API 参考

def test():
    import guan
    current_version = guan.get_current_version('guan')
    print(f'Congratulations on successfully installing Guan package! The installed version is guan-{current_version}.')

def fundamental_constants():
    constants = {}
    constants['c'] = 2.99792458e8             # 真空光速，单位：m/s（米每秒）
    constants['h'] = 6.62607015e-34           # 普朗克常数，单位：J·s（焦耳·秒）
    constants['hbar'] = 1.054571817e-34       # 约化普朗克常数 ħ = h / (2π)，单位：J·s（焦耳·秒）
    constants['q'] = 1.602176634e-19          # 基本电荷（元电荷），单位：C（库仑）
    constants['eV'] = 1.602176634e-19         # 1 电子伏特（eV）对应的焦耳值，即 1 eV = q J
    constants['k'] = 1.380649e-23             # 玻尔兹曼常数，单位：J/K（焦耳每开尔文）
    constants['NA'] = 6.02214076e23           # 阿伏伽德罗常数，单位：mol⁻¹（每摩尔的粒子数）
    constants['G'] = 6.67430e-11              # 万有引力常数，单位：m³/(kg·s²)
    constants['mu0'] = 1.25663706212e-6       # 真空磁导率 μ₀ ≈ 4π × 10⁻⁷，单位：H/m（亨利每米）
    constants['eps0'] = 8.8541878128e-12      # 真空介电常数 ε₀ = 1 / (μ₀ c²)，单位：F/m（法拉每米）
    constants['me'] = 9.1093837015e-31        # 电子静止质量，单位：kg（千克）
    constants['mp'] = 1.67262192595e-27       # 质子静止质量，单位：kg（千克）
    constants['mn'] = 1.67492749804e-27       # 中子静止质量，单位：kg（千克）
    constants['alpha'] = 7.2973525693e-3      # 精细结构常数 α = e² / (4π ε₀ ħ c) ≈ 1/137，无量纲
    constants['a0'] = 5.29177210903e-11       # 玻尔半径，单位：m
    constants['T0'] = 273.15                  # 标准温度参考点（0°C 对应的开尔文温度偏移），单位：K（开尔文）
    return constants

def sigma_0():
    import numpy as np
    return np.eye(2)

def sigma_x():
    import numpy as np
    return np.array([[0, 1],[1, 0]])

def sigma_y():
    import numpy as np
    return np.array([[0, -1j],[1j, 0]])

def sigma_z():
    import numpy as np
    return np.array([[1, 0],[0, -1]])

def sigma_00():
    import numpy as np
    import guan
    return np.kron(guan.sigma_0(), guan.sigma_0())

def sigma_0x():
    import numpy as np
    import guan
    return np.kron(guan.sigma_0(), guan.sigma_x())

def sigma_0y():
    import numpy as np
    import guan
    return np.kron(guan.sigma_0(), guan.sigma_y())

def sigma_0z():
    import numpy as np
    import guan
    return np.kron(guan.sigma_0(), guan.sigma_z())

def sigma_x0():
    import numpy as np
    import guan
    return np.kron(guan.sigma_x(), guan.sigma_0())

def sigma_xx():
    import numpy as np
    import guan
    return np.kron(guan.sigma_x(), guan.sigma_x())

def sigma_xy():
    import numpy as np
    import guan
    return np.kron(guan.sigma_x(), guan.sigma_y())

def sigma_xz():
    import numpy as np
    import guan
    return np.kron(guan.sigma_x(), guan.sigma_z())

def sigma_y0():
    import numpy as np
    import guan
    return np.kron(guan.sigma_y(), guan.sigma_0())

def sigma_yx():
    import numpy as np
    import guan
    return np.kron(guan.sigma_y(), guan.sigma_x())

def sigma_yy():
    import numpy as np
    import guan
    return np.kron(guan.sigma_y(), guan.sigma_y())

def sigma_yz():
    import numpy as np
    import guan
    return np.kron(guan.sigma_y(), guan.sigma_z())

def sigma_z0():
    import numpy as np
    import guan
    return np.kron(guan.sigma_z(), guan.sigma_0())

def sigma_zx():
    import numpy as np
    import guan
    return np.kron(guan.sigma_z(), guan.sigma_x())

def sigma_zy():
    import numpy as np
    import guan
    return np.kron(guan.sigma_z(), guan.sigma_y())

def sigma_zz():
    import numpy as np
    import guan
    return np.kron(guan.sigma_z(), guan.sigma_z())

def one_dimensional_fourier_transform(k, unit_cell, hopping):
    import numpy as np
    import cmath
    unit_cell = np.array(unit_cell)
    hopping = np.array(hopping)
    hamiltonian = unit_cell+hopping*cmath.exp(1j*k)+hopping.transpose().conj()*cmath.exp(-1j*k)
    return hamiltonian

def two_dimensional_fourier_transform_for_square_lattice(k1, k2, unit_cell, hopping_1, hopping_2):
    import numpy as np
    import cmath
    unit_cell = np.array(unit_cell)
    hopping_1 = np.array(hopping_1)
    hopping_2 = np.array(hopping_2)
    hamiltonian = unit_cell+hopping_1*cmath.exp(1j*k1)+hopping_1.transpose().conj()*cmath.exp(-1j*k1)+hopping_2*cmath.exp(1j*k2)+hopping_2.transpose().conj()*cmath.exp(-1j*k2)
    return hamiltonian

def three_dimensional_fourier_transform_for_cubic_lattice(k1, k2, k3, unit_cell, hopping_1, hopping_2, hopping_3):
    import numpy as np
    import cmath
    unit_cell = np.array(unit_cell)
    hopping_1 = np.array(hopping_1)
    hopping_2 = np.array(hopping_2)
    hopping_3 = np.array(hopping_3)
    hamiltonian = unit_cell+hopping_1*cmath.exp(1j*k1)+hopping_1.transpose().conj()*cmath.exp(-1j*k1)+hopping_2*cmath.exp(1j*k2)+hopping_2.transpose().conj()*cmath.exp(-1j*k2)+hopping_3*cmath.exp(1j*k3)+hopping_3.transpose().conj()*cmath.exp(-1j*k3)
    return hamiltonian

def one_dimensional_fourier_transform_with_k(unit_cell, hopping):
    import functools
    import guan
    hamiltonian_function = functools.partial(guan.one_dimensional_fourier_transform, unit_cell=unit_cell, hopping=hopping)
    return hamiltonian_function

def two_dimensional_fourier_transform_for_square_lattice_with_k1_k2(unit_cell, hopping_1, hopping_2):
    import functools
    import guan
    hamiltonian_function = functools.partial(guan.two_dimensional_fourier_transform_for_square_lattice, unit_cell=unit_cell, hopping_1=hopping_1, hopping_2=hopping_2)
    return hamiltonian_function

def three_dimensional_fourier_transform_for_cubic_lattice_with_k1_k2_k3(unit_cell, hopping_1, hopping_2, hopping_3):
    import functools
    import guan
    hamiltonian_function = functools.partial(guan.three_dimensional_fourier_transform_for_cubic_lattice, unit_cell=unit_cell, hopping_1=hopping_1, hopping_2=hopping_2, hopping_3=hopping_3)
    return hamiltonian_function

def calculate_one_dimensional_reciprocal_lattice_vector(a1):
    import numpy as np
    b1 = 2*np.pi/a1
    return b1

def calculate_two_dimensional_reciprocal_lattice_vectors(a1, a2):
    import numpy as np
    a1 = np.array(a1)
    a2 = np.array(a2)
    a1 = np.append(a1, 0)
    a2 = np.append(a2, 0)
    a3 = np.array([0, 0, 1])
    b1 = 2*np.pi*np.cross(a2, a3)/np.dot(a1, np.cross(a2, a3))
    b2 = 2*np.pi*np.cross(a3, a1)/np.dot(a1, np.cross(a2, a3))
    b1 = np.delete(b1, 2)
    b2 = np.delete(b2, 2)
    return b1, b2

def calculate_three_dimensional_reciprocal_lattice_vectors(a1, a2, a3):
    import numpy as np
    a1 = np.array(a1)
    a2 = np.array(a2)
    a3 = np.array(a3)
    b1 = 2*np.pi*np.cross(a2, a3)/np.dot(a1, np.cross(a2, a3))
    b2 = 2*np.pi*np.cross(a3, a1)/np.dot(a1, np.cross(a2, a3))
    b3 = 2*np.pi*np.cross(a1, a2)/np.dot(a1, np.cross(a2, a3))
    return b1, b2, b3

def calculate_one_dimensional_reciprocal_lattice_vector_with_sympy(a1):
    import sympy
    b1 = 2*sympy.pi/a1
    return b1

def calculate_two_dimensional_reciprocal_lattice_vectors_with_sympy(a1, a2):
    import sympy
    a1 = sympy.Matrix(1, 3, [a1[0], a1[1], 0])
    a2 = sympy.Matrix(1, 3, [a2[0], a2[1], 0])
    a3 = sympy.Matrix(1, 3, [0, 0, 1])
    cross_a2_a3 = a2.cross(a3)
    cross_a3_a1 = a3.cross(a1)
    b1 = 2*sympy.pi*cross_a2_a3/a1.dot(cross_a2_a3)
    b2 = 2*sympy.pi*cross_a3_a1/a1.dot(cross_a2_a3)
    b1 = sympy.Matrix(1, 2, [b1[0], b1[1]])
    b2 = sympy.Matrix(1, 2, [b2[0], b2[1]])
    return b1, b2

def calculate_three_dimensional_reciprocal_lattice_vectors_with_sympy(a1, a2, a3):
    import sympy
    cross_a2_a3 = a2.cross(a3)
    cross_a3_a1 = a3.cross(a1)
    cross_a1_a2 = a1.cross(a2)
    b1 = 2*sympy.pi*cross_a2_a3/a1.dot(cross_a2_a3)
    b2 = 2*sympy.pi*cross_a3_a1/a1.dot(cross_a2_a3)
    b3 = 2*sympy.pi*cross_a1_a2/a1.dot(cross_a2_a3)
    return b1, b2, b3

def hamiltonian_of_finite_size_system_along_one_direction(N, on_site=0, hopping=1, period=0):
    import numpy as np
    on_site = np.array(on_site)
    hopping = np.array(hopping)
    if on_site.shape==():
        dim = 1
    else:
        dim = on_site.shape[0]
    hamiltonian = np.zeros((N*dim, N*dim), dtype=complex)
    for i0 in range(N):
        hamiltonian[i0*dim+0:i0*dim+dim, i0*dim+0:i0*dim+dim] = on_site
    for i0 in range(N-1):
        hamiltonian[i0*dim+0:i0*dim+dim, (i0+1)*dim+0:(i0+1)*dim+dim] = hopping
        hamiltonian[(i0+1)*dim+0:(i0+1)*dim+dim, i0*dim+0:i0*dim+dim] = hopping.transpose().conj()
    if period == 1:
        hamiltonian[(N-1)*dim+0:(N-1)*dim+dim, 0:dim] = hopping
        hamiltonian[0:dim, (N-1)*dim+0:(N-1)*dim+dim] = hopping.transpose().conj()
    return hamiltonian

def hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N1, N2, on_site=0, hopping_1=1, hopping_2=1, period_1=0, period_2=0):
    import numpy as np
    on_site = np.array(on_site)
    hopping_1 = np.array(hopping_1)
    hopping_2 = np.array(hopping_2)
    if on_site.shape==():
        dim = 1
    else:
        dim = on_site.shape[0]
    hamiltonian = np.zeros((N1*N2*dim, N1*N2*dim), dtype=complex)    
    for i1 in range(N1):
        for i2 in range(N2):
            hamiltonian[i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim, i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim] = on_site
    for i1 in range(N1-1):
        for i2 in range(N2):
            hamiltonian[i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim, (i1+1)*N2*dim+i2*dim+0:(i1+1)*N2*dim+i2*dim+dim] = hopping_1
            hamiltonian[(i1+1)*N2*dim+i2*dim+0:(i1+1)*N2*dim+i2*dim+dim, i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim] = hopping_1.transpose().conj()
    for i1 in range(N1):
        for i2 in range(N2-1):
            hamiltonian[i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim, i1*N2*dim+(i2+1)*dim+0:i1*N2*dim+(i2+1)*dim+dim] = hopping_2
            hamiltonian[i1*N2*dim+(i2+1)*dim+0:i1*N2*dim+(i2+1)*dim+dim, i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim] = hopping_2.transpose().conj()
    if period_1 == 1:
        for i2 in range(N2):
            hamiltonian[(N1-1)*N2*dim+i2*dim+0:(N1-1)*N2*dim+i2*dim+dim, i2*dim+0:i2*dim+dim] = hopping_1
            hamiltonian[i2*dim+0:i2*dim+dim, (N1-1)*N2*dim+i2*dim+0:(N1-1)*N2*dim+i2*dim+dim] = hopping_1.transpose().conj()
    if period_2 == 1:
        for i1 in range(N1):
            hamiltonian[i1*N2*dim+(N2-1)*dim+0:i1*N2*dim+(N2-1)*dim+dim, i1*N2*dim+0:i1*N2*dim+dim] = hopping_2
            hamiltonian[i1*N2*dim+0:i1*N2*dim+dim, i1*N2*dim+(N2-1)*dim+0:i1*N2*dim+(N2-1)*dim+dim] = hopping_2.transpose().conj()
    return hamiltonian

def hamiltonian_of_finite_size_system_along_three_directions_for_cubic_lattice(N1, N2, N3, on_site=0, hopping_1=1, hopping_2=1, hopping_3=1, period_1=0, period_2=0, period_3=0):
    import numpy as np
    on_site = np.array(on_site)
    hopping_1 = np.array(hopping_1)
    hopping_2 = np.array(hopping_2)
    hopping_3 = np.array(hopping_3)
    if on_site.shape==():
        dim = 1
    else:
        dim = on_site.shape[0]
    hamiltonian = np.zeros((N1*N2*N3*dim, N1*N2*N3*dim), dtype=complex) 
    for i1 in range(N1):
        for i2 in range(N2):
            for i3 in range(N3):
                hamiltonian[i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim, i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim] = on_site
    for i1 in range(N1-1):
        for i2 in range(N2):
            for i3 in range(N3):
                hamiltonian[i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim, (i1+1)*N2*N3*dim+i2*N3*dim+i3*dim+0:(i1+1)*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_1
                hamiltonian[(i1+1)*N2*N3*dim+i2*N3*dim+i3*dim+0:(i1+1)*N2*N3*dim+i2*N3*dim+i3*dim+dim, i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_1.transpose().conj()
    for i1 in range(N1):
        for i2 in range(N2-1):
            for i3 in range(N3):
                hamiltonian[i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim, i1*N2*N3*dim+(i2+1)*N3*dim+i3*dim+0:i1*N2*N3*dim+(i2+1)*N3*dim+i3*dim+dim] = hopping_2
                hamiltonian[i1*N2*N3*dim+(i2+1)*N3*dim+i3*dim+0:i1*N2*N3*dim+(i2+1)*N3*dim+i3*dim+dim, i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_2.transpose().conj()
    for i1 in range(N1):
        for i2 in range(N2):
            for i3 in range(N3-1):
                hamiltonian[i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim, i1*N2*N3*dim+i2*N3*dim+(i3+1)*dim+0:i1*N2*N3*dim+i2*N3*dim+(i3+1)*dim+dim] = hopping_3
                hamiltonian[i1*N2*N3*dim+i2*N3*dim+(i3+1)*dim+0:i1*N2*N3*dim+i2*N3*dim+(i3+1)*dim+dim, i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_3.transpose().conj()
    if period_1 == 1:
        for i2 in range(N2):
            for i3 in range(N3):
                hamiltonian[(N1-1)*N2*N3*dim+i2*N3*dim+i3*dim+0:(N1-1)*N2*N3*dim+i2*N3*dim+i3*dim+dim, i2*N3*dim+i3*dim+0:i2*N3*dim+i3*dim+dim] = hopping_1
                hamiltonian[i2*N3*dim+i3*dim+0:i2*N3*dim+i3*dim+dim, (N1-1)*N2*N3*dim+i2*N3*dim+i3*dim+0:(N1-1)*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_1.transpose().conj()
    if period_2 == 1:
        for i1 in range(N1):
            for i3 in range(N3):
                hamiltonian[i1*N2*N3*dim+(N2-1)*N3*dim+i3*dim+0:i1*N2*N3*dim+(N2-1)*N3*dim+i3*dim+dim, i1*N2*N3*dim+i3*dim+0:i1*N2*N3*dim+i3*dim+dim] = hopping_2
                hamiltonian[i1*N2*N3*dim+i3*dim+0:i1*N2*N3*dim+i3*dim+dim, i1*N2*N3*dim+(N2-1)*N3*dim+i3*dim+0:i1*N2*N3*dim+(N2-1)*N3*dim+i3*dim+dim] = hopping_2.transpose().conj()
    if period_3 == 1:
        for i1 in range(N1):
            for i2 in range(N2):
                hamiltonian[i1*N2*N3*dim+i2*N3*dim+(N3-1)*dim+0:i1*N2*N3*dim+i2*N3*dim+(N3-1)*dim+dim, i1*N2*N3*dim+i2*N3*dim+0:i1*N2*N3*dim+i2*N3*dim+dim] = hopping_3
                hamiltonian[i1*N2*N3*dim+i2*N3*dim+0:i1*N2*N3*dim+i2*N3*dim+dim, i1*N2*N3*dim+i2*N3*dim+(N3-1)*dim+0:i1*N2*N3*dim+i2*N3*dim+(N3-1)*dim+dim] = hopping_3.transpose().conj()
    return hamiltonian

def hamiltonian_of_finite_size_ssh_model(N, v=0.6, w=1, onsite_1=0, onsite_2=0, period=1):
    import numpy as np
    hamiltonian = np.zeros((2*N, 2*N))
    for i in range(N):
        hamiltonian[i*2+0, i*2+0] = onsite_1
        hamiltonian[i*2+1, i*2+1] = onsite_2
        hamiltonian[i*2+0, i*2+1] = v
        hamiltonian[i*2+1, i*2+0] = v
    for i in range(N-1):
        hamiltonian[i*2+1, (i+1)*2+0] = w
        hamiltonian[(i+1)*2+0, i*2+1] = w
    if period==1:
        hamiltonian[0, 2*N-1] = w
        hamiltonian[2*N-1, 0] = w
    return hamiltonian

def get_hopping_term_of_graphene_ribbon_along_zigzag_direction(N, eta=0):
    import numpy as np
    hopping = np.zeros((4*N, 4*N), dtype=complex)
    for i0 in range(N):
        hopping[4*i0+0, 4*i0+0] = eta
        hopping[4*i0+1, 4*i0+1] = eta
        hopping[4*i0+2, 4*i0+2] = eta
        hopping[4*i0+3, 4*i0+3] = eta
        hopping[4*i0+1, 4*i0+0] = 1
        hopping[4*i0+2, 4*i0+3] = 1
    return hopping

