Annotation of OpenXM/src/asir-contrib/packages/doc/gtt_ekn/gtt_ekn-ja.texi, Revision 1.2
1.2 ! takayama 1: %% $OpenXM: OpenXM/src/asir-contrib/packages/doc/gtt_ekn/gtt_ekn-ja.texi,v 1.1 2016/03/21 00:16:10 takayama Exp $
1.1 takayama 2: %% ptex gtt_ekn.texi (.texi $B$^$G$D$1$k(B. platex $B$G$J$/(B ptex)
3: %% $B0J2<%3%a%s%H$O(B @comment $B$G;O$a$k(B. \input texinfo $B0J9_$OIaDL$N(B tex $BL?Na$O;H$($J$$(B.
4: \input texinfo
5: @iftex
6: @catcode`@#=6
7: @def@fref#1{@xrefX[#1,,@code{#1},,,]}
8: @def@b#1{{@bf@gt #1}}
9: @catcode`@#=@other
10: @end iftex
11: @overfullrule=0pt
12: @c -*-texinfo-*-
13: @comment %**start of header
14: @comment --- $B$*$^$8$J$$=*$j(B ---
15:
16: @comment --- GNU info $B%U%!%$%k$NL>A0(B ---
17: @setfilename xyzman
18:
19: @comment --- $B%?%$%H%k(B ---
20: @settitle 2$B85J,3dI=(BHGM
21:
22: @comment %**end of header
23: @comment %@setchapternewpage odd
24:
25: @comment --- $B$*$^$8$J$$(B ---
26: @ifinfo
27: @macro fref{name}
28: @ref{\name\,,@code{\name\}}
29: @end macro
30: @end ifinfo
31:
32: @iftex
33: @comment @finalout
34: @end iftex
35:
36: @titlepage
37: @comment --- $B$*$^$8$J$$=*$j(B ---
38:
39: @comment --- $B%?%$%H%k(B, $B%P!<%8%g%s(B, $BCx<TL>(B, $BCx:n8"I=<((B ---
40: @title 2$B85J,3dI=(BHGM$B4X?t(B
41: @subtitle Risa/Asir 2$B85J,3dI=(BHGM$B4X?t@bL@=q(B
42: @subtitle 1.0 $BHG(B
1.2 ! takayama 43: @subtitle 2016 $BG/(B 3 $B7n(B 22 $BF|(B
1.1 takayama 44:
45: @author by Y.Goto, Y.Tachibana, N.Takayama
46: @page
47: @vskip 0pt plus 1filll
48: Copyright @copyright{} Risa/Asir committers
49: 2004--2010. All rights reserved.
50: @end titlepage
51:
52: @comment --- $B$*$^$8$J$$(B ---
53: @synindex vr fn
54: @comment --- $B$*$^$8$J$$=*$j(B ---
55:
56: @comment --- @node $B$O(B GNU info, HTML $BMQ(B ---
57: @comment --- @node $B$N0z?t$O(B node-name, next, previous, up ---
58: @node Top,, (dir), (dir)
59:
60: @comment --- @menu $B$O(B GNU info, HTML $BMQ(B ---
61: @comment --- chapter $BL>$r@53N$KJB$Y$k(B ---
62: @comment --- $B$3$NJ8=q$G$O(B chapter XYZ, Chapter Index $B$,$"$k(B.
63: @comment --- Chapter XYZ $B$K$O(B section XYZ$B$K$D$$$F(B, section XYZ$B$K4X$9$k4X?t$,$"$k(B.
64: @menu
65: * 2$B85J,3dI=(BHGM$B$N4X?t@bL@=q$K$D$$$F(B::
66: * 2$B85J,3dI=(BHGM$B$N4X?t(B::
67: * Index::
68: @end menu
69:
70: @comment --- chapter $B$N3+;O(B ---
71: @comment --- $B?F(B chapter $BL>$r@53N$K(B. $B?F$,$J$$>l9g$O(B Top ---
72: @node 2$B85J,3dI=(BHGM$B$N4X?t@bL@=q$K$D$$$F(B,,, Top
73: @chapter 2$B85J,3dI=(BHGM$B$N4X?t@bL@=q$K$D$$$F(B
74:
75: $B$3$N@bL@=q$G$O(B
76: HGM(holonomic gradient method) $B$rMQ$$$?(B2$B85J,3dI=$N4X?t$K$D$$$F@bL@$9$k(B.
77: ChangeLog $B$N9`L\$O(B www.openxm.org $B$N(B cvsweb $B$G(B
78: $B%=!<%9%3!<%I$rFI$`;~$N=u$1$K$J$k>pJs$,=q$+$l$F$$$k(B.
79:
80: $BK\J8Cf$G0zMQ$7$F$$$kJ88%$rNs5s$9$k(B.
81: @itemize @bullet
82: @item [GM2016]
83: Y.Goto, K.Matsumoto, Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications, arxiv:1602.01637 (version 1)
84: @item [T2016]
85: Y.Tachibana, $B:9J,%[%m%N%_%C%/8{G[K!$N%b%8%e%i!<%a%=%C%I$K$h$k7W;;$N9bB.2=(B,
86: 2016, $B?@8MBg3X=$;NO@J8(B.
87: @item [GTT2016]
88: Y.Goto, Y.Tachibana, N.Takayama, 2$B85J,3dI=$KBP$9$k:9J,%[%m%N%_%C%/8{G[K!$N<BAu(B,
89: $B?tM}8&9V5fO?(B($B7G:\M=Dj(B).
90: @item [TKT2015]
91: N.Takayama, S.Kuriki, A.Takemura,
92: $A$-hypergeometric distributions and Newton polytopes.
93: arxiv:1510.02269
94: @end itemize
95:
96: $B$3$N%^%K%e%"%k$G@bL@$9$k4X?t$rMQ$$$?%W%m%0%i%`Nc$O(B
97: gtt_ekn/test-t1.rr
98: $B$J$I(B.
99:
100: @node 2$B85J,3dI=(BHGM$B$N4X?t(B,,, Top
101: @chapter 2$B85J,3dI=(BHGM$B$N4X?t(B
102:
103: @comment --- section ``$B<B83E*4X?t(B'' $B$N(B subsection xyz_abc
104: @comment --- subsection xyz_pqr xyz_stu $B$,$"$k(B.
