Matlab FF_OPTIM_MZOOM_SAVEZRONE Optimal Savings Share Concurrent Zooming Optimization
Fan Wang
2020-07-08
1 FF_OPTIM_MZOOM_SAVEZRONE Derivative Multisection
Go to the MLX, M, PDF, or HTML version of this file. Go back to fan’s MEconTools Toolbox (bookdown), Matlab Code Examples Repository (bookdown), or Math for Econ with Matlab Repository (bookdown).
Examples](https://fanwangecon.github.io/M4Econ/), or** Dynamic Asset This is the example vignette for function: ff_optim_mzoom_savezrone from the MEconTools Package. This functions solves for optimal savings/borrowing level given an anonymous function that provides the utility (not derivative) of a intertemporal savings problem. This is a vectorized function solves for multiple state-space elements at the same time. The function allows for controls of iteration counts, the number of evaluations per iteration, and how much to "zoom-in" for each iteration around the last iteration’s maximum/optimal choice.
Note that if first order conditions are available this method should not be used, but ff_optim_mlsec_savezrone should be used. ff_optim_mlsec_savezrone relies on bisection. In the first example below more it_mzoom_jnt_pnts values are needed to achieve the same precision than under ff_optim_mlsec_savezrone. However, increasing it_mzoom_jnt_pnts might not expensive given vectorization, should increase time cost linearly in generally. MZOOM is much more robust than bisection based methods. And by increasing the number of points evaluated per iteration, in limited number of iterations, the approximately exact optimal savings choice can be found.
The vectorized zooming savings problem rely on this function to solve for optimal savings choices:
- States Grid + Approximate Continuous Exact Savings (zoom) as Share of Cash-on-Hand Vectorized: ff_vfi_az_zoom_vec, precision and speed
1.1 Test FF_OPTIM_MZOOM_SAVEZRONE One Individual
Bisection for savings choice at one state:
% Generate the state-space and function
[fl_z1, fl_z2, fl_r, fl_beta] = deal(0.4730, 0.6252, 0.0839, 0.7365);
% ffi_intertemporal_max is a function in ff_optim_mlsec_savezrone for testing
fc_util = @(x) ffi_intertemporal_util(x, fl_z1, fl_z2, fl_r, fl_beta);
% Call Function
bl_verbose = false;
bl_timer = true;
% optimally borrowing given the parameters here
mp_mzoom_ctrlinfo = containers.Map('KeyType','char', 'ValueType','any');
mp_mzoom_ctrlinfo('it_mzoom_jnt_pnts') = 15;
mp_mzoom_ctrlinfo('it_mzoom_max_iter') = 10;
mp_mzoom_ctrlinfo('it_mzoom_zm_ratio') = 0.25;
[fl_opti_save_frac, fl_opti_save_level] = ...
ff_optim_mzoom_savezrone(fc_util, bl_verbose, bl_timer, mp_mzoom_ctrlinfo)
Elapsed time is 0.011586 seconds.
fl_opti_save_frac = 0.4241
fl_opti_save_level = -0.13161.2 Test FF_OPTIM_MZOOM_SAVEZRONE 4 Individuals 3 Iterations 50 Points Per Iteration
5 grid points per iteration, and 5 iterations.
% Generate the state-space and function
rng(123);
it_draws = 4; % must be even number
ar_z1 = exp(rand([it_draws,1])*3-1.5);
ar_z2 = exp(rand([it_draws,1])*3-1.5);
ar_r = (rand(it_draws,1)*10.0);
ar_beta = [rand(round(it_draws/2),1)*0.9+0.1; rand(round(it_draws/2),1)*0.9+1];
fc_util = @(x) ffi_intertemporal_util(x, ar_z1, ar_z2, ar_r, ar_beta);
% Call Function
bl_verbose = true;
bl_timer = true;
mp_mzoom_ctrlinfo = containers.Map('KeyType','char', 'ValueType','any');
mp_mzoom_ctrlinfo('it_mzoom_jnt_pnts') = 50;
mp_mzoom_ctrlinfo('it_mzoom_max_iter') = 3;
mp_mzoom_ctrlinfo('it_mzoom_zm_ratio') = 0;
[fl_opti_save_frac, fl_opti_save_level] = ...
