Known lattice mapping

python/libcasm/mapping/info/__init__.py

@@ -12,4 +12,6 @@
     StructureMappingResults,
     has_same_prim,
     pretty_json,
+    lattice_isotropic_strain_cost,
+    lattice_symmetry_breaking_strain_cost,
 )

python/libcasm/mapping/methods/__init__.py

@@ -1,4 +1,8 @@
 """Easy-to-use mapping methods"""
+from ._methods import (
+    map_lattices_without_reorientation,
+)
+
 from ._mapping_methods import (
     make_mapped_lattice,
     make_mapped_structure,

python/libcasm/mapping/methods/_methods.py

@@ -0,0 +1,59 @@
+import typing
+
+import libcasm.mapping.info as mapinfo
+import libcasm.xtal as xtal
+import numpy as np
+
+
+def map_lattices_without_reorientation(
+    lattice1: xtal.Lattice,
+    lattice2: xtal.Lattice,
+    transformation_matrix_to_super: typing.Optional[np.ndarray] = None,
+) -> mapinfo.LatticeMapping:
+    """Map lattices without reorienting the child.
+
+    This function may be used to find the lattice mapping from
+    an ideal structure to a deformed structure during geometric
+    relaxation via DFT. The lattice mapping has the form
+
+    .. math::
+
+        FL_1T = L_2
+
+    where :math:`F` is the deformation tensor, :math:`L_1` is
+    the ideal parent lattice, :math:`L_2` is the deformed child
+    lattice, and :math:`T` is an optional transformation matrix
+    from the parent to the child which may be provided if :math:`L2`
+    is a superlattice of :math:`L1`.
+
+    Parameters
+    ----------
+    lattice1: xtal.Lattice
+        The parent crystal lattice.
+    lattice2: xtal.Lattice
+        The child crystal lattice.
+    transformation_matrix_to_super: Optional[np.ndarray] = None
+        An integer shape=(3,3) transformation matrix that generates a superlattice of `lattice1`.
+        The transformation matrix that generates a superlattice of `lattice1`.
+        If None, :math:`T` is set to the identity matrix.
+
+    Returns
+    -------
+    lattice_mapping: mapinfo.LatticeMapping
+        The lattice mapping from the parent to the child.
+    """
+    if transformation_matrix_to_super is None:
+        transformation_matrix_to_super = np.eye(3, dtype=int)
+
+    # calculate deformation gradient
+    l1 = lattice1.column_vector_matrix()
+    l2 = lattice2.column_vector_matrix()
+    deformation_gradient = (
+        l2 @ np.linalg.inv(transformation_matrix_to_super) @ np.linalg.inv(l1)
+    )
+    lattice_mapping = mapinfo.LatticeMapping(
+        deformation_gradient=deformation_gradient,
+        transformation_matrix_to_super=transformation_matrix_to_super,
+        reorientation=np.eye(3, dtype=float),
+    )
+    return lattice_mapping

python/src/mapping_info.cpp

@@ -10,6 +10,7 @@
 #include "casm/mapping/AtomMapping.hh"
 #include "casm/mapping/LatticeMapping.hh"
 #include "casm/mapping/StructureMapping.hh"
+#include "casm/mapping/lattice_cost.hh"
 #include "casm/mapping/io/json_io.hh"
 #include "pybind11_json/pybind11_json.hpp"
 
@@ -770,6 +771,42 @@ PYBIND11_MODULE(_mapping_info, m) {
       },
       "Pretty-print JSON to string.", py::arg("data"));
 
+  m.def(
+      "lattice_isotropic_strain_cost", &isotropic_strain_cost,
+      R"pbdoc(
+      Return the isotropic strain cost for a lattice deformation.
+
+      Parameters
+      ----------
+      deformation_gradient : array_like, shape=(3,3)
+          The parent-to-child deformation gradient tensor, :math:`F`, a shape=(3,3)
+          matrix.
+
+      Returns
+      -------
+      float : The isotropic strain cost for the lattice deformation given by :math:`F`.
+      )pbdoc",
+      py::arg("deformation_gradient"));
+
+    m.def(
+      "lattice_symmetry_breaking_strain_cost", &symmetry_breaking_strain_cost,
+      R"pbdoc(
+      Return the symmetry-breaking strain cost for a lattice deformation.
+
+      Parameters
+      ----------
+      deformation_gradient : array_like, shape=(3,3)
+          The parent-to-child deformation gradient tensor, :math:`F`, a shape=(3,3)
+          matrix.
+      lattice1_point_group : list[:class:`xtal::SymOp`]
+          The point group of the parent crystal lattice.
+
+      Returns
+      -------
+      float : The symmetry-breaking strain cost for the lattice deformation given by :math:`F`.
+      )pbdoc",
+      py::arg("deformation_gradient"), py::arg("lattice1_point_group"));
+
 #ifdef VERSION_INFO
   m.attr("__version__") = MACRO_STRINGIFY(VERSION_INFO);
 #else