Calculate synchronization accuracy within the chull module
[lttv.git] / lttv / lttv / sync / event_analysis_chull.c
index 223ea12f7d13dc0fb2a3073fed58a8182cdf423a..154258e00effc5af9369dc13c1c036e2d999125a 100644 (file)
@@ -40,13 +40,21 @@ typedef enum
        UPPER
 } HullType;
 
-
 typedef enum
 {
        MINIMUM,
        MAXIMUM
 } LineType;
 
+#ifdef HAVE_LIBGLPK
+struct LPAddRowInfo
+{
+       glp_prob* lp;
+       int boundType;
+       GArray* iArray, * jArray, * aArray;
+};
+#endif
+
 
 // Functions common to all analysis modules
 static void initAnalysisCHull(SyncState* const syncState);
@@ -56,8 +64,8 @@ static void analyzeMessageCHull(SyncState* const syncState, Message* const
        message);
 static AllFactors* finalizeAnalysisCHull(SyncState* const syncState);
 static void printAnalysisStatsCHull(SyncState* const syncState);
-static void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const
-       unsigned int i, const unsigned int j);
+static void writeAnalysisTraceTraceForePlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j);
 
 // Functions specific to this module
 static void openGraphFiles(SyncState* const syncState);
@@ -65,16 +73,18 @@ static void closeGraphFiles(SyncState* const syncState);
 static void writeGraphFiles(SyncState* const syncState);
 static void gfDumpHullToFile(gpointer data, gpointer userData);
 
+AllFactors* calculateAllFactors(struct _SyncState* const syncState);
+void calculateFactorsMiddle(PairFactors* const factors);
+static Factors* calculateFactorsExact(GQueue* const cu, GQueue* const cl, const
+       LineType lineType) __attribute__((pure));
+static void calculateFactorsFallback(GQueue* const cr, GQueue* const cs,
+       PairFactors* const result);
 static void grahamScan(GQueue* const hull, Point* const newPoint, const
        HullType type);
 static int jointCmp(const Point* const p1, const Point* const p2, const Point*
        const p3) __attribute__((pure));
 static double crossProductK(const Point const* p1, const Point const* p2,
        const Point const* p3, const Point const* p4) __attribute__((pure));
-static Factors* calculateFactorsExact(GQueue* const cu, GQueue* const cl, const
-       LineType lineType) __attribute__((pure));
-static void calculateFactorsFallback(GQueue* const cr, GQueue* const cs,
-       PairFactors* const result);
 static double slope(const Point* const p1, const Point* const p2)
        __attribute__((pure));
 static double intercept(const Point* const p1, const Point* const p2)
@@ -84,6 +94,36 @@ static double verticalDistance(Point* p1, Point* p2, Point* const point)
 
 static void gfPointDestroy(gpointer data, gpointer userData);
 
+// The next group of functions is only needed when computing synchronization
+// accuracy.
+#ifdef HAVE_LIBGLPK
+static AllFactors* finalizeAnalysisCHullLP(SyncState* const syncState);
+static void writeAnalysisTraceTimeBackPlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j);
+static void writeAnalysisTraceTimeForePlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j);
+static void writeAnalysisTraceTraceBackPlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j);
+
+static glp_prob* lpCreateProblem(GQueue* const lowerHull, GQueue* const
+       upperHull);
+static void gfLPAddRow(gpointer data, gpointer user_data);
+static Factors* calculateFactorsLP(glp_prob* const lp, const int direction);
+static void calculateCompleteFactorsLP(glp_prob* const lp, PairFactors*
+       factors);
+void timeCorrectionLP(glp_prob* const lp, const PairFactors* const lpFactors,
+       const uint64_t time, CorrectedTime* const correctedTime);
+
+static void gfAddAbsiscaToArray(gpointer data, gpointer user_data);
+static gint gcfCompareUint64(gconstpointer a, gconstpointer b);
+#else
+static inline AllFactors* finalizeAnalysisCHullLP(SyncState* const syncState)
+{
+       return NULL;
+}
+#endif
+
+
 
