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79 lines
3.4 KiB
79 lines
3.4 KiB
import unittest, functools
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from tinygrad import Tensor, Context
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import numpy as np
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def orthogonality_helper(A:Tensor, tolerance=1e-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=1e-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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@unittest.skip("TODO: reenable this")
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def test_svd_general(self):
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sizes = [(2,2),(5,3),(3,5),(3,4,4),(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 = a.svd()
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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([None]*len(b_shape) + [(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, size):
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with Context(IGNORE_OOB=1): # sometimes this is slow in CI
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a = Tensor.randn(size).realize()
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U,S,V = a.svd(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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# faster for parallel pytest
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def test_svd_nonfull_2_2(self): self._test_svd_nonfull((2,2))
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def test_svd_nonfull_5_3(self): self._test_svd_nonfull((5,3))
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def test_svd_nonfull_3_5(self): self._test_svd_nonfull((3,5))
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def test_svd_nonfull_2_2_2_2_3(self): self._test_svd_nonfull((2,2,2,2,3))
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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 = a.svd()
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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([None]*len(b_shape) + [(0,m-k), (0,n-k)]))
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orthogonality_helper(U,tolerance=1e-3)
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orthogonality_helper(V,tolerance=1e-3)
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reconstruction_helper([U,s_diag,V],a,tolerance=1e-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 = a.qr()
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orthogonality_helper(Q)
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reconstruction_helper([Q,R],a)
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def test_newton_schulz(self):
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coefficients = [(2, -1.5, 0.5), (2.0, -1.4, 0.2, 0.2)]#these params map to the sign function
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sizes = [(2,2), (3,2), (2,3), (2,2,2)]
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for coefs in coefficients:
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for size in sizes:
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a = Tensor.randn(size)
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b = a.newton_schulz(steps=20, params=coefs, eps=0.0)
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# ns(A) = U @ Vt -> (U @ Vt) @ (U @ Vt)t = I
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orthogonality_helper(b if size[-1] > size[-2] else b.transpose(-2, -1), tolerance=1e-3)
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if __name__ == "__main__":
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unittest.main()
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