Annotation of OpenXM/src/asir-contrib/packages/doc/gtt_ekn/gtt_ekn-ja.texi, Revision 1.1
1.1 ! takayama 1: %% $OpenXM$
! 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
! 43: @subtitle 2016 $BG/(B 3 $B7n(B 21 $BF|(B
! 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$$@bL@(B ---
! 145: @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
! 146: @comment --- @bullet $B$O9uE@IU$-(B ---
! 147: @itemize @bullet
! 148: @item
! 149: gmvector $B$O(B Gauss-Manin vector $B$NN,$G$"$k(B [GM2016].
! 150: @item
! 151: gmvector $B$NLa$jCM$O(B [GM2016] $B$N#4>O$GDj5A$5$l$F$$$k%Y%/%H%k(B F $B$G$"$k(B.
! 152: $B$?$@$7Bh0l@.J,$,(B [GM2016] $B$N#6>O$GDj5A$5$l$F$$$k5i?t(B S $B$NCM$HEy$7$/(B
! 153: $B$J$k$h$&$K%9%+%i!<G\$5$l$F$$$k(B.
! 154: @item
! 155: r1 x r2 $BJ,3dI=$r9M$($k(B.
! 156: m+1=r1, n+1=r2 $B$H$*$/(B.
! 157: $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.
! 158: $B$3$3$GOB$O9TOBNsOB$,(B @var{beta} $B$G$"$k$h$&$J(B u $BA4BN$G$H$k(B
! 159: [TKT2015], [GM2016].
! 160: S $B$O$3$N5i?t$N(B p $B$r(B
! 161: @verbatim
! 162: [[1,y11,...,y1n],
! 163: [1,y21,...,y2n],...,
! 164: [1,ym1, ...,ymn],
! 165: [1,1, ..., 1]]
! 166: @end verbatim
! 167: $B!!(B(1 $B$,(B L $B;z7?$KJB$V(B),
! 168: $B$H@55,2=$7$?5i?t$G$"$k(B.
! 169: @item
! 170: 2x(n+1)$BJ,3dI=$G(B, gmvector $B$NLa$jCM$r(B Lauricella F_D $B$G=q$/$3$H$,(B
! 171: $B0J2<$N$h$&$K$G$-$k(B
! 172: (b[2][1]-b[1][1] >= 0 $B$N>l9g(B).
! 173: $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,
! 174: b[2][i] $B$O(B i $BNsL\$NNsOB$G$"$k(B.
! 175: @comment ekn/Talks/2015-12-3-goto.tex
! 176: @verbatim
! 177: S=F_D(-b[1,1], [-b[2,2],...,-b[2,n+1]], b[2,1]-b[1,1]+1 ; y)/C,
! 178: @end verbatim
! 179: C=b[1,1]! b[2,2]! ... b[2][n+1]! (b[2,1]-b[1,1])!
! 180: $B$H$*$/(B.
! 181: 1/C $B$O(B L $B;z7?$NJ,3dI=(B
! 182: @verbatim
! 183: [[b[1,1], 0, ..., 0 ],
! 184: [b[2,1]-b[1,1],b[2,2], ..., b[2,n+1]]]
! 185: @end verbatim
! 186: $B$KBP1~(B.
! 187: gmvector $B$O(B
! 188: @verbatim
! 189: [S,(y11/a2) d_11 S,(y12/a3) d_12 S, ..., (y1n/a_(n+1)) d_1n S]
! 190: @end verbatim
! 191: $B$G$"$k(B.
! 192: $B$3$3$G(B d_ij $B$O(B yij $B$K$D$$$F$NHyJ,(B,
! 193: @verbatim
! 194: [a0, a1, ... ,a_(n+2)]
! 195: = [-b[1,2],-b[1,1],b[2,2], ..., b[2,n+1],b[2,1]]
! 196: @end verbatim
! 197: $B$G$"$k(B.
! 198: @item
! 199: $B<~JUOB(B @var{beta}$B$N;~$N@55,2=Dj?t$N%;%k3NN((B @var{p} $B$KBP$9$kCM$O(B $BB?9`<0$KB`2=$7$?(B E(k,n) $B$NCM$GI=8=$G$-$k(B. $BJ88%(B [TKT2015], [GM2016] $B;2>H(B.
! 200: @item
! 201: option crt=1 (crt = Chinese remainder theorem) $B$rM?$($k$H(B, $BJ,;67W;;$r$*$3$J$&(B
! 202: [T2016].
! 203: $BJ,;67W;;MQ$N3F<o%Q%i%a!<%?$N@_Dj$O(B
! 204: gtt_ekn.setup $B$G9T$J$&(B.
! 205: @end itemize
! 206:
! 207: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 208: $BNc(B: $B<!$O(B2 x 2 $BJ,3dI=$G9TOB$,(B [5,1], $BNsOB$,(B [3,3], $B3F%;%k$N3NN($,(B
! 209: [[1/2,1/3],[1/7,1/5]] $B$N>l9g$N(B gmvector $B$NCM$G$"$k(B.
! 210: @example
! 211: [3000] load("gtt_ekn.rr");
! 212: [3001] ekn_gtt.gmvector([[5,1],[3,3]],[[1/2,1/3],[1/7,1/5]])
! 213: [775/27783]
! 214: [200/9261]
! 215: @end example
! 216:
! 217: $B;29M(B: 2 x m $BJ,3dI=(B(Lauricella FD)$B$K$D$$$F$O%Q%C%1!<%8(B tk_fd $B$G$b2<5-$N$h$&$KF1Ey$J(B
! 218: $B7W;;$,$G$-$k(B.
! 219: $B<iHwHO0O$N0[$J$k%W%m%0%i%`F1;N$NHf3S(B, debug $BMQ;29M(B.
