Output¶

print(123)

123

printf syntax¶

print("%s" % ("Hello"))
print("%d , %03d" % (1,1))
print("%f, %.3f " % (0.2,0.2))
print("%e, %E" % (300000000,300000000))
print("%.1e, %.0E" % (300000000,300000000))

Hello
1 , 001
0.200000, 0.200 
3.000000e+08, 3.000000E+08
3.0e+08, 3E+08

Format string syntax¶

print("{x:.2f}" .format(x=64.89999)) #{[name a variable]:[assigns a format]}

64.90

Type Conversion¶

a = 1
b = 1.0
c = "c"
print(type(a))
print(type(b))
print(type(c))

<class 'int'>
<class 'float'>
<class 'str'>

print(type( str(a) ))
print(type( int(b) ))

print(round(1.89))
print(int(round(1.45)))

<class 'str'>
<class 'int'>
2
1

Complex Number¶

u = 24 + 2j

u.real

24.0

u.imag

2.0

u.conjugate()

(24-2j)

Differentiation and Integration¶

# displacement = u*t + 1/2*a*t^2; velocity = u + a*t; acceleration = a
from sympy import *
t,a,u=symbols("t a u") # to make python treat those alphabet as symbolic variables
s = u*t+Rational(1,2)*a*t**2
ds= diff(s,t) #1st deriative
print("v = %s" % (ds))
dds = diff(s,t,t) #2nd derivative
print("a = %s" % (dds))

v = a*t + u
a = a

s_ = integrate(ds, t)
print("s = %s" % (s_))

s = a*t**2/2 + t*u

#insert numbers in symbolic expression
v = lambdify([t,u,a], ds)
v(t=1,u=1,a=9.81)

10.81

Solving Equations¶

from sympy import solve
y,k,x = symbols("y k x")
y = x+1 
solve(y,x) # solve for x on x+1=0

[-1]

solve(y<3) # solve for x on x+1<3

#do substitution by expression.subs([term], [variable])
print("x+1 = %s when x = 1" % (y.subs(x, 1)))

x+1 = 2 when x = 1

Input¶

#Reading Keyboard Input
u = input("enter u=...") # use raw_input() for python 2.x
print("I just received %s" % u)

enter u=...hello
I just received hello

#assigning object with user input
p = eval(input("type what you what: "))
print(p)
print(type(p))

q = eval(input("type what you what: "))
print(q)
print(type(q))

type what you what: 1+5
6
<class 'int'>
type what you what: [1,2,3]
[1, 2, 3]
<class 'list'>

#Reading user input as part of code
string = input("type you code: ")
exec(string)

type you code: for i in range(0,5):print(i)
0
1
2
3
4

#Reading files
data = open('path/fileName.fileType', 'r') #reading line by line
for line in data:
    #operations for data

#or
line = data.readlines() 
'''
which is the same as 
line = []
for l in data:
    line.append(l)
    
and 

line = [l for l in data]
'''

#Other ways to read a file
#1.
data = open('file.txt', 'r')
for line in data:
    #do something
data.close()
#2.
with open('file.txt', 'r') as data:
    for line in data:
        #do something; no need to close the file
#3.
data = open('file.txt', 'r')
while True:
    line = data.readline()
    if not line:
        break
    #do something

# Writing data to a file
data = open('file.txt', 'w')
data.write("your data")
data.close()

Operations¶

While Loop¶

a = 0
b = 10
while a <= 7 and b != 0:
    print("a = %d, b = %d" % (a,b))
    a += 1
    b -= 1
    if a == 7:
        b == 0

a = 0, b = 10
a = 1, b = 9
a = 2, b = 8
a = 3, b = 7
a = 4, b = 6
a = 5, b = 5
a = 6, b = 4
a = 7, b = 3

For Loop¶

whatever = [1,2,3,4,5,6]
for itemsInWhatever in whatever:
    print(itemsInWhatever)

listForEx = [0]*3 #create a list with 3 zeros. i.e. [0,0,0]
for i in range(-10, 20, 5): #range(start, stop, step)
    listForEx.append(i)
print(listForEx)

