim1 * 1;
|
|
q -= q_offset;
|
|
z_dim1 = *ldz;
|
|
z_offset = 1 + z_dim1 * 1;
|
|
z__ -= z_offset;
|
|
--work;
|
|
--rwork;
|
|
|
|
/* Function Body */
|
|
if (lsame_(job, "E")) {
|
|
ilschr = FALSE_;
|
|
ischur = 1;
|
|
} else if (lsame_(job, "S")) {
|
|
ilschr = TRUE_;
|
|
ischur = 2;
|
|
} else {
|
|
ilschr = TRUE_;
|
|
ischur = 0;
|
|
}
|
|
|
|
if (lsame_(compq, "N")) {
|
|
ilq = FALSE_;
|
|
icompq = 1;
|
|
} else if (lsame_(compq, "V")) {
|
|
ilq = TRUE_;
|
|
icompq = 2;
|
|
} else if (lsame_(compq, "I")) {
|
|
ilq = TRUE_;
|
|
icompq = 3;
|
|
} else {
|
|
ilq = TRUE_;
|
|
icompq = 0;
|
|
}
|
|
|
|
if (lsame_(compz, "N")) {
|
|
ilz = FALSE_;
|
|
icompz = 1;
|
|
} else if (lsame_(compz, "V")) {
|
|
ilz = TRUE_;
|
|
icompz = 2;
|
|
} else if (lsame_(compz, "I")) {
|
|
ilz = TRUE_;
|
|
icompz = 3;
|
|
} else {
|
|
ilz = TRUE_;
|
|
icompz = 0;
|
|
}
|
|
|
|
/* Check Argument Values */
|
|
|
|
*info = 0;
|
|
i__1 = f2cmax(1,*n);
|
|
work[1].r = (doublereal) i__1, work[1].i = 0.;
|
|
lquery = *lwork == -1;
|
|
if (ischur == 0) {
|
|
*info = -1;
|
|
} else if (icompq == 0) {
|
|
*info = -2;
|
|
} else if (icompz == 0) {
|
|
*info = -3;
|
|
} else if (*n < 0) {
|
|
*info = -4;
|
|
} else if (*ilo < 1) {
|
|
*info = -5;
|
|
} else if (*ihi > *n || *ihi < *ilo - 1) {
|
|
*info = -6;
|
|
} else if (*ldh < *n) {
|
|
*info = -8;
|
|
} else if (*ldt < *n) {
|
|
*info = -10;
|
|
} else if (*ldq < 1 || ilq && *ldq < *n) {
|
|
*info = -14;
|
|
} else if (*ldz < 1 || ilz && *ldz < *n) {
|
|
*info = -16;
|
|
} else if (*lwork < f2cmax(1,*n) && ! lquery) {
|
|
*info = -18;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZHGEQZ", &i__1, (ftnlen)6);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
/* WORK( 1 ) = CMPLX( 1 ) */
|
|
if (*n <= 0) {
|
|
work[1].r = 1., work[1].i = 0.;
|
|
return;
|
|
}
|
|
|
|
/* Initialize Q and Z */
|
|
|
|
if (icompq == 3) {
|
|
zlaset_("Full", n, n, &c_b1, &c_b2, &q[q_offset], ldq);
|
|
}
|
|
if (icompz == 3) {
|
|
zlaset_("Full", n, n, &c_b1, &c_b2, &z__[z_offset], ldz);
|
|
}
|
|
|
|
/* Machine Constants */
|
|
|
|
in = *ihi + 1 - *ilo;
|
|
safmin = dlamch_("S");
|
|
ulp = dlamch_("E") * dlamch_("B");
|
|
anorm = zlanhs_("F", &in, &h__[*ilo + *ilo * h_dim1], ldh, &rwork[1]);
|
|
bnorm = zlanhs_("F", &in, &t[*ilo + *ilo * t_dim1], ldt, &rwork[1]);
|
|
/* Computing MAX */
|
|
d__1 = safmin, d__2 = ulp * anorm;
|
|
atol = f2cmax(d__1,d__2);
|
|
/* Computing MAX */
|
|
d__1 = safmin, d__2 = ulp * bnorm;
|
|
btol = f2cmax(d__1,d__2);
|
|
ascale = 1. / f2cmax(safmin,anorm);
|
|
bscale = 1. / f2cmax(safmin,bnorm);
|
|
|
|
|
|
/* Set Eigenvalues IHI+1:N */
|
|
|
|
i__1 = *n;
|
|
for (j = *ihi + 1; j <= i__1; ++j) {
|
|
absb = z_abs(&t[j + j * t_dim1]);
|
|
if (absb > safmin) {
|
|
i__2 = j + j * t_dim1;
|
|
z__2.r = t[i__2].r / absb, z__2.i = t[i__2].i / absb;
|
|
d_cnjg(&z__1, &z__2);
|
|
signbc.r = z__1.r, signbc.i = z__1.i;
|
|
i__2 = j + j * t_dim1;
|
|
t[i__2].r = absb, t[i__2].i = 0.;
|
|
if (ilschr) {
|
|
i__2 = j - 1;
|
|
zscal_(&i__2, &signbc, &t[j * t_dim1 + 1], &c__1);
|
|
zscal_(&j, &signbc, &h__[j * h_dim1 + 1], &c__1);
|
|
} else {
|
|
zscal_(&c__1, &signbc, &h__[j + j * h_dim1], &c__1);
|
|
}
|
|
if (ilz) {
|
|
zscal_(n, &signbc, &z__[j * z_dim1 + 1], &c__1);
|
|
}
|
|
} else {
|
|
i__2 = j + j * t_dim1;
|
|
t[i__2].r = 0., t[i__2].i = 0.;
