mass矩阵入门，matlab

function M = massmatrix(V,F, type)
% MASSMATRIX mass matrix for the mesh given by V and F
%
% M = massmatrix(V,F, type)
% M = massmatrix(V,T, type)
%
% Inputs:
% V #V x 3 matrix of vertex coordinates
% F #F x simplex-size matrix of indices of triangle corners
% type string containing type of mass matrix to compute
% ‘full’: full mass matrix for p.w. linear fem
% ‘barycentric’: diagonal lumped mass matrix obtained by summing 1/3
% ‘voronoi’: true voronoi area, except in cases where triangle is obtuse
% then uses 1/2, 1/4, 1/4 {simplex size 3 only}
% Output:
% M #V by #V sparse mass matrix
%
% Copyright 2011, Alec Jacobson ([e-mail])
%

function r = cross2(a,b)
% Optimizes r = cross(a,b,2), that is it computes cross products per row
% Faster than cross if I know that I’m calling it correctly
r =[a(:,2).*b(:,3)-a(:,3).*b(:,2), …
a(:,3).*b(:,1)-a(:,1).*b(:,3), …
a(:,1).*b(:,2)-a(:,2).*b(:,1)];
end

% simplex size
ss = size(F,2);
if nargin<3
switch ss
case 3
type = ‘voronoi’;
case {2,4}
type = ‘barycentric’;
end
end

switch ss
case 2
l = edge_lengths(V,F);
switch type
case {‘voronoi’,‘barycentric’}
M = sparse(F(,F(,[l l]/size(V,2),size(V,1),size(V,1));
case ‘full’
% renaming indices of vertices of triangles for convenience
i1 = F(:,1); i2 = F(:,2);
i = [i1 i2 i1 i2];
j = [i2 i1 i1 i2];
v = [l/4 l/4 l/2 l/2];
M = sparse(i,j,v,size(V,1),size(V,1));
end
case 3
% should change code below, so we don’t need this transpose
if(size(F,1) == 3)
warning(‘F seems to be 3 by #F, it should be #F by 3’);
end
F = F’;

% renaming indices of vertices of triangles for convenience
i1 = F(1,:); i2 = F(2,:); i3 = F(3,:); 
% #F x 3 matrices of triangle edge vectors, named after opposite vertices
v1 = V(i3,:) - V(i2,:);  v2 = V(i1,:) - V(i3,:); v3 = V(i2,:) - V(i1,:);
% computing the areas
if size(V,2) == 2
% 2d vertex data
  dblA = v1(:,1).*v2(:,2)-v1(:,2).*v2(:,1);
elseif size(V,2) == 3
  %n  = cross(v1,v2,2);  dblA  = multinorm(n,2);
  n  = cross(v1,v2,2);  
  
  % dblA  = norm(n,2);
  % This does correct l2 norm of rows
  dblA = (sqrt(sum((n').^2)))';
else 
  error('unsupported vertex dimension %d', size(V,2))
end
if strcmp(type,'full')
    % arrays for matrix assembly using 'sparse'
    % indices and values of the element mass matrix entries in the order 
    % (1,2), (2,1),(2,3), (3,2), (3,1), (1,3) (1,1), (2,2), (3,3);
    i = [i1 i2 i2 i3 i3 i1  i1 i2 i3];
    j = [i2 i1 i3 i2 i1 i3  i1 i2 i3];
    offd_v = dblA/24.;
    diag_v = dblA/12.;
    v = [offd_v,offd_v, offd_v,offd_v, offd_v,offd_v, diag_v,diag_v,diag_v];  
    M = sparse(i,j,v,size(V,1), size(V,1));
elseif strcmp(type,'barycentric')
    % only diagonal elements
    i = [i1 i2 i3];
    j = [i1 i2 i3];
    diag_v = dblA/6.;
    v = [diag_v,diag_v,diag_v];
    M = sparse(i,j,v,size(V,1), size(V,1));
elseif strcmp(type,'voronoi')

  % just ported version of intrinsic code

  % edges numbered same as opposite vertices
  FT = F';
  l = [ ...
    sqrt(sum((V(FT(:,2),:)-V(FT(:,3),:)).^2,2)) ...
    sqrt(sum((V(FT(:,3),:)-V(FT(:,1),:)).^2,2)) ...
    sqrt(sum((V(FT(:,1),:)-V(FT(:,2),:)).^2,2)) ...
    ];
  M = massmatrix_intrinsic(l,F',size(V,1),'voronoi');
else 
    error('bad mass matrix type')
end

% warn if any rows are all zero (probably unreferenced vertices)
if(any(sum(M,2) == 0))
  warning('Some rows have all zeros... probably unreferenced vertices..');
end

case 4
% vertices must be defined in 3D
assert(size(V,2)==3);

% should change code below, so we don't need this transpose
if(size(F,1) == 4)
  warning('F seems to be 4 by #F, it should be #F by 4');
end

switch type
case 'full'
  % e.g., from _Finite Elements for Analysis and Design_,  J. E. Akin, pp
  % 198. Or Zienkiewicz-4
  %
  % Earliest reference I could find is "Numerical Integration over
  % Simplexes and Cones", [Hammer et al. 1956]
  % 
  I = [F(:,[2 3 4 3 4 1 4 1 2 1 2 3 1 2 3 4])];
  J = [F(:,[1 1 1 2 2 2 3 3 3 4 4 4 1 2 3 4])];
  vol = abs(volume(V,F));
  VV = [repmat(vol/20,1,3*4) repmat(vol/10,1,4)];
  M = sparse(I,J,VV,size(V,1),size(V,1));
  % Uniform mid-face quadrature rules don't seem to be quadratically
  % precise
  % I = [F(:,[2 3 4 3 4 1 4 1 2 1 2 3 1 2 3 4])];
  % J = [F(:,[1 1 1 2 2 2 3 3 3 4 4 4 1 2 3 4])];
  % vol = abs(volume(V,F));
  % VV = [repmat(vol/18,1,3*4) repmat(vol/12,1,4)];
  % M = sparse(I,J,VV,size(V,1),size(V,1));
case 'barycentric'
  %a = V(F(:,1),:);
  %b = V(F(:,2),:);
  %c = V(F(:,3),:);
  %d = V(F(:,4),:);
  %% http://en.wikipedia.org/wiki/Tetrahedron#Volume
  %% volume for each tetrahedron
  %v = repmat(abs(dot((a-d),cross2(b-d,c-d),2))./6./4,1,4);
  v = repmat(abs(volume(V,F)),1,4);

