vnl : Numerics Library

The numerics library, vnl is intended to provide an environment for numerical programming which combines the ease of use of packages like Mathematica and Matlab with the speed of C and the elegance of C++. It provides a C++ interface to the high-quality Fortran routines made available in the public domain by numerical analysis researchers.

Matrix and vector classes include

• vnl_vector<T> : Standard vector class
• vnl_matrix<T> : Standard matrix class
• vnl_vector_fixed<T,N> : Fixed size vector class (of length N)
• vnl_matrix_fixed<T,N,M> : Fixed size NxM matrix class
• vnl_vector_ref<T> : Wrap user-supplied memory chunk as a vector
• vnl_matrix_ref<T> : Wrap user-supplied memory chunk as a matrix

Functions to generate special matrixes:

• vnl_identity_3x3
• vnl_rotation_matrix
• vnl_cross_product_matrix

Support for manipulating polynomials

• vnl_real_polynomial
• vnl_real_npolynomial
• vnl_rnpoly_solve
• vnl_rpoly_roots
• vnl_cpoly_roots

Useful utility functions

• Common functions and constants (in vnl_math)
• vnl_random : random number generation, with normal and box distributions.
• vnl_gamma, vnl_gamma_p, vnl_gamma_q : gamma functions
• vnl_erf

Simple matrix operations

• vnl_transpose : transpose of a matrix for direct use in a multiplication
• vnl_adjugate : return the adjugate matrix
• vnl_rank, vnl_rank_row_reduce and vnl_rank_column_reduce
• vnl_trace
• vnl_cross
• vnl_det and vnl_determinant
• vnl_inverse, vnl_inverse_transpose and vnl_matrix_inverse
• vnl_orthogonal_complement

Alternative number representations

• vnl_complex
• vnl_quaternion
• vnl_rational
• vnl_bignum
• vnl_finite

Mapping functionality

• vnl_unary_function
• vnl_identity

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vnl_algo : Computational Numerics Library

Matrix decompositions include

• vnl_svd and vnl_svd_economy : Singular value decomposition
• vnl_qr : QR decomposition
• vnl_cholesky : Cholesky decomposition (for symmetric matrices)
• vnl_ldl_cholesky : Variant on Cholesky, allowing fast updating
• vnl_symmetric_eigensystem : Eigen-decomposition
• vnl_real_eigensystem : Eigen-decomposition
• vnl_complex_eigensystem : Eigen-decomposition
• vnl_generalized_eigensystem : Eigen-decomposition
• vnl_sparse_symmetric_eigensystem
• vnl_generalized_schur

Optimisation routines include

• vnl_amoeba : Downhill simplex algorithm
• vnl_lsqr
• vnl_brent_minimizer (For 1D optimization)
• vnl_conjugate_gradient
• vnl_lbfgs
• vnl_levenberg_marquardt
• vnl_powell
• vnl_bracket_minimum (To bracket a minimum of a 1D function)

Useful utility functions

• vnl_fft_1d : 1D Fast Fourier Transform
• vnl_fft_2d : 2D Fast Fourier Transform
• vnl_convolve
• vnl_chi_squared : CDF of chi-squared distributi

Developer

Amitha Perera is responsible for co-ordinating significant changes to vnl. http://sourceforge.net/sendmessage.php?touser=237910