Theorem 1, Binary Optimal Allocation solution, for one planner inequality preference (one rho value)

This is the solution to the linear optimal allocation problem. Relative allocations, summed splined, inversion. solin, solution linear. relow, relative to the lowest allocation algoritm.

ffp_opt_solin_relow(
  df,
  svr_A_i,
  svr_alpha_i,
  svr_beta_i,
  fl_N_agg,
  fl_rho,
  svr_inpalc = "optiallocate",
  svr_expout = "optiexpoutcm"
)

Arguments

df

tibble data table including variables using svr names below each row is potentially an individual who will receive alternative allocations

svr_A_i

string name of the A_i variable, dot product of covariates and coefficients

svr_alpha_i

string name of the alpha_i variable, individual specific marginal-effects

svr_beta_i

string name of the beta_i variable, relative preference weight for each child

fl_N_agg

float total resource avaible for allocation, if not specific, sum by svr_N_i

fl_rho

float preference for equality for the planner

svr_inpalc

string variable name for newly generated input optimal allocation, single word no dash

svr_expout

string variable name for newly generated expected outcome, single word no dash

Value

a dataframe that expands the df inputs with additional results. a list with a dataframe and an array

• df_opti - Dataframe with various statistcs related to optimal allocation, all intermediary stats

• ar_opti_inpalc - Array where each element is an optimal choice for each individual

• ar_opti_expout - Array where each element is the expected outcome given optimal choices for each i

References

https://fanwangecon.github.io/PrjOptiAlloc/reference/ffp_opt_solin_relow.html https://fanwangecon.github.io/PrjOptiAlloc/articles/ffv_opt_solin_relow.html

