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lalg.py
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lalg.py
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### lalg.py
###
### Author: Job Hernandez
from math import sqrt
from operator import (
add,
sub,
mul,
)
class Number:
def __add__(self, other):
return self.add(other)
def __sub__(self, other):
return self.sub(other)
def __mul__(self, other):
return self.mul(other)
class Vector(Number):
def add(self, other):
"""
Vector Vector -> Vector
given two Vectors 'add' adds them together.
given: Vector([2,3,5]) + Vector([4,5,6])
expect: Vector([6,8,11])
"""
if isinstance(other, Vector):
return [s + t for s, t in zip(self.contents, other.contents)]
else:
raise ValueError("{} is not type Vector.".format(other))
def sub(self, other):
"""
Vector Vector -> Vector
given two Vectors 'sub' substracts them.
given: Vector([2,3,5]) Vector([4,6,7])
expect: Vector([-2,-3,-2])
"""
if isinstance(other, Vector):
return [s - t for s, t in zip(self.contents, other.contents)]
else:
raise ValueError("{} is not type Vector.".format(other))
def mul(self, other):
"""
Vector Vector -> Scalar or Vector Scalar -> Vector
computes the DOT-PRODUCT of the two given Vectors if other is of type VECTOR;
otherwise, if other is of type INT, it multiplies Vector by a scalar.
given: Vector([-6, 8]) * Vector([5, 12])
expect: 66
given: Vector([2,3,4,5]) * 3
expect: [6,9,12,15]
"""
if isinstance(other, Vector):
return sum([t * u for t, u in zip(self.contents, other.contents)])
elif isinstance(other, int):
return [other * t for t in self.contents]
else:
raise ValueError("{} is not of type VECTOR or INT.".format(other))
class M(Number):
def add(self, other):
"""
M M -> M
returns the SUM of the two given matrices.
given: M([[2,3,5], [5,6,7]]) + M([[3,4,5], [5,6,7]])
expect: [[5,7,10], [10,12,14]]
"""
if isinstance(other, M):
return [list(map(add,t,u)) for t, u in zip(self.contents, other.contents)]
else:
raise ValueError("{} is not of type M.".format(other))
def sub(self, other):
"""
M M -> M
returns the DIFFERENCE of the given two matrices.
given: M([[4,5,6], [5,6,7]]) - M([[2,3,4], [2,3,4]])
expect: [[2,2,2], [3,3,3]]
"""
if isinstance(other, M):
return [list(map(sub, t, u)) for t, u in zip(self.contents, other.contents)]
else:
raise ValueError("{} is not of type M.".format(other))
def mul(self, other):
"""
M M -> M or M Scalar -> M
returns the product of two matrices if the type of other is M; otherwise
if the type of other is INT then it returns the matrix multplied by a scalar.
given: M([[1,2,3], [4,5,6]]) * M([[7,8], [9,10], [11,12]])
expect: [[58,64], [139, 154]]
given: M([[2,3,4], [3,4,5]) * 4
expect: [[8,12,16], [12,16,20]]
"""
if isinstance(other, M):
return [compute_ith_vector(self.contents, other.contents, i) for i in range(len(self.contents))]
elif isinstance(other, int):
return [[other * i for i in x] for x in self.contents]
else:
raise ValueError("{} is not of type M.".format(other))
class Vec(Vector):
def __init__(self, contents):
self.contents = contents
def magnitude(self):
"""
Vec -> Scalar
given a Vec 'magnitude' returns the magnitude.
given: Vec([6,8])
expect: 10
"""
return sqrt(sum([x * x for x in self.contents]))
def is_unit_vector(self):
"""
Vector -> Bool
check if the Vector is a UNIT-VECTOR.
given: Vec([6,8])
expect: False
given: Vec([1,0,0])
expect: True
"""
return self.magnitude() == 1
class Matrix(M):
def __init__(self, contents):
self.contents = contents
def transpose(self):
return [get_first(self.contents, i) for i in range(len(self.contents[0]))]
def compute_ith_vector(m, m2, i):
return [sum([a * b for a, b in zip(m[i], get_column(m2, j))])
for j in range(len(m2[0]))]
def get_column(m, index):
c = []
for k in range(len(m)):
c.append(m[k][index])
return c
def get_first(m, index):
firsts = []
for i in range(len(m)):
firsts.append(m[i][index])
return firsts