Prepare for PSUT analysis
Matthew Kuperus Heun
2024-02-03
prep_psut.RmdIntroduction
After loading IEA data and ensuring that the data are balanced (see
the vignette
about loading data) and specifying many of the flows (see the vignette
about specifying flows), the analyst can prepare for physical
supply-use table (PSUT) analysis of an energy conversion chain. This
vignette shows how to use the functions in the IEATools
package for that purpose.
Adding PSUT matrix names (add_psut_matnames())
The first step to converting the IEA extended energy balance data
into PSUT matrices is identifying the matrix in which each datum
belongs. The add_psut_matnames() function performs this
task. It adds a column named “matnames” (by default but changeable by
the user) that contains one of R, U,
V, or Y to identify the Resources, Use, Make,
or Final demand matrix.
load_tidy_iea_df() %>%
add_psut_matnames() %>%
glimpse()
#> Rows: 403
#> Columns: 12
#> $ Country <chr> "GHA", "GHA", "GHA", "GHA", "GHA", "GHA", "GHA"…
#> $ Method <chr> "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM"…
#> $ Energy.type <chr> "E", "E", "E", "E", "E", "E", "E", "E", "E", "E…
#> $ Last.stage <chr> "Final", "Final", "Final", "Final", "Final", "F…
#> $ Year <dbl> 1971, 2000, 1971, 2000, 1971, 2000, 2000, 2000,…
#> $ Ledger.side <chr> "Supply", "Supply", "Supply", "Supply", "Supply…
#> $ Flow.aggregation.point <chr> "Total primary energy supply", "Total primary e…
#> $ Flow <chr> "Production", "Production", "Production", "Prod…
#> $ Product <chr> "Primary solid biofuels", "Primary solid biofue…
#> $ Unit <chr> "TJ", "TJ", "TJ", "TJ", "TJ", "TJ", "TJ", "TJ",…
#> $ E.dot <dbl> 87399.9985, 162908.9993, 10472.4010, 23792.3995…
#> $ matnames <chr> "V", "V", "V", "V", "R", "R", "R", "R", "R", "R…Note that when a matnames column already exists in
.tidy_iea_df, add_psut_matnames() returns the
input data frame without modification. This behavior allows other matrix
naming conventions.
Add matrix metadata (add_row_col_meta())
The next step is to add information to identify the rows and columns
for each datum. The add_row_col_meta() function performs
this task by adding rowname, colname,
rowtype, and coltype columns which identify
the names and types of rows and columns in the PSUT matrices.
add_row_col_meta() should be called after calling
add_psut_matnames(), because it relies on the the
matnames column to determine names and types.
load_tidy_iea_df() %>%
add_psut_matnames() %>%
add_row_col_meta() %>%
glimpse()
#> Rows: 403
#> Columns: 16
#> $ Country <chr> "GHA", "GHA", "GHA", "GHA", "GHA", "GHA", "GHA"…
#> $ Method <chr> "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM"…
#> $ Energy.type <chr> "E", "E", "E", "E", "E", "E", "E", "E", "E", "E…
#> $ Last.stage <chr> "Final", "Final", "Final", "Final", "Final", "F…
#> $ Year <dbl> 1971, 2000, 1971, 2000, 1971, 2000, 2000, 2000,…
#> $ Ledger.side <chr> "Supply", "Supply", "Supply", "Supply", "Supply…
#> $ Flow.aggregation.point <chr> "Total primary energy supply", "Total primary e…
#> $ Flow <chr> "Production", "Production", "Production", "Prod…
#> $ Product <chr> "Primary solid biofuels", "Primary solid biofue…
#> $ Unit <chr> "TJ", "TJ", "TJ", "TJ", "TJ", "TJ", "TJ", "TJ",…
#> $ E.dot <dbl> 87399.9985, 162908.9993, 10472.4010, 23792.3995…
#> $ matnames <chr> "V", "V", "V", "V", "R", "R", "R", "R", "R", "R…
#> $ rownames <chr> "Production", "Production", "Production", "Prod…
#> $ colnames <chr> "Primary solid biofuels", "Primary solid biofue…
#> $ rowtypes <chr> "Industry", "Industry", "Industry", "Industry",…
#> $ coltypes <chr> "Product", "Product", "Product", "Product", "Pr…Note that if all of rowname, colname,
rowtype, or coltype columns are already
present in .tidy_iea_data, add_row_col_meta()
returns the input data frame without modification. This behavior allows
other matrix row, column, rowtype, and coltype naming conventions.