Author

Fan Wang, http://fanwangecon.github.io

Examples

data(df_opt_dtgch_cbem4)
df <- df_opt_dtgch_cbem4
svr_A_i <- 'A_lin'
svr_alpha_i <- 'alpha_lin'
svr_beta_i <- 'beta'
fl_N_agg <- 10000
fl_rho <- -30
ls_lin_solu <- ffp_opt_solin_relow(df, svr_A_i, svr_alpha_i, svr_beta_i, fl_N_agg, fl_rho)
df_opti <- ls_lin_solu$df_opti
ar_opti_inpalc <- ls_lin_solu$ar_opti_inpalc
ar_opti_expout <- ls_lin_solu$ar_opti_expout
summary(df_opti)
#>   S.country             vil.id         indi.id        svymthRound
#>  Length:1043        Min.   : 1.00   Min.   :   2.0   Min.   :24  
#>  Class :character   1st Qu.: 7.00   1st Qu.: 298.5   1st Qu.:24  
#>  Mode  :character   Median :12.00   Median : 627.0   Median :24  
#>                     Mean   :12.52   Mean   : 634.8   Mean   :24  
#>                     3rd Qu.:17.00   3rd Qu.: 939.5   3rd Qu.:24  
#>                     Max.   :33.00   Max.   :1349.0   Max.   :24  
#>      alpha           alpha_log              A             A_log      
#>  Min.   :0.01014   Min.   :0.006687   Min.   :73.70   Min.   :4.287  
#>  1st Qu.:0.01014   1st Qu.:0.006687   1st Qu.:77.73   1st Qu.:4.334  
#>  Median :0.06018   Median :0.012090   Median :78.45   Median :4.343  
#>  Mean   :0.04108   Mean   :0.010321   Mean   :78.46   Mean   :4.343  
#>  3rd Qu.:0.06018   3rd Qu.:0.012090   3rd Qu.:79.15   3rd Qu.:4.351  
#>  Max.   :0.06619   Max.   :0.013940   Max.   :84.61   Max.   :4.417  
#>       beta              rank_val        rank_idx      lowest_rank_A 
#>  Min.   :0.0009588   Min.   :101.0   Min.   :   1.0   Min.   :73.7  
#>  1st Qu.:0.0009588   1st Qu.:107.5   1st Qu.: 261.5   1st Qu.:73.7  
#>  Median :0.0009588   Median :109.7   Median : 522.0   Median :73.7  
#>  Mean   :0.0009588   Mean   :109.8   Mean   : 522.0   Mean   :73.7  
#>  3rd Qu.:0.0009588   3rd Qu.:112.4   3rd Qu.: 782.5   3rd Qu.:73.7  
#>  Max.   :0.0009588   Max.   :118.3   Max.   :1043.0   Max.   :73.7  
#>  rela_slope_to_lowest rela_intercept_to_lowest rela_slope_to_lowest_cumsum
#>  Min.   :0.9119       Min.   :-979.72          Min.   :   1.0             
#>  1st Qu.:1.0000       1st Qu.:-758.11          1st Qu.: 259.7             
#>  Median :1.0000       Median :-100.33          Median : 534.2             
#>  Mean   :2.6236       Mean   :-340.13          Mean   : 856.5             
#>  3rd Qu.:5.6008       3rd Qu.: -76.32          3rd Qu.:1349.4             
#>  Max.   :5.6008       Max.   :   0.00          Max.   :2736.4             
#>  rela_intercept_to_lowest_cumsum rela_slope_to_lowest_cumsum_invert
#>  Min.   :-354758                 Min.   :0.0003654                 
#>  1st Qu.:-143999                 1st Qu.:0.0007410                 
#>  Median : -41684                 Median :0.0018720                 
#>  Mean   : -90708                 Mean   :0.0069946                 
#>  3rd Qu.: -16952                 3rd Qu.:0.0038500                 
#>  Max.   :      0                 Max.   :1.0000000                 
#>  rela_intercept_to_lowest_cumsum_invert rela_x_intercept
#>  Min.   :  0.00                         Min.   :  0.00  
#>  1st Qu.: 65.27                         1st Qu.: 79.37  
#>  Median : 78.03                         Median :106.26  
#>  Mean   : 83.86                         Mean   :107.34  
#>  3rd Qu.:106.71                         3rd Qu.:138.90  
#>  Max.   :129.65                         Max.   :209.85  
#>  opti_lowest_spline_knots    tot_devi      allocate_lowest  optiallocate   
#>  Min.   :     0           Min.   :-10000   Min.   :96.12   Min.   : 0.000  
#>  1st Qu.:  3664           1st Qu.: -6336   1st Qu.:96.12   1st Qu.: 0.000  
#>  Median : 15077           Median :  5077   Median :96.12   Median : 0.000  
#>  Mean   : 25808           Mean   : 15808   Mean   :96.12   Mean   : 9.588  
#>  3rd Qu.: 43446           3rd Qu.: 33446   3rd Qu.:96.12   3rd Qu.:16.688  
#>  Max.   :219471           Max.   :209471   Max.   :96.12   Max.   :96.115  
#>  allocate_total   optiexpoutcm  
#>  Min.   :10000   Min.   :75.05  
#>  1st Qu.:10000   1st Qu.:78.35  
#>  Median :10000   Median :79.48  
#>  Mean   :10000   Mean   :79.04  
#>  3rd Qu.:10000   3rd Qu.:79.73  
#>  Max.   :10000   Max.   :84.61  
print(ar_opti_inpalc)
#>    [1]  0.07757637  0.08698173  0.09955769  0.22957298  0.37913904  0.40937073
#>    [7]  0.57345270  0.60795674  0.78881136  0.94574472  1.18772710  1.72333858
