Finding the matrix tangent function using Taylor series.
Here’s a Java program that calculates the tangent function for a given matrix using the Taylor series approximation:
import java.util.Arrays;
public class MatrixTangent {
public static double[][] calculateTangent(double[][] matrix, int iterations) {
int rows = matrix.length;
int columns = matrix[0].length;
double[][] tangentMatrix = new double[rows][columns];
for (int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
tangentMatrix[i][j] = calculateTerm(matrix[i][j], iterations);
}
}
return tangentMatrix;
}
private static double calculateTerm(double value, int iterations) {
double term = 0;
double numerator = value;
double denominator = 1;
double power = value;
int sign = 1;
for (int i = 0; i < iterations; i++) {
term += sign * numerator / denominator;
numerator *= power * power;
denominator *= (2 * i + 3) * (2 * i + 2);
power *= value * value;
sign *= -1;
}
return term;
}
public static void main(String[] args) {
double[][] matrix = {
{0.5, 0.75},
{1.2, 1.8}
};
int iterations = 5;
double[][] tangentMatrix = calculateTangent(matrix, iterations);
System.out.println("Input Matrix:");
for (double[] row : matrix) {
System.out.println(Arrays.toString(row));
}
System.out.println("\nTangent Matrix (approximation):");
for (double[] row : tangentMatrix) {
System.out.println(Arrays.toString(row));
}
}
}
In this example, the `calculateTangent` method takes a matrix and the number of iterations as input. It initializes a new matrix of the same size to store the tangent values. Then, it iterates over each element of the input matrix and calls the `calculateTerm` method to compute the tangent approximation using the Taylor series.
The `calculateTerm` method implements the Taylor series approximation for the tangent function. It iterates for the specified number of iterations and accumulates the terms using the provided formula.
In the `main` method, an example matrix and the number of iterations are defined. The `calculateTangent` method is called with these inputs, and the resulting tangent matrix is printed to the console.
Please note that the Taylor series approximation for the tangent function might not provide accurate results for large values or close to singularities, as the series converges slowly in those cases.