// The need for `USE_FC_LEN_T` and `FCONE` is due to a Fortran character string
// to C incompatibility. See: Writing R Extentions: 6.6.1 Fortran character strings
#define USE_FC_LEN_T
#include <R.h>
#include <Rinternals.h>
#include <R_ext/BLAS.h>
#ifndef FCONE
#define FCONE
#endif

/**
 * Tensor Mode Crossproduct
 *
 *      C = A_(m) t(A_(m))
 *
 * For a matrix `A`, the first mode is `mcrossprod(A, 1)` equivalent to
 * `A %*% t(A)` (`tcrossprod`). On the other hand for mode two `mcrossprod(A, 2)`
 * the equivalence is `t(A) %*% A` (`crossprod`).
 *
 * @param A multi-dimensional array
 * @param m mode index (1-indexed)
 */
extern SEXP mcrossprod(SEXP A, SEXP m) {
    // get zero indexed mode
    int mode = asInteger(m) - 1;

    // get dimension attribute of A
    SEXP dim = getAttrib(A, R_DimSymbol);

    // validate mode (0-indexed, must be smaller than the tensor order)
    if (mode < 0 || length(dim) <= mode) {
        error("Illegal mode");
    }

    // the strides
    //  `stride[0] <- prod(dim(X)[seq_len(mode - 1)])`
    //  `stride[1] <- dim(X)[mode]`
    //  `stride[2] <- prod(dim(X)[-seq_len(mode)])`
    int stride[3] = {1, INTEGER(dim)[mode], 1};
    for (int i = 0; i < length(dim); ++i) {
        int size = INTEGER(dim)[i];
        stride[0] *= (i < mode) ? size : 1;
        stride[2] *= (i > mode) ? size : 1;
    }

    // create response matrix C
    SEXP C = PROTECT(allocMatrix(REALSXP, stride[1], stride[1]));

    // raw data access pointers
    double* a = REAL(A);
    double* c = REAL(C);

    // employ BLAS dsyrk (Double SYmmeric Rank K) operation
    // (C = alpha A A^T + beta C or C = alpha A^T A + beta C)
    const double zero = 0.0;
    const double one  = 1.0;
    if (mode == 0) {
        // mode 1: special case C = A_(1) A_(1)^T
        // C = 1 A A^T + 0 C
        F77_CALL(dsyrk)("U", "N", &stride[1], &stride[2],
            &one, a, &stride[1], &zero, c, &stride[1] FCONE FCONE);
    } else {
        // Other modes writen as accumulated sum of matrix products
        // initialize C to zero
        memset(c, 0, stride[1] * stride[1] * sizeof(double));

        // Sum over all modes > mode
        for (int i2 = 0; i2 < stride[2]; ++i2) {
            // C = 1 A^T A + 1 C
            F77_CALL(dsyrk)("U", "T", &stride[1], &stride[0],
                &one, &a[i2 * stride[0] * stride[1]], &stride[0],
                &one, c, &stride[1] FCONE FCONE);
        }
    }

    // Symmetric matrix result is stored in upper triangular part only
    // Copy upper triangular part to lower
    for (int j = 0; j + 1 < stride[1]; j++) {
        for (int i = j + 1; i < stride[1]; ++i) {
            c[i + j * stride[1]] = c[j + i * stride[1]];
        }
    }

    // release C to grabage collector
    UNPROTECT(1);

    return C;
}