Compute generalized inverse logit function.

inv_logit(x, min = 0, max = 1)

## Arguments

x

value(s) to be transformed

min

Lower end of logit interval

max

Upper end of logit interval

## Value

y Transformed value(s).

## Details

The generalized inverse logit function takes values on [-Inf,Inf] and transforms them to span [min, max] : $$y = p' (max-min) + min$$ $$where$$ $$p =\frac{exp(x)}{(1+exp(x))}$$

## Author

Gregory R. Warnes <greg@warnes.net>

## Examples

x <- seq(0,10, by=0.25)
xt <- jSDM::logit(x, min=0, max=10)
cbind(x,xt)
#>           x         xt
#>  [1,]  0.00       -Inf
#>  [2,]  0.25 -3.6635616
#>  [3,]  0.50 -2.9444390
#>  [4,]  0.75 -2.5123056
#>  [5,]  1.00 -2.1972246
#>  [6,]  1.25 -1.9459101
#>  [7,]  1.50 -1.7346011
#>  [8,]  1.75 -1.5505974
#>  [9,]  2.00 -1.3862944
#> [10,]  2.25 -1.2367626
#> [11,]  2.50 -1.0986123
#> [12,]  2.75 -0.9694006
#> [13,]  3.00 -0.8472979
#> [14,]  3.25 -0.7308875
#> [15,]  3.50 -0.6190392
#> [16,]  3.75 -0.5108256
#> [17,]  4.00 -0.4054651
#> [18,]  4.25 -0.3022809
#> [19,]  4.50 -0.2006707
#> [20,]  4.75 -0.1000835
#> [21,]  5.00  0.0000000
#> [22,]  5.25  0.1000835
#> [23,]  5.50  0.2006707
#> [24,]  5.75  0.3022809
#> [25,]  6.00  0.4054651
#> [26,]  6.25  0.5108256
#> [27,]  6.50  0.6190392
#> [28,]  6.75  0.7308875
#> [29,]  7.00  0.8472979
#> [30,]  7.25  0.9694006
#> [31,]  7.50  1.0986123
#> [32,]  7.75  1.2367626
#> [33,]  8.00  1.3862944
#> [34,]  8.25  1.5505974
#> [35,]  8.50  1.7346011
#> [36,]  8.75  1.9459101
#> [37,]  9.00  2.1972246
#> [38,]  9.25  2.5123056
#> [39,]  9.50  2.9444390
#> [40,]  9.75  3.6635616
#> [41,] 10.00        Inf
y <- jSDM::inv_logit(xt, min=0, max=10)
cbind(x,xt,y)
#>           x         xt     y
#>  [1,]  0.00       -Inf  0.00
#>  [2,]  0.25 -3.6635616  0.25
#>  [3,]  0.50 -2.9444390  0.50
#>  [4,]  0.75 -2.5123056  0.75
#>  [5,]  1.00 -2.1972246  1.00
#>  [6,]  1.25 -1.9459101  1.25
#>  [7,]  1.50 -1.7346011  1.50
#>  [8,]  1.75 -1.5505974  1.75
#>  [9,]  2.00 -1.3862944  2.00
#> [10,]  2.25 -1.2367626  2.25
#> [11,]  2.50 -1.0986123  2.50
#> [12,]  2.75 -0.9694006  2.75
#> [13,]  3.00 -0.8472979  3.00
#> [14,]  3.25 -0.7308875  3.25
#> [15,]  3.50 -0.6190392  3.50
#> [16,]  3.75 -0.5108256  3.75
#> [17,]  4.00 -0.4054651  4.00
#> [18,]  4.25 -0.3022809  4.25
#> [19,]  4.50 -0.2006707  4.50
#> [20,]  4.75 -0.1000835  4.75
#> [21,]  5.00  0.0000000  5.00
#> [22,]  5.25  0.1000835  5.25
#> [23,]  5.50  0.2006707  5.50
#> [24,]  5.75  0.3022809  5.75
#> [25,]  6.00  0.4054651  6.00
#> [26,]  6.25  0.5108256  6.25
#> [27,]  6.50  0.6190392  6.50
#> [28,]  6.75  0.7308875  6.75
#> [29,]  7.00  0.8472979  7.00
#> [30,]  7.25  0.9694006  7.25
#> [31,]  7.50  1.0986123  7.50
#> [32,]  7.75  1.2367626  7.75
#> [33,]  8.00  1.3862944  8.00
#> [34,]  8.25  1.5505974  8.25
#> [35,]  8.50  1.7346011  8.50
#> [36,]  8.75  1.9459101  8.75
#> [37,]  9.00  2.1972246  9.00
#> [38,]  9.25  2.5123056  9.25
#> [39,]  9.50  2.9444390  9.50
#> [40,]  9.75  3.6635616  9.75
#> [41,] 10.00        Inf 10.00