2nd Stage Optimization for Risky + Safe Asset (Saving Only) Interpolated-Percentage
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Contents
- FF_IPWKZ_EVF solves the k' vs b' problem given aggregate savings
- Default
- Parse Parameters
- Integrate E(V(coh(k',b'), z')|z, w)
- Reshape E(V(coh,z'|z,w)) to allow for maxing
- Maximize max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w)) optimal value and index
- Reindex K' and B' Choices for each State at the Optimal w'=k'+b' choice
- Graph
- Graph 1, V and EV
- Graph 2, max(EV)
- Graph 3, at max(EV) optimal choice category, color regions, borrow save
- Graph 4, Optimal K' and B' Levels
function [mt_ev_condi_z_max, mt_ev_condi_z_max_idx, mt_ev_condi_z_max_kp, mt_ev_condi_z_max_bp] = ff_ipwkz_evf(varargin)
FF_IPWKZ_EVF solves the k' vs b' problem given aggregate savings
This function follows the structure set up here: ff_wkz_evf but now we solve the second stage with percentage choice grid
We solve along a vector of w_n vector, that is an interpolation vector, not a vector of actual w choices picked in the first stage. k' choices are in terms of percentages. Compared to ff_wkz_evf where we only had an upper triangle of choices, now we have a full matrix of percentage choices.
@param mt_val matrix state_n I^2 by shock_n. This is the value matrix each row is a feasible reachable state given the choice vectors/matrix and each column is a shock state.
@param param_map container parameter container
@param support_map container support container
@param armt_map container container with states, choices and shocks grids that are inputs for grid based solution algorithm
@return mt_ev_condi_z_max matrix choice_w_n by shock_n max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w)) conditional on z and w, at the optimal k' choice (w=k'+b') what is the expected utility? This is the value result from the 2nd stage problem. Note the result integrates over z'.
@return mt_ev_condi_z_max_idx matrix choice_w_n by shock_n this is the argmax from max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w)). Given the vector of k' choices, which index maximized conditional on z and w integrating over z'/
@return mt_ev_condi_z_max_kp matrix choice_w_level_n by shock_n the k' choice at max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w))
@return mt_ev_condi_z_max_bp matrix choice_w_n by shock_n the b'=w-k' choice at max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w))
@example
@include
Default
if (~isempty(varargin)) % override when called from outside [mt_val, param_map, support_map, armt_map] = varargin{:}; else clear all; close all; % Not default parameters, but parameters that generate defaults it_param_set = 4; bl_input_override = true; [param_map, support_map] = ffs_ipwkz_set_default_param(it_param_set); support_map('bl_graph_evf') = true; support_map('bl_display_evf') = true; param_map('it_ak_perc_n') = 250; param_map('fl_w_interp_grid_gap') = (param_map('fl_w_max')-param_map('fl_b_bd'))/param_map('it_ak_perc_n'); [armt_map, func_map] = ffs_ipwkz_get_funcgrid(param_map, support_map, bl_input_override); % 1 for override % Generating Defaults params_group = values(armt_map, {'ar_a_meshk', 'ar_k_mesha', 'ar_z'}); [ar_a_meshk, ar_k_mesha, ar_z] = params_group{:}; params_group = values(func_map, {'f_util_standin'}); [f_util_standin] = params_group{:}; mt_val = f_util_standin(ar_z, ar_a_meshk, ar_k_mesha); end
Parse Parameters
params_group = values(armt_map, {'mt_z_trans', 'ar_z',...
'ar_w_level', 'ar_k_mesha', 'ar_a_meshk', 'mt_k'});
[mt_z_trans, ar_z, ar_w_level, ...
ar_k_mesha, ar_a_meshk, mt_k] = params_group{:};
params_group = values(param_map, {'it_z_n', 'fl_nan_replace', 'fl_b_bd'});
[it_z_n, fl_nan_replace, fl_b_bd] = params_group{:};
params_group = values(support_map, {'bl_graph_onebyones','bl_display_evf', 'bl_graph_evf'});
[bl_graph_onebyones, bl_display_evf, bl_graph_evf] = params_group{:};
params_group = values(support_map, {'bl_img_save', 'st_img_path', 'st_img_prefix', 'st_img_name_main', 'st_img_suffix'});
[bl_img_save, st_img_path, st_img_prefix, st_img_name_main, st_img_suffix] = params_group{:};
% append function name
st_func_name = 'ff_ipwkz_evf';
st_img_name_main = [st_func_name st_img_name_main];
Integrate E(V(coh(k',b'), z')|z, w)
Each column for a different state z, each value E(V(coh,z')|z) integrated already Here, each column is a current z, more to right higher EV dim(mt_ev_condi_z): Q by M Note that: mt_ev_condi_z = mt_val*mt_z_trans' is a mistake, that would be what we do in the ffs_ipwkz_set_functions code where we loop over current z, and for each current z, grab out a particular row from the mt_z_trans that corresponds to a current shock's transition into all future states.
here, each column of mt_val corresponds to a state z, think of that as future state z. The input mt_val is V(coh, z), we need to integrate to get E(V(coh,z')|z).
mt_ev_condi_z = mt_val*mt_z_trans'; if(bl_display_evf) disp('----------------------------------------'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp('mt_ev_condi_z: Q by M'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp(size(mt_ev_condi_z)); disp(head(array2table(mt_ev_condi_z), 20)); disp(tail(array2table(mt_ev_condi_z), 20)); end
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mt_ev_condi_z: Q by M
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62500 15
mt_ev_condi_z1 mt_ev_condi_z2 mt_ev_condi_z3 mt_ev_condi_z4 mt_ev_condi_z5 mt_ev_condi_z6 mt_ev_condi_z7 mt_ev_condi_z8 mt_ev_condi_z9 mt_ev_condi_z10 mt_ev_condi_z11 mt_ev_condi_z12 mt_ev_condi_z13 mt_ev_condi_z14 mt_ev_condi_z15
______________ ______________ ______________ ______________ ______________ ______________ ______________ ______________ ______________ _______________ _______________ _______________ _______________ _______________ _______________
-0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272
-0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272
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-0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272
-0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272
-0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272
-0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272
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-0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272
-0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272
-0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272
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mt_ev_condi_z1 mt_ev_condi_z2 mt_ev_condi_z3 mt_ev_condi_z4 mt_ev_condi_z5 mt_ev_condi_z6 mt_ev_condi_z7 mt_ev_condi_z8 mt_ev_condi_z9 mt_ev_condi_z10 mt_ev_condi_z11 mt_ev_condi_z12 mt_ev_condi_z13 mt_ev_condi_z14 mt_ev_condi_z15
______________ ______________ ______________ ______________ ______________ ______________ ______________ ______________ ______________ _______________ _______________ _______________ _______________ _______________ _______________
3.8834 3.8874 3.892 3.8973 3.9033 3.9099 3.9172 3.9254 3.9345 3.9446 3.9557 3.9681 3.9816 3.9961 4.0106
3.883 3.887 3.8917 3.897 3.9029 3.9095 3.9169 3.9251 3.9342 3.9443 3.9555 3.9679 3.9814 3.9959 4.0104
3.8826 3.8866 3.8913 3.8966 3.9026 3.9092 3.9166 3.9248 3.9339 3.944 3.9552 3.9676 3.9812 3.9957 4.0103
3.8822 3.8863 3.891 3.8963 3.9023 3.9089 3.9163 3.9245 3.9336 3.9438 3.955 3.9674 3.981 3.9955 4.0101
3.8819 3.8859 3.8906 3.8959 3.9019 3.9086 3.916 3.9242 3.9334 3.9435 3.9548 3.9672 3.9808 3.9954 4.01
3.8815 3.8855 3.8902 3.8956 3.9016 3.9082 3.9157 3.9239 3.9331 3.9432 3.9545 3.967 3.9806 3.9952 4.0098
3.8811 3.8851 3.8899 3.8952 3.9012 3.9079 3.9153 3.9236 3.9328 3.943 3.9543 3.9668 3.9804 3.995 4.0097
3.8807 3.8848 3.8895 3.8949 3.9009 3.9076 3.915 3.9233 3.9325 3.9427 3.954 3.9665 3.9802 3.9949 4.0095
3.8804 3.8844 3.8892 3.8945 3.9005 3.9072 3.9147 3.923 3.9322 3.9424 3.9538 3.9663 3.98 3.9947 4.0094
3.88 3.884 3.8888 3.8942 3.9002 3.9069 3.9144 3.9227 3.9319 3.9422 3.9535 3.9661 3.9798 3.9945 4.0092
3.8796 3.8837 3.8884 3.8938 3.8999 3.9066 3.9141 3.9224 3.9316 3.9419 3.9533 3.9659 3.9796 3.9943 4.0091
3.8792 3.8833 3.8881 3.8935 3.8995 3.9063 3.9138 3.9221 3.9314 3.9416 3.953 3.9656 3.9794 3.9941 4.0089
3.8788 3.8829 3.8877 3.8931 3.8992 3.9059 3.9134 3.9218 3.9311 3.9414 3.9528 3.9654 3.9792 3.994 4.0088
3.8785 3.8825 3.8873 3.8928 3.8988 3.9056 3.9131 3.9215 3.9308 3.9411 3.9525 3.9652 3.979 3.9938 4.0086
3.8781 3.8822 3.887 3.8924 3.8985 3.9053 3.9128 3.9212 3.9305 3.9408 3.9523 3.965 3.9788 3.9936 4.0085
3.8777 3.8818 3.8866 3.8921 3.8981 3.9049 3.9125 3.9209 3.9302 3.9406 3.952 3.9647 3.9786 3.9934 4.0083
3.8773 3.8814 3.8862 3.8917 3.8978 3.9046 3.9122 3.9206 3.9299 3.9403 3.9518 3.9645 3.9784 3.9933 4.0081
3.8769 3.881 3.8859 3.8913 3.8975 3.9043 3.9119 3.9203 3.9296 3.94 3.9515 3.9643 3.9782 3.9931 4.008
3.8765 3.8807 3.8855 3.891 3.8971 3.9039 3.9115 3.92 3.9294 3.9398 3.9513 3.964 3.978 3.9929 4.0078
3.8762 3.8803 3.8851 3.8906 3.8968 3.9036 3.9112 3.9197 3.9291 3.9395 3.951 3.9638 3.9778 3.9927 4.0077
Reshape E(V(coh,z'|z,w)) to allow for maxing
dim(mt_ev_condi_z): IxJ by M
[it_mt_bp_rown, it_mt_bp_coln] = size(mt_k); mt_ev_condi_z_full = reshape(mt_ev_condi_z, [it_mt_bp_rown, it_mt_bp_coln*it_z_n]);
Maximize max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w)) optimal value and index