! 220: @example
! 221: [3080] import("tk_fd.rr");
! 222: [3081] A=tk_fd.marginal2abc([4,5],[2,4,3]);
! 223: [-4,[-4,-3],-1] // 2$BJQ?t(B FD $B$N%Q%i%a!<%?(B. a,[b1,b2],c
! 224: [3082] tk_fd.fd_hessian2(A[0],A[1],A[2],[1/2,1/3]);
! 225: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
! 226: [4483/124416,[ 1961/15552 185/1728 ],
! 227: [ 79/288 259/864 ]
! 228: [ 259/864 47/288 ]]
! 229: // $BLaCM$O(B [F=F_D, gradient(F), Hessian(F)]
! 230:
! 231: // ekn_gt $B$G$NNc$HF1$8%Q%i%a!<%?(B.
! 232: [3543] A=tk_fd.marginal2abc([5,1],[3,3]);
! 233: [-5,[-3],-1]
! 234: [3544] tk_fd.fd_hessian2(A[0],A[1],A[2],[(1/3)*(1/7)/((1/2)*(1/5))]);
! 235: Computing Dmat(ca) for parameters B=[-3],X=[ 10/21 ]
! 236: [775/27783,[ 20/147 ],[ 17/42 ]]
! 237: @end example
! 238:
! 239: $B;29M(B: $B0lHL$N(B A $BJ,I[$N@55,2=Dj?t$K$D$$$F$N(B Hessian $B$N7W;;$O<B83E*(B package ot_hessian_ahg.rr
! 240: $B$G<BAu$N%F%9%H$,$5$l$F$$$k(B. ($B$3$l$O$^$@L$40@.$N%F%9%HHG$J$N$G=PNO7A<0Ey$b>-MhE*$K$OJQ99$5$l$k(B.)
! 241: @example
! 242: import("ot_hgm_ahg.rr");
! 243: import("ot_hessian_ahg.rr");
! 244: def htest4() @{
! 245: extern C11_A;
! 246: extern C11_Beta;
! 247: Hess=newmat(7,7);
! 248: A =C11_A;
! 249: Beta0= [b0,b1,b2,b3];
! 250: BaseIdx=[4,5,6];
! 251: X=[x0,x1,x2,x3,x4,x5,x6];
! 252: for (I=0; I<7; I++) for (J=0; J<7; J++) @{
! 253: Idx = [I,J];
! 254: H=hessian_simplify(A,Beta0,X,BaseIdx,Idx);
! 255: Hess[I][J]=H;
! 256: printf("[I,J]=%a, Hessian_ij=%a\n",Idx,H);
! 257: @}
! 258: return(Hess);
! 259: @}
! 260: [2917] C11_A;
! 261: [[0,0,0,1,1,1,1],[1,0,0,1,0,1,0],[0,1,1,0,1,0,1],[1,1,0,1,1,0,0]]
! 262: [2918] C11_Beta;
! 263: [166,36,290,214]
! 264: [2919] Ans=htest4$
! 265: [2920] Ans[0][0];
! 266: [[((b1-b0-1)*x4)/(x0^2),[4]],[((b1-b0-1)*x6)/(x0^2),[6]],
! 267: [(b1^2+(-2*b0-1)*b1+b0^2+b0)/(x0^2),[]],[(x6)/(x0),[6,0]],[(x4)/(x0),[4,0]]]
! 268: @end example
! 269:
! 270: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
! 271: @table @t
! 272: @item $B;2>H(B
! 273: @ref{gtt_ekn.setup}
! 274: @ref{gtt_ekn.pfaffian_basis}
! 275: @end table
! 276:
! 277: @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
! 278: @noindent
! 279: ChangeLog
! 280: @itemize @bullet
! 281: @item
! 282: $B$3$N4X?t$O(B
! 283: [GM2016] $B$N%"%k%4%j%:%`$*$h$S(B
! 284: [T2016] $B$K$h$k(B modular method $B$rMQ$$$?9bB.2=$r<BAu$7$?$b$N$G$"$k(B.
! 285: @item
! 286: $BJQ99$r<u$1$?%U%!%$%k$O(B
! 287: OpenXM/src/asir-contrib/packages/src/gtt_ekn.rr 1.1, gtt_ekn/ekn_pfaffian_8.rr
! 288: @end itemize
! 289:
! 290:
! 291: @comment **********************************************************
! 292: @node gtt_ekn.nc,,, $BD64v2?4X?t(BE(k,n)
! 293: @subsection @code{gtt_ekn.nc}
! 294: @comment --- $B:w0zMQ%-!<%o!<%I(B
! 295: @findex gtt_ekn.nc
! 296:
! 297: @table @t
! 298: @item gtt_ekn.nc(@var{beta},@var{p})
! 299: :: $B<~JUOB(B @var{beta}, $B%;%k$N3NN((B @var{p} $B$NFs85J,3dI=$N>r7oIU$-3NN($N@55,2=Dj?t(B Z
! 300: $B$*$h$S$=$NHyJ,$NCM$rLa$9(B.
! 301: @end table
! 302:
! 303: @comment --- $B0z?t$N4JC1$J@bL@(B --- $B0J2<$^$@=q$$$F$J$$(B.
! 304: @table @var
! 305: @item return
! 306: $B%Y%/%H%k(B [Z,[[d_11 Z, d_12 Z, ...], ..., [d_m1 Z, d_m2 Z, ...., d_mn Z]]]
! 307: @item beta
! 308: $B9TOB(B, $BNsOB$N%j%9%H(B. $B@.J,$O$9$Y$F@5$G$"$k$3$H(B.
! 309: @item p
! 310: $BFs85J,3dI=$N%;%k$N3NN($N%j%9%H(B
! 311: @end table
! 312:
! 313: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 314: @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
! 315: @comment --- @bullet $B$O9uE@IU$-(B ---
! 316: @itemize @bullet
! 317: @item
! 318: r1 x r2 $BJ,3dI=$r9M$($k(B.
! 319: m=r1, n=r2 $B$H$*$/(B.
! 320: $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.
! 321: $B$3$3$GOB$O9TOBNsOB$,(B @var{beta} $B$G$"$k$h$&$J(B u $BA4BN$G$H$k(B
! 322: [TKT2015], [GM2016].