 static AnalysisModule analysisModuleCHull= {
        .name= "chull",
@@ -93,7 +133,12 @@ static AnalysisModule analysisModuleCHull= {
        .finalizeAnalysis= &finalizeAnalysisCHull,
        .printAnalysisStats= &printAnalysisStatsCHull,
        .graphFunctions= {
-               .writeTraceTraceForePlots= &writeAnalysisGraphsPlotsCHull,
+#ifdef HAVE_LIBGLPK
+               .writeTraceTimeBackPlots= &writeAnalysisTraceTimeBackPlotsCHull,
+               .writeTraceTimeForePlots= &writeAnalysisTraceTimeForePlotsCHull,
+               .writeTraceTraceBackPlots= &writeAnalysisTraceTraceBackPlotsCHull,
+#endif
+               .writeTraceTraceForePlots= &writeAnalysisTraceTraceForePlotsCHull,
        }
 };
 
@@ -140,19 +185,19 @@ static void initAnalysisCHull(SyncState* const syncState)
                        analysisData->hullArray[i][j]= g_queue_new();
                }
        }
+#ifdef HAVE_LIBGLPK
+       analysisData->lps= NULL;
+#endif
 
        if (syncState->stats)
        {
-               analysisData->stats= malloc(sizeof(AnalysisStatsCHull));
-               analysisData->stats->dropped= 0;
-               analysisData->stats->allFactors= NULL;
+               analysisData->stats= calloc(1, sizeof(AnalysisStatsCHull));
        }
 
        if (syncState->graphsStream)
        {
-               analysisData->graphsData= malloc(sizeof(AnalysisGraphsDataCHull));
+               analysisData->graphsData= calloc(1, sizeof(AnalysisGraphsDataCHull));
                openGraphFiles(syncState);
-               analysisData->graphsData->allFactors= NULL;
        }
 }
 
@@ -330,22 +375,51 @@ static void destroyAnalysisCHull(SyncState* const syncState)
        }
        free(analysisData->hullArray);
 
+#ifdef HAVE_LIBGLPK
+       if (analysisData->lps != NULL)
+       {
+               for (i= 0; i < syncState->traceNb; i++)
+               {
+                       unsigned int j;
+
+                       for (j= 0; j < i; j++)
+                       {
+                               // There seems to be a memory leak in glpk, valgrind reports a
+                               // loss (reachable) even if the problem is deleted
+                               glp_delete_prob(analysisData->lps[i][j]);
+                       }
+                       free(analysisData->lps[i]);
+               }
+               free(analysisData->lps);
+       }
+#endif
+
        if (syncState->stats)
        {
                freeAllFactors(analysisData->stats->allFactors, syncState->traceNb);
+               freeAllFactors(analysisData->stats->geoFactors, syncState->traceNb);
+
+#ifdef HAVE_LIBGLPK
+               freeAllFactors(analysisData->stats->lpFactors, syncState->traceNb);
+#endif
 
                free(analysisData->stats);
        }
 
        if (syncState->graphsStream)
        {
-               if (analysisData->graphsData->hullPoints != NULL)
+               AnalysisGraphsDataCHull* graphs= analysisData->graphsData;
+
+               if (graphs->hullPoints != NULL)
                {
                        closeGraphFiles(syncState);
                }
 
-               freeAllFactors(analysisData->graphsData->allFactors,
-                       syncState->traceNb);
+               freeAllFactors(graphs->allFactors, syncState->traceNb);
+
+#ifdef HAVE_LIBGLPK
+               freeAllFactors(graphs->lpFactors, syncState->traceNb);
+#endif
 
                free(analysisData->graphsData);
        }
@@ -486,7 +560,7 @@ static void grahamScan(GQueue* const hull, Point* const newPoint, const
 static AllFactors* finalizeAnalysisCHull(SyncState* const syncState)
 {
        AnalysisDataCHull* analysisData;
-       AllFactors* allFactors;
+       AllFactors* geoFactors, * lpFactors;
 
        analysisData= (AnalysisDataCHull*) syncState->analysisData;
 
