Contents
function [Ar, Br, Cr] = bt_mor_rail_tol(k,tol,shifts,istest)
% bt_mor_FDM_tol computes a reduced order model via the standard Lyapunov % balanced truncation (see e.g. [1]) for a finite difference discretized % convection diffusion model on the unit square described in [2]. % % Usage: % [Ar, Br, Cr] = bt_mor_rail_tol(k,tol,max_ord,n0,test) % % Inputs % % k refinement level of the model to use % (0 - 5, i.e. 109 - 79841 Dofs) % (optional, defaults to 3, i.e. 5177 Dofs) % % tol truncation tolerance for the Hankel singular values % (optional; defaults to 1e-6) % % shifts shift selection used in ADI; possible choices: % 'heur' : Penzl heuristic shifts % 'projection' : projection shifts using the last columns % of the solution factor % (optional, defaults to 'heur') % % istest flag to determine whether this demo runs as a CI test or % interactive demo % (optional, defaults to 0, i.e. interactive demo) % % Outputs % % Ar, Br, Cr the reduced order system matrices. % % References % [1] A. C. Antoulas, Approximation of Large-Scale Dynamical Systems, Vol. % 6 of Adv. Des. Control, SIAM Publications, Philadelphia, PA, 2005. % https://doi.org/10.1137/1.9780898718713 % % [2] J. Saak, Effiziente numerische Lösung eines % Optimalsteuerungsproblems für die Abkühlung von Stahlprofilen, % Diplomarbeit, Fachbereich 3/Mathematik und Informatik, Universität % Bremen, D-28334 Bremen (Sep. 2003). % https://doi.org/10.5281/zenodo.1187040 % % [3] P. Benner, J. Saak, A semi-discretized heat transfer model for % optimal cooling of steel profiles, in: P. Benner, V. Mehrmann, D. % Sorensen (Eds.), Dimension Reduction of Large-Scale Systems, Vol. 45 % of Lect. Notes Comput. Sci. Eng., Springer-Verlag, Berlin/Heidelberg, % Germany, 2005, pp. 353–356. https://doi.org/10.1007/3-540-27909-1_19 % % [4] J. Saak, Efficient numerical solution of large scale algebraic matrix % equations in PDE control and model order reduction, Dissertation, % Technische Universität Chemnitz, Chemnitz, Germany (Jul. 2009). % URL http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200901642 %
% % This file is part of the M-M.E.S.S. project % (http://www.mpi-magdeburg.mpg.de/projects/mess). % Copyright © 2009-2022 Jens Saak, Martin Koehler, Peter Benner and others. % All rights reserved. % License: BSD 2-Clause License (see COPYING) % narginchk(0,4); % BT tolerance and maximum order for the ROM if nargin<1, k=3; end if nargin<2, tol=1e-5; end if nargin<3, shifts='heur'; end if nargin<4, istest=0; end % ADI tolerance and maximum iteration number opts.adi.maxiter = 100; % maximum iteration number opts.adi.res_tol = 1e-10; % residual norm tolerance opts.adi.rel_diff_tol = 1e-16; % relative change norm tolerance opts.adi.info = 1; % turn output on opts.norm = 'fro'; % Frobenius norm for stopping criteria oper = operatormanager('default');
Problem data
eqn = mess_get_linear_rail(k); % load system matrices n = oper.size(eqn, opts); % number of equations
Shift Parameters
opts.shifts.num_desired=25; % number of parameters for % 'heur' and 'wachspress' switch lower(shifts) case 'heur' opts.shifts.method = 'heur'; opts.shifts.num_Ritz=50; % number Arnoldi steps with F opts.shifts.num_hRitz=25; % Arnoldi steps with inv(F) opts.shifts.b0=ones(n,1); % initial guess for Arnoldi case 'wachspress' opts.shifts.method = 'wachspress'; opts.shifts.wachspress = 'T'; case 'projection' opts.shifts.method = 'projection'; end
Compute low-rank factor of Controllability Gramian
eqn.type='N'; % Lyapunov eq. for Controllability Gram. t_mess_lradi = tic; outB = mess_lradi(eqn, opts, oper); % run ADI iteration t_elapsed1 = toc(t_mess_lradi); fprintf(1,'mess_lradi took %6.2f seconds \n',t_elapsed1); % residual norm plot if istest if min(outB.res)>=opts.adi.res_tol error('MESS:TEST:accuracy','unexpectedly inaccurate result'); end else figure(1); semilogy(outB.res,'LineWidth',3); title('A X E^T + E X A^T = -BB^T'); xlabel('number of iterations'); ylabel('normalized residual norm'); pause(1); end disp('size outB.Z:'); disp(size(outB.Z));
ADI step: 1 normalized residual: 9.540736e-01 relative change in Z: 1.000000e+00 ADI step: 2 normalized residual: 9.022193e-01 relative change in Z: 7.017286e-01 ADI step: 3 normalized residual: 8.376322e-01 relative change in Z: 5.940307e-01 ADI step: 4 normalized residual: 7.288196e-01 relative change in Z: 5.901053e-01 ADI step: 5 normalized residual: 6.307259e-01 relative change in Z: 4.849749e-01 ADI step: 6 normalized residual: 5.436156e-01 relative change in Z: 4.476573e-01 ADI step: 7 normalized residual: 4.550657e-01 relative change in Z: 4.706104e-01 ADI step: 8 normalized residual: 3.869504e-01 relative change in Z: 4.017214e-01 ADI step: 9 normalized residual: 3.235731e-01 relative change in Z: 3.896615e-01 ADI step: 10 normalized residual: 2.589330e-01 relative change in Z: 4.125858e-01 