! 323: 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.
! 324: d_ij Z $B$G(B Z $B$NJQ?t(B p_ij $B$K$D$$$F$NJPHyJ,$rI=$9(B.
! 325: @item
! 326: nc $B$O(B gmvector $B$NCM$r85$K(B, [GM2016] $B$N(B Prop
! 327: 7.1 $B$K4p$E$$$F(B Z $B$NCM$r7W;;$9$k(B.
! 328: @item
! 329: option crt=1 (crt = Chinese remainder theorem) $B$rM?$($k$H(B, $BJ,;67W;;$r$*$3$J$&(B.
! 330: $BJ,;67W;;MQ$N3F<o%Q%i%a!<%?$N@_Dj$O(B
! 331: gtt_ekn.setup $B$G9T$J$&(B.
! 332: @end itemize
! 333:
! 334: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 335: $BNc(B: 2x3 $BJ,3dI=$G$N(B Z $B$H$=$NHyJ,$N7W;;(B.
! 336: @example
! 337: [2237] gtt_ekn.nc([[4,5],[2,4,3]],[[1,1/2,1/3],[1,1,1]]);
! 338: [4483/124416,[ 353/7776 1961/15552 185/1728 ]
! 339: [ 553/20736 1261/15552 1001/13824 ]]
! 340: @end example
! 341:
! 342: $B;29M(B: 2 x m $BJ,3dI=(B(Lauricella FD)$B$K$D$$$F$O%Q%C%1!<%8(B tk_fd $B$G$b2<5-$N$h$&$KF1Ey$J(B
! 343: $B7W;;$,$G$-$k(B.
! 344: @example
! 345: [3076] import("tk_fd.rr");
! 346: [3077] A=tk_fd.marginal2abc([4,5],[2,4,3]);
! 347: [-4,[-4,-3],-1]
! 348: [3078] tk_fd.ahmat_abc(A[0],A[1],A[2],[[1,1/2,1/3],[1,1,1]]);
! 349: RS=[ 4 5 ], CSnew=[ 2 4 3 ], Ynew=[ 1 1/2 1/3 ]
! 350: [ 1 1 1 ]
! 351: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
! 352: [4483/124416,[[353/7776,1961/15552,185/1728],
! 353: [553/20736,1261/15552,1001/13824]]]
! 354: // $BLaCM$O(B [Z, [[d_11 Z, d_12 Z, d_13 Z],
! 355: // [d_21 Z, d_22 Z, d_23 Z]]] $B$NCM(B.
! 356: // $B$3$3$G(B d_ij $B$O(B i,j $B@.J,$K$D$$$F$NHyJ,$rI=$9(B.
! 357: @end example
! 358:
! 359: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
! 360: @table @t
! 361: @item $B;2>H(B
! 362: @ref{gtt_ekn.setup}
! 363: @ref{gtt_ekn.lognc}
! 364: @end table
! 365:
! 366: @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
! 367: @noindent
! 368: ChangeLog
! 369: @itemize @bullet
! 370: @item
! 371: $BJQ99$r<u$1$?%U%!%$%k$O(B
! 372: OpenXM/src/asir-contrib/packages/src/gtt_ekn.rr 1.1, gtt_ekn/ekn_eval.rr
! 373: @end itemize
! 374:
! 375:
! 376: @comment **********************************************************
! 377: @node gtt_ekn.lognc,,, $BD64v2?4X?t(BE(k,n)
! 378: @subsection @code{gtt_ekn.lognc}
! 379: @comment --- $B:w0zMQ%-!<%o!<%I(B
! 380: @findex gtt_ekn.lognc
! 381:
! 382: @table @t
! 383: @item gtt_ekn.lognc(@var{beta},@var{p})
! 384: :: $B<~JUOB(B @var{beta}, $B%;%k$N3NN((B @var{p} $B$NFs85J,3dI=$N>r7oIU$-3NN($N@55,2=Dj?t(B Z
! 385: $B$N(B log $B$N6a;wCM$*$h$S$=$NHyJ,$N6a;wCM$rLa$9(B.
! 386: @end table
! 387:
! 388: @comment --- $B0z?t$N4JC1$J@bL@(B --- $B0J2<$^$@=q$$$F$J$$(B.
! 389: @table @var
! 390: @item return
! 391: $B%Y%/%H%k(B [log(Z), [[d_11 log(Z), d_12 log(Z), ...], [d_21 log(Z),...], ... ]
! 392: @item beta
! 393: $B9TOB(B, $BNsOB$N%j%9%H(B. $B@.J,$O$9$Y$F@5$G$"$k$3$H(B.
! 394: @item p
! 395: $BFs85J,3dI=$N%;%k$N3NN($N%j%9%H(B
! 396: @end table
! 397:
! 398: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 399: @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
! 400: @comment --- @bullet $B$O9uE@IU$-(B ---
! 401: @itemize @bullet
! 402: @item
! 403: $B>r7oIU$-:GL`?dDj$KMxMQ$9$k(B [TKT2015].
! 404: @item option crt=1 (crt = Chinese remainder theorem) $B$rM?$($k$H(B, $BJ,;67W;;$r$*$3$J$&(B.
! 405: $BJ,;67W;;MQ$N3F<o%Q%i%a!<%?$N@_Dj$O(B
! 406: gtt_ekn.setup $B$G9T$J$&(B.
! 407: @end itemize
! 408:
! 409: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 410: $BNc(B: 2 $B!_(B 3 $BJ,3dI=$G$NNc(B. $BBh0l@.J,$N$_6a;wCM(B.
! 411: @example
! 412: [2238] gtt_ekn.lognc([[4,5],[2,4,3]],[[1,1/2,1/3],[1,1,1]]);
! 413: [-3.32333832422461674630,[ 5648/4483 15688/4483 13320/4483 ]
! 414: [ 3318/4483 10088/4483 9009/4483 ]]
! 415: @end example
! 416:
! 417: $B;29M(B: 2 x m $BJ,3dI=(B(Lauricella FD)$B$K$D$$$F$O%Q%C%1!<%8(B tk_fd $B$G$b2<5-$N$h$&$KF1Ey$J(B
! 418: $B7W;;$,$G$-$k(B.
