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++. Its dependent, vnl_algo, 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
vnl_c_vector<T> : underlying implementor class: math on blocks of memory
vnl_diag_matrix<T> : Diagonal matrix class
vnl_diag_matrix_fixed<T,N> : Fixed size NxN diagonal matrix class
vnl_sym_matrix<T> : Symmetric matrix class
vnl_sparse_matrix<T> : Efficient storage for matrices with many zeroes
vnl_crs_index : like vnl_sparse_matrix<T>, but without the data
vnl_linear_system : interface for large, sparse systems of linear equations

Functions to generate special matrixes or vectors:

vnl_identity_3x3
vnl_rotation_matrix
vnl_cross_product_matrix
vnl_int_matrix
vnl_double_2, vnl_float_3, vnl_int_4, ...: fixed-size, fixed-type vectors
vnl_double_2x3, vnl_float_3x3, vnl_int_4x3, ...: fixed-size, fixed-type matrices

Polynomial representations:

Useful utility functions and constants

Common functions and constants (in vnl_math), like pi, sqrt2, ln10, euler, ...
vnl_random : random number generation, with normal and box distributions.
vnl_gamma, vnl_gamma_p, vnl_gamma_q, vnl_beta : gamma and beta functions
vnl_erf
vnl_bessel
vnl_matrix_exp : compute the exponential of a square matrix
vnl_power : compute the nth power of a small vnl_matrix_fixed
vnl_operators.h contains vector and matrix comparison functions
vnl_copy : easy conversion between vectors/matrices with different datatypes

Computational functionality:

vnl_definite_integral : computes the surface area under a given function (see also vnl_simpson_integral in vnl_algo)

Simple matrix operations

vnl_transpose : transpose of a matrix for direct use in a multiplication
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
vnl_file_matrix and vnl_file_vector : load from a file
class vnl_fastops, with functions like AtA, ABt, Ab, inc_X_by_AtA, ...
vnl_linear_operators_3.h : contains 3D linear algebra operations

Alternative number representations

vnl_complex, vnl_complexify, vnl_real, vnl_imag : represent and manipulate complex numbers
vnl_quaternion<T>
vnl_rational : numbers represented as the quotient of two integers
vnl_bignum : arbitrary size integers, binary representation
vnl_decnum : arbitrary size integers, decimal representation and arithmetic
vnl_finite<N> : modulo-N arithmetic, e.g. for finite fields

Mapping functionality

vnl_cost_function : R^n --> R. Used by minimizers
vnl_least_squares_function, vnl_least_squares_cost_function : minimizer interface
vnl_identity
vnl_hungarian_algorithm : Find best column to row assignment given a cost matrix

Miscellaneous

vnl_sample : sampling from uniform, binomial and normal distributions
vnl_matlab_print : pretty-print matrices and vectors in matlab-style format
vnl_matlab_read : import data from files in the .mat format of Matlab
vnl_matlab_write, vnl_matlab_filewrite : export data in the .mat format of Matlab

vnl_algo : Computational Numerics Library

Matrix decompositions include:

vnl_svd, vnl_svd_fixed, 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 : least squares algorithm for (large, sparse) linear systems
vnl_sparse_lu : LU decomposition to solve a (sparse) linear system
vnl_brent_minimizer : minimizes a 1D function without using derivatives
vnl_powell : minimizes an N-D function without using derivatives
vnl_conjugate_gradient
vnl_lbfgs, vnl_lbfgsb : Broyden Fletcher Goldfarb Shannon minimization
vnl_levenberg_marquardt and vnl_sparse_lm : Levenberg-Marquardt nonlinear least squares
vnl_bracket_minimum : bracket a minimum of a 1D function
vnl_solve_qp : several quadratic programming problem solving functions

Support for manipulating polynomials:

Useful utility functions:

vnl_fft_1d : 1D Fast Fourier Transform
vnl_fft_2d : 2D Fast Fourier Transform
vnl_determinant (but see also vnl_determinant in library vnl)
vnl_matrix_inverse (but see also vnl_matrix_inverse in library vnl)
vnl_adjugate : return the adjugate (or adjoint, or cofactors) matrix
vnl_convolve
vnl_chi_squared : CDF of chi-squared distribution
vnl_fit_parabola : given three points, return 2nd degree fitting polynomial

Developers

Gehua Yang and Peter Vanroose are responsible for co-ordinating significant changes to vnl. http://sourceforge.net/sendmessage.php?touser=717688 http://sourceforge.net/sendmessage.php?touser=290414