ff_optim_mzoom_savezrone(fc_util, bl_verbose, bl_timer, mp_mzoom_ctrlinfo);
iter cl_row_names_a Var1 Var2 Var3 Var4
____ ______________ ________ ________ ________ ________
1 "point=1" 1e-05 1e-05 1e-05 1e-05
1 "point=2" 0.020418 0.020418 0.020418 0.020418
1 "point=3" 0.040826 0.040826 0.040826 0.040826
1 "point=4" 0.061233 0.061233 0.061233 0.061233
1 "point=5" 0.081641 0.081641 0.081641 0.081641
1 "point=6" 0.10205 0.10205 0.10205 0.10205
1 "point=7" 0.12246 0.12246 0.12246 0.12246
1 "point=8" 0.14286 0.14286 0.14286 0.14286
1 "point=9" 0.16327 0.16327 0.16327 0.16327
1 "point=10" 0.18368 0.18368 0.18368 0.18368
1 "point=11" 0.20409 0.20409 0.20409 0.20409
1 "point=12" 0.2245 0.2245 0.2245 0.2245
1 "point=13" 0.2449 0.2449 0.2449 0.2449
1 "point=14" 0.26531 0.26531 0.26531 0.26531
1 "point=15" 0.28572 0.28572 0.28572 0.28572
1 "point=16" 0.30613 0.30613 0.30613 0.30613
1 "point=17" 0.32653 0.32653 0.32653 0.32653
1 "point=18" 0.34694 0.34694 0.34694 0.34694
1 "point=19" 0.36735 0.36735 0.36735 0.36735
1 "point=20" 0.38776 0.38776 0.38776 0.38776
1 "point=21" 0.40817 0.40817 0.40817 0.40817
1 "point=22" 0.42857 0.42857 0.42857 0.42857
1 "point=23" 0.44898 0.44898 0.44898 0.44898
1 "point=24" 0.46939 0.46939 0.46939 0.46939
1 "point=25" 0.4898 0.4898 0.4898 0.4898
1 "point=26" 0.5102 0.5102 0.5102 0.5102
1 "point=27" 0.53061 0.53061 0.53061 0.53061
1 "point=28" 0.55102 0.55102 0.55102 0.55102
1 "point=29" 0.57143 0.57143 0.57143 0.57143
1 "point=30" 0.59183 0.59183 0.59183 0.59183
1 "point=31" 0.61224 0.61224 0.61224 0.61224
1 "point=32" 0.63265 0.63265 0.63265 0.63265
1 "point=33" 0.65306 0.65306 0.65306 0.65306
1 "point=34" 0.67347 0.67347 0.67347 0.67347
1 "point=35" 0.69387 0.69387 0.69387 0.69387
1 "point=36" 0.71428 0.71428 0.71428 0.71428
1 "point=37" 0.73469 0.73469 0.73469 0.73469
1 "point=38" 0.7551 0.7551 0.7551 0.7551
1 "point=39" 0.7755 0.7755 0.7755 0.7755
1 "point=40" 0.79591 0.79591 0.79591 0.79591
1 "point=41" 0.81632 0.81632 0.81632 0.81632
1 "point=42" 0.83673 0.83673 0.83673 0.83673
1 "point=43" 0.85714 0.85714 0.85714 0.85714
1 "point=44" 0.87754 0.87754 0.87754 0.87754
1 "point=45" 0.89795 0.89795 0.89795 0.89795
1 "point=46" 0.91836 0.91836 0.91836 0.91836
1 "point=47" 0.93877 0.93877 0.93877 0.93877
1 "point=48" 0.95917 0.95917 0.95917 0.95917
1 "point=49" 0.97958 0.97958 0.97958 0.97958
1 "point=50" 0.99999 0.99999 0.99999 0.99999
2 "point=1" 0.30693 0.12326 0.55182 0.61304
2 "point=2" 0.30773 0.12406 0.55262 0.61384
2 "point=3" 0.30853 0.12486 0.55342 0.61464
2 "point=4" 0.30933 0.12566 0.55422 0.61544
2 "point=5" 0.31013 0.12646 0.55502 0.61624
2 "point=6" 0.31093 0.12726 0.55582 0.61704
2 "point=7" 0.31173 0.12806 0.55662 0.61784
2 "point=8" 0.31253 0.12886 0.55742 0.61865
2 "point=9" 0.31333 0.12966 0.55822 0.61945
2 "point=10" 0.31413 0.13046 0.55902 0.62025
2 "point=11" 0.31493 0.13126 0.55982 0.62105
2 "point=12" 0.31573 0.13206 0.56062 0.62185
2 "point=13" 0.31653 0.13286 0.56142 0.62265
2 "point=14" 0.31733 0.13366 0.56222 0.62345
2 "point=15" 0.31813 0.13446 0.56302 0.62425
2 "point=16" 0.31893 0.13526 0.56382 0.62505
2 "point=17" 0.31973 0.13606 0.56462 0.62585
2 "point=18" 0.32053 0.13686 0.56542 0.62665
2 "point=19" 0.32133 0.13766 0.56623 0.62745
2 "point=20" 0.32213 0.13846 0.56703 0.62825
2 "point=21" 0.32293 0.13926 0.56783 0.62905
2 "point=22" 0.32373 0.14006 0.56863 0.62985