#>   [13]  1.72596536  1.83338817  1.86118932  1.99739447  2.36937909  2.21002823
#>   [19]  2.22658220  2.25865571  2.27164659  2.32435018  2.36268923  2.49921118
#>   [25]  2.75067459  2.75232017  3.03810958  2.91468088  3.08197835  3.14794474
#>   [31]  3.16655921  3.41367458  3.48902389  3.50471723  3.53843632  3.71599977
#>   [37]  3.73606358  3.92138680  3.98521701  4.01505622  4.18350867  4.63430784
#>   [43]  4.28194105  4.28213729  5.01812142  4.68493291 29.09408447  4.92274105
#>   [49]  5.58179423  5.16405903  5.84083063  6.02879352  6.19193048  5.67960670
#>   [55]  6.23528873  5.72368989  6.28782991  5.76214950  5.99376777  6.30171654
#>   [61]  6.30598890  6.37030971  6.42785194  6.53102484  6.61995374  6.79393166
#>   [67]  6.87878444  7.00501796  7.03350594  7.03660087  7.12020055  7.12292544
#>   [73]  7.33447990  8.06910174  7.53142033  7.59797544  7.79840328  7.87222756
#>   [79]  8.72175751  8.77789413  8.78121516  8.04649984  8.57290221  9.40242763
#>   [85]  8.65136889  8.69844889  8.69940765  9.63269419  8.83097040  8.91931059
#>   [91]  8.93645327  8.93839321  9.97909466  9.14270094 10.17345907 10.27500454
#>   [97]  9.41172195 10.45913145  9.57359206 10.62599646  9.77372554 10.76984561
#>  [103] 10.77784134 10.00708752 11.15908938 10.25827901 11.26136566 10.28143776
#>  [109] 10.34634728 10.38063265 10.39612975 10.40978502 10.42547836 11.50581362
#>  [115] 11.54641516 10.66689446 11.70847286 11.71295640 11.74801982 10.74157938
#>  [121] 10.81955546 10.83185951 11.90540282 66.88513801 10.96806466 12.06267789
#>  [127] 12.06384040 11.03044552 12.10646785 12.11030383 12.12062457 12.16006361
#>  [133] 12.19885508 11.16655255 11.19155312 11.20685398 11.22487974 11.29200112
#>  [139] 12.43871159 12.49006558 11.39198096 11.51229654 11.52246441 11.73848746
#>  [145] 11.78740929 12.94238712 11.96730516 11.96875451 13.14974575 13.17435582
#>  [151] 13.39919220 13.69861428 12.50746092 12.52838537 13.75199419 13.77298414
#>  [157] 12.56858868 12.64550789 13.91032384 12.71719599 12.81793835 12.81987829
#>  [163] 14.14880199 14.17576175 14.18343371 13.05159468 13.17714137 14.49468750
#>  [169] 13.23566479 14.53804576 13.26646275 14.62916256 14.64096959 13.39704431
#>  [175] 14.71044888 14.80496996 13.55756320 14.87796145 15.15296463 15.26644974
#>  [181] 14.00898629 15.66784900 15.67349504 15.70331945 15.76545057 15.83066218
#>  [187] 15.90003355 15.91399910 14.52502456 15.97345675 16.02075891 14.67886298
#>  [193] 14.69745501 14.70791724 16.14191597 16.18421965 16.28692763 16.34884290
#>  [199] 16.34927460 14.92443089 16.39892645 15.01849278 15.10383616 16.63003175
#>  [205] 16.64591528 16.72987508 16.75491686 17.01065691 17.07767858 15.58500034
#>  [211] 17.10804262 17.40149489 16.13426710 17.96975916 16.60157977 18.40184624
#>  [217] 18.42262033 16.82052396 18.46192676 18.52522039 18.68079332 17.03743008
#>  [223] 18.74654456 18.97265137 19.02305871 19.04042853 17.39506320 19.10115661
#>  [229] 19.16188469 19.16210054 19.16604445 19.23201154 19.29379420 19.31937561
#>  [235] 19.40301163 17.73682918 19.47591988 19.52651839 19.56231262 17.97959651
#>  [241] 19.72450292 19.76340233 19.82156486 19.95784998 19.98172925 19.98694359
#>  [247] 20.00995945 18.36272080 18.37492673 20.15977842 20.17885038 20.20410801
#>  [253] 20.39790811 20.40752274 18.64704267 20.46228100 20.48083801 20.67593322
#>  [259] 20.70554178 18.95587451 20.81754060 20.84322994 19.07957937 19.13189049
#>  [265] 21.03394954 19.18584720 19.21723387 21.09246054 21.11185627 21.26326945
#>  [271] 21.26421611 21.39688110 21.43267533 19.57334196 21.49437474 21.61307419
#>  [277] 19.76370005 21.80657519 22.06796128 22.18025920 22.27456442 22.30057753
#>  [283] 22.34309706 20.51698018 22.51944409 22.82140704 22.86168480 22.98176260
#>  [289] 23.08257727 23.12477302 23.15875719 23.16642914 23.20116879 23.27959048
#>  [295] 23.28631578 23.34758349 23.64209033 23.66553790 23.66564582 23.74917392
#>  [301] 23.91795692 23.96420450 23.99724201 24.00629232 24.12574725 24.21013875
#>  [307] 24.25009273 24.35334034 24.42762695 24.62293801 24.79436981 24.95899305
#>  [313] 22.77613371 25.36892767 25.42144417 25.47058107 25.73407632 25.87592423
#>  [319] 25.93249256 26.15562680 26.26238661 26.29818084 26.29861254 26.41966168
#>  [325] 26.51267179 26.79483197 26.81838746 26.97298906 26.99473449 27.03341805
#>  [331] 27.05759642 27.08647417 27.10416777 27.21284557 27.24769314 27.25377089
