AUTO の中身
($AUTO)/src/README
README : This file.
autlib1.f : Auto library routines (including main program)
autlib2.f : Auto library routines (bvp linear equation routines)
autlib3.f : Auto library routines (interface routines)
autlib4.f : Auto library routines (Floquet routines)
autlib5.f : Auto library routines (HomPack)
stdat.f : A subroutine for starting orbits from numerical data
eispack.f : contains EISPACK routines needed by AUTO
autlab.f : A utility program for rewriting AUTO data files
86to97.f : A utility program to convert AUTO86 Data-files
94to97.f : A utility program to convert older AUTO94 Data-files
double.f : A utility program for ``doubling'' solutions in q.xxx
Makefile : To compile the source files
($AUTO)/src/autlib4.c
#include "auto_f2c.h"
#include "auto_c.h"/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* Floquet Multiplier Computation (Tom Fairgrieve, U. of Toronto) */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* References: */
/* T. F. Fairgrieve, PhD Thesis, University of Toronto, 1994. */
/* T. F. Fairgrieve, A. D. Jepson, O.K. Floquet multipliers, */
/* SIAM J. Numer. Anal. 28. No. 5, 1991, 1446-1462. *//* Please inform Tom Fairgrieve (tff@na.utoronto.ca) of any */
/* modifications to or errors in these routines. */
/* Mailing Address: T.F. Fairgrieve, Department of Computer Science, */
/* University of Toronto, Toronto, Ontario, CANADA M5S 1A4C */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* Routines included in this file: *//* subroutine flowkm : new routine to compute floquet multipliers */
/* subroutine dhhpr : compute a Householder matrix */
/* subroutine dhhap : appy a Householder matrix */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* Required library routines (included in the file eispack.f) : *//* subroutine qzhes : QZ reduction to Hessenberg form (EISPACK)*/
/* subroutine qzit : QZ reduction to quasi-upper triangular form (EISPACK)*/
/* subroutine qzval : QZ calculation of eigenvalues (EISPACK)*/
/* function epslon : machine constant routine (EISPACK)*/
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* function dnrm2 : compute l2-norm of a vector (BLAS-1)*/
/* function ddot : dot product of two vectors (BLAS-1)*/
/* subroutine dscal : scale a vector by a constant (BLAS-1)*/
/* function idamax : find index of element with max abs value (BLAS-1)*/
/* subroutine daxpy : constant times a vector plus a vector (BLAS-1)*/
/* subroutine drot : apply a plane rotation (BLAS-1)*/
/* subroutine dswap : swap two vectors (BLAS-1)*/
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* subroutine dgemc : matrix-matrix copy */
/* subroutine xerbla : BLAS error handling routine (BLAS-2)*/
/* function lsame : compare character strings (BLAS-2)*/
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* subroutine dgemm : matrix-matrix multiply (BLAS-3)*/
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* subroutines ezsvd, ndrotg, ndsvd, prse, sig22, sigmin, sndrtg : */
/* Demmel-Kahan svd routines */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
($AUTO)/include/auto_c.h
ほどんどの関数の定義．
...
doublereal dnrm2(integer n, doublereal *dx, integer *incx);
doublereal ddot(integer n, doublereal *dx, integer *incx, doublereal *dy, integer *incy);
...
($AUTO)/src/eispack.c
auto_c.h で定義された関数の一部の実装．
/* eispack.f -- translated by f2c (version 19970805).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
AUTO on Mac のエラー
Mac で AUTO を実行しようとした時に起きたエラーの解決策．
エラー 1 : /usr/bin/ld: Undefined symbols : _main
$ auto
AUTO> ld("ab")
AUTO> run()
make: [ab.o] Error 1 (ignored)
...
/usr/bin/ld: Undefined symbols:
_main
collect2: ld returned 1 exit status
make: [ab.exe] Error 1 (ignored)
make: ./ab.exe: Command not found
make: [run] Error 127 (ignored)
..
