Annotation of OpenXM/src/hgm/mh/src/jack-n.c, Revision 1.12
1.1 takayama 1: #include <stdio.h>
2: #include <stdlib.h>
3: #define _ISOC99_SOURCE
4: #include <math.h>
5: #include <string.h>
6: #include "sfile.h"
7: /*
1.12 ! takayama 8: $OpenXM: OpenXM/src/hgm/mh/src/jack-n.c,v 1.11 2013/03/05 05:26:07 takayama Exp $
! 9: Ref: copied from this11/misc-2011/A1/wishart/Prog
! 10: jack-n.c, translated from mh.rr or tk_jack.rr in the asir-contrib. License: LGPL
! 11: Koev-Edelman for higher order derivatives.
! 12: cf. 20-my-note-mh-jack-n.pdf, /Movies/oxvh/priv-j1/2011-12-14-ke-mh-jack.mov
! 13: Todo:
! 14: 1. Cash the transposes of partitions.
! 15: 2. Use the recurrence to obtain beta().
! 16: 3. Easier input data file format for mh-n.c
! 17: Changelog:
! 18: 2012.02.21, porting to OpenXM/src/hgm
! 19: 2011.12.22, --table option, which is experimental.
! 20: 2011.12.19, bug fix. jjk() should return double. It can become more than max int.
! 21: 2011.12.15, mh.r --> jack-n.c
1.1 takayama 22: */
23:
1.3 takayama 24: /****** from mh-n.c *****/
25: static int JK_byFile=1;
1.6 takayama 26: static int JK_deallocate=0;
1.3 takayama 27: #define M_n_default 3
1.4 takayama 28: #define Sample_default 1
1.3 takayama 29: static int M_n=0;
1.1 takayama 30: /* global variables. They are set in setParam() */
1.2 takayama 31: static int Mg; /* n */
32: static int Mapprox; /* m, approximation degree */
33: static double *Beta; /* beta[0], ..., beta[m-1] */
34: static double *Ng; /* freedom n. c=(m+1)/2+n/2; Note that it is a pointer */
35: static double X0g; /* initial point */
36: static double *Iv; /* Initial values of mhg sorted by mhbase() in rd.rr at beta*x0 */
37: static double Ef; /* exponential factor at beta*x0 */
38: static double Hg; /* step size of rk defined in rk.c */
39: static int Dp; /* Data sampling period */
40: static double Xng=0.0; /* the last point */
1.4 takayama 41: static int Sample = Sample_default;
1.1 takayama 42:
43: /* for sample inputs */
1.2 takayama 44: static double *Iv2;
45: static double Ef2;
1.1 takayama 46:
47: #ifdef NAN
48: #else
1.2 takayama 49: #define NAN 3.40282e+38 /* for old 32 bit machines. Todo, configure */
1.1 takayama 50: #endif
51:
52: /* #define M_n 3 defined in the Makefile */ /* number of variables */
53: #define M_n0 3 /* used for tests. Must be equal to M_n */
54: #define M_m_MAX 200
1.3 takayama 55: #define M_nmx M_m_MAX /* maximal of M_n */
1.1 takayama 56: #define A_LEN 1 /* (a_1) , (a_1, ..., a_p)*/
57: #define B_LEN 1 /* (b_1) */
1.9 takayama 58: static int Debug = 0;
1.5 takayama 59: static int Alpha = 2; /* 2 implies the zonal polynomial */
1.2 takayama 60: static int *Darray = NULL;
61: static int **Parray = NULL; /* array of partitions of size M_n */
62: static int *ParraySize = NULL; /* length of each partitions */
1.3 takayama 63: static int M_kap[M_nmx];
1.2 takayama 64: static int M_m=M_m_MAX-2; /* | | <= M_m, bug do check of M_m <=M_m_MAX-2 */
1.1 takayama 65: void (*M_pExec)(void);
1.3 takayama 66: static int HS_mu[M_nmx];
67: static int HS_n=M_nmx; /* It is initialized to M_n in jk_main */
1.1 takayama 68: void (*HS_hsExec)(void);
1.3 takayama 69: static double M_x[M_nmx];
1.1 takayama 70:
71: /* They are used in pmn */
1.2 takayama 72: static int *P_pki=NULL;
73: static int P_pmn=0;
1.1 takayama 74:
75: /* It is used genDarray2(), list partitions... */
1.2 takayama 76: static int DR_parray=0;
1.1 takayama 77:
78: /* Used in genBeta() and enumeration of horizontal strip. */
1.2 takayama 79: static double *M_beta_0=NULL; /* M_beta[0][*] value of beta_{kappa,mu}, M_beta[1][*] N_mu */
80: static int *M_beta_1=NULL;
81: static int M_beta_pt=0;
1.3 takayama 82: static int M_beta_kap[M_nmx];
1.2 takayama 83: static int UseTable = 0;
84:
85: static double **M_jack;
86: static int M_df=1; /* Compute differentials? */
87: static int M_2n=0; /* 2^N */
1.1 takayama 88:
1.3 takayama 89: static double Xarray[M_nmx][M_m_MAX];
1.1 takayama 90: /* (x_1, ..., x_n) */
91: /* Xarray[i][0] x_{i+1}^0, Xarray[i][1], x_{i+1}^1, ... */
92:
1.2 takayama 93: static double *M_qk=NULL; /* saves pochhammerb */
94: static double M_rel_error=0.0; /* relative errors */
1.1 takayama 95:
1.2 takayama 96: /* prototypes */
97: static void *mymalloc(int size);
1.10 takayama 98: static int myfree(void *p);
99: static int myerror(char *s);
1.2 takayama 100: static double jack1(int K);
101: static double jack1diff(int k);
102: static double xval(int i,int p); /* x_i^p */
103: static int mysum(int L[]);
104: static int plength(int P[]);
105: static int plength_t(int P[]);
1.3 takayama 106: static void ptrans(int P[M_nmx],int Pt[]);
1.10 takayama 107: static int test_ptrans();
1.2 takayama 108: static int huk(int K[],int I,int J);
109: static int hdk(int K[],int I,int J);
110: static double jjk(int K[]);
111: static double ppoch(double A,int K[]);
112: static double ppoch2(double A,double B,int K[]);
113: static double mypower(double x,int n);
114: static double qk(int K[],double A[A_LEN],double B[B_LEN]);
115: static int bb(int N[],int K[],int M[],int I,int J);
116: static double beta(int K[],int M[]);
1.10 takayama 117: static int printp(int kappa[]);
118: static int printp2(int kappa[]);
119: static int test_beta();
1.2 takayama 120: static double q3_10(int K[],int M[],int SK);
121: static double q3_5(double A[],double B[],int K[],int I);
122: static void mtest4();
123: static void mtest4b();
124: static int nk(int KK[]);
125: static int plength2(int P1[],int P2[]);
126: static int myeq(int P1[],int P2[]);
127: static int pListPartition(int M,int N);
128: static int pListPartition2(int Less,int From,int To, int M);
129: static void pExec_0();
130: static int pListHS(int Kap[],int N);
131: static int pListHS2(int From,int To,int Kap[]);
132: static void hsExec_0();
133: static int pmn(int M,int N);
134: static int *cloneP(int a[]);
1.10 takayama 135: static int copyP(int p[],int a[]);
1.2 takayama 136: static void pExec_darray(void);
1.10 takayama 137: static int genDarray2(int M,int N);
138: static int isHStrip(int Kap[],int Nu[]);
1.2 takayama 139: static void hsExec_beta(void);
1.10 takayama 140: static int genBeta(int Kap[]);
141: static int checkBeta1();
1.2 takayama 142: static int psublen(int Kap[],int Mu[]);
1.10 takayama 143: static int genJack(int M,int N);
144: static int checkJack1(int M,int N);
145: static int checkJack2(int M,int N);
146: static int mtest1b();
1.2 takayama 147:
148: static int imypower(int x,int n);
1.10 takayama 149: static int usage();
150: static int setParamDefault();
151: static int next(struct SFILE *fp,char *s,char *msg);
1.2 takayama 152: static int gopen_file(void);
153: static int setParam(char *fname);
1.8 takayama 154: static int showParam(struct SFILE *fp,int fd);
1.2 takayama 155: static double iv_factor(void);
156: static double gammam(double a,int n);
157: static double mypower(double a,int n);
158:
159: double mh_t(double A[A_LEN],double B[B_LEN],int N,int M);
160: double mh_t2(int J);
1.3 takayama 161: struct MH_RESULT *jk_main(int argc,char *argv[]);
162: int jk_freeWorkArea();
163: int jk_initializeWorkArea();
164:
165: int jk_freeWorkArea() {
166: /* bug, p in the cloneP will not be deallocated.
1.12 ! takayama 167: Nk in genDarray2 will not be deallocated.
