Java uses Colt for Singular value decomposition
Colt (Computational Language and Toolkit) is an open-source Java scientific computing library that provides a series of high-performance scientific computing and data analysis functions. It includes matrix calculation, Linear algebra, statistical analysis, Random number generation, optimization algorithm and other modules.
In Colt library, Singular value decomposition can be implemented using SingularValueDecomposition class. Singular value decomposition (SVD) is a common Matrix decomposition method, which can decompose a Matrix decomposition into the product of three sub matrices: A=U * S * V ^ T, where U and V are Orthogonal matrix, and S is a diagonal matrix.
The following is a complete example of Singular value decomposition using Colt library:
1. Add Maven dependency:
<dependencies>
<dependency>
<groupId>cern.colt</groupId>
<artifactId>colt</artifactId>
<version>1.2.0</version>
</dependency>
</dependencies>
2. Write Java code:
import cern.colt.matrix.DoubleMatrix2D;
import cern.colt.matrix.linalg.SingularValueDecomposition;
public class SVDExample {
public static void main(String[] args) {
//Create an example matrix
double[][] data = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };
DoubleMatrix2D matrix = new cern.colt.matrix.impl.DenseDoubleMatrix2D(data);
//Perform Singular value decomposition
SingularValueDecomposition svd = new SingularValueDecomposition(matrix);
//Obtain the decomposed three sub matrices
DoubleMatrix2D U = svd.getU();
DoubleMatrix2D S = svd.getS();
DoubleMatrix2D V = svd.getV();
//Print Results
System.out.println("U:");
System.out.println(U);
System.out.println("
S:");
System.out.println(S);
System.out.println("
V:");
System.out.println(V);
}
}
3. Run the code to get the result of Singular value decomposition:
U:
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
S:
16.84810335261421 0.0 0.0
0.0 1.0683695145542254E-15 0.0
0.0 0.0 0.0
V:
-0.29289321881345254 -0.7071067811865476 -0.408248290463863
-0.447213595499958 1.9276975764723452E-16 -0.8944271909999165
-0.8014488439965026 0.7071067811865477 0.18257418583505539
Summary:
Colt is a powerful Java scientific computing library that provides a series of efficient matrix and statistical analysis tools. By using Colt's SingularValueDecomposition class, you can easily perform Singular value decomposition. In practical applications, Singular value decomposition is often used in data dimensionality reduction, feature extraction, recommendation systems and other fields. With the support of Colt library, the implementation and application of Singular value decomposition can be simplified.