105: @menu
106: * gtt_ekn.gmvector::
107: * gtt_ekn.nc::
108: * gtt_ekn.lognc::
109: * gtt_ekn.expectation::
110: * gtt_ekn.setup::
111: * gtt_ekn.upAlpha::
112: @end menu
113:
114: @node $BD64v2?4X?t(BE(k,n),,, 2$B85J,3dI=(BHGM$B$N4X?t(B
115: @section $BD64v2?4X?t(BE(k,n)
116:
117: @comment **********************************************************
118: @comment --- $B"~"~"~"~(B $B$N@bL@(B
119: @comment --- $B8D!9$N4X?t$N@bL@$N3+;O(B ---
120: @comment --- section $BL>$r@53N$K(B ---
121: @node gtt_ekn.gmvector,,, $BD64v2?4X?t(BE(k,n)
122: @subsection @code{gtt_ekn.gmvector}
123: @comment --- $B:w0zMQ%-!<%o!<%I(B
124: @findex gtt_ekn.gmvector
125:
126: @table @t
127: @item gtt_ekn.gmvector(@var{beta},@var{p})
128: :: $B<~JUOB(B @var{beta}, $B%;%k$N3NN((B @var{p} $B$NFs85J,3dI=$KIU?o$9$kD64v2?4X?t(B
129: E(k,n) $B$NCM$*$h$S$=$NHyJ,$NCM$rLa$9(B.
130: @item gtt_ekn.ekn_cBasis_2(@var{beta},@var{p})
131: $B$NJLL>$G$"$k(B.
132: @end table
133:
134: @comment --- $B0z?t$N4JC1$J@bL@(B --- $B0J2<$^$@=q$$$F$J$$(B.
135: @table @var
136: @item return
137: $B%Y%/%H%k(B, $BD64v2?4X?t$NCM$H$=$NHyJ,(B. $B>\$7$/$O2<5-(B.
138: @item beta
139: $B9TOB(B, $BNsOB$N%j%9%H(B. $B@.J,$O$9$Y$F@5$G$"$k$3$H(B.
140: @item p
141: $BFs85J,3dI=$N%;%k$N3NN($N%j%9%H(B
142: @end table
143:
144: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
145: @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
146: @comment --- @bullet $B$O9uE@IU$-(B ---
147: @itemize @bullet
148: @item
149: gmvector $B$O(B Gauss-Manin vector $B$NN,$G$"$k(B [GM2016].
150: @item
1.2 ! takayama 151: gmvector $B$NLa$jCM$O(B
! 152: [GM2016] $B$N(B 6$B>O(B p.23 $B$N%Y%/%H%k(B S$B$G$"$k(B.
! 153: $B$3$l$O(B
! 154: [GM2016] $B$N#4>O$GDj5A$5$l$F$$$k%Y%/%H%k(B F $B$NDj?tG\$G$"$j(B,
! 155: $B$=$NDj?t$O(B
! 156: $BBh0l@.J,$,(B [GM2016] $B$N#6>O$GDj5A$5$l$F$$$k5i?t(B S $B$NCM$HEy$7$/(B
! 157: $B$J$k$h$&$K7h$a$i$l$F$$$k(B.
1.1 takayama 158: @item
159: r1 x r2 $BJ,3dI=$r9M$($k(B.
160: m+1=r1, n+1=r2 $B$H$*$/(B.
161: $B@55,2=Dj?t(B Z $B$OJ,3dI=(B u $B$r(B (m+1) $B!_(B (n+1) $B9TNs$H$9$k$H$-(B p^u/u! $B$NOB$G$"$k(B.
162: $B$3$3$GOB$O9TOBNsOB$,(B @var{beta} $B$G$"$k$h$&$J(B u $BA4BN$G$H$k(B
163: [TKT2015], [GM2016].
1.2 ! takayama 164: S $B$O$3$NB?9`<0(B Z $B$N(B p $B$r(B
1.1 takayama 165: @verbatim
166: [[1,y11,...,y1n],
167: [1,y21,...,y2n],...,
168: [1,ym1, ...,ymn],
169: [1,1, ..., 1]]
170: @end verbatim
171: $B!!(B(1 $B$,(B L $B;z7?$KJB$V(B),
172: $B$H@55,2=$7$?5i?t$G$"$k(B.
173: @item
174: 2x(n+1)$BJ,3dI=$G(B, gmvector $B$NLa$jCM$r(B Lauricella F_D $B$G=q$/$3$H$,(B
175: $B0J2<$N$h$&$K$G$-$k(B
176: (b[2][1]-b[1][1] >= 0 $B$N>l9g(B).
177: $B$3$3$G(B b[1][1], b[1][2] $B$O(B, $B$=$l$>$l(B 1 $B9TL\$N9TOB(B, 2 $B9TL\$N9TOB(B,
178: b[2][i] $B$O(B i $BNsL\$NNsOB$G$"$k(B.
179: @comment ekn/Talks/2015-12-3-goto.tex
180: @verbatim
181: S=F_D(-b[1,1], [-b[2,2],...,-b[2,n+1]], b[2,1]-b[1,1]+1 ; y)/C,
182: @end verbatim
183: C=b[1,1]! b[2,2]! ... b[2][n+1]! (b[2,1]-b[1,1])!
184: $B$H$*$/(B.
185: 1/C $B$O(B L $B;z7?$NJ,3dI=(B
186: @verbatim
187: [[b[1,1], 0, ..., 0 ],
188: [b[2,1]-b[1,1],b[2,2], ..., b[2,n+1]]]
189: @end verbatim
190: $B$KBP1~(B.
191: gmvector $B$O(B
192: @verbatim
193: [S,(y11/a2) d_11 S,(y12/a3) d_12 S, ..., (y1n/a_(n+1)) d_1n S]
194: @end verbatim
195: $B$G$"$k(B.
196: $B$3$3$G(B d_ij $B$O(B yij $B$K$D$$$F$NHyJ,(B,
197: @verbatim
198: [a0, a1, ... ,a_(n+2)]
199: = [-b[1,2],-b[1,1],b[2,2], ..., b[2,n+1],b[2,1]]
200: @end verbatim
201: $B$G$"$k(B.
202: @item
203: $B<~JUOB(B @var{beta}$B$N;~$N@55,2=Dj?t$N%;%k3NN((B @var{p} $B$KBP$9$kCM$O(B $BB?9`<0$KB`2=$7$?(B E(k,n) $B$NCM$GI=8=$G$-$k(B. $BJ88%(B [TKT2015], [GM2016] $B;2>H(B.
204: @item
205: option crt=1 (crt = Chinese remainder theorem) $B$rM?$($k$H(B, $BJ,;67W;;$r$*$3$J$&(B
206: [T2016].
207: $BJ,;67W;;MQ$N3F<o%Q%i%a!<%?$N@_Dj$O(B
208: gtt_ekn.setup $B$G9T$J$&(B.
209: @end itemize
210:
211: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
212: $BNc(B: $B<!$O(B2 x 2 $BJ,3dI=$G9TOB$,(B [5,1], $BNsOB$,(B [3,3], $B3F%;%k$N3NN($,(B
213: [[1/2,1/3],[1/7,1/5]] $B$N>l9g$N(B gmvector $B$NCM$G$"$k(B.