2 "point=23" 0.32453 0.14086 0.56943 0.63065
2 "point=24" 0.32533 0.14166 0.57023 0.63145
2 "point=25" 0.32613 0.14246 0.57103 0.63225
2 "point=26" 0.32693 0.14326 0.57183 0.63305
2 "point=27" 0.32773 0.14406 0.57263 0.63385
2 "point=28" 0.32853 0.14487 0.57343 0.63465
2 "point=29" 0.32934 0.14567 0.57423 0.63545
2 "point=30" 0.33014 0.14647 0.57503 0.63625
2 "point=31" 0.33094 0.14727 0.57583 0.63705
2 "point=32" 0.33174 0.14807 0.57663 0.63785
2 "point=33" 0.33254 0.14887 0.57743 0.63865
2 "point=34" 0.33334 0.14967 0.57823 0.63945
2 "point=35" 0.33414 0.15047 0.57903 0.64025
2 "point=36" 0.33494 0.15127 0.57983 0.64105
2 "point=37" 0.33574 0.15207 0.58063 0.64185
2 "point=38" 0.33654 0.15287 0.58143 0.64265
2 "point=39" 0.33734 0.15367 0.58223 0.64345
2 "point=40" 0.33814 0.15447 0.58303 0.64425
2 "point=41" 0.33894 0.15527 0.58383 0.64506
2 "point=42" 0.33974 0.15607 0.58463 0.64586
2 "point=43" 0.34054 0.15687 0.58543 0.64666
2 "point=44" 0.34134 0.15767 0.58623 0.64746
2 "point=45" 0.34214 0.15847 0.58703 0.64826
2 "point=46" 0.34294 0.15927 0.58783 0.64906
2 "point=47" 0.34374 0.16007 0.58863 0.64986
2 "point=48" 0.34454 0.16087 0.58943 0.65066
2 "point=49" 0.34534 0.16167 0.59023 0.65146
2 "point=50" 0.34614 0.16247 0.59103 0.65226
3 "point=1" 0.32937 0.13129 0.57426 0.62348
3 "point=2" 0.3294 0.13132 0.57429 0.62351
3 "point=3" 0.32943 0.13135 0.57432 0.62354
3 "point=4" 0.32946 0.13139 0.57435 0.62357
3 "point=5" 0.32949 0.13142 0.57439 0.6236
3 "point=6" 0.32952 0.13145 0.57442 0.62364
3 "point=7" 0.32955 0.13148 0.57445 0.62367
3 "point=8" 0.32959 0.13151 0.57448 0.6237
3 "point=9" 0.32962 0.13154 0.57451 0.62373
3 "point=10" 0.32965 0.13157 0.57454 0.62376
3 "point=11" 0.32968 0.13161 0.57457 0.62379
3 "point=12" 0.32971 0.13164 0.5746 0.62382
3 "point=13" 0.32974 0.13167 0.57464 0.62385
3 "point=14" 0.32977 0.1317 0.57467 0.62389
3 "point=15" 0.32981 0.13173 0.5747 0.62392
3 "point=16" 0.32984 0.13176 0.57473 0.62395
3 "point=17" 0.32987 0.13179 0.57476 0.62398
3 "point=18" 0.3299 0.13182 0.57479 0.62401
3 "point=19" 0.32993 0.13186 0.57482 0.62404
3 "point=20" 0.32996 0.13189 0.57486 0.62407
3 "point=21" 0.32999 0.13192 0.57489 0.62411
3 "point=22" 0.33003 0.13195 0.57492 0.62414
3 "point=23" 0.33006 0.13198 0.57495 0.62417
3 "point=24" 0.33009 0.13201 0.57498 0.6242
3 "point=25" 0.33012 0.13204 0.57501 0.62423
3 "point=26" 0.33015 0.13208 0.57504 0.62426
3 "point=27" 0.33018 0.13211 0.57508 0.62429
3 "point=28" 0.33021 0.13214 0.57511 0.62433
3 "point=29" 0.33025 0.13217 0.57514 0.62436
3 "point=30" 0.33028 0.1322 0.57517 0.62439
3 "point=31" 0.33031 0.13223 0.5752 0.62442
3 "point=32" 0.33034 0.13226 0.57523 0.62445
3 "point=33" 0.33037 0.1323 0.57526 0.62448
3 "point=34" 0.3304 0.13233 0.5753 0.62451
3 "point=35" 0.33043 0.13236 0.57533 0.62455
3 "point=36" 0.33046 0.13239 0.57536 0.62458
3 "point=37" 0.3305 0.13242 0.57539 0.62461
3 "point=38" 0.33053 0.13245 0.57542 0.62464
3 "point=39" 0.33056 0.13248 0.57545 0.62467
3 "point=40" 0.33059 0.13252 0.57548 0.6247
3 "point=41" 0.33062 0.13255 0.57551 0.62473
3 "point=42" 0.33065 0.13258 0.57555 0.62477
3 "point=43" 0.33068 0.13261 0.57558 0.6248
3 "point=44" 0.33072 0.13264 0.57561 0.62483
3 "point=45" 0.33075 0.13267 0.57564 0.62486
3 "point=46" 0.33078 0.1327 0.57567 0.62489
3 "point=47" 0.33081 0.13273 0.5757 0.62492
