# Copyright (c) 2021 PaddlePaddle Authors. All Rights Reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. import unittest import numpy as np from eager_op_test import OpTest import paddle def valid_eigh_result(A, eigh_value, eigh_vector, uplo): assert A.ndim == 2 or A.ndim == 3 if A.ndim == 2: valid_single_eigh_result(A, eigh_value, eigh_vector, uplo) return for batch_A, batch_w, batch_v in zip(A, eigh_value, eigh_vector): valid_single_eigh_result(batch_A, batch_w, batch_v, uplo) def valid_single_eigh_result(A, eigh_value, eigh_vector, uplo): FP32_MAX_RELATIVE_ERR = 5e-5 FP64_MAX_RELATIVE_ERR = 1e-14 if A.dtype == np.single or A.dtype == np.csingle: rtol = FP32_MAX_RELATIVE_ERR else: rtol = FP64_MAX_RELATIVE_ERR M, N = A.shape triangular_func = np.tril if uplo == 'L' else np.triu if not np.iscomplexobj(A): # Reconstruct A by filling triangular part A = triangular_func(A) + triangular_func(A, -1).T else: # Reconstruct A to Hermitian matrix A = triangular_func(A) + np.matrix(triangular_func(A, -1)).H # Diagonal matrix of eigen value T = np.diag(eigh_value) # A = Q*T*Q' residual = A - (eigh_vector @ T @ np.linalg.inv(eigh_vector)) # ||A - Q*T*Q'|| / (N*||A||) < rtol np.testing.assert_array_less( np.linalg.norm(residual, np.inf) / (N * np.linalg.norm(A, np.inf)), rtol ) # ||I - Q*Q'|| / M < rtol residual = np.eye(M) - eigh_vector @ np.linalg.inv(eigh_vector) np.testing.assert_array_less(np.linalg.norm(residual, np.inf) / M, rtol) class TestEighOp(OpTest): def setUp(self): paddle.enable_static() self.op_type = "eigh" self.python_api = paddle.linalg.eigh self.init_input() self.init_config() np.random.seed(123) out_w, out_v = np.linalg.eigh(self.x_np, self.UPLO) self.inputs = {"X": self.x_np} self.attrs = {"UPLO": self.UPLO} self.outputs = {'Eigenvalues': out_w, "Eigenvectors": out_v} def init_config(self): self.UPLO = 'L' def init_input(self): self.x_shape = (10, 10) self.x_type = np.float64 self.x_np = np.random.random(self.x_shape).astype(self.x_type) # def test_check_output(self): # self.check_output(no_check_set=['Eigenvectors']) def test_grad(self): self.check_grad(["X"], ["Eigenvalues"]) class TestEighUPLOCase(TestEighOp): def init_config(self): self.UPLO = 'U' class TestEighGPUCase(unittest.TestCase): def setUp(self): self.x_shape = [32, 32] self.dtype = "float32" self.UPLO = "L" np.random.seed(123) self.x_np = np.random.random(self.x_shape).astype(self.dtype) def test_check_output_gpu(self): if paddle.is_compiled_with_cuda(): paddle.disable_static(place=paddle.CUDAPlace(0)) input_real_data = paddle.to_tensor(self.x_np) actual_w, actual_v = paddle.linalg.eigh(input_real_data, self.UPLO) valid_eigh_result( self.x_np, actual_w.numpy(), actual_v.numpy(), self.UPLO ) class TestEighAPI(unittest.TestCase): def setUp(self): self.init_input_data() self.UPLO = 'L' self.rtol = 1e-5 # for test_eigh_grad self.atol = 1e-5 # for test_eigh_grad self.place = ( paddle.CUDAPlace(0) if paddle.is_compiled_with_cuda() else paddle.CPUPlace() ) np.random.seed(123) def init_input_shape(self): self.x_shape = [5, 5] def init_input_data(self): self.init_input_shape() self.dtype = "float32" self.real_data = np.random.random(self.x_shape).astype(self.dtype) complex_data = np.random.random(self.x_shape).astype( self.dtype ) + 1j * np.random.random(self.x_shape).astype(self.dtype) self.trans_dims = list(range(len(self.x_shape) - 2)) + [ len(self.x_shape) - 1, len(self.x_shape) - 2, ] # build a random conjugate matrix self.complex_symm = np.divide( complex_data + np.conj(complex_data.transpose(self.trans_dims)), 2 ) def check_static_float_result(self): main_prog = paddle.static.Program() startup_prog = paddle.static.Program() with paddle.static.program_guard(main_prog, startup_prog): input_x = paddle.static.data( 'input_x', shape=self.x_shape, dtype=self.dtype ) output_w, output_v = paddle.linalg.eigh(input_x) exe = paddle.static.Executor(self.place) actual_w, actual_v = exe.run( main_prog, feed={"input_x": self.real_data}, fetch_list=[output_w, output_v], ) valid_eigh_result(self.real_data, actual_w, actual_v, self.UPLO) def check_static_complex_result(self): main_prog = paddle.static.Program() startup_prog = paddle.static.Program() with paddle.static.program_guard(main_prog, startup_prog): x_dtype = np.complex64 if self.dtype == "float32" else np.complex128 input_x = paddle.static.data( 'input_x', shape=self.x_shape, dtype=x_dtype ) output_w, output_v = paddle.linalg.eigh(input_x) exe = paddle.static.Executor(self.place) actual_w, actual_v = exe.run( main_prog, feed={"input_x": self.complex_symm}, fetch_list=[output_w, output_v], ) valid_eigh_result(self.complex_symm, actual_w, actual_v, self.UPLO) def test_in_static_mode(self): paddle.enable_static() self.check_static_float_result() self.check_static_complex_result() def test_in_dynamic_mode(self): paddle.disable_static() input_real_data = paddle.to_tensor(self.real_data) actual_w, actual_v = paddle.linalg.eigh(input_real_data) valid_eigh_result( self.real_data, actual_w.numpy(), actual_v.numpy(), self.UPLO ) input_complex_data = paddle.to_tensor(self.complex_symm) actual_w, actual_v = paddle.linalg.eigh(input_complex_data) valid_eigh_result( self.complex_symm, actual_w.numpy(), actual_v.numpy(), self.UPLO ) def test_eigh_grad(self): paddle.disable_static() x = paddle.to_tensor(self.complex_symm, stop_gradient=False) w, v = paddle.linalg.eigh(x) (w.sum() + paddle.abs(v).sum()).backward() np.testing.assert_allclose( abs(x.grad.numpy()), abs(x.grad.numpy().conj().transpose(self.trans_dims)), rtol=self.rtol, atol=self.atol, ) class TestEighBatchAPI(TestEighAPI): def init_input_shape(self): self.x_shape = [2, 5, 5] class TestEighAPIError(unittest.TestCase): def test_error(self): main_prog = paddle.static.Program() startup_prog = paddle.static.Program() with paddle.static.program_guard(main_prog, startup_prog): # input maxtrix must greater than 2 dimensions input_x = paddle.static.data( name='x_1', shape=[12], dtype='float32' ) self.assertRaises(ValueError, paddle.linalg.eigh, input_x) # input matrix must be square matrix input_x = paddle.static.data( name='x_2', shape=[12, 32], dtype='float32' ) self.assertRaises(ValueError, paddle.linalg.eigh, input_x) # uplo must be in 'L' or 'U' input_x = paddle.static.data( name='x_3', shape=[4, 4], dtype="float32" ) uplo = 'R' self.assertRaises(ValueError, paddle.linalg.eigh, input_x, uplo) # x_data cannot be integer input_x = paddle.static.data( name='x_4', shape=[4, 4], dtype="int32" ) self.assertRaises(TypeError, paddle.linalg.eigh, input_x) if __name__ == "__main__": unittest.main()