def square_matrix():
    from numpy import zeros, linalg, linspace, sqrt, sin, pi, sum, sort
    A = zeros([5, 5])

    n = 0
    while n <= 4:
        A[n, n] = 2
        n = n + 1

    n = 0
    while n <= 3:
        A[n, n + 1] = 1
        A[n + 1, n] = 1
        n = n + 1

    H = (1/ (1/4)) * A
    return H


def lowest_eigenvectors(square_matrix, number_of_eigenvectors=3):
    from numpy import linalg, linspace, sqrt, sin, pi, sum, sort, argsort

    M_rows = len(square_matrix)
    count = 0
    while count < M_rows:
        M_columns = len(square_matrix[count])
        if not M_rows == M_columns:
            return print("Square matrix must have M rows and M columns, M >= 1.")

    (V, D) = linalg.eig(square_matrix)
    ordered_indices = argsort(V)
    eigenvalues = (V[ordered_indices[0:number_of_eigenvectors]])
    eigenvectors = (D[ordered_indices[0:number_of_eigenvectors]])
    return eigenvalues, eigenvectors

ce81168685d42b63355450913856950e68e85df0
<mask token>

def square_matrix():
    from numpy import zeros, linalg, linspace, sqrt, sin, pi, sum, sort
    A = zeros([5, 5])
    n = 0
    while n <= 4:
        A[n, n] = 2
        n = n + 1
    n = 0
    while n <= 3:
        A[n, n + 1] = 1
        A[n + 1, n] = 1
        n = n + 1
    H = 1 / (1 / 4) * A
    return H


<mask token>

def square_matrix():
    from numpy import zeros, linalg, linspace, sqrt, sin, pi, sum, sort
    A = zeros([5, 5])
    n = 0
    while n <= 4:
        A[n, n] = 2
        n = n + 1
    n = 0
    while n <= 3:
        A[n, n + 1] = 1
        A[n + 1, n] = 1
        n = n + 1
    H = 1 / (1 / 4) * A
    return H


def lowest_eigenvectors(square_matrix, number_of_eigenvectors=3):
    from numpy import linalg, linspace, sqrt, sin, pi, sum, sort, argsort
    M_rows = len(square_matrix)
    count = 0
    while count < M_rows:
        M_columns = len(square_matrix[count])
        if not M_rows == M_columns:
            return print(
                'Square matrix must have M rows and M columns, M >= 1.')
    V, D = linalg.eig(square_matrix)
    ordered_indices = argsort(V)
    eigenvalues = V[ordered_indices[0:number_of_eigenvectors]]
    eigenvectors = D[ordered_indices[0:number_of_eigenvectors]]
    return eigenvalues, eigenvectors

def square_matrix():
    from numpy import zeros, linalg, linspace, sqrt, sin, pi, sum, sort
    A = zeros([5, 5])

    n = 0
    while n <= 4:
        A[n, n] = 2
        n = n + 1

    n = 0
    while n <= 3:
        A[n, n + 1] = 1
        A[n + 1, n] = 1
        n = n + 1

    H = (1/ (1/4)) * A
    return H


def lowest_eigenvectors(square_matrix, number_of_eigenvectors=3):
    from numpy import linalg, linspace, sqrt, sin, pi, sum, sort, argsort

    M_rows = len(square_matrix)
    count = 0
    while count < M_rows:
        M_columns = len(square_matrix[count])
        if not M_rows == M_columns:
            return print("Square matrix must have M rows and M columns, M >= 1.")

    (V, D) = linalg.eig(square_matrix)
    ordered_indices = argsort(V)
    eigenvalues = (V[ordered_indices[0:number_of_eigenvectors]])
    eigenvectors = (D[ordered_indices[0:number_of_eigenvectors]])
    return eigenvalues, eigenvectors