  % only diagonal elements
  M = sparse(F(:),F(:),v/4,size(V,1),size(V,1));
case 'voronoi'
  pa = V(F(:,1),:);
  pb = V(F(:,2),:);
  pc = V(F(:,3),:);
  pd = V(F(:,4),:);
  % as if pd is the origin
  a = pa-pd;
  b = pb-pd;
  c = pc-pd;
  % circumcenter:
  % http://en.wikipedia.org/wiki/Tetrahedron#More_vector_formulas_in_a_general_tetrahedron
  cc = pd + bsxfun(@rdivide, ...
    bsxfun(@times,sum(a.*a,2),cross2(b,c)) + ...
    bsxfun(@times,sum(b.*b,2),cross2(c,a)) + ...
    bsxfun(@times,sum(c.*c,2),cross2(a,b)), ...
    2*sum(a.*cross2(b,c),2));
  % get correct sign
  sa = sign(sum((pa-pb).*cross2(pc-pb,pd-pb),2)/6);
  sb = sign(sum((pb-pc).*cross2(pd-pc,pa-pc),2)/6);
  sc = sign(sum((pc-pd).*cross2(pa-pd,pb-pd),2)/6);
  sd = sign(sum((pd-pa).*cross2(pb-pa,pc-pa),2)/6);
  % get area of sub-tet and correct sign
  la = sa.*sum((cc-pb).*cross2(pc-pb,pd-pb),2)/6;
  lb = sb.*sum((cc-pc).*cross2(pd-pc,pa-pc),2)/6;
  lc = sc.*sum((cc-pd).*cross2(pa-pd,pb-pd),2)/6;
  ld = sd.*sum((cc-pa).*cross2(pb-pa,pc-pa),2)/6;
  v = abs(sum(a.*cross2(b,c),2)/6);
  %max(abs((la+lb+lc+ld - v)))
  assert(all((la+lb+lc+ld - v)<10*eps));
  % partial volumes attached to each corner
  pv = [(lb+lc+ld)/3 (lc+ld+la)/3 (ld+la+lb)/3 (la+lb+lc)/3];
  M = sparse(F,F,pv,size(V,1),size(V,1));
otherwise
  error('bad mass matrix type')
end

end
end

clear all;
mesh_source = ‘C:\Users\lixiaohu\Desktop\101028\101028_l\TOOTH_0.obj’;
[v,F] = load_mesh(mesh_source);

massmatrix(v,F,‘barycentric’)