#>  [337] 27.33983985 27.40539992 27.76852265 27.79113149 27.81968547 28.74521058
#>  [343] 28.91547986 29.11965007 29.17038118 29.17527174 29.20307023 29.23878122
#>  [349] 29.27435959 29.31144893 29.59849967 29.86010161 30.05211633 30.13180845
#>  [355] 30.13267185 30.19702006 30.25871948 30.33927500 30.34981160 30.36474848
#>  [361] 30.45638023 30.72457487 30.75793615 31.02388902 31.07578264 31.30648091
#>  [367] 31.36623766 31.41005230 31.41472700 31.44457609 31.47769685 31.47983069
#>  [373] 31.50997888 31.63561948 31.72927714 31.97702146 31.99087908 32.01910928
#>  [379] 32.05490351 32.07005624 32.26547524 32.29381336 32.59301959 32.79578676
#>  [385] 32.96327465 32.98183166 33.03361735 33.08572682 33.17522473 33.23127811
#>  [391] 33.42796753 33.60207279 33.97907783 34.03672542 34.05622908 34.05717573
#>  [397] 34.10428672 34.52740673 34.79816691 34.91548800 34.98464351 35.09650973
#>  [403] 35.52135656 35.59210629 35.71058988 35.73052525 35.84452531 35.92243204
#>  [409] 36.05893301 36.38369597 36.43526581 37.89785242 37.99332015 39.04043403
#>  [415] 39.06931179 39.30692653 39.40485187 39.69360475 40.09095218 40.35169071
#>  [421] 40.53006366 41.48532993 41.61767115 41.72869864 41.84750601 41.99040850
#>  [427] 42.15203450 42.31230682 42.49184227 43.04700440 43.41823079 43.42536311
#>  [433] 43.52958206 43.75995655 44.31787539 44.73726735 45.33716609 45.54166008
#>  [439] 46.06216580 46.22786831 46.34367843 47.70258573 47.85389098 47.92104527
#>  [445] 48.12113896 49.11209154 50.86289140 51.31969648 51.85651745 52.00857818
#>  [451] 53.66688288 53.78077502 53.87518816 54.07957422 54.57568573 55.37570285
#>  [457] 55.69941122 56.74460711 59.43684030 59.75852277 60.61170394 62.79799515
#>  [463] 66.89981739 78.77746473 80.91304951 81.64666783 96.11543459  0.00000000
#>  [469]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [475]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [481]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [487]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [493]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [499]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [505]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [511]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [517]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [523]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [529]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [535]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [541]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [547]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [553]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [559]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [565]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [571]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [577]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [583]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [589]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [595]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [601]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [607]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [613]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [619]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [625]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [631]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [637]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [643]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [649]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [655]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [661]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [667]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [673]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [679]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [685]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [691]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [697]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [703]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [709]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [715]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [721]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [727]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [733]