[0, 0, 0, -10, -5, 0, 5, 10, 15]

String Opeation¶

#splitting a string
string = "1 2 3 4 5"
words = string.split()
print(words)

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

Error Exception¶

try:
    #do something that may have errors. e.g. opening a file
    file = open('IAmNotExists.txt','r')
except:
    print("It doesn't exist")

It doesn't exist

#if weren't use exception...
file = open('IAmNotExists.txt','r')
print("It really doesn't exit")

---------------------------------------------------------------------------
FileNotFoundError                         Traceback (most recent call last)
<ipython-input-203-9b3c8838629f> in <module>
      1 #if weren't use exception...
----> 2 file = open('IAmNotExists.txt','r')
      3 print("It really doesn't exit")

FileNotFoundError: [Errno 2] No such file or directory: 'IAmNotExists.txt'

#Exeption for specific errors
try:
    #do something
    list = [1,2]
    print(list[int(input())])
except IndexError:
    print("Don't have such value")
except ValueError:
    print("Please input number")

print("--------------------------------")
try:
    #do something
    list = [1,2]
    print(list[int(input())])
except IndexError:
    print("Don't have such value")
except ValueError:
    print("Please input number")
    
print("--------------------------------")
try:
    #do something
    list = [1,2]
    print(list[int(input())])
except IndexError:
    print("Don't have such value")
except ValueError:
    print("Please input number")

3
Don't have such value
--------------------------------
a
Please input number
--------------------------------
0
1

#Raising Exception
try:
    l = [1,2]
    a = input()
    print(l[int(a)])
          
except IndexError:
    raise IndexError\
        ("Don't have such value")
if int(a) < 0:
    raise ValueError("Don't do that")

-1
2

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-215-d0dcdeb9390a> in <module>
      9         ("Don't have such value")
     10 if int(a) < 0:
---> 11     raise ValueError("Don't do that")

ValueError: Don't do that

#more firendly way
try:
    l = [1,2]
    a = input()
    print(l[int(a)])
          
except IndexError as e:
    print(e)

3
list index out of range

Data Structures¶

List¶

C = [1,2,3,4,5,6,7] #position: [0,1,2,3,4,and so on]
print(C)
for items in C:
    print(items)

[1, 2, 3, 4, 5, 6, 7]
1
2
3
4
5
6
7

#add an element in the end of the list
C.append(8)
C

[1, 2, 3, 4, 5, 6, 7, 8]

#adding two lists
C += [1,2,3] # same as C = C + [1,2,3]
C

[1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3]

#insert an element by assign a position for it
C.insert(2, 100) #assign 100 to position 2
C

[1, 2, 100, 3, 4, 5, 6, 7, 8]

#delete an element such at position 2
del C[2]
C

[1, 2, 3, 4, 5, 6, 7, 8]

#get the length of the list
len(C)

8

#get the index of an element
C.index(7) #element 7 locates at position 6

6

#Is 9 in the list?
print(9 in C)
#Is 1 in the list?
print(1 in C)

False
True

''' PYTHON ALLOWS NEGATIVE INDEX! '''
#negative index = index starting from the right
C[-1] == C[len(C)-1]

True

#nameing elements of the list
a,b,c,d,e,f,g,h = C
print("%d,%d,%d,%d,%d,%d,%d,%d" % (a,b,c,d,e,f,g,h))

1,2,3,4,5,6,7,8

#another way to create a list
D = [1+i for i in range(3)]
D

[1, 2, 3]

#operating two lists at the same time
list1 = [1,2,3,4]
list2 = [7,8,9]
for elementFrom1, elementFrom2 in zip(list1, list2):
    print("%d, %d" % (elementFrom1, elementFrom2))

