Пример #1
0
def angle_hessian(xyz, iangles):
    n_atoms, three = xyz.shape
    if three != 3:
        raise TypeError('xyz must be of length 3 in the last dimension.')
    n_angles, three = iangles.shape
    if three != 3:
        raise TypeError('angles must have 3 columns.')

    qa = internal.angles(xyz.reshape(1, n_atoms, 3), iangles).flatten()
    jacobian = internal_derivs.angle_derivs(xyz, iangles)

    hessian = np.zeros((n_angles, n_atoms, 3, n_atoms, 3))
    for i, (m, o, n) in enumerate(iangles):
        u_prime = xyz[m] - xyz[o]
        v_prime = xyz[n] - xyz[o]
        lambda_u = np.linalg.norm(u_prime)
        lambda_v = np.linalg.norm(v_prime)
        u = u_prime / lambda_u
        v = v_prime / lambda_v
        jac = jacobian[i]

        cos = np.cos(qa[i])
        sin = np.sin(qa[i])
        uv = np.outer(u, v)
        uu = np.outer(u, u)
        vv = np.outer(v, v)
        eye = np.eye(3)

        term1 = (uv + uv.T + (-3 * uu + eye) * cos) / (lambda_u**2 * sin)
        term2 = (uv + uv.T + (-3 * vv + eye) * cos) / (lambda_v**2 * sin)
        term3 = (uu + vv - uv * cos - eye) / (lambda_u * lambda_v * sin)
        term4 = (uu + vv - uv.T * cos - eye) / (lambda_u * lambda_v * sin)
        hessian[i] = -(cos / sin) * np.outer(
            jac.flatten(), jac.flatten()).reshape(n_atoms, 3, n_atoms, 3)

        for a in [m, n, o]:
            for b in [m, n, o]:
                sign6(a, m, o, b, m, o)
                hessian[i, a, :, b, :] += sign6(a, m, o, b, m, o) * term1
                hessian[i, a, :, b, :] += sign6(a, n, o, b, n, o) * term2
                hessian[i, a, :, b, :] += sign6(a, m, o, b, n, o) * term3
                hessian[i, a, :, b, :] += sign6(a, n, o, b, m, o) * term4

    return hessian
Пример #2
0
def angle_hessian(xyz, iangles):
    n_atoms, three = xyz.shape
    if three != 3:
        raise TypeError('xyz must be of length 3 in the last dimension.')
    n_angles, three = iangles.shape
    if three != 3:
        raise TypeError('angles must have 3 columns.')
    
    qa = internal.angles(xyz.reshape(1, n_atoms, 3), iangles).flatten()
    jacobian = internal_derivs.angle_derivs(xyz, iangles)
    
    hessian = np.zeros((n_angles, n_atoms, 3, n_atoms, 3))
    for i, (m, o, n) in enumerate(iangles):
        u_prime = xyz[m] - xyz[o]
        v_prime = xyz[n] - xyz[o]
        lambda_u = np.linalg.norm(u_prime)
        lambda_v = np.linalg.norm(v_prime)
        u = u_prime / lambda_u
        v = v_prime / lambda_v
        jac = jacobian[i]

        cos = np.cos(qa[i])
        sin = np.sin(qa[i])
        uv = np.outer(u, v)
        uu = np.outer(u, u)
        vv = np.outer(v, v)
        eye = np.eye(3)
        
        term1 = (uv + uv.T + (-3 * uu + eye) * cos) / (lambda_u**2 * sin)
        term2 = (uv + uv.T + (-3 * vv + eye) * cos) / (lambda_v**2 * sin)
        term3 = (uu + vv - uv   * cos - eye) / (lambda_u * lambda_v * sin)
        term4 = (uu + vv - uv.T * cos - eye) / (lambda_u * lambda_v * sin)
        hessian[i] = -(cos / sin) * np.outer(jac.flatten(), jac.flatten()).reshape(n_atoms, 3, n_atoms, 3)
        
        for a in [m, n, o]:
            for b in [m, n, o]:
                sign6(a,m,o, b,m,o)
                hessian[i, a, :, b, :] += sign6(a,m,o, b,m,o) * term1
                hessian[i, a, :, b, :] += sign6(a,n,o, b,n,o) * term2
                hessian[i, a, :, b, :] += sign6(a,m,o, b,n,o) * term3
                hessian[i, a, :, b, :] += sign6(a,n,o, b,m,o) * term4
    
    return hessian
Пример #3
0
    xyz = np.random.randn(4, 3)
    xyz2 = xyz.copy()
    xyz2[1, 1] += h
    ibonds = np.array([[0, 1], [0, 2]])
    iangles = np.array([[0, 1, 2], [1, 2, 3]])
    idihedrals = np.array([[0, 1, 2, 3]])

    # print 'TESTING BOND HESSIAN'
    # jac1 = internal_derivs.bond_derivs(xyz, ibonds)
    # jac2 = internal_derivs.bond_derivs(xyz2, ibonds)
    # hessian = bond_hessian(xyz, ibonds)
    # print ((jac2-jac1)/h)[0]
    # print hessian[0, 1, 1]

    print '\nTESTING ANGLE HESSIAN'
    jac1 = internal_derivs.angle_derivs(xyz, iangles)
    jac2 = internal_derivs.angle_derivs(xyz2, iangles)
    hessian = angle_hessian(xyz, iangles)
    print((jac2 - jac1) / h)[0]
    print
    print hessian[0, 1, 1]

    print '\nTESTING DIHEDRAL HESSIAN'
    jac1, hessian = dihedral_hessian(xyz, idihedrals)
    jac2, hessian = dihedral_hessian(xyz2, idihedrals)

    print 'These matricies should match'
    print((jac2 - jac1) / h)[0]
    print
    print hessian[0][1, 1]
Пример #4
0
    xyz2 = xyz.copy()
    xyz2[1,1] += h
    ibonds = np.array([[0,1], [0,2]])
    iangles = np.array([[0,1,2], [1,2,3]])
    idihedrals = np.array([[0,1,2,3]])

    # print 'TESTING BOND HESSIAN'
    # jac1 = internal_derivs.bond_derivs(xyz, ibonds)
    # jac2 = internal_derivs.bond_derivs(xyz2, ibonds)
    # hessian = bond_hessian(xyz, ibonds)
    # print ((jac2-jac1)/h)[0]
    # print hessian[0, 1, 1]
    
    
    print '\nTESTING ANGLE HESSIAN'
    jac1 = internal_derivs.angle_derivs(xyz, iangles)
    jac2 = internal_derivs.angle_derivs(xyz2, iangles)
    hessian = angle_hessian(xyz, iangles)
    print ((jac2-jac1)/h)[0]
    print
    print hessian[0, 1, 1] 
    
    print '\nTESTING DIHEDRAL HESSIAN'
    jac1, hessian = dihedral_hessian(xyz, idihedrals)
    jac2, hessian = dihedral_hessian(xyz2, idihedrals)

    print 'These matricies should match'
    print ((jac2-jac1)/h)[0]
    print 
    print hessian[0][1,1]