とりあえずの解決法
Makefile の編集．
EXE = $(PGM).exe
の行を，
EXE = ./$(PGM).exe
と書き直す．
解決法（AUTO のコマンドをいじる）
成功時（$ make でのコンパイルメッセージ）
gcc -D_THREAD_SAFE -DPTHREADS -O -I/Users/hoge/prog/auto/include -c ab.c
gcc -D_THREAD_SAFE -DPTHREADS -O -I/Users/hoge/prog/auto/include ab.o -o ab.exe -L/Users/hoge/prog/auto/lib -lauto -lauto_f2c -lm
gcc -pthread -DPTHREADS -O -I/Users/hoge/prog/auto/include -c -o ab.o ab.c
gcc -pthread -DPTHREADS -O -I/Users/hoge/prog/auto/include ab.o -o ab.exe /Users/hoge/prog/auto/lib/*.o -L/Users/hoge/prog/auto/lib -lauto_f2c -lm
を比べると，
/Users/hoge/prog/auto/lib*.o を読み込んでいないのが，エラーの原因であることが分かる．
AUTO> run() をした時に，実行されている make のための Makefile は，
$(AUTO_DIR)/cmds/cmds.make を使っているらしいので，
このファイルの LIBS に，$(AUTO_DIR)/lib/*.o を追加する．
20行めくらい？
LIBS = -L$(AUTO_DIR)/lib -lauto -lauto_f2c -lm
↓編集後
LIBS = $(AUTO_DIR)/lib/*.o -L$(AUTO_DIR)/lib -lauto -lauto_f2c -lm
エラー 2 : plot できず？
これは，他のが原因だったかもしれない．
一応，これだけはやっておいたらいいかも．
以下，おそらく不要．
tkinter のインストール
http://people.ucsc.edu/~jacobkm/tkinter_osx_howto.html
1. Install Fink.
2. Add "unstable/main" to the "Trees:" line in /sw/etc/fink.conf
3. From the command line:[localhost:~] jacob% fink selfupdate
(say yes to "packages from CVS")
[localhost:~] jacob% fink install xfree86-base （なし）
[localhost:~] jacob% fink install xfree86-rootless （なし）
[localhost:~] jacob% fink install windowmaker
[localhost:~] jacob% fink install python （2.5 をインストール？ 2.3 以下じゃないと，AUTO 動作に問題あるらしいので，在れば不要）4. Make sure XDarwin is running (run /Aplications/XDarwin)
5. From the command line:
AUTO の出力
fort.7 （=> b.hoge) ：安定性の交代，分岐点の種類が見易い．
fort.8 （=> s.hoge）：軌道の座標．
fort.9 （=> d.hoge）：固有値，L2-norm, max(1) max(2), period
autlib1.c の，wrtbv8 内で出力
軌道の空間座標値は，ups[j][k] (0 <= j < ntst),(0 <= k < ncol) 内にある．
fort.8
4 30 4 6 2 1 201 3 412 50 4 50 ← *0
0.0000000000E+00 8.4126672680E-01 5.2580555883E+00 ← *1-A
...
9.9862932262E-01 8.3118721821E-01 5.1313960895E+00
9.9931466131E-01 8.3612426003E-01 5.1933992065E+00 ← *1-B
1.0000000000E+00 8.4126672680E-01 5.2580555883E+00 ← *2
1 10 ← *3
-4.6120475941E-03 1.5955207440E+00 ← *4-A
-1.5890722484E-01 -6.7386091320E-02
-1.5003073620E-01 4.9295602685E-02
-1.4041373599E-01 1.7584396443E-01
-1.3000897365E-01 3.1288396581E-01
-1.1877311309E-01 4.6098383219E-01
...
autlib1.c
wrtbv8(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, doublereal *rldot, integer *ndxloc, doublereal **ups, doublereal **udotps, doublereal *tm, doublereal *dtm)
{
...
fprintf(fp8,"%5ld",ibr); // *0
fprintf(fp8,"%5ld",mtot);
fprintf(fp8,"%5ld",itp);
fprintf(fp8,"%5ld",lab);
fprintf(fp8,"%5ld",nfpr);
fprintf(fp8,"%5ld",isw);
fprintf(fp8,"%5ld",ntpl);
fprintf(fp8,"%5ld",nar);
fprintf(fp8,"%7ld",nrowpr);
fprintf(fp8,"%5ld",ntst);
fprintf(fp8,"%5ld",ncol);
fprintf(fp8,"%5d\n",NPARX); // *0
for(j = 0; j < ntst; ++j){ //NTST（メッシュ区間数）in c.xxx
rn = 1. / ncol;
for(i = 0; i < ncol; ++i){ //NCOL（区間内点数）in c.xxx
k1 = i * ndim;
k2 = (i + 1) * ndim;
t = tm[j] + i * rn * dtm[j];
fprintf(fp8," %19.10E",t);
for(k = k1; k < k2; ++k){
...