@@ -496,21 +570,50 @@ static AllFactors* finalizeAnalysisCHull(SyncState* const syncState)
                closeGraphFiles(syncState);
        }
 
-       allFactors= calculateAllFactors(syncState);
+       geoFactors= calculateAllFactors(syncState);
+       lpFactors= finalizeAnalysisCHullLP(syncState);
 
        if (syncState->stats)
        {
-               allFactors->refCount++;
-               analysisData->stats->allFactors= allFactors;
+               geoFactors->refCount++;
+               analysisData->stats->geoFactors= geoFactors;
+
+               if (lpFactors != NULL)
+               {
+                       lpFactors->refCount++;
+                       analysisData->stats->allFactors= lpFactors;
+               }
+               else
+               {
+                       geoFactors->refCount++;
+                       analysisData->stats->allFactors= geoFactors;
+               }
        }
 
        if (syncState->graphsStream)
        {
-               allFactors->refCount++;
-               analysisData->graphsData->allFactors= allFactors;
+               if (lpFactors != NULL)
+               {
+                       lpFactors->refCount++;
+                       analysisData->graphsData->allFactors= lpFactors;
+               }
+               else
+               {
+                       geoFactors->refCount++;
+                       analysisData->graphsData->allFactors= geoFactors;
+               }
        }
 
-       return allFactors;
+       if (lpFactors != NULL)
+       {
+               freeAllFactors(geoFactors, syncState->traceNb);
+               return lpFactors;
+       }
+       else
+       {
+               freeAllFactors(lpFactors, syncState->traceNb);
+               return geoFactors;
+       }
 }
 
 
@@ -603,7 +706,7 @@ static void printAnalysisStatsCHull(SyncState* const syncState)
                                                        1.));
                                }
                        }
-                       else if (factorsCHull->type == SCREWED)
+                       else if (factorsCHull->type == FAIL)
                        {
                                printf("\n");
 
@@ -632,6 +735,47 @@ static void printAnalysisStatsCHull(SyncState* const syncState)
                        }
                }
        }
+
+#ifdef HAVE_LIBGLPK
+       printf("\tFactor comparison:\n"
+               "\t\tTrace pair  Factors type  Differences (lp - chull)\n"
+               "\t\t                          a0                    a1\n"
+               "\t\t                          Min        Max        Min        Max\n");
+
+       for (i= 0; i < syncState->traceNb; i++)
+       {
+               for (j= 0; j < i; j++)
+               {
+                       PairFactors* geoFactors=
+                               &analysisData->stats->geoFactors->pairFactors[i][j];
+                       PairFactors* lpFactors=
+                               &analysisData->stats->lpFactors->pairFactors[i][j];
+
+                       printf("\t\t%3d - %-3d   ", i, j);
+                       if (lpFactors->type == geoFactors->type)
+                       {
+                               if (lpFactors->type == ACCURATE)
+                               {
+                                       printf("%-13s %-10.4g %-10.4g %-10.4g %.4g\n",
+                                               approxNames[lpFactors->type],
+                                               lpFactors->min->offset - geoFactors->min->offset,
+                                               lpFactors->max->offset - geoFactors->max->offset,
+                                               lpFactors->min->drift - geoFactors->min->drift,
+                                               lpFactors->max->drift - geoFactors->max->drift);
+                               }
+                               else if (lpFactors->type == ABSENT)
+                               {
+                                       printf("%s\n", approxNames[lpFactors->type]);
+                               }
+                       }
+                       else
+                       {
+                               printf("Different! %s and %s\n", approxNames[lpFactors->type],
+                                       approxNames[geoFactors->type]);
+                       }
+               }
+       }
+#endif
 }
 
 
@@ -718,19 +862,19 @@ static double crossProductK(const Point const* p1, const Point const* p2,
  *   syncState     container for synchronization data.
  *
  * Returns:
- *   AllFactors*, see the documentation for the member allFactors of
+ *   AllFactors*, see the documentation for the member geoFactors of
  *   AnalysisStatsCHull.
  */
 AllFactors* calculateAllFactors(SyncState* const syncState)
 {
        unsigned int traceNumA, traceNumB;
-       AllFactors* allFactors;
+       AllFactors* geoFactors;
        AnalysisDataCHull* analysisData;
 
        analysisData= (AnalysisDataCHull*) syncState->analysisData;
 
