TNT

The Template Numerical Toolkit (TNT) is a series of C++ templates that implement matrices and vectors. You can get the code and documentation from [1]. The most useful basic data type is TNT::Array2D, which is the preferred matrix data type. TNT::Array1D is occasionally useful for vectors that you are using with TNT code. Operators and []s are overloaded for matrices like you would expect, and an the templates handle memory allocation and sizing. The associated JAMA templates (same URL) provide Cholesky, Eigenvalue, LU, QR, and SVD decompositions.

The nice things about this library are that it is simple, free, and implemented entirely as templates (so you just specify -I/path/to/tnt and include the headers). On the down side, it's a bit limited in what it provides, and bjbrown has encountered a couple of bugs. He thinks they were in QR and Eigenvalue decompositions, and if they aren't fix in the official distro, e-mail him for the fixes.

Oddly, the library doesn't transpose matrices. It also doesn't invert them. Here's the simplest matrix inversion (and determinant) code:

#include <assert.h>
#include <tnt_array1d.h>
#include <tnt_array2d.h>
#include <jama_lu.h>

TNT::Array2D<float> invert(TNT::Array2D<float> &M) {
  assert(M.dim1() == M.dim2()); // square matrices only please

  // create identity matrix
  TNT::Array2D<float> id(M.dim1(), M.dim2(), 0);
  for (int i = 0; i < M.dim1(); i++) id[i][i] = 1;

  // solve for inverse with LU decomposition
  JAMA::LU lu(M);
  assert(LU.det() > THRESHOLD); // non-singularity
  return lu.solve(id);
}