Move an ECC from final to useful as its last stage

This function uses a matrix method to move from final energy/exergy to useful energy/exergy as the last stage of an energy conversion chain.

move_last_stage_to_useful(
  .sutdata,
  wide_C_data,
  wide_eta_fu_data,
  last_stage = IEATools::iea_cols$last_stage,
  unit = IEATools::iea_cols$unit,
  final = IEATools::last_stages$final,
  useful = IEATools::last_stages$useful,
  industry_type = IEATools::row_col_types$industry_type,
  product_type = IEATools::row_col_types$product_type,
  R = IEATools::psut_cols$R,
  U_eiou = IEATools::psut_cols$U_eiou,
  U_excl_eiou = IEATools::psut_cols$U_excl_eiou,
  V = IEATools::psut_cols$V,
  Y = IEATools::psut_cols$Y,
  s_units = IEATools::psut_cols$s_units,
  matnames = IEATools::mat_meta_cols$matnames,
  matvals = IEATools::mat_meta_cols$matvals,
  sut_meta_cols = IEATools::sut_meta_cols,
  C_eiou = IEATools::template_cols$C_eiou,
  C_Y = IEATools::template_cols$C_Y,
  eta_fu = IEATools::template_cols$eta_fu,
  phi_u = IEATools::template_cols$phi_u,
  sep = IEATools::specify_notation$arrow,
  tol = 0.001,
  .Y_f_vec_hat_C_Y = ".Y_f_vec_hat_C_Y",
  .U_eiou_f_vec_hat_C_eiou = ".U_eiou_f_vec_hat_C_eiou",
  .eta_fu_hat = ".eta_fu_hat",
  .add_to_U_f = ".add_to_U_f",
  .add_to_U_eiou = ".add_to_U_eiou",
  .add_to_V_f = ".add_to_V_f",
  .useful = "_useful"
)

Arguments

.sutdata	A wide data frame of PSUT matrices that represent an energy conversion chain. Matrices should be in column identified by their names. The last stage of these ECCs should be final (not useful). .sutdata is likely the result of calling (in sequence) load_tidy_iea_df() %>% specify_all() %>% prep_psut()
wide_C_data	a wide data frame of final-to-useful allocation matrices, probably the result of calling form_C_mats().
wide_eta_fu_data	a wide data frame of final-to-useful machine efficiency matrices, probably the result of calling form_eta_fu_phi_u_vecs.
last_stage, unit	See IEATools::iea_cols$last_stage. Each of these should be a column in all of .tidy_psut_data, C_data, and eta_fu_data.
final, useful	See IEATools::last_stages.
industry_type, product_type	See IEATools::row_col_types
R, U_eiou, U_excl_eiou, V, Y, s_units	See IEATools::psut_cols. These matrices should be found in the matvals column of the .tidy_psut_data data frame.
matnames, matvals	See IEATools::mat_meta_cols.
sut_meta_cols	See IEATools::sut_meta_cols.
C_eiou, C_Y, eta_fu, phi_u	See IEATools::template_cols. C_eiou and C_Y matrices should be found in the matvals column of the C_Y_data data frame. eta_fu and phi_u should be found in the matvals column of the eta_fu_data data frame.
sep	The string separator between prefix and suffix of compound row and column names. Default is specify_notation$arrow, -> tion$arrow". The default value matches the default value for the separgument ofmatsbyname::vectorize_byname(), because matsbyname::vectorize_byname()` will be used for further manipulations.
tol	the allowable error in energy balances. Default is 1e-3.
.Y_f_vec_hat_C_Y	an internal matrix name for the product of the Y_f_vec_hat and C_Y matrices. Default is ".Y_f_vec_hat_C_Y".
.U_eiou_f_vec_hat_C_eiou	an internal matrix name for the product of the U_eiou_f_vec_hat and C_eiou matrices. Default is ".U_eiou_f_vec_hat_C_eiou".
.eta_fu_hat	an internal matrix name. Default is ".eta_fu_hat".
.add_to_U_f	an internal matrix name for the a matrix to be added to the U_excl_eiou_f matrix to form the useful form of the U_excl_eiou matrix. Default is ".add_to_U_f".
.add_to_U_eiou	an internal matrix name for the a matrix to be added to the U_eiou_f matrix to form the useful form of the U_eiou matrix. Default is ".add_to_U_eiou".
.add_to_V_f	an internal matrix name for a matrix to add to the Y_f matrix. Default is ".add_to_V_f".
.useful	A suffix applied to versions of PSUT matrices where useful is the last stage. Default is "_useful".

