N lowest eigenvalues of the tridiagonal matrix in python，,''' r = lamR

N lowest eigenvalues of the tridiagonal matrix in python，,''' r = lamR

''' 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 onesfrom 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