Python cvxpy.Parameter() Examples

def _generate_cvxpy_problem(self):
        '''
        Generate QP problem
        '''

        x = cvxpy.Variable(self.n)
        y = cvxpy.Variable(self.m)
        t = cvxpy.Variable(self.n)

        # Create parameeter and assign value
        lambda_cvxpy = cvxpy.Parameter()
        lambda_cvxpy.value = self.lambda_param

        objective = cvxpy.Minimize(cvxpy.quad_form(y, spa.eye(self.m))
                                   + self.lambda_param * (np.ones(self.n) * t))
        constraints = [y == self.Ad * x - self.bd,
                       -t <= x, x <= t]
        problem = cvxpy.Problem(objective, constraints)

        return problem, (x, y, t), lambda_cvxpy 

def test_example(self):
        n, m = 2, 3
        x = cp.Variable(n)
        A = cp.Parameter((m, n))
        b = cp.Parameter(m)
        constraints = [x >= 0]
        objective = cp.Minimize(0.5 * cp.pnorm(A @ x - b, p=1))
        problem = cp.Problem(objective, constraints)
        assert problem.is_dpp()

        cvxpylayer = CvxpyLayer(problem, parameters=[A, b], variables=[x])
        A_tch = torch.randn(m, n, requires_grad=True)
        b_tch = torch.randn(m, requires_grad=True)

        # solve the problem
        solution, = cvxpylayer(A_tch, b_tch)

        # compute the gradient of the sum of the solution with respect to A, b
        solution.sum().backward() 

def test_simple_batch_socp(self):
        set_seed(243)
        n = 5
        m = 1
        batch_size = 4

        P_sqrt = cp.Parameter((n, n), name='P_sqrt')
        q = cp.Parameter((n, 1), name='q')
        A = cp.Parameter((m, n), name='A')
        b = cp.Parameter((m, 1), name='b')

        x = cp.Variable((n, 1), name='x')

        objective = 0.5 * cp.sum_squares(P_sqrt @ x) + q.T @ x
        constraints = [A@x == b, cp.norm(x) <= 1]
        prob = cp.Problem(cp.Minimize(objective), constraints)

        prob_tch = CvxpyLayer(prob, [P_sqrt, q, A, b], [x])

        P_sqrt_tch = torch.randn(batch_size, n, n, requires_grad=True)
        q_tch = torch.randn(batch_size, n, 1, requires_grad=True)
        A_tch = torch.randn(batch_size, m, n, requires_grad=True)
        b_tch = torch.randn(batch_size, m, 1, requires_grad=True)

        torch.autograd.gradcheck(prob_tch, (P_sqrt_tch, q_tch, A_tch, b_tch)) 

def test_lml(self):
        tf.random.set_seed(0)
        k = 2
        x = cp.Parameter(4)
        y = cp.Variable(4)
        obj = -x * y - cp.sum(cp.entr(y)) - cp.sum(cp.entr(1. - y))
        cons = [cp.sum(y) == k]
        problem = cp.Problem(cp.Minimize(obj), cons)
        lml = CvxpyLayer(problem, [x], [y])
        x_tf = tf.Variable([1., -1., -1., -1.], dtype=tf.float64)

        with tf.GradientTape() as tape:
            y_opt = lml(x_tf, solver_args={'eps': 1e-10})[0]
            loss = -tf.math.log(y_opt[1])

        def f():
            problem.solve(solver=cp.SCS, eps=1e-10)
            return -np.log(y.value[1])

        grad = tape.gradient(loss, [x_tf])
        numgrad = numerical_grad(f, [x], [x_tf])
        np.testing.assert_almost_equal(grad, numgrad, decimal=3) 

def test_entropy_maximization(self):
        set_seed(243)
        n, m, p = 5, 3, 2

        tmp = np.random.rand(n)
        A_np = np.random.randn(m, n)
        b_np = A_np.dot(tmp)
        F_np = np.random.randn(p, n)
        g_np = F_np.dot(tmp) + np.random.rand(p)

        x = cp.Variable(n)
        A = cp.Parameter((m, n))
        b = cp.Parameter(m)
        F = cp.Parameter((p, n))
        g = cp.Parameter(p)
        obj = cp.Maximize(cp.sum(cp.entr(x)) - .01 * cp.sum_squares(x))
        constraints = [A * x == b,
                       F * x <= g]
        prob = cp.Problem(obj, constraints)
        layer = CvxpyLayer(prob, [A, b, F, g], [x])

