comments in experiment

experiments/talk/minVariance2.py

@@ -5,18 +5,17 @@
 
 
 def f():
-    L = np.linalg.cholesky(A)
-
+    U = uu
     x = cp.Variable(n)
 
-    objective = cp.Minimize(cp.norm2(L.T @ x))
+    objective = cp.Minimize(cp.norm2(U @ x))
     constraints = [cp.sum(x) == 1, x >= 0]
     prob = cp.Problem(objective, constraints)
     prob.solve(solver)
 
 
 def g():
-    L.value = np.linalg.cholesky(A)
+    U.value = uu
     prob.solve(solver)
 
 
@@ -25,27 +24,45 @@ def g():
     C = np.random.rand(n, n)
     A = C @ C.T
 
+    uu = np.transpose(np.linalg.cholesky(A))
+
+    # check all eigenvalue are positive
     result = np.linalg.eigh(A)
     assert np.all(result.eigenvalues > 0)
 
     for solver in [cp.MOSEK, cp.CLARABEL, cp.ECOS]:
         print(solver)
+
+        # solve one problem
         execution_time = timeit.timeit(f, number=1)
         print(f"{execution_time:.6f} seconds")
 
+        # solve 10 problems, each time the problem is reconstructed
+        # Should take 10times longer than the previous one
         execution_time = timeit.timeit(f, number=10)
         print(f"{execution_time:.6f} seconds")
 
+        # construct the problem once with parameters
         x = cp.Variable(n)
-        L = cp.Parameter((n, n))
+        # would be good if the parameter could be an upper triangular matrix
+        # rather than just a matrix
+        U = cp.Parameter((n, n))
 
-        objective = cp.Minimize(cp.norm2(L.T @ x))
+        # construct the problem
+        objective = cp.Minimize(cp.norm2(U @ x))
         constraints = [cp.sum(x) == 1, x >= 0]
-
         prob = cp.Problem(objective, constraints)
 
+        # could we know construct the problem
+        xxx = prob.get_problem_data(solver)
+        # what can we do with xxx?
+
+        # solve the problem only once, should be faster
+        # than the previous one, but not for CLARABEL and ECOS
         execution_time = timeit.timeit(g, number=1)
         print(f"{execution_time:.6f} seconds")
+        # assert False
 
-        execution_time = timeit.timeit(g, number=100)
+        # solve the problem 10 times
+        execution_time = timeit.timeit(g, number=10)
         print(f"{execution_time:.6f} seconds")