potrf_blocked_right_looking.hpp

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//
// Copyright (c) 2025, University of Colorado Denver. All rights reserved.
//
// This file is part of <T>LAPACK.
// <T>LAPACK is free software: you can redistribute it and/or modify it under
// the terms of the BSD 3-Clause license. See the accompanying LICENSE file.
 
#ifndef TLAPACK_POTRF_BLOCKED_RL_HH
#define TLAPACK_POTRF_BLOCKED_RL_HH
 
#include "tlapack/base/utils.hpp"
#include "tlapack/blas/herk.hpp"
#include "tlapack/blas/trsm.hpp"
#include "tlapack/lapack/potf2.hpp"
#include "tlapack/lapack/potrf_blocked.hpp"
 
namespace tlapack {
 
template <TLAPACK_UPLO uplo_t, TLAPACK_SMATRIX matrix_t>
int potrf_rl(uplo_t uplo, matrix_t& A, const BlockedCholeskyOpts& opts = {})
{
    using T = type_t<matrix_t>;
    using real_t = real_type<T>;
    using idx_t = size_type<matrix_t>;
    using range = pair<idx_t, idx_t>;
 
    // Constants
    const real_t one(1);
    const idx_t n = nrows(A);
    const idx_t nb = opts.nb;
 
    // check arguments
    tlapack_check(uplo == Uplo::Lower || uplo == Uplo::Upper);
    tlapack_check(nrows(A) == ncols(A));
 
    // Quick return
    if (n <= 0) return 0;
 
    // Unblocked code
    else if (nb >= n)
        return potf2(uplo, A);
 
    // Blocked code
    else {
        if (uplo == Uplo::Upper) {
            for (idx_t j = 0; j < n; j += nb) {
                idx_t jb = min(nb, n - j);
 
                // Define AJJ
                auto AJJ = slice(A, range{j, j + jb}, range{j, j + jb});
 
                int info = potf2(UPPER_TRIANGLE, AJJ);
                if (info != 0) {
                    tlapack_error(
                        info + j,
                        "The leading minor of the reported order is not "
                        "positive definite,"
                        " and the factorization could not be completed.");
                    return info + j;
                }
 
                if (j + jb < n) {
                    auto B = slice(A, range{j, j + jb}, range{j + jb, n});
                    auto C = slice(A, range{j + jb, n}, range{j + jb, n});
 
                    trsm(LEFT_SIDE, UPPER_TRIANGLE, CONJ_TRANS, NON_UNIT_DIAG,
                         one, AJJ, B);
                    herk(UPPER_TRIANGLE, CONJ_TRANS, -one, B, one, C);
                }
            }
        }
        else {
            for (idx_t j = 0; j < n; j += nb) {
                idx_t jb = min(nb, n - j);
 
                // Define AJJ
                auto AJJ = slice(A, range{j, j + jb}, range{j, j + jb});
 
                int info = potf2(LOWER_TRIANGLE, AJJ);
                if (info != 0) {
                    tlapack_error(
                        info + j,
                        "The leading minor of the reported order is not "
                        "positive definite,"
                        " and the factorization could not be completed.");
                    return info + j;
                }
 
                if (j + jb < n) {
                    auto B = slice(A, range{j + jb, n}, range{j, j + jb});
                    auto C = slice(A, range{j + jb, n}, range{j + jb, n});
 
                    trsm(RIGHT_SIDE, LOWER_TRIANGLE, CONJ_TRANS, NON_UNIT_DIAG,
                         one, AJJ, B);
                    herk(LOWER_TRIANGLE, NO_TRANS, -one, B, one, C);
                }
            }
        }
 
        return 0;
    }
}
 
}  // namespace tlapack
 
#endif  // TLAPACK_POTRF_BLOCKED_RL_HH