OpenXM/src/hgm/mh/src/jack-n.c - diff

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Diff for /OpenXM/src/hgm/mh/src/jack-n.c between version 1.3 and 1.31

version 1.3, 2013/02/21 07:30:56

version 1.31, 2015/04/02 00:11:32

Line 5

#include <string.h>

#include "sfile.h"

$OpenXM: OpenXM/src/hgm/mh/src/jack-n.c,v 1.2 2013/02/20 07:53:44 takayama Exp $

$OpenXM: OpenXM/src/hgm/mh/src/jack-n.c,v 1.30 2015/03/24 07:49:06 takayama Exp $

Ref: copied from this11/misc-2011/A1/wishart/Prog

jack-n.c, translated from mh.rr or tk_jack.rr in the asir-contrib. License: LGPL

Koev-Edelman for higher order derivatives.

cf. 20-my-note-mh-jack-n.pdf, /Movies/oxvh/priv-j1/2011-12-14-ke-mh-jack.mov

Todo:

1. Cash the transposes of partitions.

2. Use the recurrence to obtain beta().

3. Easier input data file format for mh-n.c

Changelog:

2012.02.21, porting to OpenXM/src/hgm

2014.03.15 http://fe.math.kobe-u.ac.jp/Movies/oxvh/2014-03-11-jack-n-c-automatic see also hgm/doc/ref.html, @s/2014/03/15-my-note-jack-automatic-order-F_A-casta.pdf.

2011.12.22, --table option, which is experimental.

2014.03.14, --automatic option. Output estimation data.

2011.12.19, bug fix. jjk() should return double. It can become more than max int.

2012.02.21, porting to OpenXM/src/hgm

2011.12.15, mh.r --> jack-n.c

2011.12.22, --table option, which is experimental.

2011.12.19, bug fix. jjk() should return double. It can become more than max int.

2011.12.15, mh.r --> jack-n.c

/****** from mh-n.c *****/

static int JK_byFile=1;

static int JK_deallocate=0;

#define M_n_default 3

#define Sample_default 1

static int M_n=0;

/* global variables. They are set in setParam() */

static int Mg; /* n */

Line 36 static double Ef; /* exponential factor at beta*x0 *

Line 40 static double Ef; /* exponential factor at beta*x0 *

static double Hg; /* step size of rk defined in rk.c */

static int Dp; /* Data sampling period */

static double Xng=0.0; /* the last point */

static int Sample = 1;

static int Sample = Sample_default;

/* for sample inputs */

static double *Iv2;

Line 54 static double Ef2;

Line 58 static double Ef2;

#define A_LEN 1 /* (a_1) , (a_1, ..., a_p)*/

#define B_LEN 1 /* (b_1) */

static int Debug = 0;

static int Alpha = 2;;

static int Alpha = 2; /* 2 implies the zonal polynomial */

static int *Darray = NULL;

static int **Parray = NULL; /* array of partitions of size M_n */

static int *ParraySize = NULL; /* length of each partitions */

Line 91 static double Xarray[M_nmx][M_m_MAX];

Line 95 static double Xarray[M_nmx][M_m_MAX];

static double *M_qk=NULL; /* saves pochhammerb */

static double M_rel_error=0.0; /* relative errors */

/* For automatic degree and X0g setting. */

If automatic == 1, then the series is reevaluated as long as t_success!=1

by increasing X0g (evaluation point) and M_m (approx degree);

static int M_automatic=1;

/* Estimated degree bound for series expansion. See mh_t */

static int M_m_estimated_approx_deg=0;

/* Let F(i) be the approximation up to degree i.

The i-th series_error is defined

by |(F(i)-F(i-1))/F(i-1)|.

static double M_series_error;

M_series_error < M_assigend_series_error (A) is required for the

estimated_approx_deg.

static double M_assigned_series_error=M_ASSIGNED_SERIES_ERROR_DEFAULT;

Let Ef be the exponential factor ( Ef=(4)/1F1 of [HNTT] )

If F(M_m)*Ef < x0value_min (B), the success=0 and X0g is increased.

Note that minimal double is about 2e-308

static double M_x0value_min=1e-60;

estimated_X0g is the suggested value of X0g.

static double M_estimated_X0g=0.0;

X0g should be less than M_X0g_bound.

static double M_X0g_bound = 1e+100;

success is set to 1 when (A) and (B) are satisfied.

static int M_mh_t_success=1;

recommended_abserr is the recommended value of the absolute error

for the Runge-Kutta method. It is defined as

assigend_series_error(standing for significant digits)*Ig[0](initial value)

static double M_recommended_abserr;

recommended_relerr is the recommended value of the relative error

for the Runge-Kutta method..

static double M_recommended_relerr;

max of beta(i)*x/2

static double M_beta_i_x_o2_max;

minimum of |beta_i-beta_j|

static double M_beta_i_beta_j_min;

Value of matrix hg

static double M_mh_t_value;

Show the process of updating degree.

int M_show_autosteps=1;

/* prototypes */

static void *mymalloc(int size);

static myfree(void *p);

static int myfree(void *p);

static myerror(char *s);

static int myerror(char *s);

static double jack1(int K);

static double jack1diff(int k);

static double xval(int i,int p); /* x_i^p */

Line 102 static int mysum(int L[]);

Line 170 static int mysum(int L[]);

static int plength(int P[]);

static int plength_t(int P[]);

static void ptrans(int P[M_nmx],int Pt[]);

static test_ptrans();

static int test_ptrans();

static int huk(int K[],int I,int J);

static int hdk(int K[],int I,int J);

static double jjk(int K[]);

Line 112 static double mypower(double x,int n);

Line 180 static double mypower(double x,int n);

static double qk(int K[],double A[A_LEN],double B[B_LEN]);

static int bb(int N[],int K[],int M[],int I,int J);

static double beta(int K[],int M[]);

static printp(int kappa[]);

static int printp(int kappa[]);

static printp2(int kappa[]);

static int printp2(int kappa[]);

static test_beta();

static int test_beta();

static double q3_10(int K[],int M[],int SK);

static double q3_5(double A[],double B[],int K[],int I);

static void mtest4();

Line 130 static int pListHS2(int From,int To,int Kap[]);

Line 198 static int pListHS2(int From,int To,int Kap[]);

static void hsExec_0();

static int pmn(int M,int N);

static int *cloneP(int a[]);

static copyP(int p[],int a[]);

static int copyP(int p[],int a[]);

static void pExec_darray(void);

static genDarray2(int M,int N);

static int genDarray2(int M,int N);

static isHStrip(int Kap[],int Nu[]);

static int isHStrip(int Kap[],int Nu[]);

static void hsExec_beta(void);

static genBeta(int Kap[]);

static int genBeta(int Kap[]);

static checkBeta1();

static int checkBeta1();

static int psublen(int Kap[],int Mu[]);

static genJack(int M,int N);

static int genJack(int M,int N);

static checkJack1(int M,int N);

static int checkJack1(int M,int N);

static checkJack2(int M,int N);

static int checkJack2(int M,int N);

static mtest1b();

static int mtest1b();

static int imypower(int x,int n);

static usage();

static int usage();

static setParamDefault();

static int setParamDefault();

static next(struct SFILE *fp,char *s,char *msg);

static int next(struct SFILE *fp,char *s,char *msg);

static int gopen_file(void);

static int setParam(char *fname);

static int showParam(struct SFILE *fp);

static int showParam(struct SFILE *fp,int fd);

static double iv_factor(void);

static double gammam(double a,int n);

static double mypower(double a,int n);

Line 157 static double mypower(double a,int n);

Line 225 static double mypower(double a,int n);

double mh_t(double A[A_LEN],double B[B_LEN],int N,int M);

double mh_t2(int J);

struct MH_RESULT *jk_main(int argc,char *argv[]);

struct MH_RESULT *jk_main2(int argc,char *argv[],int automode,double newX0g,int newDegree);

int jk_freeWorkArea();

int jk_initializeWorkArea();

int jk_freeWorkArea() {

/* bug, p in the cloneP will not be deallocated.

