Mathpaqs / News: Recent posts

Mathpaqs is a collection of mathematical packages in the Ada programming language.

What's new:

• Discrete_Random_Simulation: after linear - O(n) - and dichotomic (binary) - O(log(n)) - searches, added the alias method which is O(1). Concretely, the simulation of a discrete, finite random variable of any number of states is as fast as simulating a flip-or-coin !...

• Added Test_Discrete_Random_Simulation with timing and error measurement.

What's new:

• Added special functions Beta and Phi in the numerics part (Beta_function, Test_Beta, Phi_function)
• Added the Beta distribution in the random distribution part (Generic_Random_Functions)

The main change in this release is in the Copulas package.
It is now possible to use a vector of pseudo-random generators, one for each dimension.
This way, each independent dimension has a reproducible sequence when using a fixed seed.
Then, results can be reproduced even if a dimension is added or removed.

• Added Gamma special function: see Gamma_function package; code courtesy of Stephen L. Moshier
• Added Normal_inverse_CDF to random functions (as complement to the Box-Muller method)

Two additions in the latest release:

• Formulas, a generic formula package with parsing, evaluation and simplification

• Contours, a generic contour plot package

Enjoy!

Formulas is a package for parsing formulas in real numbers, evaluating them quickly in parsed form, and simplifying them if desired.

Recent additions (check-ins around #60 to #70) :

New simplification rules

X + -Y -> X - Y
X - -Y -> X + Y
-cst -> cst (fold unary minus into constant)
cst - cst -> cst
X + n -> X - {abs n} where n < 0
X - n -> X + {abs n} where n < 0
-n -> {abs n} where n < 0
X + {X + Y} -> 2 * X + Y
X + {Y + X} -> 2 * X + Y... read more