If some but not all of rowname, colname,
rowtype, and coltype columns are present in in
.tidy_iea_data, add_row_col_meta()returns an
error.
Collapse to matrices (collapse_to_tidy_psut())
After identifying row and column names and types, the next step is to
collapse the data into PSUT matrices. The
collapse_to_tidy_psut() function performs this task using
the matsindf::collapse_to_matrices() function internally.
The matvals column is added to the data frame and contain
matrix names for each row of the data frame.
collapse_to_tidy_psut() ensures that all entries in each
matrix are non-negative.
Tidy_PSUT <-
load_tidy_iea_df() %>%
specify_all() %>%
add_psut_matnames() %>%
add_row_col_meta() %>%
collapse_to_tidy_psut()
Tidy_PSUT %>%
glimpse()
#> Rows: 20
#> Columns: 7
#> $ Country <chr> "GHA", "GHA", "GHA", "GHA", "GHA", "GHA", "GHA", "GHA", "G…
#> $ Method <chr> "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "P…
#> $ Energy.type <chr> "E", "E", "E", "E", "E", "E", "E", "E", "E", "E", "E", "E"…
#> $ Last.stage <chr> "Final", "Final", "Final", "Final", "Final", "Final", "Fin…
#> $ Year <dbl> 1971, 1971, 1971, 1971, 1971, 2000, 2000, 2000, 2000, 2000…
#> $ matnames <chr> "R", "U_EIOU", "U_feed", "V", "Y", "R", "U_EIOU", "U_feed"…
#> $ matvals <list> <<matrix[9 x 8]>>, <<matrix[2 x 2]>>, <<matrix[6 x 5]>>, …
class(Tidy_PSUT$matvals[[1]])
#> [1] "matrix" "array"
Tidy_PSUT$matvals[[1]]
#> Aviation gasoline Crude oil
#> Imports [of Aviation gasoline] 44.7988 0.0
#> Imports [of Crude oil] 0.0000 38359.8
#> Imports [of Kerosene type jet fuel excl. biofuels] 0.0000 0.0
#> Imports [of Lubricants] 0.0000 0.0
#> Imports [of Other kerosene] 0.0000 0.0
#> Resources [of Hydro] 0.0000 0.0
#> Resources [of Primary solid biofuels] 0.0000 0.0
#> Statistical differences 0.0000 0.0
#> Stock changes [of Gas/diesel oil excl. biofuels] 0.0000 0.0
#> Kerosene type jet fuel excl. biofuels
#> Imports [of Aviation gasoline] 0.0000
#> Imports [of Crude oil] 0.0000
#> Imports [of Kerosene type jet fuel excl. biofuels] 892.0019
#> Imports [of Lubricants] 0.0000
#> Imports [of Other kerosene] 0.0000
#> Resources [of Hydro] 0.0000
#> Resources [of Primary solid biofuels] 0.0000
#> Statistical differences 0.0000
#> Stock changes [of Gas/diesel oil excl. biofuels] 0.0000
#> Lubricants Other kerosene
#> Imports [of Aviation gasoline] 0.0000 0.0000
#> Imports [of Crude oil] 0.0000 0.0000
#> Imports [of Kerosene type jet fuel excl. biofuels] 0.0000 0.0000
#> Imports [of Lubricants] 755.9979 0.0000
#> Imports [of Other kerosene] 0.0000 43.7981
#> Resources [of Hydro] 0.0000 0.0000
#> Resources [of Primary solid biofuels] 0.0000 0.0000
#> Statistical differences 0.0000 0.0000
#> Stock changes [of Gas/diesel oil excl. biofuels] 0.0000 0.0000
#> Hydro [from Resources]
#> Imports [of Aviation gasoline] 0.0
#> Imports [of Crude oil] 0.0
#> Imports [of Kerosene type jet fuel excl. biofuels] 0.0
#> Imports [of Lubricants] 0.0
#> Imports [of Other kerosene] 0.0
#> Resources [of Hydro] 10472.4
#> Resources [of Primary solid biofuels] 0.0
#> Statistical differences 0.0
#> Stock changes [of Gas/diesel oil excl. biofuels] 0.0
#> Primary solid biofuels [from Resources]
#> Imports [of Aviation gasoline] 0
#> Imports [of Crude oil] 0
#> Imports [of Kerosene type jet fuel excl. biofuels] 0
#> Imports [of Lubricants] 0
#> Imports [of Other kerosene] 0
#> Resources [of Hydro] 0
#> Resources [of Primary solid biofuels] 87400
#> Statistical differences 0
#> Stock changes [of Gas/diesel oil excl. biofuels] 0
#> Gas/diesel oil excl. biofuels
#> Imports [of Aviation gasoline] 0.0000
#> Imports [of Crude oil] 0.0000
#> Imports [of Kerosene type jet fuel excl. biofuels] 0.0000
#> Imports [of Lubricants] 0.0000
#> Imports [of Other kerosene] 0.0000
#> Resources [of Hydro] 0.0000
#> Resources [of Primary solid biofuels] 0.0000
#> Statistical differences 822.7020
#> Stock changes [of Gas/diesel oil excl. biofuels] 476.2987
#> attr(,"rowtype")
#> [1] "Industry"
#> attr(,"coltype")
#> [1] "Product"Generate S_units matrices
(extract_S_units_from_tidy())
A matrix of Products and Units can be obtained from a tidy IEA data
frame with the extract_S_units_from_tidy() function.
