Name  Description 

covariance(input1, input2)  
covarianceMatrix(mat, ans, pool)  These overloads allow for correlation and covariance matrices to be computed
with the results being stored in a preallocated variable, ans. ans must
be either a SciD matrix or a randomaccess range of ranges with assignable
elements of a floating point type. It must have the same number of rows
as the number of vectors in mat and must have at least enough columns in
each row to support storing the lower triangle. If ans is a full rectangular
matrix/range of ranges, only the lower triangle results will be stored.

kendallCor(input1, input2)  Kendall's Taub, O(N log N) version. This is a nonparametric measure
of monotonic association and can be defined in terms of the
bubble sort distance, or the number of swaps that would be needed in a
bubble sort to sort input2 into the same order as input1.

kendallCorDestructive(input1, input2)  Kendall's Taub O(N log N), overwrites input arrays with undefined data but
uses only O(log N) stack space for sorting, not O(N) space to duplicate
input. R1 and R2 must be either SortedRange structs with the default predicate
or arrays.

kendallCorDestructiveLowLevel(input1, input2, needTies)  
kendallMatrix(mat, ans, pool)  These overloads allow for correlation and covariance matrices to be computed
with the results being stored in a preallocated variable, ans. ans must
be either a SciD matrix or a randomaccess range of ranges with assignable
elements of a floating point type. It must have the same number of rows
as the number of vectors in mat and must have at least enough columns in
each row to support storing the lower triangle. If ans is a full rectangular
matrix/range of ranges, only the lower triangle results will be stored.

partial(vec1, vec2, conditionsIn)  Computes the partial correlation between vec1, vec2 given
conditions. conditions can be either a tuple of ranges, a range of ranges,
or (for a single condition) a single range.

pearsonCor(input1, input2)  Convenience function for calculating Pearson correlation.
When the term correlation is used unqualified, it is
usually referring to this quantity. This is a parametric correlation
metric and should not be used with extremely illbehaved data.
This function works with any pair of input ranges.

pearsonMatrix(mat, ans, pool)  These overloads allow for correlation and covariance matrices to be computed
with the results being stored in a preallocated variable, ans. ans must
be either a SciD matrix or a randomaccess range of ranges with assignable
elements of a floating point type. It must have the same number of rows
as the number of vectors in mat and must have at least enough columns in
each row to support storing the lower triangle. If ans is a full rectangular
matrix/range of ranges, only the lower triangle results will be stored.

spearmanCor(input1, input2)  Spearman's rank correlation. Nonparametric. This is essentially the
Pearson correlation of the ranks of the data, with ties dealt with by
averaging.

spearmanMatrix(mat, ans, pool)  These overloads allow for correlation and covariance matrices to be computed
with the results being stored in a preallocated variable, ans. ans must
be either a SciD matrix or a randomaccess range of ranges with assignable
elements of a floating point type. It must have the same number of rows
as the number of vectors in mat and must have at least enough columns in
each row to support storing the lower triangle. If ans is a full rectangular
matrix/range of ranges, only the lower triangle results will be stored.
