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++. 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