Nk in genDarray2 will not be deallocated.

int i;

JK_deallocate=1;

if (Darray) {myfree(Darray); Darray=NULL;}

if (Parray) {myfree(Parray); Parray=NULL;}

if (ParraySize) {myfree(ParraySize); ParraySize=NULL;}

if (M_beta_0) {myfree(M_beta_0); M_beta_0=NULL;}

if (M_beta_1) {myfree(M_beta_1); M_beta_1=NULL;}

if (M_jack) {

for (i=0; M_jack[i] != NULL; i++) {

myfree(M_jack[i]); M_jack[i] = NULL;

if (Debug) oxprintf("Free M_jack[%d]\n",i);

}

myfree(M_jack[i]); M_jack[i] = NULL;

myfree(M_jack); M_jack=NULL;

}

myfree(M_jack); M_jack=NULL;

}

if (M_qk) {myfree(M_qk); M_qk=NULL;}

if (P_pki) {myfree(P_pki); P_pki=NULL;}

JK_deallocate=0;

return(0);

}

int jk_initializeWorkArea() {

int i,j;

JK_deallocate=1;

xval(0,0);

JK_deallocate=0;

Darray=NULL;

Parray=NULL;

ParraySize=NULL;

Line 191 int jk_initializeWorkArea() {

Line 267 int jk_initializeWorkArea() {

for (i=0; i<M_nmx; i++) M_kap[i]=HS_mu[i]=0;

for (i=0; i<M_nmx; i++) M_x[i]=0;

for (i=0; i<M_nmx; i++) for (j=0; j<M_m_MAX; j++) Xarray[i][j]=0;

for (i=0; i<M_nmx; i++) M_beta_kap[i]=0;

M_m=M_m_MAX-2;

Alpha = 2;

HS_n=M_nmx;

Line 201 int jk_initializeWorkArea() {

Line 278 int jk_initializeWorkArea() {

M_df=1;

M_2n=0;

M_rel_error=0.0;

Sample = Sample_default;

Xng=0.0;

M_n=0;

return(0);

}

static void *mymalloc(int size) {

void *p;

if (Debug) printf("mymalloc(%d)\n",size);

if (Debug) oxprintf("mymalloc(%d)\n",size);

p = (void *)malloc(size);

p = (void *)mh_malloc(size);

if (p == NULL) {

fprintf(stderr,"No more memory.\n");

oxprintfe("No more memory.\n");

mh_exit(-1);

}

return(p);

}

static myfree(void *p) { free(p); }

static int myfree(void *p) {

static myerror(char *s) { fprintf(stderr,"%s: type in control-C\n",s); getchar(); getchar();}

if (Debug) oxprintf("myFree at %p\n",p);

return(mh_free(p));

}

static int myerror(char *s) { oxprintfe("%s: type in control-C\n",s); getchar(); getchar(); return(0);}

static double jack1(int K) {

double F;

Line 247 static double xval(int ii,int p) { /* x_i^p */

Line 331 static double xval(int ii,int p) { /* x_i^p */

extern double M_x[];

double F;

int i,j;

static init=0;

static int init=0;

if (JK_deallocate) { init=0; return(0.0);}

if (!init) {

for (i=1; i<=M_n; i++) {

for (j=0; j<M_m_MAX; j++) {

if (j != 0) {

Xarray[i-1][j] = M_x[i-1]*Xarray[i-1][j-1];

}else{

Xarray[i-1][0] = 1;

}

init = 1;

Line 264 static double xval(int ii,int p) { /* x_i^p */

Line 349 static double xval(int ii,int p) { /* x_i^p */

if (p > M_m_MAX-2) myerror("xval, p is too large.");

if (p < 0) {

myerror("xval, p is negative.");

printf("ii=%d, p=%d\n",ii,p);

oxprintf("ii=%d, p=%d\n",ii,p);

mh_exit(-1);

}

return(Xarray[ii-1][p]);

Line 279 static int mysum(int L[]) {

Line 364 static int mysum(int L[]) {

}

(3,2,2,0,0) --> 3

static int plength(int P[]) {

int I;

Line 298 static int plength_t(int P[]) {

Line 383 static int plength_t(int P[]) {

}

ptrans(P) returns Pt

static void ptrans(int P[M_nmx],int Pt[]) { /* Pt[M_m] */

extern int M_m;

Line 313 static void ptrans(int P[M_nmx],int Pt[]) { /* Pt[M_m]

Line 398 static void ptrans(int P[M_nmx],int Pt[]) { /* Pt[M_m]

}

static test_ptrans() {

static int test_ptrans() {

extern int M_m;

int p[M_n0]={5,3,2};

int pt[10];

int i;

M_m = 10;

ptrans(p,pt);

if (Debug) {for (i=0; i<10; i++) printf("%d,",pt[i]); printf("\n");}

if (Debug) {for (i=0; i<10; i++) oxprintf("%d,",pt[i]); oxprintf("\n");}

return(0);

}

Line 333 static int huk(int K[],int I,int J) {

Line 419 static int huk(int K[],int I,int J) {

int Kp[M_m_MAX];

int A,H;

A=Alpha;

/*printf("h^k(%a,%a,%a,%a)\n",K,I,J,A);*/

/*oxprintf("h^k(%a,%a,%a,%a)\n",K,I,J,A);*/

ptrans(K,Kp);

H=Kp[J-1]-I+A*(K[I-1]-J+1);

return(H);

Line 348 static int hdk(int K[],int I,int J) {

Line 434 static int hdk(int K[],int I,int J) {

int Kp[M_m_MAX];

int A,H;

A = Alpha;

/*printf("h_k(%a,%a,%a,%a)\n",K,I,J,A);*/

/*oxprintf("h_k(%a,%a,%a,%a)\n",K,I,J,A);*/

ptrans(K,Kp);

H=Kp[J-1]-I+1+A*(K[I-1]-J);

return(H);

Line 368 static double jjk(int K[]) {

Line 454 static double jjk(int K[]) {

V *= huk(K,I+1,J+1)*hdk(K,I+1,J+1);

}

if (Debug) {printp(K); printf("<--K, jjk=%lg\n",V);}

if (Debug) {printp(K); oxprintf("<--K, jjk=%lg\n",V);}

return(V);

}

Line 413 static double mypower(double x,int n) {

Line 499 static double mypower(double x,int n) {

return(v);

}

/* Q_kappa

static double qk(int K[],double A[A_LEN],double B[B_LEN]) {

extern int Alpha;

int P,Q,I;

Line 433 static double qk(int K[],double A[A_LEN],double B[B_LE

Line 519 static double qk(int K[],double A[A_LEN],double B[B_LE

}

B^nu_{kappa,mu}(i,j)

bb(N,K,M,I,J)

static int bb(int N[],int K[],int M[],int I,int J) {

int Kp[M_m_MAX]; int Mp[M_m_MAX];

Line 442 static int bb(int N[],int K[],int M[],int I,int J) {

Line 528 static int bb(int N[],int K[],int M[],int I,int J) {

ptrans(M,Mp);

printp(K); printf("K<--, "); printp2(Kp); printf("<--Kp\n");

printp(K); oxprintf("K<--, "); printp2(Kp); oxprintf("<--Kp\n");

printp(M); printf("M<--, "); printp2(Mp); printf("<--Mp\n");

printp(M); oxprintf("M<--, "); printp2(Mp); oxprintf("<--Mp\n");

if ((plength_t(Kp) < J) || (plength_t(Mp) < J)) return(hdk(N,I,J));

Line 464 static double beta(int K[],int M[]) {

Line 550 static double beta(int K[],int M[]) {

for (J=0; J<K[I]; J++) {

II = I+1; JJ = J+1;

V *= (double)bb(K,K,M,II,JJ);

/* printf("[%d,%d,%lf]\n",I,J,V); */

/* oxprintf("[%d,%d,%lf]\n",I,J,V); */

}

Line 473 static double beta(int K[],int M[]) {

Line 559 static double beta(int K[],int M[]) {

for (J=0; J<M[I]; J++) {

II = I+1; JJ = J+1;

V /= (double)bb(M,K,M,II,JJ);

/* printf("[%d,%d,%lf]\n",I,J,V);*/

/* oxprintf("[%d,%d,%lf]\n",I,J,V);*/

}

return(V);

}

static printp(int kappa[]) {

static int printp(int kappa[]) {

int i;

printf("(");

oxprintf("(");

for (i=0; i<M_n; i++) {

if (i <M_n-1) printf("%d,",kappa[i]);

if (i <M_n-1) oxprintf("%d,",kappa[i]);

else printf("%d)",kappa[i]);

else oxprintf("%d)",kappa[i]);

}

return(0);

}

static printp2(int kappa[]) {

static int printp2(int kappa[]) {

int i,ell;

printf("(");

oxprintf("(");

ell = plength_t(kappa);

for (i=0; i<ell+1; i++) {

if (i <ell+1-1) printf("%d,",kappa[i]);

if (i <ell+1-1) oxprintf("%d,",kappa[i]);

else printf("%d)",kappa[i]);

else oxprintf("%d)",kappa[i]);

}

return(0);

}

static test_beta() {

static int test_beta() {

int kappa[M_n0]={2,1,0};

int mu1[M_n0]={1,0,0};

int mu2[M_n0]={1,1,0};

int mu3[M_n0]={2,0,0};

printp(kappa); printf(","); printp(mu3); printf(": beta = %lf\n",beta(kappa,mu3));

printp(kappa); oxprintf(","); printp(mu3); oxprintf(": beta = %lf\n",beta(kappa,mu3));

printp(kappa); printf(","); printp(mu1); printf(": beta = %lf\n",beta(kappa,mu1));

printp(kappa); oxprintf(","); printp(mu1); oxprintf(": beta = %lf\n",beta(kappa,mu1));

printp(kappa); printf(","); printp(mu2); printf(": beta = %lf\n",beta(kappa,mu2));

printp(kappa); oxprintf(","); printp(mu2); oxprintf(": beta = %lf\n",beta(kappa,mu2)); return(0);

}

/* main() { test_beta(); } */

cf. w1m.rr

matrix hypergeometric by jack

N variables, up to degree M.