-       // Allocate allFactors and calculate min and max
-       allFactors= createAllFactors(syncState->traceNb);
+       // Allocate geoFactors and calculate min and max
+       geoFactors= createAllFactors(syncState->traceNb);
        for (traceNumA= 0; traceNumA < syncState->traceNb; traceNumA++)
        {
                for (traceNumB= 0; traceNumB < traceNumA; traceNumB++)
@@ -751,14 +895,14 @@ AllFactors* calculateAllFactors(SyncState* const syncState)
 
                        for (i= 0; i < sizeof(loopValues) / sizeof(*loopValues); i++)
                        {
-                               g_debug("allFactors[%u][%u].%s = calculateFactorsExact(cr= "
+                               g_debug("geoFactors[%u][%u].%s = calculateFactorsExact(cr= "
                                        "hullArray[%u][%u], cs= hullArray[%u][%u], %s)",
                                        traceNumA, traceNumB, loopValues[i].factorsOffset ==
                                        offsetof(PairFactors, min) ? "min" : "max", traceNumB,
                                        traceNumA, traceNumA, traceNumB, loopValues[i].lineType ==
                                        MINIMUM ? "MINIMUM" : "MAXIMUM");
                                *((Factors**) ((void*)
-                                               &allFactors->pairFactors[traceNumA][traceNumB] +
+                                               &geoFactors->pairFactors[traceNumA][traceNumB] +
                                                loopValues[i].factorsOffset))=
                                        calculateFactorsExact(cr, cs, loopValues[i].lineType);
                        }
@@ -772,13 +916,13 @@ AllFactors* calculateAllFactors(SyncState* const syncState)
                {
                        PairFactors* factorsCHull;
 
-                       factorsCHull= &allFactors->pairFactors[traceNumA][traceNumB];
+                       factorsCHull= &geoFactors->pairFactors[traceNumA][traceNumB];
                        if (factorsCHull->min == NULL && factorsCHull->max == NULL)
                        {
                                factorsCHull->type= APPROXIMATE;
                                calculateFactorsFallback(analysisData->hullArray[traceNumB][traceNumA],
                                        analysisData->hullArray[traceNumA][traceNumB],
-                                       &allFactors->pairFactors[traceNumA][traceNumB]);
+                                       &geoFactors->pairFactors[traceNumA][traceNumB]);
                        }
                        else if (factorsCHull->min != NULL && factorsCHull->max != NULL)
                        {
@@ -801,12 +945,12 @@ AllFactors* calculateAllFactors(SyncState* const syncState)
                        else
                        {
                                //g_assert_not_reached();
-                               factorsCHull->type= SCREWED;
+                               factorsCHull->type= FAIL;
                        }
                }
        }
 