def hamiltonian_of_finite_size_system_along_two_directions_for_graphene(N1, N2, period_1=0, period_2=0):
    import numpy as np
    import guan
    on_site = guan.hamiltonian_of_finite_size_system_along_one_direction(4)
    hopping_1 = guan.get_hopping_term_of_graphene_ribbon_along_zigzag_direction(1)
    hopping_2 = np.zeros((4, 4), dtype=complex)
    hopping_2[3, 0] = 1
    hamiltonian = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N1, N2, on_site, hopping_1, hopping_2, period_1, period_2)
    return hamiltonian

def get_onsite_and_hopping_terms_of_2d_effective_graphene_along_one_direction(qy, t=1, staggered_potential=0, eta=0, valley_index=0):
    import numpy as np
    constant = -np.sqrt(3)/2
    h00 = np.zeros((2, 2), dtype=complex)
    h00[0, 0] = staggered_potential
    h00[1, 1] = -staggered_potential
    h00[0, 1] = -1j*constant*t*np.sin(qy)
    h00[1, 0] = 1j*constant*t*np.sin(qy)
    h01 = np.zeros((2, 2), dtype=complex)
    h01[0, 0] = eta
    h01[1, 1] = eta
    if valley_index == 0:
        h01[0, 1] = constant*t*(-1j/2)
        h01[1, 0] = constant*t*(-1j/2)
    else:
        h01[0, 1] = constant*t*(1j/2)
        h01[1, 0] = constant*t*(1j/2)
    return h00, h01

def get_onsite_and_hopping_terms_of_bhz_model(A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01, a=1):
    import numpy as np
    E_s = C+M-4*(D+B)/(a**2)
    E_p = C-M-4*(D-B)/(a**2)
    V_ss = (D+B)/(a**2)
    V_pp = (D-B)/(a**2)
    V_sp = -1j*A/(2*a)
    H0 = np.zeros((4, 4), dtype=complex)
    H1 = np.zeros((4, 4), dtype=complex)
    H2 = np.zeros((4, 4), dtype=complex)
    H0[0, 0] = E_s
    H0[1, 1] = E_p
    H0[2, 2] = E_s
    H0[3, 3] = E_p
    H1[0, 0] = V_ss
    H1[1, 1] = V_pp
    H1[2, 2] = V_ss
    H1[3, 3] = V_pp
    H1[0, 1] = V_sp
    H1[1, 0] = -np.conj(V_sp)
    H1[2, 3] = np.conj(V_sp)
    H1[3, 2] = -V_sp
    H2[0, 0] = V_ss
    H2[1, 1] = V_pp
    H2[2, 2] = V_ss
    H2[3, 3] = V_pp
    H2[0, 1] = 1j*V_sp
    H2[1, 0] = 1j*np.conj(V_sp)
    H2[2, 3] = -1j*np.conj(V_sp)
    H2[3, 2] = -1j*V_sp
    return H0, H1, H2

def get_onsite_and_hopping_terms_of_half_bhz_model_for_spin_up(A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01, a=1):
    import numpy as np
    E_s = C+M-4*(D+B)/(a**2)
    E_p = C-M-4*(D-B)/(a**2)
    V_ss = (D+B)/(a**2)
    V_pp = (D-B)/(a**2)
    V_sp = -1j*A/(2*a)
    H0 = np.zeros((2, 2), dtype=complex)
    H1 = np.zeros((2, 2), dtype=complex)
    H2 = np.zeros((2, 2), dtype=complex)
    H0[0, 0] = E_s
    H0[1, 1] = E_p
    H1[0, 0] = V_ss
    H1[1, 1] = V_pp
    H1[0, 1] = V_sp
    H1[1, 0] = -np.conj(V_sp)
    H2[0, 0] = V_ss
    H2[1, 1] = V_pp
    H2[0, 1] = 1j*V_sp
    H2[1, 0] = 1j*np.conj(V_sp)
    return H0, H1, H2

def get_onsite_and_hopping_terms_of_half_bhz_model_for_spin_down(A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01, a=1):
    import numpy as np
    E_s = C+M-4*(D+B)/(a**2)
    E_p = C-M-4*(D-B)/(a**2)
    V_ss = (D+B)/(a**2)
    V_pp = (D-B)/(a**2)
    V_sp = -1j*A/(2*a)
    H0 = np.zeros((2, 2), dtype=complex)
    H1 = np.zeros((2, 2), dtype=complex)
    H2 = np.zeros((2, 2), dtype=complex)
    H0[0, 0] = E_s
    H0[1, 1] = E_p
    H1[0, 0] = V_ss
    H1[1, 1] = V_pp
    H1[0, 1] = np.conj(V_sp)
    H1[1, 0] = -V_sp
    H2[0, 0] = V_ss
    H2[1, 1] = V_pp
    H2[0, 1] = -1j*np.conj(V_sp)
    H2[1, 0] = -1j*V_sp
    return H0, H1, H2

def hamiltonian_of_simple_chain(k):
    import guan
    hamiltonian = guan.one_dimensional_fourier_transform(k, unit_cell=0, hopping=1)
    return hamiltonian

def hamiltonian_of_square_lattice(k1, k2):
    import guan
    hamiltonian = guan.two_dimensional_fourier_transform_for_square_lattice(k1, k2, unit_cell=0, hopping_1=1, hopping_2=1)
    return hamiltonian

def hamiltonian_of_square_lattice_in_quasi_one_dimension(k, N=10, period=0):
    import numpy as np
    import guan
    h00 = np.zeros((N, N), dtype=complex)  # hopping in a unit cell
    h01 = np.zeros((N, N), dtype=complex)  # hopping between unit cells
    for i in range(N-1):   
        h00[i, i+1] = 1
        h00[i+1, i] = 1
    if period == 1:
        h00[N-1, 0] = 1
        h00[0, N-1] = 1
    for i in range(N):   
        h01[i, i] = 1
    hamiltonian = guan.one_dimensional_fourier_transform(k, unit_cell=h00, hopping=h01)
    return hamiltonian

def hamiltonian_of_cubic_lattice(k1, k2, k3):
    import guan
    hamiltonian = guan.three_dimensional_fourier_transform_for_cubic_lattice(k1, k2, k3, unit_cell=0, hopping_1=1, hopping_2=1, hopping_3=1)
    return hamiltonian

def hamiltonian_of_ssh_model(k, v=0.6, w=1):
    import numpy as np
    import cmath
    hamiltonian = np.zeros((2, 2), dtype=complex)
    hamiltonian[0,1] = v+w*cmath.exp(-1j*k)
    hamiltonian[1,0] = v+w*cmath.exp(1j*k)
    return hamiltonian

def hamiltonian_of_graphene(k1, k2, staggered_potential=0, t=1, a='default'):
    import numpy as np
    import cmath
    import math
    if a == 'default':
        a = 1/math.sqrt(3)
    h0 = np.zeros((2, 2), dtype=complex)  # mass term
    h1 = np.zeros((2, 2), dtype=complex)  # nearest hopping
    h0[0, 0] = staggered_potential     
    h0[1, 1] = -staggered_potential
    h1[1, 0] = t*(cmath.exp(1j*k2*a)+cmath.exp(1j*math.sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*math.sqrt(3)/2*k1*a-1j/2*k2*a))   
    h1[0, 1] = h1[1, 0].conj()
    hamiltonian = h0 + h1
    return hamiltonian

def effective_hamiltonian_of_graphene(qx, qy, t=1, staggered_potential=0, valley_index=0):
    import numpy as np
    hamiltonian = np.zeros((2, 2), dtype=complex)
    hamiltonian[0, 0] = staggered_potential
    hamiltonian[1, 1] = -staggered_potential
    constant = -np.sqrt(3)/2
    if valley_index == 0:
        hamiltonian[0, 1] = constant*t*(qx-1j*qy)
        hamiltonian[1, 0] = constant*t*(qx+1j*qy)
    else:
        hamiltonian[0, 1] = constant*t*(-qx-1j*qy)
        hamiltonian[1, 0] = constant*t*(-qx+1j*qy)
    return hamiltonian

def effective_hamiltonian_of_graphene_after_discretization(qx, qy, t=1, staggered_potential=0, valley_index=0):
    import numpy as np
    hamiltonian = np.zeros((2, 2), dtype=complex)
    hamiltonian[0, 0] = staggered_potential
    hamiltonian[1, 1] = -staggered_potential
    constant = -np.sqrt(3)/2
    if valley_index == 0:
        hamiltonian[0, 1] = constant*t*(np.sin(qx)-1j*np.sin(qy))
        hamiltonian[1, 0] = constant*t*(np.sin(qx)+1j*np.sin(qy))
    else:
        hamiltonian[0, 1] = constant*t*(-np.sin(qx)-1j*np.sin(qy))
        hamiltonian[1, 0] = constant*t*(-np.sin(qx)+1j*np.sin(qy))
    return hamiltonian

def hamiltonian_of_graphene_with_zigzag_in_quasi_one_dimension(k, N=10, M=0, t=1, period=0):
    import numpy as np
    import guan
    h00 = np.zeros((4*N, 4*N), dtype=complex)  # hopping in a unit cell
    h01 = np.zeros((4*N, 4*N), dtype=complex)  # hopping between unit cells
    for i in range(N):
        h00[i*4+0, i*4+0] = M
        h00[i*4+1, i*4+1] = -M
        h00[i*4+2, i*4+2] = M
        h00[i*4+3, i*4+3] = -M
        h00[i*4+0, i*4+1] = t
        h00[i*4+1, i*4+0] = t
        h00[i*4+1, i*4+2] = t
        h00[i*4+2, i*4+1] = t
        h00[i*4+2, i*4+3] = t
        h00[i*4+3, i*4+2] = t
    for i in range(N-1):
        h00[i*4+3, (i+1)*4+0] = t
        h00[(i+1)*4+0, i*4+3] = t
    if period == 1:
        h00[(N-1)*4+3, 0] = t
        h00[0, (N-1)*4+3] = t
    for i in range(N):
        h01[i*4+1, i*4+0] = t
        h01[i*4+2, i*4+3] = t
    hamiltonian = guan.one_dimensional_fourier_transform(k, unit_cell=h00, hopping=h01)
    return hamiltonian

def hamiltonian_of_haldane_model(k1, k2, M=2/3, t1=1, t2=1/3, phi='default', a='default'):
    import numpy as np
    import cmath
    import math
    if phi == 'default':
        phi=math.pi/4
    if a == 'default':
        a=1/math.sqrt(3)
    h0 = np.zeros((2, 2), dtype=complex)  # mass term
    h1 = np.zeros((2, 2), dtype=complex)  # nearest hopping
    h2 = np.zeros((2, 2), dtype=complex)  # next nearest hopping
    h0[0, 0] = M
    h0[1, 1] = -M
    h1[1, 0] = t1*(cmath.exp(1j*k2*a)+cmath.exp(1j*math.sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*math.sqrt(3)/2*k1*a-1j/2*k2*a))
    h1[0, 1] = h1[1, 0].conj()
    h2[0, 0] = t2*cmath.exp(-1j*phi)*(cmath.exp(1j*math.sqrt(3)*k1*a)+cmath.exp(-1j*math.sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*math.sqrt(3)/2*k1*a-1j*3/2*k2*a))
    h2[1, 1] = t2*cmath.exp(1j*phi)*(cmath.exp(1j*math.sqrt(3)*k1*a)+cmath.exp(-1j*math.sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*math.sqrt(3)/2*k1*a-1j*3/2*k2*a))
    hamiltonian = h0 + h1 + h2 + h2.transpose().conj()
    return hamiltonian

def hamiltonian_of_haldane_model_in_quasi_one_dimension(k, N=10, M=2/3, t1=1, t2=1/3, phi='default', period=0):
    import numpy as np
    import cmath
    import math
    if phi == 'default':
        phi=math.pi/4
    h00 = np.zeros((4*N, 4*N), dtype=complex)  # hopping in a unit cell
    h01 = np.zeros((4*N, 4*N), dtype=complex)  # hopping between unit cells
    for i in range(N):
        h00[i*4+0, i*4+0] = M
        h00[i*4+1, i*4+1] = -M
        h00[i*4+2, i*4+2] = M
        h00[i*4+3, i*4+3] = -M
        h00[i*4+0, i*4+1] = t1
        h00[i*4+1, i*4+0] = t1
        h00[i*4+1, i*4+2] = t1
        h00[i*4+2, i*4+1] = t1
        h00[i*4+2, i*4+3] = t1
        h00[i*4+3, i*4+2] = t1
        h00[i*4+0, i*4+2] = t2*cmath.exp(-1j*phi)
        h00[i*4+2, i*4+0] = h00[i*4+0, i*4+2].conj()
        h00[i*4+1, i*4+3] = t2*cmath.exp(-1j*phi)
        h00[i*4+3, i*4+1] = h00[i*4+1, i*4+3].conj()
    for i in range(N-1):
        h00[i*4+3, (i+1)*4+0] = t1
        h00[(i+1)*4+0, i*4+3] = t1
        h00[i*4+2, (i+1)*4+0] = t2*cmath.exp(1j*phi)
        h00[(i+1)*4+0, i*4+2] = h00[i*4+2, (i+1)*4+0].conj()
        h00[i*4+3, (i+1)*4+1] = t2*cmath.exp(1j*phi)
        h00[(i+1)*4+1, i*4+3] = h00[i*4+3, (i+1)*4+1].conj()
    if period == 1:
        h00[(N-1)*4+3, 0] = t1
        h00[0, (N-1)*4+3] = t1
        h00[(N-1)*4+2, 0] = t2*cmath.exp(1j*phi)
        h00[0, (N-1)*4+2] = h00[(N-1)*4+2, 0].conj()
        h00[(N-1)*4+3, 1] = t2*cmath.exp(1j*phi)
        h00[1, (N-1)*4+3] = h00[(N-1)*4+3, 1].conj()
    for i in range(N):
        h01[i*4+1, i*4+0] = t1
        h01[i*4+2, i*4+3] = t1
        h01[i*4+0, i*4+0] = t2*cmath.exp(1j*phi)
        h01[i*4+1, i*4+1] = t2*cmath.exp(-1j*phi)
        h01[i*4+2, i*4+2] = t2*cmath.exp(1j*phi)
        h01[i*4+3, i*4+3] = t2*cmath.exp(-1j*phi)
        h01[i*4+1, i*4+3] = t2*cmath.exp(1j*phi)
        h01[i*4+2, i*4+0] = t2*cmath.exp(-1j*phi)
        if i != 0:
            h01[i*4+1, (i-1)*4+3] = t2*cmath.exp(1j*phi)
    for i in range(N-1):
        h01[i*4+2, (i+1)*4+0] = t2*cmath.exp(-1j*phi)
    hamiltonian = h00 + h01*cmath.exp(1j*k) + h01.transpose().conj()*cmath.exp(-1j*k)
    return hamiltonian

def hamiltonian_of_one_QAH_model(k1, k2, t1=1, t2=1, t3=0.5, m=-1):
    import numpy as np
    import math
    hamiltonian = np.zeros((2, 2), dtype=complex)
    hamiltonian[0, 1] = 2*t1*math.cos(k1)-1j*2*t1*math.cos(k2)
    hamiltonian[1, 0] = 2*t1*math.cos(k1)+1j*2*t1*math.cos(k2)
    hamiltonian[0, 0] = m+2*t3*math.sin(k1)+2*t3*math.sin(k2)+2*t2*math.cos(k1+k2)
    hamiltonian[1, 1] = -(m+2*t3*math.sin(k1)+2*t3*math.sin(k2)+2*t2*math.cos(k1+k2))
    return hamiltonian

def hamiltonian_of_bhz_model(kx, ky, A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01):
    import numpy as np
    import math
    hamiltonian = np.zeros((4, 4), dtype=complex)
    varepsilon = C-2*D*(2-math.cos(kx)-math.cos(ky))
    d3 = -2*B*(2-(M/2/B)-math.cos(kx)-math.cos(ky))
    d1_d2 = A*(math.sin(kx)+1j*math.sin(ky))
    hamiltonian[0, 0] = varepsilon+d3
    hamiltonian[1, 1] = varepsilon-d3
    hamiltonian[0, 1] = np.conj(d1_d2)
    hamiltonian[1, 0] = d1_d2
    hamiltonian[2, 2] = varepsilon+d3
    hamiltonian[3, 3] = varepsilon-d3
    hamiltonian[2, 3] = -d1_d2 
    hamiltonian[3, 2] = -np.conj(d1_d2)
    return hamiltonian

def hamiltonian_of_half_bhz_model_for_spin_up(kx, ky, A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01):
    import numpy as np
    import math
    hamiltonian = np.zeros((2, 2), dtype=complex)
    varepsilon = C-2*D*(2-math.cos(kx)-math.cos(ky))
    d3 = -2*B*(2-(M/2/B)-math.cos(kx)-math.cos(ky))
    d1_d2 = A*(math.sin(kx)+1j*math.sin(ky))
    hamiltonian[0, 0] = varepsilon+d3
    hamiltonian[1, 1] = varepsilon-d3
    hamiltonian[0, 1] = np.conj(d1_d2)
    hamiltonian[1, 0] = d1_d2
    return hamiltonian

def hamiltonian_of_half_bhz_model_for_spin_down(kx, ky, A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01):
    import numpy as np
    import math
    hamiltonian = np.zeros((2, 2), dtype=complex)
    varepsilon = C-2*D*(2-math.cos(kx)-math.cos(ky))
    d3 = -2*B*(2-(M/2/B)-math.cos(kx)-math.cos(ky))
    d1_d2 = A*(math.sin(kx)+1j*math.sin(ky))
    hamiltonian[0, 0] = varepsilon+d3
    hamiltonian[1, 1] = varepsilon-d3
    hamiltonian[0, 1] = -d1_d2 
    hamiltonian[1, 0] = -np.conj(d1_d2)
    return hamiltonian

def hamiltonian_of_bbh_model(kx, ky, gamma_x=0.5, gamma_y=0.5, lambda_x=1, lambda_y=1):
    import numpy as np
    import cmath
    # label of atoms in a unit cell
    # (2) —— (0)
    #  |      |
    # (1) —— (3)   
    hamiltonian = np.zeros((4, 4), dtype=complex)
    hamiltonian[0, 2] = gamma_x+lambda_x*cmath.exp(1j*kx)
    hamiltonian[1, 3] = gamma_x+lambda_x*cmath.exp(-1j*kx)
    hamiltonian[0, 3] = gamma_y+lambda_y*cmath.exp(1j*ky)
    hamiltonian[1, 2] = -gamma_y-lambda_y*cmath.exp(-1j*ky)
    hamiltonian[2, 0] = np.conj(hamiltonian[0, 2])
    hamiltonian[3, 1] = np.conj(hamiltonian[1, 3])
    hamiltonian[3, 0] = np.conj(hamiltonian[0, 3])
    hamiltonian[2, 1] = np.conj(hamiltonian[1, 2])
    return hamiltonian

