import numpy as np
A=np.array([[1.5,1],[3.75,4]])
B=np.array([1800,900])
x=np.linalg.solve(A,B)
print("Values of A and B variables:",x)
h=np.allclose(np.dot(A, x), B)
print("Substitution of two variables in equation to validate:",h)
Solve Problems by Coding Solutions - A Complete solution for python programming
Operations on Matrices using Python program
import numpy as np
A = np.array([[4,1,7],[2,1,8],[3 ,7,1]])
B = np.array([[6,1,1],[2,1,5],[2,3,1]])
C=A.dot(B)
print("Values of First 2D Matrix\n",A)
print("Values of Second 2D Matrix\n",B)
print("---------------------------------------------")
print("Multiplication of Matrices\n",C)
print("\n")
Ainv=np.linalg.inv(A)
Binv=np.linalg.inv(B)
print("Inverse of First Matrix\n",Ainv)
print("Inverse of Second Matrix\n",Binv)
print("\n")
AI=Ainv.dot(A)
BI=Binv.dot(B)
print("Multiplication of First Matrix and their Inverse\n",AI)
print("Multiplication of Second Matrix and their Inverse\n",BI)
AD=np.linalg.det(A)
BD=np.linalg.det(B)
print("\n")
print("Determinant of First Matricx:",AD)
print("Determinant of Second Matricx:",BD)
print("\n")
ADi=np.diag(A)
BDi=np.diag(B)
print("Diagonal Elements of First Matrix:",ADi)
print("Diagonal Elements of Second Matrix:",BDi)
SADi=np.trace(A)
SBDi=np.trace(B)
print("\n")
print("Sum of Diagonal Elements of First Matrix:",SADi)
print("Sum of Diagonal Elements of Second Matrix:",SBDi)
print("\n")
CA=np.cov(A)
CB=np.cov(B)
print("Covariance matrix of First Matrix\n",CA)
print("Covariance matrix of Second Matrix\n",CB)
print("\n")
ECA=np.linalg.eigh(CA)
ECB=np.linalg.eigh(CB)
print("First array represents eigenvalues and second array represents eigenvectors")
print("\n")
print("covariance matrix eigenvalues eigenvectors of First Matrix\n",ECA)
print("\n")
print("covariance matrix eigenvalues eigenvectors of Second Matrix\n",ECB)
A = np.array([[4,1,7],[2,1,8],[3 ,7,1]])
B = np.array([[6,1,1],[2,1,5],[2,3,1]])
C=A.dot(B)
print("Values of First 2D Matrix\n",A)
print("Values of Second 2D Matrix\n",B)
print("---------------------------------------------")
print("Multiplication of Matrices\n",C)
print("\n")
Ainv=np.linalg.inv(A)
Binv=np.linalg.inv(B)
print("Inverse of First Matrix\n",Ainv)
print("Inverse of Second Matrix\n",Binv)
print("\n")
AI=Ainv.dot(A)
BI=Binv.dot(B)
print("Multiplication of First Matrix and their Inverse\n",AI)
print("Multiplication of Second Matrix and their Inverse\n",BI)
AD=np.linalg.det(A)
BD=np.linalg.det(B)
print("\n")
print("Determinant of First Matricx:",AD)
print("Determinant of Second Matricx:",BD)
print("\n")
ADi=np.diag(A)
BDi=np.diag(B)
print("Diagonal Elements of First Matrix:",ADi)
print("Diagonal Elements of Second Matrix:",BDi)
SADi=np.trace(A)
SBDi=np.trace(B)
print("\n")
print("Sum of Diagonal Elements of First Matrix:",SADi)
print("Sum of Diagonal Elements of Second Matrix:",SBDi)
print("\n")
CA=np.cov(A)
CB=np.cov(B)
print("Covariance matrix of First Matrix\n",CA)
print("Covariance matrix of Second Matrix\n",CB)
print("\n")
ECA=np.linalg.eigh(CA)
ECB=np.linalg.eigh(CB)
print("First array represents eigenvalues and second array represents eigenvectors")
print("\n")
print("covariance matrix eigenvalues eigenvectors of First Matrix\n",ECA)
print("\n")
print("covariance matrix eigenvalues eigenvectors of Second Matrix\n",ECB)
Temperature Conversion Table
def Fah():
F=int(input('Enter the temperature on Fahrenheit(F)'))
C=(F - 32) * 5/9
K=(F - 32) * 5/9 + 273.15
print("Fahrenheit Value :",F)
print("Celsius Value :",C)
print("Kelvin Value:",K)
def Cel():
C=int(input('Enter the temperature on Celsius(C)'))
F=(C * 9/5) + 32
K=C + 273.15
print("Fahrenheit Value :",F)
print("Celsius Value :",C)
print("Kelvin Value:",K)
def Kel():
K=int(input('Enter the temperature on Kelvin(K)'))
F=(K - 273.15) * 9/5 + 32
C=K - 273.15
print("Fahrenheit Value :",F)
print("Celsius Value :",C)
print("Kelvin Value:",K)
print("\n")
print('1.Fahrenheit to Celsius & Kelvin\n2.Celsius to Fahrenheit & Kelvin\n3.Kelvin to Fahrenheit & Celsius\n4.Exit')
n=int(input('Enter the choice:'))
if n==1:
Fah()
elif n==2:
Cel()
elif n==3:
Kel()
elif n==4:
exit()
else:
print('Invalid options')
F=int(input('Enter the temperature on Fahrenheit(F)'))
C=(F - 32) * 5/9
K=(F - 32) * 5/9 + 273.15
print("Fahrenheit Value :",F)
print("Celsius Value :",C)
print("Kelvin Value:",K)
def Cel():
C=int(input('Enter the temperature on Celsius(C)'))
F=(C * 9/5) + 32
K=C + 273.15
print("Fahrenheit Value :",F)
print("Celsius Value :",C)
print("Kelvin Value:",K)
def Kel():
K=int(input('Enter the temperature on Kelvin(K)'))
F=(K - 273.15) * 9/5 + 32
C=K - 273.15
print("Fahrenheit Value :",F)
print("Celsius Value :",C)
print("Kelvin Value:",K)
print("\n")
print('1.Fahrenheit to Celsius & Kelvin\n2.Celsius to Fahrenheit & Kelvin\n3.Kelvin to Fahrenheit & Celsius\n4.Exit')
n=int(input('Enter the choice:'))
if n==1:
Fah()
elif n==2:
Cel()
elif n==3:
Kel()
elif n==4:
exit()
else:
print('Invalid options')
Newton Raphson Method
# Newton Raphson Method
# The Newton-Raphson method (also known as Newton's method) is a way
# to quickly find a good approximation for the root of a real-valued function
xcube=int(input('Enter the values for Xcube: '))
xsquare=int(input('Enter the values for Xsquare: '))
x=int(input('Enter the values for X: '))
constant=int(input('Enter the values for Constant: '))
X0=int(input('Enter the values for inital vaule X0: '))
# It can be any value, but based on the incorrectness the root convergence
# will delay. Here we can use trail and error method for input value.
X1= X0-((((xcube*X0*X0*X0)+(xsquare*X0*X0)+(x*X0)+constant)/((xcube*3*X0*X0)+(xsquare*2*X0)+x)))
print ("Root at first approximations:",X1)
X2= X1-((((xcube*X1*X1*X1)+(xsquare*X1*X1)+(x*X1)+constant)/((xcube*3*X1*X1)+(xsquare*2*X1)+x)))
print ("Root at second approximations:",X2)
X3= X2-((((xcube*X2*X2*X2)+(xsquare*X2*X2)+(x*X2)+constant)/((xcube*3*X2*X2)+(xsquare*2*X2)+x)))
print ("Root at thrid approximations:",X3)
X4= X3-((((xcube*X3*X3*X3)+(xsquare*X3*X3)+(x*X3)+constant)/((xcube*3*X3*X3)+(xsquare*2*X3)+x)))
print ("Root at fourth approximations:",X4)
X5= X4-((((xcube*X4*X4*X4)+(xsquare*X4*X4)+(x*X4)+constant)/((xcube*3*X4*X4)+(xsquare*2*X4)+x)))
print ("Root at fifth approximations:",X5)
# The Newton-Raphson method (also known as Newton's method) is a way
# to quickly find a good approximation for the root of a real-valued function
xcube=int(input('Enter the values for Xcube: '))
xsquare=int(input('Enter the values for Xsquare: '))
x=int(input('Enter the values for X: '))
constant=int(input('Enter the values for Constant: '))
X0=int(input('Enter the values for inital vaule X0: '))
# It can be any value, but based on the incorrectness the root convergence
# will delay. Here we can use trail and error method for input value.
X1= X0-((((xcube*X0*X0*X0)+(xsquare*X0*X0)+(x*X0)+constant)/((xcube*3*X0*X0)+(xsquare*2*X0)+x)))
print ("Root at first approximations:",X1)
X2= X1-((((xcube*X1*X1*X1)+(xsquare*X1*X1)+(x*X1)+constant)/((xcube*3*X1*X1)+(xsquare*2*X1)+x)))
print ("Root at second approximations:",X2)
X3= X2-((((xcube*X2*X2*X2)+(xsquare*X2*X2)+(x*X2)+constant)/((xcube*3*X2*X2)+(xsquare*2*X2)+x)))
print ("Root at thrid approximations:",X3)
X4= X3-((((xcube*X3*X3*X3)+(xsquare*X3*X3)+(x*X3)+constant)/((xcube*3*X3*X3)+(xsquare*2*X3)+x)))
print ("Root at fourth approximations:",X4)
X5= X4-((((xcube*X4*X4*X4)+(xsquare*X4*X4)+(x*X4)+constant)/((xcube*3*X4*X4)+(xsquare*2*X4)+x)))
print ("Root at fifth approximations:",X5)
To read a coordinate point in a XY coordinate system and determine its Quadrant
x=int(input('Enter the values for X'))
y=int(input('Enter the values for Y'))
if x > 0 and y > 0:
print ('x, y point lies in the First quandrant')
elif x < 0 and y > 0:
print ('x, y point lies in the Second quandrant')
elif x < 0 and y < 0:
print ('x, y point lies in the Third quandrant')
elif x > 0 and y < 0:
print ('x, y point lies in the Fourth quandrant')
elif x == 0 and y == 0:
print ('x, y point lies at the origin')
y=int(input('Enter the values for Y'))
if x > 0 and y > 0:
print ('x, y point lies in the First quandrant')
elif x < 0 and y > 0:
print ('x, y point lies in the Second quandrant')
elif x < 0 and y < 0:
print ('x, y point lies in the Third quandrant')
elif x > 0 and y < 0:
print ('x, y point lies in the Fourth quandrant')
elif x == 0 and y == 0:
print ('x, y point lies at the origin')
Reading files into Python
f = open("1.txt")
#create a text file which consists of names of students in class
# Printing file all the names
print("File contnet as in text file:",f.read())
f = open("1.txt")
# Printing file one by one letters
print("\nFile contnet one by one word fromtext file:")
next = f.read(1)
while next != "":
print(next)
next = f.read(1)
#create a text file which consists of names of students in class
# Printing file all the names
print("File contnet as in text file:",f.read())
f = open("1.txt")
# Printing file one by one letters
print("\nFile contnet one by one word fromtext file:")
next = f.read(1)
while next != "":
print(next)
next = f.read(1)
Multiplication of two Matrices
X = [[4,1,7],[2,1,8],[3 ,7,1]];
Y = [[6,8,1],[9,7,5],[2,3,1]];
result = [[0,0,0],[0,0,0],[0,0,0]];
for i in range(len(X)):
for j in range(len(Y[0])):
for k in range(len(Y)):
result[i][j] += X[i][k] * Y[k][j]
for r in result:
print(r)
Y = [[6,8,1],[9,7,5],[2,3,1]];
result = [[0,0,0],[0,0,0],[0,0,0]];
for i in range(len(X)):
for j in range(len(Y[0])):
for k in range(len(Y)):
result[i][j] += X[i][k] * Y[k][j]
for r in result:
print(r)
Mathematical operators on Numpy Array and List
import numpy as np
a = np.array([1, 2, 3])
print(type(a))
print('Numpy Array:\n',a)
print('Addition of Numpy Arrays with constant:\n',a+13)
print('Addition of Numpy Arrays:\n',a+a)
print('Multiplication of Numpy Arrays with constant:\n',a*3)
print('Multiplication of Numpy Arrays with another:\n',a*a)
print('Divison of Numpy Arrays with constant:\n', a/3)
print('Divison of Numpy Arrays with another:\n', a/a)
print('Power of Numpy Arrays with constant:\n', a**4)
print('Power of Numpy Arrays with another:\n', a**a)
print('Remainder of Numpy Arrays with constant:\n',a%2)
print('Remainder of Numpy Arrays with another:\n',a%a)
print('Subtraction of Numpy Arrays with constant:\n', a-1)
print('Subtraction of Numpy Arrays with another:\n', a-a)
try:
a1=[1, 2, 3]
print('\n',type(a1))
print('Common List:\n', a1)
print('Addition of Lists:\n',a1+a1)
print('Multiplication of List with constant:\n',a1*3)
print(a1+13) #error
print(a1*a1) #error
print(a1/3) #error
print(a1/a1) #error
print(a1**4) #error
print(a1*a1) #error
print(a1%2) #error
print(a1%a1) #error
print(a1-1) #error
print(a1-a1) #error
except TypeError:
print('TypeError')
a = np.array([1, 2, 3])
print(type(a))
print('Numpy Array:\n',a)
print('Addition of Numpy Arrays with constant:\n',a+13)
print('Addition of Numpy Arrays:\n',a+a)
print('Multiplication of Numpy Arrays with constant:\n',a*3)
print('Multiplication of Numpy Arrays with another:\n',a*a)
print('Divison of Numpy Arrays with constant:\n', a/3)
print('Divison of Numpy Arrays with another:\n', a/a)
print('Power of Numpy Arrays with constant:\n', a**4)
print('Power of Numpy Arrays with another:\n', a**a)
print('Remainder of Numpy Arrays with constant:\n',a%2)
print('Remainder of Numpy Arrays with another:\n',a%a)
print('Subtraction of Numpy Arrays with constant:\n', a-1)
print('Subtraction of Numpy Arrays with another:\n', a-a)
try:
a1=[1, 2, 3]
print('\n',type(a1))
print('Common List:\n', a1)
print('Addition of Lists:\n',a1+a1)
print('Multiplication of List with constant:\n',a1*3)
print(a1+13) #error
print(a1*a1) #error
print(a1/3) #error
print(a1/a1) #error
print(a1**4) #error
print(a1*a1) #error
print(a1%2) #error
print(a1%a1) #error
print(a1-1) #error
print(a1-a1) #error
except TypeError:
print('TypeError')
To check the number is composite number or not
n=int(input('Enter the number '))
factor=0
for i in range(1,n):
if n%i==0:
factor=i
if factor>1:
print ('The number is a composite number!')
elif n==1:
print ('The number 1 is neither prime nor composite!')
else:
print ('This is not a composite number!')
factor=0
for i in range(1,n):
if n%i==0:
factor=i
if factor>1:
print ('The number is a composite number!')
elif n==1:
print ('The number 1 is neither prime nor composite!')
else:
print ('This is not a composite number!')
Statistical and Extrema operations on Numpy Array
import numpy as np
x = np.array([11, 13, 121, 181, 99, 100])
print('Numpy Array Elements',x)
print ('Minimum Value in array',x.min())
print ('Maximum Value in array',x.max())
print ('Index of Minimum Value',x.argmin())
print ('Index of Maximum Value',x.argmax())
print ('Mean of Array Values',x.mean())
print ('Median of Array Values',np.median(x))
print ('Standard deviation of Array Values',x.std())
x = np.array([11, 13, 121, 181, 99, 100])
print('Numpy Array Elements',x)
print ('Minimum Value in array',x.min())
print ('Maximum Value in array',x.max())
print ('Index of Minimum Value',x.argmin())
print ('Index of Maximum Value',x.argmax())
print ('Mean of Array Values',x.mean())
print ('Median of Array Values',np.median(x))
print ('Standard deviation of Array Values',x.std())
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