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.
Arguments
- v
The vector to be hatized and inverted.
- keep
See
hatize_byname().- inf_becomes
A value to be substitute for any
Infproduced by the inversion process. Default is.Machine$double.xmax. Another reasonable value isInf. Set toNULLto disable substitution.
Details
Note that this function gives the same result as invert_byname(hatize_byname(v)),
except that invert_byname(hatize_byname(v)) fails due to a singular matrix error
when any of the elements of v are zero.
This function will give inf_becomes on the diagonal of the result for each zero element of v,
arguably a better answer.
The sign of Inf is preserved in the substitution.
The default value of inf_becomes is .Machine$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.
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")
#> i1 i10 i2 i3 i4 i5 i6 i7 i8 i9
#> i1 1 0.0 0.0 0.0000000 0.00 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i10 0 0.1 0.0 0.0000000 0.00 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i2 0 0.0 0.5 0.0000000 0.00 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i3 0 0.0 0.0 0.3333333 0.00 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i4 0 0.0 0.0 0.0000000 0.25 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i5 0 0.0 0.0 0.0000000 0.00 0.2 0.0000000 0.0000000 0.000 0.0000000
#> i6 0 0.0 0.0 0.0000000 0.00 0.0 0.1666667 0.0000000 0.000 0.0000000
#> i7 0 0.0 0.0 0.0000000 0.00 0.0 0.0000000 0.1428571 0.000 0.0000000
#> i8 0 0.0 0.0 0.0000000 0.00 0.0 0.0000000 0.0000000 0.125 0.0000000
#> i9 0 0.0 0.0 0.0000000 0.00 0.0 0.0000000 0.0000000 0.000 0.1111111
#> attr(,"rowtype")
#> [1] "Industries"
#> attr(,"coltype")
#> [1] "Industries"
hatinv_byname(r, keep = "colnames")
#> c1 c2 c3 c4 c5
#> c1 1 0.0 0.0000000 0.00 0.0
#> c2 0 0.5 0.0000000 0.00 0.0
#> c3 0 0.0 0.3333333 0.00 0.0
#> c4 0 0.0 0.0000000 0.25 0.0
#> c5 0 0.0 0.0000000 0.00 0.2
#> attr(,"rowtype")
#> [1] "Commodities"
#> attr(,"coltype")
#> [1] "Commodities"
# This function also works with lists.
hatinv_byname(list(v, v), keep = "rownames")
#> [[1]]
#> i1 i10 i2 i3 i4 i5 i6 i7 i8 i9
#> i1 1 0.0 0.0 0.0000000 0.00 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i10 0 0.1 0.0 0.0000000 0.00 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i2 0 0.0 0.5 0.0000000 0.00 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i3 0 0.0 0.0 0.3333333 0.00 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i4 0 0.0 0.0 0.0000000 0.25 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i5 0 0.0 0.0 0.0000000 0.00 0.2 0.0000000 0.0000000 0.000 0.0000000
#> i6 0 0.0 0.0 0.0000000 0.00 0.0 0.1666667 0.0000000 0.000 0.0000000
#> i7 0 0.0 0.0 0.0000000 0.00 0.0 0.0000000 0.1428571 0.000 0.0000000
#> i8 0 0.0 0.0 0.0000000 0.00 0.0 0.0000000 0.0000000 0.125 0.0000000
#> i9 0 0.0 0.0 0.0000000 0.00 0.0 0.0000000 0.0000000 0.000 0.1111111
#> attr(,"rowtype")
#> [1] "Industries"
#> attr(,"coltype")
#> [1] "Industries"
#>
#> [[2]]
#> i1 i10 i2 i3 i4 i5 i6 i7 i8 i9
#> i1 1 0.0 0.0 0.0000000 0.00 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i10 0 0.1 0.0 0.0000000 0.00 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i2 0 0.0 0.5 0.0000000 0.00 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i3 0 0.0 0.0 0.3333333 0.00 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i4 0 0.0 0.0 0.0000000 0.25 0.0 0.0000000 0.0000000 0.000 0.0000000
#> i5 0 0.0 0.0 0.0000000 0.00 0.2 0.0000000 0.0000000 0.000 0.0000000
#> i6 0 0.0 0.0 0.0000000 0.00 0.0 0.1666667 0.0000000 0.000 0.0000000
#> i7 0 0.0 0.0 0.0000000 0.00 0.0 0.0000000 0.1428571 0.000 0.0000000
#> i8 0 0.0 0.0 0.0000000 0.00 0.0 0.0000000 0.0000000 0.125 0.0000000
#> i9 0 0.0 0.0 0.0000000 0.00 0.0 0.0000000 0.0000000 0.000 0.1111111
#> attr(,"rowtype")
#> [1] "Industries"
#> attr(,"coltype")
#> [1] "Industries"
#>
# 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
if (FALSE) v2 %>% hatize_byname() %>% invert_byname
# Handles 0 values well
hatinv_byname(v2, keep = "rownames")
#> i0 i1
#> i0 1.797693e+308 0
#> i1 0.000000e+00 1
#> attr(,"rowtype")
#> [1] "Industries"
#> attr(,"coltype")
#> [1] "Industries"
hatinv_byname(v2, inf_becomes = 42, keep = "rownames")
#> i0 i1
#> i0 42 0
#> i1 0 1
#> attr(,"rowtype")
#> [1] "Industries"
#> attr(,"coltype")
#> [1] "Industries"
hatinv_byname(v2, inf_becomes = NA, keep = "rownames")
#> i0 i1
#> i0 NA 0
#> i1 0 1
#> attr(,"rowtype")
#> [1] "Industries"
#> attr(,"coltype")
#> [1] "Industries"
# 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")
#> r1
#> r1 0.02380952
#> attr(,"rowtype")
#> [1] "Product -> Industry"
#> attr(,"coltype")
#> [1] "Product -> Industry"
m %>%
hatinv_byname(keep = "colnames")
#> c1
#> c1 0.02380952
#> attr(,"rowtype")
#> [1] "Industry -> Product"
#> attr(,"coltype")
#> [1] "Industry -> Product"