89 lines
2.7 KiB
C
89 lines
2.7 KiB
C
// The need for `USE_FC_LEN_T` and `FCONE` is due to a Fortran character string
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// to C incompatibility. See: Writing R Extentions: 6.6.1 Fortran character strings
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#define USE_FC_LEN_T
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#include <R.h>
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#include <Rinternals.h>
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#include <R_ext/BLAS.h>
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#ifndef FCONE
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#define FCONE
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#endif
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/**
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* Tensor Mode Crossproduct
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*
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* C = A_(m) t(A_(m))
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*
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* For a matrix `A`, the first mode is `mcrossprod(A, 1)` equivalent to
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* `A %*% t(A)` (`tcrossprod`). On the other hand for mode two `mcrossprod(A, 2)`
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* the equivalence is `t(A) %*% A` (`crossprod`).
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*
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* @param A multi-dimensional array
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* @param m mode index (1-indexed)
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*/
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extern SEXP mcrossprod(SEXP A, SEXP m) {
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// get zero indexed mode
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int mode = asInteger(m) - 1;
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// get dimension attribute of A
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SEXP dim = getAttrib(A, R_DimSymbol);
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// validate mode (0-indexed, must be smaller than the tensor order)
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if (mode < 0 || length(dim) <= mode) {
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error("Illegal mode");
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}
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// the strides
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// `stride[0] <- prod(dim(X)[seq_len(mode - 1)])`
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// `stride[1] <- dim(X)[mode]`
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// `stride[2] <- prod(dim(X)[-seq_len(mode)])`
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int stride[3] = {1, INTEGER(dim)[mode], 1};
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for (int i = 0; i < length(dim); ++i) {
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int size = INTEGER(dim)[i];
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stride[0] *= (i < mode) ? size : 1;
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stride[2] *= (i > mode) ? size : 1;
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}
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// create response matrix C
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SEXP C = PROTECT(allocMatrix(REALSXP, stride[1], stride[1]));
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// raw data access pointers
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double* a = REAL(A);
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double* c = REAL(C);
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// employ BLAS dsyrk (Double SYmmeric Rank K) operation
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// (C = alpha A A^T + beta C or C = alpha A^T A + beta C)
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const double zero = 0.0;
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const double one = 1.0;
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if (mode == 0) {
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// mode 1: special case C = A_(1) A_(1)^T
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// C = 1 A A^T + 0 C
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F77_CALL(dsyrk)("U", "N", &stride[1], &stride[2],
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&one, a, &stride[1], &zero, c, &stride[1] FCONE FCONE);
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} else {
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// Other modes writen as accumulated sum of matrix products
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// initialize C to zero
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memset(c, 0, stride[1] * stride[1] * sizeof(double));
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// Sum over all modes > mode
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for (int i2 = 0; i2 < stride[2]; ++i2) {
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// C = 1 A^T A + 1 C
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F77_CALL(dsyrk)("U", "T", &stride[1], &stride[0],
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&one, &a[i2 * stride[0] * stride[1]], &stride[0],
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&one, c, &stride[1] FCONE FCONE);
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}
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}
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// Symmetric matrix result is stored in upper triangular part only
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// Copy upper triangular part to lower
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for (int j = 0; j + 1 < stride[1]; j++) {
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for (int i = j + 1; i < stride[1]; ++i) {
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c[i + j * stride[1]] = c[j + i * stride[1]];
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}
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}
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// release C to grabage collector
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UNPROTECT(1);
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return C;
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}
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