ADI step: 11 normalized residual: 1.856869e-01 relative change in Z: 4.801609e-01 ADI step: 12 normalized residual: 1.484909e-01 relative change in Z: 3.927720e-01 ADI step: 13 normalized residual: 1.132085e-01 relative change in Z: 4.410151e-01 ADI step: 14 normalized residual: 8.773470e-02 relative change in Z: 4.895876e-01 ADI step: 15 normalized residual: 7.751995e-02 relative change in Z: 4.676556e-01 ADI step: 16 normalized residual: 7.076337e-02 relative change in Z: 4.495181e-01 ADI step: 17 normalized residual: 5.919815e-02 relative change in Z: 5.280133e-01 ADI step: 18 normalized residual: 4.842990e-02 relative change in Z: 4.722096e-01 ADI step: 19 normalized residual: 3.774125e-02 relative change in Z: 4.728068e-01 ADI step: 20 normalized residual: 2.798475e-02 relative change in Z: 4.621671e-01 ADI step: 21 normalized residual: 1.961923e-02 relative change in Z: 4.213141e-01 ADI step: 22 normalized residual: 8.997049e-03 relative change in Z: 4.519668e-01 ADI step: 23 normalized residual: 5.275588e-04 relative change in Z: 4.202030e-01 ADI step: 24 normalized residual: 7.333388e-06 relative change in Z: 1.195977e-01 ADI step: 25 normalized residual: 9.877299e-07 relative change in Z: 1.393323e-02 ADI step: 26 normalized residual: 9.578007e-07 relative change in Z: 2.842105e-05 ADI step: 27 normalized residual: 9.281348e-07 relative change in Z: 2.404943e-05 ADI step: 28 normalized residual: 8.928960e-07 relative change in Z: 2.349151e-05 ADI step: 29 normalized residual: 8.299175e-07 relative change in Z: 2.997828e-05 ADI step: 30 normalized residual: 7.611381e-07 relative change in Z: 3.066412e-05 ADI step: 31 normalized residual: 6.738629e-07 relative change in Z: 3.481919e-05 ADI step: 32 normalized residual: 5.377852e-07 relative change in Z: 4.638747e-05 ADI step: 33 normalized residual: 4.322907e-07 relative change in Z: 4.584316e-05 ADI step: 34 normalized residual: 3.444620e-07 relative change in Z: 4.777012e-05 ADI step: 35 normalized residual: 2.601868e-07 relative change in Z: 5.362071e-05 ADI step: 36 normalized residual: 1.610205e-07 relative change in Z: 6.658857e-05 ADI step: 37 normalized residual: 1.137514e-07 relative change in Z: 5.390905e-05 ADI step: 38 normalized residual: 7.023969e-08 relative change in Z: 6.161001e-05 ADI step: 39 normalized residual: 2.841649e-08 relative change in Z: 6.794112e-05 ADI step: 40 normalized residual: 6.238977e-09 relative change in Z: 5.166790e-05 ADI step: 41 normalized residual: 5.548212e-10 relative change in Z: 2.904573e-05 ADI step: 42 normalized residual: 6.583571e-11 relative change in Z: 1.616275e-05 mess_lradi took 1.13 seconds size outB.Z: 5177 294

Compute low-rank factor of Observability Gramian
eqn.type = 'T'; % Lyapunov eq. for Observability Gram. t_mess_lradi = tic; outC = mess_lradi(eqn, opts, oper); % run ADI iteration t_elapsed2 = toc(t_mess_lradi); fprintf(1,'mess_lradi took %6.2f seconds \n',t_elapsed2); % residual norm plot if istest if min(outC.res)>=opts.adi.res_tol error('MESS:TEST:accuracy','unexpectedly inaccurate result'); end else figure(2); semilogy(outC.res,'LineWidth',3); title('A^T X E + E^T X A = -C^T C'); xlabel('number of iterations'); ylabel('normalized residual norm'); pause(1); end disp('size outC.Z:'); disp(size(outC.Z));
ADI step: 1 normalized residual: 8.947589e-01 relative change in Z: 1.000000e+00 ADI step: 2 normalized residual: 7.869684e-01 relative change in Z: 6.992007e-01 ADI step: 3 normalized residual: 6.682720e-01 relative change in Z: 5.768862e-01 ADI step: 4 normalized residual: 4.969198e-01 relative change in Z: 5.506452e-01 ADI step: 5 normalized residual: 3.594852e-01 relative change in Z: 4.232765e-01 ADI step: 6 normalized residual: 2.415124e-01 relative change in Z: 3.614895e-01 ADI step: 7 normalized residual: 1.359892e-01 relative change in Z: 3.409900e-01 ADI step: 8 normalized residual: 8.687926e-02 relative change in Z: 2.530866e-01 ADI step: 9 normalized residual: 5.598895e-02 relative change in Z: 2.241878e-01 ADI step: 10 normalized residual: 3.347451e-02 relative change in Z: 2.213724e-01 ADI step: 11 normalized residual: 1.558178e-02 relative change in Z: 2.415891e-01 ADI step: 12 normalized residual: 8.570039e-03 relative change in Z: 1.781169e-01 ADI step: 13 normalized residual: 3.293371e-03 relative change in Z: 1.809690e-01 ADI step: 14 normalized residual: 9.946641e-04 relative change in Z: 1.695158e-01 ADI step: 15 normalized residual: 3.995725e-04 relative change in Z: 1.259353e-01 ADI step: 16 normalized residual: 1.640396e-04 relative change in Z: 8.252576e-02 ADI step: 17 normalized residual: 7.651346e-05 relative change in Z: 6.107904e-02 ADI step: 18 normalized residual: 5.866263e-05 relative change in Z: 4.823852e-02 ADI step: 19 normalized residual: 4.640613e-05 relative change in Z: 5.171545e-02 ADI step: 