! 168: */
1.3 takayama 169: int i;
1.6 takayama 170: JK_deallocate=1;
1.3 takayama 171: if (Darray) {myfree(Darray); Darray=NULL;}
172: if (Parray) {myfree(Parray); Parray=NULL;}
173: if (ParraySize) {myfree(ParraySize); ParraySize=NULL;}
174: if (M_beta_0) {myfree(M_beta_0); M_beta_0=NULL;}
175: if (M_beta_1) {myfree(M_beta_1); M_beta_1=NULL;}
176: if (M_jack) {
1.12 ! takayama 177: for (i=0; M_jack[i] != NULL; i++) {
! 178: if (Debug) printf("Free M_jack[%d]\n",i);
! 179: myfree(M_jack[i]); M_jack[i] = NULL;
! 180: }
! 181: myfree(M_jack); M_jack=NULL;
1.3 takayama 182: }
183: if (M_qk) {myfree(M_qk); M_qk=NULL;}
184: if (P_pki) {myfree(P_pki); P_pki=NULL;}
1.6 takayama 185: JK_deallocate=0;
1.3 takayama 186: }
187: int jk_initializeWorkArea() {
188: int i,j;
1.6 takayama 189: JK_deallocate=1;
190: xval(0,0);
191: JK_deallocate=0;
1.3 takayama 192: Darray=NULL;
193: Parray=NULL;
194: ParraySize=NULL;
195: M_beta_0=NULL;
196: M_beta_1=NULL;
197: M_jack=NULL;
198: M_qk=NULL;
199: for (i=0; i<M_nmx; i++) M_kap[i]=HS_mu[i]=0;
200: for (i=0; i<M_nmx; i++) M_x[i]=0;
201: for (i=0; i<M_nmx; i++) for (j=0; j<M_m_MAX; j++) Xarray[i][j]=0;
1.5 takayama 202: for (i=0; i<M_nmx; i++) M_beta_kap[i]=0;
1.3 takayama 203: M_m=M_m_MAX-2;
204: Alpha = 2;
205: HS_n=M_nmx;
206: P_pki=NULL;
207: P_pmn=0;
208: DR_parray=0;
209: M_beta_pt=0;
210: M_df=1;
211: M_2n=0;
212: M_rel_error=0.0;
1.4 takayama 213: Sample = Sample_default;
1.5 takayama 214: Xng=0.0;
215: M_n=0;
1.3 takayama 216: }
1.2 takayama 217:
218: static void *mymalloc(int size) {
1.1 takayama 219: void *p;
220: if (Debug) printf("mymalloc(%d)\n",size);
1.8 takayama 221: p = (void *)mh_malloc(size);
1.1 takayama 222: if (p == NULL) {
223: fprintf(stderr,"No more memory.\n");
1.3 takayama 224: mh_exit(-1);
1.1 takayama 225: }
226: return(p);
227: }
1.10 takayama 228: static int myfree(void *p) {
1.8 takayama 229: if (Debug) printf("myFree at %p\n",p);
230: mh_free(p);
1.7 takayama 231: }
1.10 takayama 232: static int myerror(char *s) { fprintf(stderr,"%s: type in control-C\n",s); getchar(); getchar();}
1.1 takayama 233:
1.2 takayama 234: static double jack1(int K) {
1.1 takayama 235: double F;
236: extern int Alpha;
237: int I,J,L,II,JJ,N;
238: N = 1;
239: if (K == 0) return((double)1);
240: F = xval(1,K);
241: for (J=0; J<K; J++) {
242: II = 1; JJ = J+1;
243: F *= (N-(II-1)+Alpha*(JJ-1));
244: }
245: return(F);
246: }
1.2 takayama 247: static double jack1diff(int K) {
1.1 takayama 248: double F;
249: extern int Alpha;
250: int I,J,S,L,II,JJ,N;
251: N = 1;
252: if (K == 0) return((double)1);
253: F = K*xval(1,K-1);
254: for (J=0; J<K; J++) {
255: II = 1; JJ = J+1;
256: F *= (N-(II-1)+Alpha*(JJ-1));
257: }
258: return(F);
259: }
260:
1.2 takayama 261: static double xval(int ii,int p) { /* x_i^p */
1.1 takayama 262: extern double M_x[];
263: double F;
264: int i,j;
1.10 takayama 265: static int init=0;
1.6 takayama 266: if (JK_deallocate) { init=0; return(0.0);}
1.1 takayama 267: if (!init) {
268: for (i=1; i<=M_n; i++) {
269: for (j=0; j<M_m_MAX; j++) {
1.12 ! takayama 270: if (j != 0) {
! 271: Xarray[i-1][j] = M_x[i-1]*Xarray[i-1][j-1];
! 272: }else{
! 273: Xarray[i-1][0] = 1;
! 274: }
1.1 takayama 275: }
276: }
277: init = 1;
278: }
279: if (ii < 1) myerror("xval, index out of bound.");
280: if (p > M_m_MAX-2) myerror("xval, p is too large.");
281: if (p < 0) {
282: myerror("xval, p is negative.");
283: printf("ii=%d, p=%d\n",ii,p);
1.3 takayama 284: mh_exit(-1);
1.1 takayama 285: }
286: return(Xarray[ii-1][p]);
287: }
288:
1.2 takayama 289: static int mysum(int L[]) {
1.1 takayama 290: int S,I,N;
291: N=M_n;
292: S=0;
293: for (I=0; I<N; I++) S += L[I];
294: return(S);
295: }
296:
297: /*
1.12 ! takayama 298: (3,2,2,0,0) --> 3
1.1 takayama 299: */
1.2 takayama 300: static int plength(int P[]) {
1.1 takayama 301: int I;
302: for (I=0; I<M_n; I++) {
303: if (P[I] == 0) return(I);
304: }
305: return(M_n);
306: }
307: /* plength for transpose */
1.2 takayama 308: static int plength_t(int P[]) {
1.1 takayama 309: int I;
310: for (I=0; I<M_m; I++) {
311: if (P[I] == 0) return(I);
312: }
313: return(M_m);
314: }
315:
316: /*
1.12 ! takayama 317: ptrans(P) returns Pt
1.1 takayama 318: */
1.3 takayama 319: static void ptrans(int P[M_nmx],int Pt[]) { /* Pt[M_m] */
1.1 takayama 320: extern int M_m;
321: int i,j,len;
1.3 takayama 322: int p[M_nmx];
1.1 takayama 323: for (i=0; i<M_n; i++) p[i] = P[i];
324: for (i=0; i<M_m+1; i++) Pt[i] = 0;
325: for (i=0; i<M_m; i++) {
326: len=plength(p); Pt[i] = len;
327: if (len == 0) return;
328: for (j=0; j<len; j++) p[j] -= 1;
329: }
330: }
331:
1.10 takayama 332: static int test_ptrans() {
1.1 takayama 333: extern int M_m;
334: int p[M_n0]={5,3,2};
335: int pt[10];
336: int i;
337: M_m = 10;
338: ptrans(p,pt);
339: if (Debug) {for (i=0; i<10; i++) printf("%d,",pt[i]); printf("\n");}
340: }
341:
342:
343: /*
344: upper hook length
345: h_kappa^*(K)
346: */
1.2 takayama 347: static int huk(int K[],int I,int J) {
1.1 takayama 348: extern int Alpha;
349: int Kp[M_m_MAX];
350: int A,H;
351: A=Alpha;
352: /*printf("h^k(%a,%a,%a,%a)\n",K,I,J,A);*/
353: ptrans(K,Kp);
354: H=Kp[J-1]-I+A*(K[I-1]-J+1);
355: return(H);
356: }
357:
358: /*
359: lower hook length
360: h^kappa_*(K)
361: */
1.2 takayama 362: static int hdk(int K[],int I,int J) {
1.1 takayama 363: extern int Alpha;
364: int Kp[M_m_MAX];
365: int A,H;
366: A = Alpha;
367: /*printf("h_k(%a,%a,%a,%a)\n",K,I,J,A);*/
368: ptrans(K,Kp);
369: H=Kp[J-1]-I+1+A*(K[I-1]-J);
370: return(H);
371: }
372: /*
373: j_kappa. cf. Stanley.