|
|
}
|
|
i__2 = j;
|
|
i__3 = j + j * h_dim1;
|
|
alpha[i__2].r = h__[i__3].r, alpha[i__2].i = h__[i__3].i;
|
|
i__2 = j;
|
|
i__3 = j + j * t_dim1;
|
|
beta[i__2].r = t[i__3].r, beta[i__2].i = t[i__3].i;
|
|
/* L10: */
|
|
}
|
|
|
|
/* If IHI < ILO, skip QZ steps */
|
|
|
|
if (*ihi < *ilo) {
|
|
goto L190;
|
|
}
|
|
|
|
/* MAIN QZ ITERATION LOOP */
|
|
|
|
/* Initialize dynamic indices */
|
|
|
|
/* Eigenvalues ILAST+1:N have been found. */
|
|
/* Column operations modify rows IFRSTM:whatever */
|
|
/* Row operations modify columns whatever:ILASTM */
|
|
|
|
/* If only eigenvalues are being computed, then */
|
|
/* IFRSTM is the row of the last splitting row above row ILAST; */
|
|
/* this is always at least ILO. */
|
|
/* IITER counts iterations since the last eigenvalue was found, */
|
|
/* to tell when to use an extraordinary shift. */
|
|
/* MAXIT is the maximum number of QZ sweeps allowed. */
|
|
|
|
ilast = *ihi;
|
|
if (ilschr) {
|
|
ifrstm = 1;
|
|
ilastm = *n;
|
|
} else {
|
|
ifrstm = *ilo;
|
|
ilastm = *ihi;
|
|
}
|
|
iiter = 0;
|
|
eshift.r = 0., eshift.i = 0.;
|
|
maxit = (*ihi - *ilo + 1) * 30;
|
|
|
|
i__1 = maxit;
|
|
for (jiter = 1; jiter <= i__1; ++jiter) {
|
|
|
|
/* Check for too many iterations. */
|
|
|
|
if (jiter > maxit) {
|
|
goto L180;
|
|
}
|
|
|
|
/* Split the matrix if possible. */
|
|
|
|
/* Two tests: */
|
|
/* 1: H(j,j-1)=0 or j=ILO */
|
|
/* 2: T(j,j)=0 */
|
|
|
|
/* Special case: j=ILAST */
|
|
|
|
if (ilast == *ilo) {
|
|
goto L60;
|
|
} else {
|
|
i__2 = ilast + (ilast - 1) * h_dim1;
|
|
if ((d__1 = h__[i__2].r, abs(d__1)) + (d__2 = d_imag(&h__[ilast +
|
|
(ilast - 1) * h_dim1]), abs(d__2)) <= atol) {
|
|
i__2 = ilast + (ilast - 1) * h_dim1;
|
|
h__[i__2].r = 0., h__[i__2].i = 0.;
|
|
goto L60;
|
|
}
|
|
}
|
|
|
|
if (z_abs(&t[ilast + ilast * t_dim1]) <= btol) {
|
|
i__2 = ilast + ilast * t_dim1;
|
|
t[i__2].r = 0., t[i__2].i = 0.;
|
|
goto L50;
|
|
}
|
|
|
|
/* General case: j<ILAST */
|
|
|
|
i__2 = *ilo;
|
|
for (j = ilast - 1; j >= i__2; --j) {
|
|
|
|
/* Test 1: for H(j,j-1)=0 or j=ILO */
|
|
|
|
if (j == *ilo) {
|
|
ilazro = TRUE_;
|
|
} else {
|
|
i__3 = j + (j - 1) * h_dim1;
|
|
if ((d__1 = h__[i__3].r, abs(d__1)) + (d__2 = d_imag(&h__[j +
|
|
(j - 1) * h_dim1]), abs(d__2)) <= atol) {
|
|
i__3 = j + (j - 1) * h_dim1;
|
|
h__[i__3].r = 0., h__[i__3].i = 0.;
|
|
ilazro = TRUE_;
|
|
} else {
|
|
ilazro = FALSE_;
|
|
}
|
|
}
|
|
|
|
/* Test 2: for T(j,j)=0 */
|
|
|
|
if (z_abs(&t[j + j * t_dim1]) < btol) {
|
|
i__3 = j + j * t_dim1;
|
|
t[i__3].r = 0., t[i__3].i = 0.;
|
|
|
|
/* Test 1a: Check for 2 consecutive small subdiagonals in A */
|
|
|
|
ilazr2 = FALSE_;
|
|
if (! ilazro) {
|
|
i__3 = j + (j - 1) * h_dim1;
|
|
i__4 = j + 1 + j * h_dim1;
|
|
i__5 = j + j * h_dim1;
|
|
if (((d__1 = h__[i__3].r, abs(d__1)) + (d__2 = d_imag(&
|
|
h__[j + (j - 1) * h_dim1]), abs(d__2))) * (ascale
|
|
* ((d__3 = h__[i__4].r, abs(d__3)) + (d__4 =
|
|
d_imag(&h__[j + 1 + j * h_dim1]), abs(d__4)))) <=
|
|
((d__5 = h__[i__5].r, abs(d__5)) + (d__6 = d_imag(
|
|
&h__[j + j * h_dim1]), abs(d__6))) * (ascale *
|
|
atol)) {
|
|
ilazr2 = TRUE_;
|
|
}
|
|
}
|
|
|
|
/* If both tests pass (1 & 2), i.e., the leading diagonal */
|
|
/* element of B in the block is zero, split a 1x1 block off */
|
|
/* at the top. (I.e., at the J-th row/column) The leading */
