blob: 133cdfff4c95f016f69aae0d0170899b9ed59a83 (plain) (blame)

ofs	hex dump	ascii
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13e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1400	25 0a 25 20 55 73 61 67 65 3a 0a 25 0a 25 20 20 20 20 5b 52 2c 74 2c 53 5d 20 3d 20 66 61 63 74	%.%.Usage:.%.%....[R,t,S].=.fact
1420	6f 72 28 57 29 0a 25 0a 25 20 46 75 6e 63 74 69 6f 6e 20 74 6f 20 66 61 63 74 6f 72 20 61 20 6d	or(W).%.%.Function.to.factor.a.m
1440	61 74 72 69 78 20 6f 66 20 69 6e 70 75 74 20 64 61 74 61 20 28 57 29 20 69 6e 74 6f 20 74 68 65	atrix.of.input.data.(W).into.the
1460	20 63 61 6d 65 72 61 0a 25 20 72 6f 74 61 74 69 6f 6e 20 6d 61 74 72 69 78 20 28 52 29 2c 20 74	.camera.%.rotation.matrix.(R),.t
1480	72 61 6e 73 6c 61 74 69 6f 6e 20 28 74 29 2c 20 61 6e 64 20 74 68 65 20 73 68 61 70 65 20 6d 61	ranslation.(t),.and.the.shape.ma
14a0	74 72 69 78 20 28 53 29 2e 0a 25 20 54 68 72 65 65 2d 64 69 6d 65 6e 73 69 6f 6e 61 6c 20 76 65	trix.(S)..%.Three-dimensional.ve
14c0	72 73 69 6f 6e 2e 20 46 61 69 6c 75 72 65 20 6f 66 20 6e 6f 72 6d 61 6c 69 7a 61 74 69 6f 6e 20	rsion..Failure.of.normalization.
14e0	72 65 73 75 6c 74 73 20 69 6e 0a 25 20 65 6d 70 74 79 20 52 20 61 6e 64 20 53 2e 0a 0a 66 75 6e	results.in.%.empty.R.and.S...fun
1500	63 74 69 6f 6e 20 5b 52 2c 74 2c 53 2c 43 2c 62 5d 20 3d 20 66 61 63 74 6f 72 28 57 29 0a 0a 70	ction.[R,t,S,C,b].=.factor(W)..p
1520	74 73 20 3d 20 73 69 7a 65 28 57 2c 32 29 3b 0a 74 20 3d 20 57 2a 6f 6e 65 73 28 70 74 73 2c 31	ts.=.size(W,2);.t.=.W*ones(pts,1
1540	29 2f 70 74 73 3b 0a 57 20 3d 20 57 20 2d 20 74 2a 6f 6e 65 73 28 31 2c 70 74 73 29 3b 0a 0a 25	)/pts;.W.=.W.-.t*ones(1,pts);..%
1560	20 55 73 65 20 53 56 44 20 74 6f 20 66 61 63 74 6f 72 20 57 2e 20 0a 20 20 20 5b 61 2c 62 2c 63	.Use.SVD.to.factor.W......[a,b,c
1580	5d 20 3d 20 73 76 64 28 57 2c 30 29 3b 0a 0a 66 69 67 75 72 65 28 33 29 3b 70 6c 6f 74 28 64 69	].=.svd(W,0);..figure(3);plot(di
15a0	61 67 28 62 29 29 0a 20 0a 73 6d 61 6c 6c 62 20 3d 20 62 28 31 3a 33 2c 31 3a 33 29 3b 09 25 20	ag(b))...smallb.=.b(1:3,1:3);.%.
15c0	53 69 6e 63 65 20 57 20 69 73 20 72 61 6e 6b 20 33 2c 20 62 20 68 61 73 20 6f 6e 6c 79 20 74 68	Since.W.is.rank.3,.b.has.only.th
15e0	72 65 65 20 6d 65 61 6e 69 6e 67 66 75 6c 20 76 61 6c 75 65 73 0a 73 71 72 74 62 20 3d 20 73 71	ree.meaningful.values.sqrtb.=.sq
1600	72 74 28 73 6d 61 6c 6c 62 29 3b 0a 52 68 61 74 20 3d 20 61 28 3a 2c 31 3a 33 29 20 2a 20 73 71	rt(smallb);.Rhat.=.a(:,1:3).*.sq
1620	72 74 62 3b 0a 53 68 61 74 20 3d 20 73 71 72 74 62 20 2a 20 63 28 3a 2c 31 3a 33 29 27 3b 0a 0a	rtb;.Shat.=.sqrtb.*.c(:,1:3)';..
1640	5b 47 2c 43 5d 20 3d 20 66 69 6e 64 67 32 28 52 68 61 74 29 3b 0a 0a 69 66 20 73 69 7a 65 28 47	[G,C].=.findg2(Rhat);..if.size(G
1660	2c 31 29 20 3d 3d 20 30 2c 0a 52 20 3d 20 5b 5d 3b 0a 53 20 3d 20 5b 5d 3b 0a 65 6c 73 65 0a 20	,1).==.0,.R.=.[];.S.=.[];.else..
1680	20 52 20 3d 20 52 68 61 74 2a 47 3b 0a 20 20 53 20 3d 20 69 6e 76 28 47 29 2a 53 68 61 74 3b 0a	.R.=.Rhat*G;...S.=.inv(G)*Shat;.
16a0	0a 20 20 25 20 72 6f 74 61 74 69 6f 6e 20 6d 61 74 72 69 78 20 74 68 61 74 20 61 6c 69 67 6e 73	...%.rotation.matrix.that.aligns
16c0	20 74 68 65 20 72 65 66 65 72 65 6e 63 65 20 66 72 61 6d 65 20 77 69 74 68 20 74 68 65 20 66 69	.the.reference.frame.with.the.fi
16e0	72 73 74 20 63 61 6d 65 72 61 0a 20 20 46 20 3d 20 73 69 7a 65 28 52 2c 31 29 2f 32 3b 0a 20 20	rst.camera...F.=.size(R,1)/2;...
