add example matrix generator

Author: 0xSooki

app/generate.py

@@ -0,0 +1,40 @@
+import numpy as np
+from scipy.stats import unitary_group
+
+
+def generate_random_unitary(n):
+    """Generate a random n x n unitary matrix."""
+    return unitary_group.rvs(n, random_state=42)
+
+
+def generate_multiplicity_vectors(n, max_val=5):
+    """Generate row and column multiplicity vectors with random values from 0 to max_val,
+    ensuring their sums are equal."""
+    rng = np.random.default_rng(seed=42)
+    total = rng.integers(n, n * max_val + 1)
+    rows = np.zeros(n, dtype=np.uint64)
+    cols = np.zeros(n, dtype=np.uint64)
+    while True:
+        rows = rng.multinomial(total, np.ones(n) / n)
+        cols = rng.multinomial(total, np.ones(n) / n)
+        if np.all(rows <= max_val) and np.all(cols <= max_val):
+            break
+    return rows, cols
+
+
+n = 10
+matrix = generate_random_unitary(n)
+rows, cols = generate_multiplicity_vectors(n)
+
+data = {
+    "matrix": matrix,
+    "rows": rows,
+    "cols": cols,
+}
+
+np.save("example_data.npy", data)
+
+loaded = np.load("example_data.npy", allow_pickle=True).item()
+print("Matrix:\n", loaded["matrix"])
+print("Rows:", loaded["rows"])
+print("Cols:", loaded["cols"])