|
|
/* diagonal element of the remainder can also be zero, so */
|
|
/* this may have to be done repeatedly. */
|
|
|
|
if (ilazro || ilazr2) {
|
|
i__3 = ilast - 1;
|
|
for (jch = j; jch <= i__3; ++jch) {
|
|
i__4 = jch + jch * h_dim1;
|
|
ctemp.r = h__[i__4].r, ctemp.i = h__[i__4].i;
|
|
zlartg_(&ctemp, &h__[jch + 1 + jch * h_dim1], &c__, &
|
|
s, &h__[jch + jch * h_dim1]);
|
|
i__4 = jch + 1 + jch * h_dim1;
|
|
h__[i__4].r = 0., h__[i__4].i = 0.;
|
|
i__4 = ilastm - jch;
|
|
zrot_(&i__4, &h__[jch + (jch + 1) * h_dim1], ldh, &
|
|
h__[jch + 1 + (jch + 1) * h_dim1], ldh, &c__,
|
|
&s);
|
|
i__4 = ilastm - jch;
|
|
zrot_(&i__4, &t[jch + (jch + 1) * t_dim1], ldt, &t[
|
|
jch + 1 + (jch + 1) * t_dim1], ldt, &c__, &s);
|
|
if (ilq) {
|
|
d_cnjg(&z__1, &s);
|
|
zrot_(n, &q[jch * q_dim1 + 1], &c__1, &q[(jch + 1)
|
|
* q_dim1 + 1], &c__1, &c__, &z__1);
|
|
}
|
|
if (ilazr2) {
|
|
i__4 = jch + (jch - 1) * h_dim1;
|
|
i__5 = jch + (jch - 1) * h_dim1;
|
|
z__1.r = c__ * h__[i__5].r, z__1.i = c__ * h__[
|
|
i__5].i;
|
|
h__[i__4].r = z__1.r, h__[i__4].i = z__1.i;
|
|
}
|
|
ilazr2 = FALSE_;
|
|
i__4 = jch + 1 + (jch + 1) * t_dim1;
|
|
if ((d__1 = t[i__4].r, abs(d__1)) + (d__2 = d_imag(&t[
|
|
jch + 1 + (jch + 1) * t_dim1]), abs(d__2)) >=
|
|
btol) {
|
|
if (jch + 1 >= ilast) {
|
|
goto L60;
|
|
} else {
|
|
ifirst = jch + 1;
|
|
goto L70;
|
|
}
|
|
}
|
|
i__4 = jch + 1 + (jch + 1) * t_dim1;
|
|
t[i__4].r = 0., t[i__4].i = 0.;
|
|
/* L20: */
|
|
}
|
|
goto L50;
|
|
} else {
|
|
|
|
/* Only test 2 passed -- chase the zero to T(ILAST,ILAST) */
|
|
/* Then process as in the case T(ILAST,ILAST)=0 */
|
|
|
|
i__3 = ilast - 1;
|
|
for (jch = j; jch <= i__3; ++jch) {
|
|
i__4 = jch + (jch + 1) * t_dim1;
|
|
ctemp.r = t[i__4].r, ctemp.i = t[i__4].i;
|
|
zlartg_(&ctemp, &t[jch + 1 + (jch + 1) * t_dim1], &
|
|
c__, &s, &t[jch + (jch + 1) * t_dim1]);
|
|
i__4 = jch + 1 + (jch + 1) * t_dim1;
|
|
t[i__4].r = 0., t[i__4].i = 0.;
|
|
if (jch < ilastm - 1) {
|
|
i__4 = ilastm - jch - 1;
|
|
zrot_(&i__4, &t[jch + (jch + 2) * t_dim1], ldt, &
|
|
t[jch + 1 + (jch + 2) * t_dim1], ldt, &
|
|
c__, &s);
|
|
}
|
|
i__4 = ilastm - jch + 2;
|
|
zrot_(&i__4, &h__[jch + (jch - 1) * h_dim1], ldh, &
|
|
h__[jch + 1 + (jch - 1) * h_dim1], ldh, &c__,
|
|
&s);
|
|
if (ilq) {
|
|
d_cnjg(&z__1, &s);
|
|
zrot_(n, &q[jch * q_dim1 + 1], &c__1, &q[(jch + 1)
|
|
* q_dim1 + 1], &c__1, &c__, &z__1);
|
|
}
|
|
i__4 = jch + 1 + jch * h_dim1;
|
|
ctemp.r = h__[i__4].r, ctemp.i = h__[i__4].i;
|
|
zlartg_(&ctemp, &h__[jch + 1 + (jch - 1) * h_dim1], &
|
|
c__, &s, &h__[jch + 1 + jch * h_dim1]);
|
|
i__4 = jch + 1 + (jch - 1) * h_dim1;
|
|
h__[i__4].r = 0., h__[i__4].i = 0.;
|
|
i__4 = jch + 1 - ifrstm;
|
|
zrot_(&i__4, &h__[ifrstm + jch * h_dim1], &c__1, &h__[
|
|
ifrstm + (jch - 1) * h_dim1], &c__1, &c__, &s)
|
|
;
|
|
i__4 = jch - ifrstm;
|
|
zrot_(&i__4, &t[ifrstm + jch * t_dim1], &c__1, &t[
|
|
ifrstm + (jch - 1) * t_dim1], &c__1, &c__, &s)
|
|
;
|
|
if (ilz) {
|
|
zrot_(n, &z__[jch * z_dim1 + 1], &c__1, &z__[(jch
|
|
- 1) * z_dim1 + 1], &c__1, &c__, &s);
|
|
}
|
|
/* L30: */
|
|
}
|
|
goto L50;
|
|
}
|
|
} else if (ilazro) {
|
|
|
|
/* Only test 1 passed -- work on J:ILAST */
|
|
|
|
ifirst = j;
|
|
goto L70;
|
|
}
|
|
|
|
/* Neither test passed -- try next J */
|
|
|
|
/* L40: */
|
|
}
|
|
|
|
