Mathematics

Function Summary

A collection of functions provides basic column-oriented data analysis capabilities. These functions are located in the MATLAB datafun directory.

This section also gives you some hints about using row and column data, and provides some basic examples. This table lists the functions.

Basic Data Analysis Function Summary  

Function	Description
cumprod	Cumulative product of elements.
cumsum	Cumulative sum of elements.
cumtrapz	Cumulative trapezoidal numerical integration.
diff	Difference function and approximate derivative.
max	Largest component.
mean	Average or mean value.
median	Median value.
min	Smallest component.
prod	Product of elements.
sort	Sort in ascending order.
sortrows	Sort rows in ascending order.
std	Standard deviation.
sum	Sum of elements.
trapz	Trapezoidal numerical integration.

To use the Data Statistics Tool to calculate the maximum, minimum, mean, median, range, and standard deviation on plotted data, and create plots of these statistics, see Using the Data Statistics Tool in the MATLAB graphics documentation.

Working with Row and Column Data

For vector input arguments to these functions, it does not matter whether the vectors are oriented in row or column direction. For array arguments, however, the functions operate column by column on the data in the array. This means, for example, that if you apply max to an array, the result is a row vector containing the maximum values over each column.

Note    You can add more functions to this list using M-files, but when doing so, you must exercise care to handle the row-vector case. If you are writing your own column-oriented M-files, check other M-files; for example, mean.m and diff.m.

Basic Examples

Continuing with the vehicle traffic count example, the statements

• mx = max(count)
  mu = mean(count)
  sigma = std(count)
  

result in

• mx =
            114          145          257
  
  mu = 
        32.0000      46.5417      65.5833
  
  sigma =
        25.3703      41.4057      68.0281
  

To locate the index at which the minimum or maximum occurs, a second output parameter can be specified. For example,

• [mx,indx] = min(count)
  mx =
        7     9     7
  
  indx =
        2    23    24
  

shows that the lowest vehicle count is recorded at 02h00 for the first observation point (column one) and at 23h00 and 24h00 for the other observation points.

You can subtract the mean from each column of the data using an outer product involving a vector of n ones.

• [n,p] = size(count)
  e = ones(n,1)
  x = count - e*mu
  

Rearranging the data may help you evaluate a vector function over an entire data set. For example, to find the smallest value in the entire data set, use

• min(count(:))
  

which produces

• ans =
        7
  

The syntax count(:) rearranges the 24-by-3 matrix into a 72-by-1 column vector.

Basic Data Analysis Functions

Covariance and Correlation Coefficients