        A_tch, b_tch, F_tch, g_tch = map(
            lambda x: torch.from_numpy(x).requires_grad_(True), [
                A_np, b_np, F_np, g_np])
        torch.autograd.gradcheck(
            lambda *x: layer(*x, solver_args={"eps": 1e-12,
                                              "max_iters": 10000}),
            (A_tch,
             b_tch,
             F_tch,
             g_tch),
            eps=1e-4,
            atol=1e-3,
            rtol=1e-3) 

def _generate_cvxpy_problem(self):
        '''
        Generate QP problem
        '''

        x = cvxpy.Variable(self.n)
        y = cvxpy.Variable(self.m)
        t = cvxpy.Variable(self.n)

        # Create parameeter and assign value
        lambda_cvxpy = cvxpy.Parameter()
        lambda_cvxpy.value = self.lambda_param

        objective = cvxpy.Minimize(cvxpy.quad_form(y, spa.eye(self.m))
                                   + self.lambda_param * (np.ones(self.n) * t))
        constraints = [y == self.Ad * x - self.bd,
                       -t <= x, x <= t]
        problem = cvxpy.Problem(objective, constraints)

        return problem, (x, y, t), lambda_cvxpy 

def _generate_cvxpy_problem(self):
        '''
        Generate QP problem
        '''

        x = cvxpy.Variable(self.n)
        y = cvxpy.Variable(self.k)

        # Create parameters m
        mu = cvxpy.Parameter(self.n)
        mu.value = self.mu

        objective = cvxpy.Minimize(cvxpy.quad_form(x, self.D) +
                                   cvxpy.quad_form(y, spa.eye(self.k)) +
                                   - 1 / self.gamma * (mu.T * x))
        constraints = [np.ones(self.n) * x == 1,
                       self.F.T * x == y,
                       0 <= x, x <= 1]
        problem = cvxpy.Problem(objective, constraints)

        return problem, mu 

def __call__(self, *parameters, solver_args={}):
        """Solve problem (or a batch of problems) corresponding to `parameters`

        Args:
          parameters: a sequence of tf.Tensors; the n-th Tensor specifies
                      the value for the n-th CVXPY Parameter. These Tensors
                      can be batched: if a Tensor has 3 dimensions, then its
                      first dimension is interpreted as the batch size.
          solver_args: a dict of optional arguments, to send to `diffcp`. Keys
                       should be the names of keyword arguments.

        Returns:
          a list of optimal variable values, one for each CVXPY Variable
          supplied to the constructor.
        """
        if len(parameters) != len(self.params):
            raise ValueError('A tensor must be provided for each CVXPY '
                             'parameter; received %d tensors, expected %d' % (
                                 len(parameters), len(self.params)))
        compute = tf.custom_gradient(
            lambda *parameters: self._compute(parameters, solver_args))
        return compute(*parameters) 

def running_example():
    print("running example")
    m = 20
    n = 10
    x = cp.Variable((n, 1))
    F = cp.Parameter((m, n))
    g = cp.Parameter((m, 1))
    lambd = cp.Parameter((1, 1), nonneg=True)
    objective_fn = cp.norm(F @ x - g) + lambd * cp.norm(x)
    constraints = [x >= 0]
    problem = cp.Problem(cp.Minimize(objective_fn), constraints)
    assert problem.is_dcp()
    assert problem.is_dpp()
    print("is_dpp: ", problem.is_dpp())

    F_t = torch.randn(m, n, requires_grad=True)
    g_t = torch.randn(m, 1, requires_grad=True)
    lambd_t = torch.rand(1, 1, requires_grad=True)
    layer = CvxpyLayer(problem, parameters=[F, g, lambd], variables=[x])
    x_star, = layer(F_t, g_t, lambd_t)
    x_star.sum().backward()
    print("F_t grad: ", F_t.grad)
    print("g_t grad: ", g_t.grad) 

def relu():
    # print(f'--- {sys._getframe().f_code.co_name} ---')
    print('relu')
    npr.seed(0)

    n = 4
    _x = cp.Parameter(n)
    _y = cp.Variable(n)
    obj = cp.Minimize(cp.sum_squares(_y - _x))
    cons = [_y >= 0]
    prob = cp.Problem(obj, cons)