/* todo

def mhgj(A,B,N,M) {

F = 0;

P = partition_a(N,M);

for (I=0; I<length(P); I++) {

K = P[I];

F += qk(K,A,B)*jack(K,N);

}

return(F);

}

Line 571 static double q3_5(double A[],double B[],int K[],int I

Line 659 static double q3_5(double A[],double B[],int K[],int I

V=1;

for (J=1; J<=P; J++) {

V *= (A[J-1]+C);

}

for (J=1; J<=Q; J++) {

V /= (B[J-1]+C);

}

for (J=1; J<=K[I-1]-1; J++) {

Ej = D-J*Alpha+Kp[J-1];

Gj = Ej+1;

V *= (Gj-Alpha)*Ej/(Gj*(Ej+Alpha));

}

for (J=1; J<=I-1; J++) {

Fj=K[J-1]*Alpha-J-D;

Hj=Fj+Alpha;

Lj=Hj*Fj;

V *= (Lj-Fj)/(Lj+Hj);

}

return(V);

}

Line 600 static void mtest4() {

Line 688 static void mtest4() {

double V1,V2;

V1=q3_5(A,B,K,I);

V2=qk(K,A,B)/qk(Ki,A,B);

printf("%lf== %lf?\n",V1,V2);

oxprintf("%lf== %lf?\n",V1,V2);

}

static void mtest4b() {

int K[M_n0]={3,2,0};

Line 610 static void mtest4b() {

Line 698 static void mtest4b() {

double V1,V2;

V1=q3_10(K,M,SK);

V2=beta(K,N)/beta(K,M);

printf("%lf== %lf?\n",V1,V2);

oxprintf("%lf== %lf?\n",V1,V2);

}

/* main() { mtest4(); mtest4b(); } */

/* nk in (4.1),

static int nk(int KK[]) {

extern int *Darray;

int N,I,Ki;

Line 670 static int pListPartition(int M,int N) {

Line 758 static int pListPartition(int M,int N) {

int I;

/* initialize */

if (M_n != N) {

fprintf(stderr,"M_n != N\n"); mh_exit(-1);

oxprintfe("M_n != N\n"); mh_exit(-1);

}

M_m = M;

/* M_plist = []; */

Line 689 static int pListPartition(int M,int N) {

Line 777 static int pListPartition(int M,int N) {

static int pListPartition2(int Less,int From,int To, int M) {

int I,R;

mh_check_intr(100);

if (To < From) {

(*M_pExec)(); return(0);

}

for (I=1; (I<=Less) && (I<=M) ; I++) {

M_kap[From-1] = I;

Line 704 static int pListPartition2(int Less,int From,int To, i

Line 793 static int pListPartition2(int Less,int From,int To, i

static void pExec_0() {

if (Debug) {

printf("M_kap=");

oxprintf("M_kap=");

printp(M_kap);

printf("\n");

oxprintf("\n");

}

/* Test.

Compare pListPartition(4,3); genDarray(4,3);

Compare pListPartition(5,3); genDarray(5,3);

main() {

M_pExec = pExec_0;

pListPartition(5,3);

}

Line 735 static int pListHS(int Kap[],int N) {

Line 824 static int pListHS(int Kap[],int N) {

HS_n = N;

/* Clear HS_mu. Do not forget when N < M_n */

for (i=0; i<M_n; i++) HS_mu[i] = 0;

pListHS2(1,N,Kap);

return(pListHS2(1,N,Kap));

}

static int pListHS2(int From,int To,int Kap[]) {

Line 751 static int pListHS2(int From,int To,int Kap[]) {

Line 840 static int pListHS2(int From,int To,int Kap[]) {

static void hsExec_0() {

int i;

if(Debug) {printf("hsExec: "); printp(HS_mu); printf("\n");}

if(Debug) {oxprintf("hsExec: "); printp(HS_mu); oxprintf("\n");}

}

pListHS([0,4,2,1],3);

main() {

int Kap[3]={4,2,1};

HS_hsExec = hsExec_0;

pListHS(Kap,3);

}

/* The number of partitions <= M, with N parts.

(0,0,...,0) is excluded.

#define aP_pki(i,j) P_pki[(i)*(M+1)+(j)]

static int pmn(int M,int N) {

Line 789 static int pmn(int M,int N) {

Line 878 static int pmn(int M,int N) {

}

P_pmn=S;

if (Debug) {

printf("P_pmn=%d\n",P_pmn);

oxprintf("P_pmn=%d\n",P_pmn);

for (i=0; i<=Min_m_n; i++) {

for (j=0; j<=M; j++) printf("%d,",aP_pki(i,j));

for (j=0; j<=M; j++) oxprintf("%d,",aP_pki(i,j));

printf("\n");

oxprintf("\n");

}

myfree(P_pki); P_pki=NULL;

Line 800 static int pmn(int M,int N) {

Line 889 static int pmn(int M,int N) {

}

main() {pmn(4,3); printf("P_pmn=%d\n",P_pmn);}

main() {pmn(4,3); oxprintf("P_pmn=%d\n",P_pmn);}

static int *cloneP(int a[]) {

Line 810 static int *cloneP(int a[]) {

Line 899 static int *cloneP(int a[]) {

for (i=0; i<M_n; i++) p[i] = a[i];

return(p);

}

static copyP(int p[],int a[]) {

static int copyP(int p[],int a[]) {

int i;

for (i=0; i<M_n; i++) p[i] = a[i];

return(0);

}

static void pExec_darray(void) {

Line 827 static void pExec_darray(void) {

Line 917 static void pExec_darray(void) {

ParraySize[DR_parray] = mysum(K);

DR_parray++;

}

static genDarray2(int M,int N) {

static int genDarray2(int M,int N) {

extern int *Darray;

extern int **Parray;

extern int DR_parray;

Line 840 static genDarray2(int M,int N) {

Line 930 static genDarray2(int M,int N) {

M_m = M;

Pmn = pmn(M,N)+1;

if (Debug) printf("Degree M = %d, N of vars N = %d, Pmn+1=%d\n",M,N,Pmn);

if (Debug) oxprintf("Degree M = %d, N of vars N = %d, Pmn+1=%d\n",M,N,Pmn);

Darray=(int *) mymalloc(sizeof(int)*Pmn);

for (i=0; i<Pmn; i++) Darray[i] = 0;

Parray=(int **) mymalloc(sizeof(int *)*Pmn);

Line 855 static genDarray2(int M,int N) {

Line 945 static genDarray2(int M,int N) {

Nk = (int *) mymalloc(sizeof(int)*(Pmn+1));

for (I=0; I<Pmn; I++) Nk[I] = I;

for (I=0; I<Pmn; I++) {

K = L[I]; /* N_K = I; D[N_K] = N_(K,1) */

mh_check_intr(100);

Ksize = plength(K);

K = L[I]; /* N_K = I; D[N_K] = N_(K,1) */

if (Ksize >= M_n) {

Ksize = plength(K);

if (Debug) {fprintf(stderr,"Ksize >= M_n\n");}

if (Ksize >= M_n) {

continue;

if (Debug) {oxprintfe("Ksize >= M_n\n");}

}

continue;

for (i=0; i<M_n; i++) Kone[i] = 0;

}

for(J=0; J<Ksize; J++) Kone[J]=K[J]; Kone[Ksize] = 1;

for (i=0; i<M_n; i++) Kone[i] = 0;

for (J=0; J<Pmn; J++) {

for(J=0; J<Ksize; J++) Kone[J]=K[J]; Kone[Ksize] = 1;

if (myeq(L[J],Kone)) Darray[I] = J; /* J is the next of I */

for (J=0; J<Pmn; J++) {

}

if (myeq(L[J],Kone)) Darray[I] = J; /* J is the next of I */

}

if (Debug) {

printf("Darray=\n");

oxprintf("Darray=\n");

for (i=0; i<Pmn; i++) printf("%d\n",Darray[i]);

for (i=0; i<Pmn; i++) oxprintf("%d\n",Darray[i]);

printf("-----------\n");

oxprintf("-----------\n");

}

return(0);

}

/* main() { genDarray2(4,3);} */

/* M_beta_0[*] value of beta_{kappa,mu}, M_beta_1[*] N_mu */

static isHStrip(int Kap[],int Nu[]) {

static int isHStrip(int Kap[],int Nu[]) {

int N1,N2,I,P;

