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Version with example.

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v1j4y 2021-02-02 14:36:43 +01:00
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testing_svd.org
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@ -139,6 +139,39 @@ def generateBlockRandomPointsAtShftApart(n,L1,dmin,shift):
None
#+end_example
#+begin_src python :noweb yes :results file :exports results
import numpy as np
# matplotlib related
import matplotlib.pyplot as plt
<<generateBlocks>>
L1 = 1.0
n = 100 # number of points
dmin = 0.1 # min dist between points
Ls = np.array([L1,L1,L1]) # lengths of the box
shift = -10.0
kappa = 2.0
rlist = generateBlockRandomPointsAtShftApart(n,L1,dmin,shift)
print(rlist.shape)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
xs = rlist.T[0]
ys = rlist.T[1]
zs = rlist.T[2]
ax.scatter(xs, ys, zs, marker='o')
fig.savefig('/tmp/test8.png')
#plt.show()
return '/tmp/test8.png'
#+end_src
#+RESULTS:
[[file:/tmp/test8.png]]
#+begin_src python :noweb yes :results file :exports results
# matplotlib related
@ -328,7 +361,7 @@ print(rlist.shape)
rij = np.zeros(shape=(rlist.shape[0],rlist.shape[0]))
def funcF(x,y):
return(np.exp(-kappa * np.sqrt(np.abs(np.dot(x,y)))))
return(np.exp(-kappa * np.linalg.norm(x-y)))
rij = np.array([[funcF(xval, yval) for yval in rlist] for xval in rlist])
@ -351,12 +384,32 @@ import numpy
a = numpy.array([[1,2,3],[4,5,6],[7,8,9]])
b = numpy.array([[11,12,13],[14,15,16],[17,18,19]])
print(list(zip(a,b))[0][1])
print(numpy.square(a[:,0]))
def stepExp(a):
def myexp(x):
if numpy.abs(x) > 1e+0:
return numpy.zeros_like(x)
else:
return numpy.exp(x)
res = numpy.array([[myexp(x) for x in y] for y in a])
return(res)
print(numpy.exp(a))
print(stepExp(a))
#+end_src
#+RESULTS:
#+begin_example
[11 12 13]
[ 1 16 49]
[[2.71828183e+00 7.38905610e+00 2.00855369e+01]
[5.45981500e+01 1.48413159e+02 4.03428793e+02]
[1.09663316e+03 2.98095799e+03 8.10308393e+03]]
[[2.71828183 0. 0. ]
[0. 0. 0. ]
[0. 0. 0. ]]
#+end_example
** Gaussian metric
@ -371,7 +424,7 @@ import matplotlib.pyplot as plt
<<generateBlocks>>
L1 = 1.0
n = 50 # number of points
n = 100 # number of points
dmin = 0.1 # min dist between points
Ls = np.array([L1,L1,L1]) # lengths of the box
shift = -10.0
@ -383,21 +436,31 @@ print(rlist.shape)
rij = np.zeros(shape=(rlist.shape[0],rlist.shape[0]))
def funcF(x,y):
return(np.exp(-kappa * np.sqrt(np.abs(np.dot(x,y)))))
return(np.exp(-kappa * np.linalg.norm(x-y)))
def funcFG(x,y):
return(np.exp(-kappa * np.abs(np.dot(x,y))))
return(np.exp(-kappa * np.square(np.linalg.norm(x-y))))
def funcFGD(x,y):
rij = np.exp(-kappa * 0.1 * np.square(np.linalg.norm(x-y)))
return(rij)
rijSlater = np.array([[funcF(xval, yval) for yval in rlist] for xval in rlist])
rijGaussian = np.array([[funcFG(xval, yval) for yval in rlist] for xval in rlist])
rijDeltafn = np.array([[funcFGD(xval, yval) for yval in rlist] for xval in rlist])
u,dS,vt = np.linalg.svd(rijSlater)
dS = dS/np.linalg.norm(dS)
u,dG,vt = np.linalg.svd(rijGaussian)
dG = dG/np.linalg.norm(dG)
u,dGD,vt = np.linalg.svd(rijDeltafn)
dGD = dGD/np.linalg.norm(dGD)
#print(d)
#plt.imshow(rij)
#plt.colorbar()
#plt.show()
plt.plot(range(dG.shape[0]),np.array([dS,dG]).T)
plt.plot(range(dG.shape[0]),np.array([dS,dG,dGD]).T)
plt.yscale('log')
plt.savefig('/tmp/plot4.png')
return '/tmp/plot4.png'
@ -405,3 +468,159 @@ return '/tmp/plot4.png'
#+RESULTS:
[[file:/tmp/plot4.png]]
** Palying around
Calculate the matrix of the \(FG(r_1,r_2)\) metric i.e. the gaussian metric.
