Squashed 'third_party/osqp/' content from commit 33454b3e23
Change-Id: I056df0582ca06664e86554c341a94c47ab932001
git-subtree-dir: third_party/osqp
git-subtree-split: 33454b3e236f1f44193bfbbb6b8c8e71f8f04e9a
Signed-off-by: Austin Schuh <austin.linux@gmail.com>
diff --git a/docs/examples/update-matrices.rst b/docs/examples/update-matrices.rst
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+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
+ osqp_cleanup(work);
+ 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;
+ };