From 0e5e050166a221712cb4047625652bf0210e7c61 Mon Sep 17 00:00:00 2001
From: Michael Schneeberger <michael.schneeberger@fhnw.ch>
Date: Mon, 8 May 2023 11:53:28 +0200
Subject: allow sos expression to have more than 1 column

---
 sumofsquares/init/initsosexpr.py                      |  6 ++++--
 sumofsquares/mixins/sosexpropmixin.py                 | 11 +++++++++++
 sumofsquares/sosexprbase/impl.py                      |  1 +
 sumofsquares/sosexprbase/init/initsosexprbase.py      | 15 ++++++++++-----
 sumofsquares/sosexprbase/mixins/exprfrommonommixin.py | 14 +++++++++++++-
 5 files changed, 39 insertions(+), 8 deletions(-)

diff --git a/sumofsquares/init/initsosexpr.py b/sumofsquares/init/initsosexpr.py
index c858549..214bb0d 100644
--- a/sumofsquares/init/initsosexpr.py
+++ b/sumofsquares/init/initsosexpr.py
@@ -25,14 +25,16 @@ def init_param_expr(
     name: str, 
     variables: polymatrix.Expression,
     monom: polymatrix.Expression | None = None,
-    n_rows: int | None = None,
+    n_row: int | None = None,
+    n_col: int | None = None,
 ):
     return ParamSOSExprImpl(
         underlying=init_param_sos_expr_base(
             name=name,
             monom=monom,
             variables=variables,
-            n_rows=n_rows,
+            n_row=n_row,
+            n_col=n_col,
         ),
     )
 
diff --git a/sumofsquares/mixins/sosexpropmixin.py b/sumofsquares/mixins/sosexpropmixin.py
index a345284..2020043 100644
--- a/sumofsquares/mixins/sosexpropmixin.py
+++ b/sumofsquares/mixins/sosexpropmixin.py
@@ -131,3 +131,14 @@ class SOSExprOPMixin(SOSExprMixin):
                 dependence=self.dependence,
             ),
         )
+    
+    def set_variables(self, variables):
+        return dataclasses.replace(
+            self,
+            underlying=init_sos_expr_base(
+                expr=self.expr,
+                variables=variables,
+                dependence=self.dependence,
+            ),
+        )
+
diff --git a/sumofsquares/sosexprbase/impl.py b/sumofsquares/sosexprbase/impl.py
index 02f220f..5a3a800 100644
--- a/sumofsquares/sosexprbase/impl.py
+++ b/sumofsquares/sosexprbase/impl.py
@@ -19,3 +19,4 @@ class ParamSOSExprBaseImpl(ParamSOSExprBase):
     monom: polymatrix.Expression
     variables: polymatrix.Expression
     param_matrix: polymatrix.Expression
+    n_row: int
diff --git a/sumofsquares/sosexprbase/init/initsosexprbase.py b/sumofsquares/sosexprbase/init/initsosexprbase.py
index 6b7f299..9dade7e 100644
--- a/sumofsquares/sosexprbase/init/initsosexprbase.py
+++ b/sumofsquares/sosexprbase/init/initsosexprbase.py
@@ -30,20 +30,24 @@ def init_param_sos_expr_base(
     name: str, 
     variables: polymatrix.Expression,
     monom: polymatrix.Expression | None = None,
-    n_rows: int | None = None,
+    n_row: int | None = None,
+    n_col: int | None = None,
 ):
     if monom is None:
         monom = polymatrix.from_(1)
 
-    if n_rows is None:
-        n_rows = 1
+    if n_row == None:
+        n_row = 1
 
-    if n_rows is 1:
+    if n_col == None:
+        n_col = 1
+
+    if n_row == 1 and n_col == 1:
         param = monom.parametrize(f'{name}')
         param_matrix = param.T
 
     else:
-        params = tuple(monom.parametrize(f'{name}_{row+1}') for row in range(n_rows))
+        params = tuple(monom.parametrize(f'{name}_{row+1}_{col+1}') for col in range(n_col) for row in range(n_row))
         param = polymatrix.v_stack(params)
         param_matrix = polymatrix.v_stack(tuple(param.T for param in params))
 
@@ -53,4 +57,5 @@ def init_param_sos_expr_base(
         monom=monom,
         variables=variables,
         param_matrix=param_matrix,
+        n_row=n_row,
     )
diff --git a/sumofsquares/sosexprbase/mixins/exprfrommonommixin.py b/sumofsquares/sosexprbase/mixins/exprfrommonommixin.py
index 354f46f..6e6e80b 100644
--- a/sumofsquares/sosexprbase/mixins/exprfrommonommixin.py
+++ b/sumofsquares/sosexprbase/mixins/exprfrommonommixin.py
@@ -11,6 +11,18 @@ class ExprFromMonomMixin(ParameterMixin, ExprBaseMixin):
     def param_matrix(self) -> polymatrix.Expression:
         ...
 
+    @property
+    @abc.abstractmethod
+    def n_row(self) -> int:
+        ...
+
     @property
     def expr(self) -> polymatrix.Expression:
-        return (self.param_matrix @ self.monom).cache()
+        expr_vec = (self.param_matrix @ self.monom).cache()
+
+        if self.n_row == 1:
+            return expr_vec
+        
+        else:
+            return expr_vec.reshape(self.n_row, -1)
+
-- 
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