""" The typical Lotka-Volterra Model simulated using scipy """

__author__ = 'Orestes (o.gutierrez-al-khudhairy@imperial.ac.uk)'

__version__ = '0.0.1'

import numpy

import sys #allows us to use input arguments

import scipy as sc

import scipy.integrate as integrate

import math

import pylab as p #Contains matplotlib for plotting

#import matplotlip.pylab as p #Some people might need to do this

counter=0 #counter

#create initial plant species)

X= sc.array([10])

a = sc.array([-0.05])

t = sc.linspace(0, 10, 1000)

m = sc.array([1])

counter=0

def dX_dt(X, t, param1, param2):

return (A.dot(X) + X*growth)

def store(old, new):

return(X)

spec = len(m)

X_mat = sc.zeroes(T_len,Max_N) #pre-allocate array

Spec = 1

while (spec < Max_N):

Spec = len(m)

#time step counter

counter=counter+1

print(spec)

print(counter)

#integration process

X_new, infodict = integrate.odeint(dX_dt, X, t, args= (m,a) , full_output=True)

globals()['Populations%s' % counter]= X_new

#X_s_new =X_new.T

#if (spec == 1):

# if (counter ==1):

# X_store=X_s_new

# else:

# X=X.reshape(1,1)

# X_store=sc.hstack((X,X_s_new))

#else:

# X_store= store(X,X_s_new)

#create species that want to invade

prob = numpy.random.rand(1)

### CREATION OF INVADER ###

if (prob <0.75):

print("New species incoming")

# Assign initial population density of invader

X=sc.hstack((X_new[len(X)-1][:],math.floor(numpy.random.rand(1)*10))) #only store the last values of old populations using X[len(X)-1][:]

m = sc.hstack((m, numpy.random.rand(1))) #create reproduction rates

if(numpy.random.rand(1) < 0.3): #make paramter negative for certain prob

m[len(m)-1] = -1*m[len(m)-1]

#inter/intra-specific parameterisation

new_a_row = sc.zeros(len(X))

new_a_col = sc.zeros(len(X)-1)

#make parameters negative with certain probability

for k in range(len(X)):

new_a_row[k] = numpy.random.rand(1)

if(numpy.random.rand(1) < 0.3):

new_a_row[k] = -1*new_a_row[k]

for k in range(len(X)-1):

new_a_col[k] = numpy.random.rand(1)

if(numpy.random.rand(1) < 0.3):

new_a_col[k] = -1*new_a_col[k]

#store new parameters

if (len(a)==1):

a = sc.hstack((a,new_a_col))

else:

a = sc.hstack((a,new_a_col.reshape(spec,1)))

a = sc.vstack((a,new_a_row))

else:

X=X_new[len(X)-1][:]#only store the last population numbers, don't need the historical time-series anymore.

spec = len(m)

#prepare calculation of survival of species

if (spec > 1):

A_surv = sc.zeros((spec,spec))

for i in range(spec):

for j in range(spec):

A_surv[i][j] =a[i][j]*X[j]

#delete species that go extinct

for x in range(spec):

if (sum(A_surv[x]-m[x])<=0):

print("Extinction incoming")

sc.delete(a, (x), axis=0)

sc.delete(a, (x), axis=1)

sc.delete(X, (x), axis=0)

sc.delete(m, (x), axis=0)

x, y, z= X_new.T# What's this for? Retrieves necessairy population time series data needed for potting

f1 = p.figure() #Open empty figure object

p.plot(t, x, 'g-', label='x density') # Plot

p.plot(t, y, 'b-', label='y density')

p.plot(t, z, 'r-', label='z density')

p.grid()

p.legend(loc='best')

p.xlabel('Time')

#p.text(-30,3.5,"a=",fontsize='small', color='green')

#p.text(-20,3.5,a,fontsize='small', color='red')

#p.text(-30,2.5,"b_x=",fontsize='small', color='green')

#p.text(-20,2.5,b_x ,fontsize='small', color='red')

#p.text(-30,1.5,"d_x=",fontsize='small', color='green')

#p.text(-20,1.5,d_x ,fontsize='small', color='red')

#p.text(-30,0.5,"b_y=",fontsize='small', color='green')

#p.text(-20,0.5,b_y ,fontsize='small', color='red')

#p.text(-30,-1.5,"d_y=",fontsize='small', color='green')

#p.text(-20,-1.5,d_y ,fontsize='small', color='red')

p.ylabel('Population')

p.title('x-y population dynamics')

#p.show()

f1.savefig('MultiSpecies_Dynamics.pdf') #Save figure