-       return allFactors;
+       return geoFactors;
 }
 
 
@@ -1137,7 +1281,7 @@ static double intercept(const Point* const p1, const Point* const p2)
  *   i:            first trace number
  *   j:            second trace number, garanteed to be larger than i
  */
-void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
+void writeAnalysisTraceTraceForePlotsCHull(SyncState* const syncState, const unsigned
        int i, const unsigned int j)
 {
        AnalysisDataCHull* analysisData;
@@ -1209,7 +1353,7 @@ void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
                                        factorsCHull->max->offset, factorsCHull->max->drift);
                }
        }
-       else if (factorsCHull->type == SCREWED)
+       else if (factorsCHull->type == FAIL)
        {
                if (factorsCHull->min != NULL && factorsCHull->min->drift != -INFINITY)
                {
@@ -1237,3 +1381,480 @@ void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
                g_assert_not_reached();
        }
 }
+
+
+#ifdef HAVE_LIBGLPK
+/*
+ * Create the linear programming problem containing the constraints defined by
+ * two half-hulls. The objective function and optimization directions are not
+ * written.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ *   i:            first trace number
+ *   j:            second trace number, garanteed to be larger than i
+ * Returns:
+ *   A new glp_prob*, this problem must be freed by the caller with
+ *   glp_delete_prob()
+ */
+static glp_prob* lpCreateProblem(GQueue* const lowerHull, GQueue* const
+       upperHull)
+{
+       unsigned int it;
+       const int zero= 0;
+       const double zeroD= 0.;
+       glp_prob* lp= glp_create_prob();
+       unsigned int hullPointNb= g_queue_get_length(lowerHull) +
+               g_queue_get_length(upperHull);
+       GArray* iArray= g_array_sized_new(FALSE, FALSE, sizeof(int), hullPointNb +
+               1);
+       GArray* jArray= g_array_sized_new(FALSE, FALSE, sizeof(int), hullPointNb +
+               1);
+       GArray* aArray= g_array_sized_new(FALSE, FALSE, sizeof(double),
+               hullPointNb + 1);
+       struct {
+               GQueue* hull;
+               struct LPAddRowInfo rowInfo;
+       } loopValues[2]= {
+               {lowerHull, {lp, GLP_UP, iArray, jArray, aArray}},
+               {upperHull, {lp, GLP_LO, iArray, jArray, aArray}},
+       };
+
+       // Create the LP problem
+       glp_term_out(GLP_OFF);
+       if (hullPointNb > 0)
+       {
+               glp_add_rows(lp, hullPointNb);
+       }
+       glp_add_cols(lp, 2);
+
+       glp_set_col_name(lp, 1, "a0");
+       glp_set_col_bnds(lp, 1, GLP_FR, 0., 0.);
+       glp_set_col_name(lp, 2, "a1");
+       glp_set_col_bnds(lp, 2, GLP_LO, 0., 0.);
+
+       // Add row constraints
+       g_array_append_val(iArray, zero);
+       g_array_append_val(jArray, zero);
+       g_array_append_val(aArray, zeroD);
+
+       for (it= 0; it < sizeof(loopValues) / sizeof(*loopValues); it++)
+       {
+               g_queue_foreach(loopValues[it].hull, &gfLPAddRow,
+                       &loopValues[it].rowInfo);
+       }
+
+       g_assert_cmpuint(iArray->len, ==, jArray->len);
+       g_assert_cmpuint(jArray->len, ==, aArray->len);
+       g_assert_cmpuint(aArray->len - 1, ==, hullPointNb * 2);
+
+       glp_load_matrix(lp, aArray->len - 1, &g_array_index(iArray, int, 0),
+               &g_array_index(jArray, int, 0), &g_array_index(aArray, double, 0));
+
+       glp_scale_prob(lp, GLP_SF_AUTO);
+
+       g_array_free(iArray, TRUE);
+       g_array_free(jArray, TRUE);
+       g_array_free(aArray, TRUE);
+
+       return lp;
+}
+
+
+/*
+ * A GFunc for g_queue_foreach(). Add constraints and bounds for one row.
+ *
+ * Args:
+ *   data          Point*, synchronization point for which to add an LP row
+ *                 (a constraint)
+ *   user_data     LPAddRowInfo*
+ */
+static void gfLPAddRow(gpointer data, gpointer user_data)
+{
+       Point* p= data;
+       struct LPAddRowInfo* rowInfo= user_data;
+       int indexes[2];
+       double constraints[2];
+
+       indexes[0]= g_array_index(rowInfo->iArray, int, rowInfo->iArray->len - 1) + 1;
+       indexes[1]= indexes[0];
+
+       if (rowInfo->boundType == GLP_UP)
+       {
+               glp_set_row_bnds(rowInfo->lp, indexes[0], GLP_UP, 0., p->y);