/* (Drop-through is "impossible") */
|
|
|
|
*info = (*n << 1) + 1;
|
|
goto L210;
|
|
|
|
/* T(ILAST,ILAST)=0 -- clear H(ILAST,ILAST-1) to split off a */
|
|
/* 1x1 block. */
|
|
|
|
L50:
|
|
i__2 = ilast + ilast * h_dim1;
|
|
ctemp.r = h__[i__2].r, ctemp.i = h__[i__2].i;
|
|
zlartg_(&ctemp, &h__[ilast + (ilast - 1) * h_dim1], &c__, &s, &h__[
|
|
ilast + ilast * h_dim1]);
|
|
i__2 = ilast + (ilast - 1) * h_dim1;
|
|
h__[i__2].r = 0., h__[i__2].i = 0.;
|
|
i__2 = ilast - ifrstm;
|
|
zrot_(&i__2, &h__[ifrstm + ilast * h_dim1], &c__1, &h__[ifrstm + (
|
|
ilast - 1) * h_dim1], &c__1, &c__, &s);
|
|
i__2 = ilast - ifrstm;
|
|
zrot_(&i__2, &t[ifrstm + ilast * t_dim1], &c__1, &t[ifrstm + (ilast -
|
|
1) * t_dim1], &c__1, &c__, &s);
|
|
if (ilz) {
|
|
zrot_(n, &z__[ilast * z_dim1 + 1], &c__1, &z__[(ilast - 1) *
|
|
z_dim1 + 1], &c__1, &c__, &s);
|
|
}
|
|
|
|
/* H(ILAST,ILAST-1)=0 -- Standardize B, set ALPHA and BETA */
|
|
|
|
L60:
|
|
absb = z_abs(&t[ilast + ilast * t_dim1]);
|
|
if (absb > safmin) {
|
|
i__2 = ilast + ilast * t_dim1;
|
|
z__2.r = t[i__2].r / absb, z__2.i = t[i__2].i / absb;
|
|
d_cnjg(&z__1, &z__2);
|
|
signbc.r = z__1.r, signbc.i = z__1.i;
|
|
i__2 = ilast + ilast * t_dim1;
|
|
t[i__2].r = absb, t[i__2].i = 0.;
|
|
if (ilschr) {
|
|
i__2 = ilast - ifrstm;
|
|
zscal_(&i__2, &signbc, &t[ifrstm + ilast * t_dim1], &c__1);
|
|
i__2 = ilast + 1 - ifrstm;
|
|
zscal_(&i__2, &signbc, &h__[ifrstm + ilast * h_dim1], &c__1);
|
|
} else {
|
|
zscal_(&c__1, &signbc, &h__[ilast + ilast * h_dim1], &c__1);
|
|
}
|
|
if (ilz) {
|
|
zscal_(n, &signbc, &z__[ilast * z_dim1 + 1], &c__1);
|
|
}
|
|
} else {
|
|
i__2 = ilast + ilast * t_dim1;
|
|
t[i__2].r = 0., t[i__2].i = 0.;
|
|
}
|
|
i__2 = ilast;
|
|
i__3 = ilast + ilast * h_dim1;
|
|
alpha[i__2].r = h__[i__3].r, alpha[i__2].i = h__[i__3].i;
|
|
i__2 = ilast;
|
|
i__3 = ilast + ilast * t_dim1;
|
|
beta[i__2].r = t[i__3].r, beta[i__2].i = t[i__3].i;
|
|
|
|
/* Go to next block -- exit if finished. */
|
|
|
|
--ilast;
|
|
if (ilast < *ilo) {
|
|
goto L190;
|
|
}
|
|
|
|
/* Reset counters */
|
|
|
|
iiter = 0;
|
|
eshift.r = 0., eshift.i = 0.;
|
|
if (! ilschr) {
|
|
ilastm = ilast;
|
|
if (ifrstm > ilast) {
|
|
ifrstm = *ilo;
|
|
}
|
|
}
|
|
goto L160;
|
|
|
|
/* QZ step */
|
|
|
|
/* This iteration only involves rows/columns IFIRST:ILAST. We */
|
|
/* assume IFIRST < ILAST, and that the diagonal of B is non-zero. */
|
|
|
|
L70:
|
|
++iiter;
|
|
if (! ilschr) {
|
|
ifrstm = ifirst;
|
|
}
|
|
|
|
/* Compute the Shift. */
|
|
|
|
/* At this point, IFIRST < ILAST, and the diagonal elements of */
|
|
/* T(IFIRST:ILAST,IFIRST,ILAST) are larger than BTOL (in */
|
|
/* magnitude) */
|
|
|
|
if (iiter / 10 * 10 != iiter) {
|
|
|
|
/* The Wilkinson shift (AEP p.512), i.e., the eigenvalue of */
|
|
/* the bottom-right 2x2 block of A inv(B) which is nearest to */
|
|
/* the bottom-right element. */
|
|
|
|
/* We factor B as U*D, where U has unit diagonals, and */
|
|
/* compute (A*inv(D))*inv(U). */
|
|
|
|
i__2 = ilast - 1 + ilast * t_dim1;
|
|
z__2.r = bscale * t[i__2].r, z__2.i = bscale * t[i__2].i;
|
|
i__3 = ilast + ilast * t_dim1;
|
|
z__3.r = bscale * t[i__3].r, z__3.i = bscale * t[i__3].i;
|
|
z_div(&z__1, &z__2, &z__3);
|
|
u12.r = z__1.r, u12.i = z__1.i;
|
|
i__2 = ilast - 1 + (ilast - 1) * h_dim1;
|
|
z__2.r = ascale * h__[i__2].r, z__2.i = ascale * h__[i__2].i;