Maximization, find optimal k'/b' combination given z and w=k'+b'
[ar_ev_condi_z_max, ar_ev_condi_z_max_idx] = max(mt_ev_condi_z_full); mt_ev_condi_z_max = reshape(ar_ev_condi_z_max, [it_mt_bp_coln, it_z_n]); mt_ev_condi_z_max_idx = reshape(ar_ev_condi_z_max_idx, [it_mt_bp_coln, it_z_n]); if(bl_display_evf) disp('----------------------------------------'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp('mt_ev_condi_z_full: J by IxM'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp(size(mt_ev_condi_z_full)); % disp(head(array2table(mt_ev_condi_z_full), 20)); % disp(tail(array2table(mt_ev_condi_z_full), 20)); disp('----------------------------------------'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp('mt_ev_condi_z_max: I by M'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp(size(mt_ev_condi_z_max)); disp(head(array2table(mt_ev_condi_z_max), 20)); disp(tail(array2table(mt_ev_condi_z_max), 20)); disp('----------------------------------------'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp('mt_ev_condi_z_max_idx: I by M'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp(size(mt_ev_condi_z_max_idx)); disp(head(array2table(mt_ev_condi_z_max_idx), 20)); disp(tail(array2table(mt_ev_condi_z_max_idx), 20)); end
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mt_ev_condi_z_full: J by IxM
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250 3750
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mt_ev_condi_z_max: I by M
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250 15
mt_ev_condi_z_max1 mt_ev_condi_z_max2 mt_ev_condi_z_max3 mt_ev_condi_z_max4 mt_ev_condi_z_max5 mt_ev_condi_z_max6 mt_ev_condi_z_max7 mt_ev_condi_z_max8 mt_ev_condi_z_max9 mt_ev_condi_z_max10 mt_ev_condi_z_max11 mt_ev_condi_z_max12 mt_ev_condi_z_max13 mt_ev_condi_z_max14 mt_ev_condi_z_max15
__________________ __________________ __________________ __________________ __________________ __________________ __________________ __________________ __________________ ___________________ ___________________ ___________________ ___________________ ___________________ ___________________
-0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272
-0.13586 -0.10537 -0.0705 -0.032211 0.0091691 0.053609 0.10116 0.15188 0.20581 0.26296 0.32333 0.38682 0.45299 0.52035 0.58524
0.1196 0.14992 0.18459 0.22267 0.26384 0.30806 0.35539 0.40588 0.45957 0.51649 0.57663 0.63989 0.70583 0.77298 0.83767
0.30837 0.33746 0.37075 0.40738 0.44702 0.48968 0.5354 0.58425 0.6363 0.69156 0.75004 0.81165 0.87598 0.94157 1.0048
0.46102 0.48875 0.52054 0.55555 0.59351 0.63443 0.67836 0.72539 0.77558 0.82897 0.88558 0.94532 1.0078 1.0716 1.1333
0.59015 0.61659 0.64694 0.68041 0.71677 0.75601 0.79822 0.84349 0.89188 0.94345 0.99822 1.0561 1.1168 1.1789 1.239
0.70247 0.72773 0.75677 0.78883 0.8237 0.8614 0.90201 0.94564 0.99235 1.0422 1.0953 1.1515 1.2104 1.2709 1.3294
0.80209 0.82629 0.85413 0.88491 0.91843 0.95471 0.99386 1.036 1.0811 1.1294 1.1809 1.2355 1.2928 1.3517 1.4088
0.89172 0.91496 0.94171 0.97133 1.0036 1.0386 1.0764 1.1171 1.1609 1.2077 1.2577 1.3108 1.3667 1.4241 1.4798
0.97327 0.99563 1.0214 1.05 1.0811 1.1149 1.1515 1.191 1.2334 1.2789 1.3275 1.3792 1.4337 1.4898 1.5442
1.0482 1.0697 1.0946 1.1222 1.1523 1.185 1.2205 1.2588 1.3 1.3442 1.3916 1.442 1.4952 1.55 1.6033
1.1179 1.1382 1.1622 1.1889 1.2181 1.2499 1.2843 1.3215 1.3616 1.4047 1.4508 1.5 1.552 1.6057 1.6579
1.1831 1.2021 1.2252 1.2511 1.2794 1.3103 1.3437 1.3799 1.419 1.461 1.506 1.5541 1.605 1.6575 1.7086
1.2443 1.2622 1.2841 1.3093 1.3368 1.3668 1.3993 1.4346 1.4727 1.5137 1.5577 1.6047 1.6546 1.706 1.7562
1.3019 1.3188 1.3396 1.3639 1.3907 1.4199 1.4516 1.486 1.5232 1.5633 1.6063 1.6524 1.7012 1.7516 1.8009
1.3564 1.3724 1.3922 1.4155 1.4416 1.4701 1.501 1.5346 1.5709 1.6101 1.6522 1.6974 1.7452 1.7948 1.8431
1.4081 1.4233 1.4421 1.4643 1.4898 1.5176 1.5478 1.5806 1.6161 1.6545 1.6958 1.74 1.787 1.8356 1.8832
1.4572 1.4717 1.4896 1.5109 1.5355 1.5627 1.5922 1.6243 1.6591 1.6967 1.7372 1.7806 1.8267 1.8745 1.9213
1.504 1.5179 1.535 1.5553 1.5791 1.6057 1.6346 1.666 1.7001 1.7369 1.7766 1.8192 1.8646 1.9116 1.9576
1.5488 1.562 1.5784 1.5979 1.6208 1.6467 1.675 1.7058 1.7392 1.7753 1.8143 1.8562 1.9008 1.947 1.9923
mt_ev_condi_z_max1 mt_ev_condi_z_max2 mt_ev_condi_z_max3 mt_ev_condi_z_max4 mt_ev_condi_z_max5 mt_ev_condi_z_max6 mt_ev_condi_z_max7 mt_ev_condi_z_max8 mt_ev_condi_z_max9 mt_ev_condi_z_max10 mt_ev_condi_z_max11 mt_ev_condi_z_max12 mt_ev_condi_z_max13 mt_ev_condi_z_max14 mt_ev_condi_z_max15
__________________ __________________ __________________ __________________ __________________ __________________ __________________ __________________ __________________ ___________________ ___________________ ___________________ ___________________ ___________________ ___________________
3.874 3.8753 3.877 3.879 3.8814 3.8842 3.8876 3.8916 3.8964 3.9021 3.9089 3.9169 3.9263 3.937 3.9485
3.8783 3.8796 3.8812 3.8832 3.8856 3.8884 3.8918 3.8958 3.9006 3.9063 3.913 3.921 3.9304 3.941 3.9524
3.8825 3.8838 3.8855 3.8874 3.8898 3.8926 3.896 3.9 3.9048 3.9104 3.9171 3.9251 3.9344 3.945 3.9564
3.8868 3.8881 3.8897 3.8917 3.894 3.8968 3.9002 3.9042 3.9089 3.9145 3.9212 3.9291 3.9384 3.949 3.9603
3.891 3.8923 3.8939 3.8959 3.8982 3.901 3.9043 3.9083 3.913 3.9186 3.9253 3.9332 3.9424 3.953 3.9642
3.8952 3.8965 3.8981 3.9 3.9024 3.9051 3.9085 3.9124 3.9171 3.9227 3.9293 3.9372 3.9464 3.9569 3.9681
3.8994 3.9006 3.9022 3.9042 3.9065 3.9093 3.9126 3.9165 3.9212 3.9268 3.9334 3.9412 3.9504 3.9608 3.972
3.9035 3.9048 3.9064 3.9083 3.9106 3.9134 3.9167 3.9206 3.9253 3.9308 3.9374 3.9452 3.9543 3.9648 3.9759
3.9077 3.9089 3.9105 3.9124 3.9148 3.9175 3.9208 3.9247 3.9293 3.9349 3.9414 3.9492 3.9583 3.9686 3.9797
3.9118 3.913 3.9146 3.9166 3.9188 3.9216 3.9249 3.9287 3.9334 3.9389 3.9454 3.9531 3.9622 3.9725 3.9836
3.9159 3.9172 3.9187 3.9206 3.9229 3.9257 3.9289 3.9328 3.9374 3.9429 3.9494 3.9571 3.9661 3.9764 3.9874
3.92 3.9212 3.9228 3.9247 3.927 3.9297 3.933 3.9368 3.9414 3.9469 3.9533 3.961 3.97 3.9803 3.9912
3.9241 3.9253 3.9269 3.9288 3.931 3.9337 3.937 3.9408 3.9454 3.9508 3.9573 3.9649 3.9739 3.9841 3.995
3.9281 3.9294 3.9309 3.9328 3.9351 3.9378 3.941 3.9448 3.9494 3.9548 3.9612 3.9688 3.9777 3.9879 3.9988
3.9322 3.9334 3.935 3.9368 3.9391 3.9418 3.945 3.9488 3.9533 3.9587 3.9651 3.9727 3.9816 3.9917 4.0025
3.9362 3.9374 3.939 3.9408 3.9431 3.9458 3.9489 3.9527 3.9573 3.9626 3.969 3.9766 3.9854 3.9955 4.0063
3.9402 3.9414 3.943 3.9448 3.9471 3.9497 3.9529 3.9567 3.9612 3.9665 3.9729 3.9804 3.9892 3.9993 4.01
3.9442 3.9454 3.947 3.9488 3.951 3.9537 3.9569 3.9606 3.9651 3.9704 3.9768 3.9843 3.993 4.0031 4.0138
3.9482 3.9494 3.9509 3.9528 3.955 3.9576 3.9608 3.9645 3.969 3.9743 3.9806 3.9881 3.9968 4.0068 4.0175
3.9521 3.9533 3.9549 3.9567 3.9589 3.9616 3.9647 3.9684 3.9729 3.9782 3.9844 3.9919 4.0006 4.0106 4.0212
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mt_ev_condi_z_max_idx: I by M
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250 15
mt_ev_condi_z_max_idx1 mt_ev_condi_z_max_idx2 mt_ev_condi_z_max_idx3 mt_ev_condi_z_max_idx4 mt_ev_condi_z_max_idx5 mt_ev_condi_z_max_idx6 mt_ev_condi_z_max_idx7 mt_ev_condi_z_max_idx8 mt_ev_condi_z_max_idx9 mt_ev_condi_z_max_idx10 mt_ev_condi_z_max_idx11 mt_ev_condi_z_max_idx12 mt_ev_condi_z_max_idx13 mt_ev_condi_z_max_idx14 mt_ev_condi_z_max_idx15
______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
233 250 250 250 250 250 250 250 250 250 250 250 250 250 250
212 249 250 250 250 250 250 250 250 250 250 250 250 250 250
195 229 250 250 250 250 250 250 250 250 250 250 250 250 250
180 211 250 250 250 250 250 250 250 250 250 250 250 250 250
167 196 233 250 250 250 250 250 250 250 250 250 250 250 250
156 184 218 250 250 250 250 250 250 250 250 250 250 250 250
146 172 205 244 250 250 250 250 250 250 250 250 250 250 250
138 162 193 230 250 250 250 250 250 250 250 250 250 250 250
130 153 182 217 250 250 250 250 250 250 250 250 250 250 250
123 145 173 206 245 250 250 250 250 250 250 250 250 250 250
mt_ev_condi_z_max_idx1 mt_ev_condi_z_max_idx2 mt_ev_condi_z_max_idx3 mt_ev_condi_z_max_idx4 mt_ev_condi_z_max_idx5 mt_ev_condi_z_max_idx6 mt_ev_condi_z_max_idx7 mt_ev_condi_z_max_idx8 mt_ev_condi_z_max_idx9 mt_ev_condi_z_max_idx10 mt_ev_condi_z_max_idx11 mt_ev_condi_z_max_idx12 mt_ev_condi_z_max_idx13 mt_ev_condi_z_max_idx14 mt_ev_condi_z_max_idx15
______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________
11 13 15 18 21 25 30 36 42 51 60 72 86 101 118
11 13 15 18 21 25 30 36 42 50 60 72 85 101 118
11 13 15 18 21 25 30 35 42 50 60 71 85 100 117
11 13 15 18 21 25 30 35 42 50 60 71 84 100 117
11 13 15 18 21 25 29 35 42 50 59 71 84 100 116
11 13 15 18 21 25 29 35 42 50 59 70 84 99 116
11 12 15 17 21 25 29 35 41 49 59 70 83 99 115
11 12 15 17 21 24 29 35 41 49 59 70 83 98 115
11 12 15 17 21 24 29 34 41 49 58 69 83 98 114
11 12 15 17 20 24 29 34 41 49 58 69 82 97 114
11 12 14 17 20 24 29 34 41 49 58 69 82 97 113
10 12 14 17 20 24 29 34 41 48 58 69 82 97 113
10 12 14 17 20 24 29 34 40 48 57 68 81 96 112
10 12 14 17 20 24 28 34 40 48 57 68 81 96 112
10 12 14 17 20 24 28 34 40 48 57 68 81 96 112
10 12 14 17 20 24 28 34 40 48 57 68 80 95 111
10 12 14 17 20 24 28 33 40 47 56 67 80 95 111
10 12 14 17 20 24 28 33 40 47 56 67 80 94 110
10 12 14 17 20 23 28 33 39 47 56 67 79 94 110
10 12 14 17 20 23 28 33 39 47 56 66 79 94 109