S_units_df <- load_tidy_iea_df() %>%
specify_all() %>%
extract_S_units_from_tidy()
S_units_df %>%
glimpse()
#> Rows: 4
#> Columns: 6
#> $ Country <chr> "GHA", "GHA", "ZAF", "ZAF"
#> $ Method <chr> "PCM", "PCM", "PCM", "PCM"
#> $ Energy.type <chr> "E", "E", "E", "E"
#> $ Last.stage <chr> "Final", "Final", "Final", "Final"
#> $ Year <dbl> 1971, 2000, 1971, 2000
#> $ S_units <list> <<matrix[16 x 1]>>, <<matrix[18 x 1]>>, <<matrix[24 x 1]>>…
S_units_df$S_units[[1]]
#> TJ
#> Aviation gasoline 1
#> Charcoal 1
#> Crude oil 1
#> Electricity 1
#> Fuel oil 1
#> Gas/diesel oil excl. biofuels 1
#> Hydro 1
#> Hydro [from Resources] 1
#> Kerosene type jet fuel excl. biofuels 1
#> Liquefied petroleum gases (LPG) 1
#> Lubricants 1
#> Motor gasoline excl. biofuels 1
#> Other kerosene 1
#> Primary solid biofuels 1
#> Primary solid biofuels [from Resources] 1
#> Refinery gas 1
#> attr(,"rowtype")
#> [1] "Product"
#> attr(,"coltype")
#> [1] "Unit"Putting it all together (prep_psut())
prep_psut() is a convenience function. It converts a
tidy IEA data frame that has gone through specify_all()
into a PSUT data frame by collapsing the IEA data into PSUT matrices (R,
U, V, and Y).
This function bundles several others: 1.
add_psut_matnames() 2. add_row_col_meta() 3.
collapse_to_tidy_psut()
Furthermore, it extracts S_units matrices using
extract_S_units_from_tidy() and adds those matrices to the
data frame.
Simple <- load_tidy_iea_df() %>%
specify_all() %>%
prep_psut() %>%
pivot_longer(cols = c(R, U_EIOU, U_feed, V, Y, S_units), names_to = "matnames", values_to = "matvals")
S_units <- load_tidy_iea_df() %>%
specify_all() %>%
extract_S_units_from_tidy()
Complicated <- load_tidy_iea_df() %>%
specify_all() %>%
add_psut_matnames() %>%
add_row_col_meta() %>%
collapse_to_tidy_psut() %>%
spread(key = matnames, value = matvals) %>%
full_join(S_units, by = c("Method", "Energy.type", "Last.stage",
"Country", "Year")) %>%
gather(key = matnames, value = matvals, R, U_EIOU, U_feed,
V, Y, S_units)