def hamiltonian_of_kagome_lattice(kx, ky, t=1):
    import numpy as np
    import math
    k1_dot_a1 = kx
    k2_dot_a2 = kx/2+ky*math.sqrt(3)/2
    k3_dot_a3 = -kx/2+ky*math.sqrt(3)/2
    hamiltonian = np.zeros((3, 3), dtype=complex)
    hamiltonian[0, 1] = 2*math.cos(k1_dot_a1)
    hamiltonian[0, 2] = 2*math.cos(k2_dot_a2)
    hamiltonian[1, 2] = 2*math.cos(k3_dot_a3)
    hamiltonian = hamiltonian + hamiltonian.transpose().conj()
    hamiltonian = -t*hamiltonian
    return hamiltonian

def hamiltonian_of_hyperhoneycomb_lattice(kx, ky, kz, t=1, a=1):
    import cmath
    import numpy as np
    hamiltonian = np.zeros((4, 4), dtype=complex)
    fx = (t*cmath.exp(1j*np.sqrt(3)/2*kx*a)+t*cmath.exp(-1j*np.sqrt(3)/2*kx*a))*cmath.exp(1j*kz/2*a)
    fy = (t*cmath.exp(1j*np.sqrt(3)/2*ky*a)+t*cmath.exp(-1j*np.sqrt(3)/2*ky*a))*cmath.exp(1j*kz/2*a)
    fz = cmath.exp(1j*kz*a)
    hamiltonian[0, 1] = fx
    hamiltonian[1, 0] = np.conj(fx)
    hamiltonian[2, 3] = fy
    hamiltonian[3, 2] = np.conj(fy)
    hamiltonian[1, 2] = fz
    hamiltonian[2, 1] = np.conj(fz)
    hamiltonian[3, 0] = fz
    hamiltonian[0, 3] = np.conj(fz)
    return hamiltonian

def calculate_eigenvalue(hamiltonian, hermitian=True):
    import numpy as np
    if np.array(hamiltonian).shape==():
        eigenvalue = np.real(hamiltonian)
    else:
        if hermitian:
            eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
        else:
            eigenvalue, eigenvector = np.linalg.eig(hamiltonian)
    return eigenvalue

def calculate_eigenvalue_with_one_parameter(x_array, hamiltonian_function, print_show=0):
    import numpy as np
    dim_x = np.array(x_array).shape[0]
    i0 = 0
    if np.array(hamiltonian_function(0)).shape==():
        eigenvalue_array = np.zeros((dim_x, 1))
        for x0 in x_array:
            hamiltonian = hamiltonian_function(x0)
            eigenvalue_array[i0, 0] = np.real(hamiltonian)
            i0 += 1
    else:
        dim = np.array(hamiltonian_function(0)).shape[0]
        eigenvalue_array = np.zeros((dim_x, dim))
        for x0 in x_array:
            if print_show==1:
                print(x0)
            hamiltonian = hamiltonian_function(x0)
            eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
            eigenvalue_array[i0, :] = eigenvalue
            i0 += 1
    return eigenvalue_array

def calculate_eigenvalue_with_two_parameters(x_array, y_array, hamiltonian_function, print_show=0, print_show_more=0):  
    import numpy as np
    dim_x = np.array(x_array).shape[0]
    dim_y = np.array(y_array).shape[0]
    if np.array(hamiltonian_function(0,0)).shape==():
        eigenvalue_array = np.zeros((dim_y, dim_x, 1))
        i0 = 0
        for y0 in y_array:
            j0 = 0
            for x0 in x_array:
                hamiltonian = hamiltonian_function(x0, y0)
                eigenvalue_array[i0, j0, 0] = np.real(hamiltonian)
                j0 += 1
            i0 += 1
    else:
        dim = np.array(hamiltonian_function(0, 0)).shape[0]
        eigenvalue_array = np.zeros((dim_y, dim_x, dim))
        i0 = 0
        for y0 in y_array:
            j0 = 0
            if print_show==1:
                print(y0)
            for x0 in x_array:
                if print_show_more==1:
                    print(x0)
                hamiltonian = hamiltonian_function(x0, y0)
                eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
                eigenvalue_array[i0, j0, :] = eigenvalue
                j0 += 1
            i0 += 1
    return eigenvalue_array

def calculate_eigenvector(hamiltonian, hermitian=True):
    import numpy as np
    if hermitian:
        eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
    else:
        eigenvalue, eigenvector = np.linalg.eig(hamiltonian)
    return eigenvector

def schmidt_orthogonalization(eigenvector):
    import numpy as np
    num = eigenvector.shape[1]
    for i in range(num):
        for i0 in range(i):
            eigenvector[:, i] = eigenvector[:, i] - eigenvector[:, i0]*np.dot(eigenvector[:, i].transpose().conj(), eigenvector[:, i0])/(np.dot(eigenvector[:, i0].transpose().conj(),eigenvector[:, i0]))
        eigenvector[:, i] = eigenvector[:, i]/np.linalg.norm(eigenvector[:, i])
    return eigenvector

def orthogonalization_with_qr(eigenvector):
    import numpy as np
    Q, R = np.linalg.qr(eigenvector)
    return Q

def orthogonalization_with_svd(eigenvector):
    import numpy as np
    U, sigma, VT = np.linalg.svd(eigenvector)
    return U

def orthogonalization_with_scipy_linalg_orth(eigenvector):
    import scipy
    Q = scipy.linalg.orth(eigenvector)
    return Q

def verify_orthogonality(eigenvector):
    import numpy as np
    identity = np.eye(eigenvector.shape[1])
    product = np.dot(eigenvector.transpose().conj(), eigenvector)
    return np.allclose(product, identity)

def find_vector_with_the_same_gauge_with_binary_search(vector_target, vector_ref, show_error=1, show_times=0, show_phase=0, n_test=1000, precision=1e-6):
    import numpy as np
    import cmath
    phase_1_pre = 0
    phase_2_pre = np.pi
    for i0 in range(n_test):
        test_1 = np.sum(np.abs(vector_target*cmath.exp(1j*phase_1_pre) - vector_ref))
        test_2 = np.sum(np.abs(vector_target*cmath.exp(1j*phase_2_pre) - vector_ref))
        if test_1 < precision:
            phase = phase_1_pre
            if show_times==1:
                print('Binary search times=', i0)
            break
        if i0 == n_test-1:
            phase = phase_1_pre
            if show_error==1:
                print('Gauge not found with binary search times=', i0)
        if test_1 < test_2:
            if i0 == 0:
                phase_1 = phase_1_pre-(phase_2_pre-phase_1_pre)/2
                phase_2 = phase_1_pre+(phase_2_pre-phase_1_pre)/2
            else:
                phase_1 = phase_1_pre
                phase_2 = phase_1_pre+(phase_2_pre-phase_1_pre)/2
        else:
            if i0 == 0:
                phase_1 = phase_2_pre-(phase_2_pre-phase_1_pre)/2
                phase_2 = phase_2_pre+(phase_2_pre-phase_1_pre)/2
            else:
                phase_1 = phase_2_pre-(phase_2_pre-phase_1_pre)/2
                phase_2 = phase_2_pre 
        phase_1_pre = phase_1
        phase_2_pre = phase_2
    vector_target = vector_target*cmath.exp(1j*phase)
    if show_phase==1:
        print('Phase=', phase)
    return vector_target

def find_vector_with_fixed_gauge_by_making_one_component_real(vector, index=None):
    import numpy as np
    import cmath
    vector = np.array(vector)
    if index == None:
        index = np.argmax(np.abs(vector))
    angle = cmath.phase(vector[index])
    vector = vector*cmath.exp(-1j*angle)
    return vector

def find_vector_array_with_fixed_gauge_by_making_one_component_real(vector_array):
    import numpy as np
    import guan
    vector_sum = 0
    Num_k = np.array(vector_array).shape[0]
    for i0 in range(Num_k):
        vector_sum += np.abs(vector_array[i0])
    index = np.argmax(np.abs(vector_sum))
    for i0 in range(Num_k):
        vector_array[i0] = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector_array[i0], index=index)
    return vector_array

def loop_find_vector_with_fixed_gauge_by_making_one_component_real(vector, precision=0.005, index=None):
    import numpy as np
    import cmath
    vector = np.array(vector)
    if index == None:
        index = np.argmax(np.abs(vector))
    sign_pre = np.sign(np.imag(vector[index]))
    for phase in np.arange(0, 2*np.pi, precision):
        sign =  np.sign(np.imag(vector[index]*cmath.exp(1j*phase)))
        if np.abs(np.imag(vector[index]*cmath.exp(1j*phase))) < 1e-9 or sign == -sign_pre:
            break
        sign_pre = sign
    vector = vector*cmath.exp(1j*phase)
    if np.real(vector[index]) < 0:
        vector = -vector
    return vector

def loop_find_vector_array_with_fixed_gauge_by_making_one_component_real(vector_array, precision=0.005):
    import numpy as np
    import guan
    vector_sum = 0
    Num_k = np.array(vector_array).shape[0]
    for i0 in range(Num_k):
        vector_sum += np.abs(vector_array[i0])
    index = np.argmax(np.abs(vector_sum))
    for i0 in range(Num_k):
        vector_array[i0] = guan.loop_find_vector_with_fixed_gauge_by_making_one_component_real(vector_array[i0], precision=precision, index=index)
    return vector_array

def rotation_of_degenerate_vectors(vector1, vector2, index1=None, index2=None, precision=0.01, criterion=0.01, show_theta=0):
    import numpy as np
    import math
    import cmath
    vector1 = np.array(vector1)
    vector2 = np.array(vector2)
    if index1 == None:
        index1 = np.argmax(np.abs(vector1))
    if index2 == None:
        index2 = np.argmax(np.abs(vector2))
    if np.abs(vector1[index2])>criterion or np.abs(vector2[index1])>criterion:
        for theta in np.arange(0, 2*math.pi, precision):
            if show_theta==1:
                print(theta)
            for phi1 in np.arange(0, 2*math.pi, precision):
                for phi2 in np.arange(0, 2*math.pi, precision):
                    vector1_test = cmath.exp(1j*phi1)*vector1*math.cos(theta)+cmath.exp(1j*phi2)*vector2*math.sin(theta)
                    vector2_test = -cmath.exp(-1j*phi2)*vector1*math.sin(theta)+cmath.exp(-1j*phi1)*vector2*math.cos(theta)
                    if np.abs(vector1_test[index2])<criterion and np.abs(vector2_test[index1])<criterion:
                        vector1 = vector1_test
                        vector2 = vector2_test
                        break
                if np.abs(vector1_test[index2])<criterion and np.abs(vector2_test[index1])<criterion:
                    break
            if np.abs(vector1_test[index2])<criterion and np.abs(vector2_test[index1])<criterion:
                break
    return vector1, vector2

def rotation_of_degenerate_vectors_array(vector1_array, vector2_array, precision=0.01, criterion=0.01, show_theta=0):
    import numpy as np
    import guan
    Num_k = np.array(vector1_array).shape[0]
    vector1_sum = 0
    for i0 in range(Num_k):
        vector1_sum += np.abs(vector1_array[i0])
    index1 = np.argmax(np.abs(vector1_sum))
    vector2_sum = 0
    for i0 in range(Num_k):
        vector2_sum += np.abs(vector2_array[i0])
    index2 = np.argmax(np.abs(vector2_sum))
    for i0 in range(Num_k):
        vector1_array[i0], vector2_array[i0] = guan.rotation_of_degenerate_vectors(vector1=vector1_array[i0], vector2=vector2_array[i0], index1=index1, index2=index2, precision=precision, criterion=criterion, show_theta=show_theta)
    return vector1_array, vector2_array

def find_close_values_in_one_array(array, precision=1e-2):
    new_array = []
    i0 = 0
    for a1 in array:
        j0 = 0
        for a2 in array:
            if j0>i0 and abs(a1-a2)<precision: 
                new_array.append([a1, a2])
            j0 +=1
        i0 += 1
    return new_array

def find_degenerate_points(k_array, eigenvalue_array, precision=1e-2):
    import guan
    degenerate_k_array = []
    degenerate_eigenvalue_array = []
    i0 = 0
    for k in k_array:
        degenerate_points = guan.find_close_values_in_one_array(eigenvalue_array[i0], precision=precision)
        if len(degenerate_points) != 0:
            degenerate_k_array.append(k)
            degenerate_eigenvalue_array.append(degenerate_points)
        i0 += 1
    return degenerate_k_array, degenerate_eigenvalue_array

def green_function(fermi_energy, hamiltonian, broadening, self_energy=0):
    import numpy as np
    if np.array(hamiltonian).shape==():
        dim = 1
    else:
        dim = np.array(hamiltonian).shape[0]
    green = np.linalg.inv((fermi_energy+broadening*1j)*np.eye(dim)-hamiltonian-self_energy)
    return green

def green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening, self_energy=0):
    import numpy as np
    h01 = np.array(h01)
    if np.array(h00).shape==():
        dim = 1
    else:
        dim = np.array(h00).shape[0]   
    green_nn_n = np.linalg.inv((fermi_energy+broadening*1j)*np.identity(dim)-h00-np.dot(np.dot(h01.transpose().conj(), green_nn_n_minus), h01)-self_energy)
    return green_nn_n

def green_function_in_n(green_in_n_minus, h01, green_nn_n):
    import numpy as np
    green_in_n = np.dot(np.dot(green_in_n_minus, h01), green_nn_n)
    return green_in_n

def green_function_ni_n(green_nn_n, h01, green_ni_n_minus):
    import numpy as np
    h01 = np.array(h01)
    green_ni_n = np.dot(np.dot(green_nn_n, h01.transpose().conj()), green_ni_n_minus)
    return green_ni_n

def green_function_ii_n(green_ii_n_minus, green_in_n_minus, h01, green_nn_n, green_ni_n_minus):
    import numpy as np
    green_ii_n = green_ii_n_minus+np.dot(np.dot(np.dot(np.dot(green_in_n_minus, h01), green_nn_n), h01.transpose().conj()),green_ni_n_minus)
    return green_ii_n

def transfer_matrix(fermi_energy, h00, h01):
    import numpy as np
    h01 = np.array(h01)
    if np.array(h00).shape==():
        dim = 1
    else:
        dim = np.array(h00).shape[0]
    transfer = np.zeros((2*dim, 2*dim), dtype=complex)
    if dim == 1:
        transfer[0:dim, 0:dim] = np.dot(1/h01, fermi_energy*np.identity(dim)-h00)
        transfer[0:dim, dim:2*dim] = np.dot(-1/h01, h01.transpose().conj())
    else:
        transfer[0:dim, 0:dim] = np.dot(np.linalg.inv(h01), fermi_energy*np.identity(dim)-h00)
        transfer[0:dim, dim:2*dim] = np.dot(-1*np.linalg.inv(h01), h01.transpose().conj())
    transfer[dim:2*dim, 0:dim] = np.identity(dim)
    transfer[dim:2*dim, dim:2*dim] = 0
    return transfer

def surface_green_function_of_lead(fermi_energy, h00, h01):
    import numpy as np
    h01 = np.array(h01)
    if np.array(h00).shape==():
        dim = 1
    else:
        dim = np.array(h00).shape[0]
    fermi_energy = fermi_energy+1e-9*1j
    transfer = transfer_matrix(fermi_energy, h00, h01)
    eigenvalue, eigenvector = np.linalg.eig(transfer)
    ind = np.argsort(np.abs(eigenvalue))
    temp = np.zeros((2*dim, 2*dim), dtype=complex)
    i0 = 0
    for ind0 in ind:
        temp[:, i0] = eigenvector[:, ind0]
        i0 += 1
    s1 = temp[dim:2*dim, 0:dim]
    s2 = temp[0:dim, 0:dim]
    s3 = temp[dim:2*dim, dim:2*dim]
    s4 = temp[0:dim, dim:2*dim]
    right_lead_surface = np.linalg.inv(fermi_energy*np.identity(dim)-h00-np.dot(np.dot(h01, s2), np.linalg.inv(s1)))
    left_lead_surface = np.linalg.inv(fermi_energy*np.identity(dim)-h00-np.dot(np.dot(h01.transpose().conj(), s3), np.linalg.inv(s4)))
    return right_lead_surface, left_lead_surface

def self_energy_of_lead(fermi_energy, h00, h01):
    import numpy as np
    import guan
    h01 = np.array(h01)
    right_lead_surface, left_lead_surface = guan.surface_green_function_of_lead(fermi_energy, h00, h01)
    right_self_energy = np.dot(np.dot(h01, right_lead_surface), h01.transpose().conj())
    left_self_energy = np.dot(np.dot(h01.transpose().conj(), left_lead_surface), h01)
    gamma_right = (right_self_energy - right_self_energy.transpose().conj())*1j
    gamma_left = (left_self_energy - left_self_energy.transpose().conj())*1j
    return right_self_energy, left_self_energy, gamma_right, gamma_left

def self_energy_of_lead_with_h_LC_and_h_CR(fermi_energy, h00, h01, h_LC, h_CR):
    import numpy as np
    import guan
    h_LC = np.array(h_LC)
    h_CR = np.array(h_CR)
    right_lead_surface, left_lead_surface = guan.surface_green_function_of_lead(fermi_energy, h00, h01)
    right_self_energy = np.dot(np.dot(h_CR, right_lead_surface), h_CR.transpose().conj())
    left_self_energy = np.dot(np.dot(h_LC.transpose().conj(), left_lead_surface), h_LC)
    gamma_right = (right_self_energy - right_self_energy.transpose().conj())*1j
    gamma_left = (left_self_energy - left_self_energy.transpose().conj())*1j
    return right_self_energy, left_self_energy, gamma_right, gamma_left

def self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00, h01, h_lead_to_center):
    import numpy as np
    import guan
    h_lead_to_center = np.array(h_lead_to_center)
    right_lead_surface, left_lead_surface = guan.surface_green_function_of_lead(fermi_energy, h00, h01)
    self_energy = np.dot(np.dot(h_lead_to_center.transpose().conj(), right_lead_surface), h_lead_to_center)
    gamma = (self_energy - self_energy.transpose().conj())*1j
    return self_energy, gamma

def green_function_with_leads(fermi_energy, h00, h01, h_LC, h_CR, center_hamiltonian):
    import numpy as np
    import guan
    dim = np.array(center_hamiltonian).shape[0]
    right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead_with_h_LC_and_h_CR(fermi_energy, h00, h01, h_LC, h_CR)
    green = np.linalg.inv(fermi_energy*np.identity(dim)-center_hamiltonian-left_self_energy-right_self_energy)
    return green, gamma_right, gamma_left

def electron_correlation_function_green_n_for_local_current(fermi_energy, h00, h01, h_LC, h_CR, center_hamiltonian):
    import numpy as np
    import guan
    right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead_with_h_LC_and_h_CR(fermi_energy, h00, h01, h_LC, h_CR)
    green = guan.green_function(fermi_energy, center_hamiltonian, broadening=0, self_energy=left_self_energy+right_self_energy)
    G_n = np.imag(np.dot(np.dot(green, gamma_left), green.transpose().conj()))
    return G_n

def total_density_of_states(fermi_energy, hamiltonian, broadening=0.01):
    import numpy as np
    import math
    import guan
    green = guan.green_function(fermi_energy, hamiltonian, broadening)
    total_dos = -np.trace(np.imag(green))/math.pi
    return total_dos