20 normalized residual: 3.395949e-05 relative change in Z: 5.643950e-02 ADI step: 21 normalized residual: 2.243128e-05 relative change in Z: 5.605705e-02 ADI step: 22 normalized residual: 8.819108e-06 relative change in Z: 6.394259e-02 ADI step: 23 normalized residual: 5.508455e-07 relative change in Z: 5.602514e-02 ADI step: 24 normalized residual: 4.772787e-07 relative change in Z: 1.453525e-02 ADI step: 25 normalized residual: 4.760426e-07 relative change in Z: 1.692512e-03 ADI step: 26 normalized residual: 4.159229e-07 relative change in Z: 2.342674e-04 ADI step: 27 normalized residual: 3.695560e-07 relative change in Z: 1.862429e-04 ADI step: 28 normalized residual: 3.259978e-07 relative change in Z: 1.603995e-04 ADI step: 29 normalized residual: 2.677560e-07 relative change in Z: 1.779658e-04 ADI step: 30 normalized residual: 2.229204e-07 relative change in Z: 1.562560e-04 ADI step: 31 normalized residual: 1.782333e-07 relative change in Z: 1.578359e-04 ADI step: 32 normalized residual: 1.177680e-07 relative change in Z: 1.973753e-04 ADI step: 33 normalized residual: 7.738125e-08 relative change in Z: 1.851612e-04 ADI step: 34 normalized residual: 5.040355e-08 relative change in Z: 1.827358e-04 ADI step: 35 normalized residual: 3.110822e-08 relative change in Z: 1.944998e-04 ADI step: 36 normalized residual: 1.304615e-08 relative change in Z: 2.265926e-04 ADI step: 37 normalized residual: 6.283452e-09 relative change in Z: 1.642206e-04 ADI step: 38 normalized residual: 2.575653e-09 relative change in Z: 1.637633e-04 ADI step: 39 normalized residual: 9.134495e-10 relative change in Z: 1.638016e-04 ADI step: 40 normalized residual: 1.833310e-10 relative change in Z: 1.222578e-04 ADI step: 41 normalized residual: 1.380298e-11 relative change in Z: 6.394106e-05 mess_lradi took 1.13 seconds size outC.Z: 5177 246

Compute reduced system matrices
Perform Square Root Method
opts.srm.tol=tol; opts.srm.max_ord=n; opts.srm.info=2; [TL,TR,HSV] = mess_square_root_method(eqn,opts,oper,outB.Z,outC.Z);
reduced system order: 59 (max possible/allowed: 246/5177)
compute ROM matrices
Ar = TL'*oper.mul_A(eqn, opts, 'N', TR, 'N'); Br = TL'*eqn.B; Cr = eqn.C*TR; Er = eye(size(Ar,1));
Plots
ROM.A=Ar; ROM.E=Er; ROM.B=Br; ROM.C=Cr; if istest opts.sigma.info=0; else opts.sigma.info=2; end opts.sigma.fmin=-6; opts.sigma.fmax=4; out = mess_sigma_plot(eqn, opts, oper, ROM); err = out.err; if istest if max(err)>tol error('MESS:TEST:accuracy','unexpectedly inaccurate result'); end else figure; semilogy(HSV,'LineWidth',3); title('Computed Hankel singular values'); xlabel('index'); ylabel('magnitude'); end
Computing TFMs of original and reduced order systems and MOR errors Step 10 / 100 Step 20 / 100 Step 30 / 100 Step 40 / 100 Step 50 / 100 Step 60 / 100 Step 70 / 100 Step 80 / 100 Step 90 / 100 Step 100 / 100 ans = Columns 1 through 7 -0.0000 0.0000 0.0000 -0.0001 0.0000 0.0000 0.0001 -0.0000 -0.0000 0.0000 0.0002 -0.0001 -0.0000 -0.0003 -0.0000 -0.0001 -0.0020 0.0000 0.0001 -0.0018 0.0000 0.0001 0.0000 0.0001 -0.0049 0.0039 0.0003 0.0021 -0.0001 0.0001 0.0002 0.0038 -0.0035 -0.0001 -0.0009 -0.0000 -0.0000 -0.0015 0.0002 -0.0002 -0.0022 -0.0000 -0.0001 0.0001 0.0000 0.0011 -0.0008 -0.0001 -0.0063 0.0001 0.0004 0.0002 -0.0012 -0.0013 -0.0006 -0.0004 -0.0001 -0.0000 0.0005 0.0062 -0.0055 0.0006 0.0006 0.0000 0.0001 0.0024 -0.0017 0.0012 0.0039 -0.0001 0.0000 0.0002 0.0067 -0.0001 -0.0011 0.0083 -0.0001 0.0001 0.0000 0.0003 -0.0074 0.0068 0.0009 0.0006 -0.0001 -0.0000 0.0023 0.0044 -0.0041 0.0023 -0.0012 0.0001 0.0001 0.0009 -0.0108 0.0091 0.0015 0.0032 -0.0001 0.0001 -0.0000 0.0028 -0.0024 -0.0004 -0.0156 0.0001 0.0005 0.0036 -0.0015 -0.0028 0.0044 0.0015 -0.0000 0.0000 0.0069 0.0001 0.0004 0.0122 -0.0011 0.0000 0.0000 -0.0005 -0.0049 0.0044 -0.0006 -0.0020 0.0000 0.0000 0.0009 -0.0009 0.0008 0.0022 -0.0008 -0.0000 -0.0000 -0.0001 0.0033 -0.0034 -0.0003 0.0063 -0.0000 -0.0001 -0.0039 0.0001 0.0005 -0.0044 -0.0002 0.0000 -0.0000 -0.0031 -0.0002 0.0001 -0.0068 -0.0004 -0.0000 -0.0002 -0.0029 0.0008 0.0009 -0.0051 0.0002 0.0000 -0.0001 -0.0040 -0.0006 0.0009 -0.0075 0.0004 0.0000 0.0000 0.0005 -0.0050 0.0047 0.0014 0.0016 -0.0000 -0.0001 0.0007 0.0019 -0.0008 0.0017 0.0011 -0.0000 -0.0002 -0.0024 0.0004 0.0007 -0.0050 -0.0001 -0.0000 0.0000 0.0001 0.0006 -0.0000 0.0004 -0.0068 0.0000 0.0001 -0.0004 0.0002 -0.0006 -0.0015 -0.0002 -0.0000 0.0000 -0.0003 0.0024 -0.0025 -0.0009 -0.0001 -0.0000 -0.0000 0.0010 0.0007 -0.0002 0.0025 0.0000 0.0000 -0.0000 -0.0008 -0.0003 -0.0001 -0.0028 -0.0003 0.0000 0.0001 0.0005 -0.0003 -0.0003 0.0009 -0.0004 0.0000 0.0001 0.0014 -0.0002 -0.0004 0.0038 -0.0001 -0.0000 0.0000 -0.0019 0.0001 0.0002 -0.0023 -0.0000 0.0000 0.0000 -0.0001 -0.0014 0.0012 -0.0001 0.0007 -0.0000 -0.0001 -0.0003 0.0002 -0.0002 -0.0024 -0.0004 0.0000 0.0000 0.0000 -0.0016 0.0011 -0.0002 