https://github.com/blab/antibody-response-pulse/
In [1]:
'''
author: Alvason Zhenhua Li
date: 03/23/2015
Home-made machinery for solving partial differential equations
'''
import numpy as np
# define RK4 for an array (3, n) of coupled differential equations
def AlvaRungeKutta4XT(pde_array, initial_Out, minX_In, maxX_In, totalPoint_X, minT_In, maxT_In, totalPoint_T, event_table):
global event_active
event_active = 0.0
global event_OAS
event_OAS = 0.0
global event_OAS_B
event_OAS_B = 0.0
# primary size of pde equations
outWay = pde_array.shape[0]
# initialize the whole memory-space for output and input
inWay = 1; # one layer is enough for storing "x" and "t" (only two list of variable)
# define the first part of array as output memory-space
gOutIn_array = np.zeros([outWay + inWay, totalPoint_X, totalPoint_T])
# loading starting output values
for i in range(outWay):
gOutIn_array[i, :, :] = initial_Out[i, :, :]
# griding input X value
gridingInput_X = np.linspace(minX_In, maxX_In, num = totalPoint_X, retstep = True)
# loading input values to (define the final array as input memory-space)
gOutIn_array[-inWay, :, 0] = gridingInput_X[0]
# step-size (increment of input X)
dx = gridingInput_X[1]
# griding input T value
gridingInput_T = np.linspace(minT_In, maxT_In, num = totalPoint_T, retstep = True)
# loading input values to (define the final array as input memory-space)
gOutIn_array[-inWay, 0, :] = gridingInput_T[0]
# step-size (increment of input T)
dt = gridingInput_T[1]
# starting
# initialize the memory-space for local try-step
dydt1_array = np.zeros([outWay, totalPoint_X])
dydt2_array = np.zeros([outWay, totalPoint_X])
dydt3_array = np.zeros([outWay, totalPoint_X])
dydt4_array = np.zeros([outWay, totalPoint_X])
# initialize the memory-space for keeping current value
currentOut_Value = np.zeros([outWay, totalPoint_X])
for tn in range(totalPoint_T - 1):
event_parameter = event_table[0][0]
event_1st = event_table[1]
event_2nd = event_table[2]
tn_unit = totalPoint_T/(maxT_In - minT_In)
activeTime = event_parameter[2]
originVirus = event_parameter[5]
# keep initial value at the moment of tn
currentOut_Value[:, :] = np.copy(gOutIn_array[:-inWay, :, tn])
currentIn_T_Value = np.copy(gOutIn_array[-inWay, 0, tn])
# first try-step
for i in range(outWay):
for xn in range(totalPoint_X):
###
# cutoff --- set virus = 0 if viral population < 1
if gOutIn_array[0, xn, tn] < 1.0:
gOutIn_array[0, xn, tn] = 0.0
# post-infection --- replace pre-parameter by post-parameter
event_active = event_parameter[0]
event_OAS = 0.0
event_OAS_B = 0.0
if xn == 1 and event_1st[xn, 0] > 1.0 and tn > int((event_1st[xn, 1] + activeTime)*tn_unit):
event_active = event_parameter[1]
# 1st-infection --- set viral infection if tn == specific time
if tn == int(event_1st[xn, 1]*tn_unit):
gOutIn_array[0, xn, tn] = event_1st[xn, 0]
# 2nd-infection --- set viral infection if tn == specific time
if tn == int(event_2nd[xn, 1]*tn_unit):
gOutIn_array[0, xn, tn] = event_2nd[xn, 0]
# OAS-infection
if tn == int(event_1st[xn, 1]*tn_unit):
gOutIn_array[0, originVirus, tn] = event_1st[xn, 0]
event_OAS = event_parameter[3]
