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A python function for create the energy landscape between two conformations using linear interpolation morphing
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| """ | |
| Mahd Sadjadi (2018) | |
| This is a set of functions to compute the | |
| energy barrier between two spring networks. | |
| The morphing is done using the linear interpolation. | |
| Example: | |
| ------- | |
| s1 = np.random.rand(10,2) | |
| s2 = np.random.rand(10,2) | |
| b = np.random.randint(low=0,high=10,size=(15,2)) | |
| lambdas, energies, morpheds = basinBuilder(s1,s2,b) | |
| """ | |
| import numpy as np | |
| def energy(sites, bonds, L0): | |
| """ | |
| Compute the energy of a given spring networks | |
| with free boundary conditions. | |
| Inputs: | |
| ------- | |
| sites: coordinates of vertices (N*dim) | |
| bonds: a list of spring ends (M*2) | |
| L0: rest/natural length of springs (M*1) | |
| Output: | |
| ------- | |
| energy: energy of the spring network. | |
| """ | |
| dim = sites1.shape[1] | |
| dr = np.diff(sites[bonds],axis=1).reshape(-1,dim) # vectors | |
| L = np.linalg.norm(dr,axis=1) | |
| energy = 0.5*np.sum((L-L0)**2) | |
| return energy | |
| def basinBuilder(sites1, sites2, bonds, L0=None, low=-0.5, high=1.5, npoint=100): | |
| """ | |
| Compute the energy and barrier parameter | |
| between two given conformations of a spring | |
| network. | |
| with free boundary conditions. | |
| Inputs: | |
| ------- | |
| sites1: first conformation coordinates (N*dim) | |
| sites2: second conformation coordinates (N*dim) | |
| bonds: a list of spring ends (M*2) | |
| L0: rest/natural length of springs (M*) | |
| if not provided, the lengths are computed | |
| from the first conformation. | |
| low: the lowest value of mo | |
| hing paramter | |
| high: the highest value of morphing paramter | |
| npoint: number of morphings | |
| Output: | |
| ------- | |
| lambdas: morphing paramter | |
| morpheds: a list of morphed coordinates | |
| energy: energy of the spring network. | |
| """ | |
| if L0 is None: | |
| dim = sites1.shape[1] | |
| dr = np.diff(sites1[bonds],axis=1).reshape(-1,dim) # vectors | |
| L0 = np.linalg.norm(dr,axis=1) | |
| diff = sites2 - sites1 | |
| lambdas = np.linspace(low,high,npoint) | |
| morpheds = sites1 + np.einsum('i,jk->ijk', lambdas, diff) | |
| energies = [energy(morphed,bonds,L0) for morphed in morpheds] | |
| return lambdas, energies, morpheds |
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