0.0034 -0.0000 -0.0000 0.0000 0.0007 -0.0003 -0.0000 -0.0034 0.0000 0.0000 0.0005 -0.0003 0.0001 0.0012 0.0005 -0.0000 0.0000 0.0003 0.0005 -0.0004 0.0013 -0.0010 0.0000 0.0000 -0.0001 -0.0005 0.0002 0.0002 0.0016 -0.0000 -0.0000 0.0000 0.0001 -0.0003 -0.0011 -0.0004 0.0000 0.0001 0.0001 -0.0002 -0.0003 0.0001 -0.0005 0.0000 0.0000 0.0001 -0.0006 0.0002 0.0000 0.0018 0.0000 -0.0000 0.0002 -0.0003 0.0004 0.0003 0.0012 -0.0000 -0.0000 0.0001 0.0002 -0.0000 0.0005 -0.0004 -0.0000 0.0000 0.0005 0.0003 -0.0003 0.0006 -0.0006 -0.0000 -0.0000 -0.0007 0.0001 0.0001 -0.0010 -0.0000 -0.0000 -0.0000 0.0005 0.0000 -0.0000 0.0000 -0.0005 0.0000 -0.0000 0.0004 -0.0000 -0.0000 0.0002 0.0006 0.0000 0.0000 -0.0001 -0.0001 0.0001 -0.0000 0.0005 0.0000 0.0000 0.0003 -0.0001 -0.0001 -0.0000 -0.0000 -0.0000 -0.0000 0.0001 0.0001 0.0002 0.0001 0.0002 0.0000 -0.0000 -0.0002 -0.0000 0.0000 -0.0002 -0.0000 0.0000 -0.0000 -0.0001 -0.0004 0.0004 -0.0001 0.0002 0.0000 0.0000 0.0006 -0.0001 -0.0000 0.0009 -0.0000 0.0000 -0.0000 -0.0004 -0.0000 0.0000 -0.0007 -0.0000 0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0002 0.0000 Columns 8 through 14 -0.0000 0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0001 -0.0000 -0.0000 0.0000 0.0001 0.0001 -0.0001 0.0002 0.0002 0.0006 0.0026 0.0067 0.0003 0.0023 0.0008 -0.0009 0.0061 -0.0017 -0.0000 -0.0074 0.0045 -0.0108 -0.0007 -0.0056 0.0012 -0.0009 0.0070 -0.0041 0.0091 -0.0004 0.0008 0.0049 0.0085 0.0009 0.0026 0.0015 -0.0003 -0.0002 0.0001 -0.0000 0.0016 -0.0018 0.0048 -0.0128 0.0008 -0.0000 -0.0009 0.0015 0.0017 -0.0029 0.0007 -0.0141 0.0003 -0.0052 0.0183 -0.0126 0.0260 0.0001 0.0004 -0.0140 -0.0202 -0.0059 -0.0032 -0.0090 -0.0010 -0.0044 -0.0178 -0.0686 -0.0025 -0.0320 -0.0106 0.0016 0.0184 -0.0058 -0.0025 -0.0301 0.0170 -0.0453 0.0017 -0.0124 -0.0016 -0.0305 0.0171 -0.0300 0.0254 -0.0027 0.0268 -0.0087 -0.0099 -0.0454 0.0255 -0.0775 -0.0059 0.0002 0.0007 0.0002 0.0070 -0.0064 0.0195 -0.0271 -0.0047 -0.0168 -0.0496 0.0063 -0.0162 -0.0140 0.0104 -0.0078 -0.0392 -0.0970 -0.0100 -0.0443 -0.0147 -0.0020 0.0162 -0.0012 0.0075 -0.0253 0.0215 -0.0424 -0.0000 0.0012 -0.0096 -0.0124 -0.0066 0.0006 -0.0101 0.0002 -0.0144 0.0034 0.0007 0.0253 -0.0143 0.0363 -0.0008 0.0003 0.0017 0.0690 0.0040 0.0479 0.0171 -0.0037 0.0072 0.0275 0.0473 0.0029 0.0189 0.0033 0.0101 0.0038 0.0200 0.0462 0.0004 0.0169 0.0129 -0.0013 0.0083 0.0269 0.0673 0.0003 0.0364 0.0034 0.0020 0.0149 -0.0077 -0.0086 -0.0331 0.0187 -0.0598 0.0090 -0.0068 -0.0029 -0.0137 0.0071 -0.0181 0.0187 0.0065 0.0043 0.0186 0.0413 -0.0001 0.0158 0.0087 0.0007 0.0027 -0.0019 -0.0023 -0.0044 -0.0019 0.0029 -0.0035 0.0035 0.0183 -0.0006 0.0030 -0.0102 -0.0016 -0.0027 -0.0085 0.0018 0.0062 0.0188 -0.0071 0.0317 0.0040 -0.0030 -0.0051 -0.0194 0.0007 -0.0139 0.0038 -0.0041 0.0015 0.0034 0.0182 0.0017 0.0114 0.0003 -0.0039 -0.0003 -0.0036 -0.0095 0.0000 -0.0030 -0.0039 -0.0035 -0.0024 -0.0106 -0.0264 -0.0005 -0.0097 -0.0052 -0.0005 0.0031 0.0141 0.0306 0.0020 0.0171 0.0062 -0.0002 0.0048 -0.0003 0.0023 -0.0110 0.0087 -0.0180 -0.0002 0.0016 0.0090 0.0053 0.0020 -0.0049 0.0009 -0.0003 0.0035 -0.0002 -0.0004 -0.0105 0.0065 -0.0198 0.0003 -0.0001 0.0001 -0.0010 0.0031 -0.0036 0.0068 -0.0003 -0.0007 -0.0051 -0.0087 -0.0018 -0.0019 -0.0042 -0.0007 -0.0024 -0.0054 -0.0048 0.0026 -0.0013 0.0061 -0.0013 0.0002 -0.0015 0.0014 -0.0015 0.0050 -0.0050 -0.0014 0.0008 0.0047 -0.0012 0.0014 -0.0054 -0.0004 -0.0042 0.0001 -0.0015 -0.0007 0.0010 0.0024 -0.0019 -0.0011 0.0006 -0.0001 -0.0026 -0.0020 0.0004 -0.0071 0.0019 0.0004 -0.0011 -0.0034 -0.0027 -0.0012 -0.0051 0.0009 -0.0007 -0.0024 -0.0006 -0.0003 0.0005 0.0023 0.0001 -0.0011 -0.0019 -0.0083 0.0012 -0.0068 0.0016 0.0008 0.0004 0.0028 0.0130 0.0009 0.0079 0.0042 0.0007 0.0008 0.0020 -0.0097 -0.0012 -0.0100 -0.0032 0.0008 0.0000 0.0011 -0.0081 -0.0004 -0.0078 -0.0029 -0.0003 0.0000 -0.0003 0.0014 -0.0002 0.0020 -0.0010 -0.0010 0.0006 0.0018 -0.0073 -0.0003 -0.0068 -0.0036 0.0022 -0.0001 -0.0002 -0.0016 -0.0009 -0.0021 0.0002 -0.0001 -0.0001 -0.0005 0.0042 0.0002 0.0038 0.0012 0.0001 0.0015 -0.0001 0.0022 -0.0029 0.0038 -0.0052 -0.0005 0.0000 -0.0016 -0.0121 -0.0012 -0.0078 -0.0045 -0.0004 0.0002 0.0007 0.0083 0.0005 0.0061 0.0018 -0.0000 0.0004 0.0017 -0.0003 -0.0001 -0.0013 -0.0007 Columns 15 through 21 0.0001 -0.0000 0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0004 0.0002 0.0000 -0.0000 0.0000 0.0001 -0.0000 -0.0000 0.0036 0.0071 -0.0005 0.0009 -0.0001 -0.0043 0.0028 -0.0012 -0.0000 -0.0049 -0.0009 0.0032 0.0001 -0.0016 -0.0026 0.0004 0.0046 0.0008 -0.0037 0.0005 -0.0003 0.0048 0.0126 -0.0006 0.0022 -0.0003 -0.0047 -0.0156 0.0015 -0.0010 -0.0012 -0.0007 0.0062 -0.0002 -0.0059 -0.0271 0.0102 -0.0021 -0.0000 0.0002 -0.0007 0.0023 -0.0054 -0.0082 0.0165 0.0012 -0.0148 0.0018 0.0002 -0.0178 -0.0418 -0.0011 -0.0098 0.0037 0.0083 0.0004 -0.0462 -0.0914 