From: Ian Jackson <ijackson@chiark.greenend.org.uk>
Date: Fri, 7 Mar 2014 14:52:13 +0000 (+0000)
Subject: wip lp
X-Git-Tag: v1~21
X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ianmdlvl/git?p=matchsticks-search.git;a=commitdiff_plain;h=34b443b35453ef92904c2ec6d22a998d6078d028

wip lp
---

diff --git a/main.c b/main.c
index 6465f9b..e246752 100644
--- a/main.c
+++ b/main.c
@@ -20,18 +20,24 @@ static void prep(void) {
   adjmatrix = xmalloc(sizeof(*adjmatrix)*n);
 }
 
+static AdjWord one_adj_bit(int bitnum) {
+  return (AdjWord)1 << j;
+}
+
 static int count_set_adj_bits(AdjWord w) {
   int j, total;
   for (j=0, total=0; j<m; j++)
-    total += !!(w & ((AdjWord)1 << j));
+    total += !!(w & one_adj_bit(j));
   return total;
 }
 
 static void optimise(void) {
-  int i;
-  for (i=0; i<n; i++) {
+  int i, totalfrags;
+  for (i=0, totalfrags=0; i<n; i++) {
+    int frags = count_set_adj_bits(adjmatrix[i]);
+    totalfrags += frags;
     printf("%"PRADJ" ", adjmatrix[i]);
-    double maxminsize = (double)m / count_set_adj_bits(adjmatrix[i]);
+    double maxminsize = (double)m / frags;
     if (maxminsize < best) {
       printf(" too fine\n");
       return;
@@ -46,17 +52,90 @@ static void optimise(void) {
    * fragment from old match i and making it part of new match j.
    *
    * The structural variables (columns) are:
-   *   x_fragsz_i_j    the size of that fragment
-   *   x_minimum       minimum size of any fragment
+   *   x_minimum        minimum size of any fragment (bounded below by 0)
+   *   x_morefrag_i_j   the amount by which the size of the fragment
+   *                     i,j exceeds the minimum size (bounded below by 0)
    *
-   * The auxiliary variables (rows, constraints) are:
+   * The auxiliary variables (rows) are:
    *   x_total_i       total length for each input match (fixed variable)
    *   x_total_j       total length for each output match (fixed variable)
-   *   x_fragmin_i_j   amount by which fragment is > minimum (lower bound 0)
    *
-   * The objective function is simply to maximise x_minimum
+   * The objective function is simply
+   *   maximise x_minimum
+   *
+   * We use X_ and Y_ to refer to GLPK's (1-based) column and row indices.
+   * ME_ refers to entries in the list of constraint matrix elements
+   * which we build up as we go.
    */
 
+  glp_prob *prob = glp_create_prob();
+
+  int Y_totals_i = glp_add_rows(prob, i);
+  int Y_totals_j = glp_add_rows(prob, j);
+  int X_minimum = glp_add_cols(prob, 1);
+  int rows = glp_get_num_rows(prob);
+  int cols = glp_get_num_rows(cols);
+
+  int next_matrix_entry = 1; /* wtf GLPK! */
+  int matrix_entries_size = next_matrix_entry + i + j + totalfrags*2;
+  double matrix_entries[matrix_entries_size];
+  int matrix_entries_XY[2][matrix_entries_size];
+
+#define ADD_MATRIX_ENTRY(Y,X) ({			\
+      assert(matrix_entries_size < next_matrix_entry);	\
+      matrix_entries_XY[0][next_matrix_entry] = X;	\
+      matrix_entries_XY[1][next_matrix_entry] = Y;	\
+      matrix_entries[next_matrix_entry] = 0;		\
+      next_matrix_entry++;				\
+    })
+
+  int ME_totals_i__minimum = next_matrix_entry;
+  for (i=0; i<n; i++) ADD_MATRIX_ENTRY(Y_totals_i+i, X_minimum);
+
+  int ME_totals_j__minimum = next_matrix_entry;
+  for (j=0; j<m; j++) ADD_MATRIX_ENTRY(Y_totals_j+j, X_minimum);
+
+  /* \forall_i x_totals_i = m */
+  /* \forall_i x_totals_j = n */
+  for (i=0; i<n; i++) glp_set_row_bounds(prob, Y_totals_i+i, GLP_FX, m,m);
+  for (j=0; j<m; j++) glp_set_row_bounds(prob, Y_totals_j+j, GLP_FX, n,n);
+
+  /* x_minimum >= 0 */
+  glp_set_col_bounds(prob, X_minimum, GLP_LB, 0, 0);
+
+  /* objective is maximising x_minimum */
+  glp_set_obj_dir(prob, GLP_MAX);
+  glp_set_obj_coef(prob, X_minimum, 1);
+
+  for (i=0; i<n; j++) {
+    for (j=0; j<m; j++) {
+      if (!(adjmatrix[i] & one_adj_bit(j)))
+	continue;
+      /* x_total_i += x_minimum */
+      /* x_total_j += x_minimum */
+      matrix_entries[ ME_totals_i__minimum + i ] ++;
+      matrix_entries[ ME_totals_j__minimum + j ] ++;
+
+      /* x_morefrag_i_j >= 0 */
+      int X_morefrag_i_j = glp_add_cols(prob, 1);
+      glp_set_col_bnds(prob, X_morefrag_i_j, GLP_LO, 0, 0);
+
+      /* x_total_i += x_morefrag_i_j */
+      /* x_total_j += x_morefrag_i_j */
+      int ME_totals_i__mf_i_j = ADD_MATRIX_ENTRY(Y_totals_i+i, X_morefrag_i_j);
+      int ME_totals_j__mf_i_j = ADD_MATRIX_ENTRY(Y_totals_j+j, X_morefrag_i_j);
+      matrix_entries[ME_totals_i__mf_i_j] = 1;
+      matrix_entries[ME_totals_j__mf_i_j] = 1;
+    }
+  }
+
+  assert(next_matrix_entry == matrix_entries_size);
+
+  for (row=1; row<=rows; row++) {
+    glp_load_matrix(prob, next_matrix_entry,
+		    matrix_entries_XY[1], matrix_entries_XY[0],
+		    matrix_entries);
+
   printf("nyi\n");
 }