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pl - added parallelization #12

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2906447
parallel_edits
peterlee6925 Feb 17, 2023
c83f3f4
minor_updates
peterlee6925 Feb 21, 2023
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126 changes: 68 additions & 58 deletions PLoM_library.py
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Original file line number Diff line number Diff line change
@@ -1,5 +1,6 @@
# -*- coding: utf-8 -*-
#JGA
#Edited by Peter Lee 2/21/2023
from matplotlib import pyplot as plt
import numpy as np
from scipy import integrate
Expand All @@ -8,6 +9,8 @@
from ctypes import *
import os
from general import Logfile, DBServer
from multiprocessing import Pool
import defs

from sys import platform
if platform == "linux" or platform == "linux2":
Expand Down Expand Up @@ -67,19 +70,16 @@ def K(eta, epsilon):
[1., 1.]]), array([[2., 0.],
[0., 2.]]))
"""
# use parallel process for KDE
# variable number of works
import multiprocessing
num_cpu = multiprocessing.cpu_count()
pool = Pool(num_cpu)
N = eta.shape[1]
K = np.zeros((N,N))
b = np.zeros((N,N))
for i in range(0,N):
row_sum = 0
for j in range(0,N):
if j != i:
K[i,j] = kernel((eta[:,i]),((eta[:,j])), epsilon)
row_sum = row_sum + K[i,j]
else:
K[i,j] = 1
row_sum = row_sum + 1
b[i,i] = row_sum
# use functions in defs.py
results = pool.map(defs.splat_f, ((i, j, eta, epsilon) for i in range(N) for j in range(N)))
K = np.array(results).reshape(N, N)
b = np.diag(np.sum(K,1))
return K, b

def g(K, b):
Expand All @@ -100,15 +100,16 @@ def g(K, b):
g = np.multiply(g, sqrt_norm)
return g, eigenvalues

def m(eigenvalues):
def m(eigenvalues, beta=0.1):
"""
>>> m(np.array([1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.05, 0.025]))
11
"""
i = 2
m = 0
print('beta = {}'.format(beta))
while i < len(eigenvalues) and m == 0:
if eigenvalues[i] <= eigenvalues[1]*0.1:
if eigenvalues[i] <= eigenvalues[1]*beta:
return i+1
i = i+1
if m == 0:
Expand Down Expand Up @@ -153,10 +154,10 @@ def PCA(x, tol):
x_mean = mean(x)
(phi,mu,v) = np.linalg.svd(x-x_mean)
mu = mu/sqrt(len(x[0])-1)
plt.figure()
plt.plot(np.arange(len(mu)), mu)
plt.xlabel('# eigenvalue of X covariance')
plt.show()
#plt.figure()
#plt.plot(np.arange(len(mu)), mu)
#plt.xlabel('# eigenvalue of X covariance')
#plt.show()
error = 1
i = 0
errors = [1]
Expand All @@ -169,11 +170,11 @@ def PCA(x, tol):
error = error - (mu[i]**2)/sum((mu**2))
i = i+1
errors.append(error)
plt.figure()
plt.semilogy(np.arange(len(mu)+1), errors)
plt.xlabel('# eigenvalue of Covariance matrix of X')
plt.ylabel('Error of the PCA associated with the eigenvalue')
plt.show()
#plt.figure()
#plt.semilogy(np.arange(len(mu)+1), errors)
#plt.xlabel('# eigenvalue of Covariance matrix of X')
#plt.ylabel('Error of the PCA associated with the eigenvalue')
#plt.show()
mu = mu[0:nu]
phi = phi[:,0:nu]
mu_sqrt_inv = (np.diag(1/(mu))) #no need to do the sqrt because we use the singularvalues
Expand Down Expand Up @@ -252,7 +253,7 @@ def generator(z_init, y_init, a, n_mc, x_mean, eta, s_v, hat_s_v, mu, phi, g, ps
if seed_num:
np.random.seed(seed_num)
delta_t = 2*pi*hat_s_v/20
print('delta t: ', delta_t)
#print('delta t: ', delta_t)
f_0 = 1.5
l_0 = 10#200
M_0 = 10#20
Expand Down Expand Up @@ -298,42 +299,51 @@ def L(y, g_c, x_mean, eta, s_v, hat_s_v, mu, phi, psi, lambda_i, D_x_g_c): #grad
nu = eta.shape[0]
N = eta.shape[1]
L = np.zeros((nu,N))
for l in range(0,N):
yl = np.resize(y[:,l],(len(y[:,l]),1))
rho_ = rhoctypes(yl, np.resize(np.transpose(eta),(nu*N,1)),\
nu, N, s_v, hat_s_v)
rho_ = 1e250*rho_
# compute the D_x_g_c if D_x_g_c is not 0 (KZ)
if D_x_g_c:
grad_g_c = D_x_g_c(x_mean+np.resize(phi.dot(np.diag(mu)).dot(yl), (x_mean.shape)))
else:
# not constraints and no D_x_g_c
grad_g_c = np.zeros((x_mean.shape[0],1))
if rho_ < 1e-250:
closest = 1e30
for i in range(0,N):
if closest > np.linalg.norm((hat_s_v/s_v)*np.resize(eta[:,i],yl.shape)-yl):
closest = np.linalg.norm((hat_s_v/s_v)*np.resize(eta[:,i],yl.shape)-yl)
vector = (hat_s_v/s_v)*np.resize(eta[:,i],yl.shape)-yl
#KZ L[:,l] = ( np.resize(vector/(hat_s_v**2),(nu))\
# -np.resize(np.diag(mu).dot(np.transpose(phi)).\
# dot(D_x_g_c(x_mean+np.resize(phi.dot(np.diag(mu)).dot(yl), (x_mean.shape)))).\
# dot(psi).dot(lambda_i), (nu)))
L[:,l] = ( np.resize(vector/(hat_s_v**2),(nu))\
-np.resize(np.diag(mu).dot(np.transpose(phi)).\
dot(grad_g_c).dot(psi).dot(lambda_i), (nu)))

