MSDS Spring 2018

DATA 605 Fundamentals of Computational Mathematics

Jiadi Li

HW #1 - Problem Set 2:Solution for A System of Equations

Write a function to solve for x in a system of equations with 3 variables and 3 constraints

systemSolution3by3 <- function(matrixA, vectorB){
  newA <- cbind(matrixA,vectorB)
  r <- nrow(newA)
  c <- ncol(newA)
  i <- 2
  j <- 1
  k <- 1
  while(k <= r) {
    while (i <= r) {
      if (newA[i,j]!=0) {
        multiplier <- (-newA[i,j]/newA[k,j])
            while (j <= c) {
              newA[i,j] <- newA[i,j] + newA[k,j]*multiplier
              j <- j+1
            }
        }
          i <- i+1
          j <- 1
      }
    k <- k+1
    i <- k+1
    j <- k
  }
  solution_vectorX <- c(1:r)
  solution_vectorX[3] <- newA[r,c]/newA[r,c-1]
  solution_vectorX[2] <- (newA[2,4]-newA[2,3]*solution_vectorX[3])/newA[2,2]
  solution_vectorX[1] <- (newA[1,4]-newA[1,3]*solution_vectorX[3]-newA[1,2]*solution_vectorX[2])/newA[1,1]

  
  return(solution_vectorX)
}

Test the function with an example system

testA <- matrix(c(1,2,-1,1,-1,-2,3,5,4),nrow=3)
testB <- c(1,2,6)
systemSolution3by3(testA,testB)

## [1] -1.5454545 -0.3181818  0.9545455

testsolutionX <- solve(testA)%*%testB #testing the answer with built-in function