0.0072 -0.0103 0.0010 0.0791 0.0040 0.0078 -0.0103 -0.0271 -0.0063 0.0245 0.0043 -0.0058 -0.0148 -0.0429 0.0220 0.0011 -0.0133 0.0532 0.0185 -0.0142 -0.0140 -0.0436 -0.0099 0.0341 0.0192 -0.1010 -0.0123 0.0050 -0.0114 -0.0058 0.0540 -0.0032 -0.0125 -0.1811 -0.0506 0.0032 -0.0189 -0.0130 0.0582 0.0048 -0.0513 -0.2462 0.0169 -0.0470 0.0100 0.1275 -0.0148 0.0053 0.0160 -0.0362 -0.0049 0.0421 -0.0103 -0.0041 -0.0183 -0.0491 -0.0040 -0.0172 0.0112 -0.0005 0.0424 -0.0097 0.0072 0.0363 0.0107 -0.0663 -0.0053 -0.0029 0.0405 0.0951 -0.0080 -0.0010 -0.0042 -0.2331 -0.0096 0.0521 0.1781 -0.0166 0.0463 0.0038 -0.0407 0.0122 0.1321 0.1171 -0.0056 0.0378 -0.0007 -0.0674 0.0002 0.0874 0.2148 -0.0231 0.0526 0.0030 -0.1248 0.0206 0.0060 -0.0383 -0.0403 -0.0185 0.0485 0.0214 0.0219 0.0452 -0.0655 0.0249 -0.0048 -0.0264 0.0450 0.0060 0.1155 0.1292 -0.0098 0.0460 0.0040 -0.0654 -0.0648 0.0126 -0.0177 -0.0139 -0.0108 0.0607 0.0032 -0.0081 0.0063 0.0838 -0.0047 0.0377 0.0013 0.1389 -0.0070 -0.0196 0.0216 0.0225 0.0087 -0.0367 -0.0422 0.0061 0.0048 -0.0727 0.0122 -0.0167 -0.0049 0.0674 -0.0100 -0.0100 0.0675 -0.0098 0.0179 0.0024 -0.0846 -0.0087 -0.0450 -0.0197 -0.0006 -0.0097 0.0039 0.0200 -0.0047 -0.0707 -0.0897 0.0071 -0.0364 -0.0004 0.0661 -0.0020 0.0475 0.1086 -0.0082 0.0253 -0.0005 -0.0417 0.0094 0.0018 0.0084 -0.0111 -0.0024 0.0250 -0.0040 -0.0059 0.0213 0.0589 -0.0053 0.0340 0.0009 0.0331 0.0398 -0.0070 0.0082 -0.0012 0.0020 0.0042 0.0084 -0.0387 0.0083 -0.0060 -0.0085 -0.0012 0.0152 0.0049 0.0063 -0.0207 -0.0375 0.0027 -0.0146 -0.0014 0.0088 -0.0117 -0.0197 -0.0360 0.0047 -0.0185 0.0002 -0.0188 0.0164 -0.0157 0.0006 0.0010 -0.0050 -0.0096 -0.0192 -0.0074 -0.0028 0.0288 -0.0026 0.0181 0.0032 0.0376 -0.0110 -0.0378 0.0061 -0.0036 -0.0047 0.0024 -0.0146 0.0183 -0.0143 0.0020 0.0011 0.0019 -0.0083 0.0142 0.0164 0.0099 -0.0148 0.0011 -0.0008 -0.0058 0.0125 -0.0030 0.0029 -0.0165 0.0020 -0.0082 0.0045 -0.0155 -0.0064 -0.0090 -0.0241 0.0028 -0.0041 0.0011 0.0291 0.0003 0.0229 0.0322 -0.0019 0.0064 -0.0013 -0.0505 -0.0047 0.0030 -0.0078 -0.0008 0.0086 0.0084 0.0722 0.0073 0.0007 -0.0097 0.0023 0.0062 -0.0045 0.0562 0.0047 -0.0031 0.0022 -0.0000 -0.0010 -0.0040 -0.0109 -0.0016 -0.0107 0.0005 -0.0008 0.0073 0.0018 0.0571 0.0050 0.0170 -0.0107 0.0017 0.0002 -0.0003 0.0094 -0.0003 0.0022 0.0055 -0.0007 -0.0018 -0.0004 -0.0293 0.0025 0.0037 0.0044 -0.0049 -0.0006 0.0049 -0.0102 -0.0008 -0.0173 -0.0272 0.0010 -0.0042 0.0028 0.0596 -0.0013 0.0053 0.0205 -0.0023 0.0025 -0.0003 -0.0462 -0.0001 0.0029 0.0072 -0.0007 0.0048 0.0008 0.0180 Columns 22 through 28 0.0000 0.0000 -0.0000 -0.0000 -0.0000 0.0000 0.0001 -0.0001 -0.0001 -0.0000 0.0001 0.0000 -0.0001 -0.0002 -0.0030 -0.0029 -0.0039 0.0005 0.0008 -0.0026 0.0002 -0.0001 0.0007 -0.0006 -0.0051 0.0018 0.0004 0.0007 0.0002 0.0008 0.0008 0.0047 -0.0010 0.0007 0.0002 -0.0068 -0.0051 -0.0076 0.0014 0.0017 -0.0049 0.0004 -0.0004 0.0002 0.0006 0.0023 0.0011 -0.0001 -0.0072 -0.0037 0.0101 -0.0015 0.0020 0.0090 0.0066 0.0007 0.0072 0.0042 0.0088 0.0147 -0.0073 0.0049 0.0030 0.0276 0.0212 0.0290 -0.0081 -0.0041 0.0207 -0.0021 0.0382 0.0405 0.0582 -0.0076 -0.0144 0.0393 -0.0024 0.0022 -0.0000 -0.0001 -0.0329 0.0073 -0.0003 -0.0034 0.0137 0.0137 0.0300 0.0196 -0.0186 0.0155 -0.0027 0.0018 0.0114 0.0010 -0.0597 0.0189 0.0086 0.0045 -0.0094 0.0113 0.0004 0.0206 0.0242 0.0054 -0.0717 0.0477 0.1301 0.0816 0.0058 0.0408 0.1196 0.0138 0.1639 0.1140 0.2105 -0.0382 -0.0689 0.1336 -0.0196 -0.0161 -0.0055 -0.0222 -0.0416 0.0276 -0.0102 -0.0162 0.0511 0.0396 0.0579 -0.0191 -0.0062 0.0464 -0.0108 0.0052 0.0013 0.0037 0.0427 -0.0263 0.0047 0.0606 -0.0005 -0.0368 -0.0743 0.0149 0.0406 -0.0523 0.0032 -0.1740 -0.1272 -0.2168 0.0324 0.0621 -0.1660 0.0090 -0.1226 -0.1736 -0.1869 0.0171 -0.0098 -0.2121 0.0048 -0.2057 -0.1886 -0.3117 0.0337 0.0900 -0.2738 0.0247 0.0292 0.0162 0.0323 -0.1192 0.0093 0.0281 0.0123 0.0546 -0.0152 0.0758 0.0127 -0.1106 0.0138 0.0052 -0.1569 -0.2039 -0.2503 0.0227 0.0081 -0.3137 0.0049 0.0084 0.0038 0.0201 -0.0146 0.0264 0.0042 -0.1461 -0.1530 -0.0780 -0.1685 0.0362 0.0387 -0.1088 0.0065 -0.0048 0.0097 -0.0071 0.0839 0.0074 -0.0033 0.0033 0.0688 0.0385 0.1112 -0.0121 -0.0845 0.1023 -0.0150 -0.0613 -0.0333 -0.1002 0.0216 0.0937 -0.1163 0.0116 0.0267 0.0674 0.0591 -0.0021 0.0333 0.1076 -0.0086 0.1154 0.1559 0.2016 -0.0221 -0.0224 0.3132 -0.0141 -0.1263 -0.1204 -0.2323 0.0369 0.0554 -0.1908 0.0110 -0.0106 -0.0091 -0.0223 -0.0625 0.0404 -0.0207 -0.0079 -0.1073 -0.0909 -0.1393 0.0308 0.0356 -0.2241 0.0091 -0.0101 -0.0069 -0.0174 -0.0756 0.0352 -0.0207 0.0743 -0.0020 -0.0012 0.0053 0.0338 -0.0116 -0.0060 -0.0884 0.0542 0.0568 0.0904 -0.0235 -0.0175 0.1238 0.0072 0.0635 0.0638 0.0948 0.0092 -0.0172 0.1456 -0.0349 0.0147 0.0240 0.0117 -0.0169 0.0182 0.0522 0.0503 -0.0601 -0.0329 -0.0681 0.0204 0.0375 -0.1032 -0.0036 0.0050 0.0493 0.0125 0.0100 