214: @example
215: [3000] load("gtt_ekn.rr");
216: [3001] ekn_gtt.gmvector([[5,1],[3,3]],[[1/2,1/3],[1/7,1/5]])
217: [775/27783]
218: [200/9261]
219: @end example
220:
221: $B;29M(B: 2 x m $BJ,3dI=(B(Lauricella FD)$B$K$D$$$F$O%Q%C%1!<%8(B tk_fd $B$G$b2<5-$N$h$&$KF1Ey$J(B
222: $B7W;;$,$G$-$k(B.
223: $B<iHwHO0O$N0[$J$k%W%m%0%i%`F1;N$NHf3S(B, debug $BMQ;29M(B.
224: @example
225: [3080] import("tk_fd.rr");
226: [3081] A=tk_fd.marginal2abc([4,5],[2,4,3]);
227: [-4,[-4,-3],-1] // 2$BJQ?t(B FD $B$N%Q%i%a!<%?(B. a,[b1,b2],c
228: [3082] tk_fd.fd_hessian2(A[0],A[1],A[2],[1/2,1/3]);
229: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
230: [4483/124416,[ 1961/15552 185/1728 ],
231: [ 79/288 259/864 ]
232: [ 259/864 47/288 ]]
233: // $BLaCM$O(B [F=F_D, gradient(F), Hessian(F)]
234:
235: // ekn_gt $B$G$NNc$HF1$8%Q%i%a!<%?(B.
236: [3543] A=tk_fd.marginal2abc([5,1],[3,3]);
237: [-5,[-3],-1]
238: [3544] tk_fd.fd_hessian2(A[0],A[1],A[2],[(1/3)*(1/7)/((1/2)*(1/5))]);
239: Computing Dmat(ca) for parameters B=[-3],X=[ 10/21 ]
240: [775/27783,[ 20/147 ],[ 17/42 ]]
241: @end example
242:
243: $B;29M(B: $B0lHL$N(B A $BJ,I[$N@55,2=Dj?t$K$D$$$F$N(B Hessian $B$N7W;;$O<B83E*(B package ot_hessian_ahg.rr
244: $B$G<BAu$N%F%9%H$,$5$l$F$$$k(B. ($B$3$l$O$^$@L$40@.$N%F%9%HHG$J$N$G=PNO7A<0Ey$b>-MhE*$K$OJQ99$5$l$k(B.)
245: @example
246: import("ot_hgm_ahg.rr");
247: import("ot_hessian_ahg.rr");
248: def htest4() @{
249: extern C11_A;
250: extern C11_Beta;
251: Hess=newmat(7,7);
252: A =C11_A;
253: Beta0= [b0,b1,b2,b3];
254: BaseIdx=[4,5,6];
255: X=[x0,x1,x2,x3,x4,x5,x6];
256: for (I=0; I<7; I++) for (J=0; J<7; J++) @{
257: Idx = [I,J];
258: H=hessian_simplify(A,Beta0,X,BaseIdx,Idx);
259: Hess[I][J]=H;
260: printf("[I,J]=%a, Hessian_ij=%a\n",Idx,H);
261: @}
262: return(Hess);
263: @}
264: [2917] C11_A;
265: [[0,0,0,1,1,1,1],[1,0,0,1,0,1,0],[0,1,1,0,1,0,1],[1,1,0,1,1,0,0]]
266: [2918] C11_Beta;
267: [166,36,290,214]
268: [2919] Ans=htest4$
269: [2920] Ans[0][0];
270: [[((b1-b0-1)*x4)/(x0^2),[4]],[((b1-b0-1)*x6)/(x0^2),[6]],
271: [(b1^2+(-2*b0-1)*b1+b0^2+b0)/(x0^2),[]],[(x6)/(x0),[6,0]],[(x4)/(x0),[4,0]]]
272: @end example
273:
274: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
275: @table @t
276: @item $B;2>H(B
277: @ref{gtt_ekn.setup}
278: @ref{gtt_ekn.pfaffian_basis}
279: @end table
280:
281: @comment --- ChangeLog $B$r=q$/(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
282: @noindent
283: ChangeLog
284: @itemize @bullet
285: @item
286: $B$3$N4X?t$O(B
287: [GM2016] $B$N%"%k%4%j%:%`$*$h$S(B
288: [T2016] $B$K$h$k(B modular method $B$rMQ$$$?9bB.2=$r<BAu$7$?$b$N$G$"$k(B.
289: @item
290: $BJQ99$r<u$1$?%U%!%$%k$O(B
291: OpenXM/src/asir-contrib/packages/src/gtt_ekn.rr 1.1, gtt_ekn/ekn_pfaffian_8.rr
292: @end itemize
293:
294:
295: @comment **********************************************************
296: @node gtt_ekn.nc,,, $BD64v2?4X?t(BE(k,n)
297: @subsection @code{gtt_ekn.nc}
298: @comment --- $B:w0zMQ%-!<%o!<%I(B
299: @findex gtt_ekn.nc
300:
301: @table @t
302: @item gtt_ekn.nc(@var{beta},@var{p})
303: :: $B<~JUOB(B @var{beta}, $B%;%k$N3NN((B @var{p} $B$NFs85J,3dI=$N>r7oIU$-3NN($N@55,2=Dj?t(B Z
304: $B$*$h$S$=$NHyJ,$NCM$rLa$9(B.
305: @end table
306:
307: @comment --- $B0z?t$N4JC1$J@bL@(B --- $B0J2<$^$@=q$$$F$J$$(B.
308: @table @var
309: @item return
310: $B%Y%/%H%k(B [Z,[[d_11 Z, d_12 Z, ...], ..., [d_m1 Z, d_m2 Z, ...., d_mn Z]]]
311: @item beta
312: $B9TOB(B, $BNsOB$N%j%9%H(B. $B@.J,$O$9$Y$F@5$G$"$k$3$H(B.
313: @item p
314: $BFs85J,3dI=$N%;%k$N3NN($N%j%9%H(B
315: @end table
316:
317: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
318: @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
319: @comment --- @bullet $B$O9uE@IU$-(B ---
320: @itemize @bullet
321: @item
322: r1 x r2 $BJ,3dI=$r9M$($k(B.
323: m=r1, n=r2 $B$H$*$/(B.
324: $B@55,2=Dj?t(B Z $B$OJ,3dI=(B u $B$r(B m $B!_(B n $B9TNs$H$9$k$H$-(B p^u/u! $B$NOB$G$"$k(B.
325: $B$3$3$GOB$O9TOBNsOB$,(B @var{beta} $B$G$"$k$h$&$J(B u $BA4BN$G$H$k(B
326: [TKT2015], [GM2016].
327: p^u $B$O(B p_ij^u_ij $B$N@Q(B, u! $B$O(B u_ij! $B$N@Q$G$"$k(B.
328: d_ij Z $B$G(B Z $B$NJQ?t(B p_ij $B$K$D$$$F$NJPHyJ,$rI=$9(B.
329: @item
330: nc $B$O(B gmvector $B$NCM$r85$K(B, [GM2016] $B$N(B Prop
331: 7.1 $B$K4p$E$$$F(B Z $B$NCM$r7W;;$9$k(B.
