def linearize(self, inputs, outputs, partials):
num_elements = self.metadata['num_elements']
num_nodes = num_elements + 1
size = 2 * num_nodes + 2
self.lu = lu_factor(inputs['K'])
partials['d', 'K'] = np.outer(np.ones(size), outputs['d']).flatten()
partials['d', 'd'] = inputs['K']
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