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [739]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [745]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [751]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [757]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [763]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [769]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [775]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [781]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [787]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [793]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [799]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [805]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [811]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [817]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [823]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [829]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [835]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [841]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [847]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [853]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [859]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [865]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [871]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [877]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [883]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [889]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [895]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [901]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [907]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [913]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [919]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [925]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [931]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [937]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [943]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [949]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [955]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [961]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [967]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [973]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [979]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [985]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [991]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#>  [997]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> [1003]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> [1009]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> [1015]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> [1021]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> [1027]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> [1033]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> [1039]  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
print(ar_opti_expout)
#>    [1] 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650
#>    [9] 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650
#>   [17] 79.48187 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650
#>   [25] 79.72650 79.72650 79.48187 79.72650 79.72650 79.72650 79.72650 79.72650
#>   [33] 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650
#>   [41] 79.72650 79.48187 79.72650 79.72650 79.48187 79.72650 75.04579 79.72650
#>   [49] 79.48187 79.72650 79.48187 79.48187 79.48187 79.72650 79.48187 79.72650
#>   [57] 79.48187 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650
#>   [65] 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650 79.72650
#>   [73] 79.72650 79.48187 79.72650 79.72650 79.72650 79.72650 79.48187 79.48187
#>   [81] 79.48187 79.72650 79.72650 79.48187 79.72650 79.72650 79.72650 79.48187
#>   [89] 79.72650 79.72650 79.72650 79.72650 79.48187 79.72650 79.48187 79.48187
#>   [97] 79.72650 79.48187 79.72650 79.48187 79.72650 79.48187 79.48187 79.72650
#>  [105] 79.48187 79.72650 79.48187 79.72650 79.72650 79.72650 79.72650 79.72650
#>  [113] 79.72650 79.48187 79.48187 79.72650 79.48187 79.48187 79.48187 79.72650
#>  [121] 79.72650 79.72650 79.48187 75.04579 79.72650 79.48187 79.48187 79.72650
#>  [129] 79.48187 79.48187 79.48187 79.48187 79.48187 79.72650 79.72650 79.72650
