lange.hpp

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//
// Copyright (c) 2021-2023, 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_LANGE_HH
#define TLAPACK_LANGE_HH
 
#include "tlapack/lapack/lassq.hpp"
 
namespace tlapack {
 
template <TLAPACK_NORM norm_t, TLAPACK_SMATRIX matrix_t>
auto lange(norm_t normType, const matrix_t& A)
{
    using T = type_t<matrix_t>;
    using real_t = real_type<T>;
    using idx_t = size_type<matrix_t>;
 
    // constants
    const idx_t m = nrows(A);
    const idx_t n = ncols(A);
 
    // check arguments
    tlapack_check_false(normType != Norm::Fro && normType != Norm::Inf &&
                        normType != Norm::Max && normType != Norm::One);
 
    // quick return
    if (m == 0 || n == 0) return real_t(0);
 
    // Norm value
    real_t norm(0);
 
    if (normType == Norm::Max) {
        for (idx_t j = 0; j < n; ++j) {
            for (idx_t i = 0; i < m; ++i) {
                real_t temp = abs(A(i, j));
 
                if (temp > norm)
                    norm = temp;
                else {
                    if (isnan(temp)) return temp;
                }
            }
        }
    }
    else if (normType == Norm::Inf) {
        for (idx_t i = 0; i < m; ++i) {
            real_t sum(0);
            for (idx_t j = 0; j < n; ++j)
                sum += abs(A(i, j));
 
            if (sum > norm)
                norm = sum;
            else {
                if (isnan(sum)) return sum;
            }
        }
    }
    else if (normType == Norm::One) {
        for (idx_t j = 0; j < n; ++j) {
            real_t sum(0);
            for (idx_t i = 0; i < m; ++i)
                sum += abs(A(i, j));
 
            if (sum > norm)
                norm = sum;
            else {
                if (isnan(sum)) return sum;
            }
        }
    }
    else {
        real_t scale(0), sum(1);
        for (idx_t j = 0; j < n; ++j)
            lassq(col(A, j), scale, sum);
        norm = scale * sqrt(sum);
    }
 
    return norm;
}
 
}  // namespace tlapack
 
#endif  // TLAPACK_LANGE_HH