N1 = plength(Kap); N2 = plength(Nu);

if (N2 > N1) return(0);

Line 898 static void hsExec_beta(void) {

Line 990 static void hsExec_beta(void) {

int Nu[M_nmx];

int rrMax;

hsExec_0();

/* printf("M_beta_pt=%a\n",M_beta_pt); */

/* oxprintf("M_beta_pt=%a\n",M_beta_pt); */

/* Mu = cdr(vtol(HS_mu)); */

Mu = HS_mu; /* buggy? need cloneP */

if (M_beta_pt == 0) {

Line 920 static void hsExec_beta(void) {

Line 1012 static void hsExec_beta(void) {

Done=0;

for (J=M_beta_pt-1; J>=0; J--) {

if (M_beta_1[J] == Nnu) {

K=I+1;

if (Debug) {

printf("Found at J=%d, K=%d, q3_10(Kap,Nu,K)=%lf,Nu,Mu= \n",

oxprintf("Found at J=%d, K=%d, q3_10(Kap,Nu,K)=%lf,Nu,Mu= \n",

J,K,q3_10(M_beta_kap,Nu,K));

printp(Nu); printf("\n");

printp(Nu); oxprintf("\n");

printp(Mu); printf("\n");

printp(Mu); oxprintf("\n");

}

/* Check other conditions. See Numata's mail on Dec 24, 2011. */

rrMax = Nu[I]-1;

if ((plength_t(Kapt) < rrMax) || (plength_t(Nut) < rrMax)) {

if (Debug) printf(" is not taken (length). \n");

if (Debug) oxprintf(" is not taken (length). \n");

break;

}

OK=1;

for (RR=0; RR<rrMax; RR++) {

if (Kapt[RR] != Nut[RR]) { OK=0; break;}

}

if (!OK) { if (Debug) printf(" is not taken.\n"); break; }

if (!OK) { if (Debug) oxprintf(" is not taken.\n"); break; }

/* check done. */

M_beta_0[M_beta_pt]=M_beta_0[J]*q3_10(M_beta_kap,Nu,K);

Done = 1; break;

}

if (Done) break; else Nu[I]--;

}

if (!Done) {

if (Debug) printf("BUG: not found M_beta_pt=%d.\n",M_beta_pt);

if (Debug) oxprintf("BUG: not found M_beta_pt=%d.\n",M_beta_pt);

/* M_beta_0[M_beta_pt] = NAN; /* error("Not found."); */

/* M_beta_0[M_beta_pt] = NAN; error("Not found."); */

M_beta_0[M_beta_pt] = beta(M_beta_kap,Mu);

}

/* Fix the bug of mh.rr */

M_beta_pt++;

}

static genBeta(int Kap[]) {

static int genBeta(int Kap[]) {

extern double *M_beta_0;

extern int *M_beta_1;

extern int M_beta_pt;

extern int M_beta_kap[];

extern int P_pmn;

int I,J,N;

if (Debug) {printp(Kap); printf("<-Kappa, P_pmn=%d\n",P_pmn);}

if (Debug) {printp(Kap); oxprintf("<-Kappa, P_pmn=%d\n",P_pmn);}

/* M_beta = newmat(2,P_pmn+1); */

M_beta_0 = (double *)mymalloc(sizeof(double)*(P_pmn+1));

M_beta_1 = (int *)mymalloc(sizeof(double)*(P_pmn+1));

M_beta_1 = (int *)mymalloc(sizeof(int)*(P_pmn+1));

M_beta_pt = 0;

for (I=0; I<=P_pmn; I++) {M_beta_0[I] = NAN; M_beta_1[I] = -1;}

N = plength(Kap);

HS_hsExec = hsExec_beta;

copyP(M_beta_kap,Kap);

pListHS(Kap,N);

pListHS(Kap,N); return(0);

}

genDarray2(4,3);

Line 977 static genBeta(int Kap[]) {

Line 1069 static genBeta(int Kap[]) {

genBeta([2,1,1]);

static checkBeta1() {

static int checkBeta1() {

int Kap[3] = {2,2,0};

int Kap2[3] = {2,1,0};

int I;

Line 988 static checkBeta1() {

Line 1080 static checkBeta1() {

for (I=0; I<M_beta_pt; I++) {

Mu = Parray[M_beta_1[I]];

Beta_km = M_beta_0[I];

if (Debug) {

printp(Kap); printf("<--Kap, ");

printp(Kap); oxprintf("<--Kap, ");

printp(Mu); printf("<--Mu,");

printp(Mu); oxprintf("<--Mu,");

printf("Beta_km(by table)=%lf, beta(Kap,Mu)=%lf\n",Beta_km,beta(Kap,Mu));

oxprintf("Beta_km(by table)=%lf, beta(Kap,Mu)=%lf\n",Beta_km,beta(Kap,Mu));

}

if (Debug) printf("-------------------------------------\n");

if (Debug) oxprintf("-------------------------------------\n");

genBeta(Kap2);

for (I=0; I<M_beta_pt; I++) {

Mu = Parray[M_beta_1[I]];

Beta_km = M_beta_0[I];

if (Debug) {

printp(Kap2); printf("<--Kap, ");

printp(Kap2); oxprintf("<--Kap, ");

printp(Mu); printf("<--Mu,");

printp(Mu); oxprintf("<--Mu,");

printf("Beta_km(by table)=%lf, beta(Kap,Mu)=%lf\n",Beta_km,beta(Kap2,Mu));

oxprintf("Beta_km(by table)=%lf, beta(Kap,Mu)=%lf\n",Beta_km,beta(Kap2,Mu));

}

return(0);

}

def checkBeta2() {

genDarray2(3,3);

Kap = [2,1,0];

printf("Kap=%a\n",Kap);

oxprintf("Kap=%a\n",Kap);

genBeta(Kap);

for (I=0; I<M_beta_pt; I++) {

Mu = Parray[M_beta[1][I]];

Beta_km = M_beta[0][I];

printf("Mu=%a,",Mu);

oxprintf("Mu=%a,",Mu);

printf("Beta_km(by table)=%a, beta(Kap,Mu)=%a\n",Beta_km,beta(Kap,Mu));

oxprintf("Beta_km(by table)=%a, beta(Kap,Mu)=%a\n",Beta_km,beta(Kap,Mu));

}

/* main() { checkBeta1(); } */

Line 1040 static int psublen(int Kap[],int Mu[]) {

Line 1133 static int psublen(int Kap[],int Mu[]) {

/* Table of Jack polynomials

Jack[1]* one variable.

Jack[2]* two variables.

...

Jack[M_n]* n variables.

Jack[P][J]*

D^J(P variables jack of p variables). Example. J=001 d_1, 010 d_2, 100 d_3

0<=J<=2^{M_n}-1

Jack[P][J][nk(Kappa)] Jack_Kappa, Kappa is a partition.

0<=nk(Kappa)<=pmn(M_m,M_n)

#define aM_jack(i,j,k) ((M_jack[i])[(j)*(Pmn+1)+(k)])

static genJack(int M,int N) {

static int genJack(int M,int N) {

extern double **M_jack;

extern int M_2n;

extern int P_pmn;

Line 1061 static genJack(int M,int N) {

Line 1154 static genJack(int M,int N) {

int *Kap,*Mu;

double Jack,Beta_km;

int Nk,JJ;

if (Debug) oxprintf("genJack(%d,%d)\n",M,N);

M_jack = (double **) mymalloc(sizeof(double *)*(N+2));

M_2n = imypower(2,N);

Pmn = pmn(M,N); /*P_pmn is initializeded.

