adjR2: Gridwise adjusted R2 for O2PLS
In selbouhaddani/O2PLS: O2PLS: Two-Way Orthogonal Partial Least Squares

Description Usage Arguments Details Value

For (a grid of) values for a, nx and ny, loocv calculates the R2 of the joint part. Parallel computing is supported on Windows with package parallel.

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adjR2(X, Y, a = 1:2, a2 = 1, b2 = 1, func = o2m, parall = F,
  cl = NULL, stripped = TRUE, p_thresh = 3000, q_thresh = p_thresh,
  tol = 1e-10, max_iterations = 100)

`X`	Numeric matrix. Vectors will be coerced to matrix with `as.matrix` (if this is possible)
`Y`	Numeric matrix. Vectors will be coerced to matrix with `as.matrix` (if this is possible)
`a`	Vector of integers. Contains the numbers of joint components.
`a2`	Vector of integers. Contains the numbers of orthogonal components in X.
`b2`	Vector of integers. Contains the numbers of orthogonal components in Y.
`func`	Function to fit the O2PLS model with. Only `o2m` and `o2m_stripped` are supported.
`parall`	Integer. Should a parallel cluster be set up using package `parallel` (Windows)? Best is to leave it to `FALSE`.
`cl`	Object of class '`cluster`'. If parall is `TRUE` and `cl` is not `NULL`, calculations are parallelized over workers in cl.
`stripped`	Logical. Use the stripped version of o2m (usually when cross-validating)?
`p_thresh`	Integer. If `X` has more than `p_thresh` columns, a power method optimization is used, see `o2m2`
`q_thresh`	Integer. If `Y` has more than `q_thresh` columns, a power method optimization is used, see `o2m2`
`tol`	double. Threshold for power method iteration
`max_iterations`	Integer, Maximum number of iterations for power method

The use of this function is to calculate the R2 of the joint part, while varying the number of orthogonal components. Adding more joint components will increase the R2!

A parallelized version is built in -tested on windows-, use package parallel and set parall=TRUE to activate this. There should not be already a cluster object with the name cl. In case of some error, don't forget to invoke stopCluster(cl) to end the cluster. See Task Manager (Windows) to verify that the workers are spanned/ended.

See loocv for more intuition.

Matrix with two rows: