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linalg.py
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linalg.py
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from fractions import Fraction
import os
#elementary reduction matrices
erm = []
def display(matrix):
for row in matrix:
for column,entry in enumerate(row):
#add bar for augmented matrix
# if column == len(row)-1:
# print(' |',end='')
#add space to positive numbers to balance '-'
if entry >= 0:
print(' ',end='')
#display entry according to its format
if isinstance(entry,int):
print(' ' + str(entry),end=' ')
elif entry.denominator == 1:
print(' ' + str(entry.numerator),end=' ')
else:
print(str(entry.numerator) + '/' + str(entry.denominator),end=' ')
print()
def swap(matrix):
display(matrix)
#read input
print('first row:',end='')
x = int(input()) - 1
print('second row:',end='')
y = int(input()) - 1
#swap rows
aux = matrix[x]
matrix[x] = matrix[y]
matrix[y] = aux
#create permutaion matrix
i = idMatrix(len(matrix))
aux = i[x]
i[x] = i[y]
i[y] = aux
erm.append(i)
def scale(matrix):
display(matrix)
#read input
print('scalar:',end='')
m = input()
print('row to scale:',end='')
rowX = int(input()) - 1
#scale rowX
for i in range(0,len(matrix[rowX])):
matrix[rowX][i] *= Fraction(m)
#create permutaion matrix
id = idMatrix(len(matrix))
for i in (range(0,len(id[rowX]))):
id[rowX][i] *= Fraction(m)
erm.append(id)
def combination(matrix):
display(matrix)
#read input
print('scalar:',end='')
m = input()
print('row to add:',end='')
rowX = int(input()) - 1
print('row to be modified:',end='')
rowY = int(input()) - 1
#add scaled rowX to rowY
for i in range(0,len(matrix[rowX])):
matrix[rowY][i] += matrix[rowX][i] * Fraction(m)
#create permutation matrix
id = idMatrix(len(matrix))
for i in range(0,len(id[rowX])):
id[rowY][i] += id[rowX][i] * Fraction(m)
erm.append(id)
def write(matrix):
#read dimensions
rows = int(input('number of rows: '))
cols = int(input('number of columns: '))
#read the entries
for row in range(0,rows):
matrix.append([])
for col in range(0,cols):
x = input('matrix['+str(row+1)+']['+str(col+1)+']')
matrix[row].append(Fraction(x))
def idMatrix(rows):
i = [[]]
rows -= 1
for row in range(0,rows):
i.append([])
for col in range(0,rows):
x = 0
if row == col:
x = 1
i[row].append(Fraction(x))
return i
def displayERM():
for i in range(len(erm)-1,-1,-1):
display(erm[i])
def matrixProduct(m1,m2):
result = [[]]
for i in range(0,len(m1)-1):
result.append([])
for j in range(0,len(m1)-1):
s = 0
for k in range (0,len(m1)-1):
s += m1[i][k] * m2[k][j]
result[i].append(s)
return result
def inverse():
m = [[1,0,0],[0,1,0],[0,0,1]]
for i in erm:
m = matrixProduct(i,m)
print("Inverse")
display(m)
def main():
os.system('clear')
#matrix to be used
a = [[]]
write(a)
os.system('clear')
while True:
display(a)
#read input
print('1.swap')
print('2.scale')
print('3.combination')
print('0.exit')
operation = input()
#choose operation
if operation == '1':
swap(a)
if operation == '2':
scale(a)
if operation == '3':
combination(a)
if operation == '0':
displayERM()
display(a)
inverse()
break
if __name__ == '__main__':
main()