(4592,4592) 0.033451
(4593,4593) 0.018297
(4594,4594) 0.059208
(4595,4595) 0.126
(4596,4596) 0.15465
(4597,4597) 0.24073
(4598,4598) 0.20689
(4599,4599) 0.12835
(4600,4600) 0.1287
(4601,4601) 0.089461
(4602,4602) 0.13076
(4603,4603) 0.12632
(4604,4604) 0.15629
(4605,4605) 0.18538
(4606,4606) 0.045072
(4607,4607) 0.044621
(4608,4608) 0.01189
(4609,4609) 0.081306
(4610,4610) 0.13137
(4611,4611) 0.066875
(4612,4612) 0.070747
(4613,4613) 0.13602
(4614,4614) 0.035903
(4615,4615) 0.089015
(4616,4616) 0.18846
(4617,4617) 0.20401
(4618,4618) 0.14487
(4619,4619) 0.16409
(4620,4620) 0.18081
(4621,4621) 0.26814
(4622,4622) 0.31501
(4623,4623) 0.36441
(4624,4624) 0.20949
(4625,4625) 0.2264
(4626,4626) 0.15011
(4627,4627) 0.19432
(4628,4628) 0.19907
(4629,4629) 0.13658
(4630,4630) 0.31603
(4631,4631) 0.16798
(4632,4632) 0.21317
(4633,4633) 0.12932
(4634,4634) 0.25533
(4635,4635) 0.27766
(4636,4636) 0.12725
(4637,4637) 0.23106
(4638,4638) 0.17924
(4639,4639) 0.14798
(4640,4640) 0.11679
(4641,4641) 0.24793
(4642,4642) 0.21979
(4643,4643) 0.20105
(4644,4644) 0.15137
(4645,4645) 0.064404
(4646,4646) 0.14623
(4647,4647) 0.21603
(4648,4648) 0.17891
(4649,4649) 0.17528
(4650,4650) 0.072994
(4651,4651) 0.19146
(4652,4652) 0.15995
(4653,4653) 0.15465
(4654,4654) 0.076551
(4655,4655) 0.023715
(4656,4656) 0.014295
(4657,4657) 0.025876
(4658,4658) 0.091234
(4659,4659) 0.063501
(4660,4660) 0.11813
(4661,4661) 0.03099
(4662,4662) 0.0047765
(4663,4663) 0.014873
(4664,4664) 0.004479
(4665,4665) 0.010133
(4666,4666) 0.010514
(4667,4667) 0.015758
(4668,4668) 0.035992
(4669,4669) 0.0063828
(4670,4670) 0.016875
(4671,4671) 0.013173
(4672,4672) 0.0073152
(4673,4673) 0.015478
(4674,4674) 0.015032
(4675,4675) 0.0061446
(4676,4676) 0.013652
(4677,4677) 0.0092215
(4678,4678) 0.015346
(4679,4679) 0.01324
(4680,4680) 0.027328
(4681,4681) 0.022611
(4682,4682) 0.037459
(4683,4683) 0.02517
(4684,4684) 0.026819
(4685,4685) 0.02
(4686,4686) 0.016032
(4687,4687) 0.033259
(4688,4688) 0.025533
(4689,4689) 0.031606
(4690,4690) 0.033422
(4691,4691) 0.014274
(4692,4692) 0.021129
(4693,4693) 0.046034
(4694,4694) 0.087901
(4695,4695) 0.10114
(4696,4696) 0.046829
(4697,4697) 0.042822
(4698,4698) 0.030123
(4699,4699) 0.02054
(4700,4700) 0.023307
(4701,4701) 0.019246
(4702,4702) 0.020744
(4703,4703) 0.017407
(4704,4704) 0.013046
(4705,4705) 0.01198
(4706,4706) 0.0097031
(4707,4707) 0.0091544
(4708,4708) 0.0091334
(4709,4709) 0.011651
(4710,4710) 0.0091792
(4711,4711) 0.009987
(4712,4712) 0.010952
(4713,4713) 0.010096
(4714,4714) 0.041806
(4715,4715) 0.02213
(4716,4716) 0.0046906
(4717,4717) 0.090688
(4718,4718) 0.065118
(4719,4719) 0.10442
(4720,4720) 0.044184
(4721,4721) 0.018866
(4722,4722) 0.017706
(4723,4723) 0.0051337
(4724,4724) 0.038473
(4725,4725) 0.0068161
(4726,4726) 0.0068763
(4727,4727) 0.048872
(4728,4728) 0.11653
(4729,4729) 0.081416
(4730,4730) 0.13716
(4731,4731) 0.044513
(4732,4732) 0.023162
(4733,4733) 0.063823
(4734,4734) 0.084417
(4735,4735) 0.027731
(4736,4736) 0.11592
(4737,4737) 0.1607
(4738,4738) 0.173
(4739,4739) 0.24473
(4740,4740) 0.26243
(4741,4741) 0.17026
(4742,4742) 0.17206
(4743,4743) 0.15749
(4744,4744) 0.1527
(4745,4745) 0.10929
(4746,4746) 0.17525
(4747,4747) 0.18821
(4748,4748) 0.16802
(4749,4749) 0.067374
(4750,4750) 0.1276
(4751,4751) 0.12436
(4752,4752) 0.072337
(4753,4753) 0.2012
(4754,4754) 0.28476
(4755,4755) 0.28309
(4756,4756) 0.21426
(4757,4757) 0.28012
(4758,4758) 0.32076
(4759,4759) 0.25887
(4760,4760) 0.22036
(4761,4761) 0.17147
(4762,4762) 0.2161
(4763,4763) 0.13079
(4764,4764) 0.11031
(4765,4765) 0.10691
(4766,4766) 0.11774
(4767,4767) 0.089357
(4768,4768) 0.18975
(4769,4769) 0.2227
(4770,4770) 0.17912
(4771,4771) 0.090236
(4772,4772) 0.26201
(4773,4773) 0.14762
(4774,4774) 0.12492
(4775,4775) 0.18956
(4776,4776) 0.13555
(4777,4777) 0.084399
(4778,4778) 0.29832
(4779,4779) 0.34672
(4780,4780) 0.17707
(4781,4781) 0.23551
(4782,4782) 0.13136
(4783,4783) 0.11586
(4784,4784) 0.20031
(4785,4785) 0.1138
(4786,4786) 0.11987
(4787,4787) 0.14032
(4788,4788) 0.16503
(4789,4789) 0.17968
(4790,4790) 0.10389
(4791,4791) 0.092776
(4792,4792) 0.15167
(4793,4793) 0.073636
(4794,4794) 0.045311
(4795,4795) 0.12882
(4796,4796) 0.16306
(4797,4797) 0.17572
(4798,4798) 0.057008
(4799,4799) 0.018731
(4800,4800) 0.055022
(4801,4801) 0.10574
(4802,4802) 0.035932
(4803,4803) 0.026026
(4804,4804) 0.048152
(4805,4805) 0.029696
(4806,4806) 0.013271
(4807,4807) 0.0092558
(4808,4808) 0.014717
(4809,4809) 0.014008
(4810,4810) 0.015114
(4811,4811) 0.019046
(4812,4812) 0.019144
(4813,4813) 0.014217
(4814,4814) 0.009361
(4815,4815) 0.013643
(4816,4816) 0.011461
(4817,4817) 0.010446
(4818,4818) 0.010341
(4819,4819) 0.0069153
(4820,4820) 0.0051441
(4821,4821) 0.011023
(4822,4822) 0.015279
(4823,4823) 0.015439
(4824,4824) 0.010702
(4825,4825) 0.014457
(4826,4826) 0.015914
(4827,4827) 0.014813
(4828,4828) 0.0089324
(4829,4829) 0.021484
(4830,4830) 0.03098
(4831,4831) 0.023949
