1126 lines
32 KiB
C
1126 lines
32 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
static integer c__0 = 0;
|
|
static integer c_n1 = -1;
|
|
|
|
/* > \brief <b> SGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors f
|
|
or GE matrices</b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download SGEES + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgees.f
|
|
"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgees.f
|
|
"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgees.f
|
|
"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, WR, WI, */
|
|
/* VS, LDVS, WORK, LWORK, BWORK, INFO ) */
|
|
|
|
/* CHARACTER JOBVS, SORT */
|
|
/* INTEGER INFO, LDA, LDVS, LWORK, N, SDIM */
|
|
/* LOGICAL BWORK( * ) */
|
|
/* REAL A( LDA, * ), VS( LDVS, * ), WI( * ), WORK( * ), */
|
|
/* $ WR( * ) */
|
|
/* LOGICAL SELECT */
|
|
/* EXTERNAL SELECT */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > SGEES computes for an N-by-N real nonsymmetric matrix A, the */
|
|
/* > eigenvalues, the real Schur form T, and, optionally, the matrix of */
|
|
/* > Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T). */
|
|
/* > */
|
|
/* > Optionally, it also orders the eigenvalues on the diagonal of the */
|
|
/* > real Schur form so that selected eigenvalues are at the top left. */
|
|
/* > The leading columns of Z then form an orthonormal basis for the */
|
|
/* > invariant subspace corresponding to the selected eigenvalues. */
|
|
/* > */
|
|
/* > A matrix is in real Schur form if it is upper quasi-triangular with */
|
|
/* > 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the */
|
|
/* > form */
|
|
/* > [ a b ] */
|
|
/* > [ c a ] */
|
|
/* > */
|
|
/* > where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc). */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOBVS */
|
|
/* > \verbatim */
|
|
/* > JOBVS is CHARACTER*1 */
|
|
/* > = 'N': Schur vectors are not computed; */
|
|
/* > = 'V': Schur vectors are computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SORT */
|
|
/* > \verbatim */
|
|
/* > SORT is CHARACTER*1 */
|
|
/* > Specifies whether or not to order the eigenvalues on the */
|
|
/* > diagonal of the Schur form. */
|
|
/* > = 'N': Eigenvalues are not ordered; */
|
|
/* > = 'S': Eigenvalues are ordered (see SELECT). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SELECT */
|
|
/* > \verbatim */
|
|
/* > SELECT is a LOGICAL FUNCTION of two REAL arguments */
|
|
/* > SELECT must be declared EXTERNAL in the calling subroutine. */
|
|
/* > If SORT = 'S', SELECT is used to select eigenvalues to sort */
|
|
/* > to the top left of the Schur form. */
|
|
/* > If SORT = 'N', SELECT is not referenced. */
|
|
/* > An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if */
|
|
/* > SELECT(WR(j),WI(j)) is true; i.e., if either one of a complex */
|
|
/* > conjugate pair of eigenvalues is selected, then both complex */
|
|
/* > eigenvalues are selected. */
|
|
/* > Note that a selected complex eigenvalue may no longer */
|
|
/* > satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since */
|
|
/* > ordering may change the value of complex eigenvalues */
|
|
/* > (especially if the eigenvalue is ill-conditioned); in this */
|
|
