Change a vector of multivariate polynomials into a function.

Transforms an mpolyList object into a function which can be evaluated.

# S3 method for mpolyList
as.function(x, varorder = vars(x), vector = TRUE,
  silent = FALSE, ..., plus_pad = 1L, times_pad = 1L, squeeze = TRUE)

# S3 method for bezier
as.function(x, ...)

Arguments

x	an object of class mpoly
varorder	the order of the variables
vector	whether the function should take a vector argument (TRUE) or a series of arguments (FALSE)
silent	logical; if TRUE, suppresses output
...	any additional arguments
plus_pad	number of spaces to the left and right of plus sign
times_pad	number of spaces to the left and right of times sign
squeeze	minify code in the created function

See also

plug(), as.function.mpolyList()

Examples

# basic examples
(mpolyList <- mp(c("2 x + 1", "x - z^2")))
#> 2 x  +  1
#> x  -  z^2
(f <- as.function(mpolyList))
#> f(.) with . = (x, z)
#> function (.) 
#> {
#>     c(2 * .[1] + 1, .[1] - .[2]^2)
#> }
#> <environment: 0x7fae3e5b1a00>
f(c(1,2)) # -> (2*1 + 1, 1-2^2) = 3 -3
#> [1]  3 -3

f <- as.function(mpolyList, varorder = c("x","y","z"))
#> f(.) with . = (x, y, z)
f(c(1,0,2)) # -> 3 -3
#> [1]  3 -3
f(c(1,4,2)) # -> 3 -3
#> [1]  3 -3

f <- as.function(mpolyList, varorder = c("x","y","z"), vector = FALSE)
f(1, 0, 2) # -> 3 -3
#> [1]  3 -3
f(1, 4, 2) # -> 3 -3
#> [1]  3 -3



# making a gradient function (useful for optim)
mpoly <- mp("x + y^2 + y z")
mpolyList <- gradient(mpoly)
f <- as.function(mpolyList, varorder = vars(mpoly))
#> f(.) with . = (x, y, z)
f(c(0,2,3)) # -> 1 7 2
#> [1] 1 7 2



# a univariate mpolyList creates a vectorized function
ps <- mp(c("x", "x^2", "x^3"))
f <- as.function(ps)
f
#> function (.) 
#> {
#>     if (length(.) > 1) 
#>         return(t(sapply(., f)))
#>     c(., .^2, .^3)
#> }
#> <environment: 0x7fae3f233058>
s <- seq(-1, 1, length.out = 11)
f(s)
#>       [,1] [,2]   [,3]
#>  [1,] -1.0 1.00 -1.000
#>  [2,] -0.8 0.64 -0.512
#>  [3,] -0.6 0.36 -0.216
#>  [4,] -0.4 0.16 -0.064
#>  [5,] -0.2 0.04 -0.008
#>  [6,]  0.0 0.00  0.000
#>  [7,]  0.2 0.04  0.008
#>  [8,]  0.4 0.16  0.064
#>  [9,]  0.6 0.36  0.216
#> [10,]  0.8 0.64  0.512
#> [11,]  1.0 1.00  1.000

# another example
ps <- chebyshev(1:3)
#> Loading required package: polynom
#> 
#> Attaching package: ‘polynom’
#> The following object is masked from ‘package:mpoly’:
#> 
#>     LCM
f <- as.function(ps)
f(s)
#>       [,1]  [,2]   [,3]
#>  [1,] -1.0  1.00 -1.000
#>  [2,] -0.8  0.28  0.352
#>  [3,] -0.6 -0.28  0.936
#>  [4,] -0.4 -0.68  0.944
#>  [5,] -0.2 -0.92  0.568
#>  [6,]  0.0 -1.00  0.000
#>  [7,]  0.2 -0.92 -0.568
#>  [8,]  0.4 -0.68 -0.944
#>  [9,]  0.6 -0.28 -0.936
#> [10,]  0.8  0.28 -0.352
#> [11,]  1.0  1.00  1.000

# the binomial pmf as an algebraic (polynomial) map
# from [0,1] to [0,1]^size
# p |-> {choose(size, x) p^x (1-p)^(size-x)}_{x = 0, ..., size}
abinom <- function(size, indet = "p"){
  chars4mp <- vapply(as.list(0:size), function(x){
    sprintf("%d %s^%d (1-%s)^%d", choose(size, x), indet, x, indet, size-x)
  }, character(1))
  mp(chars4mp)
}
(ps <- abinom(2, "p")) # = mp(c("(1-p)^2", "2 p (1-p)", "p^2"))
#> p^2  -  2 p  +  1
#> -2 p^2  +  2 p
#> p^2
f <- as.function(ps)

f(.5) # P[X = 0], P[X = 1], and P[X = 2] for X ~ Bin(2, .5)
#> [1] 0.25 0.50 0.25
dbinom(0:2, 2, .5)
#> [1] 0.25 0.50 0.25

f(.75) # P[X = 0], P[X = 1], and P[X = 2] for X ~ Bin(2, .75)
#> [1] 0.0625 0.3750 0.5625
dbinom(0:2, 2, .75)
#> [1] 0.0625 0.3750 0.5625

# as the degree gets larger, you'll need to be careful when evaluating
# the polynomial.  as.function() is not currently optimized for
# stable numerical evaluation of polynomials; it evaluates them in
# the naive way
all.equal(
  as.function(abinom(10))(.5),
  dbinom(0:10, 10, .5)
)
#> [1] TRUE

all.equal(
  as.function(abinom(30))(.5),
  dbinom(0:30, 20, .5)
)
#> [1] "Mean relative difference: 1.375229"


# the function produced is vectorized:
number_of_probs <- 11
probs <- seq(0, 1, length.out = number_of_probs)
(mat <- f(probs))
#>       [,1] [,2] [,3]
#>  [1,] 1.00 0.00 0.00
#>  [2,] 0.81 0.18 0.01
#>  [3,] 0.64 0.32 0.04
#>  [4,] 0.49 0.42 0.09
#>  [5,] 0.36 0.48 0.16
#>  [6,] 0.25 0.50 0.25
#>  [7,] 0.16 0.48 0.36
#>  [8,] 0.09 0.42 0.49
#>  [9,] 0.04 0.32 0.64
#> [10,] 0.01 0.18 0.81
#> [11,] 0.00 0.00 1.00
colnames(mat) <- sprintf("P[X = %d]", 0:2)
rownames(mat) <- sprintf("p = %.2f", s)
mat
#>           P[X = 0] P[X = 1] P[X = 2]
#> p = -1.00     1.00     0.00     0.00
#> p = -0.80     0.81     0.18     0.01
#> p = -0.60     0.64     0.32     0.04
#> p = -0.40     0.49     0.42     0.09
#> p = -0.20     0.36     0.48     0.16
#> p = 0.00      0.25     0.50     0.25
#> p = 0.20      0.16     0.48     0.36
#> p = 0.40      0.09     0.42     0.49
#> p = 0.60      0.04     0.32     0.64
#> p = 0.80      0.01     0.18     0.81
#> p = 1.00      0.00     0.00     1.00