fprintf(fp8,"%19.10E",ups[j][k]); // *1 （A-B)
}
fprintf(fp8, "\n");
}
}
fprintf(fp8," %19.10E",tm[ntst]); // *2 の 1つめ
for(i = 0; i < ndim; ++9){
...
fprintf(fp8,"%19.10E",ups[ntst][i]); // *2 の２つめ以降
}
fprintf(fp8,"\n");
/* Write the free parameter indices: */
for (i = 0; i < nfpr; ++i) {
fprintf(fp8,"%5ld",icp[i]); // *3
}
fprintf(fp8,"\n");
/* Write the direction of the branch: */
fprintf(fp8," ");
for (i = 0; i < nfpr; ++i) {
if((i>0)&&((i)%7==0)){
fprintf(fp8,"\n ");
}
fprintf(fp8,"%19.10E",rldot[i]); // *4 A-
}
fprintf(fp8,"\n");
AUTO から，shooting point を得る．
wrtbv8(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, doublereal *rldot, integer *ndxloc, doublereal **ups, doublereal **udotps, doublereal *tm, doublereal *dtm)
{
...
mtot = ntot % 10000;
fprintf(fp8,"%5ld",ibr);
fprintf(fp8,"%5ld",mtot);
fprintf(fp8,"%5ld",itp);
fprintf(fp8,"%5ld",lab);
fprintf(fp8,"%5ld",nfpr);
fprintf(fp8,"%5ld",isw);
fprintf(fp8,"%5ld",ntpl);
fprintf(fp8,"%5ld",nar);
fprintf(fp8,"%7ld",nrowpr);
fprintf(fp8,"%5ld",ntst);
fprintf(fp8,"%5ld",ncol);
fprintf(fp8,"%5d\n",NPARX);
// この下を追記．
// LABEL XXX の時のメッシュ点を splXXX.dat を出力する．
//========================================================
// uniker : output the data of the orbit
// ntst hooting points are got from AUTO
// v[0],..., v[ntst-1]
// v[ntst] sim v[0]
char char_fname_sp[20];
sprintf(char_fname_sp, "spl%03d.dat", mtot);
FILE *fsp=fopen(char_fname_sp,"w");
if(fsp == NULL) {
printf("# ERROR: Could not open spXXX.dat");
abort();
}
double period = par[10];
//tm[j] in [0.0, 1.0]
double s_j; // in [0.0, T]
double h_j; // = s[j+1] - s[j]
for (j = 0; j < ntst; ++j) {
s_j = period*tm[j];
h_j = period*(tm[j+1] - tm[j]);
fprintf(fsp," %ld", j);
fprintf(fsp,"%19.10E", tm[j]);
fprintf(fsp,"%19.10E", s_j);
fprintf(fsp,"%19.10E", h_j);
for (i = 0; i < ndim; ++i) {
fprintf(fsp,"%19.10E", ups[j][i]);
}
fprintf(fsp,"\n");
}
s_j = period*tm[ntst]; // period*1.0
h_j = period - s_j; // 0.0
fprintf(fsp," %ld", ntst);
fprintf(fsp,"%19.10E", tm[ntst]);
fprintf(fsp,"%19.10E", s_j);
fprintf(fsp,"%19.10E", h_j);
for (i = 0; i < ndim; ++i) {
fprintf(fsp,"%19.10E", ups[ntst][i]);
}
fprintf(fsp,"\n");
//========================================================
// ここまで．この後は，元々の処理が続く
/* Write the entire solution on unit 8 : */
for (j = 0; j < ntst; ++j) {
rn = 1. / ncol;
for (i = 0; i < ncol; ++i) {
k1 = i * ndim;
k2 = (i + 1) * ndim;
t = tm[j] + i * rn * dtm[j];
fprintf(fp8," %19.10E",t);
...
