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Calculate several input-output matrices

Source: R/io.R
calc_io_mats.Rd

This function bundles several others and calculates matrices that describe the structure of an energy conversion chain.

Usage

calc_io_mats(
  .sutdata = NULL,
  direction = c("upstream", "demand", "Leontief", "downstream", "supply", "Ghosh"),
  method = c("solve", "QR", "SVD"),
  tol = .Machine$double.eps,
  method_q_calculation = c("sum_U_Y_rows", "sum_R_V_cols"),
  R = "R",
  U = "U",
  U_feed = "U_feed",
  V = "V",
  Y = "Y",
  S_units = "S_units",
  y = "y",
  q = "q",
  f = "f",
  g = "g",
  h = "h",
  r = "r",
  W = "W",
  K = "K",
  Z = "Z",
  C = "C",
  D = "D",
  A = "A",
  L_ixp = "L_ixp",
  L_pxp = "L_pxp",
  O = "O",
  Z_feed = "Z_feed",
  K_feed = "K_feed",
  A_feed = "A_feed",
  L_ixp_feed = "L_ixp_feed",
  L_pxp_feed = "L_pxp_feed",
  Z_s = "Z_s",
  C_s = "C_s",
  D_s = "D_s",
  D_feed_s = "D_feed_s",
  B = "B",
  G_ixp = "G_ixp",
  G_pxp = "G_pxp",
  O_s = "O_s"
)

Arguments

.sutdata

A data frame of supply-use table matrices with matrices arranged in columns.

direction

A string that identifies the directionality of the IO matrices. See details. Default is "upstream".

method

One of "solve", "QR", or "SVD". Default is "solve". See details.

tol

The tolerance for detecting linear dependencies during matrix inversion. Default is .Machine$double.eps.

method_q_calculation

Specifies the method with which the q vector should be calculated. See details.

R

The resources (R) matrix or name of the column in .sutmats that contains same. Default is "R".

U

The use (U) matrix or name of the column in .sutmats that contains same. Default is "U".

U_feed

The feed portion of the use matrix (U_feed) or name of the column in .sutmats that contains same. Default is "U_feed".

V

The make (V) matrix or name of the column in .sutmatsthat contains same. Default is "V".

Y

The final demand (Y) matrix or name of the column in .sutmats that contains same. Default is "Y".

S_units

The unit summation matrix (S_units) or name of the column in .sutmats that contains same. Default is "S_units".

y

The name for the y vector on output. Default is "y". y is calculated by rowsums(Y).

q

The name for the q vector on output. Default is "q". q is calculated by rowsums(U) + y.

f

The name for the f vector on output. Default is "f". f is calculated by colsums(U).

g

The name for the g vector on output. Default is "g". g is calculated by rowsums(V).

h

The name for the h vector on output. Default is "h". h is calculated by colsums(transpose(R)).

r

The name for the r vector on output. Default is "r". r is calculated by rowsums(R).

W

The name for the W matrix on output. Default is "W". W is calculated by transpose(V) - U.

K

The name for the K matrix on output. Default is "K". K is calculated by U * f_hat_inv.

Z

The name fort the Z matrix on output. Default is "Z". Z is calculated by U * g_hat_inv.

C

The name for the C matrix on output. Default is "C". C is calculated by transpose(V) * g_hat_inv.

D

The name for the D matrix on output. Default is "D". D is calculated by V * q_hat_inv.

A

The name for the A matrix on output. Default is "A". A is calculated by Z * D.

L_ixp

The name for the L_ixp matrix on output. Default is "L_ixp". L_ixp is calculated by D * L_pxp.

L_pxp

The name for the L_pxp_feed matrix on output. Default is "L_pxp_feed". L_pxp is calculated by (I - Z*D)^-1.

O

name for the O matrix on output. Default is "O". O is calculated by R * h_hat_inv.

Z_feed

The name for the Z_feed matrix on output. Default is "Z_feed". Z_feed is calculated by U_feed * g_hat_inv.