#+begin_src python :noweb yes :results file :exports results
import numpy as np
from functools import reduce
import matplotlib.pyplot as plt
<<generateBlocks>>
L1 = 1.0
n = 100 # number of points
dmin = 0.1 # min dist between points
Ls = np.array([L1,L1,L1]) # lengths of the box
shift = -1.0
kappa = 2.0
rlist = generateBlockRandomPointsAtShftApart(n,L1,dmin,shift)
print(rlist.shape)
rij = np.zeros(shape=(rlist.shape[0],rlist.shape[0]))
def funcF(x,y):
rij = np.exp(-kappa * np.linalg.norm(x-y))
return(rij)
def funcFG(x,y):
rij = np.exp(-kappa * np.square(np.linalg.norm(x-y)))
return(rij)
def myexp(x):
if np.abs(x) > 1e-0:
return np.exp(-x)
else:
return np.exp(x)
def funcFGD(x,y):
rij = myexp(-kappa * np.square(np.linalg.norm(x-y)))
return(rij)
rijSlater = np.array([[funcF(xval, yval) for yval in rlist] for xval in rlist])
#rijSlater = rijSlater/np.max(rijSlater)
rijGaussian = np.array([[funcFG(xval, yval) for yval in rlist] for xval in rlist])
#rijGaussian = rijGaussian/np.max(rijGaussian)
rijDeltafn = np.array([[funcFGD(xval, yval) for yval in rlist] for xval in rlist])
#rijDeltafn = rijDeltafn/np.max(rijDeltafn)
u,dS,vt = np.linalg.svd(rijSlater)
dS = dS/np.linalg.norm(dS)
u,dG,vt = np.linalg.svd(rijGaussian)
dG = dG/np.linalg.norm(dG)
u,dGD,vt = np.linalg.svd(rijDeltafn)
dGD = dGD/np.linalg.norm(dGD)
#print(d)
#plt.imshow(rij)
#plt.colorbar()
#plt.show()
plt.plot(range(dG.shape[0]),np.array([dS,dG,dGD]).T)
plt.yscale('log')
plt.savefig('/tmp/plot5.png')
return '/tmp/plot5.png'
#+end_src
#+RESULTS:
[[file:/tmp/plot5.png]]
#+begin_src python :results file :exports results
import numpy
import matplotlib.pyplot as plt
def myexp2(x):
if numpy.abs(x) > 1e-0:
return numpy.exp(-x)
else:
return numpy.exp(x)
def myexp(x):
return(numpy.array([myexp2(y) for y in x]))
kappa = 1.0/2.0
xstart = 0.0
xend = 2.0
xstep = 0.1
s = numpy.array(list(map(lambda x : myexp(-x * numpy.power(numpy.arange(xstart,xend,xstep),2)), [10,5,1,0.5,0.1]))).T
#s = numpy.exp(-kappa * numpy.arange(0,1,0.1))
t = numpy.arange(xstart,xend,xstep)
fig, ax = plt.subplots()
ax.plot(t, s)
ax.set(xlabel=r'$r_{12}$', ylabel=r'$F(r_1,r_2)$',
title='Comparison of Kappa')
ax.set_yscale('log')
ax.grid()
fig.savefig('/tmp/test7.png')
#plt.show()
return '/tmp/test7.png'
#+end_src
#+RESULTS:
[[file:/tmp/test7.png]]
** Testing SVD for custom matrices
#+begin_src python :results output
import numpy
import matplotlib.pyplot as plt
a = numpy.array([[0,100,200],[100,0,200],[100,200,0]])
b = numpy.exp(-a)
print("Matrix A")
print(a)
print("Matrix Exp(A)")
print(numpy.around(b,10))
u,d,vt = numpy.linalg.svd(a)
d = d/numpy.linalg.norm(d)
print("Singular values of A")
print(numpy.around(d,3))
print("Singular vectors of A")
print(numpy.around(u,3))
u,d,vt = numpy.linalg.svd(b)
d = d/numpy.linalg.norm(d)
print("Singular values of Exp(A)")
print(numpy.around(d,3))
print("Singular vectors of Exp(A)")
print(numpy.around(u,3))
#+end_src
#+RESULTS:
#+begin_example
Matrix A
[[ 0 100 200]
[100 0 200]
[100 200 0]]
Matrix Exp(A)
[[1. 0. 0.]
[0. 1. 0.]
[0. 0. 1.]]
Singular values of A
[0.813 0.53 0.24 ]
Singular vectors of A
[[-0.67 0.142 0.728]
[-0.626 0.42 -0.657]
[-0.399 -0.896 -0.193]]
Singular values of Exp(A)
[0.577 0.577 0.577]
Singular vectors of Exp(A)
[[-1. 0. -0. ]
[-0. -0.894 -0.447]
[-0. -0.447 0.894]]
#+end_example