1, 7
2, 8
3, 9

#nested list (aka. a table)
'''
1 2 3 
4 5 6
'''
R = [1,2,3]
C = [4,5,6]
table1 = [R,C]
for r, c in zip(R,C):
    print("%d %d"%(r,c))

print("------------------------------------")
    
for r in range(0, 3):
    for c in range (0, 3):
        if c == 2:
            print(table1[r-1][c-1], end="\n")
        else:
            print(table1[r-1][c-1], end="")

1 4
2 5
3 6
------------------------------------
645
312
645

table2=[[row, column] for row, column in zip(R, C)]
import pprint
pprint.pprint(table2)

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

#example 
L = []
L.append([1,2,3])
L.append([4])
L.append([5,6,7,8,9])

#method 1
for i in range(len(L)):
    for j in range(len(L[i])):
        print(L[i][j])
print("-----------------")
#method 2
for l in L:
    for LElement in l:
        print(LElement)

1
2
3
4
5
6
7
8
9
-----------------
1
2
3
4
5
6
7
8
9

#reading sublists
P = [0,1,2,3,4,5,6,7,8]
print(P[2:]) #print sublist such start at position 2 to the end of the list
print(P[2:4])#print sublist such start at position 2 and end up with position 4-1 (i.e. position 3)
print(P[:4])#print sublist such start at the begining of the list and end up with position 4-1
print(P[:])#the whole lsit
print(P[1:-2])#allow negative index

[2, 3, 4, 5, 6, 7, 8]
[2, 3]
[0, 1, 2, 3]
[0, 1, 2, 3, 4, 5, 6, 7, 8]
[1, 2, 3, 4, 5, 6]

Tuples¶

t = (1, 2, 3, "a", "b", "c")
for element in t:
    print(element)

1
2
3
a
b
c

#adding tuples
t += (-1,-2)
print(t)

(1, 2, 3, 'a', 'b', 'c', -1, -2)

#indexing
print(t[0])
print(t[2:])

1
(3, 'a', 'b', 'c', -1, -2)

Functions¶

#define a function
def function(data):
    return "I received "+str(data)

print(function("a apple"))
print(function(100))

I received a apple
I received 100

#Global Variable and Local Variable

imAGlobalVariable = 10
def abc():
    imALocalVariable = 100
    print("I can read global variable %d" % imAGlobalVariable)
abc()
print("I can read global variable %d but I cannot read loval variable in function abc" % (imAGlobalVariable))

I can read global variable 10
I can read global variable 10 but I cannot read loval variable in function abc

f = 0
def plusOne():
    f = 1 #this is a 'new' local variable
    print("f = %d inside function plusOne" % f)

plusOne()
print("f = %d outside function plusOne" % f)

f = 1 inside function plusOne
f = 0 outside function plusOne

f = 0
def plusOne():
    global f
    f = 1 #this is the global variable
    print("f = %d inside function plusOne" % f)

plusOne()
print("f = %d outside function plusOne" % f)

f = 1 inside function plusOne
f = 1 outside function plusOne

#defaulting parameters of function
def summation(input1, input2, input3 = 100):
    return input1 + input2 + input3

print(summation(1,2)) #1+2+100
print(summation(1,2,3)) #1+2+3

103
6

#Lambda Function
f = lambda x: x+1
'''
which is the same as 
def f(x):
    return x+1
'''
print(f(1))

2

Modules¶

#import xxx, where xxx is a module
#e.g.
import math
print(math.factorial(3))
'''
same as
from math import factorial
print(factorial(3))

'''

6

#supposed there is a module named "IAmAFile" with functions named "abc" and "efg"
import IAmAFile #import both functions "abc" and "efg"
from IAmAFile import * #import both functions "abc" and "efg"
from IAmAFile import abc #import function "abc"

#Test Block

def f1():
    return "I am a function in a module"

if __name__ == "__main__":
    #do anything
    print("Testing Testing...")
    print(f1())