374: */
1.2 takayama 375: static double jjk(int K[]) {
1.1 takayama 376: extern int Alpha;
377: int A,L,I,J;
378: double V;
379: A=Alpha;
380: V=1;
381: L=plength(K);
382: for (I=0; I<L; I++) {
383: for (J=0; J<K[I]; J++) {
384: V *= huk(K,I+1,J+1)*hdk(K,I+1,J+1);
385: }
386: }
387: if (Debug) {printp(K); printf("<--K, jjk=%lg\n",V);}
388: return(V);
389: }
390: /*
391: (a)_kappa^\alpha, Pochhammer symbol
392: Note that ppoch(a,[n]) = (a)_n, Alpha=2
393: */
1.2 takayama 394: static double ppoch(double A,int K[]) {
1.1 takayama 395: extern int Alpha;
396: double V;
397: int L,I,J,II,JJ;
398: V = 1;
399: L=plength(K);
400: for (I=0; I<L; I++) {
401: for (J=0; J<K[I]; J++) {
402: II = I+1; JJ = J+1;
403: V *= (A-((double)(II-1))/((double)Alpha)+JJ-1);
404: }
405: }
406: return(V);
407: }
1.2 takayama 408: static double ppoch2(double A,double B,int K[]) {
1.1 takayama 409: extern int Alpha;
410: double V;
411: int L,I,J,II,JJ;
412: V = 1;
413: L=plength(K);
414: for (I=0; I<L; I++) {
415: for (J=0; J<K[I]; J++) {
416: II = I+1; JJ = J+1;
417: V *= (A-((double)(II-1))/((double)Alpha)+JJ-1);
418: V /= (B-((double)(II-1))/((double)Alpha)+JJ-1);
419: }
420: }
421: return(V);
422: }
1.2 takayama 423: static double mypower(double x,int n) {
1.1 takayama 424: int i;
425: double v;
426: if (n < 0) return(1/mypower(x,-n));
427: v = 1;
428: for (i=0; i<n; i++) v *= x;
429: return(v);
430: }
431: /* Q_kappa
1.12 ! takayama 432: */
1.2 takayama 433: static double qk(int K[],double A[A_LEN],double B[B_LEN]) {
1.1 takayama 434: extern int Alpha;
435: int P,Q,I;
436: double V;
437: P = A_LEN;
438: Q = B_LEN;
439: V = mypower((double) Alpha,mysum(K))/jjk(K);
1.2 takayama 440: /* to reduce numerical errors, temporary. */
1.1 takayama 441: if (P == Q) {
442: for (I=0; I<P; I++) V = V*ppoch2(A[I],B[I],K);
443: }
444: return(V);
445:
446: for (I=0; I<P; I++) V = V*ppoch(A[I],K);
447: for (I=0; I<Q; I++) V = V/ppoch(B[I],K);
448: return(V);
449: }
450:
451: /*
1.12 ! takayama 452: B^nu_{kappa,mu}(i,j)
! 453: bb(N,K,M,I,J)
1.1 takayama 454: */
1.2 takayama 455: static int bb(int N[],int K[],int M[],int I,int J) {
1.1 takayama 456: int Kp[M_m_MAX]; int Mp[M_m_MAX];
457: ptrans(K,Kp);
458: ptrans(M,Mp);
459:
460: /*
1.12 ! takayama 461: printp(K); printf("K<--, "); printp2(Kp); printf("<--Kp\n");
! 462: printp(M); printf("M<--, "); printp2(Mp); printf("<--Mp\n");
1.1 takayama 463: */
464:
465: if ((plength_t(Kp) < J) || (plength_t(Mp) < J)) return(hdk(N,I,J));
466: if (Kp[J-1] == Mp[J-1]) return(huk(N,I,J));
467: else return(hdk(N,I,J));
468: }
469: /*
470: beta_{kappa,mu}
471: beta(K,M)
472: */
1.2 takayama 473: static double beta(int K[],int M[]) {
1.1 takayama 474: double V;
475: int L,I,J,II,JJ;
476: V = 1;
477:
478: L=plength(K);
479: for (I=0; I<L; I++) {
480: for (J=0; J<K[I]; J++) {
481: II = I+1; JJ = J+1;
482: V *= (double)bb(K,K,M,II,JJ);
483: /* printf("[%d,%d,%lf]\n",I,J,V); */
484: }
485: }
486:
487: L=plength(M);
488: for (I=0; I<L; I++) {
489: for (J=0; J<M[I]; J++) {
490: II = I+1; JJ = J+1;
491: V /= (double)bb(M,K,M,II,JJ);
492: /* printf("[%d,%d,%lf]\n",I,J,V);*/
493: }
494: }
495:
496: return(V);
497: }
1.10 takayama 498: static int printp(int kappa[]) {
1.1 takayama 499: int i;
500: printf("(");
501: for (i=0; i<M_n; i++) {
502: if (i <M_n-1) printf("%d,",kappa[i]);
503: else printf("%d)",kappa[i]);
504: }
505: }
1.10 takayama 506: static int printp2(int kappa[]) {
1.1 takayama 507: int i,ell;
508: printf("(");
509: ell = plength_t(kappa);
510: for (i=0; i<ell+1; i++) {
511: if (i <ell+1-1) printf("%d,",kappa[i]);
512: else printf("%d)",kappa[i]);
513: }
514: }
515:
1.10 takayama 516: static int test_beta() {
1.1 takayama 517: int kappa[M_n0]={2,1,0};
518: int mu1[M_n0]={1,0,0};
519: int mu2[M_n0]={1,1,0};
520: int mu3[M_n0]={2,0,0};
521: printp(kappa); printf(","); printp(mu3); printf(": beta = %lf\n",beta(kappa,mu3));
522: printp(kappa); printf(","); printp(mu1); printf(": beta = %lf\n",beta(kappa,mu1));
523: printp(kappa); printf(","); printp(mu2); printf(": beta = %lf\n",beta(kappa,mu2));
524: }
525:
526: /* main() { test_beta(); } */
527:
528:
529: /*
1.12 ! takayama 530: cf. w1m.rr
1.1 takayama 531: matrix hypergeometric by jack
532: N variables, up to degree M.
533: */
534: /* todo
1.12 ! takayama 535: def mhgj(A,B,N,M) {
! 536: F = 0;
! 537: P = partition_a(N,M);
! 538: for (I=0; I<length(P); I++) {
! 539: K = P[I];
! 540: F += qk(K,A,B)*jack(K,N);
! 541: }
! 542: return(F);
! 543: }
1.1 takayama 544: */
545:
546:
547: /* The quotient of (3.10) of Koev-Edelman K=kappa, M=mu, SK=k */
1.2 takayama 548: static double q3_10(int K[],int M[],int SK) {
1.1 takayama 549: extern int Alpha;
550: int Mp[M_m_MAX];
1.3 takayama 551: int ML[M_nmx];
552: int N[M_nmx];
1.1 takayama 553: int i,R;
554: double T,Q,V,Ur,Vr,Wr;
555: ptrans(M,Mp);
556: for (i=0; i<M_n; i++) {ML[i] = M[i]; N[i] = M[i];}
557: N[SK-1] = N[SK-1]-1;
558:
559: T = SK-Alpha*M[SK-1];
560: Q = T+1;
561: V = Alpha;
562: for (R=1; R<=SK; R++) {
563: Ur = Q-R+Alpha*K[R-1];
564: V *= Ur/(Ur+Alpha-1);
565: }
566: for (R=1; R<=SK-1; R++) {
567: Vr = T-R+Alpha*M[R-1];
568: V *= (Vr+Alpha)/Vr;
569: }
570: for (R=1; R<=M[SK-1]-1; R++) {
571: Wr = Mp[R-1]-T-Alpha*R;
572: V *= (Wr+Alpha)/Wr;
573: }
574: return(V);
575: }
576:
1.2 takayama 577: static double q3_5(double A[],double B[],int K[],int I) {
1.1 takayama 578: extern int Alpha;
579: int Kp[M_m_MAX];
580: double C,D,V,Ej,Fj,Gj,Hj,Lj;
581: int J,P,Q;
582: ptrans(K,Kp);
583: P=A_LEN;; Q = B_LEN;
584: C = -((double)(I-1))/Alpha+K[I-1]-1;
585: D = K[I-1]*Alpha-I;
586:
587: V=1;
588:
589: for (J=1; J<=P; J++) {
1.12 ! takayama 590: V *= (A[J-1]+C);
1.1 takayama 591: }
592: for (J=1; J<=Q; J++) {
1.12 ! takayama 593: V /= (B[J-1]+C);
1.1 takayama 594: }
595:
596: for (J=1; J<=K[I-1]-1; J++) {
1.12 ! takayama 597: Ej = D-J*Alpha+Kp[J-1];
! 598: Gj = Ej+1;
! 599: V *= (Gj-Alpha)*Ej/(Gj*(Ej+Alpha));
1.1 takayama 600: }
601: for (J=1; J<=I-1; J++) {
1.12 ! takayama 602: Fj=K[J-1]*Alpha-J-D;
! 603: Hj=Fj+Alpha;
! 604: Lj=Hj*Fj;
! 605: V *= (Lj-Fj)/(Lj+Hj);
1.1 takayama 606: }
607: return(V);
608: }
609:
1.2 takayama 610: static void mtest4() {
1.1 takayama 611: double A[A_LEN] = {1.5};
612: double B[B_LEN]={6.5};
613: int K[M_n0] = {3,2,0};
614: int I=2;
615: int Ki[M_n0]={3,1,0};
616: double V1,V2;
617: V1=q3_5(A,B,K,I);
618: V2=qk(K,A,B)/qk(Ki,A,B);
619: printf("%lf== %lf?\n",V1,V2);
620: }
1.2 takayama 621: static void mtest4b() {
1.1 takayama 622: int K[M_n0]={3,2,0};
623: int M[M_n0]={2,1,0};
624: int N[M_n0]={2,0};
625: int SK=2;
626: double V1,V2;
627: V1=q3_10(K,M,SK);
628: V2=beta(K,N)/beta(K,M);
629: printf("%lf== %lf?\n",V1,V2);
630: }
631:
632: /* main() { mtest4(); mtest4b(); } */
633:
634: /* nk in (4.1),
1.12 ! takayama 635: */
1.2 takayama 636: static int nk(int KK[]) {
1.1 takayama 637: extern int *Darray;
638: int N,I,Ki;
1.3 takayama 639: int Kpp[M_nmx];
1.1 takayama 640: int i;
641: N = plength(KK);
642: if (N == 0) return(0);
643: if (N == 1) return(KK[0]);
644: for (i=0; i<M_n; i++) Kpp[i] = 0;
645: for (I=0; I<N-1; I++) Kpp[I] = KK[I];
646: Ki = KK[N-1];
647: /* K = (Kpp,Ki) */
648: return(Darray[nk(Kpp)]+Ki-1);
649: }
1.2 takayama 650: static int plength2(int P1[],int P2[]) {
1.1 takayama 651: int S1,S2;
652: S1 = plength(P1); S2 = plength(P2);
653: if (S1 > S2) return(1);
654: else if (S1 == S2) {
655: S1=mysum(P1); S2=mysum(P2);
656: if(S1 > S2) return(1);
657: else if (S1 == S2) return(0);
658: else return(-1);
659: }
660: else return(-1);
661: }
1.2 takayama 662: static int myeq(int P1[],int P2[]) {
1.1 takayama 663: int I,L1;
664: if ((L1=plength(P1)) != plength(P2)) return(0);
665: for (I=0; I<L1; I++) {
666: if (P1[I] != P2[I]) return(0);
667: }
668: return(1);
669: }
670: /*
671: M is a degree, N is a number of variables
672: genDarray(3,3);
673: N(0)=0;
674: N(1)=1;
675: N(2)=2;
676: N(3)=3;
677: N(1,1)=4; D[1] = 4
678: N(2,1)=5; D[2] = 5;
679: N(1,1,1)=6; D[4] = 6;
680: still buggy.