# Simple and Complicated are same.
full_join(Simple %>% rename(matval_simple = matvals),
Complicated %>% rename(matval_complicated = matvals),
by = c("Method", "Energy.type", "Last.stage", "Country", "Year", "matnames")) %>%
dplyr::mutate(
same = matsbyname::equal_byname(matval_simple, matval_complicated)
) %>%
magrittr::extract2("same") %>%
as.logical() %>%
all()
#> [1] TRUE
Simple %>%
glimpse()
#> Rows: 24
#> Columns: 9
#> $ Country <chr> "GHA", "GHA", "GHA", "GHA", "GHA", "GHA", "GHA", "GHA", "G…
#> $ Method <chr> "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "P…
#> $ Energy.type <chr> "E", "E", "E", "E", "E", "E", "E", "E", "E", "E", "E", "E"…
#> $ Last.stage <chr> "Final", "Final", "Final", "Final", "Final", "Final", "Fin…
#> $ Year <dbl> 1971, 1971, 1971, 1971, 1971, 1971, 2000, 2000, 2000, 2000…
#> $ U <list> <<matrix[8 x 5]>>, <<matrix[8 x 5]>>, <<matrix[8 x 5]>>, …
#> $ r_EIOU <list> <<matrix[8 x 5]>>, <<matrix[8 x 5]>>, <<matrix[8 x 5]>>, …
#> $ matnames <chr> "R", "U_EIOU", "U_feed", "V", "Y", "S_units", "R", "U_EIOU…
#> $ matvals <list> <<matrix[9 x 8]>>, <<matrix[2 x 2]>>, <<matrix[6 x 5]>>, …
# U_EIOU for Ghana in 1971
Simple$matvals[[5]]
#> Exports to World aviation bunkers [of Aviation gasoline]
#> Aviation gasoline 44.7988
#> Charcoal 0.0000
#> Crude oil 0.0000
#> Electricity 0.0000
#> Fuel oil 0.0000
#> Gas/diesel oil excl. biofuels 0.0000
#> Kerosene type jet fuel excl. biofuels 0.0000
#> Liquefied petroleum gases (LPG) 0.0000
#> Lubricants 0.0000
#> Motor gasoline excl. biofuels 0.0000
#> Other kerosene 0.0000
#> Primary solid biofuels 0.0000
#> Residential Stock changes [of Crude oil]
#> Aviation gasoline 0.0000 0.0000
#> Charcoal 4989.5980 0.0000
#> Crude oil 0.0000 852.4409
#> Electricity 590.4016 0.0000
#> Fuel oil 0.0000 0.0000
#> Gas/diesel oil excl. biofuels 0.0000 0.0000
#> Kerosene type jet fuel excl. biofuels 0.0000 0.0000
#> Liquefied petroleum gases (LPG) 141.8990 0.0000
#> Lubricants 0.0000 0.0000
#> Motor gasoline excl. biofuels 0.0000 0.0000
#> Other kerosene 3503.9999 0.0000
#> Primary solid biofuels 61299.9981 0.0000
#> Agriculture/forestry
#> Aviation gasoline 0.0000
#> Charcoal 0.0000
#> Crude oil 0.0000
#> Electricity 97.2007
#> Fuel oil 0.0000
#> Gas/diesel oil excl. biofuels 1255.7009
#> Kerosene type jet fuel excl. biofuels 0.0000
#> Liquefied petroleum gases (LPG) 0.0000
#> Lubricants 0.0000
#> Motor gasoline excl. biofuels 0.0000
#> Other kerosene 0.0000
#> Primary solid biofuels 0.0000
#> Commercial and public services
#> Aviation gasoline 0.0000
#> Charcoal 0.0000
#> Crude oil 0.0000
#> Electricity 378.0011
#> Fuel oil 0.0000
#> Gas/diesel oil excl. biofuels 389.6990
#> Kerosene type jet fuel excl. biofuels 0.0000
#> Liquefied petroleum gases (LPG) 0.0000
#> Lubricants 0.0000
#> Motor gasoline excl. biofuels 0.0000
#> Other kerosene 0.0000
#> Primary solid biofuels 0.0000
#> Industry not elsewhere specified Losses
#> Aviation gasoline 0.000 0.0000
#> Charcoal 0.000 0.0000
#> Crude oil 0.000 0.0000
#> Electricity 918.002 647.9994
#> Fuel oil 3698.401 0.0000