Testing Testing...
I am a function in a module

Plotting¶

Vector¶

Arrays¶

#numberical arrays
import numpy as np
ls = [1,2,3,4,5] # a list
n = np.array(ls) # convert a list to an array
print(n)
zn = np.zeros(3) # create an array with length of three and filled with zeros: [0 0 0]
print(zn)
z = np.linspace(1, 5, 10) # create an array with length of 10 and filled with x in [1,5] (uniformly distributed)
print(z)

[1 2 3 4 5]
[0. 0. 0.]
[1.         1.44444444 1.88888889 2.33333333 2.77777778 3.22222222
 3.66666667 4.11111111 4.55555556 5.        ]

Curve Plotting¶

#Matlab-style plotting
import numpy as np
import matplotlib.pyplot as plt
from past.builtins import xrange #for python3

def function(x):
    return x**2+1

x = np.linspace(0, 5, 100) # 100 points lay on [0, 5]
y = np.zeros(len(x)) # setting y-axis  
for i in xrange(len(x)):
    y[i] = function(x[i])
#same as y=function(X)
plt.plot(x, y)
plt.xlabel("x")
plt.ylabel("y")
plt.legend(["x^2+1"])
plt.title("Demo")
plt.axis([0, 5, 0, 50]) #[x min, x max, y min, y max]
plt.savefig("picture.png") #generate PNG
plt.show()

#plotting multiple curves
def function1(x):
    return x**2
def function2(x):
    return x+1

x = np.linspace(0, 5, 100)
y1 = function1(x)
y2 = function2(x)

plt.plot(x, y1, "r-") # 'r' = red, '-' = line
plt.plot(x, y2, "bo")
plt.show()

#putting multiple plots in one figure
plt.figure()
plt.subplot(1, 2, 1) # (rows, cloumns, row-wise counter)
x = np.linspace(0, 5, 100)
y1 = function1(x)
y2 = function2(x)
plt.plot(x, y1, "r-") # 'r' = red, '-' = line
plt.plot(x, y2, "bo")

plt.subplot(1, 2, 2)
x = np.linspace(0, 5, 100) # 100 points lay on [0, 5]
y = np.zeros(len(x)) # setting y-axis  
y = function(x)
plt.plot(x, y)

plt.show()

#Plotting with SciTools and Easyviz
from scitools.std import *
import numpy as np

def f(x):
    return x*2+x+2
x = np.linspace(0, 5, 100)
y = f(x)
plot(x,y, '-')
#fine

---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
<ipython-input-9-e9033a3d685a> in <module>
      1 #Plotting with SciTools and Easyviz
----> 2 from scitools.std import *
      3 import numpy as np
      4 
      5 def f(x):

ModuleNotFoundError: No module named 'scitools.std'

#Making Animation

Dictionaries¶

#Making Dictionaries 
dic = {"tom": 100, "jerry": 200}
print(dic["tom"])
#or
dic2 = dict(Tom=100, Jerry=200)
print(dic2["Jerry"])

print(dic)

100
200
{'tom': 100, 'jerry': 200}

#Operation

Class¶

#define a class
class IamAClass:
    def __init__(self, a):#__init__ will be called when writing A = IamAClass(3)
        self.a = a
    def output(self):
        print(self.a)

A = IamAClass(3)
A.output()
print(A.a)

3
3

#The Call Special Method
class JustAClass:
    def __call__(self, a):
        return a+1

CartonsBase

Sunday, November 3, 2024

Installing xAct (Mac)

Sunday, December 25, 2022

Quick note on installing FORM

Install WSL

Install FORM by Homebrew

Tuesday, July 7, 2020

Python Notes

Output¶

printf syntax¶

Format string syntax¶

Type Conversion¶

Complex Number¶

Differentiation and Integration¶

Solving Equations¶

Input¶

Operations¶

While Loop¶

For Loop¶

String Opeation¶

Error Exception¶

Data Structures¶

List¶

Tuples¶

Functions¶

Modules¶

Plotting¶

Vector¶

Arrays¶

Curve Plotting¶

Dictionaries¶

Class¶