Find the global bounds on the eigenvalues of a tridiagomal matrix in Python
''' lamMin,lamMax = gerschgorin(d,c).
Applies Gerschgorin's theorem to find the global bounds on
the eigenvalues of a tridiagomal matrix [A] = [c\d\c].
'''
def gerschgorin(d,c):
n = len(d)
lamMin = d[0] - abs(c[0])
lamMax = d[0] + abs(c[0])
for i in range(1,n-1):
lam = d[i] - abs(c[i]) - abs(c[i-1])
if lam < lamMin: lamMin = lam
lam = d[i] + abs(c[i]) + abs(c[i-1])
if lam > lamMax: lamMax = lam
lam = d[n-1] - abs(c[n-2])
if lam < lamMin: lamMin = lam
lam = d[n-1] + abs(c[n-2])
if lam > lamMax: lamMax = lam
return lamMin,lamMax
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