gau2grid
A collocation code for computing gaussians on a grid of the form:
out_Lp = x^l y^m z^n \sum_i coeff_i e^(exponent_i * (|center - p|)^2)
Where the returned matrix dimension are the angular momentum (L) by number of requested points (p).
import gau2grid
import numpy as np
# Build coordinates along the Z axis
>>> xyz = np.zeros((3, 5))
>>> xyz[2] = np.arange(5)
# Compute a 's' gaussian with a scaling and exponent of one at the origin
>>> ret = gau2grid.collocation(xyz, 0, [1], [1], [0, 0, 0])
>>> print(ret["PHI"])
[[ 1.00000e+00 3.67879e-01 1.83156e-02 1.23409e-04 1.12535e-07]]
# Compute a 'p' gaussian with a scaling and exponent of one at the origin
>>> ret = gau2grid.collocation(xyz, 1, [1], [1], [0, 0, 0], spherical=False)
>>> print(ret["PHI"])
[[ 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00]
[ 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00]
[ 0.00000e+00 3.67879e-01 3.66312e-02 3.70229e-04 4.50140e-07]]
# Note that the X and Y components are zero as they are orthogonal to our Z vector.The returned matrix can be in either cartesian or regular solid harmonics. There are currently three algorithms in which to compute these collocation matrices:
- Optimize C: A autogenerated C library that optimizes for cache,
vectorization, and sparsity. Fastest, requires compilation, found at
gau2grid.collocation. - Optimized/Generated NumPy: A exploratory tool to
examine the sparsity in the gaussians. No compilation required, found at
gau2grid.np_gen.collocation. - NumPy Reference: A simple NumPy-based loop
code. No compilation required, found at
gau2grid.ref.collocation.
See the documentation for more information!
Building Gau2Grid
The C library is built with CMake and has C no required dependancies other than the standard library. A CMake and build example can found below:
cmake -H. -Bobjdir
cd objdir; make -j2Several common CMake options are as follow:
-DPYTHON_EXECUTABLE- Path to the desired Python executable-DMAX_AM- Maximum angular momentum to compile to, default 6-DCMAKE_INSTALL_PREFIX- Installation directory
Python installation
The gau2grid program (without the optimized C library) can be installed using
the canonical setup.py script,
python setup.py install
Authors
This code was inspired by a number of folks and quite a few provided excellent advice.
- Daniel G. A. Smith - Code author
- Rob M. Parrish - Author of the Psi4 section which contains the original equations
- Lori A. Burns - CMake, building, and library linking
- Andy C. Simmonett - RSH coefficients
- Ben Pritchard - Generator and vectorization recommendations