3 "point=48" 0.33084 0.13277 0.57573 0.62495
3 "point=49" 0.33087 0.1328 0.57577 0.62498
3 "point=50" 0.3309 0.13283 0.5758 0.62502
iter cl_row_names_a Var1 Var2 Var3 Var4
____ ______________ _________ ________ _________ ________
1 "point=1" -3.6912 -1.9565 -12.83 -14.789
1 "point=2" 0.058694 -0.80561 -2.4984 -2.1254
1 "point=3" 0.38043 -0.72015 -1.5784 -0.99337
1 "point=4" 0.55947 -0.67935 -1.0493 -0.34024
1 "point=5" 0.67979 -0.65711 -0.68055 0.11647
1 "point=6" 0.7677 -0.64529 -0.39997 0.46531
1 "point=7" 0.8349 -0.64026 -0.17534 0.74571
1 "point=8" 0.88763 -0.6401 0.010483 0.9787
1 "point=9" 0.92959 -0.64367 0.16774 1.1768
1 "point=10" 0.96316 -0.65026 0.30302 1.3481
1 "point=11" 0.98996 -0.65938 0.4208 1.4981
1 "point=12" 1.0111 -0.67071 0.52427 1.6308
1 "point=13" 1.0275 -0.684 0.61578 1.7489
1 "point=14" 1.0397 -0.6991 0.69709 1.8547
1 "point=15" 1.0482 -0.71588 0.76958 1.9499
1 "point=16" 1.0533 -0.73426 0.83429 2.0357
1 "point=17" 1.0554 -0.75419 0.8921 2.1132
1 "point=18" 1.0546 -0.77564 0.94367 2.1833
1 "point=19" 1.0512 -0.79861 0.98955 2.2467
1 "point=20" 1.0451 -0.82309 1.0302 2.3039
1 "point=21" 1.0366 -0.8491 1.066 2.3554
1 "point=22" 1.0256 -0.87669 1.0971 2.4015
1 "point=23" 1.0123 -0.90591 1.124 2.4425
1 "point=24" 0.99654 -0.93682 1.1466 2.4788
1 "point=25" 0.97838 -0.9695 1.1652 2.5104
1 "point=26" 0.95775 -1.004 1.1798 2.5375
1 "point=27" 0.93459 -1.0406 1.1905 2.5602
1 "point=28" 0.90881 -1.0792 1.1973 2.5785
1 "point=29" 0.88029 -1.1202 1.2002 2.5925
1 "point=30" 0.84886 -1.1635 1.1991 2.6022
1 "point=31" 0.81434 -1.2096 1.1938 2.6073
1 "point=32" 0.77649 -1.2587 1.1843 2.6078
1 "point=33" 0.73504 -1.3109 1.1703 2.6035
1 "point=34" 0.68964 -1.3668 1.1514 2.594
1 "point=35" 0.63987 -1.4268 1.1274 2.5792
1 "point=36" 0.58522 -1.4913 1.0978 2.5584
1 "point=37" 0.52505 -1.5611 1.062 2.5312
1 "point=38" 0.45857 -1.6369 1.0192 2.4968
1 "point=39" 0.38475 -1.7198 0.96837 2.4541
1 "point=40" 0.3023 -1.8111 0.90834 2.4021
1 "point=41" 0.20947 -1.9126 0.83737 2.3388
1 "point=42" 0.10391 -2.0266 0.75313 2.2622
1 "point=43" -0.017693 -2.1564 0.65234 2.1687
1 "point=44" -0.16019 -2.3069 0.53016 2.0538
1 "point=45" -0.33112 -2.4857 0.37908 1.9097
1 "point=46" -0.54312 -2.7054 0.18649 1.724
1 "point=47" -0.81989 -2.9896 -0.071303 1.4729
1 "point=48" -1.2146 -3.3917 -0.44748 1.1033
1 "point=49" -1.8971 -4.0814 -1.1118 0.44547
1 "point=50" -9.5085 -11.7 -8.7054 -7.1418
2 "point=1" 1.0535 -0.64017 1.1975 2.6074
2 "point=2" 1.0536 -0.64009 1.1977 2.6075
2 "point=3" 1.0537 -0.64001 1.1979 2.6076
2 "point=4" 1.0539 -0.63995 1.198 2.6077
2 "point=5" 1.054 -0.63989 1.1982 2.6077
2 "point=6" 1.0541 -0.63983 1.1984 2.6078
2 "point=7" 1.0542 -0.63979 1.1985 2.6079
2 "point=8" 1.0543 -0.63975 1.1986 2.6079
2 "point=9" 1.0544 -0.63971 1.1988 2.608
2 "point=10" 1.0545 -0.63969 1.1989 2.608
2 "point=11" 1.0546 -0.63967 1.199 2.6081
2 "point=12" 1.0547 -0.63966 1.1992 2.6081
2 "point=13" 1.0548 -0.63965 1.1993 2.6081
2 "point=14" 1.0548 -0.63965 1.1994 2.6081
2 "point=15" 1.0549 -0.63966 1.1995 2.6081
2 "point=16" 1.055 -0.63967 1.1996 2.6081
2 "point=17" 1.0551 -0.63969 1.1997 2.6081
2 "point=18" 1.0551 -0.63971 1.1998 2.6081
2 "point=19" 1.0552 -0.63975 1.1998 2.6081
2 "point=20" 1.0552 -0.63978 1.1999 2.6081
2 "point=21" 1.0553 -0.63983 1.2 2.608
2 "point=22" 1.0553 -0.63988 1.2 2.608