681: */
682:
1.2 takayama 683: static int pListPartition(int M,int N) {
1.1 takayama 684: extern int M_m;
685: extern int M_kap[];
686: int I;
687: /* initialize */
688: if (M_n != N) {
1.3 takayama 689: fprintf(stderr,"M_n != N\n"); mh_exit(-1);
1.1 takayama 690: }
691: M_m = M;
692: /* M_plist = []; */
693: /* end of initialize */
694: (*M_pExec)(); /* exec for 0 */
695: for (I=1; I<=M_n; I++) {
696: pListPartition2(M_m,1,I,M_m);
697: }
698: /* M_plist = reverse(M_plist); */
699: return(1);
700: }
701:
702: /*
703: Enumerate all such that
704: Less >= M_kap[From], ..., M_kap[To], |(M_kap[From],...,M_kap[To])|<=M,
705: */
1.2 takayama 706: static int pListPartition2(int Less,int From,int To, int M) {
1.1 takayama 707: int I,R;
1.11 takayama 708: mh_check_intr(100);
1.1 takayama 709: if (To < From) {
1.12 ! takayama 710: (*M_pExec)(); return(0);
1.1 takayama 711: }
712: for (I=1; (I<=Less) && (I<=M) ; I++) {
713: M_kap[From-1] = I;
714: R = pListPartition2(I,From+1,To,M-I);
715: }
716: return(1);
717: }
718:
719: /*
720: partition に対してやる仕事をこちらへ書く.
721: */
1.2 takayama 722: static void pExec_0() {
1.1 takayama 723: if (Debug) {
1.12 ! takayama 724: printf("M_kap=");
! 725: printp(M_kap);
! 726: printf("\n");
1.1 takayama 727: }
728: }
729:
730: /* Test.
1.12 ! takayama 731: Compare pListPartition(4,3); genDarray(4,3);
! 732: Compare pListPartition(5,3); genDarray(5,3);
1.1 takayama 733:
734: */
735:
736: /*
1.12 ! takayama 737: main() {
1.1 takayama 738: M_pExec = pExec_0;
739: pListPartition(5,3);
1.12 ! takayama 740: }
1.1 takayama 741: */
742:
743:
744: /*
745: List all horizontal strips.
746: Kap[0] is not a dummy in C code. !(Start from Kap[1].)
747: */
1.2 takayama 748: static int pListHS(int Kap[],int N) {
1.1 takayama 749: extern int HS_n;
750: extern int HS_mu[];
751: int i;
752: HS_n = N;
753: /* Clear HS_mu. Do not forget when N < M_n */
754: for (i=0; i<M_n; i++) HS_mu[i] = 0;
755: pListHS2(1,N,Kap);
756: }
757:
1.2 takayama 758: static int pListHS2(int From,int To,int Kap[]) {
1.1 takayama 759: int More,I;
760: if (To <From) {(*HS_hsExec)(); return(0);}
761: if (From == HS_n) More=0; else More=Kap[From];
762: for (I=Kap[From-1]; I>= More; I--) {
763: HS_mu[From-1] = I;
764: pListHS2(From+1,To,Kap);
765: }
766: return(1);
767: }
768:
1.2 takayama 769: static void hsExec_0() {
1.1 takayama 770: int i;
771: if(Debug) {printf("hsExec: "); printp(HS_mu); printf("\n");}
772: }
773:
774: /*
775: pListHS([0,4,2,1],3);
776: */
777: /*
1.12 ! takayama 778: main() {
1.1 takayama 779: int Kap[3]={4,2,1};
780: HS_hsExec = hsExec_0;
781: pListHS(Kap,3);
1.12 ! takayama 782: }
1.1 takayama 783: */
784:
785: /* The number of partitions <= M, with N parts.
1.12 ! takayama 786: (0,0,...,0) is excluded.
1.1 takayama 787: */
788: #define aP_pki(i,j) P_pki[(i)*(M+1)+(j)]
1.2 takayama 789: static int pmn(int M,int N) {
1.1 takayama 790: int Min_m_n,I,K,S,T,i,j;
791: extern int P_pmn;
792: extern int *P_pki;
793: Min_m_n = (M>N?N:M);
794: /* P_pki=newmat(Min_m_n+1,M+1); */
795: P_pki = (int *) mymalloc(sizeof(int)*(Min_m_n+1)*(M+1));
796: for (i=0; i<Min_m_n+1; i++) for (j=0; j<M+1; j++) aP_pki(i,j) = 0;
797: for (I=1; I<=M; I++) aP_pki(1,I) = 1;
798: for (K=1; K<=Min_m_n; K++) aP_pki(K,0) = 0;
799: S = M;
800: for (K=2; K<=Min_m_n; K++) {
801: for (I=1; I<=M; I++) {
802: if (I-K < 0) T=0; else T=aP_pki(K,I-K);
803: aP_pki(K,I) = aP_pki(K-1,I-1)+T;
804: S += aP_pki(K,I);
805: }
806: }
807: P_pmn=S;
808: if (Debug) {
809: printf("P_pmn=%d\n",P_pmn);
810: for (i=0; i<=Min_m_n; i++) {
811: for (j=0; j<=M; j++) printf("%d,",aP_pki(i,j));
812: printf("\n");
813: }
814: }
815: myfree(P_pki); P_pki=NULL;
816: return(S);
817: }
818:
819: /*
1.12 ! takayama 820: main() {pmn(4,3); printf("P_pmn=%d\n",P_pmn);}
1.1 takayama 821: */
822:
1.2 takayama 823: static int *cloneP(int a[]) {
1.1 takayama 824: int *p;
825: int i;
826: p = (int *) mymalloc(sizeof(int)*M_n);
827: for (i=0; i<M_n; i++) p[i] = a[i];
828: return(p);
829: }
1.10 takayama 830: static int copyP(int p[],int a[]) {
1.1 takayama 831: int i;
832: for (i=0; i<M_n; i++) p[i] = a[i];
833: }
834:
1.2 takayama 835: static void pExec_darray(void) {
1.1 takayama 836: extern int DR_parray;
837: extern int M_kap[];
838: extern int **Parray;
839: extern int *ParraySize;
840: int *K;
841: pExec_0();
842: K = cloneP(M_kap);
843: Parray[DR_parray] = K;
844: ParraySize[DR_parray] = mysum(K);
845: DR_parray++;
846: }
1.10 takayama 847: static int genDarray2(int M,int N) {
1.1 takayama 848: extern int *Darray;
849: extern int **Parray;
850: extern int DR_parray;
851: extern int M_m;
852: int Pmn,I,J,Ksize,i;
853: int **L;
854: int *Nk;
855: int *K;
1.3 takayama 856: int Kone[M_nmx];
1.1 takayama 857:
858: M_m = M;
859: Pmn = pmn(M,N)+1;
860: if (Debug) printf("Degree M = %d, N of vars N = %d, Pmn+1=%d\n",M,N,Pmn);
861: Darray=(int *) mymalloc(sizeof(int)*Pmn);
862: for (i=0; i<Pmn; i++) Darray[i] = 0;
863: Parray=(int **) mymalloc(sizeof(int *)*Pmn);
864: for (i=0; i<Pmn; i++) Parray[i] = NULL;
865: ParraySize=(int *) mymalloc(sizeof(int *)*Pmn);
866: for (i=0; i<Pmn; i++) ParraySize[i] = 0;
867: DR_parray=0;
868: M_pExec = pExec_darray;
869: pListPartition(M,N); /* pExec_darray() is executed for all partitions */
870: L = Parray;
871:
872: Nk = (int *) mymalloc(sizeof(int)*(Pmn+1));
873: for (I=0; I<Pmn; I++) Nk[I] = I;
874: for (I=0; I<Pmn; I++) {
1.11 takayama 875: mh_check_intr(100);
1.12 ! takayama 876: K = L[I]; /* N_K = I; D[N_K] = N_(K,1) */
! 877: Ksize = plength(K);
! 878: if (Ksize >= M_n) {
! 879: if (Debug) {fprintf(stderr,"Ksize >= M_n\n");}
! 880: continue;
! 881: }
