Calculates downstream effects of a new level of extracted resources

This function calculates the effect of changing the resources available to an ECC, i.e. of a new resources matrix R_prime on the rest of the ECC matrices (U, V, W, and Y). New versions of the U, V, W, and Y matrices are returned, and respectively called U_prime, V_prime, W_prime, and Y_prime. This function assumes that each industry's inputs are perfectly substitutable (ps).

Usage

new_R_ps(
  .sutmats = NULL,
  method = c("solve", "QR", "SVD"),
  tol = .Machine$double.eps,
  R_prime = "R_prime",
  U = "U",
  U_feed = "U_feed",
  V = "V",
  Y = "Y",
  q = "q",
  f = "f",
  G_pxp = "G_pxp",
  G_ixp = "G_ixp",
  O_s = "O_s",
  D_s = "D_s",
  D_feed_s = "D_feed_s",
  Z_s = "Z_s",
  U_prime = "U_prime",
  U_feed_prime = "U_feed_prime",
  U_eiou_prime = "U_EIOU_prime",
  r_eiou_prime = "r_EIOU_prime",
  V_prime = "V_prime",
  Y_prime = "Y_prime"
)

Arguments

.sutmats

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

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.

R_prime

The name of the new R matrix column in the input data frame, for which the new ECC must be assessed. Default is "R_prime".

U

The name of the U matrix column in the input data frame. Default is "U".

U_feed

The name of the U_feed matrix column in the input data frame. Default is "U_feed".

V

The name of the V matrix column in the input data frame. Default is "V".

Y

The name of the Y matrix column in the input data frame. Default is "Y".

q

The name of the q vector column in the input data frame. Default is "q".

f

The name of the f vector column in the input data frame. Default is "f".

G_pxp

The name of the G_pxp matrix column in the input data frame. Default is "G_pxp".

G_ixp

The name of the G_ixp matrix column in the input data frame. Default is "G_ixp".

O_s

The name of the O_s matrix column in the input data frame. Default is "O_s", where "_s" indicates supply-sided.

D_s

The name of the D_s matrix column in the input data frame. Default is "D_s", where "_s" indicates supply-sided.

D_feed_s

The name of the D_feed_s matrix column in the input data frame. Default is "D_feed_s", where "_s" indicates supply-sided.

Z_s

The name of the Z_s matrix column in the input data frame. Default is "Z_s", where "_s" indicates supply-sided.

U_prime

The name of the output column containing the new U matrices. Default is "U_prime".

U_feed_prime

The name of the output column containing the new U_feed matrices. Default is "U_feed_prime".

U_eiou_prime

The name of the output column containing the new U_EIOU matrices. Default is "U_EIOU_prime".

r_eiou_prime

The name of the output column containing the new r_EIOU matrices. Default is "r_EIOU_prime".

V_prime

The name of the output column containing the new V matrices. Default is "V_prime".

Y_prime

The name of the output column containing the new Y matrices. Default is "Y_prime".

Value

A data frame with added columns representing each of the new U_prime, U_feed_prime, U_EIOU_prime, r_EIOU_prime, V_prime, and Y_prime matrices.

Details

Each industry must be unit-homogeneous on its inputs. If not, a matrix populated with NA is returned as the result for U_prime, V_prime, and Y_prime.

Calculating the new matrices requires a matrix inversion operation. The method argument specifies which method should be used for calculating the inverse. "solve" uses base::solve() and the value of tol. "QR" uses base::solve.qr() and the value of tol. "SVD" uses matrixcalc::svd.inverse(), ignoring the tol argument.

Both tol and method should be a single values and apply to all matrices in a.

Examples

UKEnergy2000mats %>%
  tidyr::spread(key = "matrix.name", value = "matrix") %>%
  # When Last.stage is "services", we get units problems.
  # Avoid by using only ECCs with "Final" and "Useful" as the Last.stage.
  dplyr::filter(Last.stage != IEATools::last_stages$services) %>%
  # Calculate the input-output matrices which are inputs to the new_R function.
  calc_io_mats(direction = "downstream") %>%
  # Make an R_prime matrix that gives twice the resource inputs to the economy.
  dplyr::mutate(
    R_prime = matsbyname::hadamardproduct_byname(2, R)
  ) %>%
  # Now call new_R_ps() which will calculate
  # updated U, V, and Y matrices (U_prime, V_prime, and Y_prime)
  # given R_prime.
  # Each of the *_prime matrices should be 2x their originals,
  # because R_prime is 2x relative to R.
  new_R_ps()
#> # A tibble: 2 × 34
#>   Country  Year Energy.type Last.stage R             S_units  U        U_EIOU  
#>   <chr>   <dbl> <chr>       <chr>      <list>        <list>   <list>   <list>  
#> 1 GBR      2000 E           Final      <dbl [2 × 2]> <dbl[…]> <dbl[…]> <dbl[…]>
#> 2 GBR      2000 E           Useful     <dbl [2 × 2]> <dbl[…]> <dbl[…]> <dbl[…]>
#> # ℹ 26 more variables: U_feed <list>, V <list>, Y <list>, r_EIOU <list>,
#> #   y <list>, q <list>, f <list>, g <list>, h <list>, r <list>, W <list>,
#> #   Z_s <list>, C_s <list>, D_s <list>, D_feed_s <list>, O_s <list>, B <list>,
#> #   G_pxp <list>, G_ixp <list>, R_prime <list>, U_prime <list>,
#> #   U_feed_prime <list>, U_EIOU_prime <list>, r_EIOU_prime <list>,
#> #   V_prime <list>, Y_prime <list>