# thoppe/gr_svd

Singular Value Decomposition of the Radial Distribution Function for Hard Sphere and Square Well Potentials
Python
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 Failed to load latest commit information. HS_N12 HS_N13 PDF SW_epsilon SW_phi_1well SW_phi_2well SW_phiep .gitignore README.md matplotlibrc plot_extreme_gr.py plot_singular_values.py

## Supplementary Information

Travis Hoppe, National Institutes of Health, National Institute of Diabetes and Digestive and Kidney Diseases

Archived PDF from PLoS One.

# File formats

The reduced vectors for g(r) are stored in name/, see text for a detailed description of the parameters used. Example Python programs are provided that plot the extreme parameters of g(r) in plot_extreme_gr.py and the singular values in plot_singular_values.py. Programs require the libraries numpy and matplotlib to run.

## Number singular values used, k

6 HS_N12
6 HS_N13
4 SW_epsilon
5 SW_phi_1well
5 SW_phi_2well
6 SW_Phipps


### "svd_eigenvalues.txt"

List of the k singular values

s_1
s_2
...
s_k


### "svd_u_polynomials.txt"

List of the polynomials to recreate the coefficient vectors u(param)

p11 p12 p13 ... p1k
p21 p22 p23 ... p2k
... ... ... ... ...
pk1 pk2 pk3 ... pkk


Where each row represents the polynomial

p11*x^(k+1) + p12*x^(k+0) + p13*x^(k-1) ... + p1k*x^(0)


The entries are zero-padded so they have equal columns.

For the two parameter system SW_phiep, the polynomials are stored differently to accommodate the higher dimensions. Here row is the expansion of the coefficients to

\sum_i^(k+1) \sum_j^(k+1) a_(i,j)*x^i*y*^j


Where x represents the parameter \phi and y the parameter epsilon and the matrix of coefficients a(i,j) is stored as a row flattened array

List of the m radial points for the basis vectors v(r), r_1 = \sigma and r_m = 6\sigma.

r_1
r_2
...
r_m


### "svd_v_eigenvectors.txt"

List of the k eigenvectors v(r), each has length m

v11 v12 ... v1m
v21 v22 ... v2m
... ... ... ...
vk1 vk2 ... vkm