! 882: for (i=0; i<M_n; i++) Kone[i] = 0;
! 883: for(J=0; J<Ksize; J++) Kone[J]=K[J]; Kone[Ksize] = 1;
! 884: for (J=0; J<Pmn; J++) {
! 885: if (myeq(L[J],Kone)) Darray[I] = J; /* J is the next of I */
! 886: }
1.1 takayama 887: }
888: if (Debug) {
1.12 ! takayama 889: printf("Darray=\n");
! 890: for (i=0; i<Pmn; i++) printf("%d\n",Darray[i]);
! 891: printf("-----------\n");
1.1 takayama 892: }
893: }
894:
895:
896: /* main() { genDarray2(4,3);} */
897:
898: /* M_beta_0[*] value of beta_{kappa,mu}, M_beta_1[*] N_mu */
1.10 takayama 899: static int isHStrip(int Kap[],int Nu[]) {
1.1 takayama 900: int N1,N2,I,P;
901: N1 = plength(Kap); N2 = plength(Nu);
902: if (N2 > N1) return(0);
903: for (I=0; I<N2; I++) {
904: if (I >= N1-1) P = 0; else P=Kap[I+1];
905: if (Kap[I] < Nu[I]) return(0);
906: if (Nu[I] < P) return(0);
907: }
908: return(1);
909: }
910:
1.2 takayama 911: static void hsExec_beta(void) {
1.1 takayama 912: int *Mu;
913: int N,Nmu,Nnu,Done,J,K,OK,I,RR;
914: int Kapt[M_m_MAX];
915: int Nut[M_m_MAX];
1.3 takayama 916: int Nu[M_nmx];
1.1 takayama 917: int rrMax;
918: hsExec_0();
919: /* printf("M_beta_pt=%a\n",M_beta_pt); */
920: /* Mu = cdr(vtol(HS_mu)); */
921: Mu = HS_mu; /* buggy? need cloneP */
922: if (M_beta_pt == 0) {
923: M_beta_0[0] = 1; M_beta_1[0] = nk(Mu);
924: M_beta_pt++; return;
925: }
926:
927: N = HS_n;
928: Nmu = nk(Mu);
929: M_beta_1[M_beta_pt] = Nmu;
930: ptrans(M_beta_kap,Kapt);
931: /* Mu, Nu is exchanged in this code. cf. the K-E paper */
932: copyP(Nu,Mu); /* buggy need clone? */
933: for (I=0; I<N; I++) {
934: Nu[I]++;
935: if (!isHStrip(M_beta_kap,Nu)) {Nu[I]--; continue;}
936: Nnu = nk(Nu);
937: ptrans(Nu,Nut);
938: Done=0;
939: for (J=M_beta_pt-1; J>=0; J--) {
940: if (M_beta_1[J] == Nnu) {
1.12 ! takayama 941: K=I+1;
! 942: if (Debug) {
! 943: printf("Found at J=%d, K=%d, q3_10(Kap,Nu,K)=%lf,Nu,Mu= \n",
! 944: J,K,q3_10(M_beta_kap,Nu,K));
! 945: printp(Nu); printf("\n");
! 946: printp(Mu); printf("\n");
! 947: }
! 948: /* Check other conditions. See Numata's mail on Dec 24, 2011. */
! 949: rrMax = Nu[I]-1;
! 950: if ((plength_t(Kapt) < rrMax) || (plength_t(Nut) < rrMax)) {
! 951: if (Debug) printf(" is not taken (length). \n");
! 952: break;
! 953: }
! 954: OK=1;
! 955: for (RR=0; RR<rrMax; RR++) {
! 956: if (Kapt[RR] != Nut[RR]) { OK=0; break;}
! 957: }
! 958: if (!OK) { if (Debug) printf(" is not taken.\n"); break; }
! 959: /* check done. */
! 960: M_beta_0[M_beta_pt]=M_beta_0[J]*q3_10(M_beta_kap,Nu,K);
! 961: Done = 1; break;
1.1 takayama 962: }
963: }
964: if (Done) break; else Nu[I]--;
965: }
966: if (!Done) {
967: if (Debug) printf("BUG: not found M_beta_pt=%d.\n",M_beta_pt);
968: /* M_beta_0[M_beta_pt] = NAN; /* error("Not found."); */
969: M_beta_0[M_beta_pt] = beta(M_beta_kap,Mu);
970: }
971: /* Fix the bug of mh.rr */
972: M_beta_pt++;
973: }
1.10 takayama 974: static int genBeta(int Kap[]) {
1.1 takayama 975: extern double *M_beta_0;
976: extern int *M_beta_1;
977: extern int M_beta_pt;
978: extern int M_beta_kap[];
979: extern int P_pmn;
980: int I,J,N;
981: if (Debug) {printp(Kap); printf("<-Kappa, P_pmn=%d\n",P_pmn);}
982: /* M_beta = newmat(2,P_pmn+1); */
983: M_beta_0 = (double *)mymalloc(sizeof(double)*(P_pmn+1));
1.8 takayama 984: M_beta_1 = (int *)mymalloc(sizeof(int)*(P_pmn+1));
1.1 takayama 985: M_beta_pt = 0;
986: for (I=0; I<=P_pmn; I++) {M_beta_0[I] = NAN; M_beta_1[I] = -1;}
987: N = plength(Kap);
988: HS_hsExec = hsExec_beta;
989: copyP(M_beta_kap,Kap);
990: pListHS(Kap,N);
991: }
992: /*
993: genDarray2(4,3);
994: genBeta([2,2,0]);
995: genBeta([2,1,1]);
996: */
997:
1.10 takayama 998: static int checkBeta1() {
1.1 takayama 999: int Kap[3] = {2,2,0};
1000: int Kap2[3] = {2,1,0};
1001: int I;
1002: int *Mu;
1003: double Beta_km;
1004: genDarray2(4,3);
1005: genBeta(Kap);
1006: for (I=0; I<M_beta_pt; I++) {
1007: Mu = Parray[M_beta_1[I]];
1008: Beta_km = M_beta_0[I];
1.12 ! takayama 1009: if (Debug) {
! 1010: printp(Kap); printf("<--Kap, ");
! 1011: printp(Mu); printf("<--Mu,");
! 1012: printf("Beta_km(by table)=%lf, beta(Kap,Mu)=%lf\n",Beta_km,beta(Kap,Mu));
! 1013: }
1.1 takayama 1014: }
1015: if (Debug) printf("-------------------------------------\n");
1016: genBeta(Kap2);
1017: for (I=0; I<M_beta_pt; I++) {
1018: Mu = Parray[M_beta_1[I]];
1019: Beta_km = M_beta_0[I];
1.12 ! takayama 1020: if (Debug) {
! 1021: printp(Kap2); printf("<--Kap, ");
! 1022: printp(Mu); printf("<--Mu,");
! 1023: printf("Beta_km(by table)=%lf, beta(Kap,Mu)=%lf\n",Beta_km,beta(Kap2,Mu));
! 1024: }
1.1 takayama 1025: }
1026: }
1027:
1028: /*
1.12 ! takayama 1029: def checkBeta2() {
1.1 takayama 1030: genDarray2(3,3);
1031: Kap = [2,1,0];
1032: printf("Kap=%a\n",Kap);
1033: genBeta(Kap);
1034: for (I=0; I<M_beta_pt; I++) {
1.12 ! takayama 1035: Mu = Parray[M_beta[1][I]];
! 1036: Beta_km = M_beta[0][I];
! 1037: printf("Mu=%a,",Mu);
! 1038: printf("Beta_km(by table)=%a, beta(Kap,Mu)=%a\n",Beta_km,beta(Kap,Mu));
! 1039: }
1.1 takayama 1040: }
1041: */
1042:
1043: /* main() { checkBeta1(); } */
1044:
1.2 takayama 1045: static int psublen(int Kap[],int Mu[]) {
1.1 takayama 1046: int L1,L2,A,I;
1047: L1 = plength(Kap);
1048: L2 = plength(Mu);
1049: if (L2 > L1) myerror("psub, length mismatches.");
1050: A = 0;
1051: for (I=0; I<L2; I++) {
1052: if (Kap[I] < Mu[I]) myerror("psub, not Kap >= Mu");
1053: A += Kap[I]-Mu[I];
1054: }
1055: for (I=L2; I<L1; I++) A += Kap[I];
1056: return(A);
1057: }
1058:
1059:
1060: /* Table of Jack polynomials
1.12 ! takayama 1061: Jack[1]* one variable.
! 1062: Jack[2]* two variables.
1.1 takayama 1063: ...
1.12 ! takayama 1064: Jack[M_n]* n variables.