(4832,4832) 0.018825
(4833,4833) 0.035004
(4834,4834) 0.021288
(4835,4835) 0.019627
(4836,4836) 0.030254
(4837,4837) 0.021346
(4838,4838) 0.014369
(4839,4839) 0.013473
(4840,4840) 0.010682
(4841,4841) 0.0094371
(4842,4842) 0.018945
(4843,4843) 0.027866
(4844,4844) 0.022251
(4845,4845) 0.042344
(4846,4846) 0.0058771
(4847,4847) 0.12298
(4848,4848) 0.090817
(4849,4849) 0.14664
(4850,4850) 0.16454
(4851,4851) 0.079791
(4852,4852) 0.064218
(4853,4853) 0.12648
(4854,4854) 0.15063
(4855,4855) 0.14815
(4856,4856) 0.26554
(4857,4857) 0.10102
(4858,4858) 0.17207
(4859,4859) 0.24793
(4860,4860) 0.13726
(4861,4861) 0.16129
(4862,4862) 0.12683
(4863,4863) 0.16453
(4864,4864) 0.18809
(4865,4865) 0.1089
(4866,4866) 0.097743
(4867,4867) 0.23271
(4868,4868) 0.10614
(4869,4869) 0.097154
(4870,4870) 0.14429
(4871,4871) 0.19232
(4872,4872) 0.21359
(4873,4873) 0.11725
(4874,4874) 0.14134
(4875,4875) 0.1034
(4876,4876) 0.187
(4877,4877) 0.19446
(4878,4878) 0.16764
(4879,4879) 0.23536
(4880,4880) 0.24553
(4881,4881) 0.17424
(4882,4882) 0.15295
(4883,4883) 0.14217
(4884,4884) 0.11921
(4885,4885) 0.16173
(4886,4886) 0.13769
(4887,4887) 0.097598
(4888,4888) 0.066745
(4889,4889) 0.12586
(4890,4890) 0.083043
(4891,4891) 0.060472
(4892,4892) 0.10826
(4893,4893) 0.13507
(4894,4894) 0.1666
(4895,4895) 0.1949
(4896,4896) 0.28429
(4897,4897) 0.18982
(4898,4898) 0.18617
(4899,4899) 0.27268
(4900,4900) 0.27612
(4901,4901) 0.26328
(4902,4902) 0.21654
(4903,4903) 0.17564
(4904,4904) 0.13623
(4905,4905) 0.17595
(4906,4906) 0.14636
(4907,4907) 0.14014
(4908,4908) 0.10222
(4909,4909) 0.16818
(4910,4910) 0.18423
(4911,4911) 0.26427
(4912,4912) 0.13038
(4913,4913) 0.14105
(4914,4914) 0.15799
(4915,4915) 0.19606
(4916,4916) 0.21091
(4917,4917) 0.16058
(4918,4918) 0.08958
(4919,4919) 0.031061
(4920,4920) 0.040687
(4921,4921) 0.026313
(4922,4922) 0.016567
(4923,4923) 0.005151
(4924,4924) 0.014139
(4925,4925) 0.014175
(4926,4926) 0.0058009
(4927,4927) 0.021212
(4928,4928) 0.041312
(4929,4929) 0.0066871
(4930,4930) 0.043017
(4931,4931) 0.018686
(4932,4932) 0.0247
(4933,4933) 0.018812
(4934,4934) 0.0073702
(4935,4935) 0.012212
(4936,4936) 0.0083178
(4937,4937) 0.0082259
(4938,4938) 0.0076622
(4939,4939) 0.0095738
(4940,4940) 0.010029
(4941,4941) 0.017948
(4942,4942) 0.0168
(4943,4943) 0.014797
(4944,4944) 0.018578
(4945,4945) 0.017304
(4946,4946) 0.012968
(4947,4947) 0.016904
(4948,4948) 0.01355
(4949,4949) 0.018715
(4950,4950) 0.0086532
(4951,4951) 0.013866
(4952,4952) 0.010216
(4953,4953) 0.010279
(4954,4954) 0.0049988
(4955,4955) 0.0058071
(4956,4956) 0.0058646
(4957,4957) 0.040097
(4958,4958) 0.078907
(4959,4959) 0.098576
(4960,4960) 0.10071
(4961,4961) 0.18384
(4962,4962) 0.094282
(4963,4963) 0.14549
(4964,4964) 0.14744
(4965,4965) 0.13158
(4966,4966) 0.076236
(4967,4967) 0.066851
(4968,4968) 0.16579
(4969,4969) 0.16917
(4970,4970) 0.12623
(4971,4971) 0.18081
(4972,4972) 0.167
(4973,4973) 0.19973
(4974,4974) 0.084895
(4975,4975) 0.11135
(4976,4976) 0.087015
(4977,4977) 0.09982
(4978,4978) 0.14008
(4979,4979) 0.14933
(4980,4980) 0.12237
(4981,4981) 0.12489
(4982,4982) 0.1574
(4983,4983) 0.15106
(4984,4984) 0.18512
(4985,4985) 0.17315
(4986,4986) 0.15997
(4987,4987) 0.15023
(4988,4988) 0.18313
(4989,4989) 0.15146
(4990,4990) 0.1841
(4991,4991) 0.21735
(4992,4992) 0.16702
(4993,4993) 0.12166
(4994,4994) 0.17551
(4995,4995) 0.16357
(4996,4996) 0.096236
(4997,4997) 0.16714
(4998,4998) 0.085945
(4999,4999) 0.16778
(5000,5000) 0.090591
(5001,5001) 0.071732
(5002,5002) 0.09295
(5003,5003) 0.16471
(5004,5004) 0.12407
(5005,5005) 0.092987
(5006,5006) 0.12091
(5007,5007) 0.21197
(5008,5008) 0.11066
(5009,5009) 0.12106
(5010,5010) 0.25295
(5011,5011) 0.18298
(5012,5012) 0.065457
(5013,5013) 0.20765
(5014,5014) 0.17823
(5015,5015) 0.13622
(5016,5016) 0.11886
(5017,5017) 0.087485
(5018,5018) 0.13704
(5019,5019) 0.15011
(5020,5020) 0.26166
(5021,5021) 0.185
(5022,5022) 0.11919
(5023,5023) 0.18455
(5024,5024) 0.19343
(5025,5025) 0.12477
(5026,5026) 0.1373
(5027,5027) 0.21173
(5028,5028) 0.10123
(5029,5029) 0.081943
(5030,5030) 0.033796
(5031,5031) 0.040023
(5032,5032) 0.053049
(5033,5033) 0.21136
(5034,5034) 0.071484
(5035,5035) 0.079101
(5036,5036) 0.034641
(5037,5037) 0.0048766
(5038,5038) 0.031431
(5039,5039) 0.016682
(5040,5040) 0.0030167
(5041,5041) 0.024469
(5042,5042) 0.010272
(5043,5043) 0.0097645
(5044,5044) 0.011887
(5045,5045) 0.0062786
(5046,5046) 0.0062065
(5047,5047) 0.011108
(5048,5048) 0.0053059
(5049,5049) 0.011393
(5050,5050) 0.0037759
(5051,5051) 0.0066601
(5052,5052) 0.021739
(5053,5053) 0.03994
(5054,5054) 0.0063207
(5055,5055) 0.039174
(5056,5056) 0.0084673
(5057,5057) 0.0061034
(5058,5058) 0.0082861
(5059,5059) 0.0098156
(5060,5060) 0.0066492
(5061,5061) 0.0083619
(5062,5062) 0.045237
(5063,5063) 0.0060046
(5064,5064) 0.14429
(5065,5065) 0.18361
(5066,5066) 0.11397
(5067,5067) 0.17382
(5068,5068) 0.12691
(5069,5069) 0.13842
(5070,5070) 0.15984
(5071,5071) 0.17322