! 419: @example
! 420: [3076] import("tk_fd.rr");
! 421: [3077] A=tk_fd.marginal2abc([4,5],[2,4,3]);
! 422: [-4,[-4,-3],-1]
! 423: [3078] tk_fd.log_ahmat_abc(A[0],A[1],A[2],[[1,1/2,1/3],[1,1,1]]);
! 424: RS=[ 4 5 ], CSnew=[ 2 4 3 ], Ynew=[ 1 1/2 1/3 ]
! 425: [ 1 1 1 ]
! 426: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
! 427: [-3.32333832422461674639485797719209322217260539267246045320,
! 428: [[1.2598706, 3.499442, 2.971224],
! 429: [0.7401293, 2.250278, 2.009591]]]
! 430: // $BLaCM$O(B [log(Z),
! 431: // [[d_11 log(Z), d_12 log(Z), d_13 log(Z)],
! 432: // [d_21 log(Z), d_22 log(Z), d_23 log(Z)]]]
! 433: // $B$N6a;wCM(B.
! 434: @end example
! 435:
! 436: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
! 437: @table @t
! 438: @item $B;2>H(B
! 439: @ref{gtt_ekn.setup}
! 440: @ref{gtt_ekn.nc}
! 441: @end table
! 442:
! 443: @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
! 444: @noindent
! 445: ChangeLog
! 446: @itemize @bullet
! 447: @item
! 448: $BJQ99$r<u$1$?%U%!%$%k$O(B
! 449: OpenXM/src/asir-contrib/packages/src/gtt_ekn.rr 1.1.
! 450: @end itemize
! 451:
! 452: @comment **********************************************************
! 453: @node gtt_ekn.expectation,,, $BD64v2?4X?t(BE(k,n)
! 454: @subsection @code{gtt_ekn.expectation}
! 455: @comment --- $B:w0zMQ%-!<%o!<%I(B
! 456: @findex gtt_ekn.expectation
! 457:
! 458: @table @t
! 459: @item gtt_ekn.expectation(@var{beta},@var{p})
! 460: :: $B<~JUOB(B @var{beta}, $B%;%k$N3NN((B @var{p} $B$NFs85J,3dI=$N4|BTCM$r7W;;$9$k(B.
! 461: @end table
! 462:
! 463: @comment --- $B0z?t$N4JC1$J@bL@(B --- $B0J2<$^$@=q$$$F$J$$(B.
! 464: @table @var
! 465: @item return
! 466: $BFs85J,3dI=$N3F%;%k$N4|BTCM$N%j%9%H(B.
! 467: @item beta
! 468: $B9TOB(B, $BNsOB$N%j%9%H(B. $B@.J,$O$9$Y$F@5$G$"$k$3$H(B.
! 469: @item p
! 470: $BFs85J,3dI=$N%;%k$N3NN($N%j%9%H(B
! 471: @end table
! 472:
! 473: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 474: @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
! 475: @comment --- @bullet $B$O9uE@IU$-(B ---
! 476: @itemize @bullet
! 477: @item
! 478: [GM2016] $B$N(B Algorithm 7.8 $B$N<BAu(B.
! 479: @item option crt=1 (crt = Chinese remainder theorem) $B$rM?$($k$H(B, $BJ,;67W;;$r$*$3$J$&(B.
! 480: $BJ,;67W;;MQ$N3F<o%Q%i%a!<%?$N@_Dj$O(B
! 481: gtt_ekn.setup $B$G9T$J$&(B.
! 482: @item option index $B$rM?$($k$H(B, $B;XDj$5$l$?@.J,$N4|BTCM$N$_7W;;$9$k(B.
! 483: $B$?$H$($P(B 2 x 2 $BJ,3dI=$G(B index=[[0,0],[1,1]] $B$H;XDj$9$k$H(B, 1 $B$N$"$k@.J,$N4|BTCM$N$_7W;;$9$k(B.
! 484: @end itemize
! 485:
! 486: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 487:
! 488: 2$B!_(B2, 3$B!_(B3 $B$NJ,3dI=$N4|BTCM7W;;Nc(B.
! 489: @example
! 490: [2235] gtt_ekn.expectation([[1,4],[2,3]],[[1,1/3],[1,1]]);
! 491: [ 2/3 1/3 ]
! 492: [ 4/3 8/3 ]
! 493: [2236] gtt_ekn.expectation([[4,5],[2,4,3]],[[1,1/2,1/3],[1,1,1]]);
! 494: [ 5648/4483 7844/4483 4440/4483 ]
! 495: [ 3318/4483 10088/4483 9009/4483 ]
! 496:
! 497: [2442] gtt_ekn.expectation([[4,14,9],[11,6,10]],[[1,1/2,1/3],[1,1/5,1/7],[1,1,1]]);
! 498: [ 207017568232262040/147000422096729819 163140751505489940/147000422096729819
! 499: 217843368649167296/147000422096729819 ]
! 500: [ 1185482401011137878/147000422096729819 358095302885438604/147000422096729819
! 501: 514428205457640984/147000422096729819 ]
! 502: [ 224504673820628091/147000422096729819 360766478189450370/147000422096729819
! 503: 737732646860489910/147000422096729819 ]
! 504: @end example
! 505:
! 506: $B;29M(B: 2 x m $BJ,3dI=(B(Lauricella FD)$B$K$D$$$F$O%Q%C%1!<%8(B tk_fd $B$G$b2<5-$N$h$&$KF1Ey$J(B
! 507: $B7W;;$,$G$-$k(B.
