laplace
-
constexpr Complex laplace(Complex (*f)(Complex), const Complex &z, const Complex &a = 1) noexcept
Performs the Laplace integral transform [1] of a complex function.
Parameters
Returns
- type Complex
A complex number.
The Laplace transform performs the following integral transform on a function \(f\):
\[\mathcal{L}\{f\}(z) = \int_{0}^{\infty}f(t)e^{-zt}dt\]
Example
auto fn = [](Complex t) { return sin(t); };
Complex z = 1;
std::cout << laplace(fn, z) << "\n";
Output:
0.501173 + 0j // True result: 1 / (z^2 + a^2) = 0.5 + 0j
References