text: # Copyright 2016 The TensorFlow 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.
  # ==============================================================================
  """Tests for tensorflow.ops.math_ops.matrix_inverse."""
  
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  import numpy as np
  
  from tensorflow.python.client import session
  from tensorflow.python.eager import context
  from tensorflow.python.framework import constant_op
  from tensorflow.python.framework import errors_impl
  from tensorflow.python.framework import ops
  from tensorflow.python.framework import test_util
  from tensorflow.python.ops import array_ops
  from tensorflow.python.ops import control_flow_ops
  from tensorflow.python.ops import gradient_checker_v2
  from tensorflow.python.ops import linalg_ops
  from tensorflow.python.ops import math_ops
  from tensorflow.python.ops import stateless_random_ops
  from tensorflow.python.ops import variables
  from tensorflow.python.platform import benchmark
  from tensorflow.python.platform import test
  
  
  def _AddTest(test_class, op_name, testcase_name, fn):
    test_name = "_".join(["test", op_name, testcase_name])
    if hasattr(test_class, test_name):
      raise RuntimeError("Test %s defined more than once" % test_name)
    setattr(test_class, test_name, fn)
  
  
  class QrOpTest(test.TestCase):
  
    @test_util.run_in_graph_and_eager_modes(use_gpu=True)
    def testWrongDimensions(self):
      # The input to svd should be a tensor of at least rank 2.
      scalar = constant_op.constant(1.)
      with self.assertRaisesRegex((ValueError, errors_impl.InvalidArgumentError),
                                  "rank.* 2.*0"):
        linalg_ops.qr(scalar)
      vector = constant_op.constant([1., 2.])
      with self.assertRaisesRegex((ValueError, errors_impl.InvalidArgumentError),
                                  "rank.* 2.*1"):
        linalg_ops.qr(vector)
  
    @test_util.run_in_graph_and_eager_modes(use_gpu=True)
    def testConcurrentExecutesWithoutError(self):
      seed = [42, 24]
      all_ops = []
      for full_matrices_ in True, False:
        for rows_ in 4, 5:
          for cols_ in 4, 5:
            matrix_shape = [rows_, cols_]
            matrix1 = stateless_random_ops.stateless_random_normal(
                matrix_shape, seed)
            matrix2 = stateless_random_ops.stateless_random_normal(
                matrix_shape, seed)
            self.assertAllEqual(matrix1, matrix2)
            q1, r1 = linalg_ops.qr(matrix1, full_matrices=full_matrices_)
            q2, r2 = linalg_ops.qr(matrix2, full_matrices=full_matrices_)
            all_ops += [q1, q2, r1, r2]
      val = self.evaluate(all_ops)
      for i in range(0, len(val), 2):
        self.assertAllClose(val[i], val[i + 1])
  
  
  def _GetQrOpTest(dtype_, shape_, full_matrices_, use_static_shape_):
  
    is_complex = dtype_ in (np.complex64, np.complex128)
    is_single = dtype_ in (np.float32, np.complex64)
  
    def CompareOrthogonal(self, x, y, rank):
      if is_single:
        atol = 5e-4
      else:
        atol = 5e-14
      # We only compare the first 'rank' orthogonal vectors since the
      # remainder form an arbitrary orthonormal basis for the
      # (row- or column-) null space, whose exact value depends on
      # implementation details. Notice that since we check that the
      # matrices of singular vectors are unitary elsewhere, we do
      # implicitly test that the trailing vectors of x and y span the
      # same space.
      x = x[..., 0:rank]
      y = y[..., 0:rank]
      # Q is only unique up to sign (complex phase factor for complex matrices),
      # so we normalize the sign first.
      sum_of_ratios = np.sum(np.divide(y, x), -2, keepdims=True)
      phases = np.divide(sum_of_ratios, np.abs(sum_of_ratios))
      x *= phases
      self.assertAllClose(x, y, atol=atol)
  
    def CheckApproximation(self, a, q, r):
      if is_single:
        tol = 1e-5
      else:
        tol = 1e-14
      # Tests that a ~= q*r.
      a_recon = math_ops.matmul(q, r)
      self.assertAllClose(a_recon, a, rtol=tol, atol=tol)
  
    def CheckUnitary(self, x):
      # Tests that x[...,:,:]^H * x[...,:,:] is close to the identity.
      xx = math_ops.matmul(x, x, adjoint_a=True)
      identity = array_ops.matrix_band_part(array_ops.ones_like(xx), 0, 0)
      if is_single:
        tol = 1e-5
      else:
        tol = 1e-14
      self.assertAllClose(identity, xx, atol=tol)
  
    @test_util.run_in_graph_and_eager_modes(use_gpu=True)
    def Test(self):
      if not use_static_shape_ and context.executing_eagerly():
        return
      np.random.seed(1)
      x_np = np.random.uniform(
          low=-1.0, high=1.0, size=np.prod(shape_)).reshape(shape_).astype(dtype_)
      if is_complex:
        x_np += 1j * np.random.uniform(
            low=-1.0, high=1.0,
            size=np.prod(shape_)).reshape(shape_).astype(dtype_)
  
        if use_static_shape_:
          x_tf = constant_op.constant(x_np)
        else:
          x_tf = array_ops.placeholder(dtype_)
        q_tf, r_tf = linalg_ops.qr(x_tf, full_matrices=full_matrices_)
  
        if use_static_shape_:
          q_tf_val, r_tf_val = self.evaluate([q_tf, r_tf])
        else:
          with self.session(use_gpu=True) as sess:
            q_tf_val, r_tf_val = sess.run([q_tf, r_tf], feed_dict={x_tf: x_np})
  