1700	52 31 20 3d 20 52 28 31 2c 3a 29 3b 0a 20 20 52 31 20 3d 20 52 31 2f 6e 6f 72 6d 28 52 31 29 3b	R1.=.R(1,:);...R1.=.R1/norm(R1);
1720	0a 20 20 52 32 20 3d 20 52 28 46 2b 31 2c 3a 29 3b 0a 20 20 52 32 20 3d 20 52 32 2f 6e 6f 72 6d	...R2.=.R(F+1,:);...R2.=.R2/norm
1740	28 52 32 29 3b 0a 20 20 52 33 20 3d 20 63 72 6f 73 73 28 52 31 2c 52 32 29 3b 0a 20 20 52 33 20	(R2);...R3.=.cross(R1,R2);...R3.
1760	3d 20 52 33 2f 6e 6f 72 6d 28 52 33 29 3b 0a 20 20 50 20 3d 20 5b 52 31 3b 20 52 32 3b 20 52 33	=.R3/norm(R3);...P.=.[R1;.R2;.R3
1780	5d 3b 0a 20 20 50 20 3d 20 50 27 3b 0a 0a 20 20 52 20 3d 20 52 2a 50 3b 0a 20 20 53 20 3d 20 69	];...P.=.P';....R.=.R*P;...S.=.i
17a0	6e 76 28 50 29 2a 53 3b 0a 65 6e 64 0a 0a 0a 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	nv(P)*S;.end....................
17c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
17e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1800	66 61 63 74 6f 72 5f 74 65 73 74 2e 6d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	factor_test.m...................
1820	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1840	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1860	00 00 00 00 30 31 30 30 36 34 34 00 30 30 32 31 33 36 31 00 30 30 30 30 33 33 31 00 30 30 30 30	....0100644.0021361.0000331.0000
1880	30 30 30 31 36 36 30 00 30 35 36 35 37 32 37 37 37 31 30 00 30 31 31 33 36 35 00 20 30 00 00 00	0001660.05657277710.011365..0...
18a0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
18c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
18e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1900	00 75 73 74 61 72 20 20 00 6a 73 68 69 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	.ustar...jshi...................
1920	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1940	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1960	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1980	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
19a0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
19c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
19e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1a00	25 0a 25 20 55 73 61 67 65 3a 0a 25 0a 25 20 20 20 20 5b 52 2c 74 2c 53 5d 20 3d 20 66 61 63 74	%.%.Usage:.%.%....[R,t,S].=.fact
1a20	6f 72 28 57 29 0a 25 0a 25 20 46 75 6e 63 74 69 6f 6e 20 74 6f 20 66 61 63 74 6f 72 20 61 20 6d	or(W).%.%.Function.to.factor.a.m
1a40	61 74 72 69 78 20 6f 66 20 69 6e 70 75 74 20 64 61 74 61 20 28 57 29 20 69 6e 74 6f 20 74 68 65	atrix.of.input.data.(W).into.the
1a60	20 63 61 6d 65 72 61 0a 25 20 72 6f 74 61 74 69 6f 6e 20 6d 61 74 72 69 78 20 28 52 29 2c 20 74	.camera.%.rotation.matrix.(R),.t
1a80	72 61 6e 73 6c 61 74 69 6f 6e 20 28 74 29 2c 20 61 6e 64 20 74 68 65 20 73 68 61 70 65 20 6d 61	ranslation.(t),.and.the.shape.ma
1aa0	74 72 69 78 20 28 53 29 2e 0a 25 20 54 68 72 65 65 2d 64 69 6d 65 6e 73 69 6f 6e 61 6c 20 76 65	trix.(S)..%.Three-dimensional.ve
1ac0	72 73 69 6f 6e 2e 20 46 61 69 6c 75 72 65 20 6f 66 20 6e 6f 72 6d 61 6c 69 7a 61 74 69 6f 6e 20	rsion..Failure.of.normalization.
1ae0	72 65 73 75 6c 74 73 20 69 6e 0a 25 20 65 6d 70 74 79 20 52 20 61 6e 64 20 53 2e 0a 0a 66 75 6e	results.in.%.empty.R.and.S...fun
1b00	63 74 69 6f 6e 20 5b 52 2c 74 2c 53 2c 43 2c 62 5d 20 3d 20 66 61 63 74 6f 72 28 57 29 0a 0a 70	ction.[R,t,S,C,b].=.factor(W)..p
1b20	74 73 20 3d 20 73 69 7a 65 28 57 2c 32 29 3b 0a 74 20 3d 20 57 2a 6f 6e 65 73 28 70 74 73 2c 31	ts.=.size(W,2);.t.=.W*ones(pts,1
1b40	29 2f 70 74 73 3b 0a 57 20 3d 20 57 20 2d 20 74 2a 6f 6e 65 73 28 31 2c 70 74 73 29 3b 0a 0a 25	)/pts;.W.=.W.-.t*ones(1,pts);..%
1b60	20 55 73 65 20 53 56 44 20 74 6f 20 66 61 63 74 6f 72 20 57 2e 20 0a 20 20 20 5b 61 2c 62 2c 63	.Use.SVD.to.factor.W......[a,b,c
1b80	5d 20 3d 20 73 76 64 28 57 2c 30 29 3b 0a 0a 66 69 67 75 72 65 28 33 29 3b 70 6c 6f 74 28 64 69	].=.svd(W,0);..figure(3);plot(di
1ba0	61 67 28 62 29 29 0a 20 0a 73 6d 61 6c 6c 62 20 3d 20 62 28 31 3a 33 2c 31 3a 33 29 3b 09 25 20	ag(b))...smallb.=.b(1:3,1:3);.%.