    _x.value = npr.randn(n)

    prob.solve(solver=cp.SCS)
    print(_y.value) 

def ball_con():
    # print(f'--- {sys._getframe().f_code.co_name} ---')
    print('ball con')
    npr.seed(0)

    n = 2

    A = cp.Parameter((n, n))
    z = cp.Parameter(n)
    p = cp.Parameter(n)
    x = cp.Variable(n)
    t = cp.Variable(n)
    obj = cp.Minimize(0.5 * cp.sum_squares(x - p))
    # TODO automate introduction of variables.
    cons = [0.5 * cp.sum_squares(A * t) <= 1, t == (x - z)]
    prob = cp.Problem(obj, cons)

    L = npr.randn(n, n)
    A.value = L.T
    z.value = npr.randn(n)
    p.value = npr.randn(n)

    prob.solve(solver=cp.SCS)
    print(x.value) 

def __init__(self, m, k, n, complex=False):
        if not cvx_available:
            raise RuntimeError('Cannot initialize when cvxpy is not available.')
        # Initialize parameters and variables
        A = cvx.Parameter((m, k), complex=complex)
        B = cvx.Parameter((m, n), complex=complex)
        l = cvx.Parameter(nonneg=True)
        X = cvx.Variable((k, n), complex=complex)
        # Create the problem
        # CVXPY issue:
        #   cvx.norm does not work if axis is not 0.
        # Workaround:
        #   use cvx.norm(X.T, 2, axis=0) instead of cvx.norm(X, 2, axis=1)
        obj_func = 0.5 * cvx.norm(cvx.matmul(A, X) - B, 'fro')**2 + \
                   l * cvx.sum(cvx.norm(X.T, 2, axis=0))
        self._problem = cvx.Problem(cvx.Minimize(obj_func))
        self._A = A
        self._B = B
        self._l = l
        self._X = X 

def test_shared_parameter(self):
        set_seed(243)
        m, n = 10, 5

        A = cp.Parameter((m, n))
        x = cp.Variable(n)
        b1 = np.random.randn(m)
        b2 = np.random.randn(m)
        prob1 = cp.Problem(cp.Minimize(cp.sum_squares(A @ x - b1)))
        layer1 = CvxpyLayer(prob1, parameters=[A], variables=[x])
        prob2 = cp.Problem(cp.Minimize(cp.sum_squares(A @ x - b2)))
        layer2 = CvxpyLayer(prob2, parameters=[A], variables=[x])

        A_tch = torch.randn(m, n, requires_grad=True)
        solver_args = {
            "eps": 1e-10,
            "acceleration_lookback": 0,
            "max_iters": 10000
        }

        torch.autograd.gradcheck(lambda A: torch.cat(
            [layer1(A, solver_args=solver_args)[0],
             layer2(A, solver_args=solver_args)[0]]), (A_tch,)) 

def set_parameters(self, **kwargs):
        """
        All parameters have to be filled before calling solve().
        Takes the following arguments as keywords:

        A_bar
        B_bar
        C_bar
        S_bar
        z_bar
        X_last
        U_last
        sigma_last
        E
        weight_sigma
        weight_nu
        radius_trust_region
        """

        for key in kwargs:
            if key in self.par:
                self.par[key].value = kwargs[key]
            else:
                print(f'Parameter \'{key}\' does not exist.') 

def test_basic_gp(self):
        set_seed(243)

        x = cp.Variable(pos=True)
        y = cp.Variable(pos=True)
        z = cp.Variable(pos=True)

        a = cp.Parameter(pos=True, value=2.0)
        b = cp.Parameter(pos=True, value=1.0)
        c = cp.Parameter(value=0.5)

        objective_fn = 1/(x*y*z)
        constraints = [a*(x*y + x*z + y*z) <= b, x >= y**c]
        problem = cp.Problem(cp.Minimize(objective_fn), constraints)
        problem.solve(cp.SCS, gp=True, eps=1e-12)

        layer = CvxpyLayer(
            problem, parameters=[a, b, c], variables=[x, y, z], gp=True)
        a_tch = torch.tensor(2.0, requires_grad=True)
        b_tch = torch.tensor(1.0, requires_grad=True)
        c_tch = torch.tensor(0.5, requires_grad=True)
        with torch.no_grad():
            x_tch, y_tch, z_tch = layer(a_tch, b_tch, c_tch)

        self.assertAlmostEqual(x.value, x_tch.detach().numpy(), places=5)
        self.assertAlmostEqual(y.value, y_tch.detach().numpy(), places=5)
        self.assertAlmostEqual(z.value, z_tch.detach().numpy(), places=5)