! 1065: Jack[P][J]*
! 1066: D^J(P variables jack of p variables). Example. J=001 d_1, 010 d_2, 100 d_3
! 1067: 0<=J<=2^{M_n}-1
! 1068: Jack[P][J][nk(Kappa)] Jack_Kappa, Kappa is a partition.
! 1069: 0<=nk(Kappa)<=pmn(M_m,M_n)
1.1 takayama 1070: */
1071:
1072: #define aM_jack(i,j,k) ((M_jack[i])[(j)*(Pmn+1)+(k)])
1.10 takayama 1073: static int genJack(int M,int N) {
1.1 takayama 1074: extern double **M_jack;
1075: extern int M_2n;
1076: extern int P_pmn;
1077: extern int *M_beta_1;
1078: int Pmn,I,J,K,L,Nv,H,P;
1079: int *Kap,*Mu;
1080: double Jack,Beta_km;
1081: int Nk,JJ;
1.5 takayama 1082: if (Debug) printf("genJack(%d,%d)\n",M,N);
1.3 takayama 1083: M_jack = (double **) mymalloc(sizeof(double *)*(N+2));
1.1 takayama 1084: M_2n = imypower(2,N);
1085: Pmn = pmn(M,N); /*P_pmn is initializeded.
1086: Warning. It is reset when pmn is called.*/
1087: for (I=0; I<=N; I++) M_jack[I] = (double *)mymalloc(sizeof(double)*(M_2n*(Pmn+1))); /* newmat(M_2n,Pmn+1); */
1.3 takayama 1088: M_jack[N+1] = NULL;
1.1 takayama 1089: genDarray2(M,N); /* Darray, Parray is initialized */
1090: for (I=1; I<=N; I++) aM_jack(I,0,0) = 1;
1091: if (M_df) {
1092: for (I=1; I<=N; I++) {
1093: for (J=1; J<M_2n; J++) aM_jack(I,J,0) = 0;
1094: }
1095: }
1096:
1.3 takayama 1097: /* N must satisfies N > 0 */
1.1 takayama 1098: for (K=1; K<=M; K++) {
1099: aM_jack(1,0,K) = jack1(K);
1100: if (M_df) {
1101: aM_jack(1,1,K) = jack1diff(K); /* diff(jack([K],1),x_1); */
1102: for (J=2; J<M_2n; J++) aM_jack(1,J,K) = 0;
1103: }
1104: }
1105: for (I=1; I<=N; I++) {
1106: for (K=M+1; K<Pmn+1; K++) {
1107: aM_jack(I,0,K) = NAN;
1108: if (M_df) {
1109: for (J=1; J<M_2n; J++) {
1110: if (J >= 2^I) aM_jack(I,J,K) = 0;
1.12 ! takayama 1111: else aM_jack(I,J,K) = NAN;
1.1 takayama 1112: }
1113: }
1114: }
1115: }
1116:
1117: /* Start to evaluate the entries of the table */
1118: for (K=1; K<=Pmn; K++) {
1119: Kap = Parray[K]; /* bug. need copy? */
1120: L = plength(Kap);
1121: for (I=1; I<=L-1; I++) {
1122: aM_jack(I,0,K) = 0;
1123: if (M_df) {
1124: for (J=1; J<M_2n; J++) aM_jack(I,J,K) = 0;
1125: }
1126: }
1127: if (Debug) {printf("Kappa="); printp(Kap);}
1128: /* Enumerate horizontal strip of Kappa */
1129: genBeta(Kap); /* M_beta_pt stores the number of hs */
1130: /* Nv is the number of variables */
1131: for (Nv = (L==1?2:L); Nv <= N; Nv++) {
1132: Jack = 0;
1133: for (H=0; H<M_beta_pt; H++) {
1134: Nk = M_beta_1[H];
1135: Mu = Parray[Nk];
1.12 ! takayama 1136: if (UseTable) {
! 1137: Beta_km = M_beta_0[H];
! 1138: }else{
! 1139: Beta_km = beta(Kap,Mu);
! 1140: /* do not use the M_beta table. It's buggy. UseTable is experimental.*/
! 1141: }
1.1 takayama 1142: if (Debug) {printf("Nv(number of variables)=%d, Beta_km=%lf, Mu=",Nv,Beta_km);
1.12 ! takayama 1143: printp(Mu); printf("\n");}
1.1 takayama 1144: P = psublen(Kap,Mu);
1145: Jack += aM_jack(Nv-1,0,Nk)*Beta_km*xval(Nv,P); /* util_v(x,[Nv])^P;*/
1.12 ! takayama 1146: if (Debug) printf("xval(%d,%d)=%lf\n",Nv,P,xval(Nv,P));
1.1 takayama 1147: }
1148: aM_jack(Nv,0,K) = Jack;
1149: if (M_df) {
1150: /* The case of M_df > 0. */
1151: for (J=1; J<M_2n; J++) {
1.12 ! takayama 1152: mh_check_intr(100);
! 1153: Jack = 0;
! 1154: for (H=0; H<M_beta_pt; H++) {
! 1155: Nk = M_beta_1[H];
! 1156: Mu = Parray[Nk];
! 1157: if (UseTable) {
! 1158: Beta_km = M_beta_0[H];
! 1159: }else{
! 1160: Beta_km = beta(Kap,Mu); /* do not use the M_beta table. It's buggy. */
! 1161: }
! 1162: if (Debug) {printf("M_df: Nv(number of variables)=%d, Beta_km=%lf, Mu= ",Nv,Beta_km);
! 1163: printp(Mu); printf("\n"); }
! 1164: P = psublen(Kap,Mu);
! 1165: if (J & (1 << (Nv-1))) {
! 1166: JJ = J & ((1 << (Nv-1)) ^ 0xffff); /* NOTE!! Up to 16 bits. mh-15 */
! 1167: if (P != 0) {
! 1168: Jack += aM_jack(Nv-1,JJ,Nk)*Beta_km*P*xval(Nv,P-1);
! 1169: }
! 1170: }else{
! 1171: Jack += aM_jack(Nv-1,J,Nk)*Beta_km*xval(Nv,P);
! 1172: }
! 1173: }
! 1174: aM_jack(Nv,J,K) = Jack;
! 1175: if (Debug) printf("aM_jack(%d,%d,%d) = %lf\n",Nv,J,K,Jack);
1.1 takayama 1176: } /* end of J loop */
1177: }
1178: }
1179: }
1180: }
1181:
1182:
1183: /* checkJack1(3,3)
1.12 ! takayama 1184: */
1.10 takayama 1185: static int checkJack1(int M,int N) {
1.1 takayama 1186: int I,K;
1187: extern int P_pmn;
1188: extern double M_x[];
1189: int Pmn; /* used in aM_jack */
1190: /* initialize x vars. */
1191: for (I=1; I<=N; I++) {
1192: M_x[I-1] = ((double)I)/10.0;
1193: }
1194: genJack(M,N);
1195: Pmn = P_pmn;
1196: for (I=1; I<=N; I++) {
1197: for (K=0; K<=P_pmn; K++) {
1198: printp(Parray[K]);
1199: printf("<--Kap, Nv=%d, TableJack=%lf\n",I,aM_jack(I,0,K));
1200: }
1201: }
1202: for (I=1; I<=N; I++) printf("%lf, ",M_x[I-1]);
1203: printf("<--x\n");
1204: }
1205: /*main() { checkJack1(3,3); }*/
1206:
1207:
1.10 takayama 1208: static int checkJack2(int M,int N) {
1.1 takayama 1209: int I,K,J;
1210: extern int P_pmn;
1211: extern double M_x[];
1.10 takayama 1212: extern int M_df;
1.1 takayama 1213: int Pmn; /* used in aM_jack */
1214: M_df=1;
1215: /* initialize x vars. */
1216: for (I=1; I<=N; I++) {
1217: M_x[I-1] = ((double)I)/10.0;
1218: }
1219: genJack(M,N);
1220: Pmn = P_pmn;
1221: for (I=1; I<=N; I++) {
1222: for (K=0; K<=P_pmn; K++) {
1223: printp(Parray[K]);
1224: printf("<--Kap, Nv=%d, TableJack=%lf\n",I,aM_jack(I,0,K));
1225: }
1226: }
1227: for (I=1; I<=N; I++) printf("%lf, ",M_x[I-1]);
1228: printf("<--x\n");
1229:
1230: for (I=1; I<=N; I++) {
1231: for (K=0; K<=P_pmn; K++) {
1232: for (J=0; J<M_2n; J++) {
1.12 ! takayama 1233: printp(Parray[K]);
! 1234: printf("<--Kap, Nv=%d,J(diff)=%d, D^J Jack=%lf\n",
! 1235: I,J,aM_jack(I,J,K));
! 1236: }
! 1237: }
1.1 takayama 1238: }
1239: }
1240:
1241: /* main() { checkJack2(3,3); } */
1242:
1243: double mh_t(double A[A_LEN],double B[B_LEN],int N,int M) {
1244: double F,F2;
1245: extern int M_df;
1246: extern int P_pmn;
1247: extern double *M_qk;
1248: extern double M_rel_error;
1249: int Pmn;
1250: int K;
1251: int *Kap;
1252: int size;
1253: F = 0; F2=0;
1254: M_df=1;
1255: genJack(M,N);
1.8 takayama 1256: M_qk = (double *)mymalloc(sizeof(double)*(P_pmn+1)); /* found a bug. */
1.1 takayama 1257: Pmn = P_pmn;
1258: size = ParraySize[P_pmn];
1259: for (K=0; K<=P_pmn; K++) {
1.11 takayama 1260: mh_check_intr(100);