Line 1089 static genJack(int M,int N) {

Line 1183 static genJack(int M,int N) {

if (M_df) {

for (J=1; J<M_2n; J++) {

if (J >= 2^I) aM_jack(I,J,K) = 0;

else aM_jack(I,J,K) = NAN;

}

Line 1105 static genJack(int M,int N) {

Line 1199 static genJack(int M,int N) {

for (J=1; J<M_2n; J++) aM_jack(I,J,K) = 0;

}

if (Debug) {printf("Kappa="); printp(Kap);}

if (Debug) {oxprintf("Kappa="); printp(Kap);}

/* Enumerate horizontal strip of Kappa */

genBeta(Kap); /* M_beta_pt stores the number of hs */

/* Nv is the number of variables */

Line 1114 static genJack(int M,int N) {

Line 1208 static genJack(int M,int N) {

for (H=0; H<M_beta_pt; H++) {

Nk = M_beta_1[H];

Mu = Parray[Nk];

if (UseTable) {

Beta_km = M_beta_0[H];

}else{

Beta_km = beta(Kap,Mu);

/* do not use the M_beta table. It's buggy. UseTable is experimental.*/

}

if (Debug) {printf("Nv(number of variables)=%d, Beta_km=%lf, Mu=",Nv,Beta_km);

if (Debug) {oxprintf("Nv(number of variables)=%d, Beta_km=%lf, Mu=",Nv,Beta_km);

printp(Mu); printf("\n");}

printp(Mu); oxprintf("\n");}

P = psublen(Kap,Mu);

Jack += aM_jack(Nv-1,0,Nk)*Beta_km*xval(Nv,P); /* util_v(x,[Nv])^P;*/

if (Debug) oxprintf("xval(%d,%d)=%lf\n",Nv,P,xval(Nv,P));

}

aM_jack(Nv,0,K) = Jack;

if (M_df) {

/* The case of M_df > 0. */

for (J=1; J<M_2n; J++) {

Jack = 0;

mh_check_intr(100);

for (H=0; H<M_beta_pt; H++) {

Jack = 0;

Nk = M_beta_1[H];

for (H=0; H<M_beta_pt; H++) {

Mu = Parray[Nk];

Nk = M_beta_1[H];

if (UseTable) {

Mu = Parray[Nk];

Beta_km = M_beta_0[H];

if (UseTable) {

}else{

Beta_km = M_beta_0[H];

Beta_km = beta(Kap,Mu); /* do not use the M_beta table. It's buggy. */

}else{

}

Beta_km = beta(Kap,Mu); /* do not use the M_beta table. It's buggy. */

if (Debug) {printf("M_df: Nv(number of variables)=%d, Beta_km=%lf, Mu= ",Nv,Beta_km);

}

printp(Mu); printf("\n"); }

if (Debug) {oxprintf("M_df: Nv(number of variables)=%d, Beta_km=%lf, Mu= ",Nv,Beta_km);

P = psublen(Kap,Mu);

printp(Mu); oxprintf("\n"); }

if (J & (1 << (Nv-1))) {

P = psublen(Kap,Mu);

JJ = J & ((1 << (Nv-1)) ^ 0xffff); /* NOTE!! Up to 16 bits. mh-15 */

if (J & (1 << (Nv-1))) {

if (P != 0) {

JJ = J & ((1 << (Nv-1)) ^ 0xffff); /* NOTE!! Up to 16 bits. mh-15 */

Jack += aM_jack(Nv-1,JJ,Nk)*Beta_km*P*xval(Nv,P-1);

if (P != 0) {

}

Jack += aM_jack(Nv-1,JJ,Nk)*Beta_km*P*xval(Nv,P-1);

}else{

}

Jack += aM_jack(Nv-1,J,Nk)*Beta_km*xval(Nv,P);

}else{

}

Jack += aM_jack(Nv-1,J,Nk)*Beta_km*xval(Nv,P);

}

aM_jack(Nv,J,K) = Jack;

}

aM_jack(Nv,J,K) = Jack;

if (Debug) oxprintf("aM_jack(%d,%d,%d) = %lf\n",Nv,J,K,Jack);

} /* end of J loop */

}

} return(0);

}

/* checkJack1(3,3)

static checkJack1(int M,int N) {

static int checkJack1(int M,int N) {

int I,K;

extern int P_pmn;

extern double M_x[];

Line 1174 static checkJack1(int M,int N) {

Line 1271 static checkJack1(int M,int N) {

for (I=1; I<=N; I++) {

for (K=0; K<=P_pmn; K++) {

printp(Parray[K]);

printf("<--Kap, Nv=%d, TableJack=%lf\n",I,aM_jack(I,0,K));

oxprintf("<--Kap, Nv=%d, TableJack=%lf\n",I,aM_jack(I,0,K));

}

for (I=1; I<=N; I++) printf("%lf, ",M_x[I-1]);

for (I=1; I<=N; I++) oxprintf("%lf, ",M_x[I-1]);

printf("<--x\n");

oxprintf("<--x\n");

return(0);

}

/*main() { checkJack1(3,3); }*/

static checkJack2(int M,int N) {

static int checkJack2(int M,int N) {

int I,K,J;

extern int P_pmn;

extern double M_x[];

extern M_df;

extern int M_df;

int Pmn; /* used in aM_jack */

M_df=1;

/* initialize x vars. */

Line 1199 static checkJack2(int M,int N) {

Line 1297 static checkJack2(int M,int N) {

for (I=1; I<=N; I++) {

for (K=0; K<=P_pmn; K++) {

printp(Parray[K]);

printf("<--Kap, Nv=%d, TableJack=%lf\n",I,aM_jack(I,0,K));

oxprintf("<--Kap, Nv=%d, TableJack=%lf\n",I,aM_jack(I,0,K));

}

for (I=1; I<=N; I++) printf("%lf, ",M_x[I-1]);

for (I=1; I<=N; I++) oxprintf("%lf, ",M_x[I-1]);

printf("<--x\n");

oxprintf("<--x\n");

for (I=1; I<=N; I++) {

for (K=0; K<=P_pmn; K++) {

for (J=0; J<M_2n; J++) {

printp(Parray[K]);

printf("<--Kap, Nv=%d,J(diff)=%d, D^J Jack=%lf\n",

oxprintf("<--Kap, Nv=%d,J(diff)=%d, D^J Jack=%lf\n",

I,J,aM_jack(I,J,K));

}

return(0);

}

/* main() { checkJack2(3,3); } */

Line 1224 double mh_t(double A[A_LEN],double B[B_LEN],int N,int

Line 1323 double mh_t(double A[A_LEN],double B[B_LEN],int N,int

extern int P_pmn;

extern double *M_qk;

extern double M_rel_error;

extern int M_m;

extern int M_m_estimated_approx_deg;

extern double M_assigned_series_error;

int Pmn;

int K;

int *Kap;

int size;

int i;

double partial_sum[M_m_MAX+1];

double iv;

double serror;

F = 0; F2=0;

M_df=1;

genJack(M,N);

M_qk = (double *)mymalloc(sizeof(double)*P_pmn);

M_qk = (double *)mymalloc(sizeof(double)*(P_pmn+1)); /* found a bug. */

Pmn = P_pmn;

size = ParraySize[P_pmn];

for (K=0; K<=P_pmn; K++) {

Kap = Parray[K];

mh_check_intr(100);

M_qk[K] = qk(Kap,A,B);

Kap = Parray[K];

F += M_qk[K]*aM_jack(N,0,K);

M_qk[K] = qk(Kap,A,B);

if (ParraySize[K] < size) F2 += M_qk[K]*aM_jack(N,0,K);

F += M_qk[K]*aM_jack(N,0,K);

if (Debug) printf("ParraySize[K] = %d, size=%d\n",ParraySize[K],size);

if (ParraySize[K] < size) F2 += M_qk[K]*aM_jack(N,0,K);

if (Debug && (ParraySize[K] == size)) printf("M_qk[K]=%lg, aM_jack=%lg\n",M_qk[K],aM_jack(N,0,K));

if (Debug) oxprintf("ParraySize[K] = %d, size=%d\n",ParraySize[K],size);

if (Debug && (ParraySize[K] == size)) oxprintf("M_qk[K]=%lg, aM_jack=%lg\n",M_qk[K],aM_jack(N,0,K));

}

M_rel_error = F-F2;

M_m_estimated_approx_deg = -1; serror=1;

for (i=0; i<=M_m; i++) {

partial_sum[i] = 0.0; partial_sum[i+1] = 0.0;

for (K=0; K<=P_pmn; K++) {

if (ParraySize[K] == i) partial_sum[i] += M_qk[K]*aM_jack(N,0,K);

}

if (i>0) partial_sum[i] += partial_sum[i-1];

if (i>0) serror = myabs((partial_sum[i]-partial_sum[i-1])/partial_sum[i-1]);

if ((i>0)&&(M_m_estimated_approx_deg < 0)&&(serror<M_assigned_series_error)) {

M_m_estimated_approx_deg = i; break;

}

if (M_m_estimated_approx_deg < 0) {

M_m_estimated_approx_deg = M_m+mymin(5,mymax(1,(int)log(serror/M_assigned_series_error))); /* Heuristic */

}

for (K=0; K<=P_pmn; K++) {

oxprintf("Kappa="); for (i=0; i<N; i++) oxprintf("%d ",Parray[K][i]); oxprintf("\n");

oxprintf("ParraySize(%d)=%d (|kappa|), M_m=%d\n",K,ParraySize[K],M_m);

}

for (i=0; i<=M_m; i++) {

oxprintf("partial_sum[%d]=%lg\n",i,partial_sum[i]);

}

M_estimated_X0g = X0g;

iv=myabs(F*iv_factor());

if (iv < M_x0value_min) M_estimated_X0g = X0g*mymax(2,log(log(1/iv))); /* This is heuristic */

M_estimated_X0g = mymin(M_estimated_X0g,M_X0g_bound);

M_mh_t_success = 1;

if (M_estimated_X0g != X0g) M_mh_t_success=0;

if (M_m_estimated_approx_deg > M_m) M_mh_t_success=0;