/* > case INFO is set to N+2 (see INFO below). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is REAL array, dimension (LDA,N) */
|
|
/* > On entry, the N-by-N matrix A. */
|
|
/* > On exit, A has been overwritten by its real Schur form T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SDIM */
|
|
/* > \verbatim */
|
|
/* > SDIM is INTEGER */
|
|
/* > If SORT = 'N', SDIM = 0. */
|
|
/* > If SORT = 'S', SDIM = number of eigenvalues (after sorting) */
|
|
/* > for which SELECT is true. (Complex conjugate */
|
|
/* > pairs for which SELECT is true for either */
|
|
/* > eigenvalue count as 2.) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WR */
|
|
/* > \verbatim */
|
|
/* > WR is REAL array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WI */
|
|
/* > \verbatim */
|
|
/* > WI is REAL array, dimension (N) */
|
|
/* > WR and WI contain the real and imaginary parts, */
|
|
/* > respectively, of the computed eigenvalues in the same order */
|
|
/* > that they appear on the diagonal of the output Schur form T. */
|
|
/* > Complex conjugate pairs of eigenvalues will appear */
|
|
/* > consecutively with the eigenvalue having the positive */
|
|
/* > imaginary part first. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] VS */
|
|
/* > \verbatim */
|
|
/* > VS is REAL array, dimension (LDVS,N) */
|
|
/* > If JOBVS = 'V', VS contains the orthogonal matrix Z of Schur */
|
|
/* > vectors. */
|
|
/* > If JOBVS = 'N', VS is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVS */
|
|
/* > \verbatim */
|
|
/* > LDVS is INTEGER */
|
|
/* > The leading dimension of the array VS. LDVS >= 1; if */
|
|
/* > JOBVS = 'V', LDVS >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is REAL array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) contains the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK >= f2cmax(1,3*N). */
|
|
/* > For good performance, LWORK must generally be larger. */
|
|
/* > */
|
|
/* > 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] BWORK */
|
|
/* > \verbatim */
|
|
/* > BWORK is LOGICAL array, dimension (N) */
|
|
/* > Not referenced if SORT = 'N'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > > 0: if INFO = i, and i is */
|
|
/* > <= N: the QR algorithm failed to compute all the */
|
|
/* > eigenvalues; elements 1:ILO-1 and i+1:N of WR and WI */
|
|
/* > contain those eigenvalues which have converged; if */
|
|
/* > JOBVS = 'V', VS contains the matrix which reduces A */
|
|
/* > to its partially converged Schur form. */
|
|
/* > = N+1: the eigenvalues could not be reordered because some */
|
|
/* > eigenvalues were too close to separate (the problem */
|
|
/* > is very ill-conditioned); */
|
|
/* > = N+2: after reordering, roundoff changed values of some */
|
|
/* > complex eigenvalues so that leading eigenvalues in */
|
|
/* > the Schur form no longer satisfy SELECT=.TRUE. This */
|
|
/* > could also be caused by underflow due to scaling. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2017 */
|
|
|
|
/* > \ingroup realGEeigen */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void sgees_(char *jobvs, char *sort, L_fp select, integer *n,
|
|
real *a, integer *lda, integer *sdim, real *wr, real *wi, real *vs,
|
|
integer *ldvs, real *work, integer *lwork, logical *bwork, integer *
|
|
info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2, i__3;
|
|
|
|
/* Local variables */
|
|
integer ibal;
|
|
real anrm;
|
|
integer idum[1], ierr, itau, iwrk, inxt, i__;
|
|
real s;
|
|
integer icond, ieval;
|
|
extern logical lsame_(char *, char *);
|
|
logical cursl;
|
|
integer i1, i2;
|
|
extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
|
|
integer *), sswap_(integer *, real *, integer *, real *, integer *
|
|
);
|
|
logical lst2sl;
|
|
extern /* Subroutine */ void slabad_(real *, real *);
|
|
logical scalea;
|
|
integer ip;
|
|
real cscale;
|
|
extern /* Subroutine */ void sgebak_(char *, char *, integer *, integer *,
|
|
integer *, real *, integer *, real *, integer *, integer *), sgebal_(char *, integer *, real *, integer *,
|
|
integer *, integer *, real *, integer *);
|
|
extern real slamch_(char *), slange_(char *, integer *, integer *,
|
|
real *, integer *, real *);
|
|
extern /* Subroutine */ void sgehrd_(integer *, integer *, integer *, real
|
|
*, integer *, real *, real *, integer *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
real bignum;
|
|
extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *,
|
|
real *, integer *, integer *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *,
|
|
real *, integer *);
|
|
logical lastsl;
|
|
extern /* Subroutine */ void sorghr_(integer *, integer *, integer *, real
|
|
*, integer *, real *, real *, integer *, integer *), shseqr_(char
|
|
*, char *, integer *, integer *, integer *, real *, integer *,
|
|
real *, real *, real *, integer *, real *, integer *, integer *);
|
|
integer minwrk, maxwrk;
|
|
real smlnum;
|
|
integer hswork;
|
|
extern /* Subroutine */ void strsen_(char *, char *, logical *, integer *,
|
|
real *, integer *, real *, integer *, real *, real *, integer *,
|
|
real *, real *, real *, integer *, integer *, integer *, integer *
|
|
);
|
|
logical wantst, lquery, wantvs;
|
|
integer ihi, ilo;
|
|
real dum[1], eps, sep;
|
|
|
|
|
|
/* -- LAPACK driver routine (version 3.7.1) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 2017 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input arguments */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--wr;
|
|
--wi;
|
|
vs_dim1 = *ldvs;
|
|
vs_offset = 1 + vs_dim1 * 1;
|
|
vs -= vs_offset;
|
|
--work;
|
|
--bwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
lquery = *lwork == -1;
|
|
wantvs = lsame_(jobvs, "V");
|
|
wantst = lsame_(sort, "S");
|
|
if (! wantvs && ! lsame_(jobvs, "N")) {
|
|
*info = -1;
|
|
} else if (! wantst && ! lsame_(sort, "N")) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -4;
|
|
} else if (*lda < f2cmax(1,*n)) {
|
|
*info = -6;
|
|
} else if (*ldvs < 1 || wantvs && *ldvs < *n) {
|
|
*info = -11;
|
|
}
|
|
|
|
/* Compute workspace */
|
|
/* (Note: Comments in the code beginning "Workspace:" describe the */
|
|
/* minimal amount of workspace needed at that point in the code, */
|
|
/* as well as the preferred amount for good performance. */
|
|
/* NB refers to the optimal block size for the immediately */
|
|
/* following subroutine, as returned by ILAENV. */
|
|
/* HSWORK refers to the workspace preferred by SHSEQR, as */
|
|
/* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
|
|
/* the worst case.) */
|
|
|
|
if (*info == 0) {
|
|
if (*n == 0) {
|
|
minwrk = 1;