! 508: @example
! 509: [3076] import("tk_fd.rr");
! 510: [3077] A=tk_fd.marginal2abc([4,5],[2,4,3]);
! 511: [-4,[-4,-3],-1]
! 512: [3078] tk_fd.expectation_abc(A[0],A[1],A[2],[[1,1/2,1/3],[1,1,1]]);
! 513: RS=[ 4 5 ], CSnew=[ 2 4 3 ], Ynew=[ 1 1/2 1/3 ]
! 514: [ 1 1 1 ]
! 515: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
! 516: [[5648/4483,7844/4483,4440/4483],
! 517: [3318/4483,10088/4483,9009/4483]]
! 518: // $B3F%;%k$N4|BTCM(B.
! 519: @end example
! 520:
! 521: $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.
! 522: ot_hgm_ahg.rr $B$K$D$$$F$N;29MJ88%(B:
! 523: K.Ohara, N.Takayama, Pfaffian Systems of A-Hypergeometric Systems II --- Holonomic Gradient Method, arxiv:1505.02947
! 524: @example
! 525: [3237] import("ot_hgm_ahg.rr");
! 526: // 2 x 2 $BJ,3dI=(B.
! 527: [3238] hgm_ahg_expected_values_contiguity([[0,0,1,1],[1,0,1,0],[0,1,0,1]],
! 528: [9,6,8],[1/2,1/3,1/5,1/7],[x1,x2,x3,x4]|geometric=1);
! 529: oohg_native=0, oohg_curl=1
! 530: [1376777025/625400597,1750225960/625400597,
! 531: 2375626557/625400597,3252978816/625400597]
! 532: // 2 x 2 $BJ,3dI=$N4|BTCM(B.
! 533:
! 534: // 2 x 3 $BJ,3dI=(B.
! 535: [3238] hgm_ahg_expected_values_contiguity(
! 536: [[0,0,0,1,1,1],[1,0,0,1,0,0],[0,1,0,0,1,0],[0,0,1,0,0,1]],
! 537: [5,2,4,3],[1,1/2,1/3,1,1,1],[x1,x2,x3,x4,x5,x6]|geometric=1);
! 538: [5648/4483,7844/4483,4440/4483,3318/4483,10088/4483,9009/4483]
! 539: // 2 x 3 $BJ,3dI=$N4|BTCM(B. $B>e$HF1$8LdBj(B.
! 540: @end example
! 541:
! 542: 3 x 3 $BJ,3dI=(B. $B9=B$E*(B0$B$,0l$D(B.
! 543: @example
! 544: /*
! 545: dojo, p.221 $B$N%G!<%?(B. $B@.@S(B3$B0J2<$N@8EL$O=8$a$F$R$H$D$K(B.
! 546: 2 1 1
! 547: 8 3 3
! 548: 0 2 6
! 549:
! 550: row sum: 4,14,8
! 551: column sum: 10,6,10
! 552: 0 $B$r0l$D4^$`$N$G(B, (3,6) $B7?$N(B A $B$+$i(B 7 $BNsL\$rH4$/(B.
! 553: */
! 554:
! 555: A=[[0,0,0,1,1,1, 0,0],
! 556: [0,0,0,0,0,0, 1,1],
! 557: [1,0,0,1,0,0, 0,0],
! 558: [0,1,0,0,1,0, 1,0],
! 559: [0,0,1,0,0,1, 0,1]];
! 560: B=[14,8,10,6,10];
! 561: hgm_ahg_expected_values_contiguity(A,B,[1,1/2,1/3,1,1/5,1/7,1,1],
! 562: $B!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(B[x1,x2,x3,x4,x5,x6,x7,x8]|geometric=1);
! 563:
! 564: // $BEz(B.
! 565: [14449864949304/9556267369631,
! 566: 10262588586540/9556267369631, 13512615942680/9556267369631,
! 567: 81112808747006/9556267369631,
! 568: 21816297744346/9556267369631, 30858636683482/9556267369631,
! 569:
! 570: 25258717886900/9556267369631,51191421070148/9556267369631]
! 571: @end example
! 572:
! 573: 3 x 3 $BJ,3dI=(B.
! 574: @example
! 575: /*
! 576: $B>e$N%G!<%?$G(B 0 $B$r(B 1 $B$KJQ99(B.
! 577: 2 1 1
! 578: 8 3 3
! 579: 1 2 6
! 580:
! 581: row sum: 4,14,9
! 582: column sum: 11,6,10
! 583: */
! 584: A=[[0,0,0,1,1,1,0,0,0],
! 585: [0,0,0,0,0,0,1,1,1],
! 586: [1,0,0,1,0,0,1,0,0],
! 587: [0,1,0,0,1,0,0,1,0],
! 588: [0,0,1,0,0,1,0,0,1]];
! 589: B=[14,9,11,6,10];
! 590: hgm_ahg_expected_values_contiguity(A,B,[1,1/2,1/3,1,1/5,1/7,1,1,1],
! 591: [x1,x2,x3,x4,x5,x6,x7,x8]|geometric=1);
! 592:
! 593: // $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.
! 594: [207017568232262040/147000422096729819,
! 595: 163140751505489940/147000422096729819,217843368649167296/147000422096729819,
! 596: 1185482401011137878/147000422096729819,
! 597: 358095302885438604/147000422096729819,514428205457640984/147000422096729819,
! 598: 224504673820628091/147000422096729819,360766478189450370/147000422096729819]
! 599:
! 600: // Z $B$d$=$NHyJ,$N7W;;$O(B hgm_ahg_contiguity $B4X?t$,$*$3$J$&$,(B, $B$3$l$N4J0W%$%s%?!<%U%'!<%9$O(B
! 601: // $B$^$@=q$$$F$J$$(B.
! 602: @end example
! 603:
! 604:
! 605:
! 606: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
! 607: @table @t
! 608: @item $B;2>H(B
! 609: @ref{gtt_ekn.setup}
! 610: @ref{gtt_ekn.nc}
! 611: @end table
! 612:
! 613: @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
! 614: @noindent
! 615: ChangeLog
! 616: @itemize @bullet
! 617: @item
! 618: $BJQ99$r<u$1$?%U%!%$%k$O(B
! 619: OpenXM/src/asir-contrib/packages/src/gtt_ekn.rr 1.1.
