37 lines
1.3 KiB
Python
Executable File
37 lines
1.3 KiB
Python
Executable File
#!/usr/bin/python
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# -*- coding:utf-8 -*-
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"""
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Implementation of the various integrators for numerical integration.
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Comes from the assumption that the problem is analytically defined in position-momentum (q-p) space for a given hamiltonian H.
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"""
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import numpy as np
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def dp_dt(m_array, q_array):
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"""
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Time derivative of the momentum, given by the position derivative of the Hamiltonian.
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dp/dt = -dH/dq
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"""
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dp_array = np.zeros(q_array.shape)
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for i in range(q_array.shape[0]):
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m_j = np.delete(m_array, i)
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q_j = np.delete(q_array, i, 0)
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dp_array = m_array[i]*np.sum((m_j/np.sum((q_j-q_array[i])**3, axis=1)).reshape((q_j.shape[0],1))*(q_j-q_array[i]), axis=0)
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return dp_array
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def frogleap(duration, step, m_array, q_array, p_array):
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"""
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Leapfrog integrator for first order partial differential equations.
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iteration : half-step drift -> full-step kick -> half-step drift
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"""
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N = np.ceil(duration/step).astype(int)
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for _ in range(N):
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# half-step drift
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q_array, p_array = q_array + step/2*p_array/m_array , p_array
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# full-step kick
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q_array, p_array = q_array , p_array - step*dp_dt(m_array, q_array)
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# half-step drift
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q_array, p_array = q_array + step/2*p_array/m_array , p_array
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return q_array, p_array
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