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66 lines
2.7 KiB
66 lines
2.7 KiB
1 day ago
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import numpy as np
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import unittest
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from tinygrad import Tensor
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from typing import List
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import functools
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def orthogonality_helper(A:Tensor,tolerance=1.0e-5):
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b_shape,m = A.shape[0:-2],A.shape[-2] #outer dimension should be the dim along orthogonality
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A_identity = (Tensor.eye(m).reshape((1,) * len(b_shape)+(m,m)).expand(b_shape+(m,m)))
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np.testing.assert_allclose((A @ A.transpose(-2,-1)).numpy(),A_identity.numpy(),atol=tolerance,rtol=tolerance)
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def reconstruction_helper(A:List[Tensor],B:Tensor, tolerance=1.0e-5):
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reconstructed_tensor = functools.reduce(Tensor.matmul, A)
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np.testing.assert_allclose(reconstructed_tensor.numpy(),B.numpy(),atol=tolerance,rtol=tolerance)
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class TestLinAlg(unittest.TestCase):
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def test_svd_general(self):
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sizes = [(2,2),(5,3),(3,5),(2,2,2,2,3)]
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for size in sizes:
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a = Tensor.randn(size).realize()
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U,S,V = Tensor.svd(a)
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b_shape,m,n = size[0:-2],size[-2],size[-1]
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k = min(m,n)
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s_diag = (S.unsqueeze(-2) * Tensor.eye(k).reshape((1,) * len(b_shape) + (k,k)))
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s_diag = s_diag.expand(b_shape + (k,k)).pad(tuple([(0,0) for _ in range(len(size)-2)] + [(0,m-k), (0,n-k)]))
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orthogonality_helper(U)
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orthogonality_helper(V)
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reconstruction_helper([U,s_diag,V],a)
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def test_svd_nonfull(self):
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sizes = [(2,2),(5,3),(3,5),(2,2,2,2,3)]
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for size in sizes:
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a = Tensor.randn(size).realize()
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U,S,V = Tensor.svd(a,full_matrices=False)
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b_shape,m,n = size[0:-2],size[-2],size[-1]
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k = min(m,n)
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s_diag = (S.unsqueeze(-2) * Tensor.eye(k).reshape((1,) * len(b_shape) + (k,k)).expand(b_shape + (k,k)))
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#reduced U,V is only orthogonal along smaller dim
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if (m < n): orthogonality_helper(U),orthogonality_helper(V)
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else: orthogonality_helper(U.transpose(-2,-1)),orthogonality_helper(V.transpose(-2,-1))
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reconstruction_helper([U,s_diag,V],a)
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@unittest.skip("very big. recommend wrapping with TinyJit around inner function")
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def test_svd_large(self):
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size = (1024,1024)
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a = Tensor.randn(size).realize()
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U,S,V = Tensor.svd(a)
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b_shape,m,n = size[0:-2],size[-2],size[-1]
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k = min(m,n)
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s_diag = (S.unsqueeze(-2) * Tensor.eye(k).reshape((1,) * len(b_shape) + (k,k)))
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s_diag = s_diag.expand(b_shape + (k,k)).pad(tuple([(0,0) for _ in range(len(size)-2)] + [(0,m-k), (0,n-k)]))
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orthogonality_helper(U,tolerance=1.0e-3)
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orthogonality_helper(V,tolerance=1.0e-3)
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reconstruction_helper([U,s_diag,V],a,tolerance=1.0e-3)
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def test_qr_general(self):
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sizes = [(3,3),(3,6),(6,3),(2,2,2,2,2)]
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for size in sizes:
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a = Tensor.randn(size).realize()
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Q,R = Tensor.qr(a)
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orthogonality_helper(Q)
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reconstruction_helper([Q,R],a)
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if __name__ == "__main__":
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unittest.main()
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