1bc0	53 69 6e 63 65 20 57 20 69 73 20 72 61 6e 6b 20 33 2c 20 62 20 68 61 73 20 6f 6e 6c 79 20 74 68	Since.W.is.rank.3,.b.has.only.th
1be0	72 65 65 20 6d 65 61 6e 69 6e 67 66 75 6c 20 76 61 6c 75 65 73 0a 73 71 72 74 62 20 3d 20 73 71	ree.meaningful.values.sqrtb.=.sq
1c00	72 74 28 73 6d 61 6c 6c 62 29 3b 0a 52 68 61 74 20 3d 20 61 28 3a 2c 31 3a 33 29 20 2a 20 73 71	rt(smallb);.Rhat.=.a(:,1:3).*.sq
1c20	72 74 62 3b 0a 53 68 61 74 20 3d 20 73 71 72 74 62 20 2a 20 63 28 3a 2c 31 3a 33 29 27 3b 0a 0a	rtb;.Shat.=.sqrtb.*.c(:,1:3)';..
1c40	5b 47 2c 43 5d 20 3d 20 66 69 6e 64 67 31 28 52 68 61 74 29 3b 0a 0a 69 66 20 73 69 7a 65 28 47	[G,C].=.findg1(Rhat);..if.size(G
1c60	2c 31 29 20 3d 3d 20 30 2c 0a 52 20 3d 20 5b 5d 3b 0a 53 20 3d 20 5b 5d 3b 0a 65 6c 73 65 0a 20	,1).==.0,.R.=.[];.S.=.[];.else..
1c80	20 52 20 3d 20 52 68 61 74 2a 47 3b 0a 20 20 53 20 3d 20 69 6e 76 28 47 29 2a 53 68 61 74 3b 0a	.R.=.Rhat*G;...S.=.inv(G)*Shat;.
1ca0	0a 20 20 25 20 72 6f 74 61 74 69 6f 6e 20 6d 61 74 72 69 78 20 74 68 61 74 20 61 6c 69 67 6e 73	...%.rotation.matrix.that.aligns
1cc0	20 74 68 65 20 72 65 66 65 72 65 6e 63 65 20 66 72 61 6d 65 20 77 69 74 68 20 74 68 65 20 66 69	.the.reference.frame.with.the.fi
1ce0	72 73 74 20 63 61 6d 65 72 61 0a 20 20 46 20 3d 20 73 69 7a 65 28 52 2c 31 29 2f 32 3b 0a 20 20	rst.camera...F.=.size(R,1)/2;...
1d00	52 31 20 3d 20 52 28 31 2c 3a 29 3b 0a 20 20 52 31 20 3d 20 52 31 2f 6e 6f 72 6d 28 52 31 29 3b	R1.=.R(1,:);...R1.=.R1/norm(R1);
1d20	0a 20 20 52 32 20 3d 20 52 28 46 2b 31 2c 3a 29 3b 0a 20 20 52 32 20 3d 20 52 32 2f 6e 6f 72 6d	...R2.=.R(F+1,:);...R2.=.R2/norm
1d40	28 52 32 29 3b 0a 20 20 52 33 20 3d 20 63 72 6f 73 73 28 52 31 2c 52 32 29 3b 0a 20 20 52 33 20	(R2);...R3.=.cross(R1,R2);...R3.
1d60	3d 20 52 33 2f 6e 6f 72 6d 28 52 33 29 3b 0a 20 20 50 20 3d 20 5b 52 31 3b 20 52 32 3b 20 52 33	=.R3/norm(R3);...P.=.[R1;.R2;.R3
1d80	5d 3b 0a 20 20 50 20 3d 20 50 27 3b 0a 0a 20 20 52 20 3d 20 52 2a 50 3b 0a 20 20 53 20 3d 20 69	];...P.=.P';....R.=.R*P;...S.=.i
1da0	6e 76 28 50 29 2a 53 3b 0a 65 6e 64 0a 0a 0a 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	nv(P)*S;.end....................
1dc0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1de0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1e00	66 69 6e 64 67 31 2e 6d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	findg1.m........................
1e20	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1e40	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1e60	00 00 00 00 30 31 30 30 36 34 34 00 30 30 32 31 33 36 31 00 30 30 30 30 33 33 31 00 30 30 30 30	....0100644.0021361.0000331.0000
1e80	30 30 30 31 36 35 32 00 30 35 36 37 34 31 36 36 30 30 33 00 30 31 30 32 31 30 00 20 30 00 00 00	0001652.05674166003.010210..0...
1ea0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1ec0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1ee0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1f00	00 75 73 74 61 72 20 20 00 6a 73 68 69 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	.ustar...jshi...................
1f20	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1f40	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1f60	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1f80	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1fa0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1fc0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
1fe0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2000	66 75 6e 63 74 69 6f 6e 20 5b 47 2c 43 5d 20 3d 20 66 69 6e 64 33 47 28 52 68 61 74 29 0a 0a 25	function.[G,C].=.find3G(Rhat)..%
2020	20 6e 75 6d 62 65 72 20 6f 66 20 66 72 61 6d 65 73 0a 46 20 3d 20 73 69 7a 65 28 52 68 61 74 2c	.number.of.frames.F.=.size(Rhat,
2040	31 29 2f 32 3b 0a 0a 25 20 42 75 69 6c 64 20 6d 61 74 72 69 78 20 51 20 73 75 63 68 20 74 68 61	1)/2;..%.Build.matrix.Q.such.tha
2060	74 20 51 20 2a 20 76 20 3d 20 5b 31 2c 2e 2e 2e 2c 31 2c 30 2c 2e 2e 2e 2c 30 5d 20 77 68 65 72	t.Q.*.v.=.[1,...,1,0,...,0].wher
2080	65 20 76 20 69 73 20 61 20 73 69 78 0a 25 20 65 6c 65 6d 65 6e 74 20 76 65 63 74 6f 72 20 63 6f	e.v.is.a.six.%.element.vector.co
20a0	6e 74 61 69 6e 67 20 61 6c 6c 20 73 69 78 20 64 69 73 74 69 6e 63 74 20 65 6c 65 6d 65 6e 74 73	ntaing.all.six.distinct.elements
20c0	20 6f 66 20 74 68 65 20 4d 61 74 72 69 78 20 43 0a 0a 63 6c 65 61 72 20 51 0a 66 6f 72 20 66 20	.of.the.Matrix.C..clear.Q.for.f.