K_feed

The name for the K_feed matrix on output. Default is "K_feed". K_feed is calculated by U_feed * f_hat_inv.

A_feed

The name for the A_feed matrix on output. Default is "A_feed". A_feed is calculated by Z_feed * D_feed.

L_ixp_feed

The name for the L_ixp_feed matrix on output. Default is "L_ixp_feed". L_ixp_feed is calculated by D_feed * L_pxp_feed.

L_pxp_feed

The name for the L_pxp_feed matrix on output. Default is "L_pxp_feed". L_pxp_feed is calculated by (I - Z_feed*D)^-1.

Z_s

The name for the Z_s matrix on output. Default is "Z_s". Z_s is calculated by transpose(V) * f_hat_inv.

C_s

The name for the C_s matrix on output. Default is "C_s". C_s is calculated by U * f_hat_inv.

D_s

The name for the D_s matrix on output. Default is "D_s". D_s is calculated by transpose(U) * q_hat_inv.

D_feed_s

The name for the D_feed_s matrix on output. Default is "D_feed_s". D_s is calculated by transpose(U_feed) * q_hat_inv.

B

The name for the B matrix on output. Default is "B". B is calculated by Z_s * D_s.

G_ixp

The name for the G_ixp matrix on output. Default is "G_ixp". G_ixp is calculated by D_s * G_pxp.

G_pxp

The name for the G_pxp matrix on output. Default is "G_pxp". G_pxp is calculated by inverse(I - A_s).

O_s

The name for the O_s matrix on output. Default is "O_s". O is calculated by q_hat_inv * Y.

Value

A list or data frame containing input-output matrices.

Details

Some calculations involve a matrix inversion step. The method argument specifies which method should be used for calculating the inverse. See matsbyname::invert_byname().

method_q_calculation specifies the method with which the q vector should be calculated. Default is "sum_U_Y_rows", corresponding to a demand-sided view of q. Alternatively, an analyst can choose to use the "sum_R_V_cols" method, corresponding to a supply-sided view of q. In the case of a balanced ECC, the method does not matter.

Input-output matrices can be calculated for either an upstream swim (demand-sided as Leontief) or a downstream swim (supply-sided as Ghosh). The direction argument defines the direction. Different IO matrices are calculated based on direction. The default is "upstream", meaning that an upstream swim is desired. Note that "upstream", "demand", and "Leontief" are synonyms. "downstream", "supply", and "Ghosh" are synonyms.

Examples

library(dplyr)
library(tidyr)
UKEnergy2000mats %>%
  spread(key = matrix.name, value = matrix) %>%
  select(Country, Year, Energy.type, Last.stage, U, U_feed, V, Y, r_EIOU, S_units) %>%
  calc_io_mats()
#> # A tibble: 4 × 30
#>   Country  Year Energy.type Last.stage U              U_feed   V        Y       
#>   <chr>   <dbl> <chr>       <chr>      <list>         <list>   <list>   <list>  
#> 1 GBR      2000 E           Final      <dbl [12 × 9]> <dbl[…]> <dbl[…]> <dbl[…]>
#> 2 GBR      2000 E           Services   <dbl[…]>       <dbl[…]> <dbl[…]> <dbl[…]>
#> 3 GBR      2000 E           Useful     <dbl[…]>       <dbl[…]> <dbl[…]> <dbl[…]>
#> 4 GBR      2000 X           Services   <dbl[…]>       <dbl[…]> <dbl[…]> <dbl[…]>
#> # ℹ 22 more variables: r_EIOU <list>, S_units <list>, y <list>, q <list>,
#> #   f <list>, g <list>, h <list>, r <list>, W <list>, Z <list>, K <list>,
#> #   C <list>, D <list>, A <list>, O <list>, L_pxp <list>, L_ixp <list>,
#> #   Z_feed <list>, K_feed <list>, A_feed <list>, L_pxp_feed <list>,
#> #   L_ixp_feed <list>