The bam_stat.py was a suggestion since it also works for DNA-seq alignments (you'll hopefully don't see spliced reads).
You can also have a look at the QC-metrics from Picard tools, or have a look at GATK.
Or you can extract the aligned reads (samtools view) and count e.g. how often each read is aligned. Without trimming you might have a high %mapping rate given by samtools flagstat, but you don't know how many reads were aligned with a high confidence to a single or few positions.
Most of the library preps have also a small section of how to deal with the analysis. Additionally, there are a plethora of publications describing their approach to DNA-Seq analysis.
Cheers,
Michael
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