Local bases (#610)

* added MatrixInterpolation class

* first version of local pod

* added frechet mean

* begin analytic tests

* few changes

* try computing for analytic case

* changed structure

* implementing projection error

* computing proj and interp error

* changed names and updated methods

* added commentaries for documentation

* changing the other files for new methods

* few changes

* Fixed pod error problem

* added a comment on pod error

* few problems resolved

* ruff error due to latest version

* module import fix

* fix ruff issue

* fixing other ruff issues

* new local pod tests added

---------

Co-authored-by: Rémi Lafage <[email protected]>

doc/_src_docs/applications/podi.rstx

@@ -27,7 +27,7 @@ Each column of the matrix corresponds to a snapshot output :math:`u(\mathbf{x_k}
 Proper Orthogonal Decomposition (POD)
 -------------------------------------
 
-The vectorial output $u$ is a vector of dimension $p$. Its POD is this decomposition:
+The vectorial output :math:`u` is a vector of dimension :math:`p`. Its POD is this decomposition:
 
 .. math ::
 	\begin{equation}\label{e:pod}
@@ -156,10 +156,16 @@ PODI class API
 
 .. autoclass:: smt.applications.podi.PODI
 
+	.. automethod:: smt.applications.podi.PODI.interp_subspaces
+
   	.. automethod:: smt.applications.podi.PODI.compute_pod
 
+	.. automethod:: smt.application.podi.PODI.compute_pod_errors
+
     .. automethod:: smt.applications.podi.PODI.get_singular_vectors
 
+	.. automethod:: smt.applications.podi.PODI.get_basis
+
 	.. automethod:: smt.applications.podi.PODI.get_singular_values
 
 	.. automethod:: smt.applications.podi.PODI.get_ev_ratio
@@ -168,8 +174,6 @@ PODI class API
 
 	.. automethod:: smt.applications.podi.PODI.set_interp_options
 
-	.. automethod:: smt.applications.podi.PODI.compute_pod
-
 	.. automethod:: smt.applications.podi.PODI.set_training_values
 
 	.. automethod:: smt.applications.podi.PODI.train

smt/applications/__init__.py

@@ -3,8 +3,8 @@
 from .mfkpls import MFKPLS
 from .mfkplsk import MFKPLSK
 from .moe import MOE, MOESurrogateModel
-from .podi import PODI
 from .vfm import VFM
+from .podi import PODI, SubspacesInterpolation
 
 __all__ = [
     "VFM",
@@ -17,4 +17,5 @@
     "EGO",
     "Evaluator",
     "PODI",
+    "SubspacesInterpolation",
 ]