import numpy as np
def qrdec(A):
n = A.shape[0]
Ap = np.copy(A)
Q = np.zeros((n, n))
R = np.zeros((n, n))
for j in range(n):
for i in range(j):
R[i, j] = Q[:, i] @ A[:, j]
Ap[:, j] -= R[i, j] * Q[:, i]
R[j, j] = mag(Ap[:, j])
Q[:, j] = Ap[:, j] / R[j, j]
return Q, R
def testqrdec(A):
n = A.shape[0]
Q, R = qrdec(A)
diffa = A - Q @ R
diffq = np.transpose(Q) @ Q - np.identity(n)
print(n, mag(diffa), mag(diffq))
if __name__ == '__main__':
for n in range(4, 10, 2):
A, bs = testcreate(n, 21)
testqrdec(A)
# Author: Alex Gezerlis
# Numerical Methods in Physics with Python (CUP, 2020)
from triang import testcreate
from invpowershift import invpowershift
from qrmet import qrmet
import numpy as np
def eig(A,eps=1.e-12):
n = A.shape[0]
eigvals = np.zeros(n)
eigvecs = np.zeros((n,n))
qreigvals = qrmet(A)
for i, qre in enumerate(qreigvals):
eigvals[i], eigvecs[:,i] = invpowershift(A,qre+eps)
return eigvals, eigvecs
def testeigall(f,A):
eigvals, eigvecs = f(A)
npeigvals, npeigvecs = np.linalg.eig(A)
print(eigvals); print(npeigvals)
print(" ")
for eigvec, npeigvec in zip(eigvecs.T,npeigvecs.T):
print(eigvec); print(npeigvec)
print(" ")
if __name__ == '__main__':
A, bs = testcreate(4,21)
testeigall(eig,A)
def jacobi(A, bs, kmax=50, tol=1.e-6):
n = bs.size
xnews = np.zeros(n)
for k in range(1, kmax):
xs = np.copy(xnews)
for i in range(n):
slt = A[i, :i] @ xs[:i]
sgt = A[i, i + 1:] @ xs[i + 1:]
xnews[i] = (bs[i] - slt - sgt) / A[i, i]
err = termcrit(xs, xnews)
print(k, xnews, err)
if err < tol:
break
else:
xnews = None
return xnews
if __name__ == '__main__':
n = 4
val = 21
A, bs = testcreate(n, val)
A += val * np.identity(n)
testsolve(jacobi, A, bs)