        torch.autograd.gradcheck(lambda a, b, c: layer(
            a, b, c, solver_args={
                "eps": 1e-12, "acceleration_lookback": 0})[0].sum(),
                (a_tch, b_tch, c_tch), atol=1e-3, rtol=1e-3) 

def test_infeasible(self):
        x = cp.Variable(1)
        param = cp.Parameter(1)
        prob = cp.Problem(cp.Minimize(param), [x >= 1, x <= -1])
        layer = CvxpyLayer(prob, [param], [x])
        param_tf = tf.ones(1)
        with self.assertRaises(diffcp.SolverError):
            layer(param_tf) 

def __init__(self, m, k, formulation='penalizedl1', nonnegative=False):
        if not cvx_available:
            raise RuntimeError('Cannot initialize when cvxpy is not available.')
        # Initialize parameters and variables
        A = cvx.Parameter((m, k))
        b = cvx.Parameter((m, 1))
        l = cvx.Parameter(nonneg=True)
        x = cvx.Variable((k, 1))
        # Create the problem
        if formulation == 'penalizedl1':
            obj_func = 0.5 * cvx.sum_squares(cvx.matmul(A, x) - b) + l * cvx.norm1(x)
            constraints = []
        elif formulation == 'constrainedl1':
            obj_func = cvx.sum_squares(cvx.matmul(A, x) - b)
            constraints = [cvx.norm1(x) <= l]
        elif formulation == 'constrainedl2':
            obj_func = cvx.norm1(x)
            constraints = [cvx.norm(cvx.matmul(A, x) - b) <= l]
        else:
            raise ValueError("Unknown formulation '{0}'.".format(formulation))
        if nonnegative:
            constraints.append(x >= 0)
        problem = cvx.Problem(cvx.Minimize(obj_func), constraints)
        self._formulation = formulation
        self._A = A
        self._b = b
        self._l = l
        self._x = x
        self._obj_func = obj_func
        self._constraints = constraints
        self._problem = problem 

def test_least_squares(self):
        set_seed(243)
        m, n = 100, 20

        A = cp.Parameter((m, n))
        b = cp.Parameter(m)
        x = cp.Variable(n)
        obj = cp.sum_squares(A@x - b) + cp.sum_squares(x)
        prob = cp.Problem(cp.Minimize(obj))
        prob_th = CvxpyLayer(prob, [A, b], [x])

        A_th = torch.randn(m, n).double().requires_grad_()
        b_th = torch.randn(m).double().requires_grad_()

        x = prob_th(A_th, b_th, solver_args={"eps": 1e-10})[0]

        def lstsq(
            A,
            b): return torch.solve(
            (A_th.t() @ b_th).unsqueeze(1),
            A_th.t() @ A_th +
            torch.eye(n).double())[0]
        x_lstsq = lstsq(A_th, b_th)

        grad_A_cvxpy, grad_b_cvxpy = grad(x.sum(), [A_th, b_th])
        grad_A_lstsq, grad_b_lstsq = grad(x_lstsq.sum(), [A_th, b_th])

        self.assertAlmostEqual(
            torch.norm(
                grad_A_cvxpy -
                grad_A_lstsq).item(),
            0.0)
        self.assertAlmostEqual(
            torch.norm(
                grad_b_cvxpy -
                grad_b_lstsq).item(),
            0.0) 

def test_logistic_regression(self):
        set_seed(243)
        N, n = 10, 2
        X_np = np.random.randn(N, n)
        a_true = np.random.randn(n, 1)
        y_np = np.round(sigmoid(X_np @ a_true + np.random.randn(N, 1) * 0.5))

        X_tch = torch.from_numpy(X_np)
        X_tch.requires_grad_(True)
        lam_tch = 0.1 * torch.ones(1, requires_grad=True, dtype=torch.double)

        a = cp.Variable((n, 1))
        X = cp.Parameter((N, n))
        lam = cp.Parameter(1, nonneg=True)
        y = y_np

        log_likelihood = cp.sum(
            cp.multiply(y, X @ a) -
            cp.log_sum_exp(cp.hstack([np.zeros((N, 1)), X @ a]).T, axis=0,
                           keepdims=True).T
        )
        prob = cp.Problem(
            cp.Minimize(-log_likelihood + lam * cp.sum_squares(a)))

        fit_logreg = CvxpyLayer(prob, [X, lam], [a])

        def layer_eps(*x):
            return fit_logreg(*x, solver_args={"eps": 1e-12})

