N lowest eigenvalues of the tridiagonal matrix in python
''' r = lamRange(d,c,N). Returns the sequence {r[0],r[1],...,r[N]} that separates the N lowest eigenvalues of the tridiagonal matrix [A] = [c\d\c]; that is, r[i] < lam[i] < r[i+1]. ''' from numpy import ones from sturmSeq import * from gerschgorin import * def lamRange(d,c,N): lamMin,lamMax = gerschgorin(d,c) r = ones(N+1) r[0] = lamMin # Search for eigenvalues in descending order for k in range(N,0,-1): # First bisection of interval(lamMin,lamMax) lam = (lamMax + lamMin)/2.0 h = (lamMax - lamMin)/2.0 for i in range(1000): # Find number of eigenvalues less than lam p = sturmSeq(d,c,lam) numLam = numLambdas(p) # Bisect again & find the half containing lam h = h/2.0 if numLam < k: lam = lam + h elif numLam > k: lam = lam - h else: break # If eigenvalue located, change the upper limit # of search and record it in [r] lamMax = lam r[k] = lam return r