Update matrices
===============


Consider the following QP


.. math::
  \begin{array}{ll}
    \mbox{minimize} & \frac{1}{2} x^T \begin{bmatrix}4 & 1\\ 1 & 2 \end{bmatrix} x + \begin{bmatrix}1 \\ 1\end{bmatrix}^T x \\
    \mbox{subject to} & \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \leq \begin{bmatrix} 1 & 1\\ 1 & 0\\ 0 & 1\end{bmatrix} x \leq \begin{bmatrix}1 \\ 0.7 \\ 0.7\end{bmatrix}
  \end{array}



We show below how to setup and solve the problem.
Then we update the matrices :math:`P` and :math:`A` and solve the updated problem


.. math::
  \begin{array}{ll}
    \mbox{minimize} & \frac{1}{2} x^T \begin{bmatrix}5 & 1.5\\ 1.5 & 1 \end{bmatrix} x + \begin{bmatrix}1 \\ 1\end{bmatrix}^T x \\
    \mbox{subject to} & \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \leq \begin{bmatrix} 1.2 & 1.1\\ 1.5 & 0\\ 0 & 0.8\end{bmatrix} x \leq \begin{bmatrix}1 \\ 0.7 \\ 0.7\end{bmatrix}
  \end{array}
  


Python
------

.. code:: python

    import osqp
    import numpy as np
    from scipy import sparse

    # Define problem data
    P = sparse.csc_matrix([[4, 1], [1, 2]])
    q = np.array([1, 1])
    A = sparse.csc_matrix([[1, 1], [1, 0], [0, 1]])
    l = np.array([1, 0, 0])
    u = np.array([1, 0.7, 0.7])

    # Create an OSQP object
    prob = osqp.OSQP()

    # Setup workspace
    prob.setup(P, q, A, l, u)

    # Solve problem
    res = prob.solve()

    # Update problem
    # NB: Update only upper triangular part of P
    P_new = sparse.csc_matrix([[5, 1.5], [1.5, 1]])
    A_new = sparse.csc_matrix([[1.2, 1.1], [1.5, 0], [0, 0.8]])
    prob.update(Px=sparse.triu(P_new).data, Ax=A_new.data)

    # Solve updated problem
    res = prob.solve()



Matlab
------

.. code:: matlab

    % Define problem data
    P = sparse([4, 1; 1, 2]);
    q = [1; 1];
    A = sparse([1, 1; 1, 0; 0, 1]);
    l = [1; 0; 0];
    u = [1; 0.7; 0.7];

    % Create an OSQP object
    prob = osqp;

    % Setup workspace
    prob.setup(P, q, A, l, u);

    % Solve problem
    res = prob.solve();

    % Update problem
    % NB: Update only upper triangular part of P
    P_new = sparse([5, 1.5; 1.5, 1]);
    A_new = sparse([1.2, 1.1; 1.5, 0; 0, 0.8]);
    prob.update('Px', nonzeros(triu(P_new)), 'Ax', nonzeros(A_new));

    % Solve updated problem
    res = prob.solve();



Julia
------

.. code:: julia

    using OSQP
    using Compat.SparseArrays, Compat.LinearAlgebra

    # Define problem data
    P = sparse([4. 1.; 1. 2.])
    q = [1.; 1.]
    A = sparse([1. 1.; 1. 0.; 0. 1.])
    l = [1.; 0.; 0.]
    u = [1.; 0.7; 0.7]

    # Crate OSQP object
    prob = OSQP.Model()

    # Setup workspace
    OSQP.setup!(prob; P=P, q=q, A=A, l=l, u=u)

    # Solve problem
    results = OSQP.solve!(prob)

    # Update problem
    # NB: Update only upper triangular part of P
    P_new = sparse([5. 1.5; 1.5 1.])
    A_new = sparse([1.2 1.1; 1.5 0.; 0. 0.8])
    OSQP.update!(prob, Px=triu(P_new).nzval, Ax=A_new.nzval)

    # Solve updated problem
    results = OSQP.solve!(prob)



R
-

.. code:: r

    library(osqp)
    library(Matrix)

    # Define problem data
    P <- Matrix(c(4., 1.,
                  1., 2.), 2, 2, sparse = TRUE)
    q <- c(1., 1.)
    A <- Matrix(c(1., 1., 0.,
                  1., 0., 1.), 3, 2, sparse = TRUE)
    l <- c(1., 0., 0.)
    u <- c(1., 0.7, 0.7)

    # Setup workspace
    model <- osqp(P, q, A, l, u)

    # Solve problem
    res <- model$Solve()

    # Update problem
    # NB: Update only upper triangular part of P
    P_new <- Matrix(c(5., 1.5,
                      1.5, 1.), 2, 2, sparse = TRUE)
    A_new <- Matrix(c(1.2, 1.5, 0.,
                      1.1, 0., 0.8), 3, 2, sparse = TRUE)
    model$Update(Px = P_new@x, Ax = A_new@x)

    # Solve updated problem
    res <- model$Solve()



C
-

.. code:: c

    #include "osqp.h"

    int main(int argc, char **argv) {
        // Load problem data
        c_float P_x[3] = {4.0, 1.0, 2.0, };
        c_float P_x_new[3] = {5.0, 1.5, 1.0, };
        c_int P_nnz = 3;
        c_int P_i[3] = {0, 0, 1, };
        c_int P_p[3] = {0, 1, 3, };
        c_float q[2] = {1.0, 1.0, };
        c_float q_new[2] = {2.0, 3.0, };
        c_float A_x[4] = {1.0, 1.0, 1.0, 1.0, };
        c_float A_x_new[4] = {1.2, 1.5, 1.1, 0.8, };
        c_int A_nnz = 4;
        c_int A_i[4] = {0, 1, 0, 2, };
        c_int A_p[3] = {0, 2, 4, };
        c_float l[3] = {1.0, 0.0, 0.0, };
        c_float l_new[3] = {2.0, -1.0, -1.0, };
        c_float u[3] = {1.0, 0.7, 0.7, };
        c_float u_new[3] = {2.0, 2.5, 2.5, };
        c_int n = 2;
        c_int m = 3;

        // Exitflag
        c_int exitflag = 0;

        // Workspace structures
        OSQPWorkspace *work;
        OSQPSettings  *settings = (OSQPSettings *)c_malloc(sizeof(OSQPSettings));
        OSQPData      *data     = (OSQPData *)c_malloc(sizeof(OSQPData));

        // Populate data
        if (data) {
            data = (OSQPData *)c_malloc(sizeof(OSQPData));
            data->n = n;
            data->m = m;
            data->P = csc_matrix(data->n, data->n, P_nnz, P_x, P_i, P_p);
            data->q = q;
            data->A = csc_matrix(data->m, data->n, A_nnz, A_x, A_i, A_p);
            data->l = l;
            data->u = u;
        }

        // Define Solver settings as default
        if (settings) osqp_set_default_settings(settings);

        // Setup workspace
        exitflag = osqp_setup(&work, data, settings);

        // Solve problem
        osqp_solve(work);

        // Update problem
        // NB: Update only upper triangular part of P
        osqp_update_P(work, P_x_new, OSQP_NULL, 3);
        osqp_update_A(work, A_x_new, OSQP_NULL, 4);

        // Solve updated problem
        osqp_solve(work);

        // Cleanup
        if (data) {
            if (data->A) c_free(data->A);
            if (data->P) c_free(data->P);
            c_free(data);
        }
        if (settings) c_free(settings);

        return exitflag;
    };