20e0	3d 20 31 3a 46 2c 0a 20 20 67 20 3d 20 66 20 2b 20 46 3b 0a 20 20 68 20 3d 20 67 20 2b 20 46 3b	=.1:F,...g.=.f.+.F;...h.=.g.+.F;
2100	0a 20 20 51 28 66 2c 3a 29 20 3d 20 7a 74 28 52 68 61 74 28 66 2c 3a 29 2c 20 52 68 61 74 28 66	...Q(f,:).=.zt(Rhat(f,:),.Rhat(f
2120	2c 3a 29 29 3b 0a 20 20 51 28 67 2c 3a 29 20 3d 20 7a 74 28 52 68 61 74 28 67 2c 3a 29 2c 20 52	,:));...Q(g,:).=.zt(Rhat(g,:),.R
2140	68 61 74 28 67 2c 3a 29 29 3b 0a 20 20 51 28 68 2c 3a 29 20 3d 20 7a 74 28 52 68 61 74 28 66 2c	hat(g,:));...Q(h,:).=.zt(Rhat(f,
2160	3a 29 2c 20 52 68 61 74 28 67 2c 3a 29 29 3b 0a 65 6e 64 0a 0a 25 20 53 6f 6c 76 65 20 66 6f 72	:),.Rhat(g,:));.end..%.Solve.for
2180	20 76 0a 72 68 73 20 3d 20 5b 6f 6e 65 73 28 32 2a 46 2c 31 29 3b 20 7a 65 72 6f 73 28 46 2c 31	.v.rhs.=.[ones(2*F,1);.zeros(F,1
21a0	29 5d 3b 0a 76 20 3d 20 51 20 5c 20 72 68 73 3b 0a 0a 25 20 43 20 69 73 20 61 20 73 79 6d 6d 65	)];.v.=.Q.\.rhs;..%.C.is.a.symme
21c0	74 72 69 63 20 33 78 33 20 6d 61 74 72 69 78 20 73 75 63 68 20 74 68 61 74 20 43 20 3d 20 47 20	tric.3x3.matrix.such.that.C.=.G.
21e0	2a 20 74 72 61 6e 73 70 6f 73 65 28 47 29 0a 43 28 31 2c 31 29 20 3d 20 76 28 31 29 3b 20 20 20	*.transpose(G).C(1,1).=.v(1);...
2200	20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 0a 43 28 31 2c 32 29 20 3d 20 76 28 32 29 3b 20 20	................C(1,2).=.v(2);..
2220	20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 0a 43 28 31 2c 33 29 20 3d 20 76 28 33 29 3b 20	.................C(1,3).=.v(3);.
2240	20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 0a 43 28 32 2c 32 29 20 3d 20 76 28 34 29 3b	..................C(2,2).=.v(4);
2260	0a 43 28 32 2c 33 29 20 3d 20 76 28 35 29 3b 0a 43 28 33 2c 33 29 20 3d 20 76 28 36 29 3b 0a 43	.C(2,3).=.v(5);.C(3,3).=.v(6);.C
2280	28 32 2c 31 29 20 3d 20 43 28 31 2c 32 29 3b 0a 43 28 33 2c 31 29 20 3d 20 43 28 31 2c 33 29 3b	(2,1).=.C(1,2);.C(3,1).=.C(1,3);
22a0	0a 43 28 33 2c 32 29 20 3d 20 43 28 32 2c 33 29 3b 0a 0a 65 20 3d 20 65 69 67 28 43 29 3b 0a 64	.C(3,2).=.C(2,3);..e.=.eig(C);.d
22c0	69 73 70 28 65 29 0a 0a 69 66 20 28 61 6e 79 28 65 3c 3d 20 30 29 29 2c 0a 20 20 43 20 3d 20 43	isp(e)..if.(any(e<=.0)),...C.=.C
22e0	20 2d 32 2a 6d 69 6e 28 65 29 2a 65 79 65 28 33 29 3b 0a 20 20 47 20 3d 20 73 71 72 74 6d 28 43	.-2*min(e)*eye(3);...G.=.sqrtm(C
2300	29 3b 0a 65 6c 73 65 0a 20 20 47 20 3d 20 73 71 72 74 6d 28 43 29 3b 0a 65 6e 64 0a 0a 25 6e 65	);.else...G.=.sqrtm(C);.end..%ne
2320	67 20 3d 20 30 3b 0a 25 69 66 20 65 28 31 29 20 3c 3d 20 30 2c 20 6e 65 67 20 3d 20 31 3b 20 65	g.=.0;.%if.e(1).<=.0,.neg.=.1;.e
2340	6e 64 0a 25 69 66 20 65 28 32 29 20 3c 3d 20 30 2c 20 6e 65 67 20 3d 20 31 3b 20 65 6e 64 0a 25	nd.%if.e(2).<=.0,.neg.=.1;.end.%
2360	69 66 20 65 28 33 29 20 3c 3d 20 30 2c 20 6e 65 67 20 3d 20 31 3b 20 65 6e 64 0a 25 69 66 20 6e	if.e(3).<=.0,.neg.=.1;.end.%if.n
2380	65 67 20 3d 3d 20 31 2c 20 47 20 3d 20 5b 5d 3b 0a 25 65 6c 73 65 20 47 20 3d 20 73 71 72 74 6d	eg.==.1,.G.=.[];.%else.G.=.sqrtm
23a0	28 43 29 3b 0a 25 65 6e 64 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	(C);.%end.......................
23c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
23e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2400	66 69 6e 64 67 32 2e 6d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	findg2.m........................