Reindex K' and B' Choices for each State at the Optimal w'=k'+b' choice
The K' and B' Optimal Choices Associated with EV opti dim(mt_ev_condi_z_max_kp): I by M
ar_add_grid = linspace(0, it_mt_bp_rown*(it_mt_bp_coln-1), it_mt_bp_coln); mt_ev_condi_z_max_idx = mt_ev_condi_z_max_idx + ar_add_grid'; if(bl_display_evf) disp('----------------------------------------'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp('mt_ev_condi_z_max_idx: I by M'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp(size(mt_ev_condi_z_max_idx)); disp(head(array2table(mt_ev_condi_z_max_idx), 20)); disp(tail(array2table(mt_ev_condi_z_max_idx), 20)); end mt_ev_condi_z_max_kp = reshape(ar_k_mesha(mt_ev_condi_z_max_idx), [it_mt_bp_coln, it_z_n]); mt_ev_condi_z_max_bp = reshape(ar_a_meshk(mt_ev_condi_z_max_idx), [it_mt_bp_coln, it_z_n]); if(bl_display_evf) disp('----------------------------------------'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp('mt_ev_condi_z_max_kp: I by M'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp(size(mt_ev_condi_z_max_kp)); disp(head(array2table(mt_ev_condi_z_max_kp), 20)); disp(tail(array2table(mt_ev_condi_z_max_kp), 20)); disp('----------------------------------------'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp('mt_ev_condi_z_max_bp: I by M'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp(size(mt_ev_condi_z_max_bp)); disp(head(array2table(mt_ev_condi_z_max_bp), 20)); disp(tail(array2table(mt_ev_condi_z_max_bp), 20)); end
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mt_ev_condi_z_max_idx: I by M
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250 15
mt_ev_condi_z_max_idx1 mt_ev_condi_z_max_idx2 mt_ev_condi_z_max_idx3 mt_ev_condi_z_max_idx4 mt_ev_condi_z_max_idx5 mt_ev_condi_z_max_idx6 mt_ev_condi_z_max_idx7 mt_ev_condi_z_max_idx8 mt_ev_condi_z_max_idx9 mt_ev_condi_z_max_idx10 mt_ev_condi_z_max_idx11 mt_ev_condi_z_max_idx12 mt_ev_condi_z_max_idx13 mt_ev_condi_z_max_idx14 mt_ev_condi_z_max_idx15
______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
750 750 750 750 750 750 750 750 750 750 750 750 750 750 750
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250
1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500
1750 1750 1750 1750 1750 1750 1750 1750 1750 1750 1750 1750 1750 1750 1750
2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000
2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250
2500 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500
2733 2750 2750 2750 2750 2750 2750 2750 2750 2750 2750 2750 2750 2750 2750
2962 2999 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000
3195 3229 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250
3430 3461 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500
3667 3696 3733 3750 3750 3750 3750 3750 3750 3750 3750 3750 3750 3750 3750
3906 3934 3968 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000
4146 4172 4205 4244 4250 4250 4250 4250 4250 4250 4250 4250 4250 4250 4250
4388 4412 4443 4480 4500 4500 4500 4500 4500 4500 4500 4500 4500 4500 4500
4630 4653 4682 4717 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750
4873 4895 4923 4956 4995 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000
mt_ev_condi_z_max_idx1 mt_ev_condi_z_max_idx2 mt_ev_condi_z_max_idx3 mt_ev_condi_z_max_idx4 mt_ev_condi_z_max_idx5 mt_ev_condi_z_max_idx6 mt_ev_condi_z_max_idx7 mt_ev_condi_z_max_idx8 mt_ev_condi_z_max_idx9 mt_ev_condi_z_max_idx10 mt_ev_condi_z_max_idx11 mt_ev_condi_z_max_idx12 mt_ev_condi_z_max_idx13 mt_ev_condi_z_max_idx14 mt_ev_condi_z_max_idx15
______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________
57511 57513 57515 57518 57521 57525 57530 57536 57542 57551 57560 57572 57586 57601 57618
57761 57763 57765 57768 57771 57775 57780 57786 57792 57800 57810 57822 57835 57851 57868
58011 58013 58015 58018 58021 58025 58030 58035 58042 58050 58060 58071 58085 58100 58117
58261 58263 58265 58268 58271 58275 58280 58285 58292 58300 58310 58321 58334 58350 58367
58511 58513 58515 58518 58521 58525 58529 58535 58542 58550 58559 58571 58584 58600 58616
58761 58763 58765 58768 58771 58775 58779 58785 58792 58800 58809 58820 58834 58849 58866
59011 59012 59015 59017 59021 59025 59029 59035 59041 59049 59059 59070 59083 59099 59115
59261 59262 59265 59267 59271 59274 59279 59285 59291 59299 59309 59320 59333 59348 59365
59511 59512 59515 59517 59521 59524 59529 59534 59541 59549 59558 59569 59583 59598 59614
59761 59762 59765 59767 59770 59774 59779 59784 59791 59799 59808 59819 59832 59847 59864
60011 60012 60014 60017 60020 60024 60029 60034 60041 60049 60058 60069 60082 60097 60113
60260 60262 60264 60267 60270 60274 60279 60284 60291 60298 60308 60319 60332 60347 60363
60510 60512 60514 60517 60520 60524 60529 60534 60540 60548 60557 60568 60581 60596 60612
60760 60762 60764 60767 60770 60774 60778 60784 60790 60798 60807 60818 60831 60846 60862
61010 61012 61014 61017 61020 61024 61028 61034 61040 61048 61057 61068 61081 61096 61112
61260 61262 61264 61267 61270 61274 61278 61284 61290 61298 61307 61318 61330 61345 61361
61510 61512 61514 61517 61520 61524 61528 61533 61540 61547 61556 61567 61580 61595 61611
61760 61762 61764 61767 61770 61774 61778 61783 61790 61797 61806 61817 61830 61844 61860
62010 62012 62014 62017 62020 62023 62028 62033 62039 62047 62056 62067 62079 62094 62110
62260 62262 62264 62267 62270 62273 62278 62283 62289 62297 62306 62316 62329 62344 62359
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mt_ev_condi_z_max_kp: I by M
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250 15
mt_ev_condi_z_max_kp1 mt_ev_condi_z_max_kp2 mt_ev_condi_z_max_kp3 mt_ev_condi_z_max_kp4 mt_ev_condi_z_max_kp5 mt_ev_condi_z_max_kp6 mt_ev_condi_z_max_kp7 mt_ev_condi_z_max_kp8 mt_ev_condi_z_max_kp9 mt_ev_condi_z_max_kp10 mt_ev_condi_z_max_kp11 mt_ev_condi_z_max_kp12 mt_ev_condi_z_max_kp13 mt_ev_condi_z_max_kp14 mt_ev_condi_z_max_kp15
_____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.2006 0.2006 0.2006 0.2006 0.2006 0.2006 0.2006 0.2006 0.2006 0.2006 0.2006 0.2006 0.2006 0.2006 0.2006
0.4012 0.4012 0.4012 0.4012 0.4012 0.4012 0.4012 0.4012 0.4012 0.4012 0.4012 0.4012 0.4012 0.4012 0.4012
0.60181 0.60181 0.60181 0.60181 0.60181 0.60181 0.60181 0.60181 0.60181 0.60181 0.60181 0.60181 0.60181 0.60181 0.60181
0.80241 0.80241 0.80241 0.80241 0.80241 0.80241 0.80241 0.80241 0.80241 0.80241 0.80241 0.80241 0.80241 0.80241 0.80241
1.003 1.003 1.003 1.003 1.003 1.003 1.003 1.003 1.003 1.003 1.003 1.003 1.003 1.003 1.003
1.2036 1.2036 1.2036 1.2036 1.2036 1.2036 1.2036 1.2036 1.2036 1.2036 1.2036 1.2036 1.2036 1.2036 1.2036
1.4042 1.4042 1.4042 1.4042 1.4042 1.4042 1.4042 1.4042 1.4042 1.4042 1.4042 1.4042 1.4042 1.4042 1.4042
1.6048 1.6048 1.6048 1.6048 1.6048 1.6048 1.6048 1.6048 1.6048 1.6048 1.6048 1.6048 1.6048 1.6048 1.6048
1.8054 1.8054 1.8054 1.8054 1.8054 1.8054 1.8054 1.8054 1.8054 1.8054 1.8054 1.8054 1.8054 1.8054 1.8054
1.8692 2.006 2.006 2.006 2.006 2.006 2.006 2.006 2.006 2.006 2.006 2.006 2.006 2.006 2.006
1.8702 2.1978 2.2066 2.2066 2.2066 2.2066 2.2066 2.2066 2.2066 2.2066 2.2066 2.2066 2.2066 2.2066 2.2066
1.876 2.2044 2.4072 2.4072 2.4072 2.4072 2.4072 2.4072 2.4072 2.4072 2.4072 2.4072 2.4072 2.4072 2.4072
1.8754 2.1998 2.6078 2.6078 2.6078 2.6078 2.6078 2.6078 2.6078 2.6078 2.6078 2.6078 2.6078 2.6078 2.6078
1.8732 2.2 2.6169 2.8084 2.8084 2.8084 2.8084 2.8084 2.8084 2.8084 2.8084 2.8084 2.8084 2.8084 2.8084
1.8742 2.2123 2.6227 3.009 3.009 3.009 3.009 3.009 3.009 3.009 3.009 3.009 3.009 3.009 3.009
1.8704 2.2052 2.6302 3.1324 3.2096 3.2096 3.2096 3.2096 3.2096 3.2096 3.2096 3.2096 3.2096 3.2096 3.2096
1.8779 2.2062 2.6304 3.1366 3.4102 3.4102 3.4102 3.4102 3.4102 3.4102 3.4102 3.4102 3.4102 3.4102 3.4102
1.8724 2.2056 2.6257 3.1328 3.6108 3.6108 3.6108 3.6108 3.6108 3.6108 3.6108 3.6108 3.6108 3.6108 3.6108
1.8694 2.2058 2.634 3.1386 3.735 3.8114 3.8114 3.8114 3.8114 3.8114 3.8114 3.8114 3.8114 3.8114 3.8114
mt_ev_condi_z_max_kp1 mt_ev_condi_z_max_kp2 mt_ev_condi_z_max_kp3 mt_ev_condi_z_max_kp4 mt_ev_condi_z_max_kp5 mt_ev_condi_z_max_kp6 mt_ev_condi_z_max_kp7 mt_ev_condi_z_max_kp8 mt_ev_condi_z_max_kp9 mt_ev_condi_z_max_kp10 mt_ev_condi_z_max_kp11 mt_ev_condi_z_max_kp12 mt_ev_condi_z_max_kp13 mt_ev_condi_z_max_kp14 mt_ev_condi_z_max_kp15
_____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________
1.8973 2.2675 2.6377 3.1931 3.7484 4.4888 5.4144 6.525 7.6357 9.3017 10.968 13.189 15.781 18.557 21.704
1.9055 2.2774 2.6492 3.2069 3.7647 4.5083 5.4379 6.5534 7.6689 9.1562 11.015 13.246 15.663 18.638 21.798
1.9138 2.2872 2.6607 3.2208 3.781 4.5279 5.4615 6.3951 7.7021 9.1958 11.063 13.117 15.731 18.532 21.706
1.922 2.2971 2.6721 3.2347 3.7973 4.5474 5.485 6.4226 7.7353 9.2355 11.111 13.173 15.611 18.612 21.8
1.9303 2.3069 2.6836 3.2486 3.8136 4.5669 5.3202 6.4502 7.7685 9.2751 10.97 13.23 15.678 18.692 21.705
1.9385 2.3168 2.6951 3.2625 3.8299 4.5864 5.3429 6.4777 7.8017 9.3148 11.017 13.097 15.745 18.582 21.798
1.9468 2.1367 2.7065 3.0864 3.8462 4.6059 5.3657 6.5053 7.6449 9.1645 11.064 13.153 15.622 18.661 21.7
1.955 2.1458 2.718 3.0995 3.8625 4.4347 5.3884 6.5329 7.6773 9.2033 11.111 13.209 15.689 18.55 21.792
1.9633 2.1548 2.7295 3.1126 3.8788 4.4534 5.4111 6.3689 7.7097 9.2421 10.966 13.073 15.755 18.628 21.693
1.9715 2.1639 2.7409 3.1256 3.7027 4.4721 5.4339 6.3957 7.7421 9.281 11.012 13.128 15.629 18.514 21.784
