Fix typo in posterior function name. Add example in README for LDA so…

…lver interface

README.md

@@ -3,8 +3,6 @@
 [![Build Status](https://travis-ci.org/trthatcher/DiscriminantAnalysis.jl.svg?branch=master)](https://travis-ci.org/trthatcher/DiscriminantAnalysis.jl)
 [![Coverage Status](https://coveralls.io/repos/trthatcher/DiscriminantAnalysis.jl/badge.svg?branch=master&service=github)](https://coveralls.io/github/trthatcher/DiscriminantAnalysis.jl?branch=master)
 
-#### Summary
-
 **DiscriminantAnalysis.jl** is a Julia package for multiple linear and quadratic 
 regularized discriminant analysis (LDA & QDA respectively). LDA and QDA are
 distribution-based classifiers with the underlying assumption that data follows
@@ -14,18 +12,41 @@ covariance matrix whereas QDA relaxes that constraint and allows for distinct
 within-class covariance matrices. This results in LDA being a linear classifier
 and QDA being a quadratic classifier.
 
-#### Documentation
+The package is currently a work in progress work in progress - see [issue #12](https://github.com/trthatcher/DiscriminantAnalysis.jl/issues/12) for the package status.
+
+## Getting Started
+
+A bare-bones implementation of LDA is currently available. The script below demonstrates how to fit an LDA model to some synthetic data using the low-level interface:
+
+```julia
+using DiscriminantAnalysis
+using Random
 
-Documentation is a work in progress.
+const DA = DiscriminantAnalysis
 
-#### Visualization
+# Generate two sets of 100 samples of a 5-dimensional random normal 
+# variable offset by +1/-1
+X = [randn(250,5) .- 1;
+     randn(250,5) .+ 1]
 
-When the data is modelled via linear discriminant analysis, the resulting
-classification boundaries are hyperplanes (lines in two dimensions):
+# Generate class labels for the two samples
+#   NOTE: classes must be indexed by integers from 1 to the number of 
+#         classes (2 in this case)
+y = repeat(1:2, inner=100)
 
-<p align="center"><img alt="Linear Discriminant Analysis" src="docs/src/assets/lda.png"  /></p>
+# Set the solver options
+dims = 1                    # use 1 for row-per-observation; 2 for columns
+canonical = true            # use true to compute the canonical coords
+compute_covariance = false  # use true to compute & store covariance
+centroids = nothing         # supply a precomputed set of class centroids
+priors = Float64[1/2; 1/2]  # prior class weights
+gamma = nothing             # gamma parameter
 
-Using quadratic discriminant analysis, the resulting classification boundaries
-are quadratics:
+# Fit a model
+model = DA.LinearDiscriminantModel{Float64}()
+DA._fit!(model, y, X, dims, canonical, compute_covariance, centroids, priors, gamma)
 
-<p align="center"><img alt="Quadratic Discriminant Analysis" src="docs/src/assets/qda.png"  /></p>
+# Get the posterior probabilities for new data
+Z = rand(10,5) .- 0.5
+Z_prob = DA.posteriors(model, Z)
+```

src/discriminants.jl

@@ -22,7 +22,7 @@ function posteriors!(Π::Matrix{T}, LDA::LinearDiscriminantModel{T}, X::Matrix{T
 end
 
 
-function posteriors!(LDA::LinearDiscriminantModel{T}, X::Matrix{T}) where T
+function posteriors(LDA::LinearDiscriminantModel{T}, X::Matrix{T}) where T
     Δ = discriminants(LDA, X)
     return _posteriors!(Δ, LDA)
 end