332: @item
333: option crt=1 (crt = Chinese remainder theorem) $B$rM?$($k$H(B, $BJ,;67W;;$r$*$3$J$&(B.
334: $BJ,;67W;;MQ$N3F<o%Q%i%a!<%?$N@_Dj$O(B
335: gtt_ekn.setup $B$G9T$J$&(B.
336: @end itemize
337:
338: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
339: $BNc(B: 2x3 $BJ,3dI=$G$N(B Z $B$H$=$NHyJ,$N7W;;(B.
340: @example
341: [2237] gtt_ekn.nc([[4,5],[2,4,3]],[[1,1/2,1/3],[1,1,1]]);
342: [4483/124416,[ 353/7776 1961/15552 185/1728 ]
343: [ 553/20736 1261/15552 1001/13824 ]]
344: @end example
345:
346: $B;29M(B: 2 x m $BJ,3dI=(B(Lauricella FD)$B$K$D$$$F$O%Q%C%1!<%8(B tk_fd $B$G$b2<5-$N$h$&$KF1Ey$J(B
347: $B7W;;$,$G$-$k(B.
348: @example
349: [3076] import("tk_fd.rr");
350: [3077] A=tk_fd.marginal2abc([4,5],[2,4,3]);
351: [-4,[-4,-3],-1]
352: [3078] tk_fd.ahmat_abc(A[0],A[1],A[2],[[1,1/2,1/3],[1,1,1]]);
353: RS=[ 4 5 ], CSnew=[ 2 4 3 ], Ynew=[ 1 1/2 1/3 ]
354: [ 1 1 1 ]
355: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
356: [4483/124416,[[353/7776,1961/15552,185/1728],
357: [553/20736,1261/15552,1001/13824]]]
358: // $BLaCM$O(B [Z, [[d_11 Z, d_12 Z, d_13 Z],
359: // [d_21 Z, d_22 Z, d_23 Z]]] $B$NCM(B.
360: // $B$3$3$G(B d_ij $B$O(B i,j $B@.J,$K$D$$$F$NHyJ,$rI=$9(B.
361: @end example
362:
363: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
364: @table @t
365: @item $B;2>H(B
366: @ref{gtt_ekn.setup}
367: @ref{gtt_ekn.lognc}
368: @end table
369:
370: @comment --- ChangeLog $B$r=q$/(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
371: @noindent
372: ChangeLog
373: @itemize @bullet
374: @item
375: $BJQ99$r<u$1$?%U%!%$%k$O(B
376: OpenXM/src/asir-contrib/packages/src/gtt_ekn.rr 1.1, gtt_ekn/ekn_eval.rr
377: @end itemize
378:
379:
380: @comment **********************************************************
381: @node gtt_ekn.lognc,,, $BD64v2?4X?t(BE(k,n)
382: @subsection @code{gtt_ekn.lognc}
383: @comment --- $B:w0zMQ%-!<%o!<%I(B
384: @findex gtt_ekn.lognc
385:
386: @table @t
387: @item gtt_ekn.lognc(@var{beta},@var{p})
388: :: $B<~JUOB(B @var{beta}, $B%;%k$N3NN((B @var{p} $B$NFs85J,3dI=$N>r7oIU$-3NN($N@55,2=Dj?t(B Z
389: $B$N(B log $B$N6a;wCM$*$h$S$=$NHyJ,$N6a;wCM$rLa$9(B.
390: @end table
391:
392: @comment --- $B0z?t$N4JC1$J@bL@(B --- $B0J2<$^$@=q$$$F$J$$(B.
393: @table @var
394: @item return
395: $B%Y%/%H%k(B [log(Z), [[d_11 log(Z), d_12 log(Z), ...], [d_21 log(Z),...], ... ]
396: @item beta
397: $B9TOB(B, $BNsOB$N%j%9%H(B. $B@.J,$O$9$Y$F@5$G$"$k$3$H(B.
398: @item p
399: $BFs85J,3dI=$N%;%k$N3NN($N%j%9%H(B
400: @end table
401:
402: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
403: @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
404: @comment --- @bullet $B$O9uE@IU$-(B ---
405: @itemize @bullet
406: @item
407: $B>r7oIU$-:GL`?dDj$KMxMQ$9$k(B [TKT2015].
408: @item option crt=1 (crt = Chinese remainder theorem) $B$rM?$($k$H(B, $BJ,;67W;;$r$*$3$J$&(B.
409: $BJ,;67W;;MQ$N3F<o%Q%i%a!<%?$N@_Dj$O(B
410: gtt_ekn.setup $B$G9T$J$&(B.
411: @end itemize
412:
413: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
414: $BNc(B: 2 $B!_(B 3 $BJ,3dI=$G$NNc(B. $BBh0l@.J,$N$_6a;wCM(B.
415: @example
416: [2238] gtt_ekn.lognc([[4,5],[2,4,3]],[[1,1/2,1/3],[1,1,1]]);
417: [-3.32333832422461674630,[ 5648/4483 15688/4483 13320/4483 ]
418: [ 3318/4483 10088/4483 9009/4483 ]]
419: @end example
420:
421: $B;29M(B: 2 x m $BJ,3dI=(B(Lauricella FD)$B$K$D$$$F$O%Q%C%1!<%8(B tk_fd $B$G$b2<5-$N$h$&$KF1Ey$J(B
422: $B7W;;$,$G$-$k(B.
423: @example
424: [3076] import("tk_fd.rr");
425: [3077] A=tk_fd.marginal2abc([4,5],[2,4,3]);
426: [-4,[-4,-3],-1]
427: [3078] tk_fd.log_ahmat_abc(A[0],A[1],A[2],[[1,1/2,1/3],[1,1,1]]);
428: RS=[ 4 5 ], CSnew=[ 2 4 3 ], Ynew=[ 1 1/2 1/3 ]
429: [ 1 1 1 ]
430: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
431: [-3.32333832422461674639485797719209322217260539267246045320,
432: [[1.2598706, 3.499442, 2.971224],
433: [0.7401293, 2.250278, 2.009591]]]
434: // $BLaCM$O(B [log(Z),
435: // [[d_11 log(Z), d_12 log(Z), d_13 log(Z)],
436: // [d_21 log(Z), d_22 log(Z), d_23 log(Z)]]]
437: // $B$N6a;wCM(B.
438: @end example
439:
440: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
441: @table @t
442: @item $B;2>H(B
443: @ref{gtt_ekn.setup}
444: @ref{gtt_ekn.nc}
445: @end table
446:
447: @comment --- ChangeLog $B$r=q$/(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
448: @noindent
449: ChangeLog
450: @itemize @bullet
451: @item
452: $BJQ99$r<u$1$?%U%!%$%k$O(B
453: OpenXM/src/asir-contrib/packages/src/gtt_ekn.rr 1.1.