(5072,5072) 0.11845
(5073,5073) 0.17704
(5074,5074) 0.21501
(5075,5075) 0.20034
(5076,5076) 0.19632
(5077,5077) 0.092441
(5078,5078) 0.17464
(5079,5079) 0.19691
(5080,5080) 0.096433
(5081,5081) 0.14756
(5082,5082) 0.14706
(5083,5083) 0.11764
(5084,5084) 0.092354
(5085,5085) 0.17203
(5086,5086) 0.15857
(5087,5087) 0.11235
(5088,5088) 0.1507
(5089,5089) 0.13509
(5090,5090) 0.11201
(5091,5091) 0.096476
(5092,5092) 0.11783
(5093,5093) 0.15366
(5094,5094) 0.10318
(5095,5095) 0.1101
(5096,5096) 0.19782
(5097,5097) 0.10072
(5098,5098) 0.12245
(5099,5099) 0.12403
(5100,5100) 0.080178
(5101,5101) 0.07751
(5102,5102) 0.14969
(5103,5103) 0.18649
(5104,5104) 0.081733
(5105,5105) 0.057565
(5106,5106) 0.13321
(5107,5107) 0.07873
(5108,5108) 0.087068
(5109,5109) 0.12343
(5110,5110) 0.1116
(5111,5111) 0.16365
(5112,5112) 0.10997
(5113,5113) 0.2156
(5114,5114) 0.21614
(5115,5115) 0.20338
(5116,5116) 0.13425
(5117,5117) 0.10603
(5118,5118) 0.10102
(5119,5119) 0.12001
(5120,5120) 0.17752
(5121,5121) 0.22265
(5122,5122) 0.18256
(5123,5123) 0.14793
(5124,5124) 0.23568
(5125,5125) 0.18371
(5126,5126) 0.22428
(5127,5127) 0.17498
(5128,5128) 0.21961
(5129,5129) 0.14923
(5130,5130) 0.23256
(5131,5131) 0.29658
(5132,5132) 0.13271
(5133,5133) 0.081477
(5134,5134) 0.11844
(5135,5135) 0.066145
(5136,5136) 0.092079
(5137,5137) 0.020559
(5138,5138) 0.041194
(5139,5139) 0.0055013
(5140,5140) 0.036286
(5141,5141) 0.017414
(5142,5142) 0.025728
(5143,5143) 0.078816
(5144,5144) 0.12718
(5145,5145) 0.078548
(5146,5146) 0.020445
(5147,5147) 0.029438
(5148,5148) 0.023106
(5149,5149) 0.10017
(5150,5150) 0.096319
(5151,5151) 0.20909
(5152,5152) 0.20728
(5153,5153) 0.22715
(5154,5154) 0.20843
(5155,5155) 0.16449
(5156,5156) 0.17807
(5157,5157) 0.20478
(5158,5158) 0.26211
(5159,5159) 0.2518
(5160,5160) 0.27926
(5161,5161) 0.17811
(5162,5162) 0.11793
(5163,5163) 0.09539
(5164,5164) 0.079121
(5165,5165) 0.14182
(5166,5166) 0.17987
(5167,5167) 0.12589
(5168,5168) 0.11581
(5169,5169) 0.1633
(5170,5170) 0.15897
(5171,5171) 0.18625
(5172,5172) 0.13734
(5173,5173) 0.089452
(5174,5174) 0.16969
(5175,5175) 0.15093
(5176,5176) 0.15188
(5177,5177) 0.089632
(5178,5178) 0.14007
(5179,5179) 0.14907
(5180,5180) 0.09785
(5181,5181) 0.11941
(5182,5182) 0.14435
(5183,5183) 0.13179
(5184,5184) 0.15681
(5185,5185) 0.13102
(5186,5186) 0.17366
(5187,5187) 0.13001
(5188,5188) 0.20787
(5189,5189) 0.13817
(5190,5190) 0.12583
(5191,5191) 0.091991
(5192,5192) 0.12338
(5193,5193) 0.10672
(5194,5194) 0.12419
(5195,5195) 0.15272
(5196,5196) 0.13871
(5197,5197) 0.13203
(5198,5198) 0.10737
(5199,5199) 0.14928
(5200,5200) 0.18407
(5201,5201) 0.17322
(5202,5202) 0.2637
(5203,5203) 0.20142
(5204,5204) 0.16046
(5205,5205) 0.21697
(5206,5206) 0.23607
(5207,5207) 0.14618
(5208,5208) 0.098932
(5209,5209) 0.19375
(5210,5210) 0.1629
(5211,5211) 0.10477
(5212,5212) 0.13114
(5213,5213) 0.061015
(5214,5214) 0.1106
(5215,5215) 0.078217
(5216,5216) 0.18974
(5217,5217) 0.16522
(5218,5218) 0.09001
(5219,5219) 0.11938
(5220,5220) 0.26892
(5221,5221) 0.26349
(5222,5222) 0.15899
(5223,5223) 0.14563
(5224,5224) 0.18158
(5225,5225) 0.1693
(5226,5226) 0.16522
(5227,5227) 0.2433
(5228,5228) 0.19455
(5229,5229) 0.17807
(5230,5230) 0.10081
(5231,5231) 0.10335
(5232,5232) 0.098404
(5233,5233) 0.12068
(5234,5234) 0.15667
(5235,5235) 0.10018
(5236,5236) 0.18136
(5237,5237) 0.15511
(5238,5238) 0.10981
(5239,5239) 0.19365
(5240,5240) 0.16192
(5241,5241) 0.15864
(5242,5242) 0.091202
(5243,5243) 0.13888
(5244,5244) 0.13729
(5245,5245) 0.12628
(5246,5246) 0.08331
(5247,5247) 0.12003
(5248,5248) 0.17226
(5249,5249) 0.11166
(5250,5250) 0.10737
(5251,5251) 0.097933
(5252,5252) 0.11893
(5253,5253) 0.07529
(5254,5254) 0.14746
(5255,5255) 0.14801
(5256,5256) 0.10792
(5257,5257) 0.10499
(5258,5258) 0.14437
(5259,5259) 0.12299
(5260,5260) 0.12192
(5261,5261) 0.27303
(5262,5262) 0.16084
(5263,5263) 0.18764
(5264,5264) 0.1882
(5265,5265) 0.2185
(5266,5266) 0.24384
(5267,5267) 0.26105
(5268,5268) 0.16756
(5269,5269) 0.11107
(5270,5270) 0.24206
(5271,5271) 0.089929
(5272,5272) 0.13044
(5273,5273) 0.24671
(5274,5274) 0.16892
(5275,5275) 0.20173
(5276,5276) 0.17375
(5277,5277) 0.18624
(5278,5278) 0.1366
(5279,5279) 0.27016
(5280,5280) 0.20176
(5281,5281) 0.10667
(5282,5282) 0.13384
(5283,5283) 0.14469
(5284,5284) 0.19075
(5285,5285) 0.095192
(5286,5286) 0.14459
(5287,5287) 0.11293
(5288,5288) 0.10722
(5289,5289) 0.089424
(5290,5290) 0.13464
(5291,5291) 0.1509
(5292,5292) 0.14551
(5293,5293) 0.13459
(5294,5294) 0.085912
(5295,5295) 0.10079
(5296,5296) 0.090828
(5297,5297) 0.13218
(5298,5298) 0.13827
(5299,5299) 0.15167
(5300,5300) 0.097888
(5301,5301) 0.10762
(5302,5302) 0.10409
(5303,5303) 0.080424
(5304,5304) 0.14125
(5305,5305) 0.071809
(5306,5306) 0.098222
(5307,5307) 0.20928
(5308,5308) 0.083478
(5309,5309) 0.0604
(5310,5310) 0.12769
(5311,5311) 0.21108
(5312,5312) 0.16046
(5313,5313) 0.14318
(5314,5314) 0.18062
(5315,5315) 0.19528
