Table of Contents

Matrix Infinity Norm

Routine Name: infNorm

Author: Philip Nelson

Language: C++

Description

infNorm calculates the infinity norm of a matrix. The infinity norm, \(|A|_{\infty }\) is the largest absolute sum of the rows of \(A\).

Input

infNorm(Matrix<T, M, N>& m) requires:

• Matrix<T, M, N> m - an MxN matrix of type T

Output

A double with the value of the infinity norm

Code

template <typename T, std::size_t M, std::size_t N>
T infNorm(Matrix<T, M, N>& m)
{
  std::array<T, N> rowSum;
  for (auto i = 0u; i < N; ++i)
    rowSum[i] = std::accumulate(
      m.begin(i), m.end(i), 0, [](T sum, T elem) { return sum + std::abs(elem); });

  return *std::max_element(rowSum.begin(), rowSum.end());
}

Example

int main()
{
  Matrix<int, 3, 3> A({
                      {6, 1, 1},
                      {4, -2, 5},
                      {2, 8, 7}
                      });

  std::cout << " A\n" << A << std::endl;
  std::cout << "Infinity Norm: " << infNorm(A) << std::endl;
}

Result

 A
|          6         1         1 |
|          4        -2         5 |
|          2         8         7 |

Infinity Norm: 17

Last Modification date: 10 February 2018