def total_density_of_states_with_fermi_energy_array(fermi_energy_array, hamiltonian, broadening=0.01, print_show=0):
    import numpy as np
    import guan
    dim = np.array(fermi_energy_array).shape[0]
    total_dos_array = np.zeros(dim)
    i0 = 0
    for fermi_energy in fermi_energy_array:
        if print_show == 1:
            print(fermi_energy)
        total_dos_array[i0] = guan.total_density_of_states(fermi_energy, hamiltonian, broadening)
        i0 += 1
    return total_dos_array

def local_density_of_states_for_square_lattice(fermi_energy, hamiltonian, N1, N2, internal_degree=1, broadening=0.01):
    import numpy as np
    import math
    import guan
    green = guan.green_function(fermi_energy, hamiltonian, broadening)
    local_dos = np.zeros((N2, N1))
    for i1 in range(N1):
        for i2 in range(N2):
            for i in range(internal_degree): 
                local_dos[i2, i1] = local_dos[i2, i1]-np.imag(green[i1*N2*internal_degree+i2*internal_degree+i, i1*N2*internal_degree+i2*internal_degree+i])/math.pi
    return local_dos

def local_density_of_states_for_cubic_lattice(fermi_energy, hamiltonian, N1, N2, N3, internal_degree=1, broadening=0.01):
    import numpy as np
    import math
    import guan
    green = guan.green_function(fermi_energy, hamiltonian, broadening)
    local_dos = np.zeros((N3, N2, N1))
    for i1 in range(N1):
        for i2 in range(N2):
            for i3 in range(N3):
                for i in range(internal_degree): 
                    local_dos[i3, i2, i1] = local_dos[i3, i2, i1]-np.imag(green[i1*N2*N3*internal_degree+i2*N3*internal_degree+i3*internal_degree+i, i1*N2*N3*internal_degree+i2*N3*internal_degree+i3*internal_degree+i])/math.pi
    return local_dos

def local_density_of_states_for_square_lattice_using_dyson_equation(fermi_energy, h00, h01, N2, N1, internal_degree=1, broadening=0.01):
    import numpy as np
    import math
    import guan
    local_dos = np.zeros((N2, N1))
    green_11_1 = guan.green_function(fermi_energy, h00, broadening)
    for i1 in range(N1):
        green_nn_n_minus = green_11_1
        green_in_n_minus = green_11_1
        green_ni_n_minus = green_11_1
        green_ii_n_minus = green_11_1
        for _ in range(i1):
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
            green_nn_n_minus = green_nn_n
        if i1!=0:
            green_in_n_minus = green_nn_n
            green_ni_n_minus = green_nn_n
            green_ii_n_minus = green_nn_n
        for _ in range(N1-1-i1):
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
            green_nn_n_minus = green_nn_n
            green_ii_n = guan.green_function_ii_n(green_ii_n_minus, green_in_n_minus, h01, green_nn_n, green_ni_n_minus)
            green_ii_n_minus = green_ii_n
            green_in_n = guan.green_function_in_n(green_in_n_minus, h01, green_nn_n)
            green_in_n_minus = green_in_n
            green_ni_n = guan.green_function_ni_n(green_nn_n, h01, green_ni_n_minus)
            green_ni_n_minus = green_ni_n
        for i2 in range(N2):
            for i in range(internal_degree):
                local_dos[i2, i1] = local_dos[i2, i1] - np.imag(green_ii_n_minus[i2*internal_degree+i, i2*internal_degree+i])/math.pi
    return local_dos

def local_density_of_states_for_square_lattice_using_dyson_equation_with_second_method(fermi_energy, h00, h01, N2, N1, internal_degree=1, broadening=0.01):
    import numpy as np
    import math
    import guan
    h01 = np.array(h01)
    if np.array(h00).shape==():
        dim = 1
    else:
        dim = np.array(h00).shape[0]   
    local_dos = np.zeros((N2, N1))
    green_11_1 = guan.green_function(fermi_energy, h00, broadening)
    for i1 in range(N1):
        green_nn_n_right_minus = green_11_1
        green_nn_n_left_minus = green_11_1
        if i1!=0:
            for _ in range(i1-1):
                green_nn_n_right = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_right_minus, broadening)
                green_nn_n_right_minus = green_nn_n_right
        if i1!=N1-1:
            for _ in range(N1-i1-2):
                G_nn_n_left = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_left_minus, broadening)
                green_nn_n_left_minus = G_nn_n_left
        if i1==0:
            green_ii_n = np.linalg.inv((fermi_energy+broadening*1j)*np.identity(dim)-h00-np.dot(np.dot(h01, green_nn_n_left_minus), h01.transpose().conj()))
        elif i1!=0 and i1!=N1-1:
            green_ii_n = np.linalg.inv((fermi_energy+broadening*1j)*np.identity(dim)-h00-np.dot(np.dot(h01.transpose().conj(), green_nn_n_right_minus), h01)-np.dot(np.dot(h01, green_nn_n_left_minus), h01.transpose().conj()))
        elif i1==N1-1: 
            green_ii_n = np.linalg.inv((fermi_energy+broadening*1j)*np.identity(dim)-h00-np.dot(np.dot(h01.transpose().conj(), green_nn_n_right_minus), h01))
        for i2 in range(N2):
            for i in range(internal_degree):
                local_dos[i2, i1] = local_dos[i2, i1] - np.imag(green_ii_n[i2*internal_degree+i, i2*internal_degree+i])/math.pi
    return local_dos

def local_density_of_states_for_cubic_lattice_using_dyson_equation(fermi_energy, h00, h01, N3, N2, N1, internal_degree=1, broadening=0.01):
    import numpy as np
    import math
    import guan
    local_dos = np.zeros((N3, N2, N1))
    green_11_1 = guan.green_function(fermi_energy, h00, broadening)
    for i1 in range(N1):
        green_nn_n_minus = green_11_1
        green_in_n_minus = green_11_1
        green_ni_n_minus = green_11_1
        green_ii_n_minus = green_11_1
        for _ in range(i1):
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
            green_nn_n_minus = green_nn_n
        if i1!=0:
            green_in_n_minus = green_nn_n
            green_ni_n_minus = green_nn_n
            green_ii_n_minus = green_nn_n
        for _ in range(N1-1-i1):
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
            green_nn_n_minus = green_nn_n
            green_ii_n = guan.green_function_ii_n(green_ii_n_minus, green_in_n_minus, h01, green_nn_n, green_ni_n_minus)
            green_ii_n_minus = green_ii_n
            green_in_n = guan.green_function_in_n(green_in_n_minus, h01, green_nn_n)
            green_in_n_minus = green_in_n
            green_ni_n = guan.green_function_ni_n(green_nn_n, h01, green_ni_n_minus)
            green_ni_n_minus = green_ni_n
        for i2 in range(N2):
            for i3 in range(N3):
                for i in range(internal_degree):
                    local_dos[i3, i2, i1] = local_dos[i3, i2, i1] -np.imag(green_ii_n_minus[i2*N3*internal_degree+i3*internal_degree+i, i2*N3*internal_degree+i3*internal_degree+i])/math.pi
    return local_dos

def local_density_of_states_for_square_lattice_with_self_energy_using_dyson_equation(fermi_energy, h00, h01, N2, N1, right_self_energy, left_self_energy, internal_degree=1, broadening=0.01):
    import numpy as np
    import math
    import guan
    local_dos = np.zeros((N2, N1))
    green_11_1 = guan.green_function(fermi_energy, h00+left_self_energy, broadening)
    for i1 in range(N1):
        green_nn_n_minus = green_11_1
        green_in_n_minus = green_11_1
        green_ni_n_minus = green_11_1
        green_ii_n_minus = green_11_1
        for i2_0 in range(i1):
            if i2_0 == N1-1-1:
                green_nn_n = guan.green_function_nn_n(fermi_energy, h00+right_self_energy, h01, green_nn_n_minus, broadening)
            else:
                green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
            green_nn_n_minus = green_nn_n
        if i1!=0:
            green_in_n_minus = green_nn_n
            green_ni_n_minus = green_nn_n
            green_ii_n_minus = green_nn_n
        for size_0 in range(N1-1-i1):
            if size_0 == N1-1-i1-1:
                green_nn_n = guan.green_function_nn_n(fermi_energy, h00+right_self_energy, h01, green_nn_n_minus, broadening)
            else:
                green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
            green_nn_n_minus = green_nn_n
            green_ii_n = guan.green_function_ii_n(green_ii_n_minus, green_in_n_minus, h01, green_nn_n, green_ni_n_minus)
            green_ii_n_minus = green_ii_n
            green_in_n = guan.green_function_in_n(green_in_n_minus, h01, green_nn_n)
            green_in_n_minus = green_in_n
            green_ni_n = guan.green_function_ni_n(green_nn_n, h01, green_ni_n_minus)
            green_ni_n_minus = green_ni_n
        for i2 in range(N2):
            for i in range(internal_degree):
                local_dos[i2, i1] = local_dos[i2, i1] - np.imag(green_ii_n_minus[i2*internal_degree+i, i2*internal_degree+i])/math.pi
    return local_dos

def calculate_conductance(fermi_energy, h00, h01, length=100):
    import numpy as np
    import copy
    import guan
    right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
    for ix in range(length):
        if ix == 0:
            green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
            green_0n_n = copy.deepcopy(green_nn_n)
        elif ix != length-1:
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0)
            green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
        else:
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
            green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
    dim = np.array(h00).shape[0]
    if dim == 1:
        conductance = np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj())
        if conductance.shape == ():
            pass
        else:
            conductance = conductance[0][0]
    else:
        conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
    return conductance

def calculate_conductance_with_fermi_energy_array(fermi_energy_array, h00, h01, length=100, print_show=0):
    import numpy as np
    import guan
    dim = np.array(fermi_energy_array).shape[0]
    conductance_array = np.zeros(dim)
    i0 = 0
    for fermi_energy in fermi_energy_array:
        conductance_array[i0] = np.real(guan.calculate_conductance(fermi_energy, h00, h01, length))
        if print_show == 1:
            print(fermi_energy, conductance_array[i0])
        i0 += 1
    return conductance_array

def calculate_conductance_with_barrier(fermi_energy, h00, h01, length=100, barrier_length=20, barrier_potential=1):
    import numpy as np
    import copy
    import guan
    right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
    dim = np.array(h00).shape[0]
    for ix in range(length):
        if ix == 0:
            green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
            green_0n_n = copy.deepcopy(green_nn_n)
        elif int(length/2-barrier_length/2)<=ix<int(length/2+barrier_length/2):
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00+barrier_potential*np.identity(dim), h01, green_nn_n, broadening=0) 
            green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
        elif ix != length-1:
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0)
            green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
        else:
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
            green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
    if dim == 1:
        conductance = np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj())
        if conductance.shape == ():
            pass
        else:
            conductance = conductance[0][0]
    else:
        conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
    return conductance

def calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensity=2.0, disorder_concentration=1.0, length=100, calculation_times=1):
    import numpy as np
    import copy
    import guan
    right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
    dim = np.array(h00).shape[0]
    conductance_averaged = 0
    for times in range(calculation_times):
        for ix in range(length+2):
            disorder = np.zeros((dim, dim))
            for dim0 in range(dim):
                if np.random.uniform(0, 1)<=disorder_concentration:
                    disorder[dim0, dim0] = np.random.uniform(-disorder_intensity, disorder_intensity)
            if ix == 0:
                green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
                green_0n_n = copy.deepcopy(green_nn_n)
            elif ix != length+1:
                green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0)
                green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
            else:
                green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
                green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
        if dim == 1:
            conductance = np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj())
            if conductance.shape == ():
                pass
            else:
                conductance = conductance[0][0]
        else:
            conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
        conductance_averaged += conductance
    conductance_averaged = conductance_averaged/calculation_times
    return conductance_averaged

def calculate_conductance_with_disorder_array(fermi_energy, h00, h01, disorder_array, length=100):
    import numpy as np
    import copy
    import guan
    right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
    dim = np.array(h00).shape[0]
    i0 = 0
    for ix in range(length+2):
        if ix == 0:
            green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
            green_0n_n = copy.deepcopy(green_nn_n)
        elif ix != length+1:
            disorder = np.diag(disorder_array[i0*dim:(i0+1)*dim])
            i0 += 1
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0)
            green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
        else:
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
            green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
    if dim == 1:
        conductance = np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj())
        if conductance.shape == ():
            pass
        else:
            conductance = conductance[0][0]
    else:
        conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
    return conductance

def calculate_conductance_with_slice_disorder(fermi_energy, h00, h01, disorder_intensity=2.0, disorder_concentration=1.0, length=100):
    import numpy as np
    import copy
    import guan
    right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
    dim = np.array(h00).shape[0]
    for ix in range(length+2):
        disorder = np.zeros((dim, dim))
        if np.random.uniform(0, 1)<=disorder_concentration:
            disorder = np.random.uniform(-disorder_intensity, disorder_intensity)*np.eye(dim)
        if ix == 0:
            green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
            green_0n_n = copy.deepcopy(green_nn_n)
        elif ix != length+1:
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0)
            green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
        else:
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
            green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
    if dim == 1:
        conductance = np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj())
        if conductance.shape == ():
            pass
        else:
            conductance = conductance[0][0]
    else:
        conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
    return conductance

def calculate_conductance_with_disorder_inside_unit_cell_which_keeps_translational_symmetry(fermi_energy, h00, h01, disorder_intensity=2.0, disorder_concentration=1.0, length=100):
    import numpy as np
    import copy
    import guan
    right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
    dim = np.array(h00).shape[0]
    disorder = np.zeros((dim, dim))
    for dim0 in range(dim):
        if np.random.uniform(0, 1)<=disorder_concentration:
            disorder[dim0, dim0] = np.random.uniform(-disorder_intensity, disorder_intensity)
    for ix in range(length+2):
        if ix == 0:
            green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
            green_0n_n = copy.deepcopy(green_nn_n)
        elif ix != length+1:
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0)
            green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
        else:
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
            green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
    if dim == 1:
        conductance = np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj())
        if conductance.shape == ():
            pass
        else:
            conductance = conductance[0][0]
    else:
        conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
    return conductance

def calculate_conductance_with_random_vacancy(fermi_energy, h00, h01, vacancy_concentration=0.5, vacancy_potential=1e9, length=100):
    import numpy as np
    import copy
    import guan
    right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
    dim = np.array(h00).shape[0]
    for ix in range(length+2):
        random_vacancy = np.zeros((dim, dim))
        for dim0 in range(dim):
            if np.random.uniform(0, 1)<=vacancy_concentration:
                random_vacancy[dim0, dim0] = vacancy_potential
        if ix == 0:
            green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
            green_0n_n = copy.deepcopy(green_nn_n)
        elif ix != length+1:
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00+random_vacancy, h01, green_nn_n, broadening=0)
            green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
        else:
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
            green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
    if dim == 1:
        conductance = np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj())
        if conductance.shape == ():
            pass
        else:
            conductance = conductance[0][0]
    else:
        conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
    return conductance

def calculate_conductance_with_disorder_intensity_array(fermi_energy, h00, h01, disorder_intensity_array, disorder_concentration=1.0, length=100, calculation_times=1, print_show=0):
    import numpy as np
    import guan
    dim = np.array(disorder_intensity_array).shape[0]
    conductance_array = np.zeros(dim)
    i0 = 0
    for disorder_intensity in disorder_intensity_array:
        for times in range(calculation_times):
            conductance_array[i0] = conductance_array[i0]+np.real(guan.calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensity=disorder_intensity, disorder_concentration=disorder_concentration, length=length))
        if print_show == 1:
            print(disorder_intensity, conductance_array[i0]/calculation_times)
        i0 += 1
    conductance_array = conductance_array/calculation_times
    return conductance_array

def calculate_conductance_with_disorder_concentration_array(fermi_energy, h00, h01, disorder_concentration_array, disorder_intensity=2.0, length=100, calculation_times=1, print_show=0):
    import numpy as np
    import guan
    dim = np.array(disorder_concentration_array).shape[0]
    conductance_array = np.zeros(dim)
    i0 = 0
    for disorder_concentration in disorder_concentration_array:
        for times in range(calculation_times):
            conductance_array[i0] = conductance_array[i0]+np.real(guan.calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensity=disorder_intensity, disorder_concentration=disorder_concentration, length=length))
        if print_show == 1:
            print(disorder_concentration, conductance_array[i0]/calculation_times)
        i0 += 1
    conductance_array = conductance_array/calculation_times
    return conductance_array

def calculate_conductance_with_scattering_length_array(fermi_energy, h00, h01, length_array, disorder_intensity=2.0, disorder_concentration=1.0, calculation_times=1, print_show=0):
    import numpy as np
    import guan
    dim = np.array(length_array).shape[0]
    conductance_array = np.zeros(dim)
    i0 = 0
    for length in length_array:
        for times in range(calculation_times):
            conductance_array[i0] = conductance_array[i0]+np.real(guan.calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensity=disorder_intensity, disorder_concentration=disorder_concentration, length=length))
        if print_show == 1:
            print(length, conductance_array[i0]/calculation_times)
        i0 += 1
    conductance_array = conductance_array/calculation_times
    return conductance_array

def get_gamma_array_and_green_for_six_terminal_transmission(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width=10, length=50, internal_degree=1, moving_step_of_leads=10):
    import numpy as np
    import guan
    #   ---------------- Geometry ----------------
    #               lead2         lead3
    #   lead1(L)                          lead4(R)  
    #               lead6         lead5 
    h00_for_lead_1 = h00_for_lead_4
    h00_for_lead_2 = h00_for_lead_2
    h00_for_lead_3 = h00_for_lead_2
    h00_for_lead_5 = h00_for_lead_2
    h00_for_lead_6 = h00_for_lead_2
    h00_for_lead_4 = h00_for_lead_4
    h01_for_lead_1 = h01_for_lead_4.transpose().conj()
    h01_for_lead_2 = h01_for_lead_2
    h01_for_lead_3 = h01_for_lead_2
    h01_for_lead_4 = h01_for_lead_4
    h01_for_lead_5 = h01_for_lead_2.transpose().conj()
    h01_for_lead_6 = h01_for_lead_2.transpose().conj()
    h_lead1_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
    h_lead2_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
    h_lead3_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
    h_lead4_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
    h_lead5_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
    h_lead6_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
    move = moving_step_of_leads # the step of leads 2,3,6,5 moving to center
    h_lead1_to_center[0:internal_degree*width, 0:internal_degree*width] = h01_for_lead_1.transpose().conj()
    h_lead4_to_center[0:internal_degree*width, internal_degree*width*(length-1):internal_degree*width*length] = h01_for_lead_4.transpose().conj()
    for i0 in range(width):
        begin_index = internal_degree*i0+0
        end_index = internal_degree*i0+internal_degree
        h_lead2_to_center[begin_index:end_index, internal_degree*(width*(move+i0)+(width-1))+0:internal_degree*(width*(move+i0)+(width-1))+internal_degree] = h01_for_lead_2.transpose().conj()[begin_index:end_index, begin_index:end_index]
        h_lead3_to_center[begin_index:end_index, internal_degree*(width*(length-move-1-i0)+(width-1))+0:internal_degree*(width*(length-move-1-i0)+(width-1))+internal_degree] = h01_for_lead_3.transpose().conj()[begin_index:end_index, begin_index:end_index]
        h_lead5_to_center[begin_index:end_index, internal_degree*(width*(length-move-1-i0)+0)+0:internal_degree*(width*(length-move-1-i0)+0)+internal_degree] = h01_for_lead_5.transpose().conj()[begin_index:end_index, begin_index:end_index]
        h_lead6_to_center[begin_index:end_index, internal_degree*(width*(i0+move)+0)+0:internal_degree*(width*(i0+move)+0)+internal_degree] = h01_for_lead_6.transpose().conj()[begin_index:end_index, begin_index:end_index]   
    self_energy1, gamma1 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_1, h01_for_lead_1, h_lead1_to_center)
    self_energy2, gamma2 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_2, h01_for_lead_1, h_lead2_to_center)
    self_energy3, gamma3 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_3, h01_for_lead_1, h_lead3_to_center)
    self_energy4, gamma4 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_4, h01_for_lead_1, h_lead4_to_center)
    self_energy5, gamma5 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_5, h01_for_lead_1, h_lead5_to_center)
    self_energy6, gamma6 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_6, h01_for_lead_1, h_lead6_to_center)
    gamma_array = [gamma1, gamma2, gamma3, gamma4, gamma5, gamma6]
    green = np.linalg.inv(fermi_energy*np.eye(internal_degree*width*length)-center_hamiltonian-self_energy1-self_energy2-self_energy3-self_energy4-self_energy5-self_energy6)
    return gamma_array, green