2420	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2440	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2460	00 00 00 00 30 31 30 30 36 34 34 00 30 30 32 31 33 36 31 00 30 30 30 30 33 33 31 00 30 30 30 30	....0100644.0021361.0000331.0000
2480	30 30 30 32 31 30 33 00 30 35 36 37 34 32 32 32 36 34 30 00 30 31 30 32 30 31 00 20 30 00 00 00	0002103.05674222640.010201..0...
24a0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
24c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
24e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2500	00 75 73 74 61 72 20 20 00 6a 73 68 69 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	.ustar...jshi...................
2520	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2540	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2560	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2580	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
25a0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
25c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
25e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2600	66 75 6e 63 74 69 6f 6e 20 5b 47 2c 43 5d 20 3d 20 66 69 6e 64 33 47 28 52 68 61 74 29 0a 0a 25	function.[G,C].=.find3G(Rhat)..%
2620	20 6e 75 6d 62 65 72 20 6f 66 20 66 72 61 6d 65 73 0a 46 20 3d 20 73 69 7a 65 28 52 68 61 74 2c	.number.of.frames.F.=.size(Rhat,
2640	31 29 2f 33 3b 0a 0a 25 20 42 75 69 6c 64 20 6d 61 74 72 69 78 20 51 20 73 75 63 68 20 74 68 61	1)/3;..%.Build.matrix.Q.such.tha
2660	74 20 51 20 2a 20 76 20 3d 20 5b 31 2c 2e 2e 2e 2c 31 2c 30 2c 2e 2e 2e 2c 30 5d 20 77 68 65 72	t.Q.*.v.=.[1,...,1,0,...,0].wher
2680	65 20 76 20 69 73 20 61 20 73 69 78 0a 25 20 65 6c 65 6d 65 6e 74 20 76 65 63 74 6f 72 20 63 6f	e.v.is.a.six.%.element.vector.co
26a0	6e 74 61 69 6e 67 20 61 6c 6c 20 73 69 78 20 64 69 73 74 69 6e 63 74 20 65 6c 65 6d 65 6e 74 73	ntaing.all.six.distinct.elements
26c0	20 6f 66 20 74 68 65 20 4d 61 74 72 69 78 20 43 0a 0a 63 6c 65 61 72 20 51 0a 66 6f 72 20 66 20	.of.the.Matrix.C..clear.Q.for.f.
26e0	3d 20 31 3a 46 2c 0a 20 20 67 20 3d 20 66 20 2b 20 46 3b 0a 20 20 68 20 3d 20 67 20 2b 20 46 3b	=.1:F,...g.=.f.+.F;...h.=.g.+.F;
2700	0a 20 20 6a 20 3d 20 68 20 2b 20 46 3b 0a 20 20 6b 20 3d 20 6a 20 2b 20 46 3b 0a 20 20 6c 20 3d	...j.=.h.+.F;...k.=.j.+.F;...l.=
2720	20 6b 20 2b 20 46 3b 0a 20 20 51 28 66 2c 3a 29 20 3d 20 7a 74 28 52 68 61 74 28 66 2c 3a 29 2c	.k.+.F;...Q(f,:).=.zt(Rhat(f,:),
2740	20 52 68 61 74 28 66 2c 3a 29 29 3b 0a 20 20 51 28 67 2c 3a 29 20 3d 20 7a 74 28 52 68 61 74 28	.Rhat(f,:));...Q(g,:).=.zt(Rhat(
2760	67 2c 3a 29 2c 20 52 68 61 74 28 67 2c 3a 29 29 3b 0a 20 20 51 28 68 2c 3a 29 20 3d 20 7a 74 28	g,:),.Rhat(g,:));...Q(h,:).=.zt(
2780	52 68 61 74 28 68 2c 3a 29 2c 20 52 68 61 74 28 68 2c 3a 29 29 3b 0a 20 20 51 28 6a 2c 3a 29 20	Rhat(h,:),.Rhat(h,:));...Q(j,:).
27a0	3d 20 7a 74 28 52 68 61 74 28 66 2c 3a 29 2c 20 52 68 61 74 28 67 2c 3a 29 29 3b 0a 20 20 51 28	=.zt(Rhat(f,:),.Rhat(g,:));...Q(
27c0	6b 2c 3a 29 20 3d 20 7a 74 28 52 68 61 74 28 66 2c 3a 29 2c 20 52 68 61 74 28 68 2c 3a 29 29 3b	k,:).=.zt(Rhat(f,:),.Rhat(h,:));
27e0	0a 20 20 51 28 6c 2c 3a 29 20 3d 20 7a 74 28 52 68 61 74 28 67 2c 3a 29 2c 20 52 68 61 74 28 68	...Q(l,:).=.zt(Rhat(g,:),.Rhat(h
2800	2c 3a 29 29 3b 0a 65 6e 64 0a 0a 25 20 53 6f 6c 76 65 20 66 6f 72 20 76 0a 72 68 73 20 3d 20 5b	,:));.end..%.Solve.for.v.rhs.=.[
2820	6f 6e 65 73 28 33 2a 46 2c 31 29 3b 20 7a 65 72 6f 73 28 33 2a 46 2c 31 29 5d 3b 0a 76 20 3d 20	ones(3*F,1);.zeros(3*F,1)];.v.=.
2840	51 20 5c 20 72 68 73 3b 0a 0a 25 20 43 20 69 73 20 61 20 73 79 6d 6d 65 74 72 69 63 20 33 78 33	Q.\.rhs;..%.C.is.a.symmetric.3x3
2860	20 6d 61 74 72 69 78 20 73 75 63 68 20 74 68 61 74 20 43 20 3d 20 47 20 2a 20 74 72 61 6e 73 70	.matrix.such.that.C.=.G.*.transp
2880	6f 73 65 28 47 29 0a 43 28 31 2c 31 29 20 3d 20 76 28 31 29 3b 20 20 20 20 20 20 20 20 20 20 20	ose(G).C(1,1).=.v(1);...........