1.9798 2.1729 2.5592 3.1387 3.7182 4.4908 5.4566 6.4224 7.7745 9.3198 11.058 13.183 15.694 18.591 21.682
1.7941 2.182 2.5699 3.1518 3.7337 4.5095 5.4794 6.4492 7.8069 9.1647 11.104 13.238 15.759 18.669 21.772
1.8015 2.191 2.5806 3.1649 3.7492 4.5283 5.5021 6.4759 7.6445 9.2027 10.956 13.098 15.63 18.552 21.668
1.8089 2.2001 2.5912 3.178 3.7647 4.547 5.3293 6.5027 7.6761 9.2407 11.001 13.152 15.695 18.628 21.757
1.8164 2.2091 2.6019 3.191 3.7802 4.5657 5.3512 6.5295 7.7077 9.2787 11.046 13.206 15.759 18.705 21.847
1.8238 2.2182 2.6126 3.2041 3.7957 4.5844 5.3731 6.5562 7.7393 9.3168 11.091 13.26 15.627 18.584 21.739
1.8313 2.2273 2.6232 3.2172 3.8112 4.6031 5.3951 6.385 7.7709 9.1568 10.939 13.117 15.69 18.66 21.828
1.8387 2.2363 2.6339 3.2303 3.8266 4.6218 5.417 6.4109 7.8025 9.194 10.983 13.17 15.754 18.537 21.718
1.8462 2.2454 2.6446 3.2433 3.8421 4.4409 5.4389 6.4369 7.6345 9.2313 11.028 13.223 15.618 18.612 21.806
1.8536 2.2544 2.6552 3.2564 3.8576 4.4588 5.4608 6.4629 7.6653 9.2685 11.072 13.076 15.681 18.687 21.693
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mt_ev_condi_z_max_bp: I by M
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250 15
mt_ev_condi_z_max_bp1 mt_ev_condi_z_max_bp2 mt_ev_condi_z_max_bp3 mt_ev_condi_z_max_bp4 mt_ev_condi_z_max_bp5 mt_ev_condi_z_max_bp6 mt_ev_condi_z_max_bp7 mt_ev_condi_z_max_bp8 mt_ev_condi_z_max_bp9 mt_ev_condi_z_max_bp10 mt_ev_condi_z_max_bp11 mt_ev_condi_z_max_bp12 mt_ev_condi_z_max_bp13 mt_ev_condi_z_max_bp14 mt_ev_condi_z_max_bp15
_____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.0002008 0.0002008 0.0002008 0.0002008 0.0002008 0.0002008 0.0002008 0.0002008 0.0002008 0.0002008 0.0002008 0.0002008 0.0002008 0.0002008 0.0002008
0.00040161 0.00040161 0.00040161 0.00040161 0.00040161 0.00040161 0.00040161 0.00040161 0.00040161 0.00040161 0.00040161 0.00040161 0.00040161 0.00040161 0.00040161
0.00060241 0.00060241 0.00060241 0.00060241 0.00060241 0.00060241 0.00060241 0.00060241 0.00060241 0.00060241 0.00060241 0.00060241 0.00060241 0.00060241 0.00060241
0.00080321 0.00080321 0.00080321 0.00080321 0.00080321 0.00080321 0.00080321 0.00080321 0.00080321 0.00080321 0.00080321 0.00080321 0.00080321 0.00080321 0.00080321
0.001004 0.001004 0.001004 0.001004 0.001004 0.001004 0.001004 0.001004 0.001004 0.001004 0.001004 0.001004 0.001004 0.001004 0.001004
0.0012048 0.0012048 0.0012048 0.0012048 0.0012048 0.0012048 0.0012048 0.0012048 0.0012048 0.0012048 0.0012048 0.0012048 0.0012048 0.0012048 0.0012048
0.0014056 0.0014056 0.0014056 0.0014056 0.0014056 0.0014056 0.0014056 0.0014056 0.0014056 0.0014056 0.0014056 0.0014056 0.0014056 0.0014056 0.0014056
0.0016064 0.0016064 0.0016064 0.0016064 0.0016064 0.0016064 0.0016064 0.0016064 0.0016064 0.0016064 0.0016064 0.0016064 0.0016064 0.0016064 0.0016064
0.0018072 0.0018072 0.0018072 0.0018072 0.0018072 0.0018072 0.0018072 0.0018072 0.0018072 0.0018072 0.0018072 0.0018072 0.0018072 0.0018072 0.0018072
0.13883 0.002008 0.002008 0.002008 0.002008 0.002008 0.002008 0.002008 0.002008 0.002008 0.002008 0.002008 0.002008 0.002008 0.002008
0.33863 0.011062 0.0022088 0.0022088 0.0022088 0.0022088 0.0022088 0.0022088 0.0022088 0.0022088 0.0022088 0.0022088 0.0022088 0.0022088 0.0022088
0.53359 0.20523 0.0024096 0.0024096 0.0024096 0.0024096 0.0024096 0.0024096 0.0024096 0.0024096 0.0024096 0.0024096 0.0024096 0.0024096 0.0024096
0.735 0.41066 0.0026104 0.0026104 0.0026104 0.0026104 0.0026104 0.0026104 0.0026104 0.0026104 0.0026104 0.0026104 0.0026104 0.0026104 0.0026104
0.93802 0.61126 0.19436 0.0028112 0.0028112 0.0028112 0.0028112 0.0028112 0.0028112 0.0028112 0.0028112 0.0028112 0.0028112 0.0028112 0.0028112
1.1378 0.79979 0.38933 0.003012 0.003012 0.003012 0.003012 0.003012 0.003012 0.003012 0.003012 0.003012 0.003012 0.003012 0.003012
1.3424 1.0076 0.58269 0.080476 0.0032129 0.0032129 0.0032129 0.0032129 0.0032129 0.0032129 0.0032129 0.0032129 0.0032129 0.0032129 0.0032129
1.5358 1.2074 0.78329 0.27705 0.0034137 0.0034137 0.0034137 0.0034137 0.0034137 0.0034137 0.0034137 0.0034137 0.0034137 0.0034137 0.0034137
1.742 1.4088 0.98872 0.48168 0.0036145 0.0036145 0.0036145 0.0036145 0.0036145 0.0036145 0.0036145 0.0036145 0.0036145 0.0036145 0.0036145
1.9459 1.6094 1.1813 0.67665 0.080274 0.0038153 0.0038153 0.0038153 0.0038153 0.0038153 0.0038153 0.0038153 0.0038153 0.0038153 0.0038153
mt_ev_condi_z_max_bp1 mt_ev_condi_z_max_bp2 mt_ev_condi_z_max_bp3 mt_ev_condi_z_max_bp4 mt_ev_condi_z_max_bp5 mt_ev_condi_z_max_bp6 mt_ev_condi_z_max_bp7 mt_ev_condi_z_max_bp8 mt_ev_condi_z_max_bp9 mt_ev_condi_z_max_bp10 mt_ev_condi_z_max_bp11 mt_ev_condi_z_max_bp12 mt_ev_condi_z_max_bp13 mt_ev_condi_z_max_bp14 mt_ev_condi_z_max_bp15
_____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________
44.287 43.917 43.547 42.992 42.436 41.696 40.77 39.66 38.549 36.883 35.217 32.996 30.404 27.628 24.481
44.48 44.108 43.736 43.179 42.621 41.877 40.948 39.832 38.717 37.229 35.37 33.139 30.722 27.748 24.587
44.673 44.299 43.926 43.366 42.805 42.058 41.125 40.191 38.884 37.391 35.523 33.469 30.855 28.055 24.88
44.865 44.49 44.115 43.552 42.99 42.24 41.302 40.365 39.052 37.552 35.676 33.614 31.176 28.175 24.988
45.058 44.681 44.304 43.739 43.174 42.421 41.668 40.538 39.219 37.713 36.018 33.758 31.31 28.296 25.283
45.25 44.872 44.494 43.926 43.359 42.602 41.846 40.711 39.387 37.874 36.172 34.091 31.443 28.606 25.391
45.443 45.253 44.683 44.303 43.543 42.784 42.024 40.884 39.745 38.225 36.326 34.236 31.767 28.728 25.689
45.635 45.445 44.872 44.491 43.728 43.156 42.202 41.057 39.913 38.387 36.48 34.381 31.902 29.041 25.798
45.828 45.636 45.062 44.679 43.912 43.338 42.38 41.422 40.081 38.549 36.825 34.718 32.036 29.163 26.098
46.02 45.828 45.251 44.866 44.289 43.52 42.558 41.596 40.25 38.711 36.98 34.864 32.363 29.478 26.208
46.213 46.02 45.634 45.054 44.475 43.702 42.736 41.77 40.418 38.873 37.135 35.01 32.499 29.601 26.511
46.6 46.212 45.824 45.242 44.66 43.884 42.914 41.944 40.587 39.229 37.289 35.156 32.634 29.725 26.621
46.793 46.403 46.014 45.429 44.845 44.066 43.092 42.118 40.95 39.392 37.639 35.496 32.964 30.043 26.927
46.986 46.595 46.204 45.617 45.031 44.248 43.466 42.292 41.119 39.554 37.794 35.643 33.101 30.167 27.038
47.18 46.787 46.394 45.805 45.216 44.43 43.645 42.467 41.288 39.717 37.95 35.79 33.237 30.291 27.149
47.373 46.979 46.584 45.993 45.401 44.612 43.824 42.641 41.457 39.88 38.105 35.936 33.57 30.612 27.458
47.566 47.17 46.774 46.18 45.586 44.794 44.003 43.013 41.627 40.241 38.459 36.281 33.707 30.737 27.57
47.76 47.362 46.964 46.368 45.772 44.977 44.181 43.187 41.796 40.404 38.615 36.429 33.844 31.061 27.88
47.953 47.554 47.155 46.556 45.957 45.358 44.36 43.362 42.165 40.568 38.772 36.576 34.181 31.187 27.993
48.146 47.746 47.345 46.744 46.142 45.541 44.539 43.537 42.335 40.732 38.928 36.924 34.319 31.313 28.307
Graph
if (bl_graph_evf)
Graph 1, V and EV
if (~bl_graph_onebyones) figure('PaperPosition', [0 0 14 4]); hold on; end for subplot_j=1:1:2 if (~bl_graph_onebyones) hAxis(subplot_j) = subplot(1,2,subplot_j); else figure('PaperPosition', [0 0 7 4]); end if (subplot_j==1) chart = plot(mt_val); end if (subplot_j==2) chart = plot(mt_ev_condi_z); end clr = jet(numel(chart)); for m = 1:numel(chart) set(chart(m),'Color',clr(m,:)) end legend2plot = fliplr([1 round(numel(chart)/3) round((2*numel(chart))/3) numel(chart)]); legendCell = cellstr(num2str(ar_z', 'shock=%3.2f')); legend(chart(legend2plot), legendCell(legend2plot), 'Location','southeast'); if (subplot_j==1) title('V(coh,zp); w(k+b),k,z'); end if (subplot_j==2) title('E_z(V(coh,zp|z))'); end ylabel('Next Period Value'); xlabel({'Index of Cash-on-Hand Discrete Point'... 'Each Segment is a w=k+b; within segment increasing k'... 'EV and V identical if shock is fully persistent'}); grid on; grid minor; end % Share y axis if (~bl_graph_onebyones) linkaxes(hAxis,'y'); end % save file if (bl_img_save) mkdir(support_map('st_img_path')); st_file_name = [st_img_prefix st_img_name_main '_vev' st_img_suffix]; saveas(gcf, strcat(st_img_path, st_file_name)); end
Graph 2, max(EV)
if(~bl_graph_onebyones) figure('PaperPosition', [0 0 7 4]); end for sub_j=1:1:1 if(sub_j==1) mt_outcome = mt_ev_condi_z_max; st_y_label = 'max_{k''}(E(V(coh(k'',b''=w-k''),z''|z,w))'; end if(~bl_graph_onebyones) subplot(1,1,sub_j) else figure('PaperPosition', [0 0 7 4]); end hold on; ar_it_z_graph = ([1 round((it_z_n)/4) round(2*((it_z_n)/4)) round(3*((it_z_n)/4)) (it_z_n)]); clr = jet(length(ar_it_z_graph)); i_ctr = 0; for i = ar_it_z_graph i_ctr = i_ctr + 1; ar_x = ar_w_level; ar_y = mt_outcome(:, i); scatter(ar_x, ar_y, 5, ... 'MarkerEdgeColor', clr(i_ctr,:), ... 'MarkerFaceColor', clr(i_ctr,:)); end grid on; grid minor; title(['2nd Stage Exp Value at Optimal K given W=K''+B''']) ylabel(st_y_label) xlabel({'Aggregate Savings'}) legendCell = cellstr(num2str(ar_z', 'shock=%3.2f')); legendCell{length(legendCell) + 1} = 'max-agg-save'; legend(legendCell([ar_it_z_graph length(legendCell)]), 'Location','southeast'); xline0 = xline(0); xline0.HandleVisibility = 'off'; yline0 = yline(0); yline0.HandleVisibility = 'off'; end % save file if (bl_img_save) mkdir(support_map('st_img_path')); st_file_name = [st_img_prefix st_img_name_main '_maxev' st_img_suffix]; saveas(gcf, strcat(st_img_path, st_file_name)); end
Warning: Ignoring extra legend entries.