#> Gas/diesel oil excl. biofuels 1645.400 0.0000
#> Kerosene type jet fuel excl. biofuels 0.000 0.0000
#> Liquefied petroleum gases (LPG) 0.000 0.0000
#> Lubricants 0.000 0.0000
#> Motor gasoline excl. biofuels 0.000 0.0000
#> Other kerosene 0.000 0.0000
#> Primary solid biofuels 6100.000 0.0000
#> Mining and quarrying Non-ferrous metals
#> Aviation gasoline 0.0000 0.000
#> Charcoal 0.0000 0.000
#> Crude oil 0.0000 0.000
#> Electricity 698.4001 7102.801
#> Fuel oil 0.0000 0.000
#> Gas/diesel oil excl. biofuels 0.0000 0.000
#> Kerosene type jet fuel excl. biofuels 0.0000 0.000
#> Liquefied petroleum gases (LPG) 0.0000 0.000
#> Lubricants 0.0000 0.000
#> Motor gasoline excl. biofuels 0.0000 0.000
#> Other kerosene 0.0000 0.000
#> Primary solid biofuels 0.0000 0.000
#> Textile and leather Domestic navigation
#> Aviation gasoline 0.0000 0.0000
#> Charcoal 0.0000 0.0000
#> Crude oil 0.0000 0.0000
#> Electricity 61.1985 0.0000
#> Fuel oil 0.0000 80.3991
#> Gas/diesel oil excl. biofuels 0.0000 432.9989
#> Kerosene type jet fuel excl. biofuels 0.0000 0.0000
#> Liquefied petroleum gases (LPG) 0.0000 0.0000
#> Lubricants 0.0000 0.0000
#> Motor gasoline excl. biofuels 0.0000 0.0000
#> Other kerosene 0.0000 0.0000
#> Primary solid biofuels 0.0000 0.0000
#> Exports [of Fuel oil]
#> Aviation gasoline 0
#> Charcoal 0
#> Crude oil 0
#> Electricity 0
#> Fuel oil 7437
#> Gas/diesel oil excl. biofuels 0
#> Kerosene type jet fuel excl. biofuels 0
#> Liquefied petroleum gases (LPG) 0
#> Lubricants 0
#> Motor gasoline excl. biofuels 0
#> Other kerosene 0
#> Primary solid biofuels 0
#> Exports to World marine bunkers [of Fuel oil]
#> Aviation gasoline 0.0000
#> Charcoal 0.0000
#> Crude oil 0.0000
#> Electricity 0.0000
#> Fuel oil 924.6004
#> Gas/diesel oil excl. biofuels 0.0000
#> Kerosene type jet fuel excl. biofuels 0.0000
#> Liquefied petroleum gases (LPG) 0.0000
#> Lubricants 0.0000
#> Motor gasoline excl. biofuels 0.0000
#> Other kerosene 0.0000
#> Primary solid biofuels 0.0000
#> Rail Stock changes [of Fuel oil]
#> Aviation gasoline 0.0000 0.0000
#> Charcoal 0.0000 0.0000
#> Crude oil 0.0000 0.0000
#> Electricity 0.0000 0.0000
#> Fuel oil 200.9999 321.6007
#> Gas/diesel oil excl. biofuels 432.9989 0.0000
#> Kerosene type jet fuel excl. biofuels 0.0000 0.0000
#> Liquefied petroleum gases (LPG) 0.0000 0.0000
#> Lubricants 0.0000 0.0000
#> Motor gasoline excl. biofuels 0.0000 0.0000
#> Other kerosene 0.0000 0.0000
#> Primary solid biofuels 0.0000 0.0000
#> Exports to World marine bunkers [of Gas/diesel oil excl. biofuels]
#> Aviation gasoline 0.000
#> Charcoal 0.000
#> Crude oil 0.000
#> Electricity 0.000
#> Fuel oil 0.000
#> Gas/diesel oil excl. biofuels 1212.401
#> Kerosene type jet fuel excl. biofuels 0.000
#> Liquefied petroleum gases (LPG) 0.000
#> Lubricants 0.000
#> Motor gasoline excl. biofuels 0.000
#> Other kerosene 0.000
#> Primary solid biofuels 0.000
#> Road
#> Aviation gasoline 0.000
#> Charcoal 0.000
#> Crude oil 0.000
#> Electricity 0.000
#> Fuel oil 0.000
#> Gas/diesel oil excl. biofuels 4979.499
