getri_uxli.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_GETRI_UXLI_HH
#define TLAPACK_GETRI_UXLI_HH
 
#include "tlapack/base/utils.hpp"
#include "tlapack/blas/copy.hpp"
#include "tlapack/blas/dotu.hpp"
#include "tlapack/blas/gemv.hpp"
 
namespace tlapack {
 
template <class T, TLAPACK_SMATRIX matrix_t>
constexpr WorkInfo getri_uxli_worksize(const matrix_t& A)
{
    if constexpr (is_same_v<T, type_t<matrix_t>>)
        return WorkInfo(ncols(A) - 1);
    else
        return WorkInfo(0);
}
 
template <TLAPACK_SMATRIX matrix_t, TLAPACK_WORKSPACE work_t>
int getri_uxli_work(matrix_t& A, work_t& work)
{
    using idx_t = size_type<matrix_t>;
    using T = type_t<matrix_t>;
    using range = pair<idx_t, idx_t>;
 
    // constant n, number of rows and also columns of A
    const idx_t n = ncols(A);
 
    // check arguments
    tlapack_check(nrows(A) == n);
 
    // Vector W
    auto [W, work2] = reshape(work, n - 1);
 
    // A has L and U in it, we will create X such that UXL=A in place of
    for (idx_t j = n - idx_t(1); j != idx_t(-1); j--) {
        // if A(j,j) is zero, then the matrix is not invertible
        if (A(j, j) == T(0)) return j + 1;
 
        if (j == n - 1) {
            A(j, j) = T(1) / A(j, j);
        }
        else {
            // X22, l21, u12 are as in method C Nick Higham
            auto X22 = tlapack::slice(A, range(j + 1, n), range(j + 1, n));
            auto l21 = tlapack::slice(A, range(j + 1, n), j);
            auto u12 = tlapack::slice(A, j, range(j + 1, n));
            auto w = tlapack::slice(W, range(0, n - j - 1));
 
            // first step of the algorithm, w holds x12
            tlapack::gemv(TRANSPOSE, T(-1) / A(j, j), X22, u12, w);
 
            // second line of the algorithm, update A(j, j)
            A(j, j) = (T(1) / A(j, j)) - tlapack::dotu(l21, w);
 
            // u12 updated, w available for use again
            tlapack::copy(w, u12);
 
            // third line of the algorithm
            tlapack::gemv(NO_TRANS, T(-1), X22, l21, w);
 
            // update l21
            tlapack::copy(w, l21);
        }
    }
 
    return 0;
}  // getri_uxli
 
template <TLAPACK_SMATRIX matrix_t>
int getri_uxli(matrix_t& A)
{
    using T = type_t<matrix_t>;
 
    // Functor
    Create<matrix_t> new_matrix;
 
    // Allocates workspace
    WorkInfo workinfo = getri_uxli_worksize<T>(A);
    std::vector<T> work_;
    auto work = new_matrix(work_, workinfo.m, workinfo.n);
 
    return getri_uxli_work(A, work);
}  // getri_uxli
 
}  // namespace tlapack
 
#endif  // TLAPACK_GETRI_UXLI_HH