454: @end itemize
455:
456: @comment **********************************************************
457: @node gtt_ekn.expectation,,, $BD64v2?4X?t(BE(k,n)
458: @subsection @code{gtt_ekn.expectation}
459: @comment --- $B:w0zMQ%-!<%o!<%I(B
460: @findex gtt_ekn.expectation
461:
462: @table @t
463: @item gtt_ekn.expectation(@var{beta},@var{p})
464: :: $B<~JUOB(B @var{beta}, $B%;%k$N3NN((B @var{p} $B$NFs85J,3dI=$N4|BTCM$r7W;;$9$k(B.
465: @end table
466:
467: @comment --- $B0z?t$N4JC1$J@bL@(B --- $B0J2<$^$@=q$$$F$J$$(B.
468: @table @var
469: @item return
470: $BFs85J,3dI=$N3F%;%k$N4|BTCM$N%j%9%H(B.
471: @item beta
472: $B9TOB(B, $BNsOB$N%j%9%H(B. $B@.J,$O$9$Y$F@5$G$"$k$3$H(B.
473: @item p
474: $BFs85J,3dI=$N%;%k$N3NN($N%j%9%H(B
475: @end table
476:
477: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
478: @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
479: @comment --- @bullet $B$O9uE@IU$-(B ---
480: @itemize @bullet
481: @item
482: [GM2016] $B$N(B Algorithm 7.8 $B$N<BAu(B.
483: @item option crt=1 (crt = Chinese remainder theorem) $B$rM?$($k$H(B, $BJ,;67W;;$r$*$3$J$&(B.
484: $BJ,;67W;;MQ$N3F<o%Q%i%a!<%?$N@_Dj$O(B
485: gtt_ekn.setup $B$G9T$J$&(B.
486: @item option index $B$rM?$($k$H(B, $B;XDj$5$l$?@.J,$N4|BTCM$N$_7W;;$9$k(B.
487: $B$?$H$($P(B 2 x 2 $BJ,3dI=$G(B index=[[0,0],[1,1]] $B$H;XDj$9$k$H(B, 1 $B$N$"$k@.J,$N4|BTCM$N$_7W;;$9$k(B.
488: @end itemize
489:
490: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
491:
492: 2$B!_(B2, 3$B!_(B3 $B$NJ,3dI=$N4|BTCM7W;;Nc(B.
493: @example
494: [2235] gtt_ekn.expectation([[1,4],[2,3]],[[1,1/3],[1,1]]);
495: [ 2/3 1/3 ]
496: [ 4/3 8/3 ]
497: [2236] gtt_ekn.expectation([[4,5],[2,4,3]],[[1,1/2,1/3],[1,1,1]]);
498: [ 5648/4483 7844/4483 4440/4483 ]
499: [ 3318/4483 10088/4483 9009/4483 ]
500:
501: [2442] gtt_ekn.expectation([[4,14,9],[11,6,10]],[[1,1/2,1/3],[1,1/5,1/7],[1,1,1]]);
502: [ 207017568232262040/147000422096729819 163140751505489940/147000422096729819
503: 217843368649167296/147000422096729819 ]
504: [ 1185482401011137878/147000422096729819 358095302885438604/147000422096729819
505: 514428205457640984/147000422096729819 ]
506: [ 224504673820628091/147000422096729819 360766478189450370/147000422096729819
507: 737732646860489910/147000422096729819 ]
508: @end example
509:
510: $B;29M(B: 2 x m $BJ,3dI=(B(Lauricella FD)$B$K$D$$$F$O%Q%C%1!<%8(B tk_fd $B$G$b2<5-$N$h$&$KF1Ey$J(B
511: $B7W;;$,$G$-$k(B.
512: @example
513: [3076] import("tk_fd.rr");
514: [3077] A=tk_fd.marginal2abc([4,5],[2,4,3]);
515: [-4,[-4,-3],-1]
516: [3078] tk_fd.expectation_abc(A[0],A[1],A[2],[[1,1/2,1/3],[1,1,1]]);
517: RS=[ 4 5 ], CSnew=[ 2 4 3 ], Ynew=[ 1 1/2 1/3 ]
518: [ 1 1 1 ]
519: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
520: [[5648/4483,7844/4483,4440/4483],
521: [3318/4483,10088/4483,9009/4483]]
522: // $B3F%;%k$N4|BTCM(B.
523: @end example
524:
525: $B;29M(B: $B0lHL$N(B A $BJ,I[$N7W;;$O(B ot_hgm_ahg.rr. $B$^$@<B83E*$J$?$a(B, module $B2=$5$l$F$$$J$$(B.
526: ot_hgm_ahg.rr $B$K$D$$$F$N;29MJ88%(B:
527: K.Ohara, N.Takayama, Pfaffian Systems of A-Hypergeometric Systems II --- Holonomic Gradient Method, arxiv:1505.02947
528: @example
529: [3237] import("ot_hgm_ahg.rr");
530: // 2 x 2 $BJ,3dI=(B.
531: [3238] hgm_ahg_expected_values_contiguity([[0,0,1,1],[1,0,1,0],[0,1,0,1]],
532: [9,6,8],[1/2,1/3,1/5,1/7],[x1,x2,x3,x4]|geometric=1);
533: oohg_native=0, oohg_curl=1
534: [1376777025/625400597,1750225960/625400597,
535: 2375626557/625400597,3252978816/625400597]
536: // 2 x 2 $BJ,3dI=$N4|BTCM(B.
537:
538: // 2 x 3 $BJ,3dI=(B.
539: [3238] hgm_ahg_expected_values_contiguity(
540: [[0,0,0,1,1,1],[1,0,0,1,0,0],[0,1,0,0,1,0],[0,0,1,0,0,1]],
541: [5,2,4,3],[1,1/2,1/3,1,1,1],[x1,x2,x3,x4,x5,x6]|geometric=1);
542: [5648/4483,7844/4483,4440/4483,3318/4483,10088/4483,9009/4483]
543: // 2 x 3 $BJ,3dI=$N4|BTCM(B. $B>e$HF1$8LdBj(B.
544: @end example
545:
546: 3 x 3 $BJ,3dI=(B. $B9=B$E*(B0$B$,0l$D(B.
547: @example
548: /*
549: dojo, p.221 $B$N%G!<%?(B. $B@.@S(B3$B0J2<$N@8EL$O=8$a$F$R$H$D$K(B.
550: 2 1 1
551: 8 3 3
552: 0 2 6
553:
554: row sum: 4,14,8
555: column sum: 10,6,10
556: 0 $B$r0l$D4^$`$N$G(B, (3,6) $B7?$N(B A $B$+$i(B 7 $BNsL\$rH4$/(B.
557: */
558:
559: A=[[0,0,0,1,1,1, 0,0],
560: [0,0,0,0,0,0, 1,1],
561: [1,0,0,1,0,0, 0,0],
562: [0,1,0,0,1,0, 1,0],
563: [0,0,1,0,0,1, 0,1]];
564: B=[14,8,10,6,10];
565: hgm_ahg_expected_values_contiguity(A,B,[1,1/2,1/3,1,1/5,1/7,1,1],
566: $B!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(B[x1,x2,x3,x4,x5,x6,x7,x8]|geometric=1);
567:
568: // $BEz(B.