|
|
i__3 = ilast - 1 + (ilast - 1) * t_dim1;
|
|
z__3.r = bscale * t[i__3].r, z__3.i = bscale * t[i__3].i;
|
|
z_div(&z__1, &z__2, &z__3);
|
|
ad11.r = z__1.r, ad11.i = z__1.i;
|
|
i__2 = ilast + (ilast - 1) * h_dim1;
|
|
z__2.r = ascale * h__[i__2].r, z__2.i = ascale * h__[i__2].i;
|
|
i__3 = ilast - 1 + (ilast - 1) * t_dim1;
|
|
z__3.r = bscale * t[i__3].r, z__3.i = bscale * t[i__3].i;
|
|
z_div(&z__1, &z__2, &z__3);
|
|
ad21.r = z__1.r, ad21.i = z__1.i;
|
|
i__2 = ilast - 1 + ilast * h_dim1;
|
|
z__2.r = ascale * h__[i__2].r, z__2.i = ascale * h__[i__2].i;
|
|
i__3 = ilast + ilast * t_dim1;
|
|
z__3.r = bscale * t[i__3].r, z__3.i = bscale * t[i__3].i;
|
|
z_div(&z__1, &z__2, &z__3);
|
|
ad12.r = z__1.r, ad12.i = z__1.i;
|
|
i__2 = ilast + ilast * h_dim1;
|
|
z__2.r = ascale * h__[i__2].r, z__2.i = ascale * h__[i__2].i;
|
|
i__3 = ilast + ilast * t_dim1;
|
|
z__3.r = bscale * t[i__3].r, z__3.i = bscale * t[i__3].i;
|
|
z_div(&z__1, &z__2, &z__3);
|
|
ad22.r = z__1.r, ad22.i = z__1.i;
|
|
z__2.r = u12.r * ad21.r - u12.i * ad21.i, z__2.i = u12.r * ad21.i
|
|
+ u12.i * ad21.r;
|
|
z__1.r = ad22.r - z__2.r, z__1.i = ad22.i - z__2.i;
|
|
abi22.r = z__1.r, abi22.i = z__1.i;
|
|
z__2.r = u12.r * ad11.r - u12.i * ad11.i, z__2.i = u12.r * ad11.i
|
|
+ u12.i * ad11.r;
|
|
z__1.r = ad12.r - z__2.r, z__1.i = ad12.i - z__2.i;
|
|
abi12.r = z__1.r, abi12.i = z__1.i;
|
|
|
|
shift.r = abi22.r, shift.i = abi22.i;
|
|
z_sqrt(&z__2, &abi12);
|
|
z_sqrt(&z__3, &ad21);
|
|
z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r *
|
|
z__3.i + z__2.i * z__3.r;
|
|
ctemp.r = z__1.r, ctemp.i = z__1.i;
|
|
temp = (d__1 = ctemp.r, abs(d__1)) + (d__2 = d_imag(&ctemp), abs(
|
|
d__2));
|
|
if (ctemp.r != 0. || ctemp.i != 0.) {
|
|
z__2.r = ad11.r - shift.r, z__2.i = ad11.i - shift.i;
|
|
z__1.r = z__2.r * .5, z__1.i = z__2.i * .5;
|
|
x.r = z__1.r, x.i = z__1.i;
|
|
temp2 = (d__1 = x.r, abs(d__1)) + (d__2 = d_imag(&x), abs(
|
|
d__2));
|
|
/* Computing MAX */
|
|
d__3 = temp, d__4 = (d__1 = x.r, abs(d__1)) + (d__2 = d_imag(&
|
|
x), abs(d__2));
|
|
temp = f2cmax(d__3,d__4);
|
|
z__5.r = x.r / temp, z__5.i = x.i / temp;
|
|
pow_zi(&z__4, &z__5, &c__2);
|
|
z__7.r = ctemp.r / temp, z__7.i = ctemp.i / temp;
|
|
pow_zi(&z__6, &z__7, &c__2);
|
|
z__3.r = z__4.r + z__6.r, z__3.i = z__4.i + z__6.i;
|
|
z_sqrt(&z__2, &z__3);
|
|
z__1.r = temp * z__2.r, z__1.i = temp * z__2.i;
|
|
y.r = z__1.r, y.i = z__1.i;
|
|
if (temp2 > 0.) {
|
|
z__1.r = x.r / temp2, z__1.i = x.i / temp2;
|
|
z__2.r = x.r / temp2, z__2.i = x.i / temp2;
|
|
if (z__1.r * y.r + d_imag(&z__2) * d_imag(&y) < 0.) {
|
|
z__3.r = -y.r, z__3.i = -y.i;
|
|
y.r = z__3.r, y.i = z__3.i;
|
|
}
|
|
}
|
|
z__4.r = x.r + y.r, z__4.i = x.i + y.i;
|
|
zladiv_(&z__3, &ctemp, &z__4);
|
|
z__2.r = ctemp.r * z__3.r - ctemp.i * z__3.i, z__2.i =
|
|
ctemp.r * z__3.i + ctemp.i * z__3.r;
|
|
z__1.r = shift.r - z__2.r, z__1.i = shift.i - z__2.i;
|
|
shift.r = z__1.r, shift.i = z__1.i;
|
|
}
|
|
} else {
|
|
|
|
/* Exceptional shift. Chosen for no particularly good reason. */
|
|
|
|
i__2 = ilast + ilast * t_dim1;
|
|
if (iiter / 20 * 20 == iiter && bscale * ((d__1 = t[i__2].r, abs(
|
|
d__1)) + (d__2 = d_imag(&t[ilast + ilast * t_dim1]), abs(
|
|
d__2))) > safmin) {
|
|
i__2 = ilast + ilast * h_dim1;
|
|
