102 lines
3.6 KiB
Python
102 lines
3.6 KiB
Python
import sympy as sp
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import time
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import random
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# in function to take arbitrary matrix input from user
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def inmat(rowcol) :
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# initialise list of lists
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mat=[[]]*rowcol
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# take input from user into list
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print("Enter line by line with entries separated by space:")
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for i in range(rowcol):
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mat[i]=input().split(" ")
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for j in range(len(mat[i])) :
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# convert list using nsimplify in order to take rational number symbolically
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mat[i][j] = sp.nsimplify(mat[i][j])
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return mat
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# multcheck function to check if two matrices are multiplied together
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def multcheck(a, b, rowcol, intmax) :
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sp.pprint(b)
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print("Multiply these two matrices together")
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# return bool based on if input equals the two matrices multiplied together
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return (sp.Matrix(inmat(rowcol)) == a*b)
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# detcheck function to check if the determinant of the matrix is correct
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def detcheck(a, b, rowcol, intmax):
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det = sp.det(a)
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# return bool based on if input equals determinant
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return (det == sp.nsimplify(input("What is the determinant of this matrix?: ")))
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# invcheck function to check if the inverse of the matrix is correct
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def invcheck(a, b, rowcol, intmax):
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det = a.det()
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if det != 0 :
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# return bool based on if input equals inverse of matrix
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print("What is the inverse of this matrix?")
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return (sp.Matrix(inmat(rowcol)) == a.inv())
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# eigcheck function to check if the eigenvalues are correct
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def eigcheck(a, b, rowcol, intmax):
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eigs = a.eigenvals()
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for i in range(len(eigs)) :
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val = sp.nsimplify(input("Input eigenvalue: "))
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if not (val in eigs and eigs[val] == sp.nsimplify(input("Input its algebraic multiplicity: "))) :
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# return false if the eigenvalue not in dictionary and wrong alg multiplicity
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return False
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return True
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# practice function
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def practice(t) :
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count = 0
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rowcol = int(input("What size of matrix do you want to practice with? "))
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intmax = int(input("What maximum size of integer do you want the matrix to be made out of? "))
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dif = float(input("What difficulty (probability for a matrix of rational values between 0, 1) do you want? "))
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# choose the function of the program that you want
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if t == "mult" :
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f = multcheck
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elif t == "det" :
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f = detcheck
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elif t == "inv" :
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f = invcheck
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elif t == "eig" :
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f = eigcheck
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else :
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exit()
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# initialise time measurement
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tic = time.perf_counter()
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# infinite loop of practice
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while True :
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# generate a random matrices
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a = sp.randMatrix(rowcol, rowcol, 0, intmax)
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b = sp.randMatrix(rowcol, rowcol, 0, intmax)
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# if determinant non-zero, radnom value less than difficulty, set a to its inverse
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if a.det() != 0 and random.random() <= dif :
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a = a.inv()
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# infinite loop until user succeeds
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while True :
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sp.pprint(a)
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# if return of function is True
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if f(a, b, rowcol, intmax) :
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# take time interval
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toc = time.perf_counter()
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tictoc=toc-tic
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# increment count
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count += 1
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# print success message
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print("Correct! You have solved", count, "problems in %.2f seconds" %tictoc)
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break
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else :
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# print failure message
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print("Try again")
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continue
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# take input from user on the type of practice they want to do
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t = input("What do you want to practice? (mult, det, inv, eig) ")
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practice(t)
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