+       }
+       else if (rowInfo->boundType == GLP_LO)
+       {
+               glp_set_row_bnds(rowInfo->lp, indexes[0], GLP_LO, p->y, 0.);
+       }
+       else
+       {
+               g_assert_not_reached();
+       }
+
+       g_array_append_vals(rowInfo->iArray, indexes, 2);
+       indexes[0]= 1;
+       indexes[1]= 2;
+       g_array_append_vals(rowInfo->jArray, indexes, 2);
+       constraints[0]= 1.;
+       constraints[1]= p->x;
+       g_array_append_vals(rowInfo->aArray, constraints, 2);
+}
+
+
+/*
+ * Calculate min or max correction factors (as possible) using an LP problem.
+ *
+ * Args:
+ *   lp:           A linear programming problem with constraints and bounds
+ *                 initialized.
+ *   direction:    The type of factors desired. Use GLP_MAX for max
+ *                 approximation factors (a1, the drift or slope is the
+ *                 largest) and GLP_MIN in the other case.
+ *
+ * Returns:
+ *   If the calculation was successful, a new Factors struct. Otherwise, NULL.
+ *   The calculation will fail if the hull assumptions are not respected.
+ */
+static Factors* calculateFactorsLP(glp_prob* const lp, const int direction)
+{
+       int retval, status;
+       Factors* factors;
+
+       glp_set_obj_coef(lp, 1, 0.);
+       glp_set_obj_coef(lp, 2, 1.);
+
+       glp_set_obj_dir(lp, direction);
+       retval= glp_simplex(lp, NULL);
+       status= glp_get_status(lp);
+
+       if (retval == 0 && status == GLP_OPT)
+       {
+               factors= malloc(sizeof(Factors));
+               factors->offset= glp_get_col_prim(lp, 1);
+               factors->drift= glp_get_col_prim(lp, 2);
+       }
+       else
+       {
+               factors= NULL;
+       }
+
+       return factors;
+}
+
+
+/*
+ * Calculate min, max and approx correction factors (as possible) using an LP
+ * problem.
+ *
+ * Args:
+ *   lp            A linear programming problem with constraints and bounds
+ *                 initialized.
+ *   factors       Resulting factors, must be preallocated
+ */
+static void calculateCompleteFactorsLP(glp_prob* const lp, PairFactors* factors)
+{
+       factors->min= calculateFactorsLP(lp, GLP_MIN);
+       factors->max= calculateFactorsLP(lp, GLP_MAX);
+
+       if (factors->min && factors->max)
+       {
+               factors->type= ACCURATE;
+               calculateFactorsMiddle(factors);
+       }
+       else if (factors->min || factors->max)
+       {
+               factors->type= INCOMPLETE;
+       }
+       else
+       {
+               factors->type= ABSENT;
+       }
+}
+
+
+/*
+ * A GFunc for g_queue_foreach()
+ *
+ * Args:
+ *   data          Point*, a convex hull point
+ *   user_data     GArray*, an array of convex hull point absisca values, as
+ *                 uint64_t
+ */
+static void gfAddAbsiscaToArray(gpointer data, gpointer user_data)
+{
+       Point* p= data;
+       GArray* a= user_data;
+       uint64_t v= p->x;
+
+       g_array_append_val(a, v);
+}
+
+
+/*
+ * A GCompareFunc for g_array_sort()
+ *
+ * Args:
+ *   a, b          uint64_t*, absisca values
+ *
+ * Returns:
+ *   "returns less than zero for first arg is less than second arg, zero for
+ *   equal, greater zero if first arg is greater than second arg"
+ *   - the great glib documentation
+ */
+static gint gcfCompareUint64(gconstpointer a, gconstpointer b)
+{
+       if (*(uint64_t*) a < *(uint64_t*) b)
+       {
+               return -1;
+       }
+       else if (*(uint64_t*) a > *(uint64_t*) b)
+       {
+               return 1;
+       }
+       else
+       {
+               return 0;
+       }
+}
+
+
+/*
+ * Compute synchronization factors using a linear programming approach.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ */
+static AllFactors* finalizeAnalysisCHullLP(SyncState* const syncState)
+{
+       AnalysisDataCHull* analysisData= syncState->analysisData;
+       unsigned int i, j;
+       AllFactors* lpFactorsArray;
+
+       lpFactorsArray= createAllFactors(syncState->traceNb);
+       
+       analysisData->lps= malloc(syncState->traceNb * sizeof(glp_prob**));
+       for (i= 0; i < syncState->traceNb; i++)
+       {
+               analysisData->lps[i]= malloc(i * sizeof(glp_prob*));
+       }
+
+       for (i= 0; i < syncState->traceNb; i++)
+       {
+               for (j= 0; j < i; j++)
+               {
+                       glp_prob* lp;