2 "point=23" 1.0553 -0.63993 1.2001 2.6079
2 "point=24" 1.0554 -0.63999 1.2001 2.6079
2 "point=25" 1.0554 -0.64006 1.2002 2.6078
2 "point=26" 1.0554 -0.64013 1.2002 2.6077
2 "point=27" 1.0555 -0.64021 1.2002 2.6077
2 "point=28" 1.0555 -0.64029 1.2003 2.6076
2 "point=29" 1.0555 -0.64038 1.2003 2.6075
2 "point=30" 1.0555 -0.64048 1.2003 2.6074
2 "point=31" 1.0555 -0.64058 1.2003 2.6073
2 "point=32" 1.0555 -0.64069 1.2003 2.6071
2 "point=33" 1.0555 -0.6408 1.2003 2.607
2 "point=34" 1.0555 -0.64091 1.2003 2.6069
2 "point=35" 1.0555 -0.64104 1.2002 2.6067
2 "point=36" 1.0554 -0.64116 1.2002 2.6066
2 "point=37" 1.0554 -0.64129 1.2002 2.6064
2 "point=38" 1.0554 -0.64143 1.2001 2.6063
2 "point=39" 1.0554 -0.64157 1.2001 2.6061
2 "point=40" 1.0553 -0.64172 1.2001 2.6059
2 "point=41" 1.0553 -0.64188 1.2 2.6057
2 "point=42" 1.0552 -0.64203 1.1999 2.6056
2 "point=43" 1.0552 -0.6422 1.1999 2.6053
2 "point=44" 1.0551 -0.64236 1.1998 2.6051
2 "point=45" 1.0551 -0.64254 1.1997 2.6049
2 "point=46" 1.055 -0.64271 1.1996 2.6047
2 "point=47" 1.0549 -0.64289 1.1995 2.6045
2 "point=48" 1.0549 -0.64308 1.1994 2.6042
2 "point=49" 1.0548 -0.64327 1.1993 2.604
2 "point=50" 1.0547 -0.64347 1.1992 2.6037
3 "point=1" 1.0555 -0.63967 1.2003 2.6081
3 "point=2" 1.0555 -0.63967 1.2003 2.6081
3 "point=3" 1.0555 -0.63967 1.2003 2.6081
3 "point=4" 1.0555 -0.63967 1.2003 2.6081
3 "point=5" 1.0555 -0.63967 1.2003 2.6081
3 "point=6" 1.0555 -0.63967 1.2003 2.6081
3 "point=7" 1.0555 -0.63967 1.2003 2.6081
3 "point=8" 1.0555 -0.63966 1.2003 2.6081
3 "point=9" 1.0555 -0.63966 1.2003 2.6081
3 "point=10" 1.0555 -0.63966 1.2003 2.6081
3 "point=11" 1.0555 -0.63966 1.2003 2.6081
3 "point=12" 1.0555 -0.63966 1.2003 2.6081
3 "point=13" 1.0555 -0.63966 1.2003 2.6081
3 "point=14" 1.0555 -0.63966 1.2003 2.6081
3 "point=15" 1.0555 -0.63966 1.2003 2.6081
3 "point=16" 1.0555 -0.63966 1.2003 2.6081
3 "point=17" 1.0555 -0.63966 1.2003 2.6081
3 "point=18" 1.0555 -0.63966 1.2003 2.6081
3 "point=19" 1.0555 -0.63966 1.2003 2.6081
3 "point=20" 1.0555 -0.63966 1.2003 2.6081
3 "point=21" 1.0555 -0.63966 1.2003 2.6081
3 "point=22" 1.0555 -0.63966 1.2003 2.6081
3 "point=23" 1.0555 -0.63966 1.2003 2.6081
3 "point=24" 1.0555 -0.63966 1.2003 2.6081
3 "point=25" 1.0555 -0.63966 1.2003 2.6081
3 "point=26" 1.0555 -0.63966 1.2003 2.6081
3 "point=27" 1.0555 -0.63966 1.2003 2.6081
3 "point=28" 1.0555 -0.63966 1.2003 2.6081
3 "point=29" 1.0555 -0.63966 1.2003 2.6081
3 "point=30" 1.0555 -0.63966 1.2003 2.6081
3 "point=31" 1.0555 -0.63965 1.2003 2.6081
3 "point=32" 1.0555 -0.63965 1.2003 2.6081
3 "point=33" 1.0555 -0.63965 1.2003 2.6081
3 "point=34" 1.0555 -0.63965 1.2003 2.6081
3 "point=35" 1.0555 -0.63965 1.2003 2.6081
3 "point=36" 1.0555 -0.63965 1.2003 2.6081
3 "point=37" 1.0555 -0.63965 1.2003 2.6081
3 "point=38" 1.0555 -0.63965 1.2003 2.6081
3 "point=39" 1.0555 -0.63965 1.2003 2.6081
3 "point=40" 1.0555 -0.63965 1.2003 2.6081
3 "point=41" 1.0555 -0.63965 1.2003 2.6081
3 "point=42" 1.0555 -0.63965 1.2003 2.6081
3 "point=43" 1.0555 -0.63965 1.2003 2.6081
3 "point=44" 1.0555 -0.63965 1.2003 2.6081
3 "point=45" 1.0555 -0.63965 1.2003 2.6081
3 "point=46" 1.0555 -0.63965 1.2003 2.6081
3 "point=47" 1.0555 -0.63965 1.2003 2.6081
3 "point=48" 1.0555 -0.63965 1.2003 2.6081
3 "point=49" 1.0555 -0.63965 1.2003 2.6081
3 "point=50" 1.0555 -0.63965 1.2003 2.6081
Elapsed time is 1.304303 seconds.
