【PLA】基于Python实现的线性代数算法库之斯密特正交化
算法包下载链接:https://download.csdn.net/download/qq_42629529/79481514
from PLA.Vector import Vector
from PLA.GramSchmidtProcess import gram_schmidt_process
from itertools import product
if __name__ == "__main__":
#1
basis1 = [Vector([2, 1]), Vector([1, 1])]
res1 = gram_schmidt_process(basis1)
for row in res1:
print(row)
res1 = [row / row.norm() for row in res1]
for row in res1:
print(row)
print(res1[0].dot(res1[1]))
print()
#2
basis2 = [Vector([2, 3]), Vector([4, 5])]
res2 = gram_schmidt_process(basis2)
res2 = [row / row.norm() for row in res2]
for row in res2:
print(row)
print(res2[0].dot(res2[1]))
print()
#3
basis3 = [Vector([1, 0, 1]), Vector([3, 1, 1]), Vector([-1, -1, -1])]
res3 = gram_schmidt_process(basis3)
res3 = [row / row.norm() for row in res3]
for row in res3:
print(row)
print(sum(res3[i].dot(res3[j]) for i, j in product(range(3), repeat=2) if i != j))
print()
#4
basis4 = [Vector([1, 1, 5, 2]), Vector([-3, 3, 4, -2]), Vector([-1, -2, 2, 5])]
res4 = gram_schmidt_process(basis4)
res4 = [row / row.norm() for row in res4]
for row in res4:
print(row)#标准正交基
print(sum(res4[i].dot(res4[j]) for i, j in product(range(3), repeat=2) if i != j))
print()
#5
basis5 = [Vector([1, 2, 3, 4]), Vector([2, 1, 1, 0]), Vector([3, 0, -1, 3])]
res5 = gram_schmidt_process(basis5)
res5 = [row / row.norm() for row in res5]
for row in res5:
print(row)
print(sum(res5[i].dot(res5[j]) for i, j in product(range(3), repeat=2) if i != j))
print()