        torch.autograd.gradcheck(layer_eps,
                                 (X_tch,
                                  lam_tch),
                                 eps=1e-4,
                                 atol=1e-3,
                                 rtol=1e-3) 

def sparse_lowrank_mse(name_size):
    name, size = name_size
    print(name, size)
    matrix = named_target_matrix(name, size)
    M = matrix
    lambda1 = cp.Parameter(nonneg=True)
    lambda2 = cp.Parameter(nonneg=True)
    L = cp.Variable((size, size))
    S = cp.Variable((size, size))
    prob = cp.Problem(cp.Minimize(cp.sum_squares(M - L - S) / size**2 + lambda1 / size * cp.norm(L, 'nuc') + lambda2 / size**2 * cp.norm(S, 1)))

    result = []
    for _ in range(ntrials):
        l1 = np.exp(np.random.uniform(np.log(1e-2), np.log(1e4)))
        l2 = np.exp(np.random.uniform(np.log(1e-2), np.log(1e4)))
        lambda1.value = l1
        lambda2.value = l2
        try:
            prob.solve()
            nnz = (np.abs(S.value) >= 1e-7).sum()
            singular_values = np.linalg.svd(L.value, compute_uv=False)
            rank = (singular_values >= 1e-7).sum()
            n_params = nnz + 2 * rank * size
            mse = np.sum((matrix - L.value - S.value)**2) / size**2
            result.append((n_params, mse))
        except:
            pass
    budget = 2 * size * np.log2(size)
    if model[name] == 'BPBP':
        budget *= 2
    eligible = [res for res in result if res[0] <= budget]
    if eligible:
        mse = min(m for (n_params, m) in eligible)
    else:
        mse = np.sum(matrix**2) / size**2
    print(name, size, 'done')
    return (name, size, mse) 

def test_sdp(self):
        set_seed(2)

        n = 3
        p = 3
        C = cp.Parameter((n, n))
        A = [cp.Parameter((n, n)) for _ in range(p)]
        b = [cp.Parameter((1, 1)) for _ in range(p)]

        C_tch = torch.randn(n, n, requires_grad=True).double()
        A_tch = [torch.randn(n, n, requires_grad=True).double()
                 for _ in range(p)]
        b_tch = [torch.randn(1, 1, requires_grad=True).double()
                 for _ in range(p)]

        X = cp.Variable((n, n), symmetric=True)
        constraints = [X >> 0]
        constraints += [
            cp.trace(A[i]@X) == b[i] for i in range(p)
        ]
        prob = cp.Problem(cp.Minimize(cp.trace(C@X) + cp.sum_squares(X)),
                          constraints)
        layer = CvxpyLayer(prob, [C] + A + b, [X])
        torch.autograd.gradcheck(lambda *x: layer(*x,
                                                  solver_args={'eps': 1e-12}),
                                 [C_tch] + A_tch + b_tch,
                                 eps=1e-6,
                                 atol=1e-3,
                                 rtol=1e-3) 

def test_not_enough_parameters(self):
        x = cp.Variable(1)
        lam = cp.Parameter(1, nonneg=True)
        lam2 = cp.Parameter(1, nonneg=True)
        objective = lam * cp.norm(x, 1) + lam2 * cp.sum_squares(x)
        prob = cp.Problem(cp.Minimize(objective))
        with self.assertRaises(ValueError):
            layer = CvxpyLayer(prob, [lam], [x])  # noqa: F841 

def test_incorrect_parameter_shape(self):
        set_seed(243)
        m, n = 100, 20

        A = cp.Parameter((m, n))
        b = cp.Parameter(m)
        x = cp.Variable(n)
        obj = cp.sum_squares(A@x - b) + cp.sum_squares(x)
        prob = cp.Problem(cp.Minimize(obj))
        prob_th = CvxpyLayer(prob, [A, b], [x])

        A_th = torch.randn(32, m, n).double().requires_grad_()
        b_th = torch.randn(20, m).double().requires_grad_()

        with self.assertRaises(ValueError):
            prob_th(A_th, b_th)

        A_th = torch.randn(32, m, n).double().requires_grad_()
        b_th = torch.randn(32, 2 * m).double().requires_grad_()

        with self.assertRaises(ValueError):
            prob_th(A_th, b_th)

        A_th = torch.randn(m, n).double().requires_grad_()
        b_th = torch.randn(2 * m).double().requires_grad_()

        with self.assertRaises(ValueError):
            prob_th(A_th, b_th)