なお，ups の中身は，以下のようになっている．
// example // dimension = 2 // 0<= j < ntst // (ncol-1) interpolated points //ups[j][0] // j_0 //ups[j][1] //ups[j][2] // j_1 //ups[j][3] //... //ups[j][(ncol-1)*dim] // j_{ncol-1} //ups[j][(ncol-1)*dim + 1] //ups[j+1][0] //ups[j+1][1] //... //ups[ntst][0] //ups[ntst][1]
AUTO の流れ：continuation は，extrbv stupbv stplbv (adapt) -> extrbv を反復しながら行っている．
main.c main
autlib1.c autoae -> cnrlae
//Generate the starting point
stpnt
pvlinewlab //Determine a suitable starting label and branch number
sthd //Write constants
stplae //Write plotting data for the starting point
stprae //Starting procedure (to get second point on first branch)
swpnt //Initialize computation of the next bifurcating branchstplae //Store plotting data for first point on the bifurcating branch
swprc //Determine the second point on the bifurcating branch
stplae //Store plotting data for second pointcontae //Provide initial approximation to the next point on the branch
solvae //Find the next solution point on the branchlcspae //Check for user supplied parameter output parameter-values
main
-> autobv （if(list.type==AUTOBV) list.type は，set_function_pointers 内で，iap の値で決定される．）
-> cnrlbv
-> rsptbv, setrtn, stdrbv, sthd, stplbv, extrbv
Ex1 : c=ab.1
AUTO > run(c="ab.1")
Starting ab ...
# call autoae
# call sthd
BR PT TY LAB PAR(1) L2-NORM U(1) U(2)
1 1 EP 1 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
1 33 LP 2 1.057390E-01 1.484391E+00 3.110230E-01 1.451441E+00
...
Ex2 : c="ab.2"
AUTO> run(c="ab.2",s="ab1")
Starting ab ...
# call autobv
# call cnrlbv
# call rsptbv
# call STPNT_TYPE_BVP(*stpnt) in rsptbv
# call stpnps
# call funi in stpnps
# call setrtn
# call sthd (output to fort.7)
# call stplbv (output to fort.8)
BR PT TY LAB PAR(1) L2-NORM MAX(1) MAX(2) PERIOD
# call extrbv
# call stplbv
# call extrbv
# call stupbv
# call stplbv
# call adapt
# call extrbv
# call stupbv
# call stplbv
# call extrbv
# call stupbv
# call stplbv
# call extrbv
# call stupbv
...
# call extrbv
# call stupbv
# call stplbv
4 30 6 1.198815E-01 3.987129E+00 9.919113E-01 7.020342E+00 2.721044E+00
# call adapt
# call extrbv
# call stupbv
stplbv -> wrtbv8 を呼んで， fort.8 に軌道座標を出力している．
軌道の座標は，rsptbv 内で計算して ups 内に保存している．
rsptbv
-> STPNT_TYPE_BVP( (*stpnt) ), adapt, stupbv
sthd では，fort.7 に出力．
continuation は，extrbv stupbv stplbv (adapt) -> extrbv を反復しながら行っている．
STPNT_TYPE_BVP in auto_c.h
/* This is the type for all functions that can be used at starting points
for BVPs */
#define STPNT_TYPE_BVP(X) int X(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, integer *ntsrs, integer *ncolrs, doublereal *rlcur, doublereal *rldot, integer *ndxloc, doublereal **ups, doublereal **udotps, doublereal **upoldp, doublereal *tm, doublereal *dtm, integer *nodir, doublereal *thl, doublereal *thu)
...
//autlib1.c
STPNT_TYPE_BVP(stpnbv);
STPNT_TYPE_BVP(stpnub);
...//autlib3.c
STPNT_TYPE_BVP(stpnps);
STPNT_TYPE_BVP(stpnpo);
STPNT_TYPE_BVP(stpnbl);
adapt
-> newmsh interp
c.ab.2 では， stpnps が呼ばれる．
stpnps
-> findlb, readlb, funi, scaleb
パラメータ変更毎に，istop==1 となれば L5 に飛んで stplae で，出力している．
istop は，
lcspae 終了後の iap->istop で更新される．
lcspae は，
Check for user supplied parameter output parameter-values
Check for fold
Check for branch point
Check for Hopf bifurcation
のために呼ばれる．
lcspae
Detection of Singular Points
// This subroutine uses the secant method to accurately locate special
// points (branch points, folds, Hopf bifurcations, user zeroes).