1.12 ! takayama 1261: Kap = Parray[K];
! 1262: M_qk[K] = qk(Kap,A,B);
! 1263: F += M_qk[K]*aM_jack(N,0,K);
! 1264: if (ParraySize[K] < size) F2 += M_qk[K]*aM_jack(N,0,K);
! 1265: if (Debug) printf("ParraySize[K] = %d, size=%d\n",ParraySize[K],size);
! 1266: if (Debug && (ParraySize[K] == size)) printf("M_qk[K]=%lg, aM_jack=%lg\n",M_qk[K],aM_jack(N,0,K));
1.1 takayama 1267: }
1268: M_rel_error = F-F2;
1269: return(F);
1270: }
1271: double mh_t2(int J) {
1272: extern double *M_qk;
1273: double F;
1274: int K;
1275: int Pmn;
1276: extern int P_pmn;
1.3 takayama 1277: if (M_qk == NULL) {myerror("Call mh_t first."); mh_exit(-1); }
1.1 takayama 1278: F = 0;
1279: Pmn = P_pmn;
1280: for (K=0; K<P_pmn; K++) {
1.12 ! takayama 1281: F += M_qk[K]*aM_jack(M_n,J,K);
1.1 takayama 1282: }
1283: return(F);
1284: }
1285:
1.10 takayama 1286: static int mtest1b() {
1.1 takayama 1287: double A[1] = {1.5};
1288: double B[1] = {1.5+5};
1289: int I,N,M,J;
1290: double F;
1291: N=3; M=6;
1292: for (I=1; I<=N; I++) {
1293: M_x[I-1] = ((double)I)/10.0;
1294: }
1295: mh_t(A,B,N,M);
1296: for (J=0; J<M_2n; J++) {
1.12 ! takayama 1297: F=mh_t2(J);
! 1298: printf("J=%d, D^J mh_t=%lf\n",J,F);
1.1 takayama 1299: }
1300: }
1301:
1302: /* main() { mtest1b(); }*/
1303:
1304:
1305:
1306:
1307: #define TEST 1
1308: #ifndef TEST
1309:
1310: #endif
1311:
1312: /****** from mh-n.c *****/
1313:
1314: #define SMAX 4096
1.3 takayama 1315: #define inci(i) { i++; if (i >= argc) { fprintf(stderr,"Option argument is not given.\n"); return(NULL); }}
1.1 takayama 1316:
1.2 takayama 1317: static int imypower(int x,int n) {
1.1 takayama 1318: int i;
1319: int v;
1.3 takayama 1320: if (n < 0) {myerror("imypower"); mh_exit(-1);}
1.1 takayama 1321: v = 1;
1322: for (i=0; i<n; i++) v *= x;
1323: return(v);
1324: }
1325:
1.11 takayama 1326: #ifdef STANDALONE2
1.1 takayama 1327: main(int argc,char *argv[]) {
1.3 takayama 1328: mh_exit(MH_RESET_EXIT);
1.12 ! takayama 1329: /* jk_main(argc,argv);
! 1330: printf("second run.\n"); */
1.2 takayama 1331: jk_main(argc,argv);
1332: }
1.3 takayama 1333: #endif
1334:
1335: struct MH_RESULT *jk_main(int argc,char *argv[]) {
1.1 takayama 1336: double *y0;
1337: double x0,xn;
1338: double ef;
1339: int i,j,rank;
1340: double a[1]; double b[1];
1341: extern double M_x[];
1342: extern double *Beta;
1343: extern int M_2n;
1.3 takayama 1344: char swork[1024];
1345: struct MH_RESULT *ans=NULL;
1346: struct SFILE *ofp = NULL;
1347: int idata=0;
1348: JK_byFile = 1;
1349: jk_initializeWorkArea();
1.1 takayama 1350: UseTable = 1;
1.3 takayama 1351: Mapprox=6;
1.1 takayama 1352: for (i=1; i<argc; i++) {
1.12 ! takayama 1353: if (strcmp(argv[i],"--idata")==0) {
! 1354: inci(i);
! 1355: setParam(argv[i]); idata=1;
! 1356: }else if (strcmp(argv[i],"--degree")==0) {
! 1357: inci(i);
! 1358: sscanf(argv[i],"%d",&Mapprox);
! 1359: }else if (strcmp(argv[i],"--x0")==0) {
! 1360: inci(i);
! 1361: sscanf(argv[i],"%lg",&X0g);
! 1362: }else if (strcmp(argv[i],"--notable")==0) {
! 1363: UseTable = 0;
! 1364: }else if (strcmp(argv[i],"--debug")==0) {
! 1365: Debug = 1;
! 1366: }else if (strcmp(argv[i],"--help")==0) {
! 1367: usage(); return(0);
! 1368: }else if (strcmp(argv[i],"--bystring")==0) {
! 1369: if (idata) {fprintf(stderr,"--bystring must come before --idata option.\n"); mh_exit(-1);}
! 1370: JK_byFile = 0;
! 1371: }else {
! 1372: fprintf(stderr,"Unknown option %s\n",argv[i]);
! 1373: usage();
! 1374: return(NULL);
! 1375: }
1.1 takayama 1376: }
1.3 takayama 1377: if (!idata) setParam(NULL);
1378:
1379: /* Initialize global variables */
1380: M_n = Mg;
1381: HS_n=M_n;
1382: if (!JK_byFile) ans = (struct MH_RESULT *)mymalloc(sizeof(struct MH_RESULT));
1383: else ans = NULL;
1384: /* Output by a file=stdout */
1385: ofp = mh_fopen("stdout","w",JK_byFile);
1.1 takayama 1386:
1.3 takayama 1387: sprintf(swork,"%%%%Use --help option to see the help.\n"); mh_fputs(swork,ofp);
1388: sprintf(swork,"%%%%Mapprox=%d\n",Mapprox); mh_fputs(swork,ofp);
1.1 takayama 1389: if (M_n != Mg) {
1.12 ! takayama 1390: myerror("Mg must be equal to M_n\n"); mh_exit(-1);
1.1 takayama 1391: }
1.8 takayama 1392: if (Debug) showParam(NULL,1);
1.1 takayama 1393: for (i=0; i<M_n; i++) {
1.12 ! takayama 1394: M_x[i] = Beta[i]*X0g;
1.1 takayama 1395: }
1396: a[0] = ((double)Mg+1.0)/2.0;
1397: b[0] = ((double)Mg+1.0)/2.0 + ((double) (*Ng))/2.0; /* bug, double check */
1398: if (Debug) printf("Calling mh_t with ([%lf],[%lf],%d,%d)\n",a[0],b[0],M_n,Mapprox);
1399: mh_t(a,b,M_n,Mapprox);
1400: if (imypower(2,M_n) != M_2n) {
1.12 ! takayama 1401: sprintf(swork,"M_n=%d,M_2n=%d\n",M_n,M_2n); mh_fputs(swork,ofp);
! 1402: myerror("2^M_n != M_2n\n"); mh_exit(-1);
1.1 takayama 1403: }
1.3 takayama 1404: sprintf(swork,"%%%%M_rel_error=%lg\n",M_rel_error); mh_fputs(swork,ofp);
1.1 takayama 1405: for (j=0; j<M_2n; j++) {
1.12 ! takayama 1406: Iv[j] = mh_t2(j);
1.1 takayama 1407: }
1408: Ef = iv_factor();
1.8 takayama 1409: showParam(ofp,0);
1.3 takayama 1410:
1411: /* return the result */
1412: if (!JK_byFile) {
1.12 ! takayama 1413: ans->x = X0g;
! 1414: ans->rank = imypower(2,Mg);
! 1415: ans->y = (double *)mymalloc(sizeof(double)*(ans->rank));
! 1416: for (i=0; i<ans->rank; i++) (ans->y)[i] = Iv[i];
! 1417: ans->size=1;
! 1418: ans->sfpp = (struct SFILE **)mymalloc(sizeof(struct SFILE *)*(ans->size));
! 1419: (ans->sfpp)[0] = ofp;
1.3 takayama 1420: }
1.7 takayama 1421: if (Debug) printf("jk_freeWorkArea() starts\n");
1.3 takayama 1422: jk_freeWorkArea();
1.7 takayama 1423: if (Debug) printf("jk_freeWorkArea() has finished.\n");
1.3 takayama 1424: return(ans);
1.1 takayama 1425: }
1426:
1.10 takayama 1427: static int usage() {
1.1 takayama 1428: fprintf(stderr,"Usages:\n");
1429: fprintf(stderr,"mh-m [--idata input_data_file --x0 x0 --degree approxm]\n");
1430: 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");
1431: fprintf(stderr,"The mh-m uses the Koev-Edelman algorithm to evalute the matrix hypergeometric function.\n");
1432: fprintf(stderr,"The degree of the approximation (Mapprox) is given by the --degree option.\n");
1433: fprintf(stderr,"Parameters are specified by the input_data_file. Otherwise, default values are used.\n");
1434: fprintf(stderr,"The format of the input_data_file. The orders of the input numbers must be kept.\n");