28a0	20 20 20 20 20 20 20 0a 43 28 31 2c 32 29 20 3d 20 76 28 32 29 3b 20 20 20 20 20 20 20 20 20 20	........C(1,2).=.v(2);..........
28c0	20 20 20 20 20 20 20 20 0a 43 28 31 2c 33 29 20 3d 20 76 28 33 29 3b 20 20 20 20 20 20 20 20 20	.........C(1,3).=.v(3);.........
28e0	20 20 20 20 20 20 20 20 20 0a 43 28 32 2c 32 29 20 3d 20 76 28 34 29 3b 0a 43 28 32 2c 33 29 20	..........C(2,2).=.v(4);.C(2,3).
2900	3d 20 76 28 35 29 3b 0a 43 28 33 2c 33 29 20 3d 20 76 28 36 29 3b 0a 43 28 32 2c 31 29 20 3d 20	=.v(5);.C(3,3).=.v(6);.C(2,1).=.
2920	43 28 31 2c 32 29 3b 0a 43 28 33 2c 31 29 20 3d 20 43 28 31 2c 33 29 3b 0a 43 28 33 2c 32 29 20	C(1,2);.C(3,1).=.C(1,3);.C(3,2).
2940	3d 20 43 28 32 2c 33 29 3b 0a 0a 65 20 3d 20 65 69 67 28 43 29 3b 0a 64 69 73 70 28 65 29 0a 0a	=.C(2,3);..e.=.eig(C);.disp(e)..
2960	0a 69 66 20 28 61 6e 79 28 65 3c 3d 20 30 29 29 2c 0a 20 20 43 20 3d 20 43 20 2d 32 2a 6d 69 6e	.if.(any(e<=.0)),...C.=.C.-2*min
2980	28 65 29 2a 65 79 65 28 33 29 3b 0a 20 20 47 20 3d 20 73 71 72 74 6d 28 43 29 3b 0a 65 6c 73 65	(e)*eye(3);...G.=.sqrtm(C);.else
29a0	0a 20 20 47 20 3d 20 73 71 72 74 6d 28 43 29 3b 0a 65 6e 64 0a 0a 25 6e 65 67 20 3d 20 30 3b 0a	...G.=.sqrtm(C);.end..%neg.=.0;.
29c0	25 69 66 20 65 28 31 29 20 3c 3d 20 30 2c 20 6e 65 67 20 3d 20 31 3b 20 65 6e 64 0a 25 69 66 20	%if.e(1).<=.0,.neg.=.1;.end.%if.
29e0	65 28 32 29 20 3c 3d 20 30 2c 20 6e 65 67 20 3d 20 31 3b 20 65 6e 64 0a 25 69 66 20 65 28 33 29	e(2).<=.0,.neg.=.1;.end.%if.e(3)
2a00	20 3c 3d 20 30 2c 20 6e 65 67 20 3d 20 31 3b 20 65 6e 64 0a 25 69 66 20 6e 65 67 20 3d 3d 20 31	.<=.0,.neg.=.1;.end.%if.neg.==.1
2a20	2c 20 47 20 3d 20 5b 5d 3b 0a 25 65 6c 73 65 20 47 20 3d 20 73 71 72 74 6d 28 43 29 3b 0a 25 65	,.G.=.[];.%else.G.=.sqrtm(C);.%e
2a40	6e 64 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	nd..............................
2a60	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2a80	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2aa0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2ac0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2ae0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2b00	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2b20	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2b40	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2b60	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2b80	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2ba0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2bc0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2be0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2c00	66 69 6e 64 47 2e 6d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	findG.m.........................
2c20	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2c40	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2c60	00 00 00 00 30 31 30 30 36 34 34 00 30 30 32 31 33 36 31 00 30 30 30 30 33 33 31 00 30 30 30 30	....0100644.0021361.0000331.0000
2c80	30 30 30 31 36 30 36 00 30 35 36 35 33 32 36 34 35 30 33 00 30 31 30 30 36 37 00 20 30 00 00 00	0001606.05653264503.010067..0...
2ca0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2cc0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2ce0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2d00	00 75 73 74 61 72 20 20 00 6a 73 68 69 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	.ustar...jshi...................
2d20	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2d40	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2d60	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2d80	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2da0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2dc0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2de0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
2e00	66 75 6e 63 74 69 6f 6e 20 47 20 3d 20 66 69 6e 64 33 47 28 52 68 61 74 29 0a 0a 25 20 6e 75 6d	function.G.=.find3G(Rhat)..%.num
2e20	62 65 72 20 6f 66 20 66 72 61 6d 65 73 0a 46 20 3d 20 73 69 7a 65 28 52 68 61 74 2c 31 29 2f 32	ber.of.frames.F.=.size(Rhat,1)/2
2e40	3b 0a 0a 25 20 42 75 69 6c 64 20 6d 61 74 72 69 78 20 51 20 73 75 63 68 20 74 68 61 74 20 51 20	;..%.Build.matrix.Q.such.that.Q.
2e60	2a 20 76 20 3d 20 5b 31 2c 2e 2e 2e 2c 31 2c 30 2c 2e 2e 2e 2c 30 5d 20 77 68 65 72 65 20 76 20	*.v.=.[1,...,1,0,...,0].where.v.
2e80	69 73 20 61 20 73 69 78 0a 25 20 65 6c 65 6d 65 6e 74 20 76 65 63 74 6f 72 20 63 6f 6e 74 61 69	is.a.six.%.element.vector.contai
2ea0	6e 67 20 61 6c 6c 20 73 69 78 20 64 69 73 74 69 6e 63 74 20 65 6c 65 6d 65 6e 74 73 20 6f 66 20	ng.all.six.distinct.elements.of.
