Remove cf4 function for deplete.CF4Integrator

The function openmc.deplete.cf4 has been removed in favor
of openmc.deplete.CF4Integrator. The CF4 integration scheme
can be peformed with

>>> from openmc.deplete import CF4Integrator
>>> CF4Integrator(operator, time, power).integrate()

docs/source/pythonapi/deplete.rst

@@ -16,7 +16,6 @@ transport-depletion coupling algorithms <http://hdl.handle.net/1721.1/113721>`_.
    :nosignatures:
    :template: myfunction.rst
 
-   integrator.cf4
    integrator.epc_rk4
    integrator.si_celi
    integrator.si_leqi
@@ -27,6 +26,7 @@ transport-depletion coupling algorithms <http://hdl.handle.net/1721.1/113721>`_.
     :template:  myclassinherit.rst
 
     integrator.PredictorIntegrator
+    integrator.CF4Integrator
     integrator.CECMIntegrator
     integrator.CELIIntegrator
     integrator.LEQIIntegrator

openmc/deplete/integrator/cf4.py

@@ -4,9 +4,86 @@ import copy
 from collections.abc import Iterable
 
 from .cram import timed_deplete
+from .abc import Integrator
 from ..results import Results
 
 
+class CF4Integrator(Integrator):
+    r"""Deplete using the CF4 algorithm.
+
+    Implements the fourth order `commutator-free Lie algorithm
+    <https://doi.org/10.1016/S0167-739X(02)00161-9>`_.
+    This algorithm is mathematically defined as:
+
+    .. math::
+        \begin{aligned}
+        F_1 &= h A(y_0) \\
+        y_1 &= \text{expm}(1/2 F_1) y_0 \\
+        F_2 &= h A(y_1) \\
+        y_2 &= \text{expm}(1/2 F_2) y_0 \\
+        F_3 &= h A(y_2) \\
+        y_3 &= \text{expm}(-1/2 F_1 + F_3) y_1 \\
+        F_4 &= h A(y_3) \\
+        y_4 &= \text{expm}( 1/4  F_1 + 1/6 F_2 + 1/6 F_3 - 1/12 F_4)
+               \text{expm}(-1/12 F_1 + 1/6 F_2 + 1/6 F_3 + 1/4  F_4) y_0
+        \end{aligned}
+    """
+
+    def __call__(self, bos_conc, bos_rates, dt, power, i):
+        """Perform the integration across one time step
+
+        Parameters
+        ----------
+        bos_conc : numpy.ndarray
+            Initial concentrations for all nuclides in [atom]
+        bos_rates : openmc.deplete.ReactionRates
+            Reaction rates from operator
+        dt : float
+            Time in [s] for the entire depletion interval
+        power : float
+            Power of the system [W]
+        i : int
+            Current depletion step index
+
+        Returns
+        -------
+        proc_time : float
+            Time spent in CRAM routines for all materials
+        conc_list : list of numpy.ndarray
+            Concentrations at each of the intermediate points with
+            the final concentration as the last element
+        op_results : list of openmc.deplete.OperatorResult
+            Eigenvalue and reaction rates from intermediate transport
+            simulations
+        """
+        # Step 1: deplete with matrix 1/2*A(y0)
+        time1, conc_eos1 = timed_deplete(
+            self.chain, bos_conc, bos_rates, dt, matrix_func=_cf4_f1)
+        res1 = self.operator(conc_eos1, power)
+
+        # Step 2: deplete with matrix 1/2*A(y1)
+        time2, conc_eos2 = timed_deplete(
+            self.chain, bos_conc, res1.rates, dt, matrix_func=_cf4_f1)
+        res2 = self.operator(conc_eos2, power)
+
+        # Step 3: deplete with matrix -1/2*A(y0)+A(y2)
+        list_rates = list(zip(bos_rates, res2.rates))
+        time3, conc_eos3 = timed_deplete(
+            self.chain, conc_eos1, list_rates, dt, matrix_func=_cf4_f2)
+        res3 = self.operator(conc_eos3, power)
+
+        # Step 4: deplete with two matrix exponentials
+        list_rates = list(zip(bos_rates, res1.rates, res2.rates, res3.rates))
+        time4, conc_inter = timed_deplete(
+            self.chain, bos_conc, list_rates, dt, matrix_func=_cf4_f3)
+        time5, conc_eos5 = timed_deplete(
+            self.chain, conc_inter, list_rates, dt, matrix_func=_cf4_f4)
+
+        return (time1 + time2 + time3 + time4 + time5,
+                [conc_eos1, conc_eos2, conc_eos3, conc_eos5],
+                [res1, res2, res3])
+
+
 # Functions to form the special matrix for depletion
 def _cf4_f1(chain, rates):
     return 1/2 * chain.form_matrix(rates)

tests/unit_tests/test_deplete_cf4.py

@@ -4,7 +4,7 @@ These tests integrate a simple test problem described in dummy_geometry.py.
 """
 
 from pytest import approx
-import openmc.deplete
+from openmc.deplete import CF4Integrator, ResultsList
 
 from tests import dummy_operator
 
@@ -18,10 +18,10 @@ def test_cf4(run_in_tmpdir):
     # Perform simulation using the cf4 algorithm
     dt = [0.75, 0.75]
     power = 1.0
-    openmc.deplete.cf4(op, dt, power, print_out=False)
+    CF4Integrator(op, dt, power).integrate()
 
     # Load the files
-    res = openmc.deplete.ResultsList(op.output_dir / "depletion_results.h5")
+    res = ResultsList(op.output_dir / "depletion_results.h5")
 
     _, y1 = res.get_atoms("1", "1")
     _, y2 = res.get_atoms("1", "2")