(5316,5316) 0.20498
(5317,5317) 0.18697
(5318,5318) 0.23472
(5319,5319) 0.13711
(5320,5320) 0.14515
(5321,5321) 0.13596
(5322,5322) 0.17682
(5323,5323) 0.15659
(5324,5324) 0.25435
(5325,5325) 0.18537
(5326,5326) 0.14712
(5327,5327) 0.1377
(5328,5328) 0.20197
(5329,5329) 0.13861
(5330,5330) 0.12632
(5331,5331) 0.11851
(5332,5332) 0.098139
(5333,5333) 0.14866
(5334,5334) 0.14376
(5335,5335) 0.16226
(5336,5336) 0.074105
(5337,5337) 0.083941
(5338,5338) 0.07672
(5339,5339) 0.18381
(5340,5340) 0.13409
(5341,5341) 0.12345
(5342,5342) 0.16185
(5343,5343) 0.12777
(5344,5344) 0.13123
(5345,5345) 0.12454
(5346,5346) 0.10847
(5347,5347) 0.076034
(5348,5348) 0.10413
(5349,5349) 0.16069
(5350,5350) 0.15747
(5351,5351) 0.13625
(5352,5352) 0.16407
(5353,5353) 0.10884
(5354,5354) 0.17416
(5355,5355) 0.16563
(5356,5356) 0.17776
(5357,5357) 0.18168
(5358,5358) 0.18438
(5359,5359) 0.15692
(5360,5360) 0.11794
(5361,5361) 0.15462
(5362,5362) 0.16086
(5363,5363) 0.19287
(5364,5364) 0.18254
(5365,5365) 0.19029
(5366,5366) 0.12511
(5367,5367) 0.21531
(5368,5368) 0.11103
(5369,5369) 0.14878
(5370,5370) 0.13486
(5371,5371) 0.1393
(5372,5372) 0.20973
(5373,5373) 0.12913
(5374,5374) 0.19322
(5375,5375) 0.15368
(5376,5376) 0.076404
(5377,5377) 0.13641
(5378,5378) 0.092887
(5379,5379) 0.12665
(5380,5380) 0.096579
(5381,5381) 0.13875
(5382,5382) 0.11379
(5383,5383) 0.094272
(5384,5384) 0.17925
(5385,5385) 0.16508
(5386,5386) 0.09837
(5387,5387) 0.12714
(5388,5388) 0.11899
(5389,5389) 0.094912
(5390,5390) 0.15192
full类型的mass矩阵是：------------------------------------------明显非对角
(5364,5363) 0.013782
(5394,5363) 0.012882
(5323,5364) 0.015093
(5324,5364) 0.017075
(5325,5364) 0.017455
(5363,5364) 0.013782
(5364,5364) 0.091269
(5365,5364) 0.014778
(5394,5364) 0.013087
(5325,5365) 0.014974
(5364,5365) 0.014778
(5365,5365) 0.095144
(5366,5365) 0.012765
(5392,5365) 0.014071
(5393,5365) 0.012986
(5394,5365) 0.012471
(5395,5365) 0.013099
(5325,5366) 0.012424
(5326,5366) 0.012078
(5365,5366) 0.012765
(5366,5366) 0.062554
(5367,5366) 0.012797
(5395,5366) 0.01249
(5326,5367) 0.01307
(5327,5367) 0.014686
(5328,5367) 0.014808
(5366,5367) 0.012797
(5367,5367) 0.10765
(5368,5367) 0.012676
(5395,5367) 0.013337
(5396,5367) 0.013668
(5397,5367) 0.012612
(5328,5368) 0.012514
(5367,5368) 0.012676
(5368,5368) 0.055516
(5369,5368) 0.010443
(5397,5368) 0.010486
(5398,5368) 0.0093972
(5328,5369) 0.012191
(5368,5369) 0.010443
(5369,5369) 0.074388
(5370,5369) 0.012145
(5371,5369) 0.013193
(5372,5369) 0.014605
(5398,5369) 0.01181
(5328,5370) 0.012694
(5329,5370) 0.011097
(5330,5370) 0.010252
(5331,5370) 0.010472
(5369,5370) 0.012145
(5370,5370) 0.067429
(5371,5370) 0.010769
(5331,5371) 0.0094873
(5332,5371) 0.0090069
(5333,5371) 0.012146
(5369,5371) 0.013193
(5370,5371) 0.010769
(5371,5371) 0.069652
(5372,5371) 0.01505
(5333,5372) 0.014174
(5369,5372) 0.014605
(5371,5372) 0.01505
(5372,5372) 0.10487
(5373,5372) 0.014324
(5374,5372) 0.01422
(5398,5372) 0.0122
(5399,5372) 0.0094327
(5400,5372) 0.010858
(5333,5373) 0.011931
(5334,5373) 0.011156
(5335,5373) 0.012705
(5372,5373) 0.014324
(5373,5373) 0.064567
(5374,5373) 0.01445
(5335,5374) 0.014673
(5372,5374) 0.01422
(5373,5374) 0.01445
(5374,5374) 0.096611
(5375,5374) 0.015192
(5400,5374) 0.011873
(5401,5374) 0.01209
(5402,5374) 0.014112
(5335,5375) 0.012578
(5374,5375) 0.015192
(5375,5375) 0.076839
(5376,5375) 0.0092275
(5377,5375) 0.011702
(5402,5375) 0.01414
(5403,5375) 0.014
(5335,5376) 0.00815
(5336,5376) 0.0061156
(5337,5376) 0.0064319
(5375,5376) 0.0092275
(5376,5376) 0.038202
(5377,5376) 0.0082772
(5337,5377) 0.0075582
(5338,5377) 0.0073082
(5375,5377) 0.011702
(5376,5377) 0.0082772
(5377,5377) 0.068205
(5378,5377) 0.0081982
(5379,5377) 0.011335
(5403,5377) 0.013827
(5338,5378) 0.0074899
(5339,5378) 0.010091
(5342,5378) 0.011042
(5377,5378) 0.0081982
(5378,5378) 0.046443
(5379,5378) 0.0096223
(5342,5379) 0.010928
(5343,5379) 0.010352
(5377,5379) 0.011335
(5378,5379) 0.0096223
(5379,5379) 0.063326
(5380,5379) 0.0093998
(5403,5379) 0.011689
(5343,5380) 0.0087881
(5344,5380) 0.0092758
(5379,5380) 0.0093998
(5380,5380) 0.048289
(5381,5380) 0.010312
(5403,5380) 0.010513
(5344,5381) 0.010645
(5345,5381) 0.011307
(5380,5381) 0.010312
(5381,5381) 0.069376
(5382,5381) 0.009759
(5403,5381) 0.010756
(5404,5381) 0.0088148
(5405,5381) 0.0077811
(5345,5382) 0.0096377
(5381,5382) 0.009759
(5382,5382) 0.056896
(5383,5382) 0.0090582
(5384,5382) 0.010758
(5405,5382) 0.0080524
(5406,5382) 0.0096308
(5345,5383) 0.0082102
(5346,5383) 0.0087062
(5349,5383) 0.010431
(5382,5383) 0.0090582
(5383,5383) 0.047136
(5384,5383) 0.01073
(5349,5384) 0.013646
(5350,5384) 0.014141
(5351,5384) 0.013222
(5382,5384) 0.010758
(5383,5384) 0.01073
(5384,5384) 0.089623
(5385,5384) 0.014108
(5406,5384) 0.013017
(5351,5385) 0.013535
(5352,5385) 0.012459
(5384,5385) 0.014108
(5385,5385) 0.082541
(5386,5385) 0.0108
(5406,5385) 0.01205
(5407,5385) 0.0097506
(5408,5385) 0.0098383