1435: fprintf(stderr," Mg: m(the number of variables), Beta: beta=sigma^(-1)/2 (diagonized), Ng: n,\n");
1436: fprintf(stderr," Iv: initial values at X0g*Beta (see our paper how to order them), are evaluated in this program. Give zeros. \n");
1437: fprintf(stderr," Ef: a scalar factor to the initial value. It is calculated by this program. Give the zero.\n");
1438: 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");
1439: fprintf(stderr," Dp: output data is stored in every Dp steps when output_data_file is specified, which is for w-m.\n");
1440: fprintf(stderr," The line started with %% is a comment line.\n");
1441: 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");
1442: fprintf(stderr," An example format of the input_data_file can be obtained by executing mh-m with no option.\n");
1443: fprintf(stderr,"\nExamples:\n");
1444: fprintf(stderr,"[1] ./mh-2 \n");
1445: fprintf(stderr,"[2] ./mh-2 --x0 0.3 \n");
1446: fprintf(stderr,"[3] ./mh-3 --x0 0.1 \n");
1447: fprintf(stderr,"[4] ./mh-3 --x0 0.1 --degree 15 \n");
1448: fprintf(stderr,"[5] ./mh-3 --idata test.txt --degree 15 \n");
1449: fprintf(stderr,"[6] ./mh-3 --degree 15 >test2.txt\n");
1450: fprintf(stderr," ./w-3 --idata test2.txt --gnuplotf test-g\n");
1451: fprintf(stderr," gnuplot -persist <test-g-gp.txt\n");
1452: }
1453:
1.10 takayama 1454: static int setParamDefault() {
1.1 takayama 1455: int rank;
1456: int i;
1.3 takayama 1457: Mg = M_n_default ;
1.1 takayama 1458: rank = imypower(2,Mg);
1459: Beta = (double *)mymalloc(sizeof(double)*Mg);
1460: for (i=0; i<Mg; i++) Beta[i] = 1.0+i;
1461: Ng = (double *)mymalloc(sizeof(double)); *Ng = 3.0;
1462: Iv = (double *)mymalloc(sizeof(double)*rank);
1463: Iv2 = (double *)mymalloc(sizeof(double)*rank);
1464: for (i=0; i<rank; i++) Iv[i] = 0;
1465: Ef = 0;
1466: Ef2 = 0.01034957388338225707;
1467: if (M_n == 2) {
1468: Iv2[0] = 1.58693;
1469: Iv2[1] = 0.811369;
1470: Iv2[2] = 0.846874;
1471: Iv2[3] = 0.413438;
1472: }
1473: X0g = (Beta[0]/Beta[Mg-1])*0.5;
1474: Hg = 0.001;
1475: Dp = 1;
1476: Xng = 10.0;
1477: }
1478:
1.10 takayama 1479: static int next(struct SFILE *sfp,char *s,char *msg) {
1.1 takayama 1480: s[0] = '%';
1481: while (s[0] == '%') {
1.12 ! takayama 1482: if (!mh_fgets(s,SMAX,sfp)) {
! 1483: fprintf(stderr,"Data format error at %s\n",msg);
! 1484: mh_exit(-1);
! 1485: }
! 1486: if (s[0] != '%') return(0);
1.1 takayama 1487: }
1488: }
1.10 takayama 1489: static int setParam(char *fname) {
1.1 takayama 1490: int rank;
1491: char s[SMAX];
1.3 takayama 1492: struct SFILE *fp;
1.1 takayama 1493: int i;
1494: if (fname == NULL) return(setParamDefault());
1495:
1496: Sample = 0;
1.3 takayama 1497: if ((fp=mh_fopen(fname,"r",JK_byFile)) == NULL) {
1.12 ! takayama 1498: if (JK_byFile) fprintf(stderr,"File %s is not found.\n",fp->s);
! 1499: mh_exit(-1);
1.1 takayama 1500: }
1501: next(fp,s,"Mg(m)");
1502: sscanf(s,"%d",&Mg);
1503: rank = imypower(2,Mg);
1504:
1505: Beta = (double *)mymalloc(sizeof(double)*Mg);
1506: for (i=0; i<Mg; i++) {
1507: next(fp,s,"Beta");
1.12 ! takayama 1508: sscanf(s,"%lf",&(Beta[i]));
1.1 takayama 1509: }
1510:
1511: Ng = (double *)mymalloc(sizeof(double));
1512: next(fp,s,"Ng(freedom parameter n)");
1513: sscanf(s,"%lf",Ng);
1514:
1515: next(fp,s,"X0g(initial point)");
1516: sscanf(s,"%lf",&X0g);
1517:
1518: Iv = (double *)mymalloc(sizeof(double)*rank);
1519: for (i=0; i<rank; i++) {
1.12 ! takayama 1520: next(fp,s,"Iv(initial values)");
! 1521: sscanf(s,"%lg",&(Iv[i]));
1.1 takayama 1522: }
1523:
1524: next(fp,s,"Ef(exponential factor)");
1525: sscanf(s,"%lg",&Ef);
1526:
1527: next(fp,s,"Hg (step size of rk)");
1528: sscanf(s,"%lf",&Hg);
1529:
1530: next(fp,s,"Dp (data sampling period)");
1531: sscanf(s,"%d",&Dp);
1532:
1533: next(fp,s,"Xng (the last point, cf. --xmax)");
1534: sscanf(s,"%lf",&Xng);
1.3 takayama 1535: mh_fclose(fp);
1.1 takayama 1536: }
1537:
1.10 takayama 1538: static int showParam(struct SFILE *fp,int fd) {
1.1 takayama 1539: int rank,i;
1.3 takayama 1540: char swork[1024];
1.8 takayama 1541: if (fd) {
1542: fp = mh_fopen("stdout","w",1);
1543: }
1.1 takayama 1544: rank = imypower(2,Mg);
1.3 takayama 1545: sprintf(swork,"%%Mg=\n%d\n",Mg); mh_fputs(swork,fp);
1.1 takayama 1546: for (i=0; i<Mg; i++) {
1.12 ! takayama 1547: sprintf(swork,"%%Beta[%d]=\n%lf\n",i,Beta[i]); mh_fputs(swork,fp);
1.1 takayama 1548: }
1.3 takayama 1549: sprintf(swork,"%%Ng=\n%lf\n",*Ng); mh_fputs(swork,fp);
1550: sprintf(swork,"%%X0g=\n%lf\n",X0g); mh_fputs(swork,fp);
1.1 takayama 1551: for (i=0; i<rank; i++) {
1.12 ! takayama 1552: sprintf(swork,"%%Iv[%d]=\n%lg\n",i,Iv[i]); mh_fputs(swork,fp);
! 1553: if (Sample && (M_n == 2) && (X0g == 0.3)) {
! 1554: sprintf(swork,"%%Iv[%d]-Iv2[%d]=%lg\n",i,i,Iv[i]-Iv2[i]); mh_fputs(swork,fp);
! 1555: }
1.3 takayama 1556: }
1557: sprintf(swork,"%%Ef=\n%lg\n",Ef); mh_fputs(swork,fp);
1558: sprintf(swork,"%%Hg=\n%lf\n",Hg); mh_fputs(swork,fp);
1559: sprintf(swork,"%%Dp=\n%d\n",Dp); mh_fputs(swork,fp);
1560: sprintf(swork,"%%Xng=\n%lf\n",Xng);mh_fputs(swork,fp);
1.1 takayama 1561: }
1562:
1.2 takayama 1563: static double gammam(double a,int n) {
1.1 takayama 1564: double v,v2;
1565: int i;
1566: v=mypower(sqrt(M_PI),(n*(n-1))/2);
1567: v2=0;
1568: for (i=1; i<=n; i++) {
1569: v2 += lgamma(a-((double)(i-1))/2.0); /* not for big n */
1570: }
1571: if (Debug) printf("gammam(%lg,%d)=%lg\n",a,n,v*exp(v2));
1572: return(v*exp(v2));
1573: }
1574:
1.2 takayama 1575: static double iv_factor(void) {
1.1 takayama 1576: double v1;
1577: double t;
1578: double b;
1579: double detSigma;
1580: double c;
1581: int i,n;
1582: n = (int) (*Ng);
1583: v1= mypower(sqrt(X0g),n*M_n);
1584: t = 0.0;
1585: for (i=0; i<M_n; i++) t += -X0g*Beta[i];
1586: v1 = v1*exp(t);
1587:
1588: b = 1; for (i=0; i<M_n; i++) b *= Beta[i];
1589: detSigma = 1.0/(b*mypower(2.0,M_n));
1590:
1591: c = gammam(((double)(M_n+1))/2.0, M_n)/
1.12 ! takayama 1592: ( mypower(sqrt(2), M_n*n)*mypower(sqrt(detSigma),n)*gammam(((double)(M_n+n+1))/2.0,M_n) );
1.1 takayama 1593: return( c*v1);
1594: }
1595:
1596:
1597:
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to jack-n.c CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM / src / hgm / mh / src