R/testmodels.R

In sensitivity: Sensitivity Analysis

# Test models for sensitivity analysis (Saltelli 2000)
#
# Gilles Pujol 2006


# The non-monotonic Sobol g-function

sobol.fun <- function(X) {
  a <- c(0, 1, 4.5, 9, 99, 99, 99, 99)
  y <- 1
  for (j in 1:8) {
    y <- y * (abs(4 * X[, j] - 2) + a[j]) / (1 + a[j])
  }
  y
}


# The non-monotonic Ishigami function

ishigami.fun <- function(X) {
  A <- 7
  B <- 0.1
  sin(X[, 1]) + A * sin(X[, 2])^2 + B * X[, 3]^4 * sin(X[, 1])
}


# The non-monotonic function of Morris

morris.fun <- function(X) {
  w <- 2 * (X - 0.5)
  w[, c(3, 5, 7)] <- 2 * (1.1 * X[, c(3, 5, 7)] /
                          (X[, c(3, 5, 7)] + .1) - 0.5)
  y <- b0
  for (i in 1 : 20) {
    y <- y + b1[i] * w[, i]
  }
  for (i in 1 : 19) {
    for (j in (i + 1) : 20) {
      y <- y + b2[i, j] * w[, i] * w[, j]
    }
  }
  for (i in 1 : 18) {
    for (j in (i + 1) : 19) {
      for (k in (j + 1) : 20) {
        y <- y + b3[i, j, k] * w[, i] * w[, j] * w[, k]
      }
    }
  }
  for (i in 1 : 17) {
    for (j in (i + 1) : 18) {
      for (k in (j + 1) : 19) {
        for (l in (k+1):20) {
          y <- y + b4[i, j, k, l] * w[, i] * w[, j] * w[, k] * w[, l]
        }
      }
    }
  }
  y
}

b0 <- rnorm(1)
b1 <- c(rep(20, 10), rnorm(10))
b2 <- rbind(cbind(matrix(-15, 6, 6),
                  matrix(rnorm(6 * 14), 6, 14)),
            matrix(rnorm(14 * 20), 14, 20))
b3 <- array(0, c(20, 20, 20))
b3[1 : 5, 1 : 5, 1 : 5] <- - 10
b4 <- array(0, c(20, 20, 20, 20))
b4[1 : 4, 1 : 4, 1 : 4, 1 : 4] <- 5

environment(morris.fun) <- new.env()
assign("b0", b0, envir = environment(morris.fun))
assign("b1", b1, envir = environment(morris.fun))
assign("b2", b2, envir = environment(morris.fun))
assign("b3", b3, envir = environment(morris.fun))
assign("b4", b4, envir = environment(morris.fun))