0.0645 0.0806 -0.0042 -0.0034 0.0115 0.0016 -0.0191 0.0157 0.0158 0.0492 0.0130 -0.0070 0.0197 -0.0251 -0.0345 -0.0090 0.0375 0.0286 0.0134 0.0368 -0.0048 -0.0164 0.0383 -0.0316 0.0218 0.0259 0.0531 0.0038 -0.0219 0.0524 -0.0160 -0.0288 -0.0475 -0.0763 0.0133 0.0148 -0.0958 0.0032 -0.0228 -0.0137 0.0021 -0.0049 -0.0168 -0.0408 -0.0233 -0.0102 -0.0062 0.0108 -0.0058 -0.0267 -0.0174 0.0234 0.0031 0.0043 -0.0013 -0.0026 0.0055 0.0095 0.0188 -0.0227 0.0023 -0.0036 0.0004 0.0074 -0.0090 0.0033 0.0067 -0.0173 0.0096 -0.0090 -0.0380 -0.0274 -0.0006 0.0036 -0.0024 -0.0094 0.0019 0.0093 -0.0050 -0.0003 -0.0034 -0.0067 -0.0131 -0.0173 0.0101 -0.0150 0.0021 0.0184 0.0369 0.0624 -0.0137 -0.0182 0.0804 -0.0062 -0.0130 -0.0183 -0.0437 0.0086 0.0285 -0.0492 0.0029 -0.0175 -0.0124 -0.0194 0.0017 0.0013 -0.0269 0.0014 Columns 29 through 35 -0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0000 0.0000 0.0000 0.0000 0.0013 -0.0007 0.0016 -0.0024 0.0005 0.0027 0.0009 0.0001 0.0024 0.0006 -0.0001 -0.0002 -0.0002 -0.0000 -0.0007 -0.0025 -0.0004 0.0000 -0.0002 -0.0005 -0.0002 -0.0005 -0.0011 0.0028 -0.0036 0.0009 0.0044 -0.0001 -0.0002 0.0004 0.0001 -0.0004 -0.0005 -0.0001 0.0001 -0.0035 -0.0027 0.0039 -0.0038 -0.0035 -0.0032 -0.0004 0.0015 -0.0084 -0.0039 0.0029 -0.0003 -0.0036 0.0015 0.0096 0.0043 -0.0087 0.0104 -0.0042 -0.0165 0.0059 -0.0347 0.0140 -0.0293 0.0451 -0.0079 -0.0455 -0.0256 0.0013 0.0193 0.0003 0.0035 0.0002 -0.0013 -0.0012 -0.0337 -0.0015 -0.0216 0.0314 -0.0019 -0.0247 -0.0244 -0.0104 0.0336 0.0014 0.0085 -0.0035 -0.0107 -0.0095 -0.0068 0.0033 0.0082 -0.0103 -0.0104 -0.0046 -0.0005 -0.0338 -0.0122 -0.0100 0.0246 -0.0414 -0.0944 -0.0098 0.0085 0.0419 -0.0982 0.1293 -0.0205 -0.1383 -0.0043 0.0008 0.0259 0.0148 -0.0127 -0.0012 0.0105 0.0001 0.0367 0.0097 -0.0158 0.0165 -0.0116 -0.0376 0.0263 0.0036 -0.0426 -0.0056 -0.0006 0.0048 0.0017 0.0052 0.2395 -0.0645 0.0958 -0.1776 0.0094 0.1322 0.1961 -0.1090 -0.0158 0.0838 -0.0923 0.0333 0.1480 -0.0796 -0.0219 -0.0052 0.0613 -0.0873 0.0627 0.1929 -0.0311 -0.0447 -0.0438 0.1651 -0.2198 0.0582 0.2952 -0.0337 0.0144 0.0846 -0.0181 0.0429 -0.0041 -0.0400 -0.0005 0.0025 0.0111 -0.0902 0.1134 0.0188 -0.0600 -0.0254 -0.0613 -0.0081 0.1125 -0.1634 0.0978 0.3439 -0.0646 0.0112 0.0628 -0.0035 0.0084 -0.0148 -0.0187 0.0055 -0.5019 0.0642 -0.0396 0.1861 0.0260 -0.0533 -0.5769 0.0700 -0.0982 0.0433 -0.1015 -0.0063 0.0587 0.1142 -0.0496 0.0507 -0.1344 0.2132 -0.0051 -0.1928 -0.1181 0.1462 -0.0878 0.1858 -0.3349 -0.0010 0.2884 0.3161 -0.0163 -0.0011 -0.0176 0.0384 -0.0542 -0.1454 -0.0032 -0.0598 0.0530 -0.1862 0.3358 -0.0994 -0.5277 -0.2165 -0.2864 0.0226 0.0440 0.0619 0.0791 0.1271 -0.7097 -0.0026 0.0809 0.0293 -0.0109 -0.0078 0.0260 -0.0198 -0.1346 -0.0392 0.1379 -0.2455 0.0560 0.4142 0.1336 -0.0019 0.0976 0.0416 -0.0235 -0.0118 0.0440 0.0468 -0.0127 -0.0470 -0.0166 -0.0077 0.0090 0.0070 0.0075 0.0724 0.0194 -0.0613 0.0905 -0.0475 -0.2113 0.1111 0.1095 -0.0190 -0.0705 0.1011 -0.0529 -0.2607 0.0461 0.0380 0.0064 0.0033 0.0147 -0.0255 -0.0881 -0.0337 -0.1179 -0.0210 0.0851 -0.1508 0.0127 0.2433 0.0930 0.0231 -0.0360 0.0429 -0.0642 -0.0688 -0.0916 0.0444 -0.0243 0.0186 0.0138 -0.0100 -0.0196 -0.0138 0.0362 0.0347 0.0217 -0.0200 0.0148 0.0238 0.0328 0.1195 0.0792 0.0076 -0.0292 0.0370 -0.0067 -0.0710 0.0515 0.0023 -0.0030 -0.0397 0.0412 -0.0220 -0.0835 0.1370 0.0329 -0.0217 0.0581 -0.0832 0.0516 0.1752 -0.1528 -0.1402 0.0346 -0.0180 0.0198 0.0076 0.0683 0.0836 -0.1003 0.0218 -0.0272 0.0369 0.0091 0.0257 0.0679 0.0218 -0.0060 0.0071 -0.0087 -0.0037 -0.0118 -0.0063 -0.1423 0.0180 -0.0043 0.0145 -0.0161 0.0096 0.0061 0.0151 0.0177 -0.0274 0.0302 0.0345 0.0456 0.0518 0.0654 -0.0155 0.0225 -0.0412 0.0050 0.0287 0.0072 0.0176 0.0138 0.0155 -0.0204 0.0077 0.0326 -0.0116 -0.0923 0.0370 -0.0720 0.1230 -0.0442 -0.1868 0.0572 0.0869 -0.0352 0.0722 -0.1289 0.0196 0.1491 0.0196 -0.0781 0.0122 -0.0017 0.0174 0.0075 0.0226 -0.0901 Columns 36 through 42 0.0000 -0.0000 0.0001 -0.0000 0.0000 -0.0000 0.0000 -0.0001 -0.0000 -0.0002 0.0001 -0.0000 0.0000 -0.0000 -0.0000 -0.0021 -0.0003 -0.0001 0.0003 0.0007 0.0004 -0.0004 -0.0000 0.0015 -0.0020 0.0003 -0.0005 0.0010 0.0009 0.0002 -0.0006 0.0013 -0.0003 0.0002 -0.0009 -0.0000 -0.0038 -0.0005 -0.0001 0.0009 0.0016 0.0006 -0.0045 0.0009 -0.0076 0.0056 -0.0007 0.0011 -0.0015 0.0002 -0.0002 0.0006 -0.0007 -0.0002 -0.0008 -0.0009 0.0051 0.0030 0.0010 0.0029 -0.0016 -0.0008 -0.0030 -0.0006 0.0143 0.0015 -0.0003 -0.0044 -0.0074 -0.0022 0.0003 0.0360 0.0053 0.0020 -0.0027 -0.0107 -0.0068 -0.0078 0.0024 0.0028 -0.0081 0.0014 -0.0026 0.0057 0.0031 0.0204 -0.0030 0.0108 -0.0007 -0.0014 -0.0083 -0.0076 0.0061 0.0178 -0.0238 0.0041 -0.0076 0.0111 -0.0501 0.0084 -0.0836 0.0601 -0.0079 0.0117 -0.0174 0.0137 0.0541 0.0262 -0.0115 -0.0126 -0.0318 -0.0177 -0.0032 0.1285 0.0063 0.0121 -0.0283 -0.0502 -0.0219 -0.0221 -0.0085 -0.0111 -0.0047 0.0034 0.0024 0.0086 -0.0065 0.0351 -0.0034 0.0030 -0.0140 -0.0199 -0.0061 0.0585 -0.0097 0.0636 -0.0323 0.0023 -0.0061 0.0005 0.0039 -0.1044 -0.0204 -0.0070 -0.0192 0.0083 0.0167 -0.0105 -0.1401 -0.0182 -0.0038 0.0508 0.0761 0.0271 -0.0094 -0.1528 -0.0262 0.0021 0.0467 0.0825 0.0386 -0.0081 -0.2793 -0.0206 -0.0250 0.0784 0.1276 0.0601 -0.0197 0.0409 0.0583 -0.0723 0.0019 -0.0368 0.0350 0.0357 0.0866 0.0295 0.0115 -0.0140 -0.0240 -0.0139 -0.0256 -0.3153 -0.0602 0.0051 0.0997 0.1762 0.0790 -0.1854 0.0574 -0.2996 0.2133 -0.0324 0.0327 -0.0531 -0.0204 0.0217 0.0207 0.0149 0.1364 0.1099 -0.0051 0.0620 -0.0816 0.0016 0.0175 -0.0172 0.0147 -0.0220 0.0063 0.2396 0.0226 0.0308 -0.0303 -0.0763 -0.0454 -0.0044 -0.3789 -0.0679 -0.0215 0.0078 0.1027 0.0619 -0.0105 0.1198 -0.0036 0.0154 -0.0403 -0.0701 -0.0465 0.0087 0.6119 0.0935 0.0269 -0.1148 -0.2828 -0.1590 -0.0364 -0.0586 0.0239 0.0162 0.2656 0.2299 0.0202 -0.2817 0.0203 -0.3891 0.2513 -0.0191 0.0897 -0.0401 0.0494 -0.7245 -0.0060 -0.1128 0.1691 0.3646 0.2199 -0.4831 0.0119 -0.8436 0.6362 -0.0947 0.2235 -0.1805 0.3470 -0.0997 0.6713 -0.5685 0.1029 -0.1749 0.2347 -0.0357 0.3288 -0.0613 0.0859 -0.1906 -0.2426 -0.1444 0.0844 0.4516 0.2023 -0.0767 -0.1664 -0.4105 -0.1258 -0.0949 0.1943 -0.2030 0.2095 -0.0867 -0.0380 -0.1976 -0.0069 -0.5757 -0.0805 -0.0334 0.1529 0.3728 0.1814 0.0288 0.0660 0.0822 -0.0661 -0.0449 -0.1587 -0.0819 -0.1705 -0.0041 -0.4152 0.3570 -0.1049 0.1682 -0.2135 -0.0110 -0.0282 -0.0734 0.0462 -0.0522 0.0434 -0.0036 -0.0769 0.2227 -0.1251 0.1365 -0.1187 -0.1298 -0.1161 0.0960 0.0367 0.1812 -0.1585 -0.0800 -0.1837 0.0758 -0.0036 -0.1253 0.0190 -0.0128 0.2004 0.1839 0.0527 -0.0296 -0.3445 -0.0879 -0.0218 0.0485 0.2765 0.2204 0.0292 -0.2207 -0.0216 -0.0193 0.0135 0.1855 0.1290 0.0025 0.0522 -0.0121 0.0328 -0.0224 -0.0324 -0.0759 -0.0043 -0.2698 -0.0501 -0.0181 0.0590 0.2447 0.1286 0.0025 -0.0356 -0.0117 -0.0010 0.0058 0.0672 0.0948 -0.0042 0.0587 0.0078 0.0098 0.0016 -0.0664 -0.0580 -0.0472 -0.0064 -0.0675 0.0381 0.0122 0.0563 -0.0338 0.0015 0.0971 -0.0101 -0.0044 -0.1691 -0.1084 0.0065 -0.0094 -0.1095 -0.0094 0.0023 0.1122 0.0768 -0.0213 -0.0078 -0.1146 -0.0173 -0.0044 0.0886 0.1625 0.0689 Columns 43 through 49 -0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0010 0.0002 -0.0002 -0.0002 0.0003 -0.0004 0.0006 -0.0002 -0.0003 0.0014 0.0007 -0.0001 -0.0005 -0.0001 0.0001 -0.0001 -0.0013 -0.0003 0.0001 0.0005 0.0000 -0.0020 0.0003 -0.0004 -0.0002 0.0007 -0.0003 0.0007 0.0003 -0.0002 -0.0007 -0.0008 0.0009 0.0001 0.0000 -0.0004 -0.0027 -0.0005 0.0021 0.0007 0.0003 0.0004 0.0023 0.0005 -0.0040 -0.0015 -0.0010 0.0018 -0.0001 0.0081 -0.0018 0.0023 0.0011 -0.0028 0.0002 -0.0017 0.0152 -0.0024 0.0036 0.0040 -0.0035 0.0075 -0.0121 0.0005 -0.0002 0.0096 0.0030 -0.0004 -0.0032 -0.0014 0.0081 0.0013 -0.0047 -0.0012 -0.0009 0.0081 -0.0085 0.0003 -0.0040 0.0184 0.0098 -0.0012 -0.0044 -0.0041 0.0019 -0.0067 -0.0080 -0.0048 0.0116 0.0007 0.0010 0.0247 -0.0288 -0.0003 0.0230 -0.0043 0.0103 -0.0089 0.0681 -0.0022 0.0146 0.0019 -0.0224 0.0123 -0.0272 -0.0062 -0.0027 0.0132 0.0051 0.0040 -0.0070 0.0013 0.0211 -0.0068 0.0061 0.0024 -0.0072 -0.0019 -0.0015 -0.0010 0.0039 -0.0150 -0.0010 -0.0089 0.0069 0.0025 -0.0278 -0.0004 -0.0140 -0.0162 -0.0004 -0.0381 0.0593 -0.0859 0.0146 -0.0115 -0.0022 0.0339 -0.0027 0.0115 -0.0860 0.0396 -0.0098 -0.0278 0.0246 -0.0136 0.0197 -0.1607 0.0227 -0.0199 -0.0106 0.0538 -0.0246 0.0460 0.0187 -0.0050 0.0638 0.0224 -0.0132 -0.0185 -0.0129 0.0488 0.0299 -0.0063 -0.0278 -0.0290 0.0179 -0.0259 -0.1907 0.0721 -0.0223 -0.0486 0.0605 -0.0288 0.0449 0.0253 -0.0057 -0.0089 -0.0280 0.0308 -0.0029 -0.0047 -0.0877 0.0077 0.0044 0.0454 0.0651 0.0974 -0.1293 -0.0255 -0.0089 -0.0710 -0.0155 0.0008 -0.0008 0.0490 0.1310 0.0192 0.0228 -0.0047 -0.0439 0.0478 -0.0834 -0.1893 -0.0284 -0.0598 -0.0164 0.0548 -0.0983 0.1755 0.0601 -0.0733 0.0020 0.0408 -0.0088 0.0130 -0.0126 0.3434 -0.1286 0.0626 0.1008 -0.0975 0.1178 -0.1898 -0.2015 0.0396 0.0238 0.0576 0.1201 0.1786 -0.2648 0.0004 -0.0237 0.0823 -0.0408 0.1205 -0.0530 -0.0130 -0.5453 0.0969 -0.1241 -0.0716 0.1531 -0.1646 0.3187 0.0166 -0.0220 -0.0158 -0.1801 0.2506 -0.0766 0.0464 -0.0905 0.0242 0.0793 0.1807 -0.1973 -0.0096 0.0224 0.3593 -0.0899 0.0418 -0.0016 -0.0908 -0.0029 -0.0247 0.4623 -0.1209 0.0690 0.1447 -0.2619 0.1135 -0.1764 0.2026 -0.1034 -0.0366 -0.0211 0.0617 0.0930 -0.1174 -0.6532 -0.0033 -0.1748 -0.0238 0.2277 -0.1736 0.4000 0.0186 -0.3214 0.0060 0.2141 0.0330 0.0262 0.0168 -0.0039 -0.0584 -0.2479 -0.1464 0.1250 0.0357 0.1264 0.0241 0.1057 -0.0148 -0.1757 0.0269 -0.0899 0.0952 0.2712 0.0012 -0.0122 -0.0204 -0.1660 0.0807 -0.1081 0.0603 -0.0320 0.0676 0.0432 -0.0927 -0.1527 0.1988 -0.1658 0.0830 0.0546 0.0144 0.0698 0.1676 -0.3483 -0.4647 0.1757 -0.1071 -0.1423 0.1383 -0.2837 0.5304 -0.2874 0.1671 -0.1063 -0.1762 0.1276 -0.2237 0.4104 