Calculates total requirements matrices (L_pxp and L_ixp or G_pxp and G_ixp)

L_pxp tells how much of a product (in a row) is required to make another product (in a column). L_ixp tells how much of an industry's output (in a row) is required to make another product (in a column). G_pxp and G_ixp are the Ghosh (downstream, supply-sided) equivalents.

Usage

calc_L(
  .sutdata = NULL,
  direction = c("upstream", "demand", "Leontief", "downstream", "supply", "Ghosh"),
  method = c("solve", "QR", "SVD"),
  tol = .Machine$double.eps,
  D = "D",
  A = "A",
  D_s = "D_s",
  B = "B",
  L_pxp = "L_pxp",
  L_ixp = "L_ixp",
  G_pxp = "G_pxp",
  G_ixp = "G_ixp"
)

calc_G(
  .sutdata = NULL,
  direction = c("upstream", "demand", "Leontief", "downstream", "supply", "Ghosh"),
  method = c("solve", "QR", "SVD"),
  tol = .Machine$double.eps,
  D = "D",
  A = "A",
  D_s = "D_s",
  B = "B",
  L_pxp = "L_pxp",
  L_ixp = "L_ixp",
  G_pxp = "G_pxp",
  G_ixp = "G_ixp"
)

Arguments

.sutdata: A data frame of supply-use table matrices with matrices arranged in columns. Default is NULL, meaning that matrices will be taken from the D and A arguments. Set to a list or data frame to pull matrices from its store.
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.
D: The D matrix or name of the column in .sutmats that contains same. D is required for direction = "upstream". Default is "D".
A: The A matrix or name of the column in .sutmats that contains same. D is required for direction = "upstream". Default is "A".
D_s: The D_s matrix or name of the column in .sutmats that contains same. D_s is required for direction = "downstream". Default is "D_s".
B: The B matrix or name of the column in .sutmats that contains same. B is required for direction = "downstream". Default is "B".
L_pxp: The name for the L_pxp matrix on output. Default is "L_pxp". L_pxp is calculated by inverse(I - A).
L_ixp: The name for the L_ixp matrix on output. Default is "L_ixp". L_ixp is calculated by D * L_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).
G_ixp: The name for the G_ixp matrix on output. Default is "G_ixp". G_ixp is calculated by D_s * G_pxp.

Value

A list or data frame containing L_pxp and L_ixp or G_pxp and G_ixp matrices.

Details

Calculating some matrices requires a matrix inversion operation. The method argument specifies which method should be used for calculating the inverse. See matsbyname::invert_byname().

Both tol and method should be single values and apply to all matrices being inverted.

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.

Upstream swim matrices are named after Leontief and are called L_pxp and L_ixp. Downstream swim matrices are named after Ghosh and are called G_pxp and G_ixp. Which matrices are returned (L or G) depends on the value of the direction argument. "upstream", "demand", or "Leontief" generates L matrices. "downstream", "supply, or "Ghosh" generates G matrices.

Note that for historical reasons, calc_L() and calc_G() are synonyms. Both will calculate L matrices or G matrices, depending on the value of the direction argument. But it is good practice to call calc_L() when doing an upstream swim and calc_G() when doing a downstream swim. Doing so clearly signals intent.