z__3.r = ascale * h__[i__2].r, z__3.i = ascale * h__[i__2].i;
|
|
i__3 = ilast + ilast * t_dim1;
|
|
z__4.r = bscale * t[i__3].r, z__4.i = bscale * t[i__3].i;
|
|
z_div(&z__2, &z__3, &z__4);
|
|
z__1.r = eshift.r + z__2.r, z__1.i = eshift.i + z__2.i;
|
|
eshift.r = z__1.r, eshift.i = z__1.i;
|
|
} else {
|
|
i__2 = ilast + (ilast - 1) * h_dim1;
|
|
z__3.r = ascale * h__[i__2].r, z__3.i = ascale * h__[i__2].i;
|
|
i__3 = ilast - 1 + (ilast - 1) * t_dim1;
|
|
z__4.r = bscale * t[i__3].r, z__4.i = bscale * t[i__3].i;
|
|
z_div(&z__2, &z__3, &z__4);
|
|
z__1.r = eshift.r + z__2.r, z__1.i = eshift.i + z__2.i;
|
|
eshift.r = z__1.r, eshift.i = z__1.i;
|
|
}
|
|
shift.r = eshift.r, shift.i = eshift.i;
|
|
}
|
|
|
|
/* Now check for two consecutive small subdiagonals. */
|
|
|
|
i__2 = ifirst + 1;
|
|
for (j = ilast - 1; j >= i__2; --j) {
|
|
istart = j;
|
|
i__3 = j + j * h_dim1;
|
|
z__2.r = ascale * h__[i__3].r, z__2.i = ascale * h__[i__3].i;
|
|
i__4 = j + j * t_dim1;
|
|
z__4.r = bscale * t[i__4].r, z__4.i = bscale * t[i__4].i;
|
|
z__3.r = shift.r * z__4.r - shift.i * z__4.i, z__3.i = shift.r *
|
|
z__4.i + shift.i * z__4.r;
|
|
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
|
|
ctemp.r = z__1.r, ctemp.i = z__1.i;
|
|
temp = (d__1 = ctemp.r, abs(d__1)) + (d__2 = d_imag(&ctemp), abs(
|
|
d__2));
|
|
i__3 = j + 1 + j * h_dim1;
|
|
temp2 = ascale * ((d__1 = h__[i__3].r, abs(d__1)) + (d__2 =
|
|
d_imag(&h__[j + 1 + j * h_dim1]), abs(d__2)));
|
|
tempr = f2cmax(temp,temp2);
|
|
if (tempr < 1. && tempr != 0.) {
|
|
temp /= tempr;
|
|
temp2 /= tempr;
|
|
}
|
|
i__3 = j + (j - 1) * h_dim1;
|
|
if (((d__1 = h__[i__3].r, abs(d__1)) + (d__2 = d_imag(&h__[j + (j
|
|
- 1) * h_dim1]), abs(d__2))) * temp2 <= temp * atol) {
|
|
goto L90;
|
|
}
|
|
/* L80: */
|
|
}
|
|
|
|
istart = ifirst;
|
|
i__2 = ifirst + ifirst * h_dim1;
|
|
z__2.r = ascale * h__[i__2].r, z__2.i = ascale * h__[i__2].i;
|
|
i__3 = ifirst + ifirst * t_dim1;
|
|
z__4.r = bscale * t[i__3].r, z__4.i = bscale * t[i__3].i;
|
|
z__3.r = shift.r * z__4.r - shift.i * z__4.i, z__3.i = shift.r *
|
|
z__4.i + shift.i * z__4.r;
|
|
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
|
|
ctemp.r = z__1.r, ctemp.i = z__1.i;
|
|
L90:
|
|
|
|
/* Do an implicit-shift QZ sweep. */
|
|
|
|
/* Initial Q */
|
|
|
|
i__2 = istart + 1 + istart * h_dim1;
|
|
z__1.r = ascale * h__[i__2].r, z__1.i = ascale * h__[i__2].i;
|
|
ctemp2.r = z__1.r, ctemp2.i = z__1.i;
|
|
zlartg_(&ctemp, &ctemp2, &c__, &s, &ctemp3);
|
|
|
|
/* Sweep */
|
|
|
|
i__2 = ilast - 1;
|
|
for (j = istart; j <= i__2; ++j) {
|
|
if (j > istart) {
|
|
i__3 = j + (j - 1) * h_dim1;
|
|
ctemp.r = h__[i__3].r, ctemp.i = h__[i__3].i;
|
|
zlartg_(&ctemp, &h__[j + 1 + (j - 1) * h_dim1], &c__, &s, &
|
|
h__[j + (j - 1) * h_dim1]);
|
|
i__3 = j + 1 + (j - 1) * h_dim1;
|
|
h__[i__3].r = 0., h__[i__3].i = 0.;
|
|
}
|
|
|
|
i__3 = ilastm;
|
|
for (jc = j; jc <= i__3; ++jc) {
|
|
i__4 = j + jc * h_dim1;
|
|
z__2.r = c__ * h__[i__4].r, z__2.i = c__ * h__[i__4].i;
|
|
i__5 = j + 1 + jc * h_dim1;
|
|
z__3.r = s.r * h__[i__5].r - s.i * h__[i__5].i, z__3.i = s.r *
|
|
h__[i__5].i + s.i * h__[i__5].r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
ctemp.r = z__1.r, ctemp.i = z__1.i;
|
|
i__4 = j + 1 + jc * h_dim1;
|
|
d_cnjg(&z__4, &s);
|
|
z__3.r = -z__4.r, z__3.i = -z__4.i;
|
|
i__5 = j + jc * h_dim1;
|
|
