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The Java Matrix Class provides the fundamental operations of numerical linear algebra. Various constructors create Matrices from two dimensional arrays of double precision floating point numbers. Various "gets" and "sets" provide access to submatrices and matrix elements. Several methods implement basic matrix arithmetic, including matrix addition and multiplication, matrix norms, and element-by-element array operations. Methods for reading and printing matrices are also included. All the operations in this version of the Matrix Class involve real matrices. Complex matrices may be handled in a future version.

Five fundamental matrix decompositions, which consist of pairs or triples of matrices, permutation vectors, and the like, produce results in five decomposition classes. These decompositions are accessed by the Matrix class to compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions. The five decompositions are:

• Cholesky Decomposition of symmetric, positive definite matrices.
• LU Decomposition of rectangular matrices.
• QR Decomposition of rectangular matrices.
• Singular Value Decomposition of rectangular matrices.
• Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.

Example of use:

Solve a linear system A x = b and compute the residual norm, ||b - A x||.

 double[][] vals = {{1.,2.,3},{4.,5.,6.},{7.,8.,10.}};
 Matrix A = new Matrix(vals);
 Matrix b = Matrix.random(3,1);
 Matrix x = A.solve(b);
 Matrix r = A.times(x).minus(b);
 double rnorm = r.normInf();
 

Adapted from the JAMA package. Additional methods are tagged with the @author tag.
author:
   The Mathworks and NIST
author:
   Fracpete (fracpete at waikato dot ac dot nz)
version:
   $Revision: 1.7 $

1. perform eigenvalue decomposition
   [V,D]=eig(A)
2. take the square root of all elements in D (only the ones with positive sign are considered for further computation)
   S=sqrt(D)
3. calculate the root
   X=V*S/V, which can be also written as X=(V'\(V*S)')'

Note: since this method uses other high-level methods, it generates several instances of matrices.

Note: This format differs from the one that can be read via the Matrix(Reader) constructor! For that format, the write(Writer) method is used (from the original weka.core.Matrix class).
Parameters:
  input - the input stream.
See Also:   Matrix.Matrix(Reader)
See Also:   Matrix.write(Writer)

1. perform eigenvalue decomposition
   [V,D]=eig(A)
2. take the square root of all elements in D (only the ones with positive sign are considered for further computation)
   S=sqrt(D)
3. calculate the root
   X=V*S/V, which can be also written as X=(V'\(V*S)')'

Note: since this method uses other high-level methods, it generates several instances of matrices. This can be problematic with large matrices.

Examples:

1.  X =
    5   -4    1    0    0
    -4    6   -4    1    0
    1   -4    6   -4    1
    0    1   -4    6   -4
    0    0    1   -4    5
    sqrt(X) =
    2   -1   -0   -0   -0 
    -1    2   -1    0   -0 
    0   -1    2   -1    0 
    -0    0   -1    2   -1 
    -0   -0   -0   -1    2 
    Matrix m = new Matrix(new double[][]{{5,-4,1,0,0},{-4,6,-4,1,0},{1,-4,6,-4,1},{0,1,-4,6,-4},{0,0,1,-4,5}});
    

2.  X =
    7   10
    15   22
    sqrt(X) =
    1.5667    1.7408
    2.6112    4.1779
    Matrix m = new Matrix(new double[][]{{7, 10},{15, 22}});