M_series_error = serror;

M_recommended_abserr = iv*M_assigned_series_error;

M_recommended_relerr = M_series_error;

if (M_show_autosteps) {

oxprintf("%%%%serror=%lg, M_assigned_series_error=%lg, M_m_estimated_approx_deg=%d,M_m=%d\n",serror,M_assigned_series_error,M_m_estimated_approx_deg,M_m);

oxprintf("%%%%x0value_min=%lg, x0g_bound=%lg\n",M_x0value_min, M_X0g_bound);

oxprintf("%%%%F=%lg,Ef=%lg,M_estimated_X0g=%lg, X0g=%lg\n",F,iv_factor(),M_estimated_X0g,X0g);

oxprintfe("%%%%(stderr) serror=%lg, M_assigned_series_error=%lg, M_m_estimated_approx_deg=%d,M_m=%d\n",serror,M_assigned_series_error,M_m_estimated_approx_deg,M_m);

oxprintfe("%%%%(stderr) x0value_min=%lg, x0g_bound=%lg\n",M_x0value_min, M_X0g_bound);

oxprintfe("%%%%(stderr) F=%lg,Ef=%lg,M_estimated_X0g=%lg, X0g=%lg\n",F,iv_factor(),M_estimated_X0g,X0g);

}

M_mh_t_value=F;

return(F);

}

double mh_t2(int J) {

Line 1255 double mh_t2(int J) {

Line 1409 double mh_t2(int J) {

F = 0;

Pmn = P_pmn;

for (K=0; K<P_pmn; K++) {

F += M_qk[K]*aM_jack(M_n,J,K);

}

return(F);

}

static mtest1b() {

static int mtest1b() {

double A[1] = {1.5};

double B[1] = {1.5+5};

int I,N,M,J;

Line 1271 static mtest1b() {

Line 1425 static mtest1b() {

}

mh_t(A,B,N,M);

for (J=0; J<M_2n; J++) {

F=mh_t2(J);

printf("J=%d, D^J mh_t=%lf\n",J,F);

oxprintf("J=%d, D^J mh_t=%lf\n",J,F);

}

return(0);

}

/* main() { mtest1b(); }*/

Line 1289 static mtest1b() {

Line 1444 static mtest1b() {

/****** from mh-n.c *****/

#define SMAX 4096

#define inci(i) { i++; if (i >= argc) { fprintf(stderr,"Option argument is not given.\n"); return(NULL); }}

#define inci(i) { i++; if (i >= argc) { oxprintfe("Option argument is not given.\n"); return(NULL); }}

static int imypower(int x,int n) {

int i;

Line 1300 static int imypower(int x,int n) {

Line 1455 static int imypower(int x,int n) {

return(v);

}

#ifdef STANDALONE

#ifdef STANDALONE2

main(int argc,char *argv[]) {

mh_exit(MH_RESET_EXIT);

/* jk_main(argc,argv);

printf("second run.\n"); */

oxprintf("second run.\n"); */

jk_main(argc,argv);

return(0);

}

#endif

struct MH_RESULT *jk_main(int argc,char *argv[]) {

int i;

struct MH_RESULT *ans;

extern int M_automatic;

extern int M_mh_t_success;

extern double M_estimated_X0g;

extern int M_m_estimated_approx_deg;

for (i=1; i<argc; i++) {

if (strcmp(argv[i],"--automatic")==0) {

inci(i);

sscanf(argv[i],"%d",&M_automatic);

break;

}

ans=jk_main2(argc,argv,0,0.0,0);

if (!M_automatic) return(ans);

if (M_mh_t_success) return(ans);

while (!M_mh_t_success) {

ans=jk_main2(argc,argv,1,M_estimated_X0g,M_m_estimated_approx_deg);

}

return(ans);

}

struct MH_RESULT *jk_main2(int argc,char *argv[],int automode,double newX0g,int newDegree) {

double *y0;

double x0,xn;

double ef;

Line 1318 struct MH_RESULT *jk_main(int argc,char *argv[]) {

Line 1497 struct MH_RESULT *jk_main(int argc,char *argv[]) {

extern double M_x[];

extern double *Beta;

extern int M_2n;

extern int M_mh_t_success;

char swork[1024];

struct MH_RESULT *ans=NULL;

struct SFILE *ofp = NULL;

int idata=0;

JK_byFile = 1;

jk_initializeWorkArea();

Debug = 0;

UseTable = 1;

Mapprox=6;

for (i=1; i<argc; i++) {

if (strcmp(argv[i],"--idata")==0) {

inci(i);

setParam(argv[i]); idata=1;

}else if (strcmp(argv[i],"--degree")==0) {

inci(i);

sscanf(argv[i],"%d",&Mapprox);

}else if (strcmp(argv[i],"--x0")==0) {

inci(i);

sscanf(argv[i],"%lg",&X0g);

}else if (strcmp(argv[i],"--notable")==0) {

UseTable = 0;

}else if (strcmp(argv[i],"--debug")==0) {

Debug = 1;

}else if (strcmp(argv[i],"--help")==0) {

usage(); return(0);

}else if (strcmp(argv[i],"--bystring")==0) {

if (idata) {fprintf(stderr,"--bystring must come before --idata option.\n"); mh_exit(-1);}

if (idata) {oxprintfe("--bystring must come before --idata option.\n"); mh_exit(-1);}

JK_byFile = 0;

}else {

}else if (strcmp(argv[i],"--automatic")==0) {

fprintf(stderr,"Unknown option %s\n",argv[i]);

inci(i); /* ignore, in this function */

usage();

}else if (strcmp(argv[i],"--assigned_series_error")==0) {

return(NULL);

inci(i);

}

sscanf(argv[i],"%lg",&M_assigned_series_error);

}else if (strcmp(argv[i],"--x0value_min")==0) {

inci(i);

sscanf(argv[i],"%lg",&M_x0value_min);

}else {

oxprintfe("Unknown option %s\n",argv[i]);

usage();

return(NULL);

}

if (!idata) setParam(NULL);

if (automode) {

Mapprox = newDegree;

X0g = newX0g;

}

/* Initialize global variables */

M_n = Mg;

HS_n=M_n;

if (!JK_byFile) ans = (struct MH_RESULT *)mymalloc(sizeof(struct MH_RESULT));

if (!JK_byFile) {

ans = (struct MH_RESULT *)mymalloc(sizeof(struct MH_RESULT));

ans->message = NULL;

ans->t_success = 0;

ans->series_error = 1.0e+10;

ans->recommended_abserr = 1.0e-10;

}

else ans = NULL;

if (M_automatic) {

/* Differentiation can be M_m in the bit pattern in the M_n variable case.*/

if (M_n > Mapprox) Mapprox=M_n;

}

/* Output by a file=stdout */

ofp = mh_fopen("stdout","w",JK_byFile);

ofp = mh_fopen("oxstdout","w",JK_byFile);

sprintf(swork,"%%%%Use --help option to see the help.\n"); mh_fputs(swork,ofp);

sprintf(swork,"%%%%Mapprox=%d\n",Mapprox); mh_fputs(swork,ofp);

if (M_n != Mg) {

myerror("Mg must be equal to M_n\n"); mh_exit(-1);

}

if (Debug) showParam(ofp);

if (Debug) showParam(NULL,1);

for (i=0; i<M_n; i++) {

M_x[i] = Beta[i]*X0g;

}

M_beta_i_x_o2_max=myabs(M_x[0]/2);

if (M_n <= 1) M_beta_i_beta_j_min = myabs(Beta[0]);

else M_beta_i_beta_j_min = myabs(Beta[1]-Beta[0]);

for (i=0; i<M_n; i++) {

if (myabs(M_x[i]/2) > M_beta_i_x_o2_max) M_beta_i_x_o2_max = myabs(M_x[i]/2);

for (j=i+1; j<M_n; j++) {

if (myabs(Beta[i]-Beta[j]) < M_beta_i_beta_j_min)

M_beta_i_beta_j_min = myabs(Beta[i]-Beta[j]);

}

a[0] = ((double)Mg+1.0)/2.0;

b[0] = ((double)Mg+1.0)/2.0 + ((double) (*Ng))/2.0; /* bug, double check */

if (Debug) printf("Calling mh_t with ([%lf],[%lf],%d,%d)\n",a[0],b[0],M_n,Mapprox);

if (Debug) oxprintf("Calling mh_t with ([%lf],[%lf],%d,%d)\n",a[0],b[0],M_n,Mapprox);

mh_t(a,b,M_n,Mapprox);

if ((!M_mh_t_success) && M_automatic) {

jk_freeWorkArea();

return NULL;

}

if (imypower(2,M_n) != M_2n) {

sprintf(swork,"M_n=%d,M_2n=%d\n",M_n,M_2n); mh_fputs(swork,ofp);

myerror("2^M_n != M_2n\n"); mh_exit(-1);

