Example: Matrix Trace and Frobenius Norm Calculator in C++

// Matrix Trace and Frobenius Norm Calculator
#include <iostream>
#include <vector>
#include <cmath> // For std::sqrt
#include <iomanip> // For std::fixed and std::setprecision

// Function to calculate the trace of a square matrix
int calculateTrace(const std::vector<std::vector<int>>& matrix, int rows, int cols) {
    if (rows != cols) {
        return -1; // Indicate an error
    }
    int trace = 0;
    for (int i = 0; i < rows; ++i) {
        trace += matrix[i][i];
    }
    return trace;
}

// Function to calculate the Frobenius norm of a matrix
double calculateFrobeniusNorm(const std::vector<std::vector<int>>& matrix, int rows, int cols) {
    double sumOfSquares = 0.0;
    for (int i = 0; i < rows; ++i) {
        for (int j = 0; j < cols; ++j) {
            sumOfSquares += static_cast<double>(matrix[i][j]) * matrix[i][j];
        }
    }
    return std::sqrt(sumOfSquares);
}

// Function to print the matrix
void printMatrix(const std::vector<std::vector<int>>& matrix) {
    std::cout << "Matrix:" << std::endl;
    for (const auto& row : matrix) {
        for (int val : row) {
            std::cout << std::setw(3) << val << " "; // Set width for alignment
        }
        std::cout << std::endl;
    }
    std::cout << std::endl;
}

int main() {
    // Step 1: Define a sample matrix
    std::vector<std::vector<int>> myMatrix = {
        {1, 2, 3},
        {4, 5, 6},
        {7, 8, 9}
    };

    int numRows = myMatrix.size();
    int numCols = myMatrix[0].size(); // Assumes matrix is not empty

    // Step 2: Print the matrix
    printMatrix(myMatrix);

    // Step 3: Calculate and display the trace
    int traceValue = calculateTrace(myMatrix, numRows, numCols);
    if (traceValue != -1) {
        std::cout << "Trace of the matrix: " << traceValue << std::endl;
    } else {
        std::cout << "Cannot calculate trace: Matrix is not square." << std::endl;
    }

    // Step 4: Calculate and display the Frobenius norm
    double normValue = calculateFrobeniusNorm(myMatrix, numRows, numCols);
    std::cout << std::fixed << std::setprecision(4); // Format output to 4 decimal places
    std::cout << "Frobenius Norm of the matrix: " << normValue << std::endl;

    return 0;
}