def calculate_six_terminal_transmission_matrix(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width=10, length=50, internal_degree=1, moving_step_of_leads=10):
    import numpy as np
    import guan
    gamma_array, green = guan.get_gamma_array_and_green_for_six_terminal_transmission(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width, length, internal_degree, moving_step_of_leads)
    transmission_matrix = np.zeros((6, 6), dtype=complex)
    channel_lead_4 = guan.calculate_conductance(fermi_energy, h00_for_lead_4, h01_for_lead_4, length=3)
    channel_lead_2 = guan.calculate_conductance(fermi_energy, h00_for_lead_2, h01_for_lead_2, length=3)
    for i0 in range(6):
        for j0 in range(6):
            if j0!=i0:
                transmission_matrix[i0, j0] = np.trace(np.dot(np.dot(np.dot(gamma_array[i0], green), gamma_array[j0]), green.transpose().conj()))
    for i0 in range(6):
        if i0 == 0 or i0 == 3:
            transmission_matrix[i0, i0] = channel_lead_4
        else:
            transmission_matrix[i0, i0] = channel_lead_2
    for i0 in range(6):
        for j0 in range(6):
            if j0!=i0:
                transmission_matrix[i0, i0] = transmission_matrix[i0, i0]-transmission_matrix[i0, j0]
    transmission_matrix = np.real(transmission_matrix)
    return transmission_matrix

def calculate_six_terminal_transmissions_from_lead_1(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width=10, length=50, internal_degree=1, moving_step_of_leads=10):
    import numpy as np
    import guan
    gamma_array, green = guan.get_gamma_array_and_green_for_six_terminal_transmission(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width, length, internal_degree, moving_step_of_leads)
    transmission_12 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[1]), green.transpose().conj())))
    transmission_13 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[2]), green.transpose().conj())))
    transmission_14 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[3]), green.transpose().conj())))
    transmission_15 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[4]), green.transpose().conj())))
    transmission_16 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[5]), green.transpose().conj())))
    return transmission_12, transmission_13, transmission_14, transmission_15, transmission_16

def if_active_channel(k_of_channel):
    import numpy as np
    if np.abs(np.imag(k_of_channel))<1e-6:
        if_active = 1
    else:
        if_active = 0
    return if_active

def get_k_and_velocity_of_channel(fermi_energy, h00, h01):
    import numpy as np
    import math
    import copy
    import guan
    if np.array(h00).shape==():
        dim = 1
    else:
        dim = np.array(h00).shape[0]
    transfer = guan.transfer_matrix(fermi_energy, h00, h01)
    eigenvalue, eigenvector = np.linalg.eig(transfer)
    k_of_channel = np.log(eigenvalue)/1j
    ind = np.argsort(np.real(k_of_channel))
    k_of_channel = np.sort(k_of_channel)
    temp = np.zeros((2*dim, 2*dim), dtype=complex)
    temp2 = np.zeros((2*dim), dtype=complex)
    i0 = 0
    for ind0 in ind:
        temp[:, i0] = eigenvector[:, ind0]
        temp2[i0] = eigenvalue[ind0]
        i0 += 1
    eigenvalue = copy.deepcopy(temp2)
    temp = temp[0:dim, :]
    factor = np.zeros(2*dim)
    for dim0 in range(dim):
        factor = factor+np.square(np.abs(temp[dim0, :]))
    for dim0 in range(2*dim):
        temp[:, dim0] = temp[:, dim0]/math.sqrt(factor[dim0])
    velocity_of_channel = np.zeros((2*dim), dtype=complex)
    for dim0 in range(2*dim):
        velocity_of_channel[dim0] = eigenvalue[dim0]*np.dot(np.dot(temp[0:dim, :].transpose().conj(), h01),temp[0:dim, :])[dim0, dim0]
    velocity_of_channel = -2*np.imag(velocity_of_channel)
    eigenvector = copy.deepcopy(temp) 
    return k_of_channel, velocity_of_channel, eigenvalue, eigenvector

def get_classified_k_velocity_u_and_f(fermi_energy, h00, h01):
    import numpy as np
    import guan
    if np.array(h00).shape==():
        dim = 1
    else:
        dim = np.array(h00).shape[0]
    k_of_channel, velocity_of_channel, eigenvalue, eigenvector = guan.get_k_and_velocity_of_channel(fermi_energy, h00, h01)
    ind_right_active = 0; ind_right_evanescent = 0; ind_left_active = 0; ind_left_evanescent = 0
    k_right = np.zeros(dim, dtype=complex); k_left = np.zeros(dim, dtype=complex)
    velocity_right = np.zeros(dim, dtype=complex); velocity_left = np.zeros(dim, dtype=complex)
    lambda_right = np.zeros(dim, dtype=complex); lambda_left = np.zeros(dim, dtype=complex)
    u_right = np.zeros((dim, dim), dtype=complex); u_left = np.zeros((dim, dim), dtype=complex)
    for dim0 in range(2*dim):
        if_active = guan.if_active_channel(k_of_channel[dim0])
        if guan.if_active_channel(k_of_channel[dim0]) == 1:
            direction = np.sign(velocity_of_channel[dim0])
        else:
            direction = np.sign(np.imag(k_of_channel[dim0]))
        if direction == 1:
            if if_active == 1:  # right-moving active channel
                k_right[ind_right_active] = k_of_channel[dim0]
                velocity_right[ind_right_active] = velocity_of_channel[dim0]
                lambda_right[ind_right_active] = eigenvalue[dim0]
                u_right[:, ind_right_active] = eigenvector[:, dim0]
                ind_right_active += 1
            else:               # right-moving evanescent channel
                k_right[dim-1-ind_right_evanescent] = k_of_channel[dim0]
                velocity_right[dim-1-ind_right_evanescent] = velocity_of_channel[dim0]
                lambda_right[dim-1-ind_right_evanescent] = eigenvalue[dim0]
                u_right[:, dim-1-ind_right_evanescent] = eigenvector[:, dim0]
                ind_right_evanescent += 1
        else:
            if if_active == 1:  # left-moving active channel
                k_left[ind_left_active] = k_of_channel[dim0]
                velocity_left[ind_left_active] = velocity_of_channel[dim0]
                lambda_left[ind_left_active] = eigenvalue[dim0]
                u_left[:, ind_left_active] = eigenvector[:, dim0]
                ind_left_active += 1
            else:               # left-moving evanescent channel
                k_left[dim-1-ind_left_evanescent] = k_of_channel[dim0]
                velocity_left[dim-1-ind_left_evanescent] = velocity_of_channel[dim0]
                lambda_left[dim-1-ind_left_evanescent] = eigenvalue[dim0]
                u_left[:, dim-1-ind_left_evanescent] = eigenvector[:, dim0]
                ind_left_evanescent += 1
    lambda_matrix_right = np.diag(lambda_right)
    lambda_matrix_left = np.diag(lambda_left)
    f_right = np.dot(np.dot(u_right, lambda_matrix_right), np.linalg.inv(u_right))
    f_left = np.dot(np.dot(u_left, lambda_matrix_left), np.linalg.inv(u_left))
    return k_right, k_left, velocity_right, velocity_left, f_right, f_left, u_right, u_left, ind_right_active

def calculate_scattering_matrix(fermi_energy, h00, h01, length=100):
    import numpy as np
    import math
    import copy
    import guan
    h01 = np.array(h01)
    if np.array(h00).shape==():
        dim = 1
    else:
        dim = np.array(h00).shape[0]
    k_right, k_left, velocity_right, velocity_left, f_right, f_left, u_right, u_left, ind_right_active = guan.get_classified_k_velocity_u_and_f(fermi_energy, h00, h01)
    right_self_energy = np.dot(h01, f_right)
    left_self_energy = np.dot(h01.transpose().conj(), np.linalg.inv(f_left))
    for i0 in range(length):
        if i0 == 0:
            green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
            green_00_n = copy.deepcopy(green_nn_n)
            green_0n_n = copy.deepcopy(green_nn_n)
            green_n0_n = copy.deepcopy(green_nn_n)
        elif i0 != length-1: 
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0) 
        else:
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
        green_00_n = guan.green_function_ii_n(green_00_n, green_0n_n, h01, green_nn_n, green_n0_n)
        green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
        green_n0_n = guan.green_function_ni_n(green_nn_n, h01, green_n0_n)
    temp = np.dot(h01.transpose().conj(), np.linalg.inv(f_right)-np.linalg.inv(f_left))
    transmission_matrix = np.dot(np.dot(np.linalg.inv(u_right), np.dot(green_n0_n, temp)), u_right) 
    reflection_matrix = np.dot(np.dot(np.linalg.inv(u_left), np.dot(green_00_n, temp)-np.identity(dim)), u_right)
    for dim0 in range(dim):
        for dim1 in range(dim):
            if_active = guan.if_active_channel(k_right[dim0])*guan.if_active_channel(k_right[dim1])
            if if_active == 1:
                transmission_matrix[dim0, dim1] = math.sqrt(np.abs(velocity_right[dim0]/velocity_right[dim1])) * transmission_matrix[dim0, dim1]
                reflection_matrix[dim0, dim1] = math.sqrt(np.abs(velocity_left[dim0]/velocity_right[dim1]))*reflection_matrix[dim0, dim1]
            else:
                transmission_matrix[dim0, dim1] = 0
                reflection_matrix[dim0, dim1] = 0
    sum_of_tran_refl_array = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)+np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
    for sum_of_tran_refl in sum_of_tran_refl_array:
        if sum_of_tran_refl > 1.001:
            print('Error Alert: scattering matrix is not normalized!')
    return transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active

def information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active):
    import numpy as np
    if np.array(transmission_matrix).shape==():
        dim = 1
    else:
        dim = np.array(transmission_matrix).shape[0]
    number_of_active_channels = ind_right_active
    number_of_evanescent_channels = dim-ind_right_active
    k_of_right_moving_active_channels = np.real(k_right[0:ind_right_active])
    k_of_left_moving_active_channels = np.real(k_left[0:ind_right_active])
    velocity_of_right_moving_active_channels = np.real(velocity_right[0:ind_right_active])
    velocity_of_left_moving_active_channels = np.real(velocity_left[0:ind_right_active])
    transmission_matrix_for_active_channels = np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active]))
    reflection_matrix_for_active_channels = np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active]))
    total_transmission_of_channels = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
    total_conductance = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])))
    total_reflection_of_channels = np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
    sum_of_transmission_and_reflection_of_channels = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0) + np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
    return number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels

def calculate_scattering_matrix_and_get_information(fermi_energy, h00, h01, length=100):
    import guan
    transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active = guan.calculate_scattering_matrix(fermi_energy, h00, h01, length=length)

    number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels = guan.information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active)

    return number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels

def print_or_write_scattering_matrix_with_information_of_scattering_matrix(number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels, print_show=1, write_file=0, filename='a', file_format='.txt'):
    if print_show == 1:
        print('\nActive channel (left or right) = ', number_of_active_channels)
        print('Evanescent channel (left or right) = ', number_of_evanescent_channels, '\n')
        print('K of right-moving active channels:\n', k_of_right_moving_active_channels)
        print('K of left-moving active channels:\n', k_of_left_moving_active_channels, '\n')
        print('Velocity of right-moving active channels:\n', velocity_of_right_moving_active_channels)
        print('Velocity of left-moving active channels:\n', velocity_of_left_moving_active_channels, '\n')
        print('Transmission matrix:\n', transmission_matrix_for_active_channels)
        print('Reflection matrix:\n', reflection_matrix_for_active_channels, '\n')
        print('Total transmission of channels:\n', total_transmission_of_channels)
        print('Total conductance = ', total_conductance, '\n')
        print('Total reflection of channels:\n', total_reflection_of_channels)
        print('Sum of transmission and reflection of channels:\n', sum_of_transmission_and_reflection_of_channels, '\n')
    if write_file == 1:
        with open(filename+file_format, 'w') as f:
            f.write('Active channel (left or right) = ' + str(number_of_active_channels) + '\n')
            f.write('Evanescent channel (left or right) = ' + str(number_of_evanescent_channels) + '\n\n')
            f.write('Channel               K                                     Velocity\n')
            for ind0 in range(number_of_active_channels):
                f.write('   '+str(ind0 + 1) + '   |    '+str(k_of_right_moving_active_channels[ind0])+'            ' + str(velocity_of_right_moving_active_channels[ind0])+'\n')
            f.write('\n')
            for ind0 in range(number_of_active_channels):
                f.write('  -' + str(ind0 + 1) + '   |    ' + str(k_of_left_moving_active_channels[ind0]) + '            ' + str(velocity_of_left_moving_active_channels[ind0]) + '\n')
            f.write('\nScattering matrix:\n              ')
            for ind0 in range(number_of_active_channels):
                f.write(str(ind0+1)+'               ')
            f.write('\n')
            for ind1 in range(number_of_active_channels):
                f.write('  '+str(ind1+1)+'    ')
                for ind2 in range(number_of_active_channels):
                    f.write('%f' % transmission_matrix_for_active_channels[ind1, ind2]+'    ')
                f.write('\n')
            f.write('\n')
            for ind1 in range(number_of_active_channels):
                f.write(' -'+str(ind1+1)+'    ')
                for ind2 in range(number_of_active_channels):
                    f.write('%f' % reflection_matrix_for_active_channels[ind1, ind2]+'    ')
                f.write('\n')
            f.write('\n')
            f.write('Total transmission of channels:\n'+str(total_transmission_of_channels)+'\n')
            f.write('Total conductance = '+str(total_conductance)+'\n')

def print_or_write_scattering_matrix(fermi_energy, h00, h01, length=100, print_show=1, write_file=0, filename='a', file_format='.txt'):
    import guan
    transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active = guan.calculate_scattering_matrix(fermi_energy, h00, h01, length=length)

    number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels = guan.information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active)

    guan.print_or_write_scattering_matrix_with_information_of_scattering_matrix(number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels, print_show=print_show, write_file=write_file, filename=filename, file_format=file_format)

def calculate_scattering_matrix_with_disorder(fermi_energy, h00, h01, length=100, disorder_intensity=2.0, disorder_concentration=1.0):
    import numpy as np
    import math
    import copy
    import guan
    h01 = np.array(h01)
    if np.array(h00).shape==():
        dim = 1
    else:
        dim = np.array(h00).shape[0]
    k_right, k_left, velocity_right, velocity_left, f_right, f_left, u_right, u_left, ind_right_active = guan.get_classified_k_velocity_u_and_f(fermi_energy, h00, h01)
    right_self_energy = np.dot(h01, f_right)
    left_self_energy = np.dot(h01.transpose().conj(), np.linalg.inv(f_left))
    for i0 in range(length):
        disorder = np.zeros((dim, dim))
        for dim0 in range(dim):
            if np.random.uniform(0, 1)<=disorder_concentration:
                disorder[dim0, dim0] = np.random.uniform(-disorder_intensity, disorder_intensity)
        if i0 == 0:
            green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
            green_00_n = copy.deepcopy(green_nn_n)
            green_0n_n = copy.deepcopy(green_nn_n)
            green_n0_n = copy.deepcopy(green_nn_n)
        elif i0 != length-1: 
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0) 
        else:
            green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
        green_00_n = guan.green_function_ii_n(green_00_n, green_0n_n, h01, green_nn_n, green_n0_n)
        green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
        green_n0_n = guan.green_function_ni_n(green_nn_n, h01, green_n0_n)
    temp = np.dot(h01.transpose().conj(), np.linalg.inv(f_right)-np.linalg.inv(f_left))
    transmission_matrix = np.dot(np.dot(np.linalg.inv(u_right), np.dot(green_n0_n, temp)), u_right) 
    reflection_matrix = np.dot(np.dot(np.linalg.inv(u_left), np.dot(green_00_n, temp)-np.identity(dim)), u_right)
    for dim0 in range(dim):
        for dim1 in range(dim):
            if_active = guan.if_active_channel(k_right[dim0])*guan.if_active_channel(k_right[dim1])
            if if_active == 1:
                transmission_matrix[dim0, dim1] = math.sqrt(np.abs(velocity_right[dim0]/velocity_right[dim1])) * transmission_matrix[dim0, dim1]
                reflection_matrix[dim0, dim1] = math.sqrt(np.abs(velocity_left[dim0]/velocity_right[dim1]))*reflection_matrix[dim0, dim1]
            else:
                transmission_matrix[dim0, dim1] = 0
                reflection_matrix[dim0, dim1] = 0
    sum_of_tran_refl_array = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)+np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
    for sum_of_tran_refl in sum_of_tran_refl_array:
        if sum_of_tran_refl > 1.001:
            print('Error Alert: scattering matrix is not normalized!')
    return transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active

def calculate_scattering_matrix_with_disorder_and_get_averaged_information(fermi_energy, h00, h01, length=100, disorder_intensity=2.0, disorder_concentration=1.0, calculation_times=1):
    import guan
    transmission_matrix_for_active_channels_averaged = 0
    reflection_matrix_for_active_channels_averaged = 0
    for i0 in range(calculation_times):
        transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active = guan.calculate_scattering_matrix_with_disorder(fermi_energy, h00, h01, length, disorder_intensity, disorder_concentration)

        number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels = guan.information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active)

        transmission_matrix_for_active_channels_averaged += transmission_matrix_for_active_channels
        reflection_matrix_for_active_channels_averaged += reflection_matrix_for_active_channels
    transmission_matrix_for_active_channels_averaged = transmission_matrix_for_active_channels_averaged/calculation_times
    reflection_matrix_for_active_channels_averaged = reflection_matrix_for_active_channels_averaged/calculation_times
    return transmission_matrix_for_active_channels_averaged, reflection_matrix_for_active_channels_averaged