// These are characterized as zeroes of the function FNCS supplied in the call.// This subroutine calls CONT and SOLVAE with varying stepsize RDS.
// The special point is assumed to have been found with sufficient
// accuracy if the ratio between RDS and the user supplied value of
// DS is less than the user-supplied toler du.
...
lcspae は，FNCS_TYPE_AE( (* fncs) ) を引数にしており，内部で次を実行する．
q1 = (*fncs)(iap, rap, par, icp, &chng, funi, m1aaloc,
aa, rlcur, rlold, rldot, u, uold, udot,
rhs, dfdu, dfdp, iuz, vuz);
FNCS_TYPE_AE は，auto_c.h 内で次のように定義されている．
/*This is the type for all functions which can be used to detect
special points for algebraic problems */
#define FNCS_TYPE_AE(X) doublereal X(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, logical *chng, FUNI_TYPE( (*funi) ), integer *m1aaloc, doublereal **aa, doublereal *rlcur, doublereal *rlold, doublereal *rldot, doublereal *u, doublereal *uold, doublereal *udot, doublereal *rhs, doublereal *dfdu, doublereal *dfdp, integer *iuz, doublereal *vuz)...
// それぞれ，fp9 への出力を担う．
FNCS_TYPE_AE(fnbpae); // BP FunctionFNCS_TYPE_AE(fnlpae); // Fold Function
FNCS_TYPE_AE(fnhbae); // Hopf Function，Eigenvalues
FNCS_TYPE_AE(fnuzae); // User Func.
fnbpae in autlib1.c は次のようなもの．
doublereal
fnbpae(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, logical *chng, FUNI_TYPE( (*funi) ), integer *m1aaloc, doublereal **aa, doublereal *rlcur, doublereal *rlold, doublereal *rldot, doublereal *u, doublereal *uold, doublereal *udot, doublereal *rhs, doublereal *dfdu, doublereal *dfdp, integer *iuz, doublereal *vuz)
{
/* System generated locals */
doublereal ret_val;/* Local variables */
integer ntop, ntot, iid, ibr;
doublereal det;
iid = iap->iid;
ibr = iap->ibr;
ntot = iap->ntot;
ntop = (ntot + 1) % 10000;det = rap->det;
ret_val = det;
*chng = TRUE_;/* If requested write additional output on unit 9 : */
if (iid >= 2 && iap->mynode == 0) {
fprintf(fp9,"%4li%6li BP Function %14.5E\n",ibr,ntop,ret_val);
}return ret_val;
} /* fnbpae_ */
iap は，次のような型 iap_type の変数である．
typedef struct {
/* 1 */ integer ndim;
/* 2 */ integer ips;
/* 3 */ integer irs;
/* 4 */ integer ilp;
/* 5 */ integer ntst;
/* 6 */ integer ncol;
/* 7 */ integer iad;
/* 8 */ integer iads;
/* 9 */ integer isp;
/* 10 */ integer isw;
/* 11 */ integer iplt;
/* 12 */ integer nbc;
/* 13 */ integer nint;#ifdef MANIFOLD
/* 13a*/ integer nalc; /* The number of arclength constraints (k) */
#endif
/* 14 */ integer nmx;
/* 15 */ integer nuzr;
/* 16 */ integer npr;
/* 17 */ integer mxbf;
/* 18 */ integer iid;
/* 19 */ integer itmx;
/* 20 */ integer itnw;
/* 21 */ integer nwtn;
/* 22 */ integer jac;
/* 23 */ integer ndm;
/* 24 */ integer nbc0;
/* 25 */ integer nnt0;
/* 26 */ integer iuzr;
/* 27 */ integer itp;
/* 28 */ integer itpst;
/* 29 */ integer nfpr;
/* 30 */ integer ibr;
/* 31 */ integer nit;
/* 32 */ integer ntot;
/* 33 */ integer nins;
/* 34 */ integer istop;
/* 35 */ integer nbif;
/* 36 */ integer ipos;
/* 37 */ integer lab;
/* 41 */ integer nicp;
/* The following are not set in init_.They have to do with the old parallel version. */
/* 38 */ integer mynode;
/* 39 */ integer numnodes;
/* 40 */ integer parallel_flag;
} iap_type;
これは，main 文の中で init 関数を用いて初期かされるが，
init 自体は，autlib1.c 内で次のように定義されている．
init(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, doublereal *thl, doublereal **thu_pointer, integer **iuz_pointer, doublereal **vuz_pointer, logical *eof,integer nalc)
{
...
