code: def minimize(
      residuals,
      variables,
      max_iterations,
      regularizer=1e-20,
      regularizer_multiplier=10.0,
      callback=None,
      name="levenberg_marquardt_minimize",
  ):
      r"""Minimizes a set of residuals in the least-squares sense.
  
      Args:
        residuals: A residual or a list/tuple of residuals. A residual is a Python
          `callable`.
        variables: A variable or a list or tuple of variables defining the starting
          point of the minimization.
        max_iterations: The maximum number of iterations.
        regularizer: The regularizer is used to damped the stepsize when the
          iterations are becoming unstable. The bigger the regularizer is the
          smaller the stepsize becomes.
        regularizer_multiplier: If an iteration does not decrease the objective a
          new regularizer is computed by scaling it by this multiplier.
        callback: A callback function that will be called at each iteration. In
          graph mode the callback should return an op or list of ops that will
          execute the callback logic. The callback needs to be of the form
          f(iteration, objective_value, variables). A callback is a Python
          `callable`. The callback could be used for logging, for example if one
          wants to print the objective value at each iteration.
        name: A name for this op. Defaults to "levenberg_marquardt_minimize".
  
      Returns:
        The value of the objective function and variables attained at the final
        iteration of the minimization procedure.
  
      Raises:
        ValueError: If max_iterations is not at least 1.
        InvalidArgumentError: This exception is only raised in graph mode if the
        Cholesky decomposition is not successful. One likely fix is to increase
        the regularizer. In eager mode this exception is catched and the regularizer
        is increased automatically.
  
      Examples:
  
        ```python
        x = tf.constant(np.random.random_sample(size=(1,2)), dtype=tf.float32)
        y = tf.constant(np.random.random_sample(size=(3,1)), dtype=tf.float32)
  
        def f1(x, y):
          return x + y
  
        def f2(x, y):
          return x * y
  
        def callback(iteration, objective_value, variables):
          def print_output(iteration, objective_value, *variables):
            print("Iteration:", iteration, "Objective Value:", objective_value)
            for variable in variables:
              print(variable)
          inp = [iteration, objective_value] + variables
          return tf.py_function(print_output, inp, [])
  
        minimize_op = minimize(residuals=(f1, f2),
                               variables=(x, y),
                               max_iterations=10,
                               callback=callback)
  
        if not tf.executing_eagerly():
          with tf.Session() as sess:
            sess.run(tf.global_variables_initializer())
            sess.run(minimize_op)
        ```
      """
      if not isinstance(variables, (tuple, list)):
          variables = [variables]
      with tf.name_scope(name):
          if not isinstance(residuals, (tuple, list)):
              residuals = [residuals]
          if isinstance(residuals, tuple):
              residuals = list(residuals)
          if isinstance(variables, tuple):
              variables = list(variables)
          variables = [
              tf.convert_to_tensor(value=variable)
              for variable in variables
          ]
          multiplier = tf.constant(
              regularizer_multiplier, dtype=variables[0].dtype
          )
  
          if max_iterations <= 0:
              raise ValueError(
                  "'max_iterations' needs to be at least 1."
              )
  
          def _cond(iteration, regularizer, objective_value, variables):
              """Returns whether any iteration still needs to be performed."""
              del regularizer, objective_value, variables
              return iteration < max_iterations
  
          def _body(iteration, regularizer, objective_value, variables):
              """Main optimization loop."""
              iteration += tf.constant(1, dtype=tf.int32)
              values, jacobian = _values_and_jacobian(
                  residuals, variables
              )
              # Solves the normal equation.
              try:
                  updates = tf.linalg.lstsq(
                      jacobian, values, l2_regularizer=regularizer
                  )
                  shapes = [
                      tf.shape(input=variable) for variable in variables
                  ]
                  splits = [
                      tf.reduce_prod(input_tensor=shape)
                      for shape in shapes
                  ]
                  updates = tf.split(
                      tf.squeeze(updates, axis=-1), splits
                  )
                  new_variables = [
                      variable - tf.reshape(update, shape)
                      for variable, update, shape in zip(
                          variables, updates, shapes
                      )
                  ]
                  new_objective_value = tf.reduce_sum(
                      input_tensor=[
                          tf.nn.l2_loss(residual(*new_variables))
                          for residual in residuals
                      ]
                  )
                  # If the new estimated solution does not decrease the objective value,
                  # no updates are performed, but a new regularizer is computed.
                  cond = tf.less(new_objective_value, objective_value)
                  regularizer = tf.where(
                      cond, x=regularizer, y=regularizer * multiplier
                  )
                  objective_value = tf.where(
                      cond, x=new_objective_value, y=objective_value
                  )
                  variables = [
                      tf.where(cond, x=new_variable, y=variable)
                      for variable, new_variable in zip(
                          variables, new_variables
                      )
                  ]
              # Note that catching InvalidArgumentError will only work in eager mode.
              except tf.errors.InvalidArgumentError:
                  regularizer *= multiplier
              if callback is not None:
                  callback_ops = callback(
                      iteration, objective_value, variables
                  )
                  if callback_ops is not None:
                      if not isinstance(callback_ops, (tuple, list)):
                          callback_ops = [callback_ops]
                      with tf.control_dependencies(callback_ops):
                          iteration = tf.identity(iteration)
                          objective_value = tf.identity(objective_value)
                          variables = [
                              tf.identity(v) for v in variables
                          ]
              return iteration, regularizer, objective_value, variables
  
          starting_value = tf.reduce_sum(
              input_tensor=[
                  tf.nn.l2_loss(residual(*variables))
                  for residual in residuals
              ]
          )
          dtype = variables[0].dtype
          initial = (
              tf.constant(
                  0, dtype=tf.int32
              ),  # Initial iteration number.
              tf.constant(
                  regularizer, dtype=dtype
              ),  # Initial regularizer.
              starting_value,  # Initial objective value.
              variables,  # Initial variables.
          )
          _, _, final_objective_value, final_variables = tf.while_loop(
              cond=_cond,
              body=_body,
              loop_vars=initial,
              parallel_iterations=1,
          )
          return final_objective_value, final_variables
  
imports: from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  from six.moves import zip
  import tensorflow
  from tensorflow_graphics.util import export_api
label_desc: Use image node_id 2 for calling a global function with example usage: minimize(residuals, variables, max_iterations, regularizer, regularizer_multiplier, callback, name) and returns: final_objective_value,  final_variables, unknown, iteration,  regularizer,  objective_value,  variables