! 620: @end itemize
! 621:
! 622:
! 623: @comment **********************************************************
! 624: @comment --- $B"~"~"~"~(B $B$N@bL@(B
! 625: @comment --- $B8D!9$N4X?t$N@bL@$N3+;O(B ---
! 626: @comment --- section $BL>$r@53N$K(B ---
! 627: @node gtt_ekn.setup,,, $BD64v2?4X?t(BE(k,n)
! 628: @subsection @code{gtt_ekn.setup}
! 629: @comment --- $B:w0zMQ%-!<%o!<%I(B
! 630: @findex gtt_ekn.setup
! 631:
! 632: @table @t
! 633: @item gtt_ekn.setup()
! 634: :: $BJ,;67W;;MQ$N4D6-@_Dj$r$*$3$J$&(B. $B8=:_$N4D6-$rJs9p$9$k(B.
! 635: @end table
! 636:
! 637: @comment --- $B0z?t$N4JC1$J@bL@(B --- $B0J2<$^$@=q$$$F$J$$(B.
! 638: @table @var
! 639: @item return
! 640:
! 641: @end table
! 642:
! 643: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 644: @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
! 645: @comment --- @bullet $B$O9uE@IU$-(B ---
! 646: @itemize @bullet
! 647: @item $B;HMQ$9$k%W%m%;%9$HAG?t$N8D?t(B, $B:G>.$NAG?t$rI=<($9$k(B. $B=`Hw$5$l$F$$$J$$>l9g$O$=$N;]$rI=<((B.
! 648: @item option nid (nid = Number of process ID)$B$rM?$($k$H;XDj$7$??t$@$1%W%m%;%9$rMQ0U$9$k(B.
! 649: @item option npl (npl = Prime List or Number of Prime List)$B$rM?$($k$H(Bnpl$B$,J8;zNs$N>l9g;XDj$5$l$?AG?t%j%9%H$N%U%!%$%k$rFI$_9~$`(B. npl$B$,<+A3?t$N>l9g$5$i$K(Boption minp (minp =MINimum Prime)$B$rM?$($k$H(Bminp$B$h$jBg$-$JAG?t$r(Bnpl$B8D@8@.$9$k(B. $B$=$N:](Boption fname (fname = File NAME)$B$rM?$($k$H@8@.$7$?AG?t%j%9%H$r(Bfname$B$H$7$FJ]B8$9$k(B.
! 650: @end itemize
! 651:
! 652: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 653: $BNc(B: $BAG?t$N%j%9%H$r@8@.$7$F%U%!%$%k(B p.txt $B$X=q$-=P$9(B.
! 654: @example
! 655: gtt_ekn.setup(|nps=2,nprm=20,minp=10^10,fgp="p.txt")$
! 656: @end example
! 657:
! 658:
! 659: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
! 660: @table @t
! 661: @item $B;2>H(B
! 662: @ref{gtt_ekn.nc}
! 663: @ref{gtt_ekn.gmvector}
! 664: @end table
! 665:
! 666: @comment --- ChangeLog $B$r=q$/(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
! 667: @noindent
! 668: ChangeLog
! 669: @itemize @bullet
! 670: @item
! 671: $BJQ99$r<u$1$?%U%!%$%k$O(B
! 672: OpenXM/src/asir-contrib/packages/src/gtt_ekn.rr 1.1,
! 673: gtt_ekn/g_mat_fac.rr
! 674:
! 675: @end itemize
! 676:
! 677: @comment **********************************************************
! 678: @comment --- $B"~"~"~"~(B $B$N@bL@(B
! 679: @comment --- $B8D!9$N4X?t$N@bL@$N3+;O(B ---
! 680: @comment --- section $BL>$r@53N$K(B ---
! 681: @node gtt_ekn.upAlpha,,, $BD64v2?4X?t(BE(k,n)
! 682: @subsection @code{gtt_ekn.upAlpha}
! 683: @comment --- $B:w0zMQ%-!<%o!<%I(B
! 684: @findex gtt_ekn.upAlpha
! 685:
! 686: @table @t
! 687: @item gtt_ekn.upAlpha(@var{i},@var{k},@var{n})
! 688: ::
! 689: @end table
! 690:
! 691: @comment --- $B0z?t$N4JC1$J@bL@(B --- $B0J2<$^$@=q$$$F$J$$(B.
! 692: @table @var
! 693: @item i a_i $B$r(B a_i+1 $B$HJQ2=$5$;$k(B contiguity relation.
! 694: @item k E(k+1,n+k+2)$B7?$ND64v2?4X?t$N(B k. $BJ,3dI=$G$O(B (k+1)$B!_(B(n+1).
! 695: @item n E(k+1,n+k+2)$B7?$ND64v2?4X?t$N(B n. $BJ,3dI=$G$O(B (k+1)$B!_(B(n+1).
! 696: @item return contiguity relation $B$N(B pfaffian_basis $B$K$D$$$F$N9TNsI=8=$rLa$9(B. [GM2016] $B$N(B Cor 6.3.
! 697: @end table
! 698:
! 699: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 700: @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
! 701: @comment --- @bullet $B$O9uE@IU$-(B ---
! 702: @itemize @bullet
! 703: @item
! 704: upAlpha $B$O!!(B[GM2016] $B$N(B Cor 6.3 $B$N9TNs(B U_i $B$rLa$9(B.
! 705: @item $B4XO"$9$k3F4X?t$N4J7i$J@bL@$HNc$b2C$($k(B.
! 706: @item a_i $B$r(B a_i-1 $B$HJQ2=$5$;$?$$>l9g$O4X?t(B downAlpha $B$rMQ$$$k(B.
! 707: @item a_i $B$HJ,3dI=$N<~JUOB$r8+$k$K$O(B, $B4X?t(B marginaltoAlpha([$B9TOB(B,$BNsOB(B]) $B$rMQ$$$k(B.
