I have the following system of equations:
x+y+z=20
z-y>0
y-x>0
I would like to know if there is any way in R to list all possible solutions for x, y, z and be able to save them in a matrix (3, m), where m represents the number of possible solutions.
All possible solutions would tell you that you can not, but yes, you can calculate some of these solutions by putting together a combination of values and testing the restrictions, for example:
# Creamos una función para validar las restricciones
fnvalid <- function(x) {
# x+y+z=20
# z-y>0
# y-x>0
if (x[1]+x[2]+x[3] == 20 &
-x[2]+x[3] > 0 &
-x[1]+x[2] > 0) {
return(TRUE)
}
return(FALSE)
}
Then we generate a matrix of 3xN with combinations of integer values for each variable, the size is to the taste of the consumer.
m <- as.matrix(expand.grid(lapply(numeric(3), function(x) c(-10:10))))
In this example we generate all combinations of integers between -10 and 10 for the three variables. Finally we apply the function per row to validate the restrictions and we obtain the values that meet all the conditions:
m[which(apply(m, MARGIN=1, fnvalid)),]
In this example, the result would be:
Var1 Var2 Var3
[1,] 5 7 8
[2,] 5 6 9
[3,] 4 7 9
[4,] 3 8 9
[5,] 4 6 10
[6,] 3 7 10
[7,] 2 8 10
[8,] 1 9 10