Fix: update the toy example in README.md (#74)

Author: yuwenchen95

README.md

@@ -118,6 +118,18 @@ from scipy import sparse
 
 import diffcp
 
+def random_cone_prog(m, n, cone_dict):
+    """Returns the problem data of a random cone program."""
+    cone_list = diffcp.cones.parse_cone_dict(cone_dict)
+    z = np.random.randn(m)
+    s_star = diffcp.cones.pi(z, cone_list, dual=False)
+    y_star = s_star - z
+    A = sparse.csc_matrix(np.random.randn(m, n))
+    x_star = np.random.randn(n)
+    b = A @ x_star + s_star
+    c = -A.T @ y_star
+    return A, b, c
+
 cone_dict = {
     diffcp.ZERO: 3,
     diffcp.POS: 3,
@@ -127,7 +139,7 @@ cone_dict = {
 m = 3 + 3 + 5
 n = 5
 
-A, b, c = diffcp.utils.random_cone_prog(m, n, cone_dict)
+A, b, c = random_cone_prog(m, n, cone_dict)
 x, y, s, D, DT = diffcp.solve_and_derivative(A, b, c, cone_dict)
 
 # evaluate the derivative