Finding the matrix inverse hyperbolic tangent function using Taylor series.

Here’s a Java program that calculates the inverse hyperbolic tangent (arctanh) of a matrix using the Taylor series expansion:

  import java.util.Arrays;

   public class MatrixInverseHyperbolicTangent {

    // Number of terms in the Taylor series expansion

    private static final int TERMS = 10;

    // Calculate the power of x with the given exponent

    private static double power(double x, int exponent) {

        double result = 1.0;

        for (int i = 0; i < exponent; i++) {

            result *= x;

        }

        return result;

    }

    // Calculate the factorial of n

    private static int factorial(int n) {

        int result = 1;

        for (int i = 2; i <= n; i++) {

            result *= i;

        }

        return result;

    }

    // Calculate the inverse hyperbolic tangent of x using Taylor series

    private static double arctanh(double x) {

        double result = 0.0;

        for (int n = 0; n < TERMS; n++) {

            double numerator = power(x, 2 * n + 1);

            double denominator = 2 * n + 1;

            double term = numerator / denominator;

            if (n % 2 == 1) {

                term *= -1;

            }

            result += term;

        }

        return result;

    }

    // Calculate the inverse hyperbolic tangent of a matrix

    private static double[][] matrixArctanh(double[][] matrix) {

        int rows = matrix.length;

        int cols = matrix[0].length;

        double[][] result = new double[rows][cols];

        for (int i = 0; i < rows; i++) {

            for (int j = 0; j < cols; j++) {

                result[i][j] = arctanh(matrix[i][j]);

            }

        }

        return result;

    }

    // Utility method to print a matrix

    private static void printMatrix(double[][] matrix) {

        for (double[] row : matrix) {

            System.out.println(Arrays.toString(row));

        }

    }

    // Test the program

    public static void main(String[] args) {

        double[][] matrix = {

            {0.5, 0.2},

            {-0.4, 0.8}

        };

        double[][] inverseArctanhMatrix = matrixArctanh(matrix);

        System.out.println("Matrix:");

        printMatrix(matrix);

        System.out.println("Inverse Hyperbolic Tangent Matrix:");

        printMatrix(inverseArctanhMatrix);

    }

}

In this program, the `arctanh()` method calculates the inverse hyperbolic tangent of a single value using the Taylor series expansion. The `matrixArctanh()` method applies the `arctanh()` function to each element of the input matrix to obtain the inverse hyperbolic tangent matrix.

The program includes a `printMatrix()` utility method to display the matrices neatly.

You can run this program to test it with your desired matrix and observe the resulting inverse hyperbolic tangent matrix.