2ec0	74 68 65 20 4d 61 74 72 69 78 20 43 0a 0a 63 6c 65 61 72 20 51 0a 66 6f 72 20 66 20 3d 20 31 3a	the.Matrix.C..clear.Q.for.f.=.1:
2ee0	46 2c 0a 20 20 67 20 3d 20 66 20 2b 20 46 3b 0a 20 20 68 20 3d 20 67 20 2b 20 46 3b 0a 20 20 51	F,...g.=.f.+.F;...h.=.g.+.F;...Q
2f00	28 66 2c 3a 29 20 3d 20 7a 74 28 52 68 61 74 28 66 2c 3a 29 2c 20 52 68 61 74 28 66 2c 3a 29 29	(f,:).=.zt(Rhat(f,:),.Rhat(f,:))
2f20	3b 0a 20 20 51 28 67 2c 3a 29 20 3d 20 7a 74 28 52 68 61 74 28 67 2c 3a 29 2c 20 52 68 61 74 28	;...Q(g,:).=.zt(Rhat(g,:),.Rhat(
2f40	67 2c 3a 29 29 3b 0a 20 20 51 28 68 2c 3a 29 20 3d 20 7a 74 28 52 68 61 74 28 66 2c 3a 29 2c 20	g,:));...Q(h,:).=.zt(Rhat(f,:),.
2f60	52 68 61 74 28 67 2c 3a 29 29 3b 0a 65 6e 64 0a 0a 25 20 53 6f 6c 76 65 20 66 6f 72 20 76 0a 72	Rhat(g,:));.end..%.Solve.for.v.r
2f80	68 73 20 3d 20 5b 6f 6e 65 73 28 32 2a 46 2c 31 29 3b 20 7a 65 72 6f 73 28 46 2c 31 29 5d 3b 0a	hs.=.[ones(2*F,1);.zeros(F,1)];.
2fa0	76 20 3d 20 51 20 5c 20 72 68 73 3b 0a 0a 25 20 43 20 69 73 20 61 20 73 79 6d 6d 65 74 72 69 63	v.=.Q.\.rhs;..%.C.is.a.symmetric
2fc0	20 33 78 33 20 6d 61 74 72 69 78 20 73 75 63 68 20 74 68 61 74 20 43 20 3d 20 47 20 2a 20 74 72	.3x3.matrix.such.that.C.=.G.*.tr
2fe0	61 6e 73 70 6f 73 65 28 47 29 0a 43 28 31 2c 31 29 20 3d 20 76 28 31 29 3b 20 20 20 20 20 20 20	anspose(G).C(1,1).=.v(1);.......
3000	20 20 20 20 20 20 20 20 20 20 20 0a 43 28 31 2c 32 29 20 3d 20 76 28 32 29 3b 20 20 20 20 20 20	............C(1,2).=.v(2);......
3020	20 20 20 20 20 20 20 20 20 20 20 20 0a 43 28 31 2c 33 29 20 3d 20 76 28 33 29 3b 20 20 20 20 20	.............C(1,3).=.v(3);.....
3040	20 20 20 20 20 20 20 20 20 20 20 20 20 0a 43 28 32 2c 32 29 20 3d 20 76 28 34 29 3b 0a 43 28 32	..............C(2,2).=.v(4);.C(2
3060	2c 33 29 20 3d 20 76 28 35 29 3b 0a 43 28 33 2c 33 29 20 3d 20 76 28 36 29 3b 0a 43 28 32 2c 31	,3).=.v(5);.C(3,3).=.v(6);.C(2,1
3080	29 20 3d 20 43 28 31 2c 32 29 3b 0a 43 28 33 2c 31 29 20 3d 20 43 28 31 2c 33 29 3b 0a 43 28 33	).=.C(1,2);.C(3,1).=.C(1,3);.C(3
30a0	2c 32 29 20 3d 20 43 28 32 2c 33 29 3b 0a 0a 65 20 3d 20 65 69 67 28 43 29 3b 0a 64 69 73 70 28	,2).=.C(2,3);..e.=.eig(C);.disp(
30c0	65 29 0a 0a 69 66 20 28 61 6e 79 28 65 3c 3d 20 30 29 29 2c 0a 20 20 47 20 3d 20 5b 5d 3b 0a 65	e)..if.(any(e<=.0)),...G.=.[];.e
30e0	6c 73 65 0a 20 20 47 20 3d 20 73 71 72 74 6d 28 43 29 3b 0a 65 6e 64 0a 0a 25 6e 65 67 20 3d 20	lse...G.=.sqrtm(C);.end..%neg.=.
3100	30 3b 0a 25 69 66 20 65 28 31 29 20 3c 3d 20 30 2c 20 6e 65 67 20 3d 20 31 3b 20 65 6e 64 0a 25	0;.%if.e(1).<=.0,.neg.=.1;.end.%
3120	69 66 20 65 28 32 29 20 3c 3d 20 30 2c 20 6e 65 67 20 3d 20 31 3b 20 65 6e 64 0a 25 69 66 20 65	if.e(2).<=.0,.neg.=.1;.end.%if.e
3140	28 33 29 20 3c 3d 20 30 2c 20 6e 65 67 20 3d 20 31 3b 20 65 6e 64 0a 25 69 66 20 6e 65 67 20 3d	(3).<=.0,.neg.=.1;.end.%if.neg.=
3160	3d 20 31 2c 20 47 20 3d 20 5b 5d 3b 0a 25 65 6c 73 65 20 47 20 3d 20 73 71 72 74 6d 28 43 29 3b	=.1,.G.=.[];.%else.G.=.sqrtm(C);
3180	0a 25 65 6e 64 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	.%end...........................
31a0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
31c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
31e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3200	73 68 6f 77 5f 33 64 70 6f 69 6e 74 73 2e 6d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	show_3dpoints.m.................
3220	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3240	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3260	00 00 00 00 30 31 30 30 36 34 34 00 30 30 32 31 33 36 31 00 30 30 30 30 33 33 31 00 30 30 30 30	....0100644.0021361.0000331.0000
3280	30 30 30 30 35 34 34 00 30 35 36 35 33 32 36 37 36 37 34 00 30 31 31 36 35 37 00 20 30 00 00 00	0000544.05653267674.011657..0...