(5352,5386) 0.010934
(5385,5386) 0.0108
(5386,5386) 0.049185
(5387,5386) 0.0094678
(5408,5386) 0.009277
(5409,5386) 0.0087068
(5352,5387) 0.010712
(5353,5387) 0.01131
(5354,5387) 0.011547
(5386,5387) 0.0094678
(5387,5387) 0.063569
(5388,5387) 0.011007
(5409,5387) 0.0095255
(5354,5388) 0.010418
(5387,5388) 0.011007
(5388,5388) 0.059497
(5389,5388) 0.0084512
(5409,5388) 0.010386
(5410,5388) 0.010291
(5411,5388) 0.0089438
(5354,5389) 0.010204
(5355,5389) 0.010645
(5388,5389) 0.0084512
(5389,5389) 0.047456
(5390,5389) 0.0096281
(5411,5389) 0.0085272
(5355,5390) 0.011992
(5357,5390) 0.014107
(5358,5390) 0.015004
(5389,5390) 0.0096281
(5390,5390) 0.07596
(5391,5390) 0.014245
(5411,5390) 0.010984
(5358,5391) 0.015514
(5359,5391) 0.014823
(5390,5391) 0.014245
(5391,5391) 0.09107
(5392,5391) 0.012763
(5411,5391) 0.012522
(5412,5391) 0.010905
(5413,5391) 0.010297
(5359,5392) 0.013363
(5365,5392) 0.014071
(5391,5392) 0.012763
(5392,5392) 0.075671
(5393,5392) 0.01319
(5395,5392) 0.011882
(5413,5392) 0.010401
(5359,5393) 0.011391
(5360,5393) 0.010396
(5361,5393) 0.010406
(5365,5393) 0.012986
(5392,5393) 0.01319
(5393,5393) 0.069567
(5394,5393) 0.011198
(5361,5394) 0.011547
(5363,5394) 0.012882
(5364,5394) 0.013087
(5365,5394) 0.012471
(5393,5394) 0.011198
(5394,5394) 0.061184
(5365,5395) 0.013099
(5366,5395) 0.01249
(5367,5395) 0.013337
(5392,5395) 0.011882
(5395,5395) 0.070807
(5396,5395) 0.011032
(5413,5395) 0.0089678
(5367,5396) 0.013668
(5395,5396) 0.011032
(5396,5396) 0.064747
(5397,5396) 0.012196
(5412,5396) 0.0091456
(5413,5396) 0.008043
(5414,5396) 0.010663
(5367,5397) 0.012612
(5368,5397) 0.010486
(5396,5397) 0.012196
(5397,5397) 0.06668
(5398,5397) 0.0098457
(5414,5397) 0.010883
(5415,5397) 0.010658
(5368,5398) 0.0093972
(5369,5398) 0.01181
(5372,5398) 0.0122
(5397,5398) 0.0098457
(5398,5398) 0.061581
(5399,5398) 0.0091343
(5415,5398) 0.009193
(5372,5399) 0.0094327
(5398,5399) 0.0091343
(5399,5399) 0.041285
(5400,5399) 0.0075495
(5415,5399) 0.0079447
(5416,5399) 0.0072239
(5372,5400) 0.010858
(5374,5400) 0.011873
(5399,5400) 0.0075495
(5400,5400) 0.04734
(5401,5400) 0.0095465
(5416,5400) 0.0075122
(5374,5401) 0.01209
(5400,5401) 0.0095465
(5401,5401) 0.06704
(5402,5401) 0.012933
(5416,5401) 0.0093803
(5417,5401) 0.01104
(5418,5401) 0.012049
(5374,5402) 0.014112
(5375,5402) 0.01414
(5401,5402) 0.012933
(5402,5402) 0.073944
(5403,5402) 0.011935
(5404,5402) 0.0098991
(5418,5402) 0.010925
(5375,5403) 0.014
(5377,5403) 0.013827
(5379,5403) 0.011689
(5380,5403) 0.010513
(5381,5403) 0.010756
(5402,5403) 0.011935
(5403,5403) 0.083124
(5404,5403) 0.010404
(5381,5404) 0.0088148
(5402,5404) 0.0098991
(5403,5404) 0.010404
(5404,5404) 0.044485
(5405,5404) 0.0070566
(5418,5404) 0.0083112
(5381,5405) 0.0077811
(5382,5405) 0.0080524
(5404,5405) 0.0070566
(5405,5405) 0.038757
(5406,5405) 0.0080685
(5418,5405) 0.0077981
(5382,5406) 0.0096308
(5384,5406) 0.013017
(5385,5406) 0.01205
(5405,5406) 0.0080685
(5406,5406) 0.06103
(5407,5406) 0.0094295
(5418,5406) 0.0088343
(5385,5407) 0.0097506
(5406,5407) 0.0094295
(5407,5407) 0.046618
(5408,5407) 0.0091228
(5417,5407) 0.0089935
(5418,5407) 0.0093217
(5385,5408) 0.0098383
(5386,5408) 0.009277
(5407,5408) 0.0091228
(5408,5408) 0.061322
(5409,5408) 0.010434
(5417,5408) 0.010389
(5419,5408) 0.012261
(5386,5409) 0.0087068
(5387,5409) 0.0095255
(5388,5409) 0.010386
(5408,5409) 0.010434
(5409,5409) 0.063096
(5410,5409) 0.011588
(5419,5409) 0.012455
(5388,5410) 0.010291
(5409,5410) 0.011588
(5410,5410) 0.06711
(5411,5410) 0.010097
(5412,5410) 0.01041
(5414,5410) 0.01187
(5419,5410) 0.012854
(5388,5411) 0.0089438
(5389,5411) 0.0085272
(5390,5411) 0.010984
(5391,5411) 0.012522
(5410,5411) 0.010097
(5411,5411) 0.062292
(5412,5411) 0.011218
(5391,5412) 0.010905
(5396,5412) 0.0091456
(5410,5412) 0.01041
(5411,5412) 0.011218
(5412,5412) 0.060921
(5413,5412) 0.0086494
(5414,5412) 0.010593
(5391,5413) 0.010297
(5392,5413) 0.010401
(5395,5413) 0.0089678
(5396,5413) 0.008043
(5412,5413) 0.0086494
(5413,5413) 0.046358
(5396,5414) 0.010663
(5397,5414) 0.010883
(5410,5414) 0.01187
(5412,5414) 0.010593
(5414,5414) 0.06865
(5415,5414) 0.011792
(5419,5414) 0.01285
(5397,5415) 0.010658
(5398,5415) 0.009193
(5399,5415) 0.0079447
(5414,5415) 0.011792
(5415,5415) 0.061582
(5416,5415) 0.0098057
(5419,5415) 0.012188
(5399,5416) 0.0072239
(5400,5416) 0.0075122
(5401,5416) 0.0093803
(5415,5416) 0.0098057
(5416,5416) 0.05694
(5417,5416) 0.011152
(5419,5416) 0.011866
(5401,5417) 0.01104
(5407,5417) 0.0089935
(5408,5417) 0.010389
(5416,5417) 0.011152
(5417,5417) 0.064409
(5418,5417) 0.010664
(5419,5417) 0.012171
(5401,5418) 0.012049
(5402,5418) 0.010925
(5404,5418) 0.0083112
(5405,5418) 0.0077981
(5406,5418) 0.0088343
(5407,5418) 0.0093217
(5417,5418) 0.010664
(5418,5418) 0.067903
(5408,5419) 0.012261
(5409,5419) 0.012455
(5410,5419) 0.012854
(5414,5419) 0.01285
(5415,5419) 0.012188
(5416,5419) 0.011866
(5417,5419) 0.012171
(5419,5419) 0.086644