0.0845 -0.0513 -0.0286 0.0004 0.0011 0.0605 -0.0792 -0.4802 -0.0038 -0.1645 -0.0160 0.2517 -0.2163 0.5132 0.0141 0.2869 0.0476 -0.2158 -0.0700 -0.0732 0.0229 0.1259 -0.0579 0.0495 0.0384 -0.0699 0.1151 -0.2501 0.0151 0.0112 -0.0205 -0.0401 0.0121 0.0756 -0.1011 0.0305 -0.0348 -0.0955 -0.0309 0.0076 -0.2764 0.6175 -0.0903 -0.0912 0.0388 0.0576 0.0143 0.1924 -0.4256 -0.2179 0.0702 -0.0431 0.0030 0.1396 -0.0128 0.0776 Columns 50 through 56 -0.0000 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0009 -0.0006 0.0001 -0.0005 -0.0001 0.0002 0.0001 -0.0002 0.0003 0.0003 0.0001 0.0000 -0.0000 0.0003 0.0003 -0.0001 -0.0003 0.0000 0.0000 -0.0000 -0.0004 -0.0017 -0.0013 0.0002 -0.0011 -0.0002 0.0005 0.0002 0.0006 -0.0005 -0.0003 -0.0000 -0.0001 0.0000 0.0003 0.0002 0.0002 -0.0000 0.0004 -0.0008 -0.0000 -0.0001 0.0022 0.0006 -0.0011 0.0012 0.0001 -0.0006 -0.0015 0.0069 0.0052 -0.0008 0.0052 0.0008 -0.0024 -0.0005 0.0143 0.0105 -0.0014 0.0065 0.0008 -0.0031 -0.0020 -0.0008 0.0019 0.0018 0.0005 0.0001 -0.0001 0.0025 0.0083 0.0037 -0.0020 0.0017 0.0003 -0.0010 -0.0028 -0.0010 0.0054 0.0037 0.0011 0.0000 -0.0002 0.0039 0.0057 -0.0056 -0.0033 -0.0001 -0.0015 0.0006 0.0034 0.0275 0.0218 -0.0034 0.0197 -0.0034 -0.0079 -0.0055 0.0577 0.0410 -0.0072 0.0366 0.0073 -0.0173 -0.0061 -0.0064 -0.0021 0.0033 -0.0025 -0.0012 0.0017 0.0056 0.0188 0.0138 -0.0024 0.0148 0.0032 -0.0069 -0.0004 -0.0015 0.0016 -0.0015 0.0006 0.0001 -0.0009 -0.0088 -0.0303 -0.0234 0.0005 0.0018 -0.0006 -0.0003 0.0052 -0.0745 -0.0540 0.0114 -0.0561 -0.0126 0.0267 0.0087 -0.0794 -0.0582 0.0107 -0.0602 -0.0002 0.0260 0.0105 -0.1400 -0.0981 0.0203 -0.0974 -0.0139 0.0450 0.0180 0.0100 0.0259 0.0095 0.0140 0.0059 -0.0062 0.0124 0.0412 0.0276 -0.0089 0.0163 0.0201 -0.0119 -0.0121 -0.1771 -0.1301 0.0247 -0.1332 -0.0076 0.0592 0.0241 0.0300 -0.0102 -0.0103 0.0065 0.0017 -0.0021 0.0154 -0.0529 -0.0359 0.0173 -0.1066 -0.0218 0.0494 -0.0001 -0.0192 -0.0241 -0.0092 -0.0022 -0.0052 0.0010 -0.0159 0.1134 0.0790 -0.0141 0.0615 0.0118 -0.0298 -0.0179 -0.1709 -0.1255 0.0143 -0.0776 -0.0092 0.0368 0.0252 0.0785 0.0569 -0.0128 0.0498 0.0108 -0.0235 -0.0069 0.3640 0.2702 -0.0466 0.2193 0.0354 -0.1037 -0.0478 -0.1180 -0.0746 0.0385 -0.2276 -0.0315 0.1009 0.0034 0.0191 -0.0568 -0.0055 -0.0237 -0.0033 0.0153 0.0675 -0.5959 -0.4214 0.0812 -0.3901 -0.0525 0.1863 0.0710 0.0486 -0.1715 -0.0539 -0.0478 -0.0089 0.0288 0.0847 -0.1436 0.0946 0.0776 -0.0006 -0.0065 0.0004 -0.0258 0.3849 0.2386 -0.0779 0.3309 0.0468 -0.1558 -0.0392 0.5388 0.4795 -0.0661 0.4833 0.0713 -0.2365 -0.0916 0.3046 0.1214 -0.0875 0.1665 0.0201 -0.0848 -0.0573 -0.7786 -0.5556 0.1150 -0.6701 -0.0052 0.3197 0.1232 0.1939 0.1740 -0.0424 0.0970 0.1114 -0.0656 -0.0066 -0.0140 -0.1403 -0.0710 -0.0722 0.0015 0.0323 -0.0752 -0.0241 -0.1096 -0.0281 -0.0421 0.0355 0.0158 0.0101 0.3127 0.2874 -0.0426 0.3038 0.0645 -0.1620 -0.0891 -0.0169 0.0195 0.0144 0.0830 0.0425 -0.0292 0.0722 -0.0147 0.0264 0.0334 -0.1334 -0.0411 0.0412 -0.0342 -0.9412 -0.7136 0.1779 -0.7535 -0.1515 0.4368 0.1963 -0.6485 -0.5989 0.0899 -0.5532 -0.1472 0.3394 0.1507 0.2099 0.1202 -0.0699 0.1559 0.0517 -0.1028 -0.0756 -0.9093 -0.7433 0.1554 -1.0524 0.0179 0.6017 0.2349 -0.2199 -0.2223 0.0738 -0.0170 -0.3702 0.1036 0.0163 0.3972 0.3479 -0.0784 0.4270 0.0593 -0.2953 -0.1228 0.0742 0.0665 -0.0260 0.0905 -0.0232 -0.0843 -0.1790 -0.4487 -0.4203 0.0769 -0.5425 0.0380 0.4789 0.2500 0.3702 0.3787 -0.0841 0.4211 0.1000 -0.4463 -0.2330 -0.4359 -0.3543 0.1002 -0.6190 -0.0189 0.3580 0.0968 Columns 57 through 59 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0007 0.0005 0.0001 0.0001 -0.0000 0.0000 0.0000 -0.0001 -0.0000 -0.0013 0.0010 -0.0001 0.0001 0.0000 0.0000 0.0004 0.0001 0.0001 0.0009 -0.0010 0.0002 0.0051 -0.0041 0.0010 0.0110 -0.0075 -0.0024 0.0009 -0.0003 -0.0002 0.0053 -0.0035 -0.0026 0.0028 -0.0010 -0.0009 0.0012 0.0009 0.0002 0.0220 -0.0141 0.0018 0.0418 -0.0331 0.0019 -0.0024 0.0032 -0.0001 0.0132 -0.0113 0.0043 -0.0018 -0.0008 0.0006 -0.0263 0.0128 0.0218 -0.0514 0.0451 -0.0139 -0.0596 0.0442 -0.0104 -0.1000 0.0802 -0.0140 0.0165 -0.0123 0.0012 0.0232 -0.0263 -0.0022 -0.1315 0.1014 -0.0244 0.0118 -0.0050 0.0013 -0.0255 0.0494 -0.0809 -0.0232 0.0116 0.0148 0.0842 -0.0635 -0.0095 -0.1371 0.0926 0.0372 0.0542 -0.0425 0.0120 0.2748 -0.2061 0.0049 -0.0489 0.0923 -0.1725 -0.0017 0.0198 -0.0089 -0.4813 0.3658 -0.0191 -0.0432 0.0540 0.0055 -0.0322 0.0121 0.0048 0.2728 -0.2395 0.1229 0.4911 -0.4134 0.1224 0.2278 -0.1760 0.0207 -0.7530 0.5827 -0.1099 0.1489 -0.1503 0.0621 -0.1340 0.0819 0.0216 -0.1176 0.0683 0.0238 0.3105 -0.2830 0.0868 -0.1007 0.0470 0.1319 0.2291 -0.1216 -0.2395 -1.1578 0.9753 -0.1317 -0.9271 0.8030 -0.0956 0.2393 -0.2318 0.0635 -1.4313 1.2185 -0.3581 -0.1752 0.3418 -0.1034 0.7237 -0.6991 0.2019 0.2489 -0.2500 -0.0075 -1.6385 1.4947 -0.0272 1.4052 -1.4887 0.1731 -0.6243 0.6921 -0.6032


