Mathpaqs is a collection of mathematical, 100% portable, packages
The list of
packages below is sorted by topics.
Mathpaqs archive, each topic has a subdirectory.
there are many possible interactions, like between Multi-precision numbers and
Algebra (see Euclidean_Ring_Tools) - it is like combining mathematics fields...
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
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
Examples of instantiation:
= Polynomials( float, 0.0,1.0, "-",... );
= Polynomials( rational, frac_0, frac_1, "-",... );
Rationals: Package for manipulation of rational
numbers. One-liner package: Frac_Euclid( integer, 0,1,
· Rationals_Order: =
G_Matrices: Generic simple matrix package, with
matrix-matrix, matrix-vector, vector operations
Generic_Real_Linear_Equations: by Jon Squire. Inversion, Cholesky
decomposition, LU decomposition, QR decomposition, SV decomposition
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
3D: B27 (quadratic)
Generic -> can be instantiated
for any precision!
ConjGrad: Fast (Bi)Conjugate Gradient iterative
methods for solving Ax=b. Generic -> applies to the matrix storage of your
choice (e.g. sparse) !
Multi_precision_integers: Multiple-precision integers
Multi_precision_integers_IO: Text_IO, for multi-precision
(Pseudo-) Random number
generation, probability models, statistics
Generic_Random_Functions: Functions facilitating computations with
various random distributions
Discrete_Random_Simulation: random generation on any discrete
Finite_distributed_random: random generation on any enumerated
U_Rand: Standalone random generator (Pure Ada 95,
replaces easily Ada's generator if it is too slow)
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: Sparse matrix package (Pure Ada 83); uses
SparseB: Low-level vector operations for Sparse package
- Pure Ada 83 [.adb] body, and
- DEC/Compaq/HP [.dec] body
mapped to BLAS
Formulas : a generic symbolic computation
package (expression parser, fast evaluation, formula simplification)
Contours : a generic contour plot package