32a0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
32c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
32e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3300	00 75 73 74 61 72 20 20 00 6a 73 68 69 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	.ustar...jshi...................
3320	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3340	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3360	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3380	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
33a0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
33c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
33e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3400	66 75 6e 63 74 69 6f 6e 20 73 68 6f 77 5f 33 64 70 6f 69 6e 74 73 28 53 29 0a 0a 0a 66 6f 72 20	function.show_3dpoints(S)...for.
3420	6a 3d 31 3a 73 69 7a 65 28 53 2c 32 29 2c 0a 20 20 78 20 3d 20 53 28 31 2c 6a 29 3b 0a 20 20 79	j=1:size(S,2),...x.=.S(1,j);...y
3440	20 3d 20 53 28 32 2c 6a 29 3b 0a 20 20 7a 20 3d 20 53 28 33 2c 6a 29 3b 0a 20 20 70 6c 6f 74 33	.=.S(2,j);...z.=.S(3,j);...plot3
3460	28 78 2c 79 2c 7a 2c 27 2a 27 29 3b 0a 20 20 68 6f 6c 64 20 6f 6e 3b 0a 20 20 70 6c 6f 74 33 28	(x,y,z,'*');...hold.on;...plot3(
3480	5b 78 2c 30 5d 2c 5b 79 2c 30 5d 2c 5b 7a 2c 30 5d 2c 27 72 27 29 3b 0a 25 20 20 70 6c 6f 74 33	[x,0],[y,0],[z,0],'r');.%..plot3
34a0	28 5b 78 2c 78 5d 2c 5b 79 2c 79 5d 2c 5b 7a 2c 30 5d 2c 27 72 27 29 3b 0a 25 20 20 70 6c 6f 74	([x,x],[y,y],[z,0],'r');.%..plot
34c0	33 28 5b 78 2c 30 5d 2c 5b 79 2c 79 5d 2c 5b 7a 2c 7a 5d 2c 27 72 27 29 3b 20 70 6c 6f 74 33 28	3([x,0],[y,y],[z,z],'r');.plot3(
34e0	5b 78 2c 78 5d 2c 5b 79 2c 30 5d 2c 5b 7a 2c 7a 5d 2c 27 72 27 29 3b 0a 20 20 74 65 78 74 28 78	[x,x],[y,0],[z,z],'r');...text(x
3500	2c 79 2c 7a 2c 69 6e 74 32 73 74 72 28 6a 29 29 0a 25 20 20 70 6c 6f 74 33 28 78 2c 79 2c 30 2c	,y,z,int2str(j)).%..plot3(x,y,0,
3520	27 63 6f 27 29 3b 0a 65 6e 64 0a 0a 67 72 69 64 20 6f 6e 0a 78 6c 61 62 65 6c 28 27 78 27 29 3b	'co');.end..grid.on.xlabel('x');
3540	0a 79 6c 61 62 65 6c 28 27 79 27 29 3b 0a 7a 6c 61 62 65 6c 28 27 7a 27 29 3b 0a 0a 68 6f 6c 64	.ylabel('y');.zlabel('z');..hold
3560	20 6f 66 66 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	.off............................
3580	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
35a0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
35c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
35e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3600	73 68 6f 77 5f 53 2e 6d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	show_S.m........................
3620	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3640	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3660	00 00 00 00 30 31 30 30 36 34 34 00 30 30 32 31 33 36 31 00 30 30 30 30 33 33 31 00 30 30 30 30	....0100644.0021361.0000331.0000
3680	30 30 30 30 36 32 30 00 30 35 36 35 36 33 37 30 35 33 37 00 30 31 30 33 30 35 00 20 30 00 00 00	0000620.05656370537.010305..0...
36a0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
36c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
36e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3700	00 75 73 74 61 72 20 20 00 6a 73 68 69 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	.ustar...jshi...................
3720	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3740	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3760	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3780	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
37a0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
37c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
37e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................................
3800	66 75 6e 63 74 69 6f 6e 20 73 68 6f 77 5f 53 28 53 2c 66 69 67 29 0a 0a 69 66 20 28 6e 61 72 67	function.show_S(S,fig)..if.(narg
3820	69 6e 20 3d 3d 20 31 29 2c 0a 20 20 66 69 67 75 72 65 28 31 29 3b 0a 65 6c 73 65 0a 20 20 66 69	in.==.1),...figure(1);.else...fi
3840	67 75 72 65 28 66 69 67 29 3b 0a 65 6e 64 0a 0a 6e 75 6d 5f 70 6f 69 6e 74 73 20 3d 20 73 69 7a	gure(fig);.end..num_points.=.siz
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3c20	67 74 68 28 74 29 2f 33 3b 0a 0a 74 73 20 3d 20 72 65 73 68 61 70 65 28 74 2c 66 72 61 6d 65 73	gth(t)/3;..ts.=.reshape(t,frames
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4000	66 75 6e 63 74 69 6f 6e 20 73 68 6f 77 5f 74 28 74 29 0a 0a 66 72 61 6d 65 73 20 3d 20 30 2e 35	function.show_t(t)..frames.=.0.5
4020	2a 6c 65 6e 67 74 68 28 74 29 3b 0a 0a 74 73 20 3d 20 72 65 73 68 61 70 65 28 74 2c 66 72 61 6d	*length(t);..ts.=.reshape(t,fram
4040	65 73 2c 32 29 3b 0a 0a 70 6c 6f 74 28 74 73 28 3a 2c 31 29 2c 74 73 28 3a 2c 32 29 29 3b 0a 68	es,2);..plot(ts(:,1),ts(:,2));.h
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12360	eb b2 89 0e 0e 0e 39 39 39 83 0e 70 01 7a c0 ed ed ed 01 34 34 34 4f 1b 1e 72 40 03 20 ea 79 6b	......999..p.z.....444O..r@...yk
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