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dpga_cpu.py
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dpga_cpu.py
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# -*- coding: utf-8 -*-
import numpy as np
from mpi4py import MPI
from scipy import linalg
import time
import tensorflow as tf
import sys
from small_world import small_world
import pandas as pd
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
size = comm.Get_size()
stop1 = 1e-4
stop2 = 1e-3
K = 2000
"dense lasso"
def dense_matrix(N, n):
#generate lasso problem
m_i = int(n / (2 * N))
np.random.seed(rank)
A_i = np.random.randn(m_i, n)
A_i /= np.sqrt(np.sum(A_i ** 2, 0))
np.random.seed(rank)
xi = np.random.randn(n, 1)
b_i = np.dot(A_i, xi) + 1e-2 * np.random.randn(m_i, 1)
lam = 0.1 * np.max(np.abs(A_i.T.dot(b_i)))
return A_i, b_i, lam, xi
def get_par(N, e, n, A_i):
seed = 0
# get the small world network in G and E matrix
G, E = small_world(N, e, seed)
# get minimum degree of G
d_min = min(np.diag(G))
# get the total number of edges in G
edges = E.shape[0]
m_i = int(n / (2 * N))
# degree of node i in G
d_i = G.diagonal()[rank]
#lipshitz constant
l_i = (linalg.norm(A_i, 2)) ** 2 # ||A_i||_2^2
#node specific parameter for DPGA
gamma_i = np.sqrt((2.6 * N) / (edges * d_min))
#step size
c_i = (l_i + gamma_i * d_i) ** (-1)
gamma_ii = 0
for j in range(d_i):
gamma_ii += ((gamma_i * gamma_i) / (gamma_i + gamma_i))
gamma_ij = -(gamma_i * gamma_i) / (gamma_i + gamma_i)
pi = np.zeros((n, 1), np.float64)
return G, E, d_i, l_i, gamma_i, c_i, gamma_ii, gamma_ij, pi
def graph_cpu(A_i, lam, c_i, b_i, n_i):
#construct computation graph for proximal gradient operator on node i
from tensorflow.python.framework import ops
ops.reset_default_graph()
with tf.device('/cpu:0'):
A_i = tf.constant(A_i, dtype=tf.float64, name='A_i')
lam = tf.constant(lam, dtype=tf.float64, name='lambda')
b_i = tf.constant(b_i, dtype=tf.float64, name='b_i')
c_i = tf.constant(c_i, dtype=tf.float64, name='c_i')
zeros = tf.zeros((1, 1), dtype=tf.float64, name='zeros')
p_i = tf.placeholder(dtype=tf.float64, shape=[n_i, 1], name='p_i')
s_i = tf.placeholder(dtype=tf.float64, shape=[n_i, 1], name='s_i')
x_i = tf.placeholder(dtype=tf.float64, shape=[n_i, 1], name='x_i')
temp = tf.matmul(A_i, x_i) - b_i
xbar_i = x_i - c_i * (p_i + s_i + tf.matmul(A_i, temp, transpose_a=True))
prox_i = tf.multiply(tf.sign(xbar_i), tf.maximum(zeros, tf.abs(xbar_i) - lam * c_i))
return prox_i, p_i, s_i, x_i
def sess_run(sess, prox_i, p_i, s_i, x_i, pi, si, xi):
xi = sess.run(prox_i, feed_dict={p_i: pi, s_i: si, x_i: xi})
return xi
def dpga_cpu(N, e, n):
A_i, b_i, lam, xi = dense_matrix(N, n)
G, E, d_i, l_i, gamma_i, c_i, gamma_ii, gamma_ij, pi = get_par(N, e, n, A_i)
t0 = time.time()
x_j = np.zeros((n, d_i), dtype=np.float64)
j = 0
#communicate information with their neighbors
for i in range(E.shape[0]):
if E[i, rank] == 1:
comm.send(xi, dest=(np.where(E[i, :] == -1))[0])
x_j[:, [j]] = comm.recv(source=(np.where(E[i, :] == -1))[0])
j += 1
elif E[i, rank] == -1:
x_j[:, [j]] = comm.recv(source=(np.where(E[i, :] == 1))[0])
comm.send(xi, dest=(np.where(E[i, :] == 1))[0])
j += 1
#get si
si = np.multiply(gamma_ii, xi)
for i in range(d_i):
si += np.multiply(gamma_ij, x_j[:, [i]])
xbar_k = np.zeros((n, K+1), np.float64)
xbar_k[:, [0]] = xi
prox_c, p_c, s_c, x_c = graph_cpu(A_i, lam, c_i, b_i, n)
sess = tf.InteractiveSession()
for i in range(d_i):
xbar_k[:, [0]] += x_j[:, [i]]
xbar_k[:, [0]] = xbar_k[:, [0]]/(d_i + 1)
#DPGA iterations
for k in range(K):
xi = sess_run(sess, prox_c, p_c, s_c, x_c, pi, si, xi)
j = 0
# communicate information with their neighbors
for i in range(E.shape[0]):
if E[i, rank] == 1:
comm.send(xi, dest=(np.where(E[i, :] == -1))[0])
x_j[:, [j]] = comm.recv(source=(np.where(E[i, :] == -1))[0])
j += 1
elif E[i, rank] == -1:
x_j[:, [j]] = comm.recv(source=(np.where(E[i, :] == 1))[0])
comm.send(xi, dest=(np.where(E[i, :] == 1))[0])
j += 1
#update si
si = np.multiply(gamma_ii, xi)
for i in range(d_i):
si += np.multiply(gamma_ij, x_j[:, [i]])
#update pi
pi += si
xbar_k[:, [k + 1]] = xi
for i in range(d_i):
xbar_k[:, [k+1]] += x_j[:, [i]]
xbar_k[:, [k + 1]] = xbar_k[:, [k + 1]]/(d_i + 1)
eps_1 = linalg.norm((xi - xbar_k[:, [k+1]]), 2)
for i in range(d_i):
eps_1 += linalg.norm((x_j[:, [i]] - xbar_k[:, [k+1]]), 2)
eps_1 = eps_1/((d_i + 1)*np.sqrt(n))
eps_2 = linalg.norm((xbar_k[:, [k+1]]-xbar_k[:, [k]]), 2)/np.sqrt(n)
#check stop condition
if eps_1 <= stop1 and eps_2 <= stop2:
print('elapsed time', time.time() - t0)
print('rank', rank, 'n:', n, 'iterations:', k)
sys.stdout.flush()
# if rank == 0:
# x_dpga = pd.DataFrame(x_i, columns=list('A'))
# x_dpga.to_csv('x_dpga.csv')
MPI.Finalize()
if __name__ == "__main__":
_, N_str, e_str, n_str = sys.argv
N = int(N_str)
e = int(e_str)
n = int(n_str)
if rank == 0:
print("Nodes:", N, "Add edges:", e, 'problem size n:', n)
dpga_cpu(N, e, n)