else:
array_pointer = cast(gradient_rhoctypes(np.zeros((nu,1)),yl,\
np.resize(np.transpose(eta),(nu*N,1)), nu, N, s_v, hat_s_v), POINTER(c_double*nu))
gradient_rho = np.frombuffer(array_pointer.contents)
#KZ L[:,l] = np.resize(1e250*gradient_rho/rho_,(nu))\
# -np.resize(np.diag(mu).dot(np.transpose(phi)).\
# dot(D_x_g_c(x_mean+np.resize(phi.dot(np.diag(mu)).dot(yl), (x_mean.shape)))).\
# dot(psi).dot(lambda_i), (nu))
L[:,l] = np.resize(1e250*gradient_rho/rho_,(nu))\
if False:
for l in range(0,N):
yl = np.resize(y[:,l],(len(y[:,l]),1))
rho_ = rhoctypes(yl, np.resize(np.transpose(eta),(nu*N,1)),\
nu, N, s_v, hat_s_v)
rho_ = 1e250*rho_
# compute the D_x_g_c if D_x_g_c is not 0 (KZ)
if D_x_g_c:
grad_g_c = D_x_g_c(x_mean+np.resize(phi.dot(np.diag(mu)).dot(yl), (x_mean.shape)))
else:
# not constraints and no D_x_g_c
grad_g_c = np.zeros((x_mean.shape[0],1))
if rho_ < 1e-250:
closest = np.inf
for i in range(0,N):
if closest > np.linalg.norm((hat_s_v/s_v)*np.resize(eta[:,i],yl.shape)-yl):
closest = np.linalg.norm((hat_s_v/s_v)*np.resize(eta[:,i],yl.shape)-yl)
vector = (hat_s_v/s_v)*np.resize(eta[:,i],yl.shape)-yl
#KZ L[:,l] = ( np.resize(vector/(hat_s_v**2),(nu))\
# -np.resize(np.diag(mu).dot(np.transpose(phi)).\
# dot(D_x_g_c(x_mean+np.resize(phi.dot(np.diag(mu)).dot(yl), (x_mean.shape)))).\
# dot(psi).dot(lambda_i), (nu)))
L[:,l] = ( np.resize(vector/(hat_s_v**2),(nu))\
-np.resize(np.diag(mu).dot(np.transpose(phi)).\
dot(grad_g_c).dot(psi).dot(lambda_i), (nu))
dot(grad_g_c).dot(psi).dot(lambda_i), (nu)))

else:
array_pointer = cast(gradient_rhoctypes(np.zeros((nu,1)),yl,\
np.resize(np.transpose(eta),(nu*N,1)), nu, N, s_v, hat_s_v), POINTER(c_double*nu))
gradient_rho = np.frombuffer(array_pointer.contents)
#KZ L[:,l] = np.resize(1e250*gradient_rho/rho_,(nu))\
# -np.resize(np.diag(mu).dot(np.transpose(phi)).\
# dot(D_x_g_c(x_mean+np.resize(phi.dot(np.diag(mu)).dot(yl), (x_mean.shape)))).\
# dot(psi).dot(lambda_i), (nu))
L[:,l] = np.resize(1e250*gradient_rho/rho_,(nu))\
-np.resize(np.diag(mu).dot(np.transpose(phi)).\
dot(grad_g_c).dot(psi).dot(lambda_i), (nu))
if True:
import multiprocessing
num_cpu = multiprocessing.cpu_count()
pool = Pool(num_cpu)
results = pool.map(defs.splat_h, ((l, y, x_mean, eta, s_v, hat_s_v, mu, phi, psi, lambda_i, D_x_g_c, nu, N) for l in range(N)))
L = np.array(results).reshape(N,nu).transpose()

return L


Expand Down
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