Lab02_slides_v2.ipynb

Kernel: SageMath (stable)

Week 02 - List And Loops

LS30A LAB 1B/1D

TA: Hao Lee

LA: Evelyn Malamut

Review

Continuous Time System

$$R' = aR+bJ+c\\J'=dR+eJ+f$$

• What is the difference between R' and R?

• What is a, b, c, d, e, f?

Ans:

• R is a state variable, R' is the rate of change

• a, e can be per-captia rate or proportionality, b and d are mostly proportionality, and c and f can be constant growth rate.

Nomenclature

• Per-captia rate: increase/ decrease rate per unit of itself.

• Proportionality: increase/ decrease rate related to anything.

e.g.,

• R's growth rate is proportional to its own population, with proportionality a

• R's per-captia growth rate is a

• R's growth rate is proportional to J, with proportionality b

• R has a constant growth rate c

Programming

Type of Data

• Variables have data types

var1 = 1
var2 = 'some string'
print(var1 + var2)

This makes no sense

Reason: They have different data types

Data Types of Variables

a = 1
print(type(a))
b = 'I am a string'
print(type(b))

<type 'sage.rings.integer.Integer'>
<type 'str'>

List

Put multiple variables together

var1 = 1
var2 = 2
var3 = 3
my_array = [var1, var2, var3]
show(my_array)

It does not need to be the same data type

var1 = 1
var2 = 'String'
var3 = plot(x^2,(x,-2,2))

my_list= [var1,var2,var3]
print(my_list)

[1, 'String', Graphics object consisting of 1 graphics primitive]

How can we retrieve variables from a list?

=> Indexing

print(my_list)
show(my_list[2])

[1, 'String', Graphics object consisting of 1 graphics primitive]

How Indexing Works?

• If starts from the beginning, index starts from 0

• If starts from the end, index starts from -1

Example

my_list = [1,2,3,4,5]
print(my_list)
print(my_list[0])
print(my_list[-2])

[1, 2, 3, 4, 5]
1
4

We can retrieve more than one element!

my_list[1:4]

[2, 3, 4]

Be careful, for index range 1:4, only elements at position 1,2,3 are retrieved.

Add components into a list

print(my_list)
my_list.append(9)
print(my_list)

[1, 2, 3, 4, 5]
[1, 2, 3, 4, 5, 9]

Plot of List

Currently we have learned plot

plot(function,(x,x_min,x_max),options)

For most data set, we do not have the function!

Example: For a data set (x1,x2,x3,x4.......,xn),(y1,y2,y3,y4,........yn), please find their relationship!

X= (1,2,3,4,5)

Y= (1,4,9,16,25)

listToPlot=[(1,1),(2,4),(3,9),(4,16),(5,25)]
fig = list_plot(listToPlot)
show(fig)

(,) IS ANNONYING

X = (1,2,3,4,5)
Y=(1,4,9,16,25)
listToPlot=zip(X,Y)
listToPlot  #just wrote the variable's name can also print it!
list_plot(listToPlot,axes_labels=['Index','Value'],title='Test Data')
# take a look at the new options we set!!!!!

Connect all the points

X = (1,2,3,4,5)
Y=(1,4,9,16,25)
listToPlot=zip(X,Y)
list_plot(listToPlot,axes_labels=['Index','Value'],title='Test Data',plotjoined=True)

Loops

Whatis loops for?

=> Doing Repeated Task for Different Things

for var in list:
    do something to var

listVar=[1,2,3,4,5,6]

curSum = 0
for var in listVar:
    curSum = curSum+var
    print(curSum)

1
3
6
10
15
21

Create list in a Loop

This is very useful when we are trying to do the following operation

for testObj in list_of_testObj:
    result = testObj_do_some_task

We want to record the results

e.g., Do square root to [1,2,3,4,5,6,7]

allResult=[] #this is call an empty list
in_list = [1.,2.,3.,4.,5.,6.,7.]
for element in in_list:
    allResult.append(sqrt(element))
print(allResult)

[1.00000000000000, 1.41421356237310, 1.73205080756888, 2.00000000000000, 2.23606797749979, 2.44948974278318, 2.64575131106459]

Animation

What animation does?

Create a list of plots and plot them!!!!!

plots=[]
power =range(15)
for z in power:
    p=plot(x^z,(x,-10,10),axes_labels=['x','y'],ymax=5000,ymin=-5000)
    plots.append(p)
a=animate(plots)
show(a)

listVar = [1,2,3]
for var in listVar:
    print(var)

1
2
3