拓扑优化代码
时间: 2023-07-28 20:06:20 浏览: 48
拓扑优化是指寻找一个分子在特定条件下最稳定的构象,常见的方法包括力场优化、分子动力学模拟、量子力学计算等。以下是一份使用Python语言实现的力场优化拓扑优化代码示例:
```python
import numpy as np
from scipy.optimize import minimize
import matplotlib.pyplot as plt
class TopologyOptimization:
def __init__(self, coords, bonds):
self.coords = coords
self.bonds = bonds
self.num_atoms = len(coords)
self.num_bonds = len(bonds)
def get_distance(self, coord1, coord2):
return np.sqrt(np.sum((coord1-coord2)**2))
def potential_energy(self, coords):
energy = 0
for i in range(self.num_bonds):
bond = self.bonds[i]
atom1 = bond[0]
atom2 = bond[1]
r = self.get_distance(coords[atom1], coords[atom2])
energy += (r-bond[2])**2
return energy
def gradient(self, coords):
grads = np.zeros_like(coords)
for i in range(self.num_bonds):
bond = self.bonds[i]
atom1 = bond[0]
atom2 = bond[1]
r = self.get_distance(coords[atom1], coords[atom2])
dE_dr = 2*(r-bond[2])
d_r_dx = (coords[atom1]-coords[atom2])/r
grads[atom1] += dE_dr*d_r_dx
grads[atom2] -= dE_dr*d_r_dx
return grads
def optimize(self):
initial_coords = self.coords.flatten()
result = minimize(self.potential_energy, initial_coords, method='BFGS', jac=self.gradient, options={'disp':True})
return result.x.reshape((-1,3))
# Example usage
# Define coordinates and bonds
coords = np.array([[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]])
bonds = np.array([[0, 1, 1.0], [0, 2, 1.0], [0, 3, 1.0]])
# Create a TopologyOptimization object and optimize
optimizer = TopologyOptimization(coords, bonds)
optimized_coords = optimizer.optimize()
# Plot the original and optimized structures
fig = plt.figure()
ax1 = fig.add_subplot(121, projection='3d')
ax2 = fig.add_subplot(122, projection='3d')
ax1.set_title('Original structure')
ax2.set_title('Optimized structure')
for i in range(len(coords)):
ax1.scatter(coords[i][0], coords[i][1], coords[i][2], color='blue')
ax2.scatter(optimized_coords[i][0], optimized_coords[i][1], optimized_coords[i][2], color='red')
for bond in bonds:
atom1 = bond[0]
atom2 = bond[1]
ax1.plot([coords[atom1][0], coords[atom2][0]], [coords[atom1][1], coords[atom2][1]], [coords[atom1][2], coords[atom2][2]], color='blue')
ax2.plot([optimized_coords[atom1][0], optimized_coords[atom2][0]], [optimized_coords[atom1][1], optimized_coords[atom2][1]], [optimized_coords[atom1][2], optimized_coords[atom2][2]], color='red')
plt.show()
```
这份代码中,首先定义了一个 `TopologyOptimization` 类,包含原子坐标和键的信息。通过定义 `potential_energy` 和 `gradient` 函数,分别计算势能和梯度,然后使用 `scipy.optimize.minimize` 函数进行优化,得到最佳构象。最后使用 Matplotlib 库绘制原始结构和最优结构的三维结构图。