z__2.r = z__3.r * h__[i__5].r - z__3.i * h__[i__5].i, z__2.i =
|
|
z__3.r * h__[i__5].i + z__3.i * h__[i__5].r;
|
|
i__6 = j + 1 + jc * h_dim1;
|
|
z__5.r = c__ * h__[i__6].r, z__5.i = c__ * h__[i__6].i;
|
|
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
|
|
h__[i__4].r = z__1.r, h__[i__4].i = z__1.i;
|
|
i__4 = j + jc * h_dim1;
|
|
h__[i__4].r = ctemp.r, h__[i__4].i = ctemp.i;
|
|
i__4 = j + jc * t_dim1;
|
|
z__2.r = c__ * t[i__4].r, z__2.i = c__ * t[i__4].i;
|
|
i__5 = j + 1 + jc * t_dim1;
|
|
z__3.r = s.r * t[i__5].r - s.i * t[i__5].i, z__3.i = s.r * t[
|
|
i__5].i + s.i * t[i__5].r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
ctemp2.r = z__1.r, ctemp2.i = z__1.i;
|
|
i__4 = j + 1 + jc * t_dim1;
|
|
d_cnjg(&z__4, &s);
|
|
z__3.r = -z__4.r, z__3.i = -z__4.i;
|
|
i__5 = j + jc * t_dim1;
|
|
z__2.r = z__3.r * t[i__5].r - z__3.i * t[i__5].i, z__2.i =
|
|
z__3.r * t[i__5].i + z__3.i * t[i__5].r;
|
|
i__6 = j + 1 + jc * t_dim1;
|
|
z__5.r = c__ * t[i__6].r, z__5.i = c__ * t[i__6].i;
|
|
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
|
|
t[i__4].r = z__1.r, t[i__4].i = z__1.i;
|
|
i__4 = j + jc * t_dim1;
|
|
t[i__4].r = ctemp2.r, t[i__4].i = ctemp2.i;
|
|
/* L100: */
|
|
}
|
|
if (ilq) {
|
|
i__3 = *n;
|
|
for (jr = 1; jr <= i__3; ++jr) {
|
|
i__4 = jr + j * q_dim1;
|
|
z__2.r = c__ * q[i__4].r, z__2.i = c__ * q[i__4].i;
|
|
d_cnjg(&z__4, &s);
|
|
i__5 = jr + (j + 1) * q_dim1;
|
|
z__3.r = z__4.r * q[i__5].r - z__4.i * q[i__5].i, z__3.i =
|
|
z__4.r * q[i__5].i + z__4.i * q[i__5].r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
ctemp.r = z__1.r, ctemp.i = z__1.i;
|
|
i__4 = jr + (j + 1) * q_dim1;
|
|
z__3.r = -s.r, z__3.i = -s.i;
|
|
i__5 = jr + j * q_dim1;
|
|
z__2.r = z__3.r * q[i__5].r - z__3.i * q[i__5].i, z__2.i =
|
|
z__3.r * q[i__5].i + z__3.i * q[i__5].r;
|
|
i__6 = jr + (j + 1) * q_dim1;
|
|
z__4.r = c__ * q[i__6].r, z__4.i = c__ * q[i__6].i;
|
|
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
|
|
q[i__4].r = z__1.r, q[i__4].i = z__1.i;
|
|
i__4 = jr + j * q_dim1;
|
|
q[i__4].r = ctemp.r, q[i__4].i = ctemp.i;
|
|
/* L110: */
|
|
}
|
|
}
|
|
|
|
i__3 = j + 1 + (j + 1) * t_dim1;
|
|
ctemp.r = t[i__3].r, ctemp.i = t[i__3].i;
|
|
zlartg_(&ctemp, &t[j + 1 + j * t_dim1], &c__, &s, &t[j + 1 + (j +
|
|
1) * t_dim1]);
|
|
i__3 = j + 1 + j * t_dim1;
|
|
t[i__3].r = 0., t[i__3].i = 0.;
|
|
|
|
/* Computing MIN */
|
|
i__4 = j + 2;
|
|
i__3 = f2cmin(i__4,ilast);
|
|
for (jr = ifrstm; jr <= i__3; ++jr) {
|
|
i__4 = jr + (j + 1) * h_dim1;
|
|
z__2.r = c__ * h__[i__4].r, z__2.i = c__ * h__[i__4].i;
|
|
i__5 = jr + j * h_dim1;
|
|
z__3.r = s.r * h__[i__5].r - s.i * h__[i__5].i, z__3.i = s.r *
|
|
h__[i__5].i + s.i * h__[i__5].r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
ctemp.r = z__1.r, ctemp.i = z__1.i;
|
|
i__4 = jr + j * h_dim1;
|
|
d_cnjg(&z__4, &s);
|
|
z__3.r = -z__4.r, z__3.i = -z__4.i;
|
|
i__5 = jr + (j + 1) * h_dim1;
|
|
z__2.r = z__3.r * h__[i__5].r - z__3.i * h__[i__5].i, z__2.i =
|
|
z__3.r * h__[i__5].i + z__3.i * h__[i__5].r;
|
|
i__6 = jr + j * h_dim1;
|
|
z__5.r = c__ * h__[i__6].r, z__5.i = c__ * h__[i__6].i;
|
|
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
|
|
h__[i__4].r = z__1.r, h__[i__4].i = z__1.i;
|
|
i__4 = jr + (j + 1) * h_dim1;
|
|
h__[i__4].r = ctemp.r, h__[i__4].i = ctemp.i;
|
|
/* L120: */
|
|
}
