Speed improvements

[eSoares]

Hello,

In the past few weeks I have been using the library for some heavy number of runs and notice some bottlenecks.
Here are some contributions to patch some of the bottlenecks found to try to make the simulation faster.

• Added caching using an LRU cache in some functions that are slow and repeatedly called with same parameters;
• Change not-equal comparison of numpy arrays to bitwise xor since they are 1's and 0's;
• Reduce iterations in the _where_c function by taking advantage of numpy function to search for a value;

Between each commit the following test was performed (based on conv_encode_decode):

# Authors: CommPy contributors
# License: BSD 3-Clause

import math
import time
from datetime import timedelta

import numpy as np

import commpy.channelcoding.convcode as cc
import commpy.channels as chan
import commpy.links as lk
import commpy.modulation as mod

# =============================================================================
# Convolutional Code 1: G(D) = [1+D^2, 1+D+D^2]
# Standard code with rate 1/2
# =============================================================================

# Number of delay elements in the convolutional encoder
memory = np.array(6, ndmin=1)

# Generator matrix
g_matrix = np.array((0o5, 0o7), ndmin=2)

# Create trellis data structure
trellis1 = cc.Trellis(memory, g_matrix)

# ==================================================================================================
# Complete example using Commpy features and compare hard and soft demodulation. Example with code 1
# ==================================================================================================

# Modem : QPSK
modem = mod.QAMModem(4)

# AWGN channel
channels = chan.SISOFlatChannel(None, (1 + 0j, 0j))

# SNR range to test
SNRs = np.arange(0, 6) + 10 * math.log10(modem.num_bits_symbol)


# Modulation function
def modulate(bits):
    return modem.modulate(cc.conv_encode(bits, trellis1, 'cont'))


# Receiver function (no process required as there are no fading)
def receiver_soft(y, h, constellation, noise_var):
    return modem.demodulate(y, 'soft', noise_var)


# Decoder function
def decoder_soft(msg):
    return cc.viterbi_decode(msg, trellis1, decoding_type='soft')


# Build model from parameters
code_rate = trellis1.k / trellis1.n
model_soft = lk.LinkModel(modulate, channels, receiver_soft,
                          modem.num_bits_symbol, modem.constellation, modem.Es,
                          decoder_soft, code_rate)

# Test
start = time.time()
BERs_soft = model_soft.link_performance(SNRs, 1000, 600, 5000, code_rate)
print(str(timedelta(seconds=(time.time() - start))))

Rough results for each commit are presented bellow:

base (the repo at master) - 0:00:42.092337
with added cache (commit fc764d5) - 0:00:33.801127
with bitwise xor improvement (commit a9d3aa7) - 0:00:31.678570
improvement where_c (commit c276ede) - 0:00:13.405827

[veeresht]

Thank you! @eSoares