}

sprintf(swork,"%%%%M_rel_error=%lg\n",M_rel_error); mh_fputs(swork,ofp);

for (j=0; j<M_2n; j++) {

Iv[j] = mh_t2(j);

}

Ef = iv_factor();

showParam(ofp);

showParam(ofp,0);

/* return the result */

if (!JK_byFile) {

ans->x = X0g;

ans->rank = imypower(2,Mg);

ans->y = (double *)mymalloc(sizeof(double)*(ans->rank));

for (i=0; i<ans->rank; i++) (ans->y)[i] = Iv[i];

ans->size=1;

ans->sfpp = (struct SFILE **)mymalloc(sizeof(struct SFILE *)*(ans->size));

(ans->sfpp)[0] = ofp;

ans->t_success = M_mh_t_success;

ans->series_error = M_series_error;

ans->recommended_abserr = M_recommended_abserr;

}

if (Debug) oxprintf("jk_freeWorkArea() starts\n");

jk_freeWorkArea();

if (Debug) oxprintf("jk_freeWorkArea() has finished.\n");

return(ans);

}

static usage() {

static int usage() {

fprintf(stderr,"Usages:\n");

oxprintfe("Usages:\n");

fprintf(stderr,"mh-m [--idata input_data_file --x0 x0 --degree approxm]\n");

oxprintfe("hgm_jack-n [--idata input_data_file --x0 x0 --degree approxm]\n");

fprintf(stderr,"\nThe command mh-m [options] generates an input for w-m, Pr({y | y<xmax}), which is the cumulative distribution function of the largest root of the m by m Wishart matrix with n degrees of freedom and the covariantce matrix sigma.\n");

oxprintfe(" [--automatic n --assigned_series_error e --x0value_min e2]\n");

fprintf(stderr,"The mh-m uses the Koev-Edelman algorithm to evalute the matrix hypergeometric function.\n");

oxprintfe("\nThe command hgm_jack-n [options] generates an input for hgm_w-n, Pr({y | y<xmax}), which is the cumulative distribution function of the largest root of the m by m Wishart matrices with n degrees of freedom and the covariantce matrix sigma.\n");

fprintf(stderr,"The degree of the approximation (Mapprox) is given by the --degree option.\n");

oxprintfe("The hgm_jack-n uses the Koev-Edelman algorithm to evalute the matrix hypergeometric function.\n");

fprintf(stderr,"Parameters are specified by the input_data_file. Otherwise, default values are used.\n");

oxprintfe("The degree of the approximation (Mapprox) is given by the --degree option.\n");

fprintf(stderr,"The format of the input_data_file. The orders of the input numbers must be kept.\n");

oxprintfe("Parameters are specified by the input_data_file. Otherwise, default values are used.\n\n");

fprintf(stderr," Mg: m(the number of variables), Beta: beta=sigma^(-1)/2 (diagonized), Ng: n,\n");

oxprintfe("The format of the input_data_file: (The orders of the input data must be kept.)\n");

fprintf(stderr," Iv: initial values at X0g*Beta (see our paper how to order them), are evaluated in this program. Give zeros. \n");

oxprintfe(" Mg: m(the number of variables), Beta: beta=sigma^(-1)/2 (diagonized), Ng: n,\n");

fprintf(stderr," Ef: a scalar factor to the initial value. It is calculated by this program. Give the zero.\n");

oxprintfe(" (Add a comment line %%Ng= before the data Ng to check the number of beta.)\n");

fprintf(stderr," Hg: h (step size) which is for w-m, X0g: starting value of x(when --x0 option is used, this value is used), Xng: terminating value of x which is for w-m.\n");

oxprintfe(" X0g: starting value of x(when --x0 option is used, this value is used)\n");

fprintf(stderr," Dp: output data is stored in every Dp steps when output_data_file is specified, which is for w-m.\n");

oxprintfe(" Iv: initial values at X0g*Beta (see our paper how to order them), are evaluated in this program. Give zeros or the symbol * to skip rank many inputs.\n");

fprintf(stderr," The line started with %% is a comment line.\n");

oxprintfe(" Ef: a scalar factor to the initial value. It is calculated by this program. Give the zero.\n");

fprintf(stderr," With the --notable option, it does not use the Lemma 3.2 of Koev-Edelman (there is a typo: kappa'_r = mu'_r for 1<=r<=mu_k).\n");

oxprintfe(" Hg: h (step size) which is for hgm_w-n, \n");

fprintf(stderr," An example format of the input_data_file can be obtained by executing mh-m with no option.\n");

oxprintfe(" Dp: output data is stored in every Dp steps when output_data_file is specified. This is for hgm_w-n.\n");

fprintf(stderr,"\nExamples:\n");

oxprintfe(" Xng: terminating value of x. This is for hgm_w-n.\n");

fprintf(stderr,"[1] ./mh-2 \n");

oxprintfe("Optional parameters automatic, ... are interpreted by a parser. See setParam() in jack-n.c and Testdata/tmp-idata2.txt as an example. Optional paramters are given as %%parameter_name=value Lines starting with %%%% or # are comment lines.\n");

fprintf(stderr,"[2] ./mh-2 --x0 0.3 \n");

oxprintfe("Parameters are redefined when they appear more than once in the idata file and the command line options.\n\n");

fprintf(stderr,"[3] ./mh-3 --x0 0.1 \n");

oxprintfe("With the --notable option, it does not use the Lemma 3.2 of Koev-Edelman (there is a typo: kappa'_r = mu'_r for 1<=r<=mu_k).\n");

fprintf(stderr,"[4] ./mh-3 --x0 0.1 --degree 15 \n");

oxprintfe("An example format of the input_data_file can be obtained by executing hgm_jack-n with no option. When there is no --idata file, all options are ignored.\n");

fprintf(stderr,"[5] ./mh-3 --idata test.txt --degree 15 \n");

oxprintfe("By --automatic option, X0g and degree are automatically determined from assigend_series_error. The current strategy is described in mh_t in jack-n.c\n");

fprintf(stderr,"[6] ./mh-3 --degree 15 >test2.txt\n");

oxprintfe("Default values for the papameters of the automatic mode: automatic=%d, assigned_series_error=%lg, x0value_min=%lg\n",M_automatic,M_assigned_series_error,M_x0value_min);

fprintf(stderr," ./w-3 --idata test2.txt --gnuplotf test-g\n");

oxprintfe("Todo: automatic mode throws away the table of Jack polynomials of the previous degrees and reevaluate them. They should be kept.\n");

fprintf(stderr," gnuplot -persist <test-g-gp.txt\n");

oxprintfe("\nExamples:\n");

oxprintfe("[1] ./hgm_jack-n \n");

oxprintfe("[2] ./hgm_jack-n --idata Testdata/tmp-idata3.txt --degree 15 --automatic 0\n");

oxprintfe("[3] ./hgm_jack-n --idata Testdata/tmp-idata2.txt --degree 15 >test2.txt\n");

oxprintfe(" ./hgm_w-n --idata test2.txt --gnuplotf test-g\n");

oxprintfe(" gnuplot -persist <test-g-gp.txt\n");

oxprintfe("[4] ./hgm_jack-n --idata Testdata/tmp-idata3.txt --automatic 1 --assigned_series_error=1e-12\n");

oxprintfe("[5] ./hgm_jack-n --idata Testdata/tmp-idata4.txt\n");

return(0);

}

static setParamDefault() {

static int setParamDefault() {

int rank;

int i;

Mg = M_n_default ;

Line 1450 static setParamDefault() {

Line 1681 static setParamDefault() {

Hg = 0.001;

Dp = 1;

Xng = 10.0;

return(0);

}

static next(struct SFILE *sfp,char *s,char *msg) {

static int next(struct SFILE *sfp,char *s,char *msg) {

static int check=1;

char *ng="%%Ng=";

int i;

s[0] = '%';

while (s[0] == '%') {

if (!mh_fgets(s,SMAX,sfp)) {

fprintf(stderr,"Data format error at %s\n",msg);

oxprintfe("Data format error at %s\n",msg);

mh_exit(-1);

}

if (s[0] != '%') return(0);

if (check && (strncmp(msg,ng,4)==0)) {

if (strncmp(s,ng,5) != 0) {

oxprintfe("Warning, there is no %%Ng= at the border of Beta's and Ng, s=%s\n",s);

}

/* check=0; */

}

if (s[0] != '%') return(0);

}

return(0);

}

static setParam(char *fname) {

static int setParam(char *fname) {

int rank;

char s[SMAX];

struct SFILE *fp;

int i;

struct mh_token tk;

if (fname == NULL) return(setParamDefault());

