sgccak: Internal function for computing the SGCCA parameters (SGCCA...
In ecamenen/r-rgcca: RGCCA and Sparse GCCA for multi-block data analysis

The function sgccak() is called by sgcca() and does not have to be used by the user. sgccak() enables the computation of SGCCA block components, outer weight vectors, etc., for each block and each dimension.

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  sgccak(A, C, c1 = rep(1, length(A)), scheme = "centroid",
    scale = FALSE, tol = .Machine$double.eps, init = "svd",
    bias = TRUE, verbose = TRUE)

`A`	A list that contains the J blocks of variables from which block components are constructed. It could be eiher the original matrices (\mathbf{X}_1, \mathbf{X}_2, …, \mathbf{X}_J) or the residual matrices (\mathbf{X}_{h1}, \mathbf{X}_{h2}, …, \mathbf{X}_{hJ}).
`C`	A design matrix that describes the relationships between blocks.
`c1`	A 1 \times J vector that contains the value of c1 applied to each block. The L1 bound on a[[j]] is \\|a_{j}\\|_{\ell_1} ≤q c_1[j] √{p_j}. with p_j the number of variables of \mathbf{X}_j and with c1[j] between 0 and 1 (larger L1 bound corresponds to less penalization).
`scheme`	Either "horst", "factorial" or "centroid" (default: centroid).
`scale`	If scale = TRUE, each block is standardized to zero means and unit variances (default: TRUE).
`init`	Mode of initialization of the SGCCA algorithm. Either by Singular Value Decompostion ("svd") or random ("random") (default: "svd").
`bias`	Logical value for biaised (1/n) or unbiaised (1/(n-1)) estimator of the var/cov.
`verbose`	Reports progress while computing, if verbose = TRUE (default: TRUE).
`tol`	Stopping value for convergence.

`Y`	A n \times J matrix of SGCCA block components.
`a`	A list of J elements. Each element contains the outer weight vector of each block.
`crit`	The values of the objective function at each iteration of the iterative procedure.
`converg`	Speed of convergence of the alogrithm to reach the tolerance.
`AVE`	Indicators of model quality based on the Average Variance Explained (AVE): AVE(for one block), AVE(outer model), AVE(inner model).
`C`	A design matrix that describes the relationships between blocks (user specified).
`scheme`	The scheme chosen by the user (user specified).