|
|
maxwrk = 1;
|
|
} else {
|
|
maxwrk = (*n << 1) + *n * ilaenv_(&c__1, "SGEHRD", " ", n, &c__1,
|
|
n, &c__0, (ftnlen)6, (ftnlen)1);
|
|
minwrk = *n * 3;
|
|
|
|
shseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[1]
|
|
, &vs[vs_offset], ldvs, &work[1], &c_n1, &ieval);
|
|
hswork = work[1];
|
|
|
|
if (! wantvs) {
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *n + hswork;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
} else {
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1,
|
|
"SORGHR", " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)
|
|
1);
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *n + hswork;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
}
|
|
}
|
|
work[1] = (real) maxwrk;
|
|
|
|
if (*lwork < minwrk && ! lquery) {
|
|
*info = -13;
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("SGEES ", &i__1, (ftnlen)5);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
*sdim = 0;
|
|
return;
|
|
}
|
|
|
|
/* Get machine constants */
|
|
|
|
eps = slamch_("P");
|
|
smlnum = slamch_("S");
|
|
bignum = 1.f / smlnum;
|
|
slabad_(&smlnum, &bignum);
|
|
smlnum = sqrt(smlnum) / eps;
|
|
bignum = 1.f / smlnum;
|
|
|
|
/* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
|
|
|
|
anrm = slange_("M", n, n, &a[a_offset], lda, dum);
|
|
scalea = FALSE_;
|
|
if (anrm > 0.f && anrm < smlnum) {
|
|
scalea = TRUE_;
|
|
cscale = smlnum;
|
|
} else if (anrm > bignum) {
|
|
scalea = TRUE_;
|
|
cscale = bignum;
|
|
}
|
|
if (scalea) {
|
|
slascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
|
|
ierr);
|
|
}
|
|
|
|
/* Permute the matrix to make it more nearly triangular */
|
|
/* (Workspace: need N) */
|
|
|
|
ibal = 1;
|
|
sgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &work[ibal], &ierr);
|
|
|
|
/* Reduce to upper Hessenberg form */
|
|
/* (Workspace: need 3*N, prefer 2*N+N*NB) */
|
|
|
|
itau = *n + ibal;
|
|
iwrk = *n + itau;
|
|
i__1 = *lwork - iwrk + 1;
|
|
sgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
|
|
&ierr);
|
|
|
|
if (wantvs) {
|
|
|
|
/* Copy Householder vectors to VS */
|
|
|
|
slacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs)
|
|
;
|
|
|
|
/* Generate orthogonal matrix in VS */
|
|
/* (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
|
|
|
|
i__1 = *lwork - iwrk + 1;
|
|
sorghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk],
|
|
&i__1, &ierr);
|
|
}
|
|
|
|
*sdim = 0;
|
|
|
|
/* Perform QR iteration, accumulating Schur vectors in VS if desired */
|
|
/* (Workspace: need N+1, prefer N+HSWORK (see comments) ) */
|
|
|
|
iwrk = itau;
|
|
i__1 = *lwork - iwrk + 1;
|
|
shseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &wr[1], &wi[1], &vs[
|
|
vs_offset], ldvs, &work[iwrk], &i__1, &ieval);
|
|
if (ieval > 0) {
|
|
*info = ieval;
|
|
}
|
|
|
|
/* Sort eigenvalues if desired */
|
|
|
|
if (wantst && *info == 0) {
|
|
if (scalea) {
|
|
slascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wr[1], n, &
|
|
ierr);
|
|
slascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wi[1], n, &
|
|
ierr);
|
|
}
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
bwork[i__] = (*select)(&wr[i__], &wi[i__]);
|
|
/* L10: */
|
|
}
|
|
|
|
/* Reorder eigenvalues and transform Schur vectors */
|
|
/* (Workspace: none needed) */
|
|
