transpose.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_TRANSPOSE_HH
#define TLAPACK_TRANSPOSE_HH
 
#include "tlapack/base/utils.hpp"
 
namespace tlapack {
struct TransposeOpts {
    // Optimization parameter. Matrices smaller than nx will not
    // be transposed using recursion. Must be at least 2.s
    size_t nx = 16;
};
 
template <TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixB_t>
void conjtranspose(matrixA_t& A, matrixB_t& B, const TransposeOpts& opts = {})
{
    using idx_t = size_type<matrixA_t>;
    using range = pair<idx_t, idx_t>;
 
    const idx_t m = nrows(A);
    const idx_t n = ncols(A);
 
    tlapack_check(m == ncols(B));
    tlapack_check(n == nrows(B));
    tlapack_check(opts.nx >= 2);
 
    if (min(m, n) <= (idx_t)opts.nx) {
        // The matrix is small, use direct method and end recursion
        for (idx_t i = 0; i < m; ++i)
            for (idx_t j = 0; j < n; ++j)
                B(j, i) = conj(A(i, j));
    }
    else {
        // The matrix is large, split into subblocks and use recursion
        const idx_t m1 = m / 2;
        const idx_t n1 = n / 2;
 
        auto A00 = slice(A, range(0, m1), range(0, n1));
        auto A01 = slice(A, range(0, m1), range(n1, n));
        auto A10 = slice(A, range(m1, m), range(0, n1));
        auto A11 = slice(A, range(m1, m), range(n1, n));
 
        auto B00 = slice(B, range(0, n1), range(0, m1));
        auto B01 = slice(B, range(0, n1), range(m1, m));
        auto B10 = slice(B, range(n1, n), range(0, m1));
        auto B11 = slice(B, range(n1, n), range(m1, m));
 
        conjtranspose(A00, B00, opts);
        conjtranspose(A01, B10, opts);
        conjtranspose(A10, B01, opts);
        conjtranspose(A11, B11, opts);
    }
}
 
template <TLAPACK_SMATRIX matrixA_t, TLAPACK_SMATRIX matrixB_t>
void transpose(matrixA_t& A, matrixB_t& B, const TransposeOpts& opts = {})
{
    using idx_t = size_type<matrixA_t>;
    using range = pair<idx_t, idx_t>;
 
    const idx_t m = nrows(A);
    const idx_t n = ncols(A);
 
    tlapack_check(m == ncols(B));
    tlapack_check(n == nrows(B));
    tlapack_check(opts.nx >= 2);
 
    if (min(m, n) <= (idx_t)opts.nx) {
        // The matrix is small, use direct method and end recursion
        for (idx_t i = 0; i < m; ++i)
            for (idx_t j = 0; j < n; ++j)
                B(j, i) = A(i, j);
    }
    else {
        // The matrix is large, split into subblocks and use recursion
        const idx_t m1 = m / 2;
        const idx_t n1 = n / 2;
 
        auto A00 = slice(A, range(0, m1), range(0, n1));
        auto A01 = slice(A, range(0, m1), range(n1, n));
        auto A10 = slice(A, range(m1, m), range(0, n1));
        auto A11 = slice(A, range(m1, m), range(n1, n));
 
        auto B00 = slice(B, range(0, n1), range(0, m1));
        auto B01 = slice(B, range(0, n1), range(m1, m));
        auto B10 = slice(B, range(n1, n), range(0, m1));
        auto B11 = slice(B, range(n1, n), range(m1, m));
 
        transpose(A00, B00, opts);
        transpose(A01, B10, opts);
        transpose(A10, B01, opts);
        transpose(A11, B11, opts);
    }
}
 
}  // namespace tlapack
 
#endif  // TLAPACK_TRANSPOSE_HH