Imperial College/Courses/Fall2009/Synthetic Biology (MRes class)/'R' Tutorial/Practical: Difference between revisions

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==Part 1: Random Walks==
Below is a basic 'R' script to simulate a random walk along the X axis.
Random walk is important to model as it is related to the phenomenon of diffusion.
* Copy and save this script into a file.
* Run this script within 'R'
<syntax type='R'>
############################
#
# Random Walk 1D / 1 Trace
#
############################
# number of samples
N <- 1000
# draw 3xN samples from normal distribution
samples_1 <- rnorm(N)
# Calculate 1D Paths
path_1 <- cumsum(samples_1)
#Plot samples, time series, and histogram
steps <- seq(1:N)
plot(steps, path_1,
type='l',
lwd = 2,
col='red',
main = "1D Random Walk",
xlab = "Steps",
ylab = "X axis",
xlim = c(0, N),
ylim = c(-50,50)
)
</syntax>
===Question===
* Modify this script so that you can overlay as many independent paths as you want (Tip = use the function capability of 'R').
Here is a modified script to model a 2D Random Walk.
<syntax type='R'>
############################
#
# Random Walk 2D
#
############################
# number of samples
N <- 1000
# draw N samples from normal distribution
x_samples <- rnorm(N, mean = 0, sd = 1)
y_samples <- rnorm(N, mean = 0, sd = 0.5)
# Calculate 1D Path in each direction
X_path <- cumsum(x_samples)
Y_path <- cumsum(y_samples)
#Plot time series, and histogram
# enable 2 plots to be displayed within the same graphics window
par(mfrow = c(1,2))
# Scatter plot for X/Y distribution
plot(x_samples, y_samples, type = 'p',
lwd = 1,
col = 'green',
main = 'X/Y distribution',
xlab = "X Samples",
ylab = "Y Samples",
xlim = c(-5, 5),
ylim = c(-5,5))
# Time Serie for the particle path
plot(X_path, Y_path,
type='l',
lwd = 2,
col='red',
main = "2D Random Walk",
xlab = "X coordinate",
ylab = "Y coordinate",
xlim = c(-50, 50),
ylim = c(-50,50)
)
</syntax>
===Question===




Revision as of 09:23, 6 October 2009

Fall 2009 - Synthetic Biology (MRes class)

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Introduction to 'R'




Part 1: Random Walks

Below is a basic 'R' script to simulate a random walk along the X axis. Random walk is important to model as it is related to the phenomenon of diffusion.

  • Copy and save this script into a file.
  • Run this script within 'R'

<syntax type='R'> 

############################
#
# Random Walk 1D / 1 Trace
#
############################

# number of samples
N <- 1000

# draw 3xN samples from normal distribution
samples_1 <- rnorm(N)

# Calculate 1D Paths 
path_1 <- cumsum(samples_1)

#Plot samples, time series, and histogram 
steps <- seq(1:N)

plot(steps, path_1,

type='l', lwd = 2, col='red', main = "1D Random Walk", xlab = "Steps", ylab = "X axis", xlim = c(0, N), ylim = c(-50,50) ) </syntax>

Question

  • Modify this script so that you can overlay as many independent paths as you want (Tip = use the function capability of 'R').

Here is a modified script to model a 2D Random Walk.

<syntax type='R'>

  3. Random Walk 2D
  1. number of samples

N <- 1000

  1. draw N samples from normal distribution

x_samples <- rnorm(N, mean = 0, sd = 1) y_samples <- rnorm(N, mean = 0, sd = 0.5)

  1. Calculate 1D Path in each direction

X_path <- cumsum(x_samples) Y_path <- cumsum(y_samples)

  1. Plot time series, and histogram
  1. enable 2 plots to be displayed within the same graphics window

par(mfrow = c(1,2))

  1. Scatter plot for X/Y distribution

plot(x_samples, y_samples, type = 'p', lwd = 1, col = 'green', main = 'X/Y distribution', xlab = "X Samples", ylab = "Y Samples", xlim = c(-5, 5), ylim = c(-5,5))

  1. Time Serie for the particle path

plot(X_path, Y_path, type='l', lwd = 2, col='red', main = "2D Random Walk", xlab = "X coordinate", ylab = "Y coordinate", xlim = c(-50, 50), ylim = c(-50,50) ) </syntax>

Question

  • Basic intro to 'R' language
    • types: vector, string, factor, data_frame
    • functions for basic stats
    • Exercises:
      • ...
  • Import / Export CSV files (other file formats ?)
    • Exercises:
      • ...
  • Fitting (least square method)
    • Exercises:
      • ...
  • Plotting (scatter plots, histograms, time series)
    • Exercises:
      • ...
  • ODE simulations (based on basic gene expression models)
    • Exercises:
      • ...
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