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#
# Licensed under the Apache License, Version 2.0 (the "License");
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#
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#
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import numpy as np
from numpy.linalg import LinAlgError
from ... import opcodes
from ...core import ExecutableTuple
from ..datasource import tensor as astensor
from ..operators import TensorHasInput, TensorOperatorMixin
class TensorLU(TensorHasInput, TensorOperatorMixin):
_op_type_ = opcodes.LU
@property
def output_limit(self):
return 3
def __call__(self, a):
import scipy.linalg
a = astensor(a)
if a.ndim != 2:
raise LinAlgError(
f"{a.ndim}-dimensional array given. Tensor must be two-dimensional"
)
if a.shape[0] > a.shape[1]:
p_shape = (a.shape[0],) * 2
l_shape = a.shape
u_shape = (a.shape[1],) * 2
elif a.shape[0] < a.shape[1]:
p_shape = (a.shape[0],) * 2
l_shape = (a.shape[0],) * 2
u_shape = a.shape
else:
p_shape, l_shape, u_shape = (a.shape,) * 3
tiny_p, tiny_l, tiny_u = scipy.linalg.lu(
np.array([[1, 2], [2, 5]], dtype=a.dtype)
)
order = a.order
p, l, u = self.new_tensors(
[a],
kws=[
{"side": "p", "dtype": tiny_p.dtype, "shape": p_shape, "order": order},
{"side": "l", "dtype": tiny_l.dtype, "shape": l_shape, "order": order},
{"side": "u", "dtype": tiny_u.dtype, "shape": u_shape, "order": order},
],
)
return ExecutableTuple([p, l, u])
[docs]
def lu(a):
"""
LU decomposition
The decomposition is::
A = P L U
where P is a permutation matrix, L lower triangular with unit diagonal elements,
and U upper triangular.
Parameters
----------
a : (M, N) array_like
Array to decompose
Returns
-------
p : (M, M) ndarray
Permutation matrix
l : (M, K) ndarray
Lower triangular or trapezoidal matrix with unit diagonal.
K = min(M, N)
u : (K, N) ndarray
Upper triangular or trapezoidal matrix
Examples
--------
>>> import maxframe.tensor as mt
>>> A = mt.array([[1,2],[2,3]])
>>> A.execute()
array([[ 1, 2],
[ 2, 3]])
>>> P, L, U = mt.linalg.lu(A)
>>> P.execute()
array([[ 0, 1],
[ 1, 0]])
>>> L.execute()
array([[ 1, 0],
[ 0.5, 1]])
>>> U.execute()
array([[ 2, 3],
[ 0, 0.5]])
>>> mt.dot(P.dot(L), U).execute() # verify that PL * U = A
array([[ 1, 2],
[ 2, 3]])
"""
op = TensorLU(sparse=a.issparse())
return op(a)