Sample = 0;

if ((fp=mh_fopen(fname,"r",JK_byFile)) == NULL) {

if (JK_byFile) fprintf(stderr,"File %s is not found.\n",fp->s);

if (JK_byFile) oxprintfe("File %s is not found.\n",fp->s);

mh_exit(-1);

}

next(fp,s,"Mg(m)");

sscanf(s,"%d",&Mg);

Line 1481 static setParam(char *fname) {

Line 1724 static setParam(char *fname) {

Beta = (double *)mymalloc(sizeof(double)*Mg);

for (i=0; i<Mg; i++) {

next(fp,s,"Beta");

sscanf(s,"%lf",&(Beta[i]));

}

Ng = (double *)mymalloc(sizeof(double));

next(fp,s,"Ng(freedom parameter n)");

next(fp,s,"%Ng= (freedom parameter n)");

sscanf(s,"%lf",Ng);

next(fp,s,"X0g(initial point)");

sscanf(s,"%lf",&X0g);

Iv = (double *)mymalloc(sizeof(double)*rank);

for (i=0; i<rank; i++) {

next(fp,s,"Iv(initial values)");

sscanf(s,"%lg",&(Iv[i]));

if (strncmp(s,"*",1)==0) {

for (i=0; i<rank; i++) Iv[i] = 0.0;

break;

}

sscanf(s,"%lg",&(Iv[i]));

}

next(fp,s,"Ef(exponential factor)");

sscanf(s,"%lg",&Ef);

if (strncmp(s,"*",1)==0) Ef=0.0;

else sscanf(s,"%lg",&Ef);

next(fp,s,"Hg (step size of rk)");

sscanf(s,"%lf",&Hg);

Line 1508 static setParam(char *fname) {

Line 1756 static setParam(char *fname) {

next(fp,s,"Xng (the last point, cf. --xmax)");

sscanf(s,"%lf",&Xng);

/* Reading the optional parameters */

while ((tk = mh_getoken(s,SMAX-1,fp)).type != MH_TOKEN_EOF) {

/* expect ID */

if (tk.type != MH_TOKEN_ID) {

oxprintfe("Syntax error at %s\n",s); mh_exit(-1);

}

if (strcmp(s,"automatic")==0) {

if (mh_getoken(s,SMAX-1,fp).type != MH_TOKEN_EQ) {

oxprintfe("Syntax error at %s\n",s); mh_exit(-1);

}

if ((tk=mh_getoken(s,SMAX-1,fp)).type != MH_TOKEN_INT) {

oxprintfe("Syntax error at %s\n",s); mh_exit(-1);

}

M_automatic = tk.ival;

continue;

}

if (strcmp(s,"assigned_series_error")==0) {

if (mh_getoken(s,SMAX-1,fp).type != MH_TOKEN_EQ) {

oxprintfe("Syntax error at %s\n",s); mh_exit(-1);

}

if ((tk=mh_getoken(s,SMAX-1,fp)).type != MH_TOKEN_DOUBLE) {

oxprintfe("Syntax error at %s\n",s); mh_exit(-1);

}

M_assigned_series_error = tk.dval;

continue;

}

if (strcmp(s,"x0value_min")==0) {

if (mh_getoken(s,SMAX-1,fp).type != MH_TOKEN_EQ) {

oxprintfe("Syntax error at %s\n",s); mh_exit(-1);

}

if ((tk=mh_getoken(s,SMAX-1,fp)).type != MH_TOKEN_DOUBLE) {

oxprintfe("Syntax error at %s\n",s); mh_exit(-1);

}

M_x0value_min = tk.dval;

continue;

}

if ((strcmp(s,"Mapprox")==0) || (strcmp(s,"degree")==0)) {

if (mh_getoken(s,SMAX-1,fp).type != MH_TOKEN_EQ) {

oxprintfe("Syntax error at %s\n",s); mh_exit(-1);

}

if ((tk=mh_getoken(s,SMAX-1,fp)).type != MH_TOKEN_INT) {

oxprintfe("Syntax error at %s\n",s); mh_exit(-1);

}

Mapprox = tk.ival;

continue;

}

if (strcmp(s,"X0g_bound")==0) {

if (mh_getoken(s,SMAX-1,fp).type != MH_TOKEN_EQ) {

oxprintfe("Syntax error at %s\n",s); mh_exit(-1);

}

if ((tk=mh_getoken(s,SMAX-1,fp)).type != MH_TOKEN_DOUBLE) {

oxprintfe("Syntax error at %s\n",s); mh_exit(-1);

}

M_X0g_bound = tk.dval;

continue;

}

if (strcmp(s,"show_autosteps")==0) {

if (mh_getoken(s,SMAX-1,fp).type != MH_TOKEN_EQ) {

oxprintfe("Syntax error at %s\n",s); mh_exit(-1);

}

if ((tk=mh_getoken(s,SMAX-1,fp)).type != MH_TOKEN_INT) {

oxprintfe("Syntax error at %s\n",s); mh_exit(-1);

}

M_show_autosteps = tk.ival;

continue;

}

oxprintfe("Unknown ID at %s\n",s); mh_exit(-1);

}

mh_fclose(fp);

return(0);

}

static showParam(struct SFILE *fp) {

static int showParam(struct SFILE *fp,int fd) {

int rank,i;

char swork[1024];

if (fd) {

fp = mh_fopen("oxstdout","w",1);

}

rank = imypower(2,Mg);

sprintf(swork,"%%Mg=\n%d\n",Mg); mh_fputs(swork,fp);

for (i=0; i<Mg; i++) {

sprintf(swork,"%%Beta[%d]=\n%lf\n",i,Beta[i]); mh_fputs(swork,fp);

}

sprintf(swork,"%%Ng=\n%lf\n",*Ng); mh_fputs(swork,fp);

sprintf(swork,"%%X0g=\n%lf\n",X0g); mh_fputs(swork,fp);

for (i=0; i<rank; i++) {

sprintf(swork,"%%Iv[%d]=\n%lg\n",i,Iv[i]); mh_fputs(swork,fp);

if (Sample && (M_n == 2) && (X0g == 0.3)) {

sprintf(swork,"%%Iv[%d]-Iv2[%d]=%lg\n",i,i,Iv[i]-Iv2[i]); mh_fputs(swork,fp);

}

sprintf(swork,"%%Ef=\n%lg\n",Ef); mh_fputs(swork,fp);

sprintf(swork,"%%Hg=\n%lf\n",Hg); mh_fputs(swork,fp);

sprintf(swork,"%%Dp=\n%d\n",Dp); mh_fputs(swork,fp);

sprintf(swork,"%%Xng=\n%lf\n",Xng);mh_fputs(swork,fp);

sprintf(swork,"%%%% Optional paramters\n"); mh_fputs(swork,fp);

sprintf(swork,"#success=%d\n",M_mh_t_success); mh_fputs(swork,fp);

sprintf(swork,"#automatic=%d\n",M_automatic); mh_fputs(swork,fp);

sprintf(swork,"#series_error=%lg\n",M_series_error); mh_fputs(swork,fp);

sprintf(swork,"#recommended_abserr\n"); mh_fputs(swork,fp);

sprintf(swork,"%%abserror=%lg\n",M_recommended_abserr); mh_fputs(swork,fp);

if (M_recommended_relerr < MH_RELERR_DEFAULT) {

sprintf(swork,"%%relerror=%lg\n",M_recommended_relerr); mh_fputs(swork,fp);

}

sprintf(swork,"#mh_t_value=%lg # Value of matrix hg at X0g.\n",M_mh_t_value); mh_fputs(swork,fp);

sprintf(swork,"# M_m=%d # Approximation degree of matrix hg.\n",M_m); mh_fputs(swork,fp);

sprintf(swork,"#beta_i_x_o2_max=%lg #max(|beta[i]*x|/2)\n",M_beta_i_x_o2_max); mh_fputs(swork,fp);

sprintf(swork,"#beta_i_beta_j_min=%lg #min(|beta[i]-beta[j]|)\n",M_beta_i_beta_j_min); mh_fputs(swork,fp);

return(0);

}

static double gammam(double a,int n) {

Line 1541 static double gammam(double a,int n) {

Line 1877 static double gammam(double a,int n) {

for (i=1; i<=n; i++) {

v2 += lgamma(a-((double)(i-1))/2.0); /* not for big n */

}

if (Debug) printf("gammam(%lg,%d)=%lg\n",a,n,v*exp(v2));

if (Debug) oxprintf("gammam(%lg,%d)=%lg\n",a,n,v*exp(v2));

return(v*exp(v2));

}

Line 1562 static double iv_factor(void) {

Line 1898 static double iv_factor(void) {

detSigma = 1.0/(b*mypower(2.0,M_n));

c = gammam(((double)(M_n+1))/2.0, M_n)/

( mypower(sqrt(2), M_n*n)*mypower(sqrt(detSigma),n)*gammam(((double)(M_n+n+1))/2.0,M_n) );

return( c*v1);

}

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