hatinv_byname: Hatize and invert a vector

In matsbyname: An Implementation of Matrix Mathematics that Respects Row and Column Names

Hatize and invert a vector

Description

When dividing rows or columns of a matrix by elements of a vector, the vector elements are placed on the diagonal of a new matrix, the diagonal matrix is inverted, and the result is pre- or post-multiplied into the matrix. This function performs the hatizing and inverting of vector v in one step and takes advantage of computational efficiencies to achieve the desired result. The computational shortcut is apparent when one observes that the matrix produced by hatizing and inverting a vector is a diagonal matrix whose non-zero elements are the numerical inverses of the individual elements of v. So this function first inverts each element of v then places the inverted elements on the diagonal of a diagonal matrix.

Usage

hatinv_byname(v, keep = NULL, inf_becomes = .Machine$double.xmax)

Arguments

v	The vector to be hatized and inverted.
keep	See hatize_byname().
inf_becomes	A value to be substitute for any Inf produced by the inversion process. Default is .Machine$double.xmax. Another reasonable value is Inf. Set to NULL to disable substitution.

Details

Note that this function gives the same result as invert_byname(hatize_byname(v)), except that invert_byname(hatize_byname(v)) fails due to a singular matrix error when any of the elements of v are zero. This function will give inf_becomes on the diagonal of the result for each zero element of v, arguably a better answer. The sign of Inf is preserved in the substitution. The default value of inf_becomes is .Machine$double.xmax. Set inf_becomes to NULL to disable this behavior.

The default behavior is helpful for cases when the result of hatinv_byname() is later multiplied by 0 to obtain 0. Multiplying Inf by 0 gives NaN which would effectively end the stream of calculations.

Value

a square diagonal matrix with inverted elements of v on the diagonal

Examples

v <- matrix(1:10, ncol = 1, dimnames = list(c(paste0("i", 1:10)), c("c1"))) %>%
  setrowtype("Industries") %>% setcoltype(NA)
r <- matrix(1:5, nrow = 1, dimnames = list(c("r1"), c(paste0("c", 1:5)))) %>%
  setrowtype(NA) %>% setcoltype("Commodities")
hatinv_byname(v, keep = "rownames")
hatinv_byname(r, keep = "colnames")
# This function also works with lists.
hatinv_byname(list(v, v), keep = "rownames")
# Watch out for 0 values
v2 <- matrix(0:1, ncol = 1, dimnames = list(c(paste0("i", 0:1)), c("p1"))) %>%
  setrowtype("Industries") %>% setcoltype(NA)
# Produces singular matrix error
## Not run: v2 %>% hatize_byname() %>% invert_byname
# Handles 0 values well
hatinv_byname(v2, keep = "rownames")
hatinv_byname(v2, inf_becomes = 42, keep = "rownames")
hatinv_byname(v2, inf_becomes = NA, keep = "rownames")
# Deals with 1x1 matrices well, if the `keep` argument is set.
m <- matrix(42, nrow = 1, ncol = 1, dimnames = list("r1", "c1")) %>% 
  setrowtype("Product -> Industry") %>% 
  setcoltype("Industry -> Product")
m %>% 
  hatinv_byname(keep = "rownames")
m %>% 
  hatinv_byname(keep = "colnames")

matsbyname documentation built on Oct. 19, 2023, 5:11 p.m.