Mathpaqs
Mathpaqs is a collection of mathematical, 100% portable, packages
in the Ada programming language.
Download:
|
You can also...
- get the corresponding crate on Alire; click here for details:
- check the mirror on GitHub.
Mathpaqs topics
The list of packages below is sorted by topics.
In the Mathpaqs archive, each topic has a subdirectory.
Of course there are many possible interactions, like between Multi-precision numbers and Algebra (see Euclidean_Ring_Tools) - it is like combining mathematics fields...
Algebra
Euclidean_Ring_Tools: Generic package: given a type with the
properties of an Euclidean ring (like integers or polynomials, with 0,1,+,* and integral division), it gives the Greatest Common
Divisor and the Bezout factors.
Frac: Generic package: given a type with the
properties of a ring, it gives the fractions of it, with operators.
Frac.Order: Supplement of generic package 'Frac': provides an order relation from one of the ring.
Frac_Euclid: Generic package: given a type with the
properties of an Euclidean
ring (with division), it gives the fractions field of it, with operators and reduction.
Frac_Euclid.Order: Supplement of generic package 'Frac_Euclid': provides an order relation from one of the
ring.
Polynomials: Generic package, creates polynomials on a field.
Examples of instantiation:
·
Float_Polynomials: = Polynomials(
float, 0.0,1.0, "-",... );
·
Rationals.Polynomials: = Polynomials(
rational, frac_0, frac_1, "-",... );
Rationals: Package for manipulation of rational
numbers. One-liner package: Frac_Euclid( integer, 0,1,
"-","+","-","*","/"); !
· Rationals_Order: = Rationals.Order("<");
Linear algebra
G_Matrices: Generic simple matrix package, with
matrix-matrix, matrix-vector, vector operations.
NB: For Ada 2005+ and real numbers implemented as floating-point numbers,
it is better to use Ada.Numerics.Generic_Real_Arrays instead.
Generic_Real_Linear_Equations: by Jon Squire. Inversion, Cholesky decomposition, LU
decomposition, QR decomposition, SV decomposition.
ConjGrad: Fast (Bi)Conjugate
Gradient iterative methods for solving Ax=b. Generic -> applies to the
matrix storage of your choice (e.g. sparse) !
Numerics
G_FEK: Parts
of the Finite Element Kernel from M.
Bercovier (original in FORTRAN);
Computes values and derivatives
of elementary functions given the element's geometry.
Available so far:
1D: L2 (linear)
2D: Q4 (linear), Q9 (quadratic)
3D: B27 (quadratic)
Generic -> can be instantiated for any precision!
Beta_Function ![[NEW]](mathpaqs_files/image005.gif){kind=small}
: The Beta
function: B(a,b), B(x,a,b),
I_x(a,b).
Gamma_Function: The Gamma function: Γ(x) and Log(Γ(x)).
Phi_Function : Gauss' Phi
function: Φ(x) and inverse.
Error_Function : Error
function: Erf(x) and complementary, ErfC(x).
Multi-precision
integers
Multi_precision_integers: Multiple-precision integers package.
Multi_precision_integers_IO:
Text_IO, for multi-precision integers.
(Pseudo-) Random
number generation, probability models, statistics
Generic_Random_Functions: Functions facilitating computations with various standard random
distributions, discrete and continuous: Beta,
Discrete_Random_Simulation: Random generation on any empirical discrete distribution.
Finite_distributed_random: Random generation on any enumerated type.
U_Rand: Standalone random generator (Pure Ada 95, replaces seamlessly the generator of an
Copulas: An
object-oriented multivariate uniform random generator with dependency model of
any kind. A few basic copulas are provided.
Samples: A package
for building samples of random values, then computing statistics from these
samples.
Estimators: Various statistical estimators.
Sparse matrices
Sparse: Sparse
matrix package (Pure Ada 83); uses SparseB
SparseB: Low-level vector operations for Sparse package
-
Pure
-
DEC/Compaq/HP [.dec] body mapped to BLAS
Miscellaneous
Formulas : A generic
symbolic computation package (expression parser, fast evaluation, formula
simplification).
Contours : A generic
contour plot package.
Project information:
For any news, change logs, support requests, update informations: visit the
project on SourceForge!
Contact:
Here is a list of other open-source projects I participate to on SourceForge. Click on the links below for details.
Some projects have GitHub mirrors too.