massmatrix(v,F,‘voronoi’)

(5035,5035) 0.073558
(5036,5036) 0.033545
(5037,5037) 0.0066607
(5038,5038) 0.031277
(5039,5039) 0.017821
(5040,5040) 0.0039136
(5041,5041) 0.024579
(5042,5042) 0.010669
(5043,5043) 0.010314
(5044,5044) 0.013004
(5045,5045) 0.0070722
(5046,5046) 0.0069226
(5047,5047) 0.013049
(5048,5048) 0.0065023
(5049,5049) 0.013007
(5050,5050) 0.0048057
(5051,5051) 0.007601
(5052,5052) 0.023436
(5053,5053) 0.040838
(5054,5054) 0.0079981
(5055,5055) 0.039569
(5056,5056) 0.0097193
(5057,5057) 0.007009
(5058,5058) 0.0098024
(5059,5059) 0.010364
(5060,5060) 0.008232
(5061,5061) 0.0095894
(5062,5062) 0.047331
(5063,5063) 0.0069232
(5064,5064) 0.12812
(5065,5065) 0.16892
(5066,5066) 0.1337
(5067,5067) 0.17569
(5068,5068) 0.14301
(5069,5069) 0.1379
(5070,5070) 0.15877
(5071,5071) 0.17087
(5072,5072) 0.13663
(5073,5073) 0.17432
(5074,5074) 0.21739
(5075,5075) 0.19958
(5076,5076) 0.20028
(5077,5077) 0.10696
(5078,5078) 0.17479
(5079,5079) 0.17198
(5080,5080) 0.11113
(5081,5081) 0.13625
(5082,5082) 0.14767
(5083,5083) 0.11759
(5084,5084) 0.10715
(5085,5085) 0.1569
(5086,5086) 0.15168
(5087,5087) 0.13128
(5088,5088) 0.14627
(5089,5089) 0.13289
(5090,5090) 0.11297
(5091,5091) 0.11038
(5092,5092) 0.11634
(5093,5093) 0.15257
(5094,5094) 0.12115
(5095,5095) 0.1225
(5096,5096) 0.17057
(5097,5097) 0.11595
(5098,5098) 0.12414
(5099,5099) 0.11984
(5100,5100) 0.092498
(5101,5101) 0.09027
(5102,5102) 0.15043
(5103,5103) 0.17005
(5104,5104) 0.09763
(5105,5105) 0.066146
(5106,5106) 0.12343
(5107,5107) 0.090215
(5108,5108) 0.099696
(5109,5109) 0.1194
(5110,5110) 0.12768
(5111,5111) 0.1479
(5112,5112) 0.13151
(5113,5113) 0.19026
(5114,5114) 0.2209
(5115,5115) 0.18604
(5116,5116) 0.13732
(5117,5117) 0.1052
(5118,5118) 0.1027
(5119,5119) 0.12021
(5120,5120) 0.17852
(5121,5121) 0.20019
(5122,5122) 0.17956
(5123,5123) 0.17586
(5124,5124) 0.2097
(5125,5125) 0.18646
(5126,5126) 0.19963
(5127,5127) 0.20049
(5128,5128) 0.20429
(5129,5129) 0.14105
(5130,5130) 0.24056
(5131,5131) 0.24687
(5132,5132) 0.1413
(5133,5133) 0.094716
(5134,5134) 0.10672
(5135,5135) 0.067549
(5136,5136) 0.087845
(5137,5137) 0.022297
(5138,5138) 0.040275
(5139,5139) 0.0066124
(5140,5140) 0.037918
(5141,5141) 0.019014
(5142,5142) 0.027291
(5143,5143) 0.071746
(5144,5144) 0.11294
(5145,5145) 0.080708
(5146,5146) 0.022297
(5147,5147) 0.031797
(5148,5148) 0.025783
(5149,5149) 0.091141
(5150,5150) 0.11206
(5151,5151) 0.18722
(5152,5152) 0.20599
(5153,5153) 0.24278
(5154,5154) 0.19342
(5155,5155) 0.16617
(5156,5156) 0.17939
(5157,5157) 0.21109
(5158,5158) 0.24359
(5159,5159) 0.24848
(5160,5160) 0.25504
(5161,5161) 0.17791
(5162,5162) 0.1177
(5163,5163) 0.093527
(5164,5164) 0.091229
(5165,5165) 0.14345
(5166,5166) 0.1635
(5167,5167) 0.1238
(5168,5168) 0.13255
(5169,5169) 0.16195
(5170,5170) 0.16406
(5171,5171) 0.17066
(5172,5172) 0.14303
(5173,5173) 0.10622
(5174,5174) 0.14873
(5175,5175) 0.1555
(5176,5176) 0.15155
(5177,5177) 0.10264
(5178,5178) 0.14031
(5179,5179) 0.13779
(5180,5180) 0.096811
(5181,5181) 0.11998
(5182,5182) 0.14492
(5183,5183) 0.1329
(5184,5184) 0.15581
(5185,5185) 0.13199
(5186,5186) 0.15666
(5187,5187) 0.15074
(5188,5188) 0.17866
(5189,5189) 0.15849
(5190,5190) 0.12058
(5191,5191) 0.10582
(5192,5192) 0.11255
(5193,5193) 0.10587
(5194,5194) 0.12443
(5195,5195) 0.15047
(5196,5196) 0.13677
(5197,5197) 0.13696
(5198,5198) 0.12435
(5199,5199) 0.15023
(5200,5200) 0.19312
(5201,5201) 0.19658
(5202,5202) 0.23604
(5203,5203) 0.19193
(5204,5204) 0.18653
(5205,5205) 0.21036
(5206,5206) 0.24116
(5207,5207) 0.17687
(5208,5208) 0.11716
(5209,5209) 0.17162
(5210,5210) 0.15246
(5211,5211) 0.12041
(5212,5212) 0.11145
(5213,5213) 0.061643
(5214,5214) 0.11875
(5215,5215) 0.091319
(5216,5216) 0.16799
(5217,5217) 0.15334
(5218,5218) 0.10661
(5219,5219) 0.14308
(5220,5220) 0.23953
(5221,5221) 0.22297
(5222,5222) 0.18481
(5223,5223) 0.16438
(5224,5224) 0.17622
(5225,5225) 0.17651
(5226,5226) 0.16448
(5227,5227) 0.23968
(5228,5228) 0.19654
(5229,5229) 0.17629
(5230,5230) 0.11653
(5231,5231) 0.10002
(5232,5232) 0.099827
(5233,5233) 0.1194
(5234,5234) 0.14342
(5235,5235) 0.11748
(5236,5236) 0.16587
(5237,5237) 0.15397
(5238,5238) 0.12698
(5239,5239) 0.17578
(5240,5240) 0.16017
(5241,5241) 0.14625
(5242,5242) 0.10422
(5243,5243) 0.12811
(5244,5244) 0.13712
(5245,5245) 0.12576
(5246,5246) 0.095763
(5247,5247) 0.12098
(5248,5248) 0.15878
(5249,5249) 0.13036
(5250,5250) 0.10537
(5251,5251) 0.11159
(5252,5252) 0.10832
(5253,5253) 0.085806
(5254,5254) 0.13684
(5255,5255) 0.14791
(5256,5256) 0.10784
(5257,5257) 0.10529
(5258,5258) 0.14672
(5259,5259) 0.12384
(5260,5260) 0.14015
(5261,5261) 0.23081
(5262,5262) 0.18409
(5263,5263) 0.19731
(5264,5264) 0.18524
(5265,5265) 0.21798
(5266,5266) 0.24472
(5267,5267) 0.22607
(5268,5268) 0.1727
(5269,5269) 0.13214
(5270,5270) 0.19187
(5271,5271) 0.10693
(5272,5272) 0.15612
(5273,5273) 0.2155
(5274,5274) 0.17021
(5275,5275) 0.21529
(5276,5276) 0.20244
(5277,5277) 0.19155
(5278,5278) 0.16274
(5279,5279) 0.22337
(5280,5280) 0.1844
(5281,5281) 0.12487
(5282,5282) 0.13549
(5283,5283) 0.14354
(5284,5284) 0.16672
(5285,5285) 0.10975
(5286,5286) 0.13083
(5287,5287) 0.11261
(5288,5288) 0.10615
(5289,5289) 0.10406
(5290,5290) 0.1321
(5291,5291) 0.15173
(5292,5292) 0.14587
(5293,5293) 0.13543
(5294,5294) 0.098621
(5295,5295) 0.098346
(5296,5296) 0.10446
(5297,5297) 0.1315
(5298,5298) 0.13797
(5299,5299) 0.13981
(5300,5300) 0.098165
(5301,5301) 0.10809
(5302,5302) 0.10386
(5303,5303) 0.092544
(5304,5304) 0.13062
(5305,5305) 0.081521
(5306,5306) 0.11477
(5307,5307) 0.1811
(5308,5308) 0.10111
(5309,5309) 0.069703
(5310,5310) 0.13089
(5311,5311) 0.19477
(5312,5312) 0.15118
(5313,5313) 0.16113
(5314,5314) 0.18574
(5315,5315) 0.19495
(5316,5316) 0.20312
(5317,5317) 0.1805
(5318,5318) 0.22142
(5319,5319) 0.1565
(5320,5320) 0.15207
(5321,5321) 0.14876
(5322,5322) 0.16767
(5323,5323) 0.17943
(5324,5324) 0.21875
(5325,5325) 0.18465
(5326,5326) 0.1346
(5327,5327) 0.1666
(5328,5328) 0.17427
(5329,5329) 0.16455
(5330,5330) 0.12037
(5331,5331) 0.11953
(5332,5332) 0.113
(5333,5333) 0.14547
(5334,5334) 0.14274
(5335,5335) 0.14997
(5336,5336) 0.086455
(5337,5337) 0.083977
(5338,5338) 0.086499
(5339,5339) 0.16021
(5340,5340) 0.13302
(5341,5341) 0.1256
(5342,5342) 0.14725
(5343,5343) 0.12801
(5344,5344) 0.13076
(5345,5345) 0.12506
(5346,5346) 0.10662
(5347,5347) 0.087328
(5348,5348) 0.10361
(5349,5349) 0.14795
(5350,5350) 0.15346
(5351,5351) 0.15594
(5352,5352) 0.1467
(5353,5353) 0.10861
(5354,5354) 0.15678
(5355,5355) 0.16808
(5356,5356) 0.17542
(5357,5357) 0.18151
(5358,5358) 0.18194
(5359,5359) 0.15941
(5360,5360) 0.13032
(5361,5361) 0.15873
(5362,5362) 0.16591
(5363,5363) 0.18005
(5364,5364) 0.18498
(5365,5365) 0.17246
(5366,5366) 0.14271
(5367,5367) 0.18724
(5368,5368) 0.12854
(5369,5369) 0.14557
(5370,5370) 0.13589
(5371,5371) 0.14153
(5372,5372) 0.18018
(5373,5373) 0.1487
(5374,5374) 0.17346
(5375,5375) 0.15391
(5376,5376) 0.088888
(5377,5377) 0.12657
(5378,5378) 0.10632
(5379,5379) 0.12546
(5380,5380) 0.11124
(5381,5381) 0.12729
(5382,5382) 0.11186
(5383,5383) 0.10896
(5384,5384) 0.16493
(5385,5385) 0.15004
(5386,5386) 0.11363
(5387,5387) 0.12579
(5388,5388) 0.11931
(5389,5389) 0.11064
(5390,5390) 0.15487
(5391,5391) 0.16464
(5392,5392) 0.16105
(5393,5393) 0.14057
(5394,5394) 0.13454
(5395,5395) 0.1352
(5396,5396) 0.13113
(5397,5397) 0.13165
(5398,5398) 0.12197
(5399,5399) 0.096035
(5400,5400) 0.11222
(5401,5401) 0.13392
(5402,5402) 0.14681
(5403,5403) 0.15226
(5404,5404) 0.10252
(5405,5405) 0.088446
(5406,5406) 0.1225
(5407,5407) 0.10696
(5408,5408) 0.12216
(5409,5409) 0.12682
(5410,5410) 0.13409
(5411,5411) 0.12347
(5412,5412) 0.11972
(5413,5413) 0.10628
(5414,5414) 0.13724
(5415,5415) 0.12445
(5416,5416) 0.11452
(5417,5417) 0.12757
(5418,5418) 0.12552
(5419,5419) 0.15994