A simple example of projecting and using MADNESS functions. More...
Include dependency graph for examples/gaussian.cc:
Functions | |
| double | gaussian (const coord_3d &r) |
| C++ function for projecting the Gaussian test function. | |
| int | main (int argc, char **argv) |
| Main function. Project the function and compute the integrals. | |
Detailed Description
A simple example of projecting and using MADNESS functions.
This example projects a simple Gaussian function,
![\[ g(\vec{x}) = e^{-|\vec{x}|^2}, \]](form_130_dark.png)
into the MADNESS adaptive basis and computes several integrals:
![\[
\int \mathrm{d}^3 \vec{x} \; g(\vec{x}) = \pi^{3/2} \doteq 5.5683279,
\]](form_131_dark.png)
![\[
\left( \int \mathrm{d}^3 \vec{x} \; g(\vec{x})^2 \right)^{1/2} = (\pi/2)^{3/4} \doteq 1.403104,
\]](form_132_dark.png)
![\[
\int \mathrm{d}^3 \vec{x} \; g(\vec{x}) \int \mathrm{d}^3 \vec{y} \; |\vec{x}-\vec{y}|^{-1} g(\vec{y}) = \pi^{5/2} 2^{1/2} \doteq 24.739429.
\]](form_133_dark.png)
Function Documentation
◆ gaussian()
C++ function for projecting the Gaussian test function.
- Parameters
-
[in] r The coordinate at which to evaluate the function.
- Returns
- The value of the Gaussian at the specified coordinate.
References madness::nonlinear_vector_solver().
◆ main()
| int main | ( | int | argc, |
| char ** | argv | ||
| ) |
Main function. Project the function and compute the integrals.
- Parameters
-
[in] argc The number of command-line arguments. [in] argv The command-line arguments.
- Returns
- Exit status.
References SafeMPI::COMM_WORLD, madness::CoulombOperator(), e(), madness::finalize(), madness::g, madness::initialize(), madness::inner(), madness::nonlinear_vector_solver(), op(), madness::print(), madness::FunctionDefaults< NDIM >::set_cubic_cell(), madness::startup(), and madness::Function< T, NDIM >::truncate().
