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from scipy.linalg import *
import numpy as np
#print("Inverse Hilbert Matrix n = 3: ")
#print(invhilbert(3))
#print("Matrix Multiplication H(3) * H^-1(3)")
#print(hilbert(3).dot(invhilbert(3)))
#print("Inverse Hilbert Matrix n = 4: ")
#print(invhilbert(4,True))
#print("Matrix Multiplication H(4) * H^-1(4)")
#print(hilbert(4).dot(invhilbert(4)))
#print("Inverse Hilbert Matrix n = 5: ")
#print(invhilbert(5,True))
#print("Matrix Multiplication H(5) * H^-1(5)")
#print(hilbert(5).dot(invhilbert(5)))
def HilbertApprox(n,m):
h = hilbert(n)
h = h.round(m)
# for i in h:
# for j in i:
# j = round(j,m)
# j = round(j,m)
# [round(i,m) for i in h[0]]
print("For H(", n, ") rounded to ", m, "decimal places:")
print(inv(h).round(m))
print("Matrix Multiplication H(",n,") * H^-1(",n,") for rounded matrix")
print(h.dot(inv(h).round(m)))
#p2 = invhilbert(n)
#print("Percentage-Error For n = ",n," m = ",m)
#print(np.divide(p2,p1)*100)
HilbertApprox(3,2)
HilbertApprox(4,2)
HilbertApprox(5,2)
#HilbertApprox(3,4)
#HilbertApprox(4,4)
#HilbertApprox(5,4)
#HilbertApprox(3,5)
#HilbertApprox(4,5)
#HilbertApprox(5,5)
#HilbertApprox(3,6)
#HilbertApprox(4,6)
#HilbertApprox(5,6)
#HilbertApprox(3,7)
#HilbertApprox(4,7)
#HilbertApprox(5,7)
#HilbertApprox(3,8)
#HilbertApprox(4,8)
#HilbertApprox(5,8)
#HilbertApprox(3,9)
#HilbertApprox(4,9)
#HilbertApprox(5,9)
#HilbertApprox(3,10)
#HilbertApprox(4,10)
#HilbertApprox(5,10)
#print(type(hilbert(2)))
#a = [1,3.004,5.2222]
#[round(i,2) for i in a]
#print(a)
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