gesvd.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_GESVD_HH
#define TLAPACK_GESVD_HH
 
#include "tlapack/base/utils.hpp"
#include "tlapack/lapack/gebrd.hpp"
#include "tlapack/lapack/svd_qr.hpp"
#include "tlapack/lapack/ungbr.hpp"
 
namespace tlapack {
 
struct GesvdOpts {
    float shapethresh = 1.6;
};
 
template <TLAPACK_SMATRIX matrix_t, TLAPACK_SVECTOR r_vector_t>
int gesvd(bool want_u,
          bool want_vt,
          matrix_t& A,
          r_vector_t& s,
          matrix_t& U,
          matrix_t& Vt,
          const GesvdOpts& opts = {})
{
    using idx_t = size_type<matrix_t>;
    using range = pair<idx_t, idx_t>;
 
    // Functors
    Create<vector_type<matrix_t>> new_vector;
    Create<vector_type<r_vector_t>> new_rvector;
 
    // constants
    const idx_t m = nrows(A);
    const idx_t n = ncols(A);
    const idx_t k = min(m, n);
    const Uplo uplo = (m >= n) ? Uplo::Upper : Uplo::Lower;
 
    // Allocate vectors
    std::vector<type_t<matrix_t>> tauv_, tauw_;
    auto tauv = new_vector(tauv_, k);
    auto tauw = new_vector(tauw_, k);
    std::vector<type_t<r_vector_t>> e_;
    auto e = new_rvector(e_, k);
 
    // Reduce A to bidiagonal form
    gebrd(A, tauv, tauw);
 
    if (m >= n) {
        // copy upper bidiagonal matrix
        for (idx_t i = 0; i < k; ++i) {
            s[i] = real(A(i, i));
            if (i + 1 < n) e[i] = real(A(i, i + 1));
        }
    }
    else {
        // copy lower bidiagonal matrix
        for (idx_t i = 0; i < k; ++i) {
            s[i] = real(A(i, i));
            if (i + 1 < m) e[i] = real(A(i + 1, i));
        }
    }
 
    if (want_u) {
        auto Ui = slice(U, range{0, m}, range{0, k});
        lacpy(Uplo::Lower, slice(A, range{0, m}, range{0, k}), Ui);
        ungbr_q(n, U, tauv);
    }
 
    if (want_vt) {
        auto Vti = slice(Vt, range{0, k}, range{0, n});
        lacpy(Uplo::Upper, slice(A, range{0, k}, range{0, n}), Vti);
        ungbr_p(m, Vt, tauw);
    }
 
    return svd_qr(uplo, want_u, want_vt, s, e, U, Vt);
}
 
}  // namespace tlapack
 
#endif  // TLAPACK_GESVD_HH