+                       unsigned int it;
+                       GQueue*** hullArray= analysisData->hullArray;
+                       PairFactors* lpFactors= &lpFactorsArray->pairFactors[i][j];
+
+                       // Create the LP problem
+                       lp= lpCreateProblem(hullArray[i][j], hullArray[j][i]);
+                       analysisData->lps[i][j]= lp;
+
+                       // Use the LP problem to find the correction factors for this pair of
+                       // traces
+                       calculateCompleteFactorsLP(lp, lpFactors);
+
+                       // If possible, compute synchronization accuracy information for
+                       // graphs
+                       if (syncState->graphsStream && lpFactors->type == ACCURATE)
+                       {
+                               int retval;
+                               char* cwd;
+                               char fileName[43];
+                               FILE* fp;
+                               GArray* xValues;
+
+                               // Open the data file
+                               snprintf(fileName, sizeof(fileName),
+                                       "analysis_chull_accuracy-%03u_and_%03u.data", j, i);
+                               fileName[sizeof(fileName) - 1]= '\0';
+
+                               cwd= changeToGraphsDir(syncState->graphsDir);
+
+                               if ((fp= fopen(fileName, "w")) == NULL)
+                               {
+                                       g_error(strerror(errno));
+                               }
+                               fprintf(fp, "#%-24s %-25s %-25s %-25s\n", "x", "middle", "min", "max");
+
+                               retval= chdir(cwd);
+                               if (retval == -1)
+                               {
+                                       g_error(strerror(errno));
+                               }
+                               free(cwd);
+
+                               // Build the list of absisca values for the points in the accuracy graph
+                               xValues= g_array_sized_new(FALSE, FALSE, sizeof(uint64_t),
+                                       g_queue_get_length(hullArray[i][j]) +
+                                       g_queue_get_length(hullArray[j][i]));
+
+                               g_queue_foreach(hullArray[i][j], &gfAddAbsiscaToArray, xValues);
+                               g_queue_foreach(hullArray[j][i], &gfAddAbsiscaToArray, xValues);
+
+                               g_array_sort(xValues, &gcfCompareUint64);
+
+                               /* For each absisca value and each optimisation direction, solve the LP
+                                * and write a line in the data file */
+                               for (it= 0; it < xValues->len; it++)
+                               {
+                                       uint64_t time;
+                                       CorrectedTime correctedTime;
+
+                                       time= g_array_index(xValues, uint64_t, it);
+                                       timeCorrectionLP(lp, lpFactors, time, &correctedTime);
+                                       fprintf(fp, "%24" PRIu64 " %24" PRIu64 " %24" PRIu64
+                                               "%24" PRIu64 "\n", time, correctedTime.time,
+                                               correctedTime.min, correctedTime.max);
+                               }
+
+                               g_array_free(xValues, TRUE);
+                               fclose(fp);
+                       }
+               }
+       }
+
+       if (syncState->stats)
+       {
+               lpFactorsArray->refCount++;
+               analysisData->stats->lpFactors= lpFactorsArray;
+       }
+
+       if (syncState->graphsStream)
+       {
+               lpFactorsArray->refCount++;
+               analysisData->graphsData->lpFactors= lpFactorsArray;
+       }
+
+       return lpFactorsArray;
+}
+
+
+/*
+ * Perform correction on one time value and calculate accuracy bounds.
+ *
+ * Args:
+ *   lp:           Linear Programming problem containing the coefficients for
+ *                 the trace pair between which to perform time correction.
+ *   lpFactors:    Correction factors for this trace pair, the factors must be
