# varsample: Samples the probability density function of variables of... In limSolve: Solving Linear Inverse Models

## Description

Uses random samples of an under- or overdetermined linear problem to estimate the distribution of equations

Based on a random sample of x (e.g. produced with `xsample`), produces the corresponding set of "variables" consisting of linear equations in the unknowns.

Var = EqA.x+EqB

## Usage

 `1` ```varsample (X, EqA, EqB=NULL) ```

## Arguments

 `X ` matrix whose rows contain the sampled values of the unknowns `x` in EqA*x-EqB. `EqA ` numeric matrix containing the coefficients that define the variables. `EqB ` numeric vector containing the right-hand side of the variable equation.

## Value

a matrix whose rows contain the sampled values of the variables.

## Author(s)

Karline Soetaert <[email protected]>

`Minkdiet`, for a description of the Mink diet example.

`varranges`, to estimate ranges of inverse variables.

`xsample`, to randomly sample the lsei problem.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```# The probability distribution of vertebrate and invertebrate # food in the diet of Mink # food items of Mink are (in that order): # fish mussels crabs shrimp rodents amphipods ducks # V I I I V I V # V= vertebrate, I = invertebrate # In matrix form: VarA <- matrix(ncol = 7, byrow = TRUE, data = c( 0, 1, 1, 1, 0, 1, 0, # invertebrates 1, 0, 0, 0, 1, 0, 1)) # vertebrates # first sample the Minkdiet problem E <- rbind(Minkdiet\$Prey, rep(1, 7)) F <- c(Minkdiet\$Mink, 1) X <- xsample(E = E, F = F, G = diag(7), H = rep(0, 7), iter = 1000)\$X #then determine Diet Composition in terms of vertebrate and invertebrate food DC <- varsample(X = X, EqA = VarA) hist(DC[,1], freq = FALSE, xlab = "fraction", main = "invertebrate food in Mink diet", col = "lightblue") ```

limSolve documentation built on Aug. 14, 2017, 3:01 p.m.