R: Samples the probability density function of variables of...

varsample {limSolve} | R Documentation

## Samples the probability density function of variables of linear inverse problems.

### 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

    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 <karline.soetaert@nioz.nl>

### See Also

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

`varranges`, to estimate ranges of inverse variables.

`xsample`, to randomly sample the lsei problem.

### Examples

    # 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")

[Package limSolve version 1.5.6 Index]