|
|
i__1 = *lwork - iwrk + 1;
|
|
strsen_("N", jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset],
|
|
ldvs, &wr[1], &wi[1], sdim, &s, &sep, &work[iwrk], &i__1,
|
|
idum, &c__1, &icond);
|
|
if (icond > 0) {
|
|
*info = *n + icond;
|
|
}
|
|
}
|
|
|
|
if (wantvs) {
|
|
|
|
/* Undo balancing */
|
|
/* (Workspace: need N) */
|
|
|
|
sgebak_("P", "R", n, &ilo, &ihi, &work[ibal], n, &vs[vs_offset], ldvs,
|
|
&ierr);
|
|
}
|
|
|
|
if (scalea) {
|
|
|
|
/* Undo scaling for the Schur form of A */
|
|
|
|
slascl_("H", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
|
|
ierr);
|
|
i__1 = *lda + 1;
|
|
scopy_(n, &a[a_offset], &i__1, &wr[1], &c__1);
|
|
if (cscale == smlnum) {
|
|
|
|
/* If scaling back towards underflow, adjust WI if an */
|
|
/* offdiagonal element of a 2-by-2 block in the Schur form */
|
|
/* underflows. */
|
|
|
|
if (ieval > 0) {
|
|
i1 = ieval + 1;
|
|
i2 = ihi - 1;
|
|
i__1 = ilo - 1;
|
|
/* Computing MAX */
|
|
i__3 = ilo - 1;
|
|
i__2 = f2cmax(i__3,1);
|
|
slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[
|
|
1], &i__2, &ierr);
|
|
} else if (wantst) {
|
|
i1 = 1;
|
|
i2 = *n - 1;
|
|
} else {
|
|
i1 = ilo;
|
|
i2 = ihi - 1;
|
|
}
|
|
inxt = i1 - 1;
|
|
i__1 = i2;
|
|
for (i__ = i1; i__ <= i__1; ++i__) {
|
|
if (i__ < inxt) {
|
|
goto L20;
|
|
}
|
|
if (wi[i__] == 0.f) {
|
|
inxt = i__ + 1;
|
|
} else {
|
|
if (a[i__ + 1 + i__ * a_dim1] == 0.f) {
|
|
wi[i__] = 0.f;
|
|
wi[i__ + 1] = 0.f;
|
|
} else if (a[i__ + 1 + i__ * a_dim1] != 0.f && a[i__ + (
|
|
i__ + 1) * a_dim1] == 0.f) {
|
|
wi[i__] = 0.f;
|
|
wi[i__ + 1] = 0.f;
|
|
if (i__ > 1) {
|
|
i__2 = i__ - 1;
|
|
sswap_(&i__2, &a[i__ * a_dim1 + 1], &c__1, &a[(
|
|
i__ + 1) * a_dim1 + 1], &c__1);
|
|
}
|
|
if (*n > i__ + 1) {
|
|
i__2 = *n - i__ - 1;
|
|
sswap_(&i__2, &a[i__ + (i__ + 2) * a_dim1], lda, &
|
|
a[i__ + 1 + (i__ + 2) * a_dim1], lda);
|
|
}
|
|
if (wantvs) {
|
|
sswap_(n, &vs[i__ * vs_dim1 + 1], &c__1, &vs[(i__
|
|
+ 1) * vs_dim1 + 1], &c__1);
|
|
}
|
|
a[i__ + (i__ + 1) * a_dim1] = a[i__ + 1 + i__ *
|
|
a_dim1];
|
|
a[i__ + 1 + i__ * a_dim1] = 0.f;
|
|
}
|
|
inxt = i__ + 2;
|
|
}
|
|
L20:
|
|
;
|
|
}
|
|
}
|
|
|
|
/* Undo scaling for the imaginary part of the eigenvalues */
|
|
|
|
i__1 = *n - ieval;
|
|
/* Computing MAX */
|
|
i__3 = *n - ieval;
|
|
i__2 = f2cmax(i__3,1);
|
|
slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[ieval +
|
|
1], &i__2, &ierr);
|
|
}
|
|
|
|
if (wantst && *info == 0) {
|
|
|
|
/* Check if reordering successful */
|
|
|
|
lastsl = TRUE_;
|
|
lst2sl = TRUE_;
|
|
*sdim = 0;
|
|
ip = 0;
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
cursl = (*select)(&wr[i__], &wi[i__]);
|
|
if (wi[i__] == 0.f) {
|
|
if (cursl) {
|
|
++(*sdim);
|
|
}
|
|
ip = 0;
|
|
if (cursl && ! lastsl) {
|
|
*info = *n + 2;
|
|
}
|
|
} else {
|
|
if (ip == 1) {
|
|
|
|
/* Last eigenvalue of conjugate pair */
|
|
|
|
cursl = cursl || lastsl;
|
|
lastsl = cursl;
|
|
if (cursl) {
|
|
*sdim += 2;
|
|
}
|
|
ip = -1;
|
|
if (cursl && ! lst2sl) {
|
|
*info = *n + 2;
|
|
}
|
|
} else {
|
|
|
|
/* First eigenvalue of conjugate pair */
|
|
|
|
ip = 1;
|
|
}
|
|
}
|
|
lst2sl = lastsl;
|
|
lastsl = cursl;
|
|
/* L30: */
|
|
}
|
|
}
|
|
|
|
work[1] = (real) maxwrk;
|
|
return;
|
|
|
|
/* End of SGEES */
|
|
|
|
} /* sgees_ */
|
|
|