Value

a version of .tidy_sut_data that contains additional rows with useful final stage ECC matrices

Examples

psut_mats <- load_tidy_iea_df() %>%
  specify_all() %>%
  prep_psut()
C_data <- load_fu_allocation_data() %>%
  form_C_mats()
eta_fu_data <- load_eta_fu_data() %>%
  form_eta_fu_phi_u_vecs()
psut_mats %>%
  move_last_stage_to_useful(wide_C_data = C_data,
                            wide_eta_fu_data = eta_fu_data)
#>   Country Method Energy.type Last.stage Year
#> 1     GHA    PCM           E      Final 1971
#> 2     GHA    PCM           E      Final 2000
#> 3     ZAF    PCM           E      Final 1971
#> 4     ZAF    PCM           E      Final 2000
#> 5     GHA    PCM           E     Useful 1971
#> 6     GHA    PCM           E     Useful 2000
#> 7     ZAF    PCM           E     Useful 1971
#> 8     ZAF    PCM           E     Useful 2000
#>                                                                                                                                                                                                                                                                                                                                                       R
#> 1                                                                                                                                                                                                                                                                                                                       250.129, 0.000, 0.000, 2087.513
#> 2                                                                                                                                                                                                                                                                                                                   568.2717, 0.0000, 0.0000, 3891.0146
#> 3                                                                                                                                                                                                                                                                         33064.4311, 0.0000, 0.0000, 0.0000, 9.6303, 0.0000, 0.0000, 0.0000, 4700.4872
#> 4 2371.9304, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 666.8167, 0.0000, 0.0000, 94.6690, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1397.7644, 0.0000, 0.0000, 0.0000, 0.0000, 276.6636, 0.0000, 0.0000, 0.0000, 3389.8747, 0.0000, 0.0000, 124554.3759, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 10775.9387
#> 5                                                                                                                                                                                                                                                                                                                       250.129, 0.000, 0.000, 2087.513
#> 6                                                                                                                                                                                                                                                                                                                   568.2717, 0.0000, 0.0000, 3891.0146
#> 7                                                                                                                                                                                                                                                                         33064.4311, 0.0000, 0.0000, 0.0000, 9.6303, 0.0000, 0.0000, 0.0000, 4700.4872
#> 8 2371.9304, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 666.8167, 0.0000, 0.0000, 94.6690, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1397.7644, 0.0000, 0.0000, 0.0000, 0.0000, 276.6636, 0.0000, 0.0000, 0.0000, 3389.8747, 0.0000, 0.0000, 124554.3759, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 10775.9387
#>                                                                                                                                                                                                                                                              U_EIOU
#> 1                                                                                                                                                                                                                                   2.4936, 0.0000, 0.0000, 19.5304
#> 2                                                                                                                                                                                                                                   3.7833, 0.0000, 0.0000, 26.4235
#> 3                                                                                                                                                                                                               52.3646, 0.0000, 305.4170, 0.0000, 0.0000, 579.9369
#> 4                                                                                                                                 237.4033, 0.0000, 0.0000, 0.0860, 0.0000, 0.0000, 1107.9965, 0.0000, 0.0000, 0.0860, 0.0000, 0.0000, 1146.2597, 0.5804, 1052.3455
#> 5                                                                                                                                                                                                             0.00000, 0.24936, 1.05978, 16.60084, 0.00000, 0.00000
#> 6                                                                                                                                                                                                       0.000000, 0.378330, 1.797068, 22.724210, 0.000000, 0.000000
#> 7                                                                                                                                                                      0.000000, 1.047292, 41.001482, 0.000000, 61.083400, 0.000000, 463.949520, 0.000000, 0.000000
#> 8 0.000000, 4.748066, 0.000000, 205.116451, 0.000000, 0.000000, 0.001720, 0.000000, 0.074304, 0.000000, 0.000000, 221.599300, 0.000000, 0.000000, 0.000000, 0.000000, 0.001720, 0.000000, 0.074304, 0.000000, 894.493675, 68.775582, 0.011608, 770.286518, 0.470124
#>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    U_excl_EIOU
#> 1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        0.0000, 0.0000, 0.0000, 477.6918, 0.0000, 11.3762, 250.1290, 0.0000, 895.8479, 0.0000, 0.0000, 0.0000
#> 2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             0.0000, 0.0000, 1094.0097, 155.7554, 568.2717, 0.0000, 1152.3862, 0.0000, 0.0000
#> 3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   0.0000, 0.0000, 0.0000, 908.5068, 1.5477, 0.0000, 0.0000, 2064.5194, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 66.8769, 0.0000, 0.0000, 0.0000, 637.3944, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 33064.4311, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 4045.7551, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1203.1751, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 15567.0427, 8.0825, 0.0000, 0.0000, 0.0000, 12082.9689, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 184.4505, 0.0000
#> 4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 2771.3005, 0.0000, 105.5938, 772.7634, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 3586.9638, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 14843.3904, 0.0000, 0.0000, 0.0000, 2371.9304, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 124554.3759, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1901.8380, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 3185.8994, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1397.7644, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 94.6690, 0.0000, 0.0000, 0.0000, 0.0000, 3389.8747, 0.0000, 45046.4069, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 666.8167, 0.0000, 0.0000, 1397.7644, 0.0000, 276.6636, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 17459.1765, 0.0000, 0.0000, 0.0000, 0.0000, 276.6636, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 7695.9740, 0.0000
#> 5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 0.000000, 0.000000, 0.000000, 0.000000, 14.995950, 0.000000, 0.000000, 202.235600, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 1.920300, 10.342000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 477.691800, 0.000000, 119.174500, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 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#> 4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     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#> 5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     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#>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         Y
#> 1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     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#> 2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     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#> 3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     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#> 4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     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#> 5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     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#> 6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     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#> 7                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     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#> 2                                                 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
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