! 708: @item
! 709: pfaffian_basis $B$O(B [GM2016] $B$N#4>O$N%Y%/%H%k(B F $B$KBP1~$9$kJPHyJ,$rLa$9(B.
! 710: @end itemize
! 711:
! 712: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 713: $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.
! 714: [2225] $B$^$G$O=PNO$rN,$7$F$$$k(B.
! 715: @example
! 716: [2221] gtt_ekn.marginaltoAlpha([[1,4],[2,3]]);
! 717: [[a_0,-4],[a_1,-1],[a_2,3],[a_3,2]]
! 718: [2222] gtt_ekn.upAlpha(1,1,1); // E(2,4) $B$N(B a_1 $BJ}8~$N(B
! 719: // contiguity $B$rI=8=$9$k9TNs(B
! 720: [2223] gtt_ekn.upAlpha(2,1,1); // E(2,4) $B$N(B a_2 $BJ}8~(B
! 721: [2224] gtt_ekn.upAlpha(3,1,1); // E(2,4) $B$N(B a_3 $BJ}8~(B
! 722: [2225] function f(x_1_1);
! 723: [2232] gtt_ekn.pfaffian_basis(f(x_1_1),1,1);
! 724: [ f(x_1_1) ]
! 725: [ (f{1}(x_1_1)*x_1_1)/(a_2) ]
! 726: [2233] function f(x_1_1,x_1_2);
! 727: f() redefined.
! 728: [2234] gtt_ekn.pfaffian_basis(f(x_1_1,x_1_2),1,2); // E(2,5), 2*3 $BJ,3dI=(B
! 729: [ f(x_1_1,x_1_2) ]
! 730: [ (f{1,0}(x_1_1,x_1_2)*x_1_1)/(a_2) ]
! 731: [ (f{0,1}(x_1_1,x_1_2)*x_1_2)/(a_3) ]
! 732: @end example
! 733:
! 734:
! 735: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
! 736: @table @t
! 737: @item $B;2>H(B
! 738: @ref{gtt_ekn.nc}
! 739: @ref{gtt_ekn.gmvector}
! 740: @end table
! 741:
! 742: @comment --- ChangeLog $B$r=q$/(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
! 743: @noindent
! 744: ChangeLog
! 745: @itemize @bullet
! 746: @item
! 747: $B$3$N4X?t$O(B [GM2016]
! 748: $B$GM?$($i$l$?%"%k%4%j%:%`$K=>$$(B contiguity relation $B$rF3=P$9$k(B.
! 749: @item
! 750: $BJQ99$r<u$1$?%U%!%$%k$O(B
! 751: OpenXM/src/asir-contrib/packages/src/gtt_ekn/ekn_pfaffian_8.rr 1.1.
! 752: @end itemize
! 753:
! 754:
! 755:
! 756: @comment --- $B$*$^$8$J$$(B ---
! 757: @node Index,,, Top
! 758: @unnumbered Index
! 759: @printindex fn
! 760: @printindex cp
! 761: @iftex
! 762: @vfill @eject
! 763: @end iftex
! 764: @summarycontents
! 765: @contents
! 766: @bye
! 767: @comment --- $B$*$^$8$J$$=*$j(B ---
! 768:
! 769:
! 770: // 2 x m $BJ,3dI=$K$*$$$F;w$?5!G=$rM-$9$k4X?t$NMxMQNc$r;29M$^$G$K5-:\$9$k(B;
! 771: // $B@55,2=Dj?t$H$=$NHyJ,4XO"(B.
! 772: // $B$=$N(B1.
! 773: [3077] A=tk_fd.marginal2abc([4,5],[2,4,3]);
! 774: [-4,[-4,-3],-1]
! 775: [3078] tk_fd.ahmat_abc(A[0],A[1],A[2],[[1,1/2,1/3],[1,1,1]]);
! 776: RS=[ 4 5 ], CSnew=[ 2 4 3 ], Ynew=[ 1 1/2 1/3 ]
! 777: [ 1 1 1 ]
! 778: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
! 779: [4483/124416,[[353/7776,1961/15552,185/1728],[553/20736,1261/15552,1001/13824]]]
! 780: // $BLaCM$O(B [Z, [[d_11 Z, d_12 Z, d_13 Z],[d_21 Z, d_22 Z, d_23 Z]]] $B$NCM(B.
! 781:
! 782: // $B$=$N(B2.
! 783: [3079] tk_fd.log_ahmat_abc(A[0],A[1],A[2],[[1,1/2,1/3],[1,1,1]]);
! 784: RS=[ 4 5 ], CSnew=[ 2 4 3 ], Ynew=[ 1 1/2 1/3 ]
! 785: [ 1 1 1 ]
! 786: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
! 787: [-3.32333832422461674639485797719209322217260539267246045320,
! 788: [[1.25987062235110417131385233102832924380994869507026544724,3.49944233772027660049074280615659156814633058219942003122,2.97122462636627258532232879768012491635065804149007361142],
! 789: [0.740129377648895828686147668971670756190051304929734552754,2.25027883113986169975462859692170421592683470890028998438,2.00959179121124247155922373410662502788311398616997546285]]]
! 790: // $BLaCM$O(B [log(Z),
! 791: // [[d_11 log(Z), d_12 log(Z), d_13 log(Z)],
! 792: // [d_21 log(Z), d_22 log(Z), d_23 log(Z)]]]
! 793: // $B$N6a;wCM(B.
! 794:
! 795: // $B$=$N(B3.
! 796: [3082] fd_hessian2(A[0],A[1],A[2],[1/2,1/3]);
! 797: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
! 798: [4483/124416,[ 1961/15552 185/1728 ],
! 799: [ 79/288 259/864 ]
! 800: [ 259/864 47/288 ]]
! 801: // $BLaCM$O(B [F=F_D, gradient(F), Hessian(F)]
! 802:
! 803: // $B;29M(B.
