impact-matrix 0.0.1

This is a Python reimplementation of the Java Jama package utilized in the original Imapct Java application - https://sourceforge.net/projects/impact/ The original Java code was implemented by The MathWorks, Inc. and the National Institute of Standards and Technology. This code implents version 5 from August 1998

Impact Matrix

This project is a Python port of the Jama Matrix library.

Jama = Java Matrix class.

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();

Author: The MathWorks, Inc. and the National Institute of Standards and Technology. Version: 5 August 1998

Conclusion

Summary of the complete Python port:

All JAMA decomposition classes are now fully implemented:

Class	Methods
Matrix	All constructors, arithmetic, norms, getters/setters, solve, inverse, etc.
CholeskyDecomposition	get_L(), is_spd(), solve()
EigenvalueDecomposition	get_V(), get_D(), get_real_eigenvalues(), get_imag_eigenvalues()
LUDecomposition	get_L(), get_U(), get_pivot(), det(), is_nonsingular(), solve()
QRDecomposition	get_Q(), get_R(), get_H(), is_full_rank(), solve()
SingularValueDecomposition	get_U(), get_V(), get_S(), norm2(), cond(),