Search Results for "function point"

This package contains simple routines for finding roots, or zeros, of scalar functions of a single real variable using floating-point math. The find_zero function provides the primary interface. The basic call is find_zero(f, x0, [M], [p]; kws...) where, typically, f is a function, x0 a starting point or bracketing interval, M is used to adjust the default algorithms used, and p can be used to pass in parameters. Bisection-like algorithms. For functions where a bracketing interval is known (one where f(a) and f(b) have alternate signs), a bracketing method, like Bisection, can be specified. ...

This package provides the @infiltrate macro, which acts as a breakpoint with negligible runtime performance overhead. Note that you cannot access other function scopes or step into further calls. Use an actual debugger if you need that level of flexibility. Running code that ends up triggering the @infiltrate REPL mode via inline evaluation in VS Code or Juno can cause issues, so it's recommended to always use the REPL directly. When the infiltration point is hit, it will drop you into an interactive REPL session that lets you inspect local variables and the call stack as well as execute arbitrary statements in the context of the current local and global scope.

...Many models in the sciences and engineering are expressed as sets of real solutions to systems of polynomial equations. We can optimize any objective whose gradient is an algebraic function using homotopy methods by computing all critical points of the objective function. An important special case is when the objective function is the euclidean distance to a given point. An example of an non-algebraic objective function whose derivative is algebraic is the Kullback–Leibler divergence. Homotopy continuation methods allow us to study the conformation space of molecules as for example cyclooctane (CH₂)₈. ...

A surrogate model is an approximation method that mimics the behavior of a computationally expensive simulation. In more mathematical terms: suppose we are attempting to optimize a function f(p), but each calculation of f is very expensive. It may be the case we need to solve a PDE for each point or use advanced numerical linear algebra machinery, which is usually costly. The idea is then to develop a surrogate model g which approximates f by training on previous data collected from evaluations of f.