Python cvxpy.Problem方法代码示例

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
def sys_norm_h2_LMI(Acl, Bdisturbance, C):
    #doesn't work very well, if problem poorly scaled Riccati works better.
    #Dullerud p 210
    n = Acl.shape[0]
    X = cvxpy.Semidef(n)
    Y = cvxpy.Semidef(n)

    constraints = [ Acl*X + X*Acl.T + Bdisturbance*Bdisturbance.T == -Y,
                  ]

    obj = cvxpy.Minimize(cvxpy.trace(Y))

    prob = cvxpy.Problem(obj, constraints)
    
    prob.solve()
    eps = 1e-16
    if np.max(np.linalg.eigvals((-Acl*X - X*Acl.T - Bdisturbance*Bdisturbance.T).value)) > -eps:
        print('Acl*X + X*Acl.T +Bdisturbance*Bdisturbance.T is not neg def.')
        return np.Inf

    if np.min(np.linalg.eigvals(X.value)) < eps:
        print('X is not pos def.')
        return np.Inf

    return np.sqrt(np.trace(C*X.value*C.T)) 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
def polish(orig_prob, polish_depth=5, polish_func=None, *args, **kwargs):
    # Fix noncvx variables and solve.
    for var in get_noncvx_vars(orig_prob):
        var.value = var.z.value
    old_val = None
    for t in range(polish_depth):
        fix_constr = []
        for var in get_noncvx_vars(orig_prob):
            fix_constr += var.restrict(var.value)
        polish_prob = cvx.Problem(orig_prob.objective, orig_prob.constraints + fix_constr)
        polish_prob.solve(*args, **kwargs)
        if polish_prob.status in [cvx.OPTIMAL, cvx.OPTIMAL_INACCURATE] and \
        (old_val is None or (old_val - polish_prob.value)/(old_val + 1) > 1e-3):
            old_val = polish_prob.value
        else:
            break

    return polish_prob.value, polish_prob.status

# Add admm method to cvx Problem. 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
def solve(self, X, missing_mask):
        X = check_array(X, force_all_finite=False)

        m, n = X.shape
        S, objective = self._create_objective(m, n)
        constraints = self._constraints(
            X=X,
            missing_mask=missing_mask,
            S=S,
            error_tolerance=self.error_tolerance)
        problem = cvxpy.Problem(objective, constraints)
        problem.solve(
            verbose=self.verbose,
            solver=cvxpy.SCS,
            max_iters=self.max_iters,
            # use_indirect, see: https://github.com/cvxgrp/cvxpy/issues/547
            use_indirect=False)
        return S.value 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
def get_sudoku_matrix(n):
    X = np.array([[cp.Variable(n**2) for i in range(n**2)] for j in range(n**2)])
    cons = ([x >= 0 for row in X for x in row] +
            [cp.sum(x) == 1 for row in X for x in row] +
            [sum(row) == np.ones(n**2) for row in X] +
            [sum([row[i] for row in X]) == np.ones(n**2) for i in range(n**2)] +
            [sum([sum(row[i:i+n]) for row in X[j:j+n]]) == np.ones(n**2) for i in range(0,n**2,n) for j in range(0, n**2, n)])
    f = sum([cp.sum(x) for row in X for x in row])
    prob = cp.Problem(cp.Minimize(f), cons)

    A = np.asarray(prob.get_problem_data(cp.ECOS)[0]["A"].todense())
    A0 = [A[0]]
    rank = 1
    for i in range(1,A.shape[0]):
        if np.linalg.matrix_rank(A0+[A[i]], tol=1e-12) > rank:
            A0.append(A[i])
            rank += 1

    return np.array(A0) 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
def get_inpaint_func_tv():
    def inpaint_func(image, mask):
        """Total variation inpainting"""
        inpainted = np.zeros_like(image)
        for c in range(image.shape[2]):
            image_c = image[:, :, c]
            mask_c = mask[:, :, c]
            if np.min(mask_c) > 0:
                # if mask is all ones, no need to inpaint
                inpainted[:, :, c] = image_c
            else:
                h, w = image_c.shape
                inpainted_c_var = cvxpy.Variable(h, w)
                obj = cvxpy.Minimize(cvxpy.tv(inpainted_c_var))
                constraints = [cvxpy.mul_elemwise(mask_c, inpainted_c_var) == cvxpy.mul_elemwise(mask_c, image_c)]
                prob = cvxpy.Problem(obj, constraints)
                # prob.solve(solver=cvxpy.SCS, max_iters=100, eps=1e-2)  # scs solver
                prob.solve()  # default solver
                inpainted[:, :, c] = inpainted_c_var.value
        return inpainted
    return inpaint_func 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
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) 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
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) 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
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) 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
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) 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
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() 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
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)) 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
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,)) 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
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 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
def fit(self, X, y):
        """
        Fit the model using X, y as training data.

        :param X: array-like, shape=(n_columns, n_samples, ) training data.
        :param y: array-like, shape=(n_samples, ) training data.
        :return: Returns an instance of self.
        """
        X, y = check_X_y(X, y, estimator=self, dtype=FLOAT_DTYPES)

        # Construct the problem.
        betas = cp.Variable(X.shape[1])
        objective = cp.Minimize(cp.sum_squares(X * betas - y))
        constraints = [sum(betas) == 1]
        if self.non_negative:
            constraints.append(0 <= betas)

        # Solve the problem.
        prob = cp.Problem(objective, constraints)
        prob.solve()
        self.coefs_ = betas.value
        return self 

# 需要导入模块: import cvxpy [as 别名]
# 或者: from cvxpy import Problem [as 别名]
def _mk_monotonic_average(xs, ys, intervals, method="increasing", **kwargs):
    """
    Creates smoothed averages of `ys` at the intervals given by `intervals`.
    :param xs: all the datapoints of a feature (represents the x-axis)
    :param ys: all the datapoints what we'd like to predict (represents the y-axis)
    :param intervals: the intervals at which we'd like to get a good average value
    :param method: the method that is used for smoothing, can be either `increasing` or `decreasing`.
    :return:
        An array as long as `intervals` that represents the average `y`-values at those intervals,
        keeping the constraint in mind.
    """
    x_internal = np.array([xs >= i for i in intervals]).T.astype(np.float)
    betas = cp.Variable(x_internal.shape[1])
    objective = cp.Minimize(cp.sum_squares(x_internal * betas - ys))
    if method == "increasing":
        constraints = [betas[i + 1] >= 0 for i in range(betas.shape[0] - 1)]
    elif method == "decreasing":
        constraints = [betas[i + 1] <= 0 for i in range(betas.shape[0] - 1)]
    else:
        raise ValueError(
            f"method must be either `increasing` or `decreasing`, got: {method}"
        )
    prob = cp.Problem(objective, constraints)
    prob.solve()
    return betas.value.cumsum()