Graph 3, at max(EV) optimal choice category, color regions, borrow save
% Borrow Vs Save [ar_z_mw, ar_w_mz] = meshgrid(ar_z, ar_w_level); mt_it_borr_idx = (mt_ev_condi_z_max_bp < 0); mt_it_riskyhalf_idx = ((mt_ev_condi_z_max_kp./mt_ev_condi_z_max_bp) > 0.5); mt_it_kzero_idx = (mt_ev_condi_z_max_kp == 0); mt_it_isnan_idx = (isnan(mt_ev_condi_z_max_kp)); figure('PaperPosition', [0 0 7 4]); % States: ar_w, ar_z % Choices: mt_ev_condi_z_max_kp, mt_ev_condi_z_max_bp hold on; it_sca_size = 10; chart_br = scatter(ar_w_mz(mt_it_borr_idx),... ar_z_mw(mt_it_borr_idx),... it_sca_size, 'blue', 'filled'); % legend([chart_br], {'Borrow'}, 'Location','northeast'); chart_khalf = scatter(ar_w_mz(~mt_it_borr_idx & mt_it_riskyhalf_idx),... ar_z_mw(~mt_it_borr_idx & mt_it_riskyhalf_idx),... it_sca_size, 'black', 'filled'); % legend([chart_khalf], {'Save >0.5 K'}, 'Location','northeast'); chart_sv = scatter(ar_w_mz(~mt_it_borr_idx & ~mt_it_riskyhalf_idx),... ar_z_mw(~mt_it_borr_idx & ~mt_it_riskyhalf_idx),... it_sca_size, 'red', 'filled'); % legend([chart_sv], {'Save <0.5 K'}, 'Location','northeast'); chart_invalid = scatter(ar_w_mz(mt_it_kzero_idx | mt_it_isnan_idx),... ar_z_mw(mt_it_kzero_idx | mt_it_isnan_idx),... it_sca_size, 'yellow', 'filled'); legend([chart_br, chart_khalf, chart_sv, chart_invalid], ... {'Borrow','Save >0.5 K','Save <0.5 K', 'k=0 or k=nan'}, 'Location','northeast'); title('Borrow and Save Regions') ylabel('Shocks') xlabel({'Total Savings w=k+b'}) grid on; % save file if (bl_img_save) mkdir(support_map('st_img_path')); st_file_name = [st_img_prefix st_img_name_main '_maxbrsv' st_img_suffix]; saveas(gcf, strcat(st_img_path, st_file_name)); end
Graph 4, Optimal K' and B' Levels
[~, ar_w_mz] = meshgrid(ar_z, ar_w_level);
for sub_j=1:1:4
if (bl_graph_onebyones)
figure('PaperPosition', [0 0 7 4]);
end
if (sub_j==1)
if(~bl_graph_onebyones)
figure('PaperPosition', [0 0 14 4]);
subplot(1,2,sub_j);
end
mt_y = mt_ev_condi_z_max_bp;
end
if (sub_j==2)
if(~bl_graph_onebyones)
subplot(1,2,sub_j);
end
mt_y = mt_ev_condi_z_max_kp;
end
if (sub_j==3)
if(~bl_graph_onebyones)
figure('PaperPosition', [0 0 14 4]);
subplot(1,2,sub_j-2);
end
mt_y = zeros(size(mt_ev_condi_z_max_bp));
mt_it_borr_idx = (mt_ev_condi_z_max_bp < 0);
mt_y(mt_it_borr_idx) = -mt_ev_condi_z_max_bp(mt_it_borr_idx)/fl_b_bd;
mt_y(~mt_it_borr_idx) = mt_ev_condi_z_max_bp(~mt_it_borr_idx)./ar_w_mz(~mt_it_borr_idx);
end
if (sub_j==4)
if(~bl_graph_onebyones)
subplot(1,2,sub_j-2);
end
mt_y = mt_ev_condi_z_max_kp./(ar_w_level'-fl_b_bd);
end
hold on;
chart = plot(ar_w_level, mt_y);
clr = jet(numel(chart));
if (length(ar_w_level) <= 100)
scatter(ar_w_mz(:), mt_y(:), 3, 'filled', 'MarkerEdgeColor', 'b', 'MarkerFaceColor', 'b');
end
for m = 1:numel(chart)
set(chart(m),'Color',clr(m,:))
end
legend2plot = fliplr([1 round(numel(chart)/3) round((2*numel(chart))/3) numel(chart)]);
legendCell = cellstr(num2str(ar_z', 'shock=%3.2f'));
xline0 = xline(0);
xline0.HandleVisibility = 'off';
yline0 = yline(0);
yline0.HandleVisibility = 'off';
grid on;
if (sub_j<=2)
hline = refline([1 0]);
hline.Color = 'k';
hline.LineStyle = ':';
hline.HandleVisibility = 'off';
end
if (sub_j==1)
title('B Choices of W');
ylabel('B Choices');
xlabel({'Total Savings w=k+b'});
legend(chart(legend2plot), legendCell(legend2plot), 'Location','northwest');
end
if (sub_j==2)
title('K Choices of W');
ylabel('K Choices');
xlabel({'Total Savings w=k+b'});
legend(chart(legend2plot), legendCell(legend2plot), 'Location','northwest');
end
if (sub_j==3)
title('B Fraction of Borrow Max and Save');
ylabel('B/bar(B) if br or B/W if sv');
xlabel({'Total Savings w=k+b'});
% set(gca, 'YScale', 'log');
ylim([-1.1 1.1]);
legend(chart(legend2plot), legendCell(legend2plot), 'Location','northwest');
end
if (sub_j==4)
title('K Fraction Choices of Total K Possible');
ylabel('K/(W-bar(b)) ');
xlabel({'Total Savings w=k+b'});
% set(gca, 'YScale', 'log');
ylim([0 1.1]);
legend(chart(legend2plot), legendCell(legend2plot), 'Location','northeast');
end
end
% save file
if (bl_img_save)
mkdir(support_map('st_img_path'));
st_file_name = [st_img_prefix st_img_name_main '_wkbopti' st_img_suffix];
saveas(gcf, strcat(st_img_path, st_file_name));
end
end
end
ans =
Columns 1 through 7
-0.8127 -0.8127 -0.8127 -0.8127 -0.8127 -0.8127 -0.8127
-0.1359 -0.1054 -0.0705 -0.0322 0.0092 0.0536 0.1012
0.1196 0.1499 0.1846 0.2227 0.2638 0.3081 0.3554
0.3084 0.3375 0.3708 0.4074 0.4470 0.4897 0.5354
0.4610 0.4888 0.5205 0.5556 0.5935 0.6344 0.6784
0.5901 0.6166 0.6469 0.6804 0.7168 0.7560 0.7982
0.7025 0.7277 0.7568 0.7888 0.8237 0.8614 0.9020
0.8021 0.8263 0.8541 0.8849 0.9184 0.9547 0.9939
0.8917 0.9150 0.9417 0.9713 1.0036 1.0386 1.0764
0.9733 0.9956 1.0214 1.0500 1.0811 1.1149 1.1515
1.0482 1.0697 1.0946 1.1222 1.1523 1.1850 1.2205
1.1179 1.1382 1.1622 1.1889 1.2181 1.2499 1.2843
1.1831 1.2021 1.2252 1.2511 1.2794 1.3103 1.3437
1.2443 1.2622 1.2841 1.3093 1.3368 1.3668 1.3993
1.3019 1.3188 1.3396 1.3639 1.3907 1.4199 1.4516
1.3564 1.3724 1.3922 1.4155 1.4416 1.4701 1.5010
1.4081 1.4233 1.4421 1.4643 1.4898 1.5176 1.5478
1.4572 1.4717 1.4896 1.5109 1.5355 1.5627 1.5922
1.5040 1.5179 1.5350 1.5553 1.5791 1.6057 1.6346
1.5488 1.5620 1.5784 1.5979 1.6208 1.6467 1.6750
1.5916 1.6043 1.6200 1.6387 1.6607 1.6860 1.7137
1.6327 1.6449 1.6600 1.6780 1.6991 1.7237 1.7508
1.6721 1.6839 1.6984 1.7157 1.7361 1.7598 1.7865
1.7100 1.7214 1.7354 1.7521 1.7717 1.7947 1.8208
1.7466 1.7575 1.7710 1.7872 1.8061 1.8283 1.8539
1.7819 1.7924 1.8055 1.8210 1.8394 1.8609 1.8859
1.8159 1.8261 1.8387 1.8538 1.8716 1.8924 1.9167
1.8489 1.8587 1.8710 1.8856 1.9028 1.9230 1.9466
1.8808 1.8903 1.9022 1.9163 1.9331 1.9527 1.9756
1.9117 1.9209 1.9324 1.9462 1.9624 1.9815 2.0038
1.9416 1.9506 1.9618 1.9752 1.9910 2.0095 2.0312
1.9707 1.9795 1.9903 2.0033 2.0187 2.0367 2.0578
1.9990 2.0075 2.0181 2.0307 2.0457 2.0632 2.0838
2.0265 2.0348 2.0451 2.0574 2.0719 2.0891 2.1091
2.0533 2.0614 2.0714 2.0834 2.0975 2.1142 2.1338
2.0794 2.0872 2.0970 2.1087 2.1225 2.1388 2.1579
2.1048 2.1124 2.1219 2.1334 2.1469 2.1628 2.1814
2.1295 2.1370 2.1463 2.1574 2.1706 2.1862 2.2044
2.1537 2.1610 2.1701 2.1810 2.1939 2.2090 2.2269
2.1773 2.1845 2.1933 2.2040 2.2165 2.2314 2.2488
2.2004 2.2074 2.2160 2.2264 2.2387 2.2533 2.2703
2.2229 2.2298 2.2382 2.2484 2.2604 2.2747 2.2914
2.2450 2.2516 2.2599 2.2699 2.2817 2.2956 2.3120
2.2666 2.2731 2.2812 2.2909 2.3025 2.3161 2.3322
2.2877 2.2941 2.3020 2.3116 2.3229 2.3362 2.3520
2.3083 2.3146 2.3224 2.3318 2.3429 2.3560 2.3714
2.3286 2.3347 2.3424 2.3515 2.3624 2.3753 2.3904
2.3485 2.3545 2.3620 2.3710 2.3816 2.3943 2.4091
2.3679 2.3738 2.3812 2.3900 2.4005 2.4129 2.4274
2.3870 2.3928 2.4000 2.4087 2.4190 2.4311 2.4455
2.4058 2.4114 2.4185 2.4270 2.4371 2.4491 2.4632
2.4242 2.4297 2.4367 2.4450 2.4550 2.4667 2.4805
2.4422 2.4477 2.4545 2.4627 2.4725 2.4840 2.4976
2.4600 2.4654 2.4721 2.4801 2.4897 2.5010 2.5144
2.4774 2.4827 2.4893 2.4972 2.5066 2.5178 2.5309
2.4945 2.4997 2.5062 2.5140 2.5233 2.5343 2.5472
2.5114 2.5165 2.5229 2.5305 2.5397 2.5505 2.5632
2.5279 2.5330 2.5392 2.5468 2.5558 2.5664 2.5789
2.5442 2.5492 2.5554 2.5628 2.5716 2.5821 2.5944
2.5603 2.5652 2.5712 2.5785 2.5872 2.5975 2.6097
2.5761 2.5809 2.5868 2.5940 2.6026 2.6127 2.6247
2.5916 2.5963 2.6022 2.6093 2.6177 2.6277 2.6395
2.6069 2.6115 2.6173 2.6243 2.6326 2.6425 2.6541
2.6220 2.6265 2.6323 2.6391 2.6473 2.6570 2.6685
2.6368 2.6413 2.6470 2.6537 2.6618 2.6714 2.6827
2.6514 2.6559 2.6614 2.6681 2.6761 2.6855 2.6967
2.6659 2.6702 2.6757 2.6823 2.6902 2.6994 2.7104
2.6801 2.6844 2.6898 2.6963 2.7040 2.7132 2.7240
2.6941 2.6983 2.7037 2.7101 2.7177 2.7268 2.7375