main 内 solvae で数値積分？ FUNI_TYPE( (*funi) ) を引数にしており，
内部で，実行している．
(*funi)(iap, rap, ndim, u, uold, icp, par, 2, f, dfdu, dfdp);
FUNI_TYPE の定義 in auto_c.h
/*This is the type for all functions which can be used as "funi" the function
which evaluates the right hand side of the equations and generatesthe Jacobian*/
#define FUNI_TYPE(X) int X(const iap_type *iap, const rap_type *rap, integer ndim, doublereal *u, const doublereal *uold, const integer *icp, doublereal *par, integer ijac, doublereal *f, doublereal *dfdu, doublereal *dfdp)...
typedef struct {
FUNI_TYPE( (*funi) );
STPNT_TYPE_AE( (*stpnt) );
PVLI_TYPE_AE( (*pvli) );
} autoae_function_list;typedef struct {
int type;
autobv_function_list bvlist;
autoae_function_list aelist;
} function_list;
.../* autlib3.c */
FUNI_TYPE(fnlp);
STPNT_TYPE_AE(stpnlp);
FUNI_TYPE(fnc1);
STPNT_TYPE_AE(stpnc1);
FUNI_TYPE(fnc2);
STPNT_TYPE_AE(stpnc2);
FUNI_TYPE(fnds);
FUNI_TYPE(fnti);
FUNI_TYPE(fnhd);
STPNT_TYPE_AE(stpnhd);
FUNI_TYPE(fnhb);
STPNT_TYPE_AE(stpnhb);
FUNI_TYPE(fnhw);
STPNT_TYPE_AE(stpnhw);
FUNI_TYPE(fnps);
BCNI_TYPE(bcps);
ICNI_TYPE(icps);int pdble(const iap_type *iap, const rap_type *rap, integer *ndim, integer *ntst, integer *ncol, integer *ndxloc, doublereal **ups, doublereal **udotps, doublereal *tm, doublereal *par);
STPNT_TYPE_BVP(stpnps);
FUNI_TYPE(fnws);
FUNI_TYPE(fnwp);
int stpnwp(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, integer *ntsr, integer *ncolrs, doublereal *rlcur, doublereal *rldot, integer *ndxloc, doublereal **ups, doublereal **udotps, doublereal **upoldp, doublereal *tm, doublereal *dtm, integer *nodir, doublereal *thl, doublereal *thu);
FUNI_TYPE(fnsp);
FUNI_TYPE(fnpe);
ICNI_TYPE(icpe);
FUNI_TYPE(fnpl);
BCNI_TYPE(bcpl);
ICNI_TYPE(icpl);
int stpnpl(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, integer *ntsr, integer *ncolrs, doublereal *rlcur, doublereal *rldot, integer *ndxloc, doublereal **ups, doublereal **udotps, doublereal **upoldp, doublereal *tm, doublereal *dtm, integer *nodir, doublereal *thl, doublereal *thu);
FUNI_TYPE(fnpd);
BCNI_TYPE(bcpd);
ICNI_TYPE(icpd);
int stpnpd(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, integer *ntsr, integer *ncolrs, doublereal *rlcur, doublereal *rldot, integer *ndxloc, doublereal **ups, doublereal **udotps, doublereal **upoldp, doublereal *tm, doublereal *dtm, integer *nodir, doublereal *thl, doublereal *thu);
FUNI_TYPE(fntr);int bctr(const iap_type *iap, const rap_type *rap, integer ndim, doublereal *par, const integer *icp, integer nbc, const doublereal *u0,const doublereal *u1, doublereal *f, integer ijac, doublereal *dbc);
ICNI_TYPE(ictr);int stpntr(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, integer *ntsr, integer *ncolrs, doublereal *rlcur, doublereal *rldot, integer *ndxloc, doublereal **ups, doublereal **udotps, doublereal **upoldp, doublereal *tm, doublereal *dtm, integer *nodir, doublereal *thl, doublereal *thu);
FUNI_TYPE(fnpo);
BCNI_TYPE(bcpo);
ICNI_TYPE(icpo);
STPNT_TYPE_BVP(stpnpo);
FUNI_TYPE(fnbl);
BCNI_TYPE(bcbl);
ICNI_TYPE(icbl);
STPNT_TYPE_BVP(stpnbl);
FUNI_TYPE(funi);
BCNI_TYPE(bcni);
ICNI_TYPE(icni);
...
