NaivePCA performs PCA for population genotype data. It implements the basic algorithm as is described by Patterson et al (2006). More precisely, suppose we have m samples of ploidy h and n biallelic markers. Let G_ij be the number of non-reference alleles for sample i at marker j. NaivePCA computes:

\mu_j  = \sum_{i=1}^m G_{ij} / m
p_j    = \mu_j / h
M_{ij} = \frac{G_{ij}-\mu_j}{\sqrt{p_j(1-p_j)}}
X_{ij} = \sum_{k=1}^n M_{ik} M_{jk} / n

and finds the eigenvectors of matrix (X_ij). Notably, if G_ij is missing data, M_ij takes zero and the computation of μ_j needs to be adjusted as well.

The input of NaivePCA looks like:

sample1  110022110100202021001122*201
sample2  2012201102*221020211*1222001

where a number represents a genotype and other characters are treated as missing data. For now, NaivePCA does not support real matrices. The output is TAB-delimited. The first column is the sample name. The i-th column gives the eigenvector corresponding the (i-1)-th largest eigenvalue.