# mgc.sims.cubic: Cubic Simulation In mgc: Multiscale Graph Correlation

## Description

A function for Generating a cubic simulation.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```mgc.sims.cubic( n, d, eps = 80, ind = FALSE, a = -1, b = 1, c.coef = c(-12, 48, 128), s = 1/3 ) ```

## Arguments

 `n` the number of samples for the simulation. `d` the number of dimensions for the simulation setting. `eps` the noise level for the simulation. Defaults to `80`. `ind` whether to sample x and y independently. Defaults to `FALSE`. `a` the lower limit for the range of the data matrix. Defaults to `-1`. `b` the upper limit for the range of the data matrix. Defaults to `1`. `c.coef` the coefficients for the cubic function, where the first value is the first order coefficient, the second value the quadratic coefficient, and the third the cubic coefficient. Defaults to `c(-12, 48, 128)`. `s` the scaling for the center of the cubic. Defaults to `1/3`.

## Value

a list containing the following:

 `X` `[n, d]` the data matrix with `n` samples in `d` dimensions. `Y` `[n]` the response array.

## Details

Given: w[i] = 1/i is a weight-vector that scales with the dimensionality. Simulates n points from Linear(X, Y), where:

X ~ U(a, b)^d

Y = c(w^TX - s)^3 + c(w^TX - s)^2 + c(w^TX - s) + κ ε

and K = 1 if d=1, and 0 otherwise controls the noise for higher dimensions.

Eric Bridgeford

## Examples

 ```1 2 3``` ```library(mgc) result <- mgc.sims.cubic(n=100, d=10) # simulate 100 samples in 10 dimensions X <- result\$X; Y <- result\$Y ```

mgc documentation built on July 1, 2020, 7:09 p.m.