N lowest eigenvalues of the tridiagonal matrix in python的代码

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''' 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] = [cdc]; that is, r[i] < lam[i] < r[i+1].

'''

from numpy import ones

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