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_container_map ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ _______ _______ _______ ________ ________ _______
ar_opti_foc_obj 1 1 2 4 1 4 4.2243 1.0561 1.3298 1.2592 -0.63965 2.6081
ar_opti_save_frac 2 2 2 4 4 1 1.664 0.416 0.2284 0.54904 0.13278 0.62461
ar_opti_save_level 3 3 2 4 1 4 0.80247 0.20062 0.37807 1.8845 -0.15125 0.64972
xxx TABLE:ar_opti_foc_obj xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4
______ ________ ______ ______
r1 1.0555 -0.63965 1.2003 2.6081
xxx TABLE:ar_opti_save_frac xxxxxxxxxxxxxxxxxx
c1
_______
r1 0.33086
r2 0.13278
r3 0.57575
r4 0.62461
xxx TABLE:ar_opti_save_level xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4
_______ _________ ________ _______
r1 0.37401 -0.070015 -0.15125 0.649721.3 Test FF_OPTIM_MZOOM_SAVEZRONE 8 Individuals 3 Iterations 10 Points Per Iteration, 0.25 zoom in ratio
10 grid points per iteration, and 3 iterations.
% Generate the state-space and function
rng(123);
it_draws = 8; % must be even number
ar_z1 = exp(rand([it_draws,1])*3-1.5);
ar_z2 = exp(rand([it_draws,1])*3-1.5);
ar_r = (rand(it_draws,1)*10.0);
ar_beta = [rand(round(it_draws/2),1)*0.9+0.1; rand(round(it_draws/2),1)*0.9+1];
fc_util = @(x) ffi_intertemporal_util(x, ar_z1, ar_z2, ar_r, ar_beta);
% Call Function
bl_verbose = true;
bl_timer = true;
mp_mzoom_ctrlinfo = containers.Map('KeyType','char', 'ValueType','any');
mp_mzoom_ctrlinfo('it_mzoom_jnt_pnts') = 10;
mp_mzoom_ctrlinfo('it_mzoom_max_iter') = 3;
mp_mzoom_ctrlinfo('it_mzoom_zm_ratio') = 0.25;
[fl_opti_save_frac, fl_opti_save_level] = ...
ff_optim_mzoom_savezrone(fc_util, bl_verbose, bl_timer, mp_mzoom_ctrlinfo);
iter cl_row_names_a Var1 Var2 Var3 Var4 Var5 Var6 Var7 Var8
____ ______________ _______ _______ _______ _______ _______ _______ _______ _______
1 "point=1" 1e-05 1e-05 1e-05 1e-05 1e-05 1e-05 1e-05 1e-05
1 "point=2" 0.11112 0.11112 0.11112 0.11112 0.11112 0.11112 0.11112 0.11112
1 "point=3" 0.22223 0.22223 0.22223 0.22223 0.22223 0.22223 0.22223 0.22223
1 "point=4" 0.33334 0.33334 0.33334 0.33334 0.33334 0.33334 0.33334 0.33334
1 "point=5" 0.44445 0.44445 0.44445 0.44445 0.44445 0.44445 0.44445 0.44445
1 "point=6" 0.55555 0.55555 0.55555 0.55555 0.55555 0.55555 0.55555 0.55555
1 "point=7" 0.66666 0.66666 0.66666 0.66666 0.66666 0.66666 0.66666 0.66666
1 "point=8" 0.77777 0.77777 0.77777 0.77777 0.77777 0.77777 0.77777 0.77777
1 "point=9" 0.88888 0.88888 0.88888 0.88888 0.88888 0.88888 0.88888 0.88888
1 "point=10" 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999
2 "point=1" 0.28788 0.20455 0.20455 0.12122 0.37121 0.37121 0.37121 0.37121
2 "point=2" 0.32576 0.24243 0.24243 0.1591 0.40909 0.40909 0.40909 0.40909
2 "point=3" 0.36364 0.28031 0.28031 0.19698 0.44697 0.44697 0.44697 0.44697
2 "point=4" 0.40152 0.31819 0.31819 0.23485 0.48485 0.48485 0.48485 0.48485
2 "point=5" 0.4394 0.35606 0.35606 0.27273 0.52273 0.52273 0.52273 0.52273
2 "point=6" 0.47727 0.39394 0.39394 0.31061 0.5606 0.5606 0.5606 0.5606
2 "point=7" 0.51515 0.43182 0.43182 0.34849 0.59848 0.59848 0.59848 0.59848
2 "point=8" 0.55303 0.4697 0.4697 0.38637 0.63636 0.63636 0.63636 0.63636
2 "point=9" 0.59091 0.50758 0.50758 0.42424 0.67424 0.67424 0.67424 0.67424