        q_dims = q_tf_val.shape
        np_q = np.ndarray(q_dims, dtype_)
        np_q_reshape = np.reshape(np_q, (-1, q_dims[-2], q_dims[-1]))
        new_first_dim = np_q_reshape.shape[0]
  
        x_reshape = np.reshape(x_np, (-1, x_np.shape[-2], x_np.shape[-1]))
        for i in range(new_first_dim):
          if full_matrices_:
            np_q_reshape[i, :, :], _ = np.linalg.qr(
                x_reshape[i, :, :], mode="complete")
          else:
            np_q_reshape[i, :, :], _ = np.linalg.qr(
                x_reshape[i, :, :], mode="reduced")
        np_q = np.reshape(np_q_reshape, q_dims)
        CompareOrthogonal(self, np_q, q_tf_val, min(shape_[-2:]))
        CheckApproximation(self, x_np, q_tf_val, r_tf_val)
        CheckUnitary(self, q_tf_val)
  
    return Test
  
  
  class QrGradOpTest(test.TestCase):
    pass
  
  
  def _GetQrGradOpTest(dtype_, shape_, full_matrices_):
  
    def RandomInput():
      a = np.random.uniform(low=-1.0, high=1.0, size=shape_).astype(dtype_)
      if dtype_ in [np.complex64, np.complex128]:
        a += 1j * np.random.uniform(
            low=-1.0, high=1.0, size=shape_).astype(dtype_)
      return a
  
    @test_util.run_in_graph_and_eager_modes(use_gpu=True)
    def Test(self):
      np.random.seed(42)
      # Optimal stepsize for central difference is O(epsilon^{1/3}).
      epsilon = np.finfo(dtype_).eps
      delta = 0.1 * epsilon**(1.0 / 3.0)
      if dtype_ in [np.float32, np.complex64]:
        tol = 3e-2
      else:
        tol = 1e-6
      # TODO(b/157171666): Sadly we have to double the computation because
      # gradient_checker_v2.compute_gradient expects a list of functions.
      funcs = [
          lambda a: linalg_ops.qr(a, full_matrices=full_matrices_)[0],
          lambda a: linalg_ops.qr(a, full_matrices=full_matrices_)[1]
      ]
      for f in funcs:
        theoretical, numerical = gradient_checker_v2.compute_gradient(
            f, [RandomInput()], delta=delta)
        self.assertAllClose(theoretical, numerical, atol=tol, rtol=tol)
  
    return Test
  
  
  class QRBenchmark(test.Benchmark):
  
    shapes = [
        (4, 4),
        (8, 8),
        (16, 16),
        (101, 101),
        (256, 256),
        (1024, 1024),
        (2048, 2048),
        (1024, 2),
        (1024, 32),
        (1024, 128),
        (1024, 512),
        (1, 8, 8),
        (10, 8, 8),
        (100, 8, 8),
        (1, 256, 256),
        (10, 256, 256),
        (100, 256, 256),
    ]
  
    def benchmarkQROp(self):
      for shape_ in self.shapes:
        with ops.Graph().as_default(), \
            session.Session(config=benchmark.benchmark_config()) as sess, \
            ops.device("/cpu:0"):
          matrix_value = np.random.uniform(
              low=-1.0, high=1.0, size=shape_).astype(np.float32)
          matrix = variables.Variable(matrix_value)
          q, r = linalg_ops.qr(matrix)
          variables.global_variables_initializer().run()
          self.run_op_benchmark(
              sess,
              control_flow_ops.group(q, r),
              min_iters=25,
              name="QR_cpu_{shape}".format(shape=shape_))
  
        if test.is_gpu_available(True):
          with ops.Graph().as_default(), \
              session.Session(config=benchmark.benchmark_config()) as sess, \
              ops.device("/device:GPU:0"):
            matrix_value = np.random.uniform(
                low=-1.0, high=1.0, size=shape_).astype(np.float32)
            matrix = variables.Variable(matrix_value)
            q, r = linalg_ops.qr(matrix)
            variables.global_variables_initializer().run()
            self.run_op_benchmark(
                sess,
                control_flow_ops.group(q, r),
                min_iters=25,
                name="QR_gpu_{shape}".format(shape=shape_))
  
  
  if __name__ == "__main__":
    for dtype in np.float32, np.float64, np.complex64, np.complex128:
      for rows in 1, 2, 5, 10, 32, 100:
        for cols in 1, 2, 5, 10, 32, 100:
          for full_matrices in False, True:
            for batch_dims in [(), (3,)] + [(3, 2)] * (max(rows, cols) < 10):
              # TF2 does not support placeholders under eager so we skip it
              for use_static_shape in [True, False]:
                shape = batch_dims + (rows, cols)
                name = "%s_%s_full_%s_static_%s" % (dtype.__name__,
                                                    "_".join(map(str, shape)),
                                                    full_matrices,
                                                    use_static_shape)
                _AddTest(QrOpTest, "Qr", name,
                         _GetQrOpTest(dtype, shape, full_matrices,
                                      use_static_shape))
  
    # TODO(pfau): Get working with complex types.
    # TODO(pfau): Get working with full_matrices when rows > cols
    # TODO(pfau): Get working with shapeholders (dynamic shapes)
    for full_matrices in False, True:
      for dtype in np.float32, np.float64:
        for rows in 1, 2, 5, 10:
          for cols in 1, 2, 5, 10:
            if rows <= cols or (not full_matrices and rows > cols):
              for batch_dims in [(), (3,)] + [(3, 2)] * (max(rows, cols) < 10):
                shape = batch_dims + (rows, cols)
                name = "%s_%s_full_%s" % (dtype.__name__,
                                          "_".join(map(str, shape)),
                                          full_matrices)
                _AddTest(QrGradOpTest, "QrGrad", name,
                         _GetQrGradOpTest(dtype, shape, full_matrices))
    test.main()
  