2.7079 2.7121 2.7174 2.7237 2.7312 2.7401 2.7507
2.7215 2.7257 2.7309 2.7371 2.7445 2.7533 2.7638
2.7350 2.7391 2.7442 2.7503 2.7577 2.7664 2.7767
2.7482 2.7523 2.7573 2.7634 2.7706 2.7792 2.7894
2.7613 2.7653 2.7703 2.7763 2.7835 2.7919 2.8020
2.7743 2.7782 2.7831 2.7890 2.7961 2.8045 2.8144
2.7870 2.7909 2.7958 2.8016 2.8086 2.8169 2.8266
2.7996 2.8035 2.8083 2.8140 2.8209 2.8291 2.8388
2.8121 2.8159 2.8206 2.8263 2.8331 2.8412 2.8507
2.8244 2.8281 2.8328 2.8384 2.8451 2.8531 2.8626
2.8365 2.8402 2.8448 2.8504 2.8570 2.8649 2.8742
2.8485 2.8522 2.8567 2.8622 2.8688 2.8766 2.8858
2.8603 2.8640 2.8685 2.8739 2.8804 2.8881 2.8972
2.8721 2.8756 2.8801 2.8855 2.8919 2.8995 2.9085
2.8836 2.8872 2.8916 2.8969 2.9032 2.9108 2.9197
2.8951 2.8986 2.9029 2.9082 2.9145 2.9219 2.9307
2.9064 2.9099 2.9142 2.9194 2.9256 2.9329 2.9417
2.9176 2.9210 2.9253 2.9304 2.9366 2.9438 2.9525
2.9287 2.9320 2.9363 2.9413 2.9474 2.9546 2.9632
2.9396 2.9429 2.9471 2.9522 2.9582 2.9653 2.9737
2.9504 2.9537 2.9579 2.9628 2.9688 2.9758 2.9842
2.9611 2.9644 2.9685 2.9734 2.9793 2.9863 2.9946
2.9717 2.9750 2.9790 2.9839 2.9897 2.9966 3.0048
2.9822 2.9854 2.9894 2.9943 3.0000 3.0068 3.0150
2.9926 2.9958 2.9997 3.0045 3.0102 3.0170 3.0250
3.0029 3.0060 3.0099 3.0147 3.0203 3.0270 3.0349
3.0130 3.0161 3.0200 3.0247 3.0303 3.0369 3.0448
3.0231 3.0262 3.0300 3.0347 3.0402 3.0468 3.0545
3.0331 3.0361 3.0399 3.0445 3.0500 3.0565 3.0642
3.0429 3.0459 3.0497 3.0543 3.0597 3.0661 3.0738
3.0527 3.0557 3.0594 3.0639 3.0693 3.0757 3.0832
3.0624 3.0653 3.0690 3.0735 3.0788 3.0851 3.0926
3.0720 3.0749 3.0785 3.0830 3.0882 3.0945 3.1019
3.0814 3.0844 3.0880 3.0924 3.0976 3.1038 3.1111
3.0908 3.0937 3.0973 3.1017 3.1068 3.1130 3.1203
3.1002 3.1030 3.1066 3.1109 3.1160 3.1221 3.1293
3.1094 3.1122 3.1157 3.1200 3.1251 3.1311 3.1383
3.1185 3.1213 3.1248 3.1290 3.1341 3.1401 3.1472
3.1276 3.1304 3.1338 3.1380 3.1430 3.1489 3.1560
3.1366 3.1393 3.1428 3.1469 3.1518 3.1577 3.1647
3.1455 3.1482 3.1516 3.1557 3.1606 3.1664 3.1734
3.1543 3.1570 3.1604 3.1644 3.1693 3.1751 3.1819
3.1630 3.1657 3.1691 3.1731 3.1779 3.1836 3.1904
3.1717 3.1744 3.1777 3.1817 3.1865 3.1921 3.1989
3.1803 3.1829 3.1862 3.1902 3.1949 3.2006 3.2072
3.1888 3.1914 3.1947 3.1986 3.2033 3.2089 3.2155
3.1973 3.1999 3.2031 3.2070 3.2116 3.2172 3.2238
3.2056 3.2082 3.2114 3.2153 3.2199 3.2254 3.2319
3.2140 3.2165 3.2197 3.2235 3.2281 3.2335 3.2400
3.2222 3.2247 3.2279 3.2317 3.2362 3.2416 3.2481
3.2304 3.2329 3.2360 3.2398 3.2443 3.2496 3.2560
3.2385 3.2410 3.2441 3.2478 3.2523 3.2576 3.2639
3.2465 3.2490 3.2521 3.2558 3.2602 3.2655 3.2718
3.2545 3.2569 3.2600 3.2637 3.2681 3.2733 3.2795
3.2624 3.2648 3.2679 3.2715 3.2759 3.2811 3.2873
3.2703 3.2727 3.2757 3.2793 3.2836 3.2888 3.2949
3.2780 3.2804 3.2834 3.2870 3.2913 3.2964 3.3025
3.2858 3.2881 3.2911 3.2947 3.2989 3.3040 3.3101
3.2934 3.2958 3.2987 3.3023 3.3065 3.3116 3.3176
3.3011 3.3034 3.3063 3.3098 3.3140 3.3190 3.3250
3.3086 3.3109 3.3138 3.3173 3.3215 3.3265 3.3324
3.3161 3.3184 3.3213 3.3247 3.3289 3.3338 3.3397
3.3236 3.3258 3.3287 3.3321 3.3362 3.3411 3.3470
3.3309 3.3332 3.3360 3.3395 3.3435 3.3484 3.3542
3.3383 3.3405 3.3433 3.3467 3.3508 3.3556 3.3613
3.3456 3.3478 3.3506 3.3539 3.3580 3.3628 3.3685
3.3528 3.3550 3.3578 3.3611 3.3651 3.3699 3.3755
3.3600 3.3622 3.3649 3.3682 3.3722 3.3769 3.3825
3.3671 3.3693 3.3720 3.3753 3.3792 3.3839 3.3895
3.3742 3.3763 3.3790 3.3823 3.3862 3.3909 3.3964
3.3812 3.3833 3.3860 3.3893 3.3932 3.3978 3.4033
3.3882 3.3903 3.3930 3.3962 3.4001 3.4046 3.4101
3.3951 3.3972 3.3999 3.4031 3.4069 3.4115 3.4169
3.4020 3.4041 3.4067 3.4099 3.4137 3.4182 3.4236
3.4088 3.4109 3.4135 3.4167 3.4205 3.4250 3.4303
3.4156 3.4177 3.4203 3.4234 3.4272 3.4316 3.4369
3.4223 3.4244 3.4270 3.4301 3.4338 3.4383 3.4435
3.4290 3.4311 3.4336 3.4367 3.4404 3.4449 3.4501
3.4357 3.4377 3.4403 3.4433 3.4470 3.4514 3.4566
3.4423 3.4443 3.4468 3.4499 3.4535 3.4579 3.4631
3.4488 3.4508 3.4534 3.4564 3.4600 3.4644 3.4695
3.4554 3.4574 3.4599 3.4629 3.4665 3.4708 3.4759
3.4618 3.4638 3.4663 3.4693 3.4729 3.4772 3.4822
3.4683 3.4702 3.4727 3.4757 3.4793 3.4835 3.4886
3.4747 3.4766 3.4791 3.4820 3.4856 3.4898 3.4948
3.4810 3.4830 3.4854 3.4883 3.4919 3.4961 3.5010
3.4873 3.4893 3.4917 3.4946 3.4981 3.5023 3.5072
3.4936 3.4955 3.4979 3.5008 3.5043 3.5085 3.5134
3.4998 3.5018 3.5041 3.5070 3.5105 3.5146 3.5195
3.5060 3.5079 3.5103 3.5132 3.5166 3.5207 3.5256
3.5122 3.5141 3.5165 3.5193 3.5227 3.5268 3.5316
3.5183 3.5202 3.5225 3.5254 3.5288 3.5328 3.5376
3.5244 3.5263 3.5286 3.5314 3.5348 3.5388 3.5436
3.5305 3.5323 3.5346 3.5374 3.5408 3.5448 3.5495
3.5365 3.5383 3.5406 3.5434 3.5467 3.5507 3.5554
3.5424 3.5443 3.5466 3.5493 3.5526 3.5566 3.5613
3.5484 3.5502 3.5525 3.5552 3.5585 3.5624 3.5671
3.5543 3.5561 3.5584 3.5611 3.5644 3.5683 3.5729
3.5602 3.5620 3.5642 3.5669 3.5702 3.5741 3.5787
3.5660 3.5678 3.5700 3.5727 3.5760 3.5798 3.5844
3.5718 3.5736 3.5758 3.5785 3.5817 3.5855 3.5901
3.5776 3.5793 3.5815 3.5842 3.5874 3.5912 3.5958
3.5833 3.5851 3.5873 3.5899 3.5931 3.5969 3.6014
3.5890 3.5907 3.5929 3.5956 3.5987 3.6025 3.6070
3.5947 3.5964 3.5986 3.6012 3.6044 3.6081 3.6126
3.6003 3.6020 3.6042 3.6068 3.6099 3.6137 3.6181
3.6059 3.6076 3.6098 3.6124 3.6155 3.6192 3.6236
3.6115 3.6132 3.6153 3.6179 3.6210 3.6247 3.6291
3.6170 3.6187 3.6209 3.6234 3.6265 3.6302 3.6345
3.6225 3.6242 3.6264 3.6289 3.6320 3.6356 3.6400
3.6280 3.6297 3.6318 3.6344 3.6374 3.6410 3.6453
3.6335 3.6352 3.6372 3.6398 3.6428 3.6464 3.6507
3.6389 3.6406 3.6426 3.6452 3.6482 3.6518 3.6560
3.6443 3.6460 3.6480 3.6505 3.6535 3.6571 3.6613
3.6497 3.6513 3.6534 3.6559 3.6588 3.6624 3.6666
3.6550 3.6566 3.6587 3.6612 3.6641 3.6677 3.6719
3.6603 3.6619 3.6640 3.6664 3.6694 3.6729 3.6771
3.6656 3.6672 3.6692 3.6717 3.6746 3.6781 3.6823
3.6708 3.6725 3.6745 3.6769 3.6798 3.6833 3.6874
3.6761 3.6777 3.6797 3.6821 3.6850 3.6885 3.6926
3.6813 3.6829 3.6849 3.6873 3.6902 3.6936 3.6977
3.6864 3.6880 3.6900 3.6924 3.6953 3.6987 3.7028
3.6916 3.6932 3.6951 3.6975 3.7004 3.7038 3.7078
3.6967 3.6983 3.7002 3.7026 3.7055 3.7088 3.7129
3.7018 3.7034 3.7053 3.7077 3.7105 3.7139 3.7179
3.7069 3.7084 3.7104 3.7127 3.7155 3.7189 3.7229
3.7119 3.7135 3.7154 3.7177 3.7205 3.7239 3.7278
3.7169 3.7185 3.7204 3.7227 3.7255 3.7288 3.7328
3.7219 3.7234 3.7254 3.7277 3.7304 3.7338 3.7377
3.7269 3.7284 3.7303 3.7326 3.7354 3.7387 3.7426
3.7318 3.7333 3.7352 3.7375 3.7403 3.7435 3.7474
3.7367 3.7382 3.7401 3.7424 3.7451 3.7484 3.7523
3.7416 3.7431 3.7450 3.7473 3.7500 3.7532 3.7571
3.7465 3.7480 3.7499 3.7521 3.7548 3.7581 3.7619
3.7513 3.7528 3.7547 3.7569 3.7596 3.7628 3.7667
3.7562 3.7576 3.7595 3.7617 3.7644 3.7676 3.7714
3.7610 3.7624 3.7643 3.7665 3.7692 3.7724 3.7761
3.7657 3.7672 3.7690 3.7713 3.7739 3.7771 3.7809
3.7705 3.7720 3.7738 3.7760 3.7786 3.7818 3.7855
3.7752 3.7767 3.7785 3.7807 3.7833 3.7865 3.7902
3.7799 3.7814 3.7832 3.7854 3.7880 3.7911 3.7948
3.7846 3.7861 3.7879 3.7900 3.7926 3.7958 3.7995
3.7893 3.7907 3.7925 3.7947 3.7973 3.8004 3.8040
3.7939 3.7954 3.7971 3.7993 3.8019 3.8050 3.8086
3.7986 3.8000 3.8017 3.8039 3.8065 3.8095 3.8132
3.8032 3.8046 3.8063 3.8085 3.8110 3.8141 3.8177
3.8077 3.8091 3.8109 3.8130 3.8156 3.8186 3.8222
3.8123 3.8137 3.8154 3.8176 3.8201 3.8231 3.8267
3.8168 3.8182 3.8200 3.8221 3.8246 3.8276 3.8312
3.8213 3.8227 3.8245 3.8266 3.8291 3.8321 3.8356
3.8258 3.8272 3.8290 3.8310 3.8335 3.8365 3.8401
3.8303 3.8317 3.8334 3.8355 3.8380 3.8410 3.8445
3.8348 3.8361 3.8379 3.8399 3.8424 3.8454 3.8489
3.8392 3.8406 3.8423 3.8443 3.8468 3.8498 3.8533
3.8436 3.8450 3.8467 3.8487 3.8512 3.8541 3.8576
3.8480 3.8494 3.8511 3.8531 3.8556 3.8585 3.8620