|
|
i__3 = j;
|
|
for (jr = ifrstm; jr <= i__3; ++jr) {
|
|
i__4 = jr + (j + 1) * t_dim1;
|
|
z__2.r = c__ * t[i__4].r, z__2.i = c__ * t[i__4].i;
|
|
i__5 = jr + j * t_dim1;
|
|
z__3.r = s.r * t[i__5].r - s.i * t[i__5].i, z__3.i = s.r * t[
|
|
i__5].i + s.i * t[i__5].r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
ctemp.r = z__1.r, ctemp.i = z__1.i;
|
|
i__4 = jr + j * t_dim1;
|
|
d_cnjg(&z__4, &s);
|
|
z__3.r = -z__4.r, z__3.i = -z__4.i;
|
|
i__5 = jr + (j + 1) * t_dim1;
|
|
z__2.r = z__3.r * t[i__5].r - z__3.i * t[i__5].i, z__2.i =
|
|
z__3.r * t[i__5].i + z__3.i * t[i__5].r;
|
|
i__6 = jr + j * t_dim1;
|
|
z__5.r = c__ * t[i__6].r, z__5.i = c__ * t[i__6].i;
|
|
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
|
|
t[i__4].r = z__1.r, t[i__4].i = z__1.i;
|
|
i__4 = jr + (j + 1) * t_dim1;
|
|
t[i__4].r = ctemp.r, t[i__4].i = ctemp.i;
|
|
/* L130: */
|
|
}
|
|
if (ilz) {
|
|
i__3 = *n;
|
|
for (jr = 1; jr <= i__3; ++jr) {
|
|
i__4 = jr + (j + 1) * z_dim1;
|
|
z__2.r = c__ * z__[i__4].r, z__2.i = c__ * z__[i__4].i;
|
|
i__5 = jr + j * z_dim1;
|
|
z__3.r = s.r * z__[i__5].r - s.i * z__[i__5].i, z__3.i =
|
|
s.r * z__[i__5].i + s.i * z__[i__5].r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
ctemp.r = z__1.r, ctemp.i = z__1.i;
|
|
i__4 = jr + j * z_dim1;
|
|
d_cnjg(&z__4, &s);
|
|
z__3.r = -z__4.r, z__3.i = -z__4.i;
|
|
i__5 = jr + (j + 1) * z_dim1;
|
|
z__2.r = z__3.r * z__[i__5].r - z__3.i * z__[i__5].i,
|
|
z__2.i = z__3.r * z__[i__5].i + z__3.i * z__[i__5]
|
|
.r;
|
|
i__6 = jr + j * z_dim1;
|
|
z__5.r = c__ * z__[i__6].r, z__5.i = c__ * z__[i__6].i;
|
|
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
|
|
z__[i__4].r = z__1.r, z__[i__4].i = z__1.i;
|
|
i__4 = jr + (j + 1) * z_dim1;
|
|
z__[i__4].r = ctemp.r, z__[i__4].i = ctemp.i;
|
|
/* L140: */
|
|
}
|
|
}
|
|
/* L150: */
|
|
}
|
|
|
|
L160:
|
|
|
|
/* L170: */
|
|
;
|
|
}
|
|
|
|
/* Drop-through = non-convergence */
|
|
|
|
L180:
|
|
*info = ilast;
|
|
goto L210;
|
|
|
|
/* Successful completion of all QZ steps */
|
|
|
|
L190:
|
|
|
|
/* Set Eigenvalues 1:ILO-1 */
|
|
|
|
i__1 = *ilo - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
absb = z_abs(&t[j + j * t_dim1]);
|
|
if (absb > safmin) {
|
|
i__2 = j + j * t_dim1;
|
|
z__2.r = t[i__2].r / absb, z__2.i = t[i__2].i / absb;
|
|
d_cnjg(&z__1, &z__2);
|
|
signbc.r = z__1.r, signbc.i = z__1.i;
|
|
i__2 = j + j * t_dim1;
|
|
t[i__2].r = absb, t[i__2].i = 0.;
|
|
if (ilschr) {
|
|
i__2 = j - 1;
|
|
zscal_(&i__2, &signbc, &t[j * t_dim1 + 1], &c__1);
|
|
zscal_(&j, &signbc, &h__[j * h_dim1 + 1], &c__1);
|
|
} else {
|
|
zscal_(&c__1, &signbc, &h__[j + j * h_dim1], &c__1);
|
|
}
|
|
if (ilz) {
|
|
zscal_(n, &signbc, &z__[j * z_dim1 + 1], &c__1);
|
|
}
|
|
} else {
|
|
i__2 = j + j * t_dim1;
|
|
t[i__2].r = 0., t[i__2].i = 0.;
|
|
}
|
|
i__2 = j;
|
|
i__3 = j + j * h_dim1;
|
|
alpha[i__2].r = h__[i__3].r, alpha[i__2].i = h__[i__3].i;
|
|
i__2 = j;
|
|
i__3 = j + j * t_dim1;
|
|
beta[i__2].r = t[i__3].r, beta[i__2].i = t[i__3].i;
|
|
/* L200: */
|
|
}
|
|
|
|
/* Normal Termination */
|
|
|
|
*info = 0;
|
|
|
|
/* Exit (other than argument error) -- return optimal workspace size */
|
|
|
|
L210:
|
|
z__1.r = (doublereal) (*n), z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
return;
|
|
|
|
/* End of ZHGEQZ */
|
|
|
|
} /* zhgeqz_ */
|
|
|