Homework 6: Section 6.5.sagews

#Carlos Gomez-Guzman
#LS30B-3, Lab 3F
#Homework 6
#UID 505130857
#Feb. 22, 2019

#Exercise 6.5.1
M=matrix([[1.2,0],[0,1.25]])
v=vector([50,50])
vlist=[v]
for i in srange(20):
    v=M*v
    vlist.append(v)
list_plot(vlist, plotjoined=True)

#Exercise 6.5.2
M=matrix([[1.2,0],[0,0.9]])
v=vector([50,50])
vlist=[v]
for i in srange(20):
    v=M*v
    vlist.append(v)
list_plot(vlist, plotjoined=True)

#Exercise 6.5.3
M=matrix([[1.2,0],[0,1.25]])
v=vector([50,50])
vlist1=[50]
vlist2=[50]
t=srange(20)
for i in t:
    v=M*v
    vlist1.append(v[0])
    vlist2.append(v[1])
list_plot(zip(t,vlist1), color="orange", legend_label="X", axes_labels=["Time","Population"], plotjoined=True, thickness=4) + list_plot(zip(t,vlist2), color="red", legend_label="Y", plotjoined=True, thickness=4)

M=matrix([[1.2,0],[0,0.9]])
v=vector([50,50])
vlist1=[50]
vlist2=[50]
t=srange(20)
for i in t:
    v=M*v
    vlist1.append(v[0])
    vlist2.append(v[1])
list_plot(zip(t,vlist1), color="orange", legend_label="X", axes_labels=["Time","Population"], plotjoined=True, thickness=4) + list_plot(zip(t,vlist2), color="red", legend_label="Y", plotjoined=True, thickness=4)

#Ecercise 6.5.4a
M=matrix([[-2,0],[0,0.5]])
v=vector([1,1])
vlist=[v]
for i in srange(5):
    v=M*v
    vlist.append(v)
list_plot(vlist, color="blue", plotjoined=True, thickness=2)

#Ecercise 6.5.4b
M=matrix([[1.3,0],[0,0.6]])
v=vector([1,1])
vlist=[v]
for i in srange(10):
    v=M*v
    vlist.append(v)
list_plot(vlist, color="blue", plotjoined=True, thickness=2)

#Ecercise 6.5.4c
M=matrix([[-0.2,0],[0,0.8]])
v=vector([1,1])
vlist=[v]
for i in srange(10):
    v=M*v
    vlist.append(v)
list_plot(vlist, color="blue", plotjoined=True, thickness=2)

#Ecercise 6.5.4d
M=matrix([[0.5,0],[0,0.8]])
v=vector([1,1])
vlist=[v]
for i in srange(10):
    v=M*v
    vlist.append(v)
list_plot(vlist, color="blue", plotjoined=True, thickness=2)

#Exercise 6.5.5
M=matrix(RDF,[[0.1,2],[0.4,0.2]])
M.eigenvectors_right()

[(-0.745823643358446, [(-0.9210218088235311, 0.38951101097585256)], 1), (1.0458236433584458, [(-0.9040077946766141, -0.4275159729927345)], 1)]