test_uni

test_uni, a Python code which defines a number of unimodal functions, each one a scalar valued function of a scalar argument. Over a specified interval [a,b], each function decreases to a minimum value and then increases. These functions are designed to test the efficiency of algorithms for locating the minimizing argument, such as bisection, golden search, or Brent's method.

There are 40 test functions. Each problem has an index number, and there are a corresponding set of routines, with names beginning with the index number. For test function 1, these would be:

• fx = p01_f(x) evaluates f(x);
• title = p01_title() returns the title of the problem;
• a, b = p01_interval() returns the initial search interval;
• x = p01_sol() returns an exact minimizer;

There is also a generic problem interface, whose routines all begin with "p00". This allows the user to call all possible problems in a single simple loop, by passing the desired index number through the generic interface.

• fx = p00_f(test,x) evaluates f(x) for the function with index test;
• title = p00_title(test) returns the title of the problem;
• a, b = p00_interval(test) returns the initial search interval;
• x = p00_sol(test) returns an exact minimizer;

These functions were selected and described by Professor Vladimir Kodnyanko of the Siberian Federal University.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

test_uni is available in a Python version.

Related Data and Programs:

glomin, a Python code which finds a global minimum of a scalar function of a scalar argument, without the use of derivative information, by Richard Brent.

golden_section, a Python code which estimates a minimizer of a function f(x), assuming f(x) is unimodular ("U-shaped") over [a,b].

local_min, a Python code which finds a local minimum of a scalar function of a scalar variable, without the use of derivative information, by Richard Brent.

local_min_rc, a Python code which finds a local minimum of a scalar function of a scalar variable, without the use of derivative information, using reverse communication (RC), by Richard Brent.

test_min, a Python code which implements test problems for minimization of a scalar function of a scalar variable.

Reference:

1. Vladimir Kodnyanko,
   Description and software implementation of optisection method for minimizing unimodal functions.
2. Vladimir Kodnyanko,
   Optimal section method for minimizing unimodal functions,
   Computational Mathematics and Modeling,
   Volume 36, pages 235-252, 16 October 2025.

Source Code:

• test_uni.py, the source code.
• test_uni.sh, runs all the tests.
• test_uni.txt, the output file.