! 804: // ygahvec $B$G6R4X?tJ,$ND4@0(B. $BFHN)$7$?4X?t$O$J$$$h$&$@(B.
! 805:
! 806: //-----------------------------------------------------------------------
! 807: // 2 x m $BJ,3dI=$K$*$$$F;w$?5!G=$rM-$9$k4X?t$NMxMQNc$r;29M$^$G$K5-:\$9$k(B;
! 808: // $B4|BTCM4XO"(B.
! 809: [3079] A=tk_fd.marginal2abc([4,5],[2,4,3]);
! 810: [-4,[-4,-3],-1]
! 811: [3080] tk_fd.expectation_abc(A[0],A[1],A[2],[[1,1/2,1/3],[1,1,1]]);
! 812: RS=[ 4 5 ], CSnew=[ 2 4 3 ], Ynew=[ 1 1/2 1/3 ]
! 813: [ 1 1 1 ]
! 814: Computing Dmat(ca) for parameters B=[-4,-3],X=[ 1/2 1/3 ]
! 815: [[5648/4483,7844/4483,4440/4483],
! 816: [3318/4483,10088/4483,9009/4483]]
! 817: // $B3F%;%k$N4|BTCM(B.
! 818:
! 819: //-----------------------------------------------------------------------
! 820: // ot_hgm_ahg.rr $B$NNc(B. $B<B83E*$J$?$a(B module $B2=$5$l$F$$$J$$(B.
! 821: [3237] import("ot_hgm_ahg.rr");
! 822: // 2 x 2 $BJ,3dI=(B.
! 823: [3238] hgm_ahg_expected_values_contiguity([[0,0,1,1],[1,0,1,0],[0,1,0,1]],
! 824: [9,6,8],[1/2,1/3,1/5,1/7],[x1,x2,x3,x4]|geometric=1);
! 825: oohg_native=0, oohg_curl=1
! 826: [1376777025/625400597,1750225960/625400597,2375626557/625400597,3252978816/625400597]
! 827: // 2 x 2 $BJ,3dI=$N4|BTCM(B.
! 828:
! 829: // 2 x 3 $BJ,3dI=(B.
! 830: [3238] hgm_ahg_expected_values_contiguity(
! 831: [[0,0,0,1,1,1],[1,0,0,1,0,0],[0,1,0,0,1,0],[0,0,1,0,0,1]],
! 832: [5,2,4,3],[1,1/2,1/3,1,1,1],[x1,x2,x3,x4,x5,x6]|geometric=1);
! 833: [5648/4483,7844/4483,4440/4483,3318/4483,10088/4483,9009/4483]
! 834: // 2 x 3 $BJ,3dI=$N4|BTCM(B. $B>e$HF1$8LdBj(B.
! 835:
! 836: /*
! 837: dojo, p.221. $B@.@S(B3$B0J2<$N@8EL$O=8$a$F$R$H$D$K(B.
! 838: 2 1 1
! 839: 8 3 3
! 840: 0 2 6
! 841:
! 842: row sum: 4,14,8
! 843: column sum: 10,6,10
! 844: 0 $B$r0l$D4^$`$N$G(B, (3,6) $B7?$N(B A $B$+$i(B 7 $BNsL\$rH4$/(B.
! 845: */
! 846: // 3 x 3 $BJ,3dI=(B. $B9=B$E*(B0$B$,0l$D(B.
! 847:
! 848: A=[[0,0,0,1,1,1, 0,0],
! 849: [0,0,0,0,0,0, 1,1],
! 850: [1,0,0,1,0,0, 0,0],
! 851: [0,1,0,0,1,0, 1,0],
! 852: [0,0,1,0,0,1, 0,1]];
! 853: B=[14,8,10,6,10];
! 854: 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);
! 855:
! 856: // $BEz(B.
! 857: [14449864949304/9556267369631,10262588586540/9556267369631,13512615942680/9556267369631,
! 858: 81112808747006/9556267369631,21816297744346/9556267369631,30858636683482/9556267369631,
! 859: 25258717886900/9556267369631,51191421070148/9556267369631]
! 860:
! 861:
! 862: /*
! 863: $B>e$N%G!<%?$G(B 0 $B$r(B 1 $B$KJQ99(B.
! 864: 2 1 1
! 865: 8 3 3
! 866: 1 2 6
! 867:
! 868: row sum: 4,14,9
! 869: column sum: 11,6,10
! 870: */
! 871: // 3 x 3 $BJ,3dI=(B.
! 872: A=[[0,0,0,1,1,1,0,0,0],
! 873: [0,0,0,0,0,0,1,1,1],
! 874: [1,0,0,1,0,0,1,0,0],
! 875: [0,1,0,0,1,0,0,1,0],
! 876: [0,0,1,0,0,1,0,0,1]];
! 877: B=[14,9,11,6,10];
! 878: 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);
! 879:
! 880: // $B4|BTCM(B, $BEz(B.
! 881: [207017568232262040/147000422096729819,163140751505489940/147000422096729819,217843368649167296/147000422096729819,
! 882: 1185482401011137878/147000422096729819,358095302885438604/147000422096729819,514428205457640984/147000422096729819,
! 883: 224504673820628091/147000422096729819,360766478189450370/147000422096729819]
! 884:
! 885: // Z $B$d$=$NHyJ,$N7W;;$O(B hgm_ahg_contiguity $B4X?t$,$*$3$J$&$,(B, $B$3$l$N4J0W%$%s%?!<%U%'!<%9$O(B
! 886: // $B$^$@=q$$$F$J$$(B.
! 887:
! 888:
! 889: 4. x_ij $B$O(B [GM2016] $B$N#1>O$G(B,
! 890: $B$?$H$($P(B 3x3 $B$N;~(B [[1,1,1],[x_11,x_12,1],[x_21,x_22,1]]
! 891: $B$H$J$C$F$$$k$,(B, [GM2016] $B$N(B Prop 7.1 $B$NBP1~$G$O(B,
! 892: 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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