569: [14449864949304/9556267369631,
570: 10262588586540/9556267369631, 13512615942680/9556267369631,
571: 81112808747006/9556267369631,
572: 21816297744346/9556267369631, 30858636683482/9556267369631,
573:
574: 25258717886900/9556267369631,51191421070148/9556267369631]
575: @end example
576:
577: 3 x 3 $BJ,3dI=(B.
578: @example
579: /*
580: $B>e$N%G!<%?$G(B 0 $B$r(B 1 $B$KJQ99(B.
581: 2 1 1
582: 8 3 3
583: 1 2 6
584:
585: row sum: 4,14,9
586: column sum: 11,6,10
587: */
588: A=[[0,0,0,1,1,1,0,0,0],
589: [0,0,0,0,0,0,1,1,1],
590: [1,0,0,1,0,0,1,0,0],
591: [0,1,0,0,1,0,0,1,0],
592: [0,0,1,0,0,1,0,0,1]];
593: B=[14,9,11,6,10];
594: hgm_ahg_expected_values_contiguity(A,B,[1,1/2,1/3,1,1/5,1/7,1,1,1],
595: [x1,x2,x3,x4,x5,x6,x7,x8]|geometric=1);
596:
597: // $B4|BTCM(B, $BEz(B. x9 $B$r;XDj$7$F$$$J$$$N$G(B, 9$BHVL\$N4|BTCM$O=PNO$7$F$J$$(B.
598: [207017568232262040/147000422096729819,
599: 163140751505489940/147000422096729819,217843368649167296/147000422096729819,
600: 1185482401011137878/147000422096729819,
601: 358095302885438604/147000422096729819,514428205457640984/147000422096729819,
602: 224504673820628091/147000422096729819,360766478189450370/147000422096729819]
603:
604: // Z $B$d$=$NHyJ,$N7W;;$O(B hgm_ahg_contiguity $B4X?t$,$*$3$J$&$,(B, $B$3$l$N4J0W%$%s%?!<%U%'!<%9$O(B
605: // $B$^$@=q$$$F$J$$(B.
606: @end example
607:
608:
609:
610: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
611: @table @t
612: @item $B;2>H(B
613: @ref{gtt_ekn.setup}
614: @ref{gtt_ekn.nc}
615: @end table
616:
617: @comment --- ChangeLog $B$r=q$/(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
618: @noindent
619: ChangeLog
620: @itemize @bullet
621: @item
622: $BJQ99$r<u$1$?%U%!%$%k$O(B
623: OpenXM/src/asir-contrib/packages/src/gtt_ekn.rr 1.1.
624: @end itemize
625:
626:
627: @comment **********************************************************
628: @comment --- $B"~"~"~"~(B $B$N@bL@(B
629: @comment --- $B8D!9$N4X?t$N@bL@$N3+;O(B ---
630: @comment --- section $BL>$r@53N$K(B ---
631: @node gtt_ekn.setup,,, $BD64v2?4X?t(BE(k,n)
632: @subsection @code{gtt_ekn.setup}
633: @comment --- $B:w0zMQ%-!<%o!<%I(B
634: @findex gtt_ekn.setup
635:
636: @table @t
637: @item gtt_ekn.setup()
638: :: $BJ,;67W;;MQ$N4D6-@_Dj$r$*$3$J$&(B. $B8=:_$N4D6-$rJs9p$9$k(B.
639: @end table
640:
641: @comment --- $B0z?t$N4JC1$J@bL@(B --- $B0J2<$^$@=q$$$F$J$$(B.
642: @table @var
643: @item return
644:
645: @end table
646:
647: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
648: @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
649: @comment --- @bullet $B$O9uE@IU$-(B ---
650: @itemize @bullet
651: @item $B;HMQ$9$k%W%m%;%9$HAG?t$N8D?t(B, $B:G>.$NAG?t$rI=<($9$k(B. $B=`Hw$5$l$F$$$J$$>l9g$O$=$N;]$rI=<((B.
1.2 ! takayama 652: @item $B$3$N%Q%C%1!<%8$G$NJ,;67W;;$OJ#?t$N(Bcpu$B$rEk:\$7$?7W;;5!$G<B9T$5$l$k$3$H$rA[Dj$7$F$$$k(B.
! 653: @item option nps ($B$^$?$O(B number_of_processes)$B$rM?$($k$H;XDj$7$??t$@$1%W%m%;%9$rMQ0U$9$k(B.
! 654: @item option nprm ($B$^$?$O(B number_of_primes)$B$rM?$($k$H(Bnprm$B$,J8;zNs$N>l9g;XDj$5$l$?AG?t%j%9%H$N%U%!%$%k$rFI$_9~$`(B. nprm$B$,<+A3?t$N>l9g$5$i$K(Boption minp (minp =MINimum Prime)$B$rM?$($k$H(Bminp$B$h$jBg$-$JAG?t$r(Bnprm$B8D@8@.$9$k(B. $B$=$N:](Boption fgp ($B$^$?$O(B file_of_generated_primes)$B$rM?$($k$H@8@.$7$?AG?t%j%9%H$r%U%!%$%kL>$r(Bfgp$B$H$7$FJ]B8$9$k(B.
! 655: @item $B>e5-$N(Boption $B$r;XDj$7$J$+$C$?>l9g<!$N%G%U%)%k%HCM$,MQ$$$i$l$k(B. nps=1. nprm=10. fgp=0.
! 656: @item option report=1$B$rM?$($k$H8=:_$N4D6-$NJs9p$N$_$r9T$&(B. setup(|report=1)$B$NJLL>$H$7$F(Breport$B4X?t$r;HMQ$9$k$3$H$b$G$-$k(B.
1.1 takayama 657: @end itemize
658:
659: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
660: $BNc(B: $BAG?t$N%j%9%H$r@8@.$7$F%U%!%$%k(B p.txt $B$X=q$-=P$9(B.