#>  [137] 79.72650 79.72650 79.48187 79.48187 79.72650 79.72650 79.72650 79.72650
#>  [145] 79.72650 79.48187 79.72650 79.72650 79.48187 79.48187 79.48187 79.48187
#>  [153] 79.72650 79.72650 79.48187 79.48187 79.72650 79.72650 79.48187 79.72650
#>  [161] 79.72650 79.72650 79.48187 79.48187 79.48187 79.72650 79.72650 79.48187
#>  [169] 79.72650 79.48187 79.72650 79.48187 79.48187 79.72650 79.48187 79.48187
#>  [177] 79.72650 79.48187 79.48187 79.48187 79.72650 79.48187 79.48187 79.48187
#>  [185] 79.48187 79.48187 79.48187 79.48187 79.72650 79.48187 79.48187 79.72650
#>  [193] 79.72650 79.72650 79.48187 79.48187 79.48187 79.48187 79.48187 79.72650
#>  [201] 79.48187 79.72650 79.72650 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [209] 79.48187 79.72650 79.48187 79.48187 79.72650 79.48187 79.72650 79.48187
#>  [217] 79.48187 79.72650 79.48187 79.48187 79.48187 79.72650 79.48187 79.48187
#>  [225] 79.48187 79.48187 79.72650 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [233] 79.48187 79.48187 79.48187 79.72650 79.48187 79.48187 79.48187 79.72650
#>  [241] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.72650
#>  [249] 79.72650 79.48187 79.48187 79.48187 79.48187 79.48187 79.72650 79.48187
#>  [257] 79.48187 79.48187 79.48187 79.72650 79.48187 79.48187 79.72650 79.72650
#>  [265] 79.48187 79.72650 79.72650 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [273] 79.48187 79.72650 79.48187 79.48187 79.72650 79.48187 79.48187 79.48187
#>  [281] 79.48187 79.48187 79.48187 79.72650 79.48187 79.48187 79.48187 79.48187
#>  [289] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [297] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [305] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [313] 79.72650 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [321] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [329] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [337] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [345] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [353] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [361] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [369] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [377] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [385] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [393] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [401] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [409] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [417] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [425] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [433] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [441] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [449] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [457] 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187 79.48187
#>  [465] 79.48187 79.48187 79.48187 79.73361 79.73949 79.74290 79.74462 79.75370
#>  [473] 75.09272 79.78232 79.78882 79.79048 79.80031 79.80101 79.80675 75.12223
#>  [481] 79.86010 79.86645 79.87024 79.88274 79.90824 79.66663 79.91848 79.95498
#>  [489] 79.96100 79.96759 79.97696 79.97840 79.99233 79.99614 80.00759 80.00903
#>  [497] 80.02731 80.05854 80.07188 75.37717 80.08700 80.11655 80.11942 80.12160
#>  [505] 80.12482 78.30534 80.17500 80.18398 80.18548 80.18778 80.18820 78.36651
#>  [513] 80.20961 80.23640 80.24788 80.27036 80.27731 80.27990 80.31003 75.61525
#>  [521] 80.33670 80.33879 78.49902 80.33999 80.36395 78.53825 75.67069 80.40841
#>  [529] 80.43347 78.59838 75.73533 80.47507 80.49621 78.67697 78.68392 78.68933
#>  [537] 78.70594 78.71795 80.56575 80.56593 80.58673 80.59173 80.59361 78.74854
#>  [545] 78.77002 75.88659 78.78695 78.80396 78.82172 78.83592 80.69424 78.85325
#>  [553] 78.86800 78.86823 78.87078 78.87194 78.87287 80.73063 78.88209 78.89190
#>  [561] 76.00335 78.89635 78.90078 80.75127 80.75767 78.90827 78.91993 78.92779
#>  [569] 78.93241 78.93804 76.05076 78.95007 78.95918 76.06796 78.96186 78.97775
#>  [577] 80.83032 78.98827 80.84773 79.00606 76.12665 76.12671 79.02993 80.88571
#>  [585] 79.03353 79.03756 79.03765 79.04114 79.05274 76.15721 80.90860 80.92110
#>  [593] 79.06816 80.92867 80.93852 80.94572 79.09631 76.21354 79.12616 79.13129
#>  [601] 79.13273 79.13894 76.25126 79.15316 79.15338 79.15546 81.01891 76.28828
#>  [609] 76.29115 76.29224 81.05269 79.19876 79.19981 79.20893 76.30844 76.32309
