From ffa4d7eacc86981dcc1a68e06ffed54f1bd9037a Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Mon, 20 May 2024 14:10:42 +0200
Subject: Create Lower triangular matrix expression

---
 polymatrix/expression/impl.py                      |  6 +++
 polymatrix/expression/init.py                      |  4 ++
 .../expression/mixins/lowertriangularexprmixin.py  | 59 ++++++++++++++++++++++
 polymatrix/polymatrix/mixins.py                    |  5 --
 4 files changed, 69 insertions(+), 5 deletions(-)
 create mode 100644 polymatrix/expression/mixins/lowertriangularexprmixin.py

diff --git a/polymatrix/expression/impl.py b/polymatrix/expression/impl.py
index 2eeea39..a1a4269 100644
--- a/polymatrix/expression/impl.py
+++ b/polymatrix/expression/impl.py
@@ -31,6 +31,7 @@ from polymatrix.expression.mixins.legendreseriesmixin import LegendreSeriesMixin
 from polymatrix.expression.mixins.linearinexprmixin import LinearInExprMixin
 from polymatrix.expression.mixins.linearmatrixinexprmixin import LinearMatrixInExprMixin
 from polymatrix.expression.mixins.linearmonomialsexprmixin import LinearMonomialsExprMixin
+from polymatrix.expression.mixins.lowertriangularexprmixin import LowerTriangularExprMixin
 from polymatrix.expression.mixins.matrixmultexprmixin import MatrixMultExprMixin
 from polymatrix.expression.mixins.maxexprmixin import MaxExprMixin
 from polymatrix.expression.mixins.parametrizeexprmixin import ParametrizeExprMixin
@@ -232,6 +233,11 @@ class LinearMonomialsExprImpl(LinearMonomialsExprMixin):
     variables: tuple
 
 
+@dataclassabc.dataclassabc(frozen=True)
+class LowerTriangularExprImpl(LowerTriangularExprMixin):
+    underlying: ExpressionBaseMixin
+
+
 @dataclassabc.dataclassabc(frozen=True)
 class LegendreSeriesImpl(LegendreSeriesMixin):
     underlying: ExpressionBaseMixin
diff --git a/polymatrix/expression/init.py b/polymatrix/expression/init.py
index 30fd3e1..825bc10 100644
--- a/polymatrix/expression/init.py
+++ b/polymatrix/expression/init.py
@@ -275,6 +275,10 @@ def init_linear_matrix_in_expr(
     )
 
 
+def init_lower_triangular_expr(underlying: ExpressionBaseMixin):
+    return polymatrix.expression.impl.LowerTriangularExprImpl(underlying)
+
+
 def init_matrix_mult_expr(
     left: ExpressionBaseMixin,
     right: ExpressionBaseMixin,
diff --git a/polymatrix/expression/mixins/lowertriangularexprmixin.py b/polymatrix/expression/mixins/lowertriangularexprmixin.py
new file mode 100644
index 0000000..74368a4
--- /dev/null
+++ b/polymatrix/expression/mixins/lowertriangularexprmixin.py
@@ -0,0 +1,59 @@
+from __future__ import annotations
+
+from abc import abstractmethod
+from math import sqrt, isclose
+from typing_extensions import override
+
+from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin
+from polymatrix.expressionstate import ExpressionState
+from polymatrix.polymatrix.index import PolyMatrixDict
+from polymatrix.polymatrix.init import init_poly_matrix
+from polymatrix.polymatrix.mixins import PolyMatrixMixin
+
+class LowerTriangularExprMixin(ExpressionBaseMixin):
+    @property
+    @abstractmethod
+    def underlying(self) -> ExpressionBaseMixin:
+        r"""
+        Construct a lower triangular matrix from a vector.
+
+        For a :math:`n\times n` lower diagonal matrix, this is a :math:`n * (n
+        + 1) / 2` dimensional vector containing the entries. The lower diagonal
+        matrix is filled from top to bottom so given the vector :math:`z` the 
+        lower triangular matrix is
+
+        .. math::
+            Z = \begin{bmatrix}
+                z_1 \\
+                z_2 & z_3 \\
+                z_4 & z_5 & z_6 \\
+                \vdots &  & & \ddots \\
+            \end{bmatrix}.
+
+        """
+
+    @override
+    def apply(self, state: ExpressionState) -> tuple[ExpressionState, PolyMatrixMixin]:
+        state, u = self.underlying.apply(state)
+
+        N, ncols = u.shape
+        if ncols > 1:
+            raise ValueError("Cannot construct lower triangular matrix from object "
+                             f"with shape {u.shape}, it must be a column vector.")
+
+        n_float = .5 * (-1 + sqrt(1 + 8 * N))
+        if not isclose(int(n_float), n_float):
+            raise ValueError("To construct a n x n lower triangular matrix, the vector "
+                             "must be n * (n + 1) / 2 column dimensional.")
+        
+        n = int(n_float)
+        p = PolyMatrixDict.empty()
+
+        for row in range(n):
+            for col in range(row):
+                p[row, col] = u.at(row + col, 1)
+
+        return state, init_poly_matrix(p, shape=(n, n))
+
+
+
diff --git a/polymatrix/polymatrix/mixins.py b/polymatrix/polymatrix/mixins.py
index 63eeb18..fa1644e 100644
--- a/polymatrix/polymatrix/mixins.py
+++ b/polymatrix/polymatrix/mixins.py
@@ -13,11 +13,6 @@ from typing_extensions import override
 from polymatrix.polymatrix.index import PolyDict, PolyMatrixDict, MatrixIndex, MonomialIndex, VariableIndex
 from polymatrix.utils.deprecation import deprecated
 
-if TYPE_CHECKING:
-    from polymatrix.expression.mixins.variablemixin import VariableMixin
-    from polymatrix.expressionstate.mixins import ExpressionStateMixin
-
-
 class PolyMatrixMixin(ABC):
     """
     Matrix with polynomial entries.
-- 
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