2 "point=10" 0.62879 0.54545 0.54545 0.46212 0.71212 0.71212 0.71212 0.71212
3 "point=1" 0.34987 0.20972 0.20972 0.15479 0.46161 0.49001 0.4332 0.49001
3 "point=2" 0.3645 0.22435 0.22435 0.16943 0.47624 0.50465 0.44783 0.50465
3 "point=3" 0.37913 0.23899 0.23899 0.18406 0.49087 0.51928 0.46247 0.51928
3 "point=4" 0.39377 0.25362 0.25362 0.1987 0.50551 0.53392 0.4771 0.53392
3 "point=5" 0.4084 0.26826 0.26826 0.21333 0.52014 0.54855 0.49174 0.54855
3 "point=6" 0.42304 0.28289 0.28289 0.22797 0.53478 0.56319 0.50637 0.56319
3 "point=7" 0.43767 0.29752 0.29752 0.2426 0.54941 0.57782 0.52101 0.57782
3 "point=8" 0.45231 0.31216 0.31216 0.25724 0.56405 0.59246 0.53564 0.59246
3 "point=9" 0.46694 0.32679 0.32679 0.27187 0.57868 0.60709 0.55027 0.60709
3 "point=10" 0.48158 0.34143 0.34143 0.28651 0.59332 0.62173 0.56491 0.62173
iter cl_row_names_a Var1 Var2 Var3 Var4 Var5 Var6 Var7 Var8
____ ______________ ________ ________ ________ ________ _______ ________ _______ _______
1 "point=1" -6.5286 -4.4312 -4.9951 -2.4407 -10.415 -15.025 -7.1352 -11.589
1 "point=2" 0.34227 -0.90966 -1.148 0.28691 1.2451 -0.53687 2.835 1.245
1 "point=3" 0.7287 -0.77242 -0.98657 0.36508 1.9879 0.4163 3.452 2.0751
1 "point=4" 0.87872 -0.76818 -0.96816 0.33477 2.3463 0.89785 3.737 2.4847
1 "point=5" 0.91222 -0.83811 -1.028 0.24031 2.5277 1.1666 3.8662 2.7023
1 "point=6" 0.85648 -0.97408 -1.1562 0.085331 2.5867 1.2933 3.8847 2.7894
1 "point=7" 0.70558 -1.1905 -1.3663 -0.14666 2.5296 1.2915 3.7944 2.7552
1 "point=8" 0.41577 -1.5358 -1.7061 -0.50502 2.319 1.1277 3.5559 2.5641
1 "point=9" -0.17716 -2.1767 -2.3424 -1.1573 1.7947 0.64395 3.0074 2.0566
1 "point=10" -9.4046 -11.446 -11.608 -10.437 -7.3721 -8.4872 -6.1808 -7.0954
2 "point=1" 0.8347 -0.78233 -0.99938 0.30205 2.4239 1.0081 3.795 2.5758
2 "point=2" 0.87277 -0.76475 -0.97586 0.34105 2.4846 1.0983 3.8381 2.6488
2 "point=3" 0.89748 -0.75933 -0.96536 0.36018 2.5303 1.1709 3.8677 2.7056
2 "point=4" 0.91044 -0.76388 -0.96549 0.36559 2.5622 1.2275 3.8849 2.7478
2 "point=5" 0.91269 -0.7771 -0.97477 0.36049 2.581 1.269 3.89 2.776
2 "point=6" 0.90477 -0.79823 -0.99237 0.34672 2.5867 1.296 3.883 2.7906
2 "point=7" 0.88684 -0.8269 -1.0178 0.32535 2.5793 1.3084 3.8637 2.7913
2 "point=8" 0.85872 -0.86304 -1.051 0.29697 2.5578 1.3055 3.831 2.7776
2 "point=9" 0.81987 -0.90685 -1.0921 0.26182 2.5209 1.2862 3.7837 2.748
2 "point=10" 0.76932 -0.95877 -1.1415 0.21989 2.4664 1.2483 3.7192 2.7003
3 "point=1" 0.88992 -0.7791 -0.99528 0.33777 2.5443 1.234 3.8584 2.7524
3 "point=2" 0.8979 -0.77144 -0.98526 0.3479 2.5562 1.251 3.8683 2.7642
3 "point=3" 0.90413 -0.7658 -0.97741 0.35543 2.5661 1.2659 3.8762 2.774
3 "point=4" 0.90869 -0.762 -0.97154 0.3607 2.5741 1.2785 3.8824 2.7817
3 "point=5" 0.91163 -0.75989 -0.96746 0.36397 2.5801 1.289 3.8867 2.7874
3 "point=6" 0.91299 -0.75934 -0.96506 0.36546 2.5842 1.2974 3.8892 2.7911
3 "point=7" 0.91281 -0.76025 -0.96421 0.36532 2.5864 1.3035 3.89 2.7927
3 "point=8" 0.91112 -0.76255 -0.96482 0.3637 2.5866 1.3074 3.889 2.7922
3 "point=9" 0.90792 -0.76615 -0.96683 0.3607 2.5849 1.3091 3.8861 2.7895
3 "point=10" 0.90324 -0.77102 -0.97016 0.35641 2.5811 1.3085 3.8815 2.7847
Elapsed time is 0.997040 seconds.