#>  [617] 76.32418 79.22959 79.23844 79.25681 79.26559 79.27642 81.15855 76.39433
#>  [625] 81.16084 81.16500 79.31479 79.31638 76.41246 79.32019 81.18115 76.41605
#>  [633] 79.32422 76.43025 79.33963 79.33995 79.34540 76.43804 79.35078 79.35601
#>  [641] 81.21669 79.37234 79.37470 79.37765 79.39466 79.40065 76.49277 79.44210
#>  [649] 79.44991 79.45076 76.54566 79.47582 79.47808 79.47947 79.48041 81.35327
#>  [657] 76.57810 79.49263 76.58325 79.49711 79.50418 76.60510 79.52303 79.52375
#>  [665] 79.52490 76.61658 76.61659 76.61918 79.53534 79.53994 81.40724 79.54352
#>  [673] 79.55294 79.56398 76.65557 79.57731 79.58435 79.59862 79.60146 76.69829
#>  [681] 79.61933 79.62682 79.62859 79.65780 76.75031 76.75675 79.69165 79.69735
#>  [689] 81.56994 79.70255 76.79124 79.72859 76.81346 79.73708 76.82148 76.82485
#>  [697] 79.75815 76.85751 76.85863 79.78821 76.86545 79.79678 79.80908 76.88868
#>  [705] 79.81400 79.81436 79.82265 76.89814 76.90105 79.84352 81.72991 79.86052
#>  [713] 76.93587 76.93914 79.86734 79.87958 79.88253 76.95930 81.76768 76.96770
#>  [721] 76.97398 76.97410 76.97503 76.98112 76.98962 76.99725 77.02021 79.95700
#>  [729] 77.03199 77.03324 77.03451 77.04278 77.06757 77.07086 77.07613 77.08902
#>  [737] 80.02808 77.11752 77.13914 81.95830 77.16132 77.17730 77.18297 77.18901
#>  [745] 77.19486 77.20135 77.20334 80.15564 80.15633 77.22010 77.22304 77.22735
#>  [753] 80.16541 77.23973 77.24234 77.25986 77.26350 77.27399 77.27682 80.21936
#>  [761] 77.28502 82.10624 77.30111 77.30315 80.24425 77.32263 77.32540 77.32702
#>  [769] 77.32958 77.34027 77.35112 77.36254 77.37350 77.38668 77.39062 80.35552
#>  [777] 77.42750 77.42873 80.37793 77.43854 77.45809 77.46988 82.31699 77.49317
#>  [785] 77.51610 80.46622 77.53989 77.54580 77.55284 77.55598 77.56532 80.52032
#>  [793] 77.57291 77.57799 77.59097 77.59099 77.59660 77.60119 77.60812 77.61631
#>  [801] 77.61664 77.62204 77.62369 80.57714 77.62612 77.62756 77.62891 77.63110
#>  [809] 77.63177 77.63213 77.63297 77.63792 77.63885 82.48301 77.64710 77.65687
#>  [817] 77.66538 77.66615 77.68510 77.68519 77.70306 77.70417 80.66141 80.66803
#>  [825] 77.72919 77.74582 77.74805 77.75001 77.75143 77.75550 77.75579 77.76104
#>  [833] 77.76381 80.72257 77.76772 77.77087 77.77210 80.73363 77.78097 77.79892
#>  [841] 77.80050 77.80788 77.80860 77.80883 77.81151 82.66567 77.81571 80.77672
#>  [849] 77.82360 77.82370 77.82972 77.83373 77.83778 77.83833 77.84043 77.84483
#>  [857] 77.84659 77.85771 77.86707 77.87311 77.87956 77.89290 77.89367 77.89820
#>  [865] 77.90775 77.91190 77.91305 77.91481 77.93637 77.93943 77.94175 77.94202
#>  [873] 77.94912 80.91568 77.95091 77.97456 77.97914 77.98546 77.99213 77.99844
#>  [881] 78.00086 78.00488 78.00809 78.01781 78.02450 81.00556 78.04462 78.06627
#>  [889] 78.07807 78.07829 78.07957 78.10010 78.10046 78.10260 78.10574 78.11050
#>  [897] 78.11672 78.11777 78.12668 78.12771 78.12803 78.12885 78.12898 78.13083
#>  [905] 78.13404 78.13666 78.13772 78.14546 78.14648 78.15364 78.15403 78.15454
#>  [913] 78.15990 78.17050 78.17562 78.17896 78.17959 78.19593 81.19769 78.22488
#>  [921] 78.22555 78.23050 78.23145 78.23374 78.24562 78.24722 78.24788 78.24811
#>  [929] 78.25378 78.25383 78.25650 78.26178 78.26257 78.26494 78.26499 78.26931
#>  [937] 78.27184 78.28061 78.28385 78.28530 78.28541 78.28645 78.28777 78.30397
#>  [945] 78.31157 78.32274 78.32474 78.32847 78.33612 78.34869 78.35063 78.35537
#>  [953] 78.36614 78.36829 78.37307 78.38329 78.39587 78.40152 78.40636 78.41266
#>  [961] 78.41340 78.41352 78.41607 78.42531 78.42745 78.42996 78.43560 78.43775
#>  [969] 78.44502 78.46064 78.46077 78.46454 78.47215 78.47367 78.48198 78.48729
#>  [977] 78.50209 78.50790 78.50797 78.50832 78.51844 78.53105 81.51984 78.54907
#>  [985] 78.54947 78.55185 78.55828 78.55875 78.56212 78.57038 78.58993 78.59732
#>  [993] 78.59735 78.60408 78.61014 78.61157 78.62410 78.63539 78.68103 78.68294
#> [1001] 78.68350 78.68774 78.69236 78.69330 78.70518 78.73668 78.74697 78.75868
#> [1009] 78.76318 78.78106 78.78464 81.78194 78.82434 78.83378 78.84038 78.87895
#> [1017] 78.88154 78.89056 78.89956 78.90591 81.93535 78.94894 78.95178 78.95991
#> [1025] 78.96625 78.97179 78.97390 78.97448 78.99004 79.03804 79.05826 79.06311
#> [1033] 79.08655 79.11331 82.14205 79.16941 79.17783 79.18255 79.20875 79.34690
#> [1041] 79.44826 79.52362 84.60875