wehub-resource-sync
46 lines
1.1 KiB
Python
Executable File
46 lines
1.1 KiB
Python
Executable File
import numpy as np
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from prml.nn.tensor.constant import Constant
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from prml.nn.tensor.tensor import Tensor
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from prml.nn.function import Function
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class Cholesky(Function):
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def forward(self, x):
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x = self._convert2tensor(x)
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self.x = x
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self.output = np.linalg.cholesky(x.value)
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if isinstance(self.x, Constant):
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return Constant(self.output)
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return Tensor(self.output, function=self)
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def backward(self, delta):
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delta_lower = np.tril(delta)
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P = phi(self.output.T @ delta_lower)
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S = np.linalg.solve(
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self.output.T,
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P @ np.linalg.inv(self.output)
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)
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dx = S + S.T + np.diag(np.diag(S))
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self.x.backward(dx)
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def phi(x):
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return 0.5 * (np.tril(x) + np.tril(x, -1))
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def cholesky(x):
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"""
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cholesky decomposition of positive-definite matrix
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x = LL^T
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Parameters
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----------
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x : (d, d) tensor_like
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positive-definite matrix
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Returns
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-------
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L : (d, d)
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cholesky decomposition
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"""
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return Cholesky().forward(x)
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