def calculate_chern_number_for_square_lattice_with_efficient_method(hamiltonian_function, precision=100, print_show=0):
    import numpy as np
    import math
    import cmath
    import guan
    if np.array(hamiltonian_function(0, 0)).shape==():
        dim = 1
    else:
        dim = np.array(hamiltonian_function(0, 0)).shape[0]   
    delta = 2*math.pi/precision
    chern_number = np.zeros(dim, dtype=complex)
    for kx in np.arange(-math.pi, math.pi, delta):
        if print_show == 1:
            print(kx)
        for ky in np.arange(-math.pi, math.pi, delta):
            H = hamiltonian_function(kx, ky)
            vector = guan.calculate_eigenvector(H)
            H_delta_kx = hamiltonian_function(kx+delta, ky) 
            vector_delta_kx = guan.calculate_eigenvector(H_delta_kx)
            H_delta_ky = hamiltonian_function(kx, ky+delta)
            vector_delta_ky = guan.calculate_eigenvector(H_delta_ky)
            H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta)
            vector_delta_kx_ky = guan.calculate_eigenvector(H_delta_kx_ky)
            for i in range(dim):
                vector_i = vector[:, i]
                vector_delta_kx_i = vector_delta_kx[:, i]
                vector_delta_ky_i = vector_delta_ky[:, i]
                vector_delta_kx_ky_i = vector_delta_kx_ky[:, i]
                Ux = np.dot(np.conj(vector_i), vector_delta_kx_i)/abs(np.dot(np.conj(vector_i), vector_delta_kx_i))
                Uy = np.dot(np.conj(vector_i), vector_delta_ky_i)/abs(np.dot(np.conj(vector_i), vector_delta_ky_i))
                Ux_y = np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i))
                Uy_x = np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i))
                F = cmath.log(Ux*Uy_x*(1/Ux_y)*(1/Uy))
                chern_number[i] = chern_number[i] + F
    chern_number = chern_number/(2*math.pi*1j)
    return chern_number

def calculate_chern_number_for_square_lattice_with_efficient_method_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision=100, print_show=0): 
    import numpy as np
    import math
    import cmath
    delta = 2*math.pi/precision
    chern_number = 0
    for kx in np.arange(-math.pi, math.pi, delta):
        if print_show == 1:
            print(kx)
        for ky in np.arange(-math.pi, math.pi, delta):
            H = hamiltonian_function(kx, ky)
            eigenvalue, vector = np.linalg.eigh(H) 
            H_delta_kx = hamiltonian_function(kx+delta, ky) 
            eigenvalue, vector_delta_kx = np.linalg.eigh(H_delta_kx) 
            H_delta_ky = hamiltonian_function(kx, ky+delta)
            eigenvalue, vector_delta_ky = np.linalg.eigh(H_delta_ky) 
            H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta)
            eigenvalue, vector_delta_kx_ky = np.linalg.eigh(H_delta_kx_ky)
            dim = len(index_of_bands)
            det_value = 1
            # first dot product
            dot_matrix = np.zeros((dim , dim), dtype=complex)
            i0 = 0
            for dim1 in index_of_bands:
                j0 = 0
                for dim2 in index_of_bands:
                    dot_matrix[i0, j0] = np.dot(np.conj(vector[:, dim1]), vector_delta_kx[:, dim2])
                    j0 += 1
                i0 += 1
            dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
            det_value = det_value*dot_matrix
            # second dot product
            dot_matrix = np.zeros((dim , dim), dtype=complex)
            i0 = 0
            for dim1 in index_of_bands:
                j0 = 0
                for dim2 in index_of_bands:
                    dot_matrix[i0, j0] = np.dot(np.conj(vector_delta_kx[:, dim1]), vector_delta_kx_ky[:, dim2])
                    j0 += 1
                i0 += 1
            dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
            det_value = det_value*dot_matrix
            # third dot product
            dot_matrix = np.zeros((dim , dim), dtype=complex)
            i0 = 0
            for dim1 in index_of_bands:
                j0 = 0
                for dim2 in index_of_bands:
                    dot_matrix[i0, j0] = np.dot(np.conj(vector_delta_kx_ky[:, dim1]), vector_delta_ky[:, dim2])
                    j0 += 1
                i0 += 1
            dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
            det_value = det_value*dot_matrix
            # four dot product
            dot_matrix = np.zeros((dim , dim), dtype=complex)
            i0 = 0
            for dim1 in index_of_bands:
                j0 = 0
                for dim2 in index_of_bands:
                    dot_matrix[i0, j0] = np.dot(np.conj(vector_delta_ky[:, dim1]), vector[:, dim2])
                    j0 += 1
                i0 += 1
            dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
            det_value= det_value*dot_matrix
            chern_number += cmath.log(det_value)
    chern_number = chern_number/(2*math.pi*1j)
    return chern_number

def calculate_chern_number_for_square_lattice_with_wilson_loop(hamiltonian_function, precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0):
    import numpy as np
    import math
    delta = 2*math.pi/precision_of_plaquettes
    chern_number = 0
    for kx in np.arange(-math.pi, math.pi, delta):
        if print_show == 1:
            print(kx)
        for ky in np.arange(-math.pi, math.pi, delta):
            vector_array = []
            # line_1
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx+delta/precision_of_wilson_loop*i0, ky) 
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            # line_2
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_wilson_loop*i0)  
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            # line_3
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx+delta-delta/precision_of_wilson_loop*i0, ky+delta)  
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            # line_4
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_wilson_loop*i0)  
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            wilson_loop = 1
            for i0 in range(len(vector_array)-1):
                wilson_loop = wilson_loop*np.dot(vector_array[i0].transpose().conj(), vector_array[i0+1])
            wilson_loop = wilson_loop*np.dot(vector_array[len(vector_array)-1].transpose().conj(), vector_array[0])
            arg = np.log(np.diagonal(wilson_loop))/1j
            chern_number = chern_number + arg
    chern_number = chern_number/(2*math.pi)
    return chern_number

def calculate_chern_number_for_square_lattice_with_wilson_loop_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0):
    import numpy as np
    import math
    delta = 2*math.pi/precision_of_plaquettes
    chern_number = 0
    for kx in np.arange(-math.pi, math.pi, delta):
        if print_show == 1:
            print(kx)
        for ky in np.arange(-math.pi, math.pi, delta):
            vector_array = []
            # line_1
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx+delta/precision_of_wilson_loop*i0, ky) 
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            # line_2
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_wilson_loop*i0)  
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            # line_3
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx+delta-delta/precision_of_wilson_loop*i0, ky+delta)  
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            # line_4
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_wilson_loop*i0)  
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)           
            wilson_loop = 1
            dim = len(index_of_bands)
            for i0 in range(len(vector_array)-1):
                dot_matrix = np.zeros((dim , dim), dtype=complex)
                i01 = 0
                for dim1 in index_of_bands:
                    i02 = 0
                    for dim2 in index_of_bands:
                        dot_matrix[i01, i02] = np.dot(vector_array[i0][:, dim1].transpose().conj(), vector_array[i0+1][:, dim2])
                        i02 += 1
                    i01 += 1
                det_value = np.linalg.det(dot_matrix)
                wilson_loop = wilson_loop*det_value
            dot_matrix_plus = np.zeros((dim , dim), dtype=complex)
            i01 = 0
            for dim1 in index_of_bands:
                i02 = 0
                for dim2 in index_of_bands:
                    dot_matrix_plus[i01, i02] = np.dot(vector_array[len(vector_array)-1][:, dim1].transpose().conj(), vector_array[0][:, dim2])
                    i02 += 1
                i01 += 1
            det_value = np.linalg.det(dot_matrix_plus)
            wilson_loop = wilson_loop*det_value
            arg = np.log(wilson_loop)/1j
            chern_number = chern_number + arg
    chern_number = chern_number/(2*math.pi)
    return chern_number

def calculate_berry_curvature_with_efficient_method(hamiltonian_function, k_min='default', k_max='default', precision=100, print_show=0):
    import numpy as np
    import cmath
    import guan
    import math
    if k_min == 'default':
        k_min = -math.pi
    if k_max == 'default':
        k_max=math.pi
    if np.array(hamiltonian_function(0, 0)).shape==():
        dim = 1
    else:
        dim = np.array(hamiltonian_function(0, 0)).shape[0]   
    delta = (k_max-k_min)/precision
    k_array = np.arange(k_min, k_max, delta)
    berry_curvature_array = np.zeros((k_array.shape[0], k_array.shape[0], dim), dtype=complex)
    i0 = 0
    for kx in k_array:
        if print_show == 1:
            print(kx)
        j0 = 0
        for ky in k_array:
            H = hamiltonian_function(kx, ky)
            vector = guan.calculate_eigenvector(H)
            H_delta_kx = hamiltonian_function(kx+delta, ky) 
            vector_delta_kx = guan.calculate_eigenvector(H_delta_kx)
            H_delta_ky = hamiltonian_function(kx, ky+delta)
            vector_delta_ky = guan.calculate_eigenvector(H_delta_ky)
            H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta)
            vector_delta_kx_ky = guan.calculate_eigenvector(H_delta_kx_ky)
            for i in range(dim):
                vector_i = vector[:, i]
                vector_delta_kx_i = vector_delta_kx[:, i]
                vector_delta_ky_i = vector_delta_ky[:, i]
                vector_delta_kx_ky_i = vector_delta_kx_ky[:, i]
                Ux = np.dot(np.conj(vector_i), vector_delta_kx_i)/abs(np.dot(np.conj(vector_i), vector_delta_kx_i))
                Uy = np.dot(np.conj(vector_i), vector_delta_ky_i)/abs(np.dot(np.conj(vector_i), vector_delta_ky_i))
                Ux_y = np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i))
                Uy_x = np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i))
                berry_curvature = cmath.log(Ux*Uy_x*(1/Ux_y)*(1/Uy))/delta/delta*1j
                berry_curvature_array[j0, i0, i] = berry_curvature
            j0 += 1
        i0 += 1
    return k_array, berry_curvature_array

def calculate_berry_curvature_with_efficient_method_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], k_min='default', k_max='default', precision=100, print_show=0):
    import numpy as np
    import cmath
    import math
    if k_min == 'default':
        k_min = -math.pi
    if k_max == 'default':
        k_max=math.pi
    delta = (k_max-k_min)/precision
    k_array = np.arange(k_min, k_max, delta)
    berry_curvature_array = np.zeros((k_array.shape[0], k_array.shape[0]), dtype=complex)
    i00 = 0
    for kx in np.arange(k_min, k_max, delta):
        if print_show == 1:
            print(kx)
        j00 = 0
        for ky in np.arange(k_min, k_max, delta):
            H = hamiltonian_function(kx, ky)
            eigenvalue, vector = np.linalg.eigh(H) 
            H_delta_kx = hamiltonian_function(kx+delta, ky) 
            eigenvalue, vector_delta_kx = np.linalg.eigh(H_delta_kx) 
            H_delta_ky = hamiltonian_function(kx, ky+delta)
            eigenvalue, vector_delta_ky = np.linalg.eigh(H_delta_ky) 
            H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta)
            eigenvalue, vector_delta_kx_ky = np.linalg.eigh(H_delta_kx_ky)
            dim = len(index_of_bands)
            det_value = 1
            # first dot product
            dot_matrix = np.zeros((dim , dim), dtype=complex)
            i0 = 0
            for dim1 in index_of_bands:
                j0 = 0
                for dim2 in index_of_bands:
                    dot_matrix[i0, j0] = np.dot(np.conj(vector[:, dim1]), vector_delta_kx[:, dim2])
                    j0 += 1
                i0 += 1
            dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
            det_value = det_value*dot_matrix
            # second dot product
            dot_matrix = np.zeros((dim , dim), dtype=complex)
            i0 = 0
            for dim1 in index_of_bands:
                j0 = 0
                for dim2 in index_of_bands:
                    dot_matrix[i0, j0] = np.dot(np.conj(vector_delta_kx[:, dim1]), vector_delta_kx_ky[:, dim2])
                    j0 += 1
                i0 += 1
            dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
            det_value = det_value*dot_matrix
            # third dot product
            dot_matrix = np.zeros((dim , dim), dtype=complex)
            i0 = 0
            for dim1 in index_of_bands:
                j0 = 0
                for dim2 in index_of_bands:
                    dot_matrix[i0, j0] = np.dot(np.conj(vector_delta_kx_ky[:, dim1]), vector_delta_ky[:, dim2])
                    j0 += 1
                i0 += 1
            dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
            det_value = det_value*dot_matrix
            # four dot product
            dot_matrix = np.zeros((dim , dim), dtype=complex)
            i0 = 0
            for dim1 in index_of_bands:
                j0 = 0
                for dim2 in index_of_bands:
                    dot_matrix[i0, j0] = np.dot(np.conj(vector_delta_ky[:, dim1]), vector[:, dim2])
                    j0 += 1
                i0 += 1
            dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
            det_value= det_value*dot_matrix
            berry_curvature = cmath.log(det_value)/delta/delta*1j
            berry_curvature_array[j00, i00] = berry_curvature
            j00 += 1
        i00 += 1
    return k_array, berry_curvature_array

def calculate_berry_curvature_with_wilson_loop(hamiltonian_function, k_min='default', k_max='default', precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0):
    import numpy as np
    import math
    if k_min == 'default':
        k_min = -math.pi
    if k_max == 'default':
        k_max=math.pi
    if np.array(hamiltonian_function(0, 0)).shape==():
        dim = 1
    else:
        dim = np.array(hamiltonian_function(0, 0)).shape[0]   
    delta = (k_max-k_min)/precision_of_plaquettes
    k_array = np.arange(k_min, k_max, delta)
    berry_curvature_array = np.zeros((k_array.shape[0], k_array.shape[0], dim), dtype=complex)
    i00 = 0
    for kx in k_array:
        if print_show == 1:
            print(kx)
        j00 = 0
        for ky in k_array:
            vector_array = []
            # line_1
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx+delta/precision_of_wilson_loop*i0, ky) 
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            # line_2
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_wilson_loop*i0)  
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            # line_3
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx+delta-delta/precision_of_wilson_loop*i0, ky+delta)  
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            # line_4
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_wilson_loop*i0)  
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            wilson_loop = 1
            for i0 in range(len(vector_array)-1):
                wilson_loop = wilson_loop*np.dot(vector_array[i0].transpose().conj(), vector_array[i0+1])
            wilson_loop = wilson_loop*np.dot(vector_array[len(vector_array)-1].transpose().conj(), vector_array[0])
            berry_curvature = np.log(np.diagonal(wilson_loop))/delta/delta*1j
            berry_curvature_array[j00, i00, :]=berry_curvature
            j00 += 1
        i00 += 1
    return k_array, berry_curvature_array

def calculate_berry_curvature_with_wilson_loop_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], k_min='default', k_max='default', precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0):
    import numpy as np
    import math
    if k_min == 'default':
        k_min = -math.pi
    if k_max == 'default':
        k_max=math.pi
    delta = (k_max-k_min)/precision_of_plaquettes
    k_array = np.arange(k_min, k_max, delta)
    berry_curvature_array = np.zeros((k_array.shape[0], k_array.shape[0]), dtype=complex)
    i000 = 0
    for kx in k_array:
        if print_show == 1:
            print(kx)
        j000 = 0
        for ky in k_array:
            vector_array = []
            # line_1
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx+delta/precision_of_wilson_loop*i0, ky) 
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            # line_2
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_wilson_loop*i0)  
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            # line_3
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx+delta-delta/precision_of_wilson_loop*i0, ky+delta)  
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)
            # line_4
            for i0 in range(precision_of_wilson_loop):
                H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_wilson_loop*i0)  
                eigenvalue, eigenvector = np.linalg.eig(H_delta)
                vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
                vector_array.append(vector_delta)           
            wilson_loop = 1
            dim = len(index_of_bands)
            for i0 in range(len(vector_array)-1):
                dot_matrix = np.zeros((dim , dim), dtype=complex)
                i01 = 0
                for dim1 in index_of_bands:
                    i02 = 0
                    for dim2 in index_of_bands:
                        dot_matrix[i01, i02] = np.dot(vector_array[i0][:, dim1].transpose().conj(), vector_array[i0+1][:, dim2])
                        i02 += 1
                    i01 += 1
                det_value = np.linalg.det(dot_matrix)
                wilson_loop = wilson_loop*det_value
            dot_matrix_plus = np.zeros((dim , dim), dtype=complex)
            i01 = 0
            for dim1 in index_of_bands:
                i02 = 0
                for dim2 in index_of_bands:
                    dot_matrix_plus[i01, i02] = np.dot(vector_array[len(vector_array)-1][:, dim1].transpose().conj(), vector_array[0][:, dim2])
                    i02 += 1
                i01 += 1
            det_value = np.linalg.det(dot_matrix_plus)
            wilson_loop = wilson_loop*det_value
            berry_curvature = np.log(wilson_loop)/delta/delta*1j
            berry_curvature_array[j000, i000]=berry_curvature
            j000 += 1
        i000 += 1
    return k_array, berry_curvature_array

def calculate_chern_number_for_honeycomb_lattice(hamiltonian_function, a=1, precision=300, print_show=0):
    import numpy as np
    import math
    import cmath
    import guan
    if np.array(hamiltonian_function(0, 0)).shape==():
        dim = 1
    else:
        dim = np.array(hamiltonian_function(0, 0)).shape[0]   
    chern_number = np.zeros(dim, dtype=complex)
    L1 = 4*math.sqrt(3)*math.pi/9/a
    L2 = 2*math.sqrt(3)*math.pi/9/a
    L3 = 2*math.pi/3/a
    delta1 = 2*L1/precision
    delta3 = 2*L3/precision
    for kx in np.arange(-L1, L1, delta1):
        if print_show == 1:
            print(kx)
        for ky in np.arange(-L3, L3, delta3):
            if (-L2<=kx<=L2) or (kx>L2 and -(L1-kx)*math.tan(math.pi/3)<=ky<=(L1-kx)*math.tan(math.pi/3)) or (kx<-L2 and  -(kx-(-L1))*math.tan(math.pi/3)<=ky<=(kx-(-L1))*math.tan(math.pi/3)):
                H = hamiltonian_function(kx, ky)
                vector = guan.calculate_eigenvector(H)
                H_delta_kx = hamiltonian_function(kx+delta1, ky) 
                vector_delta_kx = guan.calculate_eigenvector(H_delta_kx)
                H_delta_ky = hamiltonian_function(kx, ky+delta3)
                vector_delta_ky = guan.calculate_eigenvector(H_delta_ky)
                H_delta_kx_ky = hamiltonian_function(kx+delta1, ky+delta3)
                vector_delta_kx_ky = guan.calculate_eigenvector(H_delta_kx_ky)
                for i in range(dim):
                    vector_i = vector[:, i]
                    vector_delta_kx_i = vector_delta_kx[:, i]
                    vector_delta_ky_i = vector_delta_ky[:, i]
                    vector_delta_kx_ky_i = vector_delta_kx_ky[:, i]
                    Ux = np.dot(np.conj(vector_i), vector_delta_kx_i)/abs(np.dot(np.conj(vector_i), vector_delta_kx_i))
                    Uy = np.dot(np.conj(vector_i), vector_delta_ky_i)/abs(np.dot(np.conj(vector_i), vector_delta_ky_i))
                    Ux_y = np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i))
                    Uy_x = np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i))
                    F = cmath.log(Ux*Uy_x*(1/Ux_y)*(1/Uy))
                    chern_number[i] = chern_number[i] + F
    chern_number = chern_number/(2*math.pi*1j)
    return chern_number