で，funi は autlib3.c の 4363 行目から定義されている．
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* Routines for Interface with User Supplied Routines *//* (To generate Jacobian by differencing, if not supplied analytically) */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- *//* ---------- ---- */
/* Subroutine */ int
funi(const iap_type *iap, const rap_type *rap, integer ndim, doublereal *u, const doublereal *uold, const integer *icp, doublereal *par, integer ijac, doublereal *f, doublereal *dfdu, doublereal *dfdp)
{
...
user.func(ndim, u, icp, par, ijc, f, dfdu, dfdp);
...
user.func(ndim, u, icp, par, 0, f1zz, dfdu, dfdp);
...
この中で，ユーザー定義の func が実行されている．
user は， user_function_list 型の変数で，
auto_f2c.h 内で，次のように定義されている．
const user_function_list user = { func, stpnt, bcnd, icnd, fopt, pvls, 0 };
この，func, stpnt, bcnd, icnd, fopt, pvls がユーザー定義の関数与える．
function_list は，main.c 内 main 関数の中で次のように初期化されている．
...
function_list list
...
set_function_pointers(iap,&list);
set_function_pointers は次のようになっている．（autlib1.c）
int set_function_pointers(const iap_type iap,function_list *data) {
if ( (iap.ips == 0 || iap.ips == 1) && abs(iap.isw) != 2) {
/* ** Algebraic systems. */if (iap.irs == 0) {
data->type = AUTOAE;
data->aelist.funi = funi;
data->aelist.stpnt = stpnus;
data->aelist.pvli = pvlsae;
} else {
data->type = AUTOAE;
data->aelist.funi = funi;
data->aelist.stpnt = stpnae;
data->aelist.pvli = pvlsae;
}
} else if (iap.ips == 11 && abs(iap.isw) != 2) {
/* ** Waves : Spatially homogeneous solutions, */if (iap.irs == 0) {
data->type = AUTOAE;
...
imagemagick のインストール
http://www.ishihara.ne.jp/blog/archives/2006/10/index.html より転載
$ fink install libjpeg
$ fink install libpng3
1. ImageMagickのソースコード一式を以下のサイトより取得（今回は ImageMagick-6.3.0）
http://www.imagemagick.org/script/download.php
2. tarballを解凍、展開したら、以下の手順でconfigureする
$ export CPPFLAGS="-I/sw/include"
$ export LDFLAGS="-L/sw/lib"
$ ./configure --enable-lzw=yes
3. コンパイルとインストール
configureの最後でJPEG v1 --with-jpeg=yes yesと出力されているのを確認して、コンパイルとインストールを実施
$ make
$ sudo make install
Mac 用 gnuplot でタブ補完を可能にする．
Fink 使用の場合
/sw/fink/10.4/stable/main/finkinfo/sci/gnuplot.info のコンパイルパラメーター(ConfigureParams: 以下)に
--with-readline=gnu --enable-history-file
をつけてインストール。
成功！
ばっちりreadlineが使える。
すでにインストールしてあるときは、先のオプションを追加して
とすればいい。
$ fink rebuild gnuplot
$ fink install gnuplot
MacPorts 使用の場合．
最初から可能？
以下，できなければこうやればいいんじゃないかというメモ．
として，
$ sudo port edit gnuplot
のように，configure.args のところに
...
configure.args --with-readline=gnu --enable-history-file \
--with-gd --with-png --with-pdf --with-x \
--enable-datastrings --enable-histograms \
--infodir='\${prefix}/share/info' \
--mandir='\${prefix}/share/man' \
--disable-wxwidgets
...
--with-readline=gnu --enable-history-file
を加えた後，install する．
port edit gnuplot を実行した時に，
というエラーがでた場合は，
Error: No EDITOR is specified in your environment
等としてからやり直し．
$export EDITOR="emacs"
