limSolve (version 1.4)

varsample: Samples 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.

See Also

varranges,

xsample

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(nc=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")