#> Kerosene type jet fuel excl. biofuels 0.000
#> Liquefied petroleum gases (LPG) 0.000
#> Lubricants 0.000
#> Motor gasoline excl. biofuels 8467.200
#> Other kerosene 0.000
#> Primary solid biofuels 0.000
#> Exports to World aviation bunkers [of Kerosene type jet fuel excl. biofuels]
#> Aviation gasoline 0.000
#> Charcoal 0.000
#> Crude oil 0.000
#> Electricity 0.000
#> Fuel oil 0.000
#> Gas/diesel oil excl. biofuels 0.000
#> Kerosene type jet fuel excl. biofuels 1828.602
#> Liquefied petroleum gases (LPG) 0.000
#> Lubricants 0.000
#> Motor gasoline excl. biofuels 0.000
#> Other kerosene 0.000
#> Primary solid biofuels 0.000
#> Non-energy use industry/transformation/energy
#> Aviation gasoline 0.0000
#> Charcoal 0.0000
#> Crude oil 0.0000
#> Electricity 0.0000
#> Fuel oil 0.0000
#> Gas/diesel oil excl. biofuels 0.0000
#> Kerosene type jet fuel excl. biofuels 0.0000
#> Liquefied petroleum gases (LPG) 0.0000
#> Lubricants 755.9979
#> Motor gasoline excl. biofuels 0.0000
#> Other kerosene 0.0000
#> Primary solid biofuels 0.0000
#> Exports [of Motor gasoline excl. biofuels]
#> Aviation gasoline 0.0000
#> Charcoal 0.0000
#> Crude oil 0.0000
#> Electricity 0.0000
#> Fuel oil 0.0000
#> Gas/diesel oil excl. biofuels 0.0000
#> Kerosene type jet fuel excl. biofuels 0.0000
#> Liquefied petroleum gases (LPG) 0.0000
#> Lubricants 0.0000
#> Motor gasoline excl. biofuels 179.1992
#> Other kerosene 0.0000
#> Primary solid biofuels 0.0000
#> Exports [of Other kerosene]
#> Aviation gasoline 0.0000
#> Charcoal 0.0000
#> Crude oil 0.0000
#> Electricity 0.0000
#> Fuel oil 0.0000
#> Gas/diesel oil excl. biofuels 0.0000
#> Kerosene type jet fuel excl. biofuels 0.0000
#> Liquefied petroleum gases (LPG) 0.0000
#> Lubricants 0.0000
#> Motor gasoline excl. biofuels 0.0000
#> Other kerosene 175.2008
#> Primary solid biofuels 0.0000
#> attr(,"rowtype")
#> [1] "Product"
#> attr(,"coltype")
#> [1] "Industry"Conclusion
Taken together, the functions in this package make it possible to prepare IEA extended energy balance data for use with PSUT analysis techniques. A sequence of three function calls is all that is required.
wide_PSUT_mats <- load_tidy_iea_df() %>%
specify_all() %>%
prep_psut()
wide_PSUT_mats %>%
glimpse()
#> Rows: 4
#> Columns: 13
#> $ Country <chr> "GHA", "GHA", "ZAF", "ZAF"
#> $ Method <chr> "PCM", "PCM", "PCM", "PCM"
#> $ Energy.type <chr> "E", "E", "E", "E"
#> $ Last.stage <chr> "Final", "Final", "Final", "Final"
#> $ Year <dbl> 1971, 2000, 1971, 2000
#> $ Y <list> <<matrix[12 x 21]>>, <<matrix[13 x 20]>>, <<matrix[18 x 26…
#> $ S_units <list> <<matrix[16 x 1]>>, <<matrix[18 x 1]>>, <<matrix[24 x 1]>>…
#> $ R <list> <<matrix[9 x 8]>>, <<matrix[13 x 12]>>, <<matrix[6 x 6]>>,…
#> $ U <list> <<matrix[8 x 5]>>, <<matrix[7 x 5]>>, <<matrix[11 x 11]>>,…
#> $ U_feed <list> <<matrix[6 x 5]>>, <<matrix[5 x 5]>>, <<matrix[9 x 11]>>, …
#> $ U_EIOU <list> <<matrix[2 x 2]>>, <<matrix[2 x 2]>>, <<matrix[2 x 3]>>, …
#> $ r_EIOU <list> <<matrix[8 x 5]>>, <<matrix[7 x 5]>>, <<matrix[11 x 11]>>…
#> $ V <list> <<matrix[5 x 11]>>, <<matrix[5 x 11]>>, <<matrix[11 x 20]…