3.8524 3.8538 3.8554 3.8575 3.8599 3.8628 3.8663
3.8568 3.8581 3.8598 3.8618 3.8642 3.8671 3.8706
3.8611 3.8624 3.8641 3.8661 3.8685 3.8714 3.8749
3.8654 3.8668 3.8684 3.8704 3.8728 3.8757 3.8791
3.8697 3.8711 3.8727 3.8747 3.8771 3.8800 3.8834
3.8740 3.8753 3.8770 3.8790 3.8814 3.8842 3.8876
3.8783 3.8796 3.8812 3.8832 3.8856 3.8884 3.8918
3.8825 3.8838 3.8855 3.8874 3.8898 3.8926 3.8960
3.8868 3.8881 3.8897 3.8917 3.8940 3.8968 3.9002
3.8910 3.8923 3.8939 3.8959 3.8982 3.9010 3.9043
3.8952 3.8965 3.8981 3.9000 3.9024 3.9051 3.9085
3.8994 3.9006 3.9022 3.9042 3.9065 3.9093 3.9126
3.9035 3.9048 3.9064 3.9083 3.9106 3.9134 3.9167
3.9077 3.9089 3.9105 3.9124 3.9148 3.9175 3.9208
3.9118 3.9130 3.9146 3.9166 3.9188 3.9216 3.9249
3.9159 3.9172 3.9187 3.9206 3.9229 3.9257 3.9289
3.9200 3.9212 3.9228 3.9247 3.9270 3.9297 3.9330
3.9241 3.9253 3.9269 3.9288 3.9310 3.9337 3.9370
3.9281 3.9294 3.9309 3.9328 3.9351 3.9378 3.9410
3.9322 3.9334 3.9350 3.9368 3.9391 3.9418 3.9450
3.9362 3.9374 3.9390 3.9408 3.9431 3.9458 3.9489
3.9402 3.9414 3.9430 3.9448 3.9471 3.9497 3.9529
3.9442 3.9454 3.9470 3.9488 3.9510 3.9537 3.9569
3.9482 3.9494 3.9509 3.9528 3.9550 3.9576 3.9608
3.9521 3.9533 3.9549 3.9567 3.9589 3.9616 3.9647
Columns 8 through 14
-0.8127 -0.8127 -0.8127 -0.8127 -0.8127 -0.8127 -0.8127
0.1519 0.2058 0.2630 0.3233 0.3868 0.4530 0.5203
0.4059 0.4596 0.5165 0.5766 0.6399 0.7058 0.7730
0.5843 0.6363 0.6916 0.7500 0.8117 0.8760 0.9416
0.7254 0.7756 0.8290 0.8856 0.9453 1.0078 1.0716
0.8435 0.8919 0.9434 0.9982 1.0561 1.1168 1.1789
0.9456 0.9923 1.0422 1.0953 1.1515 1.2104 1.2709
1.0360 1.0811 1.1294 1.1809 1.2355 1.2928 1.3517
1.1171 1.1609 1.2077 1.2577 1.3108 1.3667 1.4241
1.1910 1.2334 1.2789 1.3275 1.3792 1.4337 1.4898
1.2588 1.3000 1.3442 1.3916 1.4420 1.4952 1.5500
1.3215 1.3616 1.4047 1.4508 1.5000 1.5520 1.6057
1.3799 1.4190 1.4610 1.5060 1.5541 1.6050 1.6575
1.4346 1.4727 1.5137 1.5577 1.6047 1.6546 1.7060
1.4860 1.5232 1.5633 1.6063 1.6524 1.7012 1.7516
1.5346 1.5709 1.6101 1.6522 1.6974 1.7452 1.7948
1.5806 1.6161 1.6545 1.6958 1.7400 1.7870 1.8356
1.6243 1.6591 1.6967 1.7372 1.7806 1.8267 1.8745
1.6660 1.7001 1.7369 1.7766 1.8192 1.8646 1.9116
1.7058 1.7392 1.7753 1.8143 1.8562 1.9008 1.9470
1.7439 1.7767 1.8122 1.8505 1.8916 1.9355 1.9810
1.7805 1.8126 1.8475 1.8851 1.9256 1.9687 2.0136
1.8156 1.8472 1.8814 1.9185 1.9583 2.0008 2.0449
1.8494 1.8805 1.9141 1.9505 1.9898 2.0316 2.0751
1.8820 1.9125 1.9457 1.9815 2.0201 2.0614 2.1043
1.9135 1.9435 1.9761 2.0114 2.0495 2.0901 2.1325
1.9439 1.9734 2.0055 2.0403 2.0778 2.1179 2.1597
1.9733 2.0024 2.0341 2.0683 2.1053 2.1449 2.1861
2.0018 2.0305 2.0617 2.0955 2.1320 2.1710 2.2117
2.0295 2.0577 2.0885 2.1218 2.1578 2.1964 2.2366
2.0563 2.0842 2.1145 2.1474 2.1829 2.2210 2.2607
2.0824 2.1099 2.1398 2.1722 2.2073 2.2449 2.2842
2.1078 2.1349 2.1644 2.1964 2.2311 2.2682 2.3070
2.1325 2.1592 2.1883 2.2200 2.2542 2.2909 2.3293
2.1567 2.1829 2.2117 2.2429 2.2768 2.3131 2.3510
2.1802 2.2060 2.2344 2.2653 2.2988 2.3346 2.3722
2.2032 2.2286 2.2566 2.2872 2.3202 2.3557 2.3928
2.2257 2.2506 2.2783 2.3085 2.3412 2.3763 2.4130
2.2477 2.2721 2.2995 2.3293 2.3617 2.3964 2.4328
2.2693 2.2931 2.3202 2.3497 2.3817 2.4160 2.4521
2.2903 2.3137 2.3404 2.3696 2.4013 2.4353 2.4709
2.3110 2.3339 2.3602 2.3891 2.4204 2.4541 2.4894
2.3312 2.3536 2.3796 2.4082 2.4392 2.4725 2.5075
2.3510 2.3730 2.3986 2.4269 2.4576 2.4906 2.5252
2.3704 2.3920 2.4172 2.4452 2.4756 2.5083 2.5426
2.3895 2.4107 2.4354 2.4631 2.4932 2.5257 2.5597
2.4082 2.4290 2.4533 2.4807 2.5106 2.5427 2.5764
2.4266 2.4470 2.4709 2.4980 2.5276 2.5594 2.5928
2.4446 2.4647 2.4881 2.5150 2.5443 2.5758 2.6089
2.4623 2.4820 2.5051 2.5316 2.5607 2.5919 2.6248
2.4797 2.4991 2.5218 2.5480 2.5768 2.6078 2.6403
2.4968 2.5159 2.5382 2.5641 2.5926 2.6233 2.6556
2.5136 2.5324 2.5543 2.5799 2.6081 2.6386 2.6707
2.5302 2.5486 2.5702 2.5954 2.6234 2.6537 2.6854
2.5464 2.5646 2.5859 2.6107 2.6385 2.6685 2.7000
2.5624 2.5803 2.6013 2.6257 2.6533 2.6830 2.7143
2.5782 2.5958 2.6164 2.6405 2.6678 2.6973 2.7284
2.5937 2.6110 2.6314 2.6551 2.6822 2.7114 2.7423
2.6090 2.6261 2.6461 2.6695 2.6963 2.7253 2.7559
2.6240 2.6409 2.6606 2.6836 2.7102 2.7390 2.7694
2.6388 2.6554 2.6749 2.6976 2.7239 2.7525 2.7826
2.6534 2.6698 2.6890 2.7114 2.7374 2.7658 2.7957
2.6678 2.6840 2.7029 2.7250 2.7507 2.7789 2.8086
2.6820 2.6979 2.7166 2.7384 2.7638 2.7918 2.8213
2.6960 2.7117 2.7301 2.7516 2.7767 2.8045 2.8338
2.7098 2.7253 2.7434 2.7647 2.7895 2.8171 2.8462
2.7234 2.7387 2.7566 2.7776 2.8020 2.8295 2.8584
2.7368 2.7519 2.7696 2.7903 2.8145 2.8417 2.8704
2.7501 2.7650 2.7824 2.8029 2.8267 2.8537 2.8823
2.7632 2.7778 2.7951 2.8153 2.8389 2.8656 2.8940
2.7761 2.7906 2.8076 2.8276 2.8508 2.8774 2.9055
2.7888 2.8031 2.8200 2.8397 2.8627 2.8890 2.9170
2.8014 2.8155 2.8322 2.8516 2.8744 2.9005 2.9283
2.8138 2.8278 2.8442 2.8635 2.8859 2.9118 2.9394
2.8261 2.8399 2.8561 2.8752 2.8974 2.9230 2.9504
2.8382 2.8518 2.8679 2.8867 2.9087 2.9340 2.9613
2.8502 2.8637 2.8795 2.8981 2.9198 2.9449 2.9720
2.8620 2.8753 2.8910 2.9094 2.9309 2.9557 2.9827
2.8737 2.8869 2.9024 2.9206 2.9418 2.9664 2.9932
2.8853 2.8983 2.9136 2.9316 2.9526 2.9769 3.0036
2.8967 2.9096 2.9247 2.9425 2.9633 2.9874 3.0138
2.9080 2.9207 2.9357 2.9533 2.9739 2.9977 3.0240
2.9192 2.9318 2.9466 2.9640 2.9844 3.0079 3.0340
2.9302 2.9427 2.9574 2.9746 2.9948 3.0181 3.0440
2.9412 2.9535 2.9680 2.9851 3.0050 3.0281 3.0538
2.9520 2.9642 2.9785 2.9954 3.0152 3.0380 3.0635
2.9627 2.9747 2.9890 3.0057 3.0252 3.0478 3.0732
2.9733 2.9852 2.9993 3.0158 3.0352 3.0576 3.0827
2.9837 2.9955 3.0095 3.0258 3.0450 3.0672 3.0921
2.9941 3.0058 3.0196 3.0358 3.0548 3.0767 3.1015
3.0044 3.0159 3.0296 3.0456 3.0644 3.0862 3.1107
3.0145 3.0260 3.0395 3.0554 3.0740 3.0956 3.1199
3.0246 3.0359 3.0493 3.0650 3.0835 3.1048 3.1289
3.0345 3.0457 3.0590 3.0746 3.0929 3.1140 3.1379
3.0444 3.0555 3.0686 3.0841 3.1022 3.1231 3.1468
3.0541 3.0651 3.0781 3.0934 3.1114 3.1322 3.1556
3.0638 3.0747 3.0876 3.1027 3.1205 3.1411 3.1644
3.0733 3.0842 3.0969 3.1119 3.1296 3.1500 3.1730
3.0828 3.0935 3.1062 3.1211 3.1385 3.1588 3.1816
3.0922 3.1028 3.1154 3.1301 3.1474 3.1675 3.1901
3.1015 3.1120 3.1245 3.1391 3.1562 3.1761 3.1986
3.1107 3.1212 3.1335 3.1480 3.1650 3.1847 3.2069
3.1199 3.1302 3.1424 3.1568 3.1736 3.1932 3.2153
3.1289 3.1392 3.1512 3.1655 3.1822 3.2016 3.2235
3.1379 3.1480 3.1600 3.1741 3.1907 3.2099 3.2317
3.1468 3.1568 3.1687 3.1827 3.1991 3.2182 3.2398
3.1556 3.1656 3.1773 3.1912 3.2075 3.2264 3.2478
3.1643 3.1742 3.1859 3.1996 3.2158 3.2346 3.2558
3.1730 3.1828 3.1944 3.2080 3.2240 3.2426 3.2637
3.1816 3.1913 3.2028 3.2163 3.2322 3.2507 3.2715
3.1901 3.1997 3.2111 3.2245 3.2403 3.2586 3.2793
3.1985 3.2081 3.2194 3.2327 3.2483 3.2665 3.2870
3.2069 3.2164 3.2276 3.2408 3.2563 3.2743 3.2947
3.2152 3.2246 3.2357 3.2488 3.2642 3.2821 3.3023
3.2234 3.2327 3.2438 3.2567 3.2720 3.2898 3.3099
3.2316 3.2408 3.2518 3.2646 3.2798 3.2974 3.3174
3.2397 3.2488 3.2597 3.2725 3.2875 3.3050 3.3248
3.2477 3.2568 3.2676 3.2803 3.2952 3.3125 3.3322
3.2557 3.2647 3.2754 3.2880 3.3028 3.3200 3.3395
3.2636 3.2725 3.2831 3.2956 3.3103 3.3274 3.3468
3.2714 3.2803 3.2908 3.3032 3.3178 3.3348 3.3540
3.2792 3.2880 3.2985 3.3108 3.3253 3.3421 3.3612
3.2869 3.2957 3.3060 3.3183 3.3326 3.3494 3.3683
3.2946 3.3033 3.3135 3.3257 3.3400 3.3566 3.3754
3.3022 3.3108 3.3210 3.3331 3.3472 3.3637 3.3824
3.3097 3.3183 3.3284 3.3404 3.3544 3.3708 3.3894
3.3172 3.3257 3.3358 3.3476 3.3616 3.3779 3.3963
3.3247 3.3331 3.3431 3.3549 3.3687 3.3849 3.4032
3.3320 3.3404 3.3503 3.3620 3.3758 3.3918 3.4100
3.3394 3.3477 3.3575 3.3691 3.3828 3.3987 3.4168