        A_th = torch.randn(32, m, n).double().requires_grad_()
        b_th = torch.randn(32, 32, m).double().requires_grad_()

        with self.assertRaises(ValueError):
            prob_th(A_th, b_th) 

def test_equality(self):
        set_seed(243)
        n = 10
        A = np.eye(n)
        x = cp.Variable(n)
        b = cp.Parameter(n)
        prob = cp.Problem(cp.Minimize(cp.sum_squares(x)), [A@x == b])
        layer = CvxpyLayer(prob, parameters=[b], variables=[x])
        b_tch = torch.randn(n, requires_grad=True)
        torch.autograd.gradcheck(lambda b: layer(
            b, solver_args={"eps": 1e-10,
                            "acceleration_lookback": 0})[0].sum(),
            (b_tch,)) 

def test_not_enough_parameters_at_call_time(self):
        x = cp.Variable(1)
        lam = cp.Parameter(1, nonneg=True)
        lam2 = cp.Parameter(1, nonneg=True)
        objective = lam * cp.norm(x, 1) + lam2 * cp.sum_squares(x)
        prob = cp.Problem(cp.Minimize(objective))
        layer = CvxpyLayer(prob, [lam, lam2], [x])  # noqa: F841
        with self.assertRaisesRegex(
                ValueError,
                'A tensor must be provided for each CVXPY parameter.*'):
            layer(lam) 

def test_too_many_variables(self):
        x = cp.Variable(1)
        y = cp.Variable(1)
        lam = cp.Parameter(1, nonneg=True)
        objective = lam * cp.norm(x, 1)
        prob = cp.Problem(cp.Minimize(objective))
        with self.assertRaises(ValueError):
            layer = CvxpyLayer(prob, [lam], [x, y])  # noqa: F841 

def test_infeasible(self):
        x = cp.Variable(1)
        param = cp.Parameter(1)
        prob = cp.Problem(cp.Minimize(param), [x >= 1, x <= -1])
        layer = CvxpyLayer(prob, [param], [x])
        param_tch = torch.ones(1)
        with self.assertRaises(diffcp.SolverError):
            layer(param_tch) 

def test_broadcasting(self):
        set_seed(243)
        n_batch, m, n = 2, 100, 20

        A = cp.Parameter((m, n))
        b = cp.Parameter(m)
        x = cp.Variable(n)
        obj = cp.sum_squares(A@x - b) + cp.sum_squares(x)
        prob = cp.Problem(cp.Minimize(obj))
        prob_th = CvxpyLayer(prob, [A, b], [x])

        A_th = torch.randn(m, n).double().requires_grad_()
        b_th = torch.randn(m).double().unsqueeze(0).repeat(n_batch, 1) \
            .requires_grad_()
        b_th_0 = b_th[0]

        x = prob_th(A_th, b_th, solver_args={"eps": 1e-10})[0]

        def lstsq(
            A,
            b): return torch.solve(
            (A.t() @ b).unsqueeze(1),
            A.t() @ A +
            torch.eye(n).double())[0]
        x_lstsq = lstsq(A_th, b_th_0)

        grad_A_cvxpy, grad_b_cvxpy = grad(x.sum(), [A_th, b_th])
        grad_A_lstsq, grad_b_lstsq = grad(x_lstsq.sum(), [A_th, b_th_0])

        self.assertAlmostEqual(
            torch.norm(
                grad_A_cvxpy / n_batch -
                grad_A_lstsq).item(),
            0.0)
        self.assertAlmostEqual(
            torch.norm(
                grad_b_cvxpy[0] -
                grad_b_lstsq).item(),
            0.0) 

def sigmoid():
    # print(f'--- {sys._getframe().f_code.co_name} ---')
    print('sigmoid')
    npr.seed(0)

    n = 4
    _x = cp.Parameter((n, 1))
    _y = cp.Variable(n)
    obj = cp.Minimize(-_x.T * _y - cp.sum(cp.entr(_y) + cp.entr(1. - _y)))
    prob = cp.Problem(obj)

    _x.value = npr.randn(n, 1)

    prob.solve(solver=cp.SCS)
    print(_y.value) 

def __init__(self, rows, cols, *args, **kwargs):
        super(NonCvxVariable, self).__init__((rows, cols,), *args, **kwargs)
        self.noncvx = True
        self.z = cvxpy.Parameter(self.shape)
        self.u = cvxpy.Parameter(self.shape)
        self.u.value = np.zeros(self.shape)