661: @example
662: gtt_ekn.setup(|nps=2,nprm=20,minp=10^10,fgp="p.txt")$
663: @end example
664:
665:
666: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
667: @table @t
668: @item $B;2>H(B
669: @ref{gtt_ekn.nc}
670: @ref{gtt_ekn.gmvector}
671: @end table
672:
673: @comment --- ChangeLog $B$r=q$/(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
674: @noindent
675: ChangeLog
676: @itemize @bullet
677: @item
678: $BJQ99$r<u$1$?%U%!%$%k$O(B
679: OpenXM/src/asir-contrib/packages/src/gtt_ekn.rr 1.1,
680: gtt_ekn/g_mat_fac.rr
681:
682: @end itemize
683:
684: @comment **********************************************************
685: @comment --- $B"~"~"~"~(B $B$N@bL@(B
686: @comment --- $B8D!9$N4X?t$N@bL@$N3+;O(B ---
687: @comment --- section $BL>$r@53N$K(B ---
688: @node gtt_ekn.upAlpha,,, $BD64v2?4X?t(BE(k,n)
689: @subsection @code{gtt_ekn.upAlpha}
690: @comment --- $B:w0zMQ%-!<%o!<%I(B
691: @findex gtt_ekn.upAlpha
692:
693: @table @t
694: @item gtt_ekn.upAlpha(@var{i},@var{k},@var{n})
695: ::
696: @end table
697:
698: @comment --- $B0z?t$N4JC1$J@bL@(B --- $B0J2<$^$@=q$$$F$J$$(B.
699: @table @var
700: @item i a_i $B$r(B a_i+1 $B$HJQ2=$5$;$k(B contiguity relation.
701: @item k E(k+1,n+k+2)$B7?$ND64v2?4X?t$N(B k. $BJ,3dI=$G$O(B (k+1)$B!_(B(n+1).
702: @item n E(k+1,n+k+2)$B7?$ND64v2?4X?t$N(B n. $BJ,3dI=$G$O(B (k+1)$B!_(B(n+1).
703: @item return contiguity relation $B$N(B pfaffian_basis $B$K$D$$$F$N9TNsI=8=$rLa$9(B. [GM2016] $B$N(B Cor 6.3.
704: @end table
705:
706: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
707: @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
708: @comment --- @bullet $B$O9uE@IU$-(B ---
709: @itemize @bullet
710: @item
711: upAlpha $B$O!!(B[GM2016] $B$N(B Cor 6.3 $B$N9TNs(B U_i $B$rLa$9(B.
712: @item $B4XO"$9$k3F4X?t$N4J7i$J@bL@$HNc$b2C$($k(B.
713: @item a_i $B$r(B a_i-1 $B$HJQ2=$5$;$?$$>l9g$O4X?t(B downAlpha $B$rMQ$$$k(B.
714: @item a_i $B$HJ,3dI=$N<~JUOB$r8+$k$K$O(B, $B4X?t(B marginaltoAlpha([$B9TOB(B,$BNsOB(B]) $B$rMQ$$$k(B.
715: @item
716: pfaffian_basis $B$O(B [GM2016] $B$N#4>O$N%Y%/%H%k(B F $B$KBP1~$9$kJPHyJ,$rLa$9(B.
717: @end itemize
718:
719: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
720: $BNc(B: $B0J2<$NNc$O(B 2$B!_(B2$BJ,3dI=(B(E(2,4)), 2$B!_(B3$BJ,3dI=(B(E(2,5))$B$N>l9g$G$"$k(B.
721: [2225] $B$^$G$O=PNO$rN,$7$F$$$k(B.
722: @example
723: [2221] gtt_ekn.marginaltoAlpha([[1,4],[2,3]]);
724: [[a_0,-4],[a_1,-1],[a_2,3],[a_3,2]]
725: [2222] gtt_ekn.upAlpha(1,1,1); // E(2,4) $B$N(B a_1 $BJ}8~$N(B
726: // contiguity $B$rI=8=$9$k9TNs(B
727: [2223] gtt_ekn.upAlpha(2,1,1); // E(2,4) $B$N(B a_2 $BJ}8~(B
728: [2224] gtt_ekn.upAlpha(3,1,1); // E(2,4) $B$N(B a_3 $BJ}8~(B
729: [2225] function f(x_1_1);
730: [2232] gtt_ekn.pfaffian_basis(f(x_1_1),1,1);
731: [ f(x_1_1) ]
732: [ (f{1}(x_1_1)*x_1_1)/(a_2) ]
733: [2233] function f(x_1_1,x_1_2);
734: f() redefined.
735: [2234] gtt_ekn.pfaffian_basis(f(x_1_1,x_1_2),1,2); // E(2,5), 2*3 $BJ,3dI=(B
736: [ f(x_1_1,x_1_2) ]
737: [ (f{1,0}(x_1_1,x_1_2)*x_1_1)/(a_2) ]
738: [ (f{0,1}(x_1_1,x_1_2)*x_1_2)/(a_3) ]
739: @end example
740:
741:
742: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
743: @table @t
744: @item $B;2>H(B
745: @ref{gtt_ekn.nc}
746: @ref{gtt_ekn.gmvector}
747: @end table
748:
749: @comment --- ChangeLog $B$r=q$/(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
750: @noindent
751: ChangeLog
752: @itemize @bullet
753: @item
754: $B$3$N4X?t$O(B [GM2016]
755: $B$GM?$($i$l$?%"%k%4%j%:%`$K=>$$(B contiguity relation $B$rF3=P$9$k(B.
756: @item
757: $BJQ99$r<u$1$?%U%!%$%k$O(B
758: OpenXM/src/asir-contrib/packages/src/gtt_ekn/ekn_pfaffian_8.rr 1.1.
759: @end itemize
760:
761:
762:
763: @comment --- $B$*$^$8$J$$(B ---
764: @node Index,,, Top
765: @unnumbered Index
766: @printindex fn
767: @printindex cp
768: @iftex
769: @vfill @eject
770: @end iftex
771: @summarycontents
772: @contents
773: @bye
774: @comment --- $B$*$^$8$J$$=*$j(B ---
775:
776:
777: // 2 x m $BJ,3dI=$K$*$$$F;w$?5!G=$rM-$9$k4X?t$NMxMQNc$r;29M$^$G$K5-:\$9$k(B;
778: // $B@55,2=Dj?t$H$=$NHyJ,4XO"(B.
779: // $B$=$N(B1.
780: [3077] A=tk_fd.marginal2abc([4,5],[2,4,3]);
781: [-4,[-4,-3],-1]
782: [3078] tk_fd.ahmat_abc(A[0],A[1],A[2],[[1,1/2,1/3],[1,1,1]]);
783: RS=[ 4 5 ], CSnew=[ 2 4 3 ], Ynew=[ 1 1/2 1/3 ]
784: [ 1 1 1 ]
785: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
786: [4483/124416,[[353/7776,1961/15552,185/1728],[553/20736,1261/15552,1001/13824]]]
787: // $BLaCM$O(B [Z, [[d_11 Z, d_12 Z, d_13 Z],[d_21 Z, d_22 Z, d_23 Z]]] $B$NCM(B.
788:
789: // $B$=$N(B2.
