From 2ce3633b355a9419a64ee05c2acd53540e176c6f Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Fri, 24 May 2024 21:19:55 +0200
Subject: Allow shape of OptVariableExpr to be an Expression

---
 sumofsquares/__init__.py |  9 ++++++--
 sumofsquares/variable.py | 53 ++++++++++++++++++++++++++++++++++++++----------
 2 files changed, 49 insertions(+), 13 deletions(-)

diff --git a/sumofsquares/__init__.py b/sumofsquares/__init__.py
index 54aec7e..6ca2b39 100644
--- a/sumofsquares/__init__.py
+++ b/sumofsquares/__init__.py
@@ -75,9 +75,14 @@ from .abc import Problem, Result, Set, Constraint, Solver
 from .constraints import BasicSemialgebraicSet, NonNegative
 from .problems import PutinarSOSProblem
 from .utils import partition
-from .variable import OptVariable, from_names as internal_from_names
+from .variable import (
+        OptVariable,
+        from_name as internal_from_name,
+        from_names as internal_from_names)
 
-# export function
+
+# export optimization variable constructors
+from_name = internal_from_name
 from_names = internal_from_names
 
 def make_sos_constraint(expr: Expression, domain: Set | None = None) -> NonNegative:
diff --git a/sumofsquares/variable.py b/sumofsquares/variable.py
index f309406..28bbc97 100644
--- a/sumofsquares/variable.py
+++ b/sumofsquares/variable.py
@@ -10,11 +10,14 @@ this extends the following parts of polymatrix:
 
 from __future__ import annotations
 
+from abc import abstractmethod
 from itertools import product
+from typing import Iterable
 from typing_extensions import override
+from dataclasses import replace
 from dataclassabc import dataclassabc
 
-from polymatrix.expression.expression import VariableExpression, init_variable_expression
+from polymatrix.expression.expression import Expression, VariableExpression, init_variable_expression
 from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin
 from polymatrix.expressionstate import ExpressionState
 from polymatrix.polymatrix.abc import PolyMatrix
@@ -31,26 +34,52 @@ class OptVariableMixin(ExpressionBaseMixin, OptVariable):
     """ Optimization (decision) variable mixin for expression object. """
 
     @override
-    def apply(self, state: ExpressionState) -> tuple[ExpressionState, PolyMatrix]:
-        state = state.register(self)
-        indices = state.get_indices(self)
-        p = PolyMatrixDict()
+    @property
+    @abstractmethod
+    def shape(self) -> tuple[int, int] | ExpressionBaseMixin:
+        """ Shape of the optimization variable expression. """
+
+    @override
+    def apply(self, state: ExpressionState) -> tuple[ExpressionState, PolyMatrixMixin]:
+        if isinstance(self.shape, ExpressionBaseMixin):
+            state, shape_pm = self.shape.apply(state)
+            if shape_pm.shape != (2, 1):
+                raise ValueError("If shape is an expression it must evaluate to a 2d row vector, "
+                                 f"but here it has shape {shape_pm.shape}")
+
+            # FIXME: should check that they are actually integers
+            nrows = int(shape_pm.at(0, 0).constant())
+            ncols = int(shape_pm.at(1, 0).constant())
+
+            # Replace shape field with computed shape
+            v = replace(self, shape=(nrows, ncols))
+            state = state.register(v) 
+            indices = state.get_indices(v)
+
+        elif isinstance(self.shape, tuple):
+            nrows, ncols = self.shape
+            state = state.register(self) 
+            indices = state.get_indices(self)
+
+        else:
+            raise ValueError("Shape must be a tuple or expression that "
+                f"evaluates to a 2d row vector, cannot be of type {type(self.shape)}")
 
-        rows, cols = self.shape
-        for (row, col), index in zip(product(range(rows), range(cols)), indices):
+        p = PolyMatrixDict()
+        for (row, col), index in zip(product(range(nrows), range(ncols)), indices):
             p[row, col] = PolyDict({
                 # Create monomial with variable to the first power
                 # with coefficient of one
                 MonomialIndex((VariableIndex(index, power=1),)): 1.
             })
 
-        return state, init_poly_matrix(p, self.shape)
+        return state, init_poly_matrix(p, shape=(nrows, ncols))
 
 
 @dataclassabc(frozen=True)
 class OptVariableImpl(OptVariableMixin):
     name: str
-    shape: tuple[int, int]
+    shape: tuple[int, int] | ExpressionBaseMixin
 
     def __str__(self):
         return self.name
@@ -60,12 +89,14 @@ def init_opt_variable_expr(name, shape):
     return OptVariableImpl(name, shape)
 
 
-def from_name(name: str, shape: tuple[int, int] = (1, 1)) -> VariableExpression:
+def from_name(name: str, shape: tuple[int, int] | ExpressionBaseMixin = (1, 1)) -> VariableExpression:
     """ Construct an optimization variable. """
+    if isinstance(shape, Expression):
+        shape = shape.underlying
     return init_variable_expression(underlying=init_opt_variable_expr(name, shape))
 
 
-def from_names(names: str, shape: tuple[int, int] = (1, 1)) -> Iterable[VariableExpression]:
+def from_names(names: str, shape: tuple[int, int]  | ExpressionBaseMixin = (1, 1)) -> Iterable[VariableExpression]:
     """ Construct one or multiple variables from comma separated a list of names. """
     for name in names.split(","):
         yield from_name(name.strip(), shape)
-- 
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