Table of Contents

Parallel 2 Condition Number Matrix Software Manual

Routine Name: parallel_condition_2_estimate

Author: Philip Nelson

Language: C++. The code can be compiled using the GNU C++ compiler (gcc). A make file is included to compile an example program

For example,

make

will produce an executable ./condition.out that can be executed.

Description/Purpose: computes the 2 condition number of a matrix.

This code uses OpenMP to parallelize the power iteration and inverse power iteration functions in order to increase computation speed.

Input: A matrix A and a max number of iterations.

Output: The 2 condition of the matrix

Usage/Example:

int main()
{
  auto A = generate_square_symmetric_diagonally_dominant_matrix(5u);

  auto condtitionNum = parallel_condition_2_estimate(A, 1000u);
  std::cout << "A\n" << A << std::endl;
  std::cout << "2 Condition Number\n" << condtitionNum << std::endl;
}

Output from the lines above

A
|      -9.17      2.89     0.378      4.41      3.44 |
|       2.89      8.95     -3.28    -0.387      6.29 |
|      0.378     -3.28      8.94      -5.1      7.99 |
|       4.41    -0.387      -5.1      6.38      6.22 |
|       3.44      6.29      7.99      6.22      11.5 |

2 Condition Number
3.65

explanation of output:

First the matrix is output, then the condition number.

Implementation/Code: The following is the code for condition_2_estimate

As you can see, the code uses the parallel power and inverse power iteration functions previously written in 6.4 and 6.5

template <typename T>
T parallel_condition_2_estimate(Matrix<T> const& A, unsigned int const& MAX)
{
  auto maxEig = parallel_power_iteration(A, MAX);
  auto minEig = parallel_inverse_power_iteration(A, MAX);
  return std::abs(maxEig / minEig);
}

Last Modified: December 2018