From 7db0d82731ababdf0b2f4d986dd54da3b4650954 Mon Sep 17 00:00:00 2001
From: y-jan137 <yousefjan24000@gmail.com>
Date: Sat, 14 Mar 2026 14:49:46 +0300
Subject: Add triangular solve

---
 examples/linear_system.cpp | 36 ++++++++++++++++++++++++++++++++++++
 1 file changed, 36 insertions(+)
 create mode 100644 examples/linear_system.cpp

(limited to 'examples/linear_system.cpp')

diff --git a/examples/linear_system.cpp b/examples/linear_system.cpp
new file mode 100644
index 0000000..184f576
--- /dev/null
+++ b/examples/linear_system.cpp
@@ -0,0 +1,36 @@
+#include "matrix.hpp"
+#include "norms.hpp"
+#include "triangular_solve.hpp"
+#include "vector.hpp"
+
+#include <iomanip>
+#include <iostream>
+
+int main() {
+    const linalg::Matrix basis = linalg::Matrix::identity(3);
+    const linalg::Matrix upper{
+        {4.0, -2.0, 1.0},
+        {0.0, 3.0, 5.0},
+        {0.0, 0.0, -2.0}
+    };
+    const linalg::Vector expected{2.0, -1.0, 3.0};
+    const linalg::Vector rhs = upper * expected;
+    const linalg::Vector x = linalg::backward_substitution(upper, rhs);
+
+    std::cout << "Week 3 triangular solve demo\n";
+    std::cout << "Identity matrix diagonal: ";
+    for (std::size_t i = 0; i < basis.rows(); ++i) {
+        std::cout << basis(i, i) << (i + 1 == basis.rows() ? '\n' : ' ');
+    }
+
+    std::cout << "Recovered solution x: ";
+    for (std::size_t i = 0; i < x.size(); ++i) {
+        std::cout << std::fixed << std::setprecision(2) << x[i]
+                  << (i + 1 == x.size() ? '\n' : ' ');
+    }
+
+    const linalg::Vector residual = (upper * x) - rhs;
+    std::cout << "Residual 2-norm = " << linalg::norm2(residual) << '\n';
+
+    return 0;
+}
-- 
cgit v1.2.3