text: # Copyright 2018 The TensorFlow Probability Authors.
  #
  # 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 root finding functions."""
  
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  # Dependency imports
  import scipy.optimize as optimize
  
  import tensorflow.compat.v2 as tf
  import tensorflow_probability as tfp
  
  
  from tensorflow_probability.python.internal import test_util
  
  
  @test_util.test_all_tf_execution_regimes
  class RootSearchTest(test_util.TestCase):
  
    def test_secant_finds_all_roots_from_one_initial_position(self):
      f = lambda x: (63 * x**5 - 70 * x**3 + 15 * x) / 8.
  
      x0, x1 = -1, 10
      guess = tf.constant([x0, x1], dtype=tf.float64)
  
      tolerance = 1e-8
      roots, value_at_roots, _ = self.evaluate(
          tfp.math.secant_root(f, guess, position_tolerance=tolerance))
  
      expected_roots = [optimize.newton(f, x0), optimize.newton(f, x1)]
      zeros = [0., 0.]
  
      self.assertAllClose(roots, expected_roots, atol=tolerance)
      self.assertAllClose(value_at_roots, zeros)
  
    def test_secant_finds_any_root_from_one_initial_position(self):
      f = lambda x: (63 * x**5 - 70 * x**3 + 15 * x) / 8.
  
      x0, x1 = -1, 10
      guess = tf.constant([x0, x1], dtype=tf.float64)
  
      tolerance = 1e-8
      # Only the root close to the first starting point will be found.
      roots, value_at_roots, _ = self.evaluate(
          tfp.math.secant_root(
              f,
              guess,
              position_tolerance=tolerance,
              stopping_policy_fn=tf.reduce_any))
  
      expected_roots = [optimize.newton(f, x0), optimize.newton(f, x1)]
  
      self.assertAllClose(roots[0], expected_roots[0], atol=tolerance)
      self.assertNotAllClose(roots[1], expected_roots[1], atol=tolerance)
  
      self.assertAllClose(value_at_roots[0], 0.)
      self.assertAllClose(value_at_roots[1], f(roots[1]))
      self.assertNotAllClose(value_at_roots[1], 0.)
  
    def test_secant_finds_all_roots_from_two_initial_positions(self):
      f = lambda x: (5 * x**3 - 3 * x) / 2.
  
      x0, x1 = -1, 10
      guess = tf.constant([x0, x1], dtype=tf.float64)
      guess_1 = tf.constant([x0 - 1, x1 - 1], dtype=tf.float64)
  
      tolerance = 1e-8
      roots, value_at_roots, _ = self.evaluate(
          tfp.math.secant_root(f, guess, guess_1, position_tolerance=tolerance))
  
      expected_roots = [optimize.newton(f, x0), optimize.newton(f, x1)]
      zeros = [0., 0.]
  
      self.assertAllClose(roots, expected_roots, atol=tolerance)
      self.assertAllClose(value_at_roots, zeros)
  
    def test_secant_finds_any_roots_from_two_initial_positions(self):
      f = lambda x: (5 * x**3 - 3 * x) / 2.
  
      x0, x1 = -1, 10
      guess = tf.constant([x0, x1], dtype=tf.float64)
      next_guess = tf.constant([x0 - 1, x1 - 1], dtype=tf.float64)
  
      tolerance = 1e-8
      roots, value_at_roots, _ = self.evaluate(
          tfp.math.secant_root(
              f,
              guess,
              next_guess,
              position_tolerance=tolerance,
              stopping_policy_fn=tf.reduce_any))
  
      expected_roots = [optimize.newton(f, x0), optimize.newton(f, x1)]
  
      self.assertAllClose(roots[0], expected_roots[0], atol=tolerance)
      self.assertNotAllClose(roots[1], expected_roots[1], atol=tolerance)
  
      self.assertAllClose(value_at_roots[0], 0.)
      self.assertAllClose(value_at_roots[1], f(roots[1]))
      self.assertNotAllClose(value_at_roots[1], 0.)
  
    def test_secant_finds_all_roots_using_float32(self):
      f = lambda x: (3 * x**2 - 1) / 2.
  
      x0, x1 = -5, 2
      guess = tf.constant([x0, x1], dtype=tf.float32)
  
      tolerance = 1e-8
      roots, value_at_roots, _ = self.evaluate(
          tfp.math.secant_root(f, guess, position_tolerance=tolerance))
  
      expected_roots = [optimize.newton(f, x0), optimize.newton(f, x1)]
      zeros = [0., 0.]
  
      self.assertAllClose(roots, expected_roots, atol=tolerance)
      self.assertAllClose(value_at_roots, zeros)
  
    def test_secant_skips_iteration(self):
      f = lambda x: (3 * x**2 - 1) / 2.
  
      x0, x1 = -5, 2
      guess = tf.constant([x0, x1], dtype=tf.float64)
  
      # Skip iteration entirely. This should be a no-op.
      guess, result = self.evaluate(
          [guess, tfp.math.secant_root(f, guess, max_iterations=0)])
  
      self.assertAllEqual(result.estimated_root, guess)
  
    def test_secant_invalid_position_tolerance(self):
      f = lambda x: (3 * x**2 - 1) / 2.
  
      guess = tf.constant(-2, dtype=tf.float64)
      with self.assertRaisesOpError(
          '`position_tolerance` must be greater than 0.'):
        self.evaluate(
            tfp.math.secant_root(
                f, guess, position_tolerance=-1e-8, validate_args=True))
  
    def test_secant_invalid_value_tolerance(self):
      f = lambda x: (3 * x**2 - 1) / 2.
  
      guess = tf.constant(-2, dtype=tf.float64)
      with self.assertRaisesOpError('`value_tolerance` must be greater than 0.'):
        self.evaluate(
            tfp.math.secant_root(
                f, guess, value_tolerance=-1e-8, validate_args=True))
  
    def test_secant_invalid_max_iterations(self):
      f = lambda x: (3 * x**2 - 1) / 2.
  
      guess = tf.constant(-2, dtype=tf.float64)
      with self.assertRaisesOpError('`max_iterations` must be nonnegative.'):
        self.evaluate(
            tfp.math.secant_root(f, guess, max_iterations=-1, validate_args=True))
  
  
  if __name__ == '__main__':
    tf.test.main()
  