def calculate_wilson_loop(hamiltonian_function, k_min='default', k_max='default', precision=100, print_show=0):
    import numpy as np
    import guan
    import math
    if k_min == 'default':
        k_min = -math.pi
    if k_max == 'default':
        k_max=math.pi
    k_array = np.linspace(k_min, k_max, precision)
    dim = np.array(hamiltonian_function(0)).shape[0]
    wilson_loop_array = np.ones(dim, dtype=complex)
    for i in range(dim):
        if print_show == 1:
            print(i)
        eigenvector_array = []
        for k in k_array:
            eigenvector  = guan.calculate_eigenvector(hamiltonian_function(k))  
            if k != k_max:
                eigenvector_array.append(eigenvector[:, i])
            else:
                eigenvector_array.append(eigenvector_array[0])
        for i0 in range(precision-1):
            F = np.dot(eigenvector_array[i0+1].transpose().conj(), eigenvector_array[i0])
            wilson_loop_array[i] = np.dot(F, wilson_loop_array[i])
    return wilson_loop_array

def fully_connected_neural_network_with_one_hidden_layer(input_size=1, hidden_size=10, output_size=1, activation='relu'):
    import torch
    global model_class_of_fully_connected_neural_network_with_one_hidden_layer
    class model_class_of_fully_connected_neural_network_with_one_hidden_layer(torch.nn.Module):
        def __init__(self, input_size, hidden_size, output_size, activation):
            super().__init__()
            self.hidden_layer = torch.nn.Linear(input_size, hidden_size)
            self.output_layer = torch.nn.Linear(hidden_size, output_size)
            self.activation = activation
        def forward(self, x):
            if self.activation == 'relu':
                hidden_output = torch.nn.functional.relu(self.hidden_layer(x))
            elif self.activation == 'leaky_relu':
                hidden_output = torch.nn.functional.leaky_relu(self.hidden_layer(x))
            elif self.activation == 'sigmoid':
                hidden_output = torch.nn.functional.sigmoid(self.hidden_layer(x))
            elif self.activation == 'tanh':
                hidden_output = torch.nn.functional.tanh(self.hidden_layer(x))
            elif self.activation == 'gelu':
                hidden_output = torch.nn.functional.gelu(self.hidden_layer(x))
            elif self.activation == 'silu':
                hidden_output = torch.nn.functional.silu(self.hidden_layer(x))
            else:
                hidden_output = self.hidden_layer(x)
            output = self.output_layer(hidden_output)
            return output
    model = model_class_of_fully_connected_neural_network_with_one_hidden_layer(input_size, hidden_size, output_size, activation)
    return model

def fully_connected_neural_network_with_two_hidden_layers(input_size=1, hidden_size_1=10, hidden_size_2=10, output_size=1, activation_1='relu', activation_2='relu'):
    import torch
    global model_class_of_fully_connected_neural_network_with_two_hidden_layers
    class model_class_of_fully_connected_neural_network_with_two_hidden_layers(torch.nn.Module):
        def __init__(self, input_size, hidden_size_1, hidden_size_2, output_size, activation_1, activation_2):
            super().__init__()
            self.hidden_layer_1 = torch.nn.Linear(input_size, hidden_size_1)
            self.hidden_layer_2 = torch.nn.Linear(hidden_size_1, hidden_size_2)
            self.output_layer = torch.nn.Linear(hidden_size_2, output_size)
            self.activation_1 = activation_1
            self.activation_2 = activation_2
        def forward(self, x):
            if self.activation_1 == 'relu':
                hidden_output_1 = torch.nn.functional.relu(self.hidden_layer_1(x))
            elif self.activation_1 == 'leaky_relu':
                hidden_output_1 = torch.nn.functional.leaky_relu(self.hidden_layer_1(x))
            elif self.activation_1 == 'sigmoid':
                hidden_output_1 = torch.nn.functional.sigmoid(self.hidden_layer_1(x))
            elif self.activation_1 == 'tanh':
                hidden_output_1 = torch.nn.functional.tanh(self.hidden_layer_1(x))
            elif self.activation_1 == 'gelu':
                hidden_output_1 = torch.nn.functional.gelu(self.hidden_layer_1(x))
            elif self.activation_1 == 'silu':
                hidden_output_1 = torch.nn.functional.silu(self.hidden_layer_1(x))
            else:
                hidden_output_1 = self.hidden_layer_1(x)
            
            if self.activation_2 == 'relu':
                hidden_output_2 = torch.nn.functional.relu(self.hidden_layer_2(hidden_output_1))
            elif self.activation_2 == 'leaky_relu':
                hidden_output_2 = torch.nn.functional.leaky_relu(self.hidden_layer_2(hidden_output_1))
            elif self.activation_2 == 'sigmoid':
                hidden_output_2 = torch.nn.functional.sigmoid(self.hidden_layer_2(hidden_output_1))
            elif self.activation_2 == 'tanh':
                hidden_output_2 = torch.nn.functional.tanh(self.hidden_layer_2(hidden_output_1))
            elif self.activation_2 == 'gelu':
                hidden_output_2 = torch.nn.functional.gelu(self.hidden_layer_2(hidden_output_1))
            elif self.activation_2 == 'silu':
                hidden_output_2 = torch.nn.functional.silu(self.hidden_layer_2(hidden_output_1))
            else:
                hidden_output_2 = self.hidden_layer_2(hidden_output_1)
            
            output = self.output_layer(hidden_output_2)
            return output
    model = model_class_of_fully_connected_neural_network_with_two_hidden_layers(input_size, hidden_size_1, hidden_size_2, output_size, activation_1, activation_2)
    return model

def fully_connected_neural_network_with_three_hidden_layers(input_size=1, hidden_size_1=10, hidden_size_2=10, hidden_size_3=10, output_size=1, activation_1='relu', activation_2='relu', activation_3='relu'):
    import torch
    global model_class_of_fully_connected_neural_network_with_three_hidden_layers
    class model_class_of_fully_connected_neural_network_with_three_hidden_layers(torch.nn.Module):
        def __init__(self, input_size, hidden_size_1, hidden_size_2, hidden_size_3, output_size, activation_1, activation_2, activation_3):
            super().__init__()
            self.hidden_layer_1 = torch.nn.Linear(input_size, hidden_size_1)
            self.hidden_layer_2 = torch.nn.Linear(hidden_size_1, hidden_size_2)
            self.hidden_layer_3 = torch.nn.Linear(hidden_size_2, hidden_size_3)
            self.output_layer = torch.nn.Linear(hidden_size_3, output_size)
            self.activation_1 = activation_1
            self.activation_2 = activation_2
            self.activation_3 = activation_3
        def forward(self, x):
            if self.activation_1 == 'relu':
                hidden_output_1 = torch.nn.functional.relu(self.hidden_layer_1(x))
            elif self.activation_1 == 'leaky_relu':
                hidden_output_1 = torch.nn.functional.leaky_relu(self.hidden_layer_1(x))
            elif self.activation_1 == 'sigmoid':
                hidden_output_1 = torch.nn.functional.sigmoid(self.hidden_layer_1(x))
            elif self.activation_1 == 'tanh':
                hidden_output_1 = torch.nn.functional.tanh(self.hidden_layer_1(x))
            elif self.activation_1 == 'gelu':
                hidden_output_1 = torch.nn.functional.gelu(self.hidden_layer_1(x))
            elif self.activation_1 == 'silu':
                hidden_output_1 = torch.nn.functional.silu(self.hidden_layer_1(x))
            else:
                hidden_output_1 = self.hidden_layer_1(x)
            
            if self.activation_2 == 'relu':
                hidden_output_2 = torch.nn.functional.relu(self.hidden_layer_2(hidden_output_1))
            elif self.activation_2 == 'leaky_relu':
                hidden_output_2 = torch.nn.functional.leaky_relu(self.hidden_layer_2(hidden_output_1))
            elif self.activation_2 == 'sigmoid':
                hidden_output_2 = torch.nn.functional.sigmoid(self.hidden_layer_2(hidden_output_1))
            elif self.activation_2 == 'tanh':
                hidden_output_2 = torch.nn.functional.tanh(self.hidden_layer_2(hidden_output_1))
            elif self.activation_2 == 'gelu':
                hidden_output_2 = torch.nn.functional.gelu(self.hidden_layer_2(hidden_output_1))
            elif self.activation_2 == 'silu':
                hidden_output_2 = torch.nn.functional.silu(self.hidden_layer_2(hidden_output_1))
            else:
                hidden_output_2 = self.hidden_layer_2(hidden_output_1)

            if self.activation_3 == 'relu':
                hidden_output_3 = torch.nn.functional.relu(self.hidden_layer_3(hidden_output_2))
            elif self.activation_3 == 'leaky_relu':
                hidden_output_3 = torch.nn.functional.leaky_relu(self.hidden_layer_3(hidden_output_2))
            elif self.activation_3 == 'sigmoid':
                hidden_output_3 = torch.nn.functional.sigmoid(self.hidden_layer_3(hidden_output_2))
            elif self.activation_3 == 'tanh':
                hidden_output_3 = torch.nn.functional.tanh(self.hidden_layer_3(hidden_output_2))
            elif self.activation_3 == 'gelu':
                hidden_output_3 = torch.nn.functional.gelu(self.hidden_layer_3(hidden_output_2))
            elif self.activation_3 == 'silu':
                hidden_output_3 = torch.nn.functional.silu(self.hidden_layer_3(hidden_output_2))
            else:
                hidden_output_3 = self.hidden_layer_3(hidden_output_2)
            
            output = self.output_layer(hidden_output_3)
            return output
    model = model_class_of_fully_connected_neural_network_with_three_hidden_layers(input_size, hidden_size_1, hidden_size_2, hidden_size_3, output_size, activation_1, activation_2, activation_3)
    return model

def convolutional_neural_network_with_two_convolutional_layers_and_two_fully_connected_layers(in_channels=1, out_channels_1=10, out_channels_2=10, kernel_size_1=3, kernel_size_2=3, stride_1=1, stride_2=1, padding_1=0, padding_2=0, pooling=1, pooling_kernel_size=2, pooling_stride=2, input_size=1, hidden_size_1=10, hidden_size_2=10, output_size=1):
    import torch
    global model_class_of_convolutional_neural_network_with_two_convolutional_layers_and_two_fully_connected_layers
    class model_class_of_convolutional_neural_network_with_two_convolutional_layers_and_two_fully_connected_layers(torch.nn.Module):
        def __init__(self, in_channels, out_channels_1, out_channels_2, kernel_size_1, kernel_size_2, stride_1, stride_2, padding_1, padding_2, pooling, pooling_kernel_size, pooling_stride, input_size, hidden_size_1, hidden_size_2, output_size):
            super().__init__()
            self.convolutional_layer_1 = torch.nn.Conv2d(in_channels=in_channels, out_channels=out_channels_1, kernel_size=kernel_size_1, stride=stride_1, padding=padding_1)
            self.convolutional_layer_2 = torch.nn.Conv2d(in_channels=out_channels_1, out_channels=out_channels_2, kernel_size=kernel_size_2, stride=stride_2, padding=padding_2)
            self.pooling_layer = torch.nn.MaxPool2d(kernel_size=pooling_kernel_size, stride=pooling_stride)
            self.hidden_layer_1 = torch.nn.Linear(input_size, hidden_size_1)
            self.hidden_layer_2 = torch.nn.Linear(hidden_size_1, hidden_size_2)
            self.output_layer = torch.nn.Linear(hidden_size_2, output_size)
            self.pooling = pooling
        def forward(self, x):
            if self.pooling == 1:
                channel_output_1 = torch.nn.functional.relu(self.pooling_layer(self.convolutional_layer_1(x))) 
                channel_output_2 = torch.nn.functional.relu(self.pooling_layer(self.convolutional_layer_2(channel_output_1)))
            else:
                channel_output_1 = torch.nn.functional.relu(self.convolutional_layer_1(x)) 
                channel_output_2 = torch.nn.functional.relu(self.convolutional_layer_2(channel_output_1))
            channel_output_2 = torch.flatten(channel_output_2, 1)
            hidden_output_1 = torch.nn.functional.relu(self.hidden_layer_1(channel_output_2))
            hidden_output_2 = torch.nn.functional.relu(self.hidden_layer_2(hidden_output_1))
            output = self.output_layer(hidden_output_2)
            return output
    model = model_class_of_convolutional_neural_network_with_two_convolutional_layers_and_two_fully_connected_layers(in_channels, out_channels_1, out_channels_2, kernel_size_1, kernel_size_2, stride_1, stride_2, padding_1, padding_2, pooling, pooling_kernel_size, pooling_stride, input_size, hidden_size_1, hidden_size_2, output_size)
    return model

def get_break_signal_from_loss_array(loss_array, patience=100, min_delta=0.001):
    break_signal = 0
    counter = 0
    num = len(loss_array)
    for i0 in range(num):
        if i0 != 0:
            if abs(loss_array[i0]-loss_array[i0-1])<min_delta:
                counter += 1
    if counter >= patience:
        break_signal = 1
    return break_signal

def train_model(model, x_data, y_data, optimizer='Adam', learning_rate=0.001, criterion='MSELoss', num_epochs=1000, print_show=1, early_stop=0, patience=100, min_delta=0.001):
    import torch
    if optimizer == 'Adam':
        optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)
    elif optimizer == 'SGD':
        optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)
    
    if criterion == 'MSELoss':
        criterion = torch.nn.MSELoss()
    elif criterion == 'CrossEntropyLoss':
        criterion = torch.nn.CrossEntropyLoss()
    loss_array = []
    for epoch in range(num_epochs):
        output = model.forward(x_data)
        loss = criterion(output, y_data)
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()
        loss_array.append(loss.item())
        if print_show == 1:
            if (epoch + 1) % 100 == 0:
                print(epoch, loss.item())
        if early_stop == 1:
            import guan
            break_signal = guan.get_break_signal_from_loss_array(loss_array, patience=patience, min_delta=min_delta)
            if break_signal:
                break
    return model, loss_array

def batch_train_model(model, train_loader, optimizer='Adam', learning_rate=0.001, criterion='MSELoss', num_epochs=1000, print_show=1, more_loss_data=0, early_stop=0, patience=100, min_delta=0.001):
    import torch
    if optimizer == 'Adam':
        optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)
    elif optimizer == 'SGD':
        optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)
    
    if criterion == 'MSELoss':
        criterion = torch.nn.MSELoss()
    elif criterion == 'CrossEntropyLoss':
        criterion = torch.nn.CrossEntropyLoss()
    loss_array = []
    losses = []
    for epoch in range(num_epochs):
        for batch_x, batch_y in train_loader:
            output = model.forward(batch_x)
            loss = criterion(output, batch_y)
            optimizer.zero_grad()
            loss.backward()
            optimizer.step()
            losses.append(loss.item())
        loss_array.append(loss.item())
        if print_show == 1:
            if (epoch + 1) % 100 == 0:
                print(epoch, loss.item())
        if early_stop == 1:
            import guan
            break_signal = guan.get_break_signal_from_loss_array(loss_array, patience=patience, min_delta=min_delta)
            if break_signal:
                break
    if more_loss_data == 0:
        return model, loss_array
    else:
        return model, losses

def save_model_parameters(model, filename='./model_parameters.pth'):
    import torch
    torch.save(model.state_dict(), filename)

def save_model(model, filename='./model.pth'):
    import torch
    torch.save(model, filename)

def save_model_with_torch_jit_script(model, filename='model_scripted_with_torch_jit.pth'):
    import torch
    scripted_model = torch.jit.script(model)
    scripted_model.save(filename)

def save_model_with_all_information(model, model_class, model_instantiation, note='', filename='./model_with_all_information.pth'):
    import torch
    import guan
    model_class_source = guan.get_source(name=model_class)
    model_class_source = 'import torch\n'+model_class_source
    model_instantiation_source = guan.get_source(name=model_instantiation)
    checkpoint = {'model_state_dict': model.state_dict(),
                  'model_class_name': model_class.__name__,
                  'model_class_source': model_class_source,
                  'model_instantiation_name':model_instantiation.__name__,
                  'model_instantiation_source': model_instantiation_source,
                  'note': note,}
    torch.save(checkpoint, filename)

def load_model_parameters(model, filename='./model_parameters.pth'):
    import torch
    model.load_state_dict(torch.load(filename))
    return model

def load_model(filename='./model.pth'):
    import torch
    model = torch.load(filename)
    return model

def load_model_with_torch_jit_script(filename='model_scripted_with_torch_jit.pth'):
    import torch
    scripted_model = torch.jit.load(filename)
    return scripted_model

def load_model_with_all_information(filename='./model_with_all_information.pth', note_print=0):
    import torch
    checkpoint = torch.load(filename)
    model_class_source = checkpoint['model_class_source']
    exec(model_class_source, globals())
    # model_class_name = checkpoint['model_class_name']
    # model_class = globals()[model_class_name]
    model_instantiation_source = checkpoint['model_instantiation_source']
    exec(model_instantiation_source, globals())
    model_instantiation_name = checkpoint['model_instantiation_name']
    model_instantiation = globals()[model_instantiation_name]
    model = model_instantiation()
    model.load_state_dict(checkpoint['model_state_dict'])
    if note_print==1:
        note = checkpoint['note']
        print(note)
    return model

def load_train_data(x_train, y_train, batch_size=32):
    from torch.utils.data import DataLoader, TensorDataset
    train_dataset = TensorDataset(x_train, y_train)
    train_loader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)
    return train_loader

def load_input_data_and_output_data_as_torch_tensors_with_pickle(index_range=[1, 2, 3], directory='./', input_filename='input_index=', output_filename='output_index=', type=None):
    import guan
    import numpy as np
    import torch
    input_data = []
    for index in index_range:
        input = guan.load_data(filename=directory+input_filename+str(index))
        input_data.append(input)
    output_data = []
    for index in index_range:
        output = guan.load_data(filename=directory+output_filename+str(index))
        output_data.append(output)
    if type == None:
        input_data = np.array(input_data)
        output_data= np.array(output_data)
    else:
        input_data = np.array(input_data).astype(type)
        output_data= np.array(output_data).astype(type)
    input_data = torch.from_numpy(input_data)
    output_data = torch.from_numpy(output_data)
    return input_data, output_data

