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refactor: InverseOfMatrix (#5446)

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refactor: InverseOfMatrix
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Alex Klymenko 2024-09-09 09:15:41 +02:00 committed by GitHub
parent bded78f888
commit 65e32641fc
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2 changed files with 52 additions and 50 deletions
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74
src/main/java/com/thealgorithms/misc/InverseOfMatrix.java
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@ -1,57 +1,29 @@
package com.thealgorithms.misc;
import java.util.Scanner;
/*
* Wikipedia link : https://en.wikipedia.org/wiki/Invertible_matrix
*
* Here we use gauss elimination method to find the inverse of a given matrix.
* To understand gauss elimination method to find inverse of a matrix:
* https://www.sangakoo.com/en/unit/inverse-matrix-method-of-gaussian-elimination
*
* We can also find the inverse of a matrix
/**
* This class provides methods to compute the inverse of a square matrix
* using Gaussian elimination. For more details, refer to:
* https://en.wikipedia.org/wiki/Invertible_matrix
*/
public final class InverseOfMatrix {
private InverseOfMatrix() {
}
public static void main(String[] argv) {
Scanner input = new Scanner(System.in);
System.out.println("Enter the matrix size (Square matrix only): ");
int n = input.nextInt();
double[][] a = new double[n][n];
System.out.println("Enter the elements of matrix: ");
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
a[i][j] = input.nextDouble();
}
}
double[][] d = invert(a);
System.out.println();
System.out.println("The inverse is: ");
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
System.out.print(d[i][j] + " ");
}
System.out.println();
}
input.close();
}
public static double[][] invert(double[][] a) {
int n = a.length;
double[][] x = new double[n][n];
double[][] b = new double[n][n];
int[] index = new int[n];
// Initialize the identity matrix
for (int i = 0; i < n; ++i) {
b[i][i] = 1;
}
// Transform the matrix into an upper triangle
// Perform Gaussian elimination
gaussian(a, index);
// Update the matrix b[i][j] with the ratios stored
// Update matrix b with the ratios stored during elimination
for (int i = 0; i < n - 1; ++i) {
for (int j = i + 1; j < n; ++j) {
for (int k = 0; k < n; ++k) {
@ -60,7 +32,7 @@ public final class InverseOfMatrix {
}
}
// Perform backward substitutions
// Perform backward substitution to find the inverse
for (int i = 0; i < n; ++i) {
x[n - 1][i] = b[index[n - 1]][i] / a[index[n - 1]][n - 1];
for (int j = n - 2; j >= 0; --j) {
@ -73,19 +45,20 @@ public final class InverseOfMatrix {
}
return x;
}
// Method to carry out the partial-pivoting Gaussian
// elimination. Here index[] stores pivoting order.
public static void gaussian(double[][] a, int[] index) {
/**
* Method to carry out the partial-pivoting Gaussian
* elimination. Here index[] stores pivoting order.
**/
private static void gaussian(double[][] a, int[] index) {
int n = index.length;
double[] c = new double[n];
// Initialize the index
// Initialize the index array
for (int i = 0; i < n; ++i) {
index[i] = i;
}
// Find the rescaling factors, one from each row
// Find the rescaling factors for each row
for (int i = 0; i < n; ++i) {
double c1 = 0;
for (int j = 0; j < n; ++j) {
@ -97,22 +70,23 @@ public final class InverseOfMatrix {
c[i] = c1;
}
// Search the pivoting element from each column
int k = 0;
// Perform pivoting
for (int j = 0; j < n - 1; ++j) {
double pi1 = 0;
int k = j;
for (int i = j; i < n; ++i) {
double pi0 = Math.abs(a[index[i]][j]);
pi0 /= c[index[i]];
double pi0 = Math.abs(a[index[i]][j]) / c[index[i]];
if (pi0 > pi1) {
pi1 = pi0;
k = i;
}
}
// Interchange rows according to the pivoting order
int itmp = index[j];
// Swap rows
int temp = index[j];
index[j] = index[k];
index[k] = itmp;
index[k] = temp;
for (int i = j + 1; i < n; ++i) {
double pj = a[index[i]][j] / a[index[j]][j];

28
src/test/java/com/thealgorithms/misc/InverseOfMatrixTest.java Normal file
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@ -0,0 +1,28 @@
package com.thealgorithms.misc;
import static org.junit.jupiter.api.Assertions.assertArrayEquals;
import java.util.stream.Stream;
import org.junit.jupiter.params.ParameterizedTest;
import org.junit.jupiter.params.provider.Arguments;
import org.junit.jupiter.params.provider.MethodSource;
class InverseOfMatrixTest {
@ParameterizedTest
@MethodSource("provideTestCases")
void testInvert(double[][] matrix, double[][] expectedInverse) {
double[][] result = InverseOfMatrix.invert(matrix);
assertMatrixEquals(expectedInverse, result);
}
private static Stream<Arguments> provideTestCases() {
return Stream.of(Arguments.of(new double[][] {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, new double[][] {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}), Arguments.of(new double[][] {{4, 7}, {2, 6}}, new double[][] {{0.6, -0.7}, {-0.2, 0.4}}));
}
private void assertMatrixEquals(double[][] expected, double[][] actual) {
for (int i = 0; i < expected.length; i++) {
assertArrayEquals(expected[i], actual[i], 1.0E-10, "Row " + i + " is not equal");
}
}
}