790: [3079] tk_fd.log_ahmat_abc(A[0],A[1],A[2],[[1,1/2,1/3],[1,1,1]]);
791: RS=[ 4 5 ], CSnew=[ 2 4 3 ], Ynew=[ 1 1/2 1/3 ]
792: [ 1 1 1 ]
793: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
794: [-3.32333832422461674639485797719209322217260539267246045320,
795: [[1.25987062235110417131385233102832924380994869507026544724,3.49944233772027660049074280615659156814633058219942003122,2.97122462636627258532232879768012491635065804149007361142],
796: [0.740129377648895828686147668971670756190051304929734552754,2.25027883113986169975462859692170421592683470890028998438,2.00959179121124247155922373410662502788311398616997546285]]]
797: // $BLaCM$O(B [log(Z),
798: // [[d_11 log(Z), d_12 log(Z), d_13 log(Z)],
799: // [d_21 log(Z), d_22 log(Z), d_23 log(Z)]]]
800: // $B$N6a;wCM(B.
801:
802: // $B$=$N(B3.
803: [3082] fd_hessian2(A[0],A[1],A[2],[1/2,1/3]);
804: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
805: [4483/124416,[ 1961/15552 185/1728 ],
806: [ 79/288 259/864 ]
807: [ 259/864 47/288 ]]
808: // $BLaCM$O(B [F=F_D, gradient(F), Hessian(F)]
809:
810: // $B;29M(B.
811: // ygahvec $B$G6R4X?tJ,$ND4@0(B. $BFHN)$7$?4X?t$O$J$$$h$&$@(B.
812:
813: //-----------------------------------------------------------------------
814: // 2 x m $BJ,3dI=$K$*$$$F;w$?5!G=$rM-$9$k4X?t$NMxMQNc$r;29M$^$G$K5-:\$9$k(B;
815: // $B4|BTCM4XO"(B.
816: [3079] A=tk_fd.marginal2abc([4,5],[2,4,3]);
817: [-4,[-4,-3],-1]
818: [3080] tk_fd.expectation_abc(A[0],A[1],A[2],[[1,1/2,1/3],[1,1,1]]);
819: RS=[ 4 5 ], CSnew=[ 2 4 3 ], Ynew=[ 1 1/2 1/3 ]
820: [ 1 1 1 ]
821: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
822: [[5648/4483,7844/4483,4440/4483],
823: [3318/4483,10088/4483,9009/4483]]
824: // $B3F%;%k$N4|BTCM(B.
825:
826: //-----------------------------------------------------------------------
827: // ot_hgm_ahg.rr $B$NNc(B. $B<B83E*$J$?$a(B module $B2=$5$l$F$$$J$$(B.
828: [3237] import("ot_hgm_ahg.rr");
829: // 2 x 2 $BJ,3dI=(B.
830: [3238] hgm_ahg_expected_values_contiguity([[0,0,1,1],[1,0,1,0],[0,1,0,1]],
831: [9,6,8],[1/2,1/3,1/5,1/7],[x1,x2,x3,x4]|geometric=1);
832: oohg_native=0, oohg_curl=1
833: [1376777025/625400597,1750225960/625400597,2375626557/625400597,3252978816/625400597]
834: // 2 x 2 $BJ,3dI=$N4|BTCM(B.
835:
836: // 2 x 3 $BJ,3dI=(B.
837: [3238] hgm_ahg_expected_values_contiguity(
838: [[0,0,0,1,1,1],[1,0,0,1,0,0],[0,1,0,0,1,0],[0,0,1,0,0,1]],
839: [5,2,4,3],[1,1/2,1/3,1,1,1],[x1,x2,x3,x4,x5,x6]|geometric=1);
840: [5648/4483,7844/4483,4440/4483,3318/4483,10088/4483,9009/4483]
841: // 2 x 3 $BJ,3dI=$N4|BTCM(B. $B>e$HF1$8LdBj(B.
842:
843: /*
844: dojo, p.221. $B@.@S(B3$B0J2<$N@8EL$O=8$a$F$R$H$D$K(B.
845: 2 1 1
846: 8 3 3
847: 0 2 6
848:
849: row sum: 4,14,8
850: column sum: 10,6,10
851: 0 $B$r0l$D4^$`$N$G(B, (3,6) $B7?$N(B A $B$+$i(B 7 $BNsL\$rH4$/(B.
852: */
853: // 3 x 3 $BJ,3dI=(B. $B9=B$E*(B0$B$,0l$D(B.
854:
855: A=[[0,0,0,1,1,1, 0,0],
856: [0,0,0,0,0,0, 1,1],
857: [1,0,0,1,0,0, 0,0],
858: [0,1,0,0,1,0, 1,0],
859: [0,0,1,0,0,1, 0,1]];
860: B=[14,8,10,6,10];
861: hgm_ahg_expected_values_contiguity(A,B,[1,1/2,1/3,1,1/5,1/7,1,1],[x1,x2,x3,x4,x5,x6,x7,x8]|geometric=1);
862:
863: // $BEz(B.
864: [14449864949304/9556267369631,10262588586540/9556267369631,13512615942680/9556267369631,
865: 81112808747006/9556267369631,21816297744346/9556267369631,30858636683482/9556267369631,
866: 25258717886900/9556267369631,51191421070148/9556267369631]
867:
868:
869: /*
870: $B>e$N%G!<%?$G(B 0 $B$r(B 1 $B$KJQ99(B.
871: 2 1 1
872: 8 3 3
873: 1 2 6
874:
875: row sum: 4,14,9
876: column sum: 11,6,10
877: */
878: // 3 x 3 $BJ,3dI=(B.
879: A=[[0,0,0,1,1,1,0,0,0],
880: [0,0,0,0,0,0,1,1,1],
881: [1,0,0,1,0,0,1,0,0],
882: [0,1,0,0,1,0,0,1,0],
883: [0,0,1,0,0,1,0,0,1]];
884: B=[14,9,11,6,10];
885: hgm_ahg_expected_values_contiguity(A,B,[1,1/2,1/3,1,1/5,1/7,1,1,1],[x1,x2,x3,x4,x5,x6,x7,x8]|geometric=1);
886:
887: // $B4|BTCM(B, $BEz(B.
888: [207017568232262040/147000422096729819,163140751505489940/147000422096729819,217843368649167296/147000422096729819,
889: 1185482401011137878/147000422096729819,358095302885438604/147000422096729819,514428205457640984/147000422096729819,
890: 224504673820628091/147000422096729819,360766478189450370/147000422096729819]
891:
892: // Z $B$d$=$NHyJ,$N7W;;$O(B hgm_ahg_contiguity $B4X?t$,$*$3$J$&$,(B, $B$3$l$N4J0W%$%s%?!<%U%'!<%9$O(B
893: // $B$^$@=q$$$F$J$$(B.
894:
895:
896: 4. x_ij $B$O(B [GM2016] $B$N#1>O$G(B,
897: $B$?$H$($P(B 3x3 $B$N;~(B [[1,1,1],[x_11,x_12,1],[x_21,x_22,1]]
898: $B$H$J$C$F$$$k$,(B, [GM2016] $B$N(B Prop 7.1 $B$NBP1~$G$O(B,
899: p = [[1,x_11,x_12],[1,x_21,x_22],[1,1,1]] $B$H$J$C$F$$$k$N$GCm0U(B.
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