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_container_map ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ______ _______ _______ ________ _________ _______
ar_opti_foc_obj 1 1 2 8 1 8 10.125 1.2656 1.731 1.3677 -0.96506 3.8892
ar_opti_save_frac 2 2 2 8 8 1 3.3843 0.42304 0.15074 0.35632 0.21333 0.59246
ar_opti_save_level 3 3 2 8 1 8 4.965 0.62062 0.71498 1.152 -0.050976 2.098
xxx TABLE:ar_opti_foc_obj xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7 c8
_______ ________ ________ _______ ______ ______ ______ ______
r1 0.91163 -0.75989 -0.96506 0.36397 2.5864 1.3074 3.8892 2.7911
xxx TABLE:ar_opti_save_frac xxxxxxxxxxxxxxxxxx
c1
_______
r1 0.4084
r2 0.26826
r3 0.28289
r4 0.21333
r5 0.54941
r6 0.59246
r7 0.50637
r8 0.56319
xxx TABLE:ar_opti_save_level xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7 c8
_______ _________ ________ _________ ______ _______ _____ _______
r1 0.53854 -0.050976 0.053729 0.0013119 1.0103 0.45895 2.098 0.855081.4 Test FF_OPTIM_MZOOM_SAVEZRONE Speed
Test Speed doing 6.25 million state-spcae points for a savings problem:
% Generate the state-space and function
rng(123);
it_draws = 6250000; % must be even number
ar_z1 = exp(rand([it_draws,1])*3-1.5);
ar_z2 = exp(rand([it_draws,1])*3-1.5);
ar_r = (rand(it_draws,1)*10.0);
ar_beta = [rand(round(it_draws/2),1)*0.9+0.1; rand(round(it_draws/2),1)*0.9+1];
% ffi_intertemporal_max is a function in ff_optim_mlsec_savezrone for testing
fc_util = @(x) ffi_intertemporal_util(x, ar_z1, ar_z2, ar_r, ar_beta);
% Call Function
bl_verbose = false;
bl_timer = true;
% set parameters
mp_mzoom_ctrlinfo = containers.Map('KeyType','char', 'ValueType','any');
mp_mzoom_ctrlinfo('it_mzoom_jnt_pnts') = 20;
mp_mzoom_ctrlinfo('it_mzoom_max_iter') = 10;
mp_mzoom_ctrlinfo('it_mzoom_zm_ratio') = 0.25;
[ar_opti_save_frac, ar_opti_save_level] = ...
ff_optim_mzoom_savezrone(fc_util, bl_verbose, bl_timer, mp_mzoom_ctrlinfo);
Elapsed time is 64.837799 seconds.
mp_container_map = containers.Map('KeyType','char', 'ValueType','any');
mp_container_map('ar_opti_save_frac') = ar_opti_save_frac;
mp_container_map('ar_opti_save_level') = ar_opti_save_level;
mp_container_map('ar_opti_save_frac_notnan') = ar_opti_save_frac(~isnan(ar_opti_save_frac));
ff_container_map_display(mp_container_map);
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_container_map ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ ________ ________ ____ __________ _______ _______ ________ ________ _______
ar_opti_save_frac 1 1 2 6.25e+06 6.25e+06 1 2.8839e+06 0.46142 0.15305 0.3317 0.090907 0.65513
ar_opti_save_frac_notnan 2 2 2 6.25e+06 6.25e+06 1 2.8839e+06 0.46142 0.15305 0.3317 0.090907 0.65513
ar_opti_save_level 3 3 2 6.25e+06 6.25e+06 1 2.9481e+06 0.47169 0.66665 1.4133 -3.9806 2.9221
figure();
histogram(ar_opti_save_frac(~isnan(ar_opti_save_frac)),100);
title('Distribution of Optimal Savings Fractions');
xlabel('Savings Fractions');
grid on;
1.5 Define Two Period Intertemporal Log Utility No Shock Utility Function
function [ar_util, ar_saveborr_level] = ...
ffi_intertemporal_util(ar_saveborr_frac, z1, z2, r, beta)
ar_saveborr_level = ar_saveborr_frac.*(z1+z2./(1+r)) - z2./(1+r);
ar_util = log(z1 - ar_saveborr_level) + beta.*log(ar_saveborr_level.*(1+r) + z2);
end