Interactive computer programs for petrologic modeling with extended Q-mode factor analysis

An extended form of Q-mode factor analysis may be used if the row-sums of the data matrix are constant and can be helpful especially in developing and testing petrologic-mixing models for igneous systems. The first step is to represent the sample compositions as unit vectors in M-dimensional space and then to project them into space of fewer dimensions (m) as determined to be appropriate from a factor-variance diagram. Compositions thought to be those of possible end-members in the petrologic system then are represented as vectors in the M-dimensional space and projected into the same space as the sample vectors. If these vectors remain close to unity in length after projection, the corresponding compositions can serve as end-member compositions for the model. After m suitable end-member compositions have been identified, each sample composition is expressed as a mixture of the end-members by computation of the composition loadings. The interactive computer programs presented are useful in these procedures because of the trial-and-error nature of the modeling procedures. ?? 1976.