# OAS+immunity --- for near term infection (memory B-cell from origin-virus is still existing)
if xn == originVirus and event_1st[xn + 1, 0] > 1.0 and tn > int(event_1st[xn + 1, 1]*tn_unit):
event_OAS = event_parameter[3] # in-rate of antibody-IgG from memory B-cell
# OAS-immunity ---
if xn > originVirus and event_1st[xn, 0] > 1.0 and tn > int(event_1st[xn, 1]*tn_unit):
event_OAS_B = event_parameter[4] # in-rate of antibody-IgG from memory B-cell
###
dydt1_array[i, xn] = pde_array[i](gOutIn_array[:, :, tn])[xn] # computing ratio
gOutIn_array[:-inWay, :, tn] = currentOut_Value[:, :] + dydt1_array[:, :]*dt/2 # update output
gOutIn_array[-inWay, 0, tn] = currentIn_T_Value + dt/2 # update input
# second half try-step
for i in range(outWay):
for xn in range(totalPoint_X):
###
# cutoff --- set virus = 0 if viral population < 1
if gOutIn_array[0, xn, tn] < 1.0:
gOutIn_array[0, xn, tn] = 0.0
# post-infection --- replace pre-parameter by post-parameter
event_active = event_parameter[0]
event_OAS = 0.0
event_OAS_B = 0.0
if xn == 1 and event_1st[xn, 0] > 1.0 and tn > int((event_1st[xn, 1] + activeTime)*tn_unit):
event_active = event_parameter[1]
# 1st-infection --- set viral infection if tn == specific time
if tn == int(event_1st[xn, 1]*tn_unit):
gOutIn_array[0, xn, tn] = event_1st[xn, 0]
# 2nd-infection --- set viral infection if tn == specific time
if tn == int(event_2nd[xn, 1]*tn_unit):
gOutIn_array[0, xn, tn] = event_2nd[xn, 0]
# OAS-infection
if tn == int(event_1st[xn, 1]*tn_unit):
gOutIn_array[0, originVirus, tn] = event_1st[xn, 0]
event_OAS = event_parameter[3]
# OAS+immunity --- for near term infection (memory B-cell from origin-virus is still existing)
if xn == originVirus and event_1st[xn + 1, 0] > 1.0 and tn > int(event_1st[xn + 1, 1]*tn_unit):
event_OAS = event_parameter[3] # in-rate of antibody-IgG from memory B-cell
# OAS-immunity ---
if xn > originVirus and event_1st[xn, 0] > 1.0 and tn > int(event_1st[xn, 1]*tn_unit):
event_OAS_B = event_parameter[4] # in-rate of antibody-IgG from memory B-cell
###
dydt2_array[i, xn] = pde_array[i](gOutIn_array[:, :, tn])[xn] # computing ratio
gOutIn_array[:-inWay, :, tn] = currentOut_Value[:, :] + dydt2_array[:, :]*dt/2 # update output
gOutIn_array[-inWay, 0, tn] = currentIn_T_Value + dt/2 # update input
# third half try-step
for i in range(outWay):
for xn in range(totalPoint_X):
###
# cutoff --- set virus = 0 if viral population < 1
if gOutIn_array[0, xn, tn] < 1.0:
gOutIn_array[0, xn, tn] = 0.0
# post-infection --- replace pre-parameter by post-parameter
event_active = event_parameter[0]
event_OAS = 0.0
event_OAS_B = 0.0
if xn == 1 and event_1st[xn, 0] > 1.0 and tn > int((event_1st[xn, 1] + activeTime)*tn_unit):
event_active = event_parameter[1]
# 1st-infection --- set viral infection if tn == specific time
if tn == int(event_1st[xn, 1]*tn_unit):
gOutIn_array[0, xn, tn] = event_1st[xn, 0]
# 2nd-infection --- set viral infection if tn == specific time
if tn == int(event_2nd[xn, 1]*tn_unit):
gOutIn_array[0, xn, tn] = event_2nd[xn, 0]
# OAS-infection
if tn == int(event_1st[xn, 1]*tn_unit):
gOutIn_array[0, originVirus, tn] = event_1st[xn, 0]
