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/src/scaling.c b/src/scaling.c
new file mode 100644
index 0000000..74616a7
--- /dev/null
+++ b/src/scaling.c
@@ -0,0 +1,192 @@
+#include "scaling.h"
+
+#if EMBEDDED != 1
+
+
+// Set values lower than threshold SCALING_REG to 1
+void limit_scaling(c_float *D, c_int n) {
+  c_int i;
+
+  for (i = 0; i < n; i++) {
+    D[i] = D[i] < MIN_SCALING ? 1.0 : D[i];
+    D[i] = D[i] > MAX_SCALING ? MAX_SCALING : D[i];
+  }
+}
+
+/**
+ * Compute infinite norm of the columns of the KKT matrix without forming it
+ *
+ * The norm is stored in the vector v = (D, E)
+ *
+ * @param P        Cost matrix
+ * @param A        Constraints matrix
+ * @param D        Norm of columns related to variables
+ * @param D_temp_A Temporary vector for norm of columns of A
+ * @param E        Norm of columns related to constraints
+ * @param n        Dimension of KKT matrix
+ */
+void compute_inf_norm_cols_KKT(const csc *P, const csc *A,
+                               c_float *D, c_float *D_temp_A,
+                               c_float *E, c_int n) {
+  // First half
+  //  [ P ]
+  //  [ A ]
+  mat_inf_norm_cols_sym_triu(P, D);
+  mat_inf_norm_cols(A, D_temp_A);
+  vec_ew_max_vec(D, D_temp_A, D, n);
+
+  // Second half
+  //  [ A']
+  //  [ 0 ]
+  mat_inf_norm_rows(A, E);
+}
+
+c_int scale_data(OSQPWorkspace *work) {
+  // Scale KKT matrix
+  //
+  //    [ P   A']
+  //    [ A   0 ]
+  //
+  // with diagonal matrix
+  //
+  //  S = [ D    ]
+  //      [    E ]
+  //
+
+  c_int   i;          // Iterations index
+  c_int   n, m;       // Number of constraints and variables
+  c_float c_temp;     // Cost function scaling
+  c_float inf_norm_q; // Infinity norm of q
+
+  n = work->data->n;
+  m = work->data->m;
+
+  // Initialize scaling to 1
+  work->scaling->c = 1.0;
+  vec_set_scalar(work->scaling->D,    1., work->data->n);
+  vec_set_scalar(work->scaling->Dinv, 1., work->data->n);
+  vec_set_scalar(work->scaling->E,    1., work->data->m);
+  vec_set_scalar(work->scaling->Einv, 1., work->data->m);
+
+
+  for (i = 0; i < work->settings->scaling; i++) {
+    //
+    // First Ruiz step
+    //
+
+    // Compute norm of KKT columns
+    compute_inf_norm_cols_KKT(work->data->P, work->data->A,
+                              work->D_temp, work->D_temp_A,
+                              work->E_temp, n);
+
+    // Set to 1 values with 0 norms (avoid crazy scaling)
+    limit_scaling(work->D_temp, n);
+    limit_scaling(work->E_temp, m);
+
+    // Take square root of norms
+    vec_ew_sqrt(work->D_temp, n);
+    vec_ew_sqrt(work->E_temp, m);
+
+    // Divide scalings D and E by themselves
+    vec_ew_recipr(work->D_temp, work->D_temp, n);
+    vec_ew_recipr(work->E_temp, work->E_temp, m);
+
+    // Equilibrate matrices P and A and vector q
+    // P <- DPD
+    mat_premult_diag(work->data->P, work->D_temp);
+    mat_postmult_diag(work->data->P, work->D_temp);
+
+    // A <- EAD
+    mat_premult_diag(work->data->A, work->E_temp);
+    mat_postmult_diag(work->data->A, work->D_temp);
+
+    // q <- Dq
+    vec_ew_prod(work->D_temp,     work->data->q, work->data->q,    n);
+
+    // Update equilibration matrices D and E
+    vec_ew_prod(work->scaling->D, work->D_temp,  work->scaling->D, n);
+    vec_ew_prod(work->scaling->E, work->E_temp,  work->scaling->E, m);
+
+    //
+    // Cost normalization step
+    //
+
+    // Compute avg norm of cols of P
+    mat_inf_norm_cols_sym_triu(work->data->P, work->D_temp);
+    c_temp = vec_mean(work->D_temp, n);
+
+    // Compute inf norm of q
+    inf_norm_q = vec_norm_inf(work->data->q, n);
+
+    // If norm_q == 0, set it to 1 (ignore it in the scaling)
+    // NB: Using the same function as with vectors here
+    limit_scaling(&inf_norm_q, 1);
+
+    // Compute max between avg norm of cols of P and inf norm of q
+    c_temp = c_max(c_temp, inf_norm_q);
+
+    // Limit scaling (use same function as with vectors)
+    limit_scaling(&c_temp, 1);
+
+    // Invert scaling c = 1 / cost_measure
+    c_temp = 1. / c_temp;
+
+    // Scale P
+    mat_mult_scalar(work->data->P, c_temp);
+
+    // Scale q
+    vec_mult_scalar(work->data->q, c_temp, n);
+
+    // Update cost scaling
+    work->scaling->c *= c_temp;
+  }
+
+
+  // Store cinv, Dinv, Einv
+  work->scaling->cinv = 1. / work->scaling->c;
+  vec_ew_recipr(work->scaling->D, work->scaling->Dinv, work->data->n);
+  vec_ew_recipr(work->scaling->E, work->scaling->Einv, work->data->m);
+
+
+  // Scale problem vectors l, u
+  vec_ew_prod(work->scaling->E, work->data->l, work->data->l, work->data->m);
+  vec_ew_prod(work->scaling->E, work->data->u, work->data->u, work->data->m);
+
+  return 0;
+}
+
+#endif // EMBEDDED
+
+c_int unscale_data(OSQPWorkspace *work) {
+  // Unscale cost
+  mat_mult_scalar(work->data->P, work->scaling->cinv);
+  mat_premult_diag(work->data->P, work->scaling->Dinv);
+  mat_postmult_diag(work->data->P, work->scaling->Dinv);
+  vec_mult_scalar(work->data->q, work->scaling->cinv, work->data->n);
+  vec_ew_prod(work->scaling->Dinv, work->data->q, work->data->q, work->data->n);
+
+  // Unscale constraints
+  mat_premult_diag(work->data->A, work->scaling->Einv);
+  mat_postmult_diag(work->data->A, work->scaling->Dinv);
+  vec_ew_prod(work->scaling->Einv, work->data->l, work->data->l, work->data->m);
+  vec_ew_prod(work->scaling->Einv, work->data->u, work->data->u, work->data->m);
+
+  return 0;
+}
+
+c_int unscale_solution(OSQPWorkspace *work) {
+  // primal
+  vec_ew_prod(work->scaling->D,
+              work->solution->x,
+              work->solution->x,
+              work->data->n);
+
+  // dual
+  vec_ew_prod(work->scaling->E,
+              work->solution->y,
+              work->solution->y,
+              work->data->m);
+  vec_mult_scalar(work->solution->y, work->scaling->cinv, work->data->m);
+
+  return 0;
+}