def load_input_data_and_output_data_as_torch_tensors_with_pickle_from_array_file(input_filename='input_file', output_filename='output_file', type=None):
    import guan
    import numpy as np
    import torch
    input_data = guan.load_data(filename=input_filename)
    output_data = guan.load_data(filename=output_filename)
    if type == None:
        input_data = np.array(input_data)
        output_data= np.array(output_data)
    else:
        input_data = np.array(input_data).astype(type)
        output_data= np.array(output_data).astype(type)
    input_data = torch.from_numpy(input_data)
    output_data = torch.from_numpy(output_data)
    return input_data, output_data

def pca_of_data(data, n_components=None, standard=1):
    from sklearn.decomposition import PCA
    if standard==1:
        from sklearn.preprocessing import StandardScaler
        scaler = StandardScaler()
        data_scaled = scaler.fit_transform(data)
    else:
        data_scaled = data
    if n_components==None:
        pca = PCA()
    else:
        pca = PCA(n_components=n_components)
    data_transformed = pca.fit_transform(data_scaled)
    explained_variance_ratio = pca.explained_variance_ratio_
    return data_transformed, explained_variance_ratio

def calculate_R2_with_definition(y_true_array, y_pred_array):
    import numpy as np
    y_mean = np.mean(y_true_array)
    SS_tot = np.sum((y_true_array - y_mean) ** 2)
    SS_res = np.sum((y_true_array - y_pred_array) ** 2)
    R2 = 1 - (SS_res / SS_tot)
    return R2

def calculate_R2_with_sklearn(y_true_array, y_pred_array):
    from sklearn.metrics import r2_score
    R2 = r2_score(y_true_array, y_pred_array)
    return R2

def calculate_R2_after_linear_regression_with_scipy(y_true_array, y_pred_array):
    from scipy import stats
    slope, intercept, r_value, p_value, std_err = stats.linregress(y_true_array, y_pred_array)
    R2 = r_value**2
    return R2

def dump_data(data, filename='a', file_format='.pkl'):
    import pickle
    with open(filename+file_format, 'wb') as f:
        pickle.dump(data, f)

def load_data(filename, file_format='.pkl'):
    import pickle
    with open(filename+file_format, 'rb') as f:
        data = pickle.load(f)
    return data

def save_npy_data(data, filename='a'):
    import numpy as np
    np.save(filename+'.npy', data)

def load_npy_data(filename):
    import numpy as np
    data = np.load(filename+'.npy')
    return data

def save_txt_data(data, filename='a'):
    import numpy as np
    np.savetxt(filename+'.txt', data)

def load_txt_data(filename):
    import numpy as np
    data = np.loadtxt(filename+'.txt')
    return data

def read_one_dimensional_data(filename='a', file_format='.txt'): 
    import numpy as np
    f = open(filename+file_format, 'r', encoding='UTF-8')
    text = f.read()
    f.close()
    row_list = np.array(text.split('\n')) 
    dim_column = np.array(row_list[0].split()).shape[0] 
    x_array = np.array([])
    y_array = np.array([])
    for row in row_list:
        column = np.array(row.split()) 
        if column.shape[0] != 0:  
            x_array = np.append(x_array, [float(column[0])], axis=0)  
            y_row = np.zeros(dim_column-1)
            for dim0 in range(dim_column-1):
                y_row[dim0] = float(column[dim0+1])
            if np.array(y_array).shape[0] == 0:
                y_array = [y_row]
            else:
                y_array = np.append(y_array, [y_row], axis=0)
    return x_array, y_array

def read_one_dimensional_complex_data(filename='a', file_format='.txt'): 
    import numpy as np
    f = open(filename+file_format, 'r', encoding='UTF-8')
    text = f.read()
    f.close()
    row_list = np.array(text.split('\n')) 
    dim_column = np.array(row_list[0].split()).shape[0] 
    x_array = np.array([])
    y_array = np.array([])
    for row in row_list:
        column = np.array(row.split()) 
        if column.shape[0] != 0:  
            x_array = np.append(x_array, [complex(column[0])], axis=0)  
            y_row = np.zeros(dim_column-1, dtype=complex)
            for dim0 in range(dim_column-1):
                y_row[dim0] = complex(column[dim0+1])
            if np.array(y_array).shape[0] == 0:
                y_array = [y_row]
            else:
                y_array = np.append(y_array, [y_row], axis=0)
    return x_array, y_array

def read_xyz_data(filename='a', file_format='.txt'): 
    import numpy as np
    f = open(filename+file_format, 'r', encoding='UTF-8')
    text = f.read()
    f.close()
    row_list = np.array(text.split('\n')) 
    x_array = np.array([])
    y_array = np.array([])
    z_array = np.array([])
    for row in row_list:
        column = np.array(row.split()) 
        if column.shape[0] != 0:  
            x_array = np.append(x_array, [float(column[0])], axis=0)
            y_array = np.append(y_array, [float(column[1])], axis=0)
            z_array = np.append(z_array, [float(column[2])], axis=0)
    return x_array, y_array, z_array

def read_two_dimensional_data(filename='a', file_format='.txt'): 
    import numpy as np
    f = open(filename+file_format, 'r', encoding='UTF-8')
    text = f.read()
    f.close()
    row_list = np.array(text.split('\n')) 
    dim_column = np.array(row_list[0].split()).shape[0] 
    x_array = np.array([])
    y_array = np.array([])
    matrix = np.array([])
    for i0 in range(row_list.shape[0]):
        column = np.array(row_list[i0].split()) 
        if i0 == 0:
            x_str = column[1::] 
            x_array = np.zeros(x_str.shape[0])
            for i00 in range(x_str.shape[0]):
                x_array[i00] = float(x_str[i00]) 
        elif column.shape[0] != 0: 
            y_array = np.append(y_array, [float(column[0])], axis=0)  
            matrix_row = np.zeros(dim_column-1)
            for dim0 in range(dim_column-1):
                matrix_row[dim0] = float(column[dim0+1])
            if np.array(matrix).shape[0] == 0:
                matrix = [matrix_row]
            else:
                matrix = np.append(matrix, [matrix_row], axis=0)
    return x_array, y_array, matrix

def read_two_dimensional_complex_data(filename='a', file_format='.txt'): 
    import numpy as np
    f = open(filename+file_format, 'r', encoding='UTF-8')
    text = f.read()
    f.close()
    row_list = np.array(text.split('\n')) 
    dim_column = np.array(row_list[0].split()).shape[0] 
    x_array = np.array([])
    y_array = np.array([])
    matrix = np.array([])
    for i0 in range(row_list.shape[0]):
        column = np.array(row_list[i0].split()) 
        if i0 == 0:
            x_str = column[1::] 
            x_array = np.zeros(x_str.shape[0], dtype=complex)
            for i00 in range(x_str.shape[0]):
                x_array[i00] = complex(x_str[i00]) 
        elif column.shape[0] != 0: 
            y_array = np.append(y_array, [complex(column[0])], axis=0)  
            matrix_row = np.zeros(dim_column-1, dtype=complex)
            for dim0 in range(dim_column-1):
                matrix_row[dim0] = complex(column[dim0+1])
            if np.array(matrix).shape[0] == 0:
                matrix = [matrix_row]
            else:
                matrix = np.append(matrix, [matrix_row], axis=0)
    return x_array, y_array, matrix

def read_two_dimensional_data_without_xy_array(filename='a', file_format='.txt'):
    import numpy as np
    matrix = np.loadtxt(filename+file_format)
    return matrix

def write_one_dimensional_data(x_array, y_array, filename='a', file_format='.txt'):
    import guan
    with open(filename+file_format, 'w', encoding='UTF-8') as f:
        guan.write_one_dimensional_data_without_opening_file(x_array, y_array, f)

def write_one_dimensional_data_without_opening_file(x_array, y_array, f):
    import numpy as np
    x_array = np.array(x_array)
    y_array = np.array(y_array)
    i0 = 0
    for x0 in x_array:
        f.write(str(x0)+'   ')
        if len(y_array.shape) == 1:
            f.write(str(y_array[i0])+'\n')
        elif len(y_array.shape) == 2:
            for j0 in range(y_array.shape[1]):
                f.write(str(y_array[i0, j0])+'   ')
            f.write('\n')
        i0 += 1

def write_xyz_data(x_array, y_array, z_array, filename='a', file_format='.txt'):
    import guan
    with open(filename+file_format, 'w', encoding='UTF-8') as f:
        write_xyz_data_without_opening_file(x_array, y_array, z_array, f)

def write_xyz_data_without_opening_file(x_array, y_array, z_array, f):
    import numpy as np
    x_array = np.array(x_array)
    y_array = np.array(y_array)
    z_array = np.array(z_array)
    i0 = 0
    for x0 in x_array:
        f.write(str(x0)+'   ')
        f.write(str(y_array[i0])+'   ')
        f.write(str(z_array[i0])+'\n')
        i0 += 1

def write_two_dimensional_data(x_array, y_array, matrix, filename='a', file_format='.txt'):
    import guan
    with open(filename+file_format, 'w', encoding='UTF-8') as f:
        guan.write_two_dimensional_data_without_opening_file(x_array, y_array, matrix, f)

def write_two_dimensional_data_without_opening_file(x_array, y_array, matrix, f):
    import numpy as np
    x_array = np.array(x_array)
    y_array = np.array(y_array)
    matrix = np.array(matrix)
    f.write('0   ')
    for x0 in x_array:
        f.write(str(x0)+'   ')
    f.write('\n')
    i0 = 0
    for y0 in y_array:
        f.write(str(y0))
        j0 = 0
        for x0 in x_array:
            f.write('   '+str(matrix[i0, j0])+'   ')
            j0 += 1
        f.write('\n')
        i0 += 1

def write_two_dimensional_data_without_xy_array(matrix, filename='a', file_format='.txt'):
    import guan
    with open(filename+file_format, 'w', encoding='UTF-8') as f:
        guan.write_two_dimensional_data_without_xy_array_and_without_opening_file(matrix, f)

def write_two_dimensional_data_without_xy_array_and_without_opening_file(matrix, f):
    for row in matrix:
        for element in row:
            f.write(str(element)+'   ')
        f.write('\n')

def make_sh_file_for_qsub(sh_filename='a', command_line='python a.py', cpu_num=1, task_name='task', cd_dir=0, pbs_q=0, queue_name='bigmem', specific_node=0, node_name='node50.cluster'):
    sh_content = \
        '#!/bin/sh\n' \
        +f'#PBS -N {task_name}\n'
    if pbs_q==1:
        sh_content += f'#PBS -q {queue_name}\n'
    if specific_node==0:
        sh_content += f'#PBS -l nodes=1:ppn={cpu_num}\n'
    else:
        sh_content += f'#PBS -l nodes={node_name}:ppn={cpu_num}\n'
    if cd_dir==1:
        sh_content += 'cd $PBS_O_WORKDIR\n'
    sh_content += command_line
    with open(sh_filename+'.sh', 'w') as f:
        f.write(sh_content)

def make_sh_file_for_sbatch(sh_filename='a', command_line='python a.py', cpu_num=1, task_name='task', cd_dir=0, sbatch_partition=0, partition_name='cpu48'):
    sh_content = \
        '#!/bin/sh\n' \
        +f'#SBATCH --job-name={task_name}\n'
    if sbatch_partition==1:
        sh_content += f'#SBATCH --partition={partition_name}\n'
    sh_content += f'#SBATCH --cpus-per-task={cpu_num}\n'
    if cd_dir==1:
        sh_content += 'cd $PBS_O_WORKDIR\n'
    sh_content += command_line
    with open(sh_filename+'.sh', 'w') as f:
        f.write(sh_content)

def make_sh_file_for_bsub(sh_filename='a', command_line='python a.py', cpu_num=1, task_name='task', cd_dir=0, bsub_q=0, queue_name='score'):
    sh_content = \
        '#!/bin/sh\n' \
        +f'#BSUB -J {task_name}\n'
    if bsub_q==1:
        sh_content += f'#BSUB -q {queue_name}\n'
    sh_content += f'#BSUB -n {cpu_num}\n'
    if cd_dir==1:
        sh_content += 'cd $PBS_O_WORKDIR\n'
    sh_content += command_line
    with open(sh_filename+'.sh', 'w') as f:
        f.write(sh_content)

def qsub_task(filename='a', file_format='.sh'):
    import os
    os.system('qsub '+filename+file_format)

def sbatch_task(filename='a', file_format='.sh'):
    import os
    os.system('sbatch '+filename+file_format)

def bsub_task(filename='a', file_format='.sh'):
    import os
    os.system('bsub < '+filename+file_format)

def copy_py_sh_file_and_qsub_task(parameter_array, py_filename='a', old_str_in_py='parameter = 0', new_str_in_py='parameter = ', sh_filename='a', task_name='task'):
    import os
    parameter_str_array = []
    for i0 in parameter_array:
        parameter_str_array.append(str(i0))
    index = 0
    for parameter_str in parameter_str_array:
        index += 1
        # copy python file
        old_file = py_filename+'.py'
        new_file = py_filename+'_'+str(index)+'.py'
        os.system('cp '+old_file+' '+new_file)
        with open(new_file, 'r') as f:
            content  = f.read()
        old_str = old_str_in_py
        new_str = new_str_in_py+parameter_str
        content = content.replace(old_str, new_str)
        with open(py_filename+'_'+str(index)+'.py', 'w') as f:
            f.write(content)
        # copy sh file
        old_file = sh_filename+'.sh'
        new_file = sh_filename+'_'+str(index)+'.sh'
        os.system('cp '+old_file+' '+new_file)
        with open(new_file, 'r') as f:
            content  = f.read()
        old_str = 'python '+py_filename+'.py'
        new_str = 'python '+py_filename+'_'+str(index)+'.py'
        content = content.replace(old_str, new_str)
        old_str = '#PBS -N '+task_name
        new_str = '#PBS -N '+task_name+'_'+str(index)
        content = content.replace(old_str, new_str)
        with open(sh_filename+'_'+str(index)+'.sh', 'w') as f: 
            f.write(content)
        # qsub task
        os.system('qsub '+new_file)

def copy_py_sh_file_and_sbatch_task(parameter_array, py_filename='a', old_str_in_py='parameter = 0', new_str_in_py='parameter = ', sh_filename='a', task_name='task'):
    import os
    parameter_str_array = []
    for i0 in parameter_array:
        parameter_str_array.append(str(i0))
    index = 0
    for parameter_str in parameter_str_array:
        index += 1
        # copy python file
        old_file = py_filename+'.py'
        new_file = py_filename+'_'+str(index)+'.py'
        os.system('cp '+old_file+' '+new_file)
        with open(new_file, 'r') as f:
            content  = f.read()
        old_str = old_str_in_py
        new_str = new_str_in_py+parameter_str
        content = content.replace(old_str, new_str)
        with open(py_filename+'_'+str(index)+'.py', 'w') as f:
            f.write(content)
        # copy sh file
        old_file = sh_filename+'.sh'
        new_file = sh_filename+'_'+str(index)+'.sh'
        os.system('cp '+old_file+' '+new_file)
        with open(new_file, 'r') as f:
            content  = f.read()
        old_str = 'python '+py_filename+'.py'
        new_str = 'python '+py_filename+'_'+str(index)+'.py'
        content = content.replace(old_str, new_str)
        old_str = '#SBATCH --job-name='+task_name
        new_str = '#SBATCH --job-name='+task_name+'_'+str(index)
        content = content.replace(old_str, new_str)
        with open(sh_filename+'_'+str(index)+'.sh', 'w') as f: 
            f.write(content)
        # sbatch task
        os.system('sbatch '+new_file)

def copy_py_sh_file_and_bsub_task(parameter_array, py_filename='a', old_str_in_py='parameter = 0', new_str_in_py='parameter = ', sh_filename='a', task_name='task'):
    import os
    parameter_str_array = []
    for i0 in parameter_array:
        parameter_str_array.append(str(i0))
    index = 0
    for parameter_str in parameter_str_array:
        index += 1
        # copy python file
        old_file = py_filename+'.py'
        new_file = py_filename+'_'+str(index)+'.py'
        os.system('cp '+old_file+' '+new_file)
        with open(new_file, 'r') as f:
            content  = f.read()
        old_str = old_str_in_py
        new_str = new_str_in_py+parameter_str
        content = content.replace(old_str, new_str)
        with open(py_filename+'_'+str(index)+'.py', 'w') as f:
            f.write(content)
        # copy sh file
        old_file = sh_filename+'.sh'
        new_file = sh_filename+'_'+str(index)+'.sh'
        os.system('cp '+old_file+' '+new_file)
        with open(new_file, 'r') as f:
            content  = f.read()
        old_str = 'python '+py_filename+'.py'
        new_str = 'python '+py_filename+'_'+str(index)+'.py'
        content = content.replace(old_str, new_str)
        old_str = '#BSUB -J '+task_name
        new_str = '#BSUB -J '+task_name+'_'+str(index)
        content = content.replace(old_str, new_str)
        with open(sh_filename+'_'+str(index)+'.sh', 'w') as f: 
            f.write(content)
        # bsub task
        os.system('bsub < '+new_file)

def write_matrix_in_markdown_format(matrix, filename='a'):
    import numpy as np
    matrix = np.array(matrix)
    dim_0 = matrix.shape[0]
    dim_1 = matrix.shape[1]
    with open(filename+'.md', 'w', encoding='UTF-8') as f:
        f.write(f'| Row\Column ')
        for i1 in range(dim_1):
            f.write(f'| column {i1+1} ')
        f.write('|\n')
        for i1 in range(dim_1+1):
            f.write('| :---: ')
        f.write('|\n')
        for i0 in range(dim_0):
            f.write(f'| row {i0+1} ')
            for i1 in range(dim_1):
                f.write(f'| {matrix[i0, i1]} ')
            f.write('|\n')

def write_matrix_in_latex_format(matrix, filename='a', format='bmatrix'):
    import numpy as np
    matrix = np.array(matrix)
    dim_0 = matrix.shape[0]
    dim_1 = matrix.shape[1]
    with open(filename+'.md', 'w', encoding='UTF-8') as f:
        f.write(f'$$\\begin{{{format}}}\n')
        for i0 in range(dim_0):
            for i1 in range(dim_1):
                if i1 != dim_1-1:
                    f.write(f'{matrix[i0, i1]} & ')
                else:
                    f.write(f'{matrix[i0, i1]} \\\\\n')
        f.write(f'\\end{{{format}}}$$')

def make_directory(directory='./test'):
    import os
    if not os.path.exists(directory):
        os.makedirs(directory)

def make_file(file_path='./a.txt'):
    import os
    if not os.path.exists(file_path):
        with open(file_path, 'w', encoding='UTF-8') as f:
            pass

def open_file(filename='a', file_format='.txt', mode='add'):
    if mode == 'add':
        f = open(filename+file_format, 'a', encoding='UTF-8')
    elif mode == 'overwrite':
        f = open(filename+file_format, 'w', encoding='UTF-8')
    return f

def print_to_file(*args, filename='print_result', file_format='.txt', print_on=True):
    if print_on==True:
        for arg in args:
            print(arg, end=' ')
        print()
    f = open(filename+file_format, 'a', encoding='UTF-8')
    for arg in args:
        f.write(str(arg)+' ')
    f.write('\n')
    f.close()