event_OAS = event_parameter[3]
# OAS+immunity --- for near term infection (memory B-cell from origin-virus is still existing)
if xn == originVirus and event_1st[xn + 1, 0] > 1.0 and tn > int(event_1st[xn + 1, 1]*tn_unit):
event_OAS = event_parameter[3] # in-rate of antibody-IgG from memory B-cell
# OAS-immunity ---
if xn > originVirus and event_1st[xn, 0] > 1.0 and tn > int(event_1st[xn, 1]*tn_unit):
event_OAS_B = event_parameter[4] # in-rate of antibody-IgG from memory B-cell
###
dydt3_array[i, xn] = pde_array[i](gOutIn_array[:, :, tn])[xn] # computing ratio
gOutIn_array[:-inWay, :, tn] = currentOut_Value[:, :] + dydt3_array[:, :]*dt # update output
gOutIn_array[-inWay, 0, tn] = currentIn_T_Value + dt # update input
# fourth try-step
for i in range(outWay):
for xn in range(totalPoint_X):
###
# cutoff --- set virus = 0 if viral population < 1
if gOutIn_array[0, xn, tn] < 1.0:
gOutIn_array[0, xn, tn] = 0.0
# post-infection --- replace pre-parameter by post-parameter
event_active = event_parameter[0]
event_OAS = 0.0
event_OAS_B = 0.0
if xn == 1 and event_1st[xn, 0] > 1.0 and tn > int((event_1st[xn, 1] + activeTime)*tn_unit):
event_active = event_parameter[1]
# 1st-infection --- set viral infection if tn == specific time
if tn == int(event_1st[xn, 1]*tn_unit):
gOutIn_array[0, xn, tn] = event_1st[xn, 0]
# 2nd-infection --- set viral infection if tn == specific time
if tn == int(event_2nd[xn, 1]*tn_unit):
gOutIn_array[0, xn, tn] = event_2nd[xn, 0]
# OAS-infection
if tn == int(event_1st[xn, 1]*tn_unit):
gOutIn_array[0, originVirus, tn] = event_1st[xn, 0]
event_OAS = event_parameter[3]
# OAS+immunity --- for near term infection (memory B-cell from origin-virus is still existing)
if xn == originVirus and event_1st[xn + 1, 0] > 1.0 and tn > int(event_1st[xn + 1, 1]*tn_unit):
event_OAS = event_parameter[3] # in-rate of antibody-IgG from memory B-cell
# OAS-immunity ---
if xn > originVirus and event_1st[xn, 0] > 1.0 and tn > int(event_1st[xn, 1]*tn_unit):
event_OAS_B = event_parameter[4] # in-rate of antibody-IgG from memory B-cell
###
dydt4_array[i, xn] = pde_array[i](gOutIn_array[:, :, tn])[xn] # computing ratio
# solid step (update the next output) by accumulate all the try-steps with proper adjustment
gOutIn_array[:-inWay, :, tn + 1] = currentOut_Value[:, :] + dt*(dydt1_array[:, :]/6
+ dydt2_array[:, :]/3
+ dydt3_array[:, :]/3
+ dydt4_array[:, :]/6)
# restore to initial value
gOutIn_array[:-inWay, :, tn] = np.copy(currentOut_Value[:, :])
gOutIn_array[-inWay, 0, tn] = np.copy(currentIn_T_Value)
# end of loop
return (gOutIn_array[:-inWay, :])
In [2]:
# min-max sorting
def AlvaMinMax(data):
totalDataPoint = np.size(data)
minMaxListing = np.zeros(totalDataPoint)
for i in range(totalDataPoint):
# searching the minimum in current array
jj = 0
minMaxListing[i] = data[jj] # suppose the 1st element [0] of current data-list is the minimum
for j in range(totalDataPoint - i):
if data[j] < minMaxListing[i]:
minMaxListing[i] = data[j]
jj = j # recording the position of selected element
# reducing the size of searching zone (removing the minmum from current array)
data = np.delete(data, jj)
return (minMaxListing)