3.3466 3.3549 3.3647 3.3762 3.3898 3.4056 3.4235
3.3539 3.3621 3.3717 3.3832 3.3967 3.4124 3.4302
3.3610 3.3692 3.3788 3.3902 3.4036 3.4192 3.4368
3.3681 3.3762 3.3858 3.3971 3.4104 3.4259 3.4434
3.3752 3.3832 3.3927 3.4039 3.4172 3.4326 3.4500
3.3822 3.3902 3.3996 3.4108 3.4239 3.4392 3.4565
3.3892 3.3971 3.4065 3.4175 3.4306 3.4458 3.4630
3.3961 3.4040 3.4133 3.4243 3.4372 3.4523 3.4694
3.4030 3.4108 3.4200 3.4310 3.4438 3.4588 3.4758
3.4098 3.4176 3.4267 3.4376 3.4504 3.4653 3.4822
3.4166 3.4243 3.4334 3.4442 3.4569 3.4717 3.4885
3.4233 3.4310 3.4400 3.4507 3.4634 3.4781 3.4947
3.4300 3.4376 3.4466 3.4572 3.4698 3.4844 3.5010
3.4367 3.4442 3.4531 3.4637 3.4762 3.4907 3.5072
3.4433 3.4508 3.4596 3.4701 3.4825 3.4970 3.5133
3.4498 3.4573 3.4661 3.4765 3.4888 3.5032 3.5194
3.4563 3.4637 3.4725 3.4829 3.4951 3.5093 3.5255
3.4628 3.4702 3.4789 3.4892 3.5013 3.5155 3.5316
3.4692 3.4765 3.4852 3.4954 3.5075 3.5216 3.5376
3.4756 3.4829 3.4915 3.5017 3.5137 3.5277 3.5435
3.4820 3.4892 3.4977 3.5079 3.5198 3.5337 3.5495
3.4883 3.4955 3.5039 3.5140 3.5259 3.5397 3.5554
3.4946 3.5017 3.5101 3.5201 3.5319 3.5456 3.5612
3.5008 3.5079 3.5163 3.5262 3.5379 3.5516 3.5671
3.5070 3.5140 3.5224 3.5322 3.5439 3.5575 3.5729
3.5131 3.5201 3.5284 3.5382 3.5498 3.5633 3.5786
3.5192 3.5262 3.5344 3.5442 3.5557 3.5691 3.5844
3.5253 3.5322 3.5404 3.5501 3.5616 3.5749 3.5901
3.5314 3.5382 3.5464 3.5560 3.5674 3.5807 3.5957
3.5374 3.5442 3.5523 3.5619 3.5732 3.5864 3.6014
3.5433 3.5501 3.5582 3.5677 3.5789 3.5921 3.6070
3.5493 3.5560 3.5640 3.5735 3.5847 3.5977 3.6125
3.5552 3.5619 3.5698 3.5793 3.5904 3.6033 3.6181
3.5610 3.5677 3.5756 3.5850 3.5960 3.6089 3.6236
3.5669 3.5735 3.5814 3.5907 3.6017 3.6145 3.6291
3.5727 3.5793 3.5871 3.5963 3.6073 3.6200 3.6345
3.5784 3.5850 3.5928 3.6020 3.6128 3.6255 3.6399
3.5842 3.5907 3.5984 3.6076 3.6184 3.6310 3.6453
3.5899 3.5963 3.6040 3.6131 3.6239 3.6364 3.6507
3.5955 3.6020 3.6096 3.6187 3.6294 3.6418 3.6560
3.6012 3.6076 3.6152 3.6242 3.6348 3.6472 3.6613
3.6068 3.6131 3.6207 3.6296 3.6402 3.6526 3.6666
3.6123 3.6187 3.6262 3.6351 3.6456 3.6579 3.6719
3.6179 3.6242 3.6317 3.6405 3.6510 3.6632 3.6771
3.6234 3.6296 3.6371 3.6459 3.6563 3.6685 3.6823
3.6289 3.6351 3.6425 3.6513 3.6616 3.6737 3.6874
3.6343 3.6405 3.6479 3.6566 3.6669 3.6789 3.6926
3.6397 3.6459 3.6532 3.6619 3.6721 3.6841 3.6977
3.6451 3.6513 3.6585 3.6672 3.6773 3.6893 3.7028
3.6505 3.6566 3.6638 3.6724 3.6825 3.6944 3.7079
3.6558 3.6619 3.6691 3.6776 3.6877 3.6995 3.7129
3.6611 3.6672 3.6743 3.6828 3.6928 3.7046 3.7179
3.6664 3.6724 3.6795 3.6880 3.6980 3.7096 3.7229
3.6716 3.6776 3.6847 3.6931 3.7030 3.7147 3.7279
3.6769 3.6828 3.6899 3.6982 3.7081 3.7197 3.7328
3.6821 3.6880 3.6950 3.7033 3.7131 3.7246 3.7377
3.6872 3.6931 3.7001 3.7084 3.7181 3.7296 3.7426
3.6924 3.6982 3.7052 3.7134 3.7231 3.7345 3.7475
3.6975 3.7033 3.7102 3.7184 3.7281 3.7394 3.7523
3.7026 3.7084 3.7152 3.7234 3.7330 3.7443 3.7571
3.7076 3.7134 3.7202 3.7284 3.7379 3.7492 3.7619
3.7127 3.7184 3.7252 3.7333 3.7428 3.7540 3.7667
3.7177 3.7234 3.7302 3.7382 3.7477 3.7588 3.7714
3.7227 3.7284 3.7351 3.7431 3.7525 3.7636 3.7762
3.7276 3.7333 3.7400 3.7480 3.7574 3.7684 3.7809
3.7326 3.7382 3.7449 3.7528 3.7621 3.7731 3.7856
3.7375 3.7431 3.7497 3.7576 3.7669 3.7778 3.7902
3.7424 3.7479 3.7546 3.7624 3.7717 3.7825 3.7949
3.7472 3.7528 3.7594 3.7672 3.7764 3.7872 3.7995
3.7521 3.7576 3.7642 3.7719 3.7811 3.7918 3.8041
3.7569 3.7624 3.7689 3.7766 3.7858 3.7965 3.8087
3.7617 3.7672 3.7737 3.7813 3.7904 3.8011 3.8132
3.7665 3.7719 3.7784 3.7860 3.7951 3.8057 3.8177
3.7712 3.7766 3.7831 3.7907 3.7997 3.8102 3.8223
3.7760 3.7813 3.7877 3.7953 3.8043 3.8148 3.8268
3.7807 3.7860 3.7924 3.7999 3.8089 3.8193 3.8312
3.7853 3.7907 3.7970 3.8045 3.8134 3.8238 3.8357
3.7900 3.7953 3.8016 3.8091 3.8180 3.8283 3.8401
3.7946 3.7999 3.8062 3.8137 3.8225 3.8328 3.8445
3.7993 3.8045 3.8108 3.8182 3.8270 3.8372 3.8489
3.8039 3.8091 3.8153 3.8227 3.8314 3.8417 3.8533
3.8084 3.8136 3.8198 3.8272 3.8359 3.8461 3.8577
3.8130 3.8182 3.8243 3.8317 3.8403 3.8505 3.8620
3.8175 3.8227 3.8288 3.8361 3.8447 3.8548 3.8663
3.8220 3.8272 3.8333 3.8405 3.8491 3.8592 3.8706
3.8265 3.8317 3.8377 3.8450 3.8535 3.8635 3.8749
3.8310 3.8361 3.8422 3.8494 3.8579 3.8678 3.8792
3.8355 3.8405 3.8466 3.8537 3.8622 3.8721 3.8834
3.8399 3.8450 3.8510 3.8581 3.8665 3.8764 3.8876
3.8443 3.8493 3.8553 3.8624 3.8708 3.8806 3.8919
3.8487 3.8537 3.8597 3.8667 3.8751 3.8849 3.8960
3.8531 3.8581 3.8640 3.8710 3.8794 3.8891 3.9002
3.8574 3.8624 3.8683 3.8753 3.8836 3.8933 3.9044
3.8618 3.8667 3.8726 3.8796 3.8878 3.8975 3.9085
3.8661 3.8710 3.8769 3.8838 3.8920 3.9017 3.9126
3.8704 3.8753 3.8811 3.8880 3.8962 3.9058 3.9167
3.8747 3.8796 3.8854 3.8923 3.9004 3.9100 3.9208
3.8789 3.8838 3.8896 3.8964 3.9046 3.9141 3.9249
3.8832 3.8880 3.8938 3.9006 3.9087 3.9182 3.9290
3.8874 3.8922 3.8980 3.9048 3.9128 3.9223 3.9330
3.8916 3.8964 3.9021 3.9089 3.9169 3.9263 3.9370
3.8958 3.9006 3.9063 3.9130 3.9210 3.9304 3.9410
3.9000 3.9048 3.9104 3.9171 3.9251 3.9344 3.9450
3.9042 3.9089 3.9145 3.9212 3.9291 3.9384 3.9490
3.9083 3.9130 3.9186 3.9253 3.9332 3.9424 3.9530
3.9124 3.9171 3.9227 3.9293 3.9372 3.9464 3.9569
3.9165 3.9212 3.9268 3.9334 3.9412 3.9504 3.9608
3.9206 3.9253 3.9308 3.9374 3.9452 3.9543 3.9648
3.9247 3.9293 3.9349 3.9414 3.9492 3.9583 3.9686
3.9287 3.9334 3.9389 3.9454 3.9531 3.9622 3.9725
3.9328 3.9374 3.9429 3.9494 3.9571 3.9661 3.9764
3.9368 3.9414 3.9469 3.9533 3.9610 3.9700 3.9803
3.9408 3.9454 3.9508 3.9573 3.9649 3.9739 3.9841
3.9448 3.9494 3.9548 3.9612 3.9688 3.9777 3.9879
3.9488 3.9533 3.9587 3.9651 3.9727 3.9816 3.9917
3.9527 3.9573 3.9626 3.9690 3.9766 3.9854 3.9955
3.9567 3.9612 3.9665 3.9729 3.9804 3.9892 3.9993
3.9606 3.9651 3.9704 3.9768 3.9843 3.9930 4.0031
3.9645 3.9690 3.9743 3.9806 3.9881 3.9968 4.0068
3.9684 3.9729 3.9782 3.9844 3.9919 4.0006 4.0106
Column 15
-0.8127
0.5852
0.8377
1.0048
1.1333
1.2390
1.3294
1.4088
1.4798
1.5442
1.6033
1.6579
1.7086
1.7562
1.8009
1.8431
1.8832
1.9213
1.9576
1.9923
2.0256
2.0575
2.0883
2.1179
2.1464
2.1740
2.2008
2.2267
2.2518
2.2761
2.2998
2.3228
2.3453
2.3671
2.3884
2.4092
2.4295
2.4493
2.4686
2.4876
2.5061
2.5243
2.5420
2.5595
2.5765
2.5933
2.6097
2.6259
2.6417
2.6573
2.6726
2.6876
2.7024
2.7169
2.7312
2.7453
2.7592
2.7728
2.7862
2.7995
2.8125
2.8254
2.8381
2.8506
2.8629
2.8750
2.8870
2.8989
2.9106
2.9221
2.9335
2.9448
2.9559
2.9668
2.9777
2.9884
2.9990
3.0095
3.0198
3.0301
3.0402
3.0502
3.0601
3.0699
3.0796
3.0892
3.0987
3.1081
3.1174
3.1266
3.1357
3.1447
3.1536
3.1625
3.1712
3.1799
3.1885
3.1971
3.2055
3.2139
3.2222
3.2304
3.2385
3.2466
3.2546
3.2625
3.2704
3.2782
3.2859
3.2936
3.3012
3.3088
3.3163
3.3237
3.3311
3.3385
3.3458
3.3530
3.3602
3.3673
3.3744
3.3814
3.3884
3.3953
3.4022
3.4090
3.4158
3.4226
3.4293
3.4359
3.4425
3.4491
3.4556
3.4621
3.4685
3.4749
3.4813
3.4876
3.4939
3.5001
3.5063
3.5125
3.5186
3.5247
3.5307
3.5367
3.5427
3.5487
3.5546
3.5604
3.5663
3.5721
3.5778
3.5836
3.5893
3.5949
3.6006
3.6062
3.6118
3.6173
3.6228
3.6283
3.6338
3.6392
3.6446
3.6500
3.6553
3.6606
3.6659
3.6711
3.6764
3.6816
3.6867
3.6919
3.6970
3.7021
3.7072
3.7122
3.7172
3.7222
3.7272
3.7321
3.7370
3.7419
3.7468
3.7516
3.7565
3.7613
3.7660
3.7708
3.7755
3.7802
3.7849
3.7896
3.7942
3.7988
3.8034
3.8080
3.8126
3.8171
3.8216
3.8261
3.8306
3.8351
3.8395
3.8439
3.8483
3.8527
3.8571
3.8614
3.8657
3.8700
3.8743
3.8786
3.8828
3.8871
3.8913
3.8955
3.8996
3.9038
3.9079
3.9121
3.9162
3.9203
3.9243
3.9284
3.9325
3.9365
3.9405
3.9445
3.9485
3.9524
3.9564
3.9603
3.9642
3.9681
3.9720
3.9759
3.9797
3.9836
3.9874
3.9912
3.9950
3.9988
4.0025
4.0063
4.0100
4.0138
4.0175
4.0212