+ *                 of type ACCURATE.
+ *   time:         Time value to correct.
+ *   correctedTime: Result of the time correction, preallocated.
+ */
+void timeCorrectionLP(glp_prob* const lp, const PairFactors* const lpFactors,
+       const uint64_t time, CorrectedTime* const correctedTime)
+{
+       unsigned int it;
+       const struct
+       {
+               int direction;
+               size_t offset;
+       } loopValues[]= {
+               {GLP_MIN, offsetof(CorrectedTime, min)},
+               {GLP_MAX, offsetof(CorrectedTime, max)}
+       };
+
+       glp_set_obj_coef(lp, 1, 1.);
+       glp_set_obj_coef(lp, 2, time);
+
+       g_assert(lpFactors->type == ACCURATE);
+
+       correctedTime->time= lpFactors->approx->offset + lpFactors->approx->drift
+               * time;
+
+       for (it= 0; it < ARRAY_SIZE(loopValues); it++)
+       {
+               int status;
+               int retval;
+
+               glp_set_obj_dir(lp, loopValues[it].direction);
+               retval= glp_simplex(lp, NULL);
+               status= glp_get_status(lp);
+
+               g_assert(retval == 0 && status == GLP_OPT);
+               *(uint64_t*) ((void*) correctedTime + loopValues[it].offset)=
+                       round(glp_get_obj_val(lp));
+       }
+}
+
+
+/*
+ * Write the analysis-specific graph lines in the gnuplot script.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ *   i:            first trace number
+ *   j:            second trace number, garanteed to be larger than i
+ */
+static void writeAnalysisTraceTimeBackPlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j)
+{
+       if (((AnalysisDataCHull*)
+                       syncState->analysisData)->graphsData->lpFactors->pairFactors[j][i].type
+               == ACCURATE)
+       {
+               fprintf(syncState->graphsStream,
+                       "\t\"analysis_chull_accuracy-%1$03u_and_%2$03u.data\" "
+                               "using 1:(($3 - $2) / clock_freq_%2$u):(($4 - $2) / clock_freq_%2$u) "
+                               "title \"Synchronization accuracy\" "
+                               "with filledcurves linewidth 2 linetype 1 "
+                               "linecolor rgb \"black\" fill solid 0.25 noborder, \\\n", i,
+                               j);
+       }
+}
+
+
+/*
+ * Write the analysis-specific graph lines in the gnuplot script.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ *   i:            first trace number
+ *   j:            second trace number, garanteed to be larger than i
+ */
+static void writeAnalysisTraceTimeForePlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j)
+{
+       if (((AnalysisDataCHull*)
+                       syncState->analysisData)->graphsData->lpFactors->pairFactors[j][i].type
+               == ACCURATE)
+       {
+               fprintf(syncState->graphsStream,
+                       "\t\"analysis_chull_accuracy-%1$03u_and_%2$03u.data\" "
+                               "using 1:(($3 - $2) / clock_freq_%2$u) notitle "
+                               "with lines linewidth 2 linetype 1 "
+                               "linecolor rgb \"gray60\", \\\n"
+                       "\t\"analysis_chull_accuracy-%1$03u_and_%2$03u.data\" "
+                               "using 1:(($4 - $2) / clock_freq_%2$u) notitle "
+                               "with lines linewidth 2 linetype 1 "
+                               "linecolor rgb \"gray60\", \\\n", i, j);
+       }
+}
+
+
+/*
+ * Write the analysis-specific graph lines in the gnuplot script.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ *   i:            first trace number
+ *   j:            second trace number, garanteed to be larger than i
+ */
+static void writeAnalysisTraceTraceBackPlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j)
+{
+       if (((AnalysisDataCHull*)
+                       syncState->analysisData)->graphsData->lpFactors->pairFactors[j][i].type
+               == ACCURATE)
+       {
+               fprintf(syncState->graphsStream,
+                       "\t\"analysis_chull_accuracy-%1$03u_and_%2$03u.data\" "
+                       "using 1:3:4 "
+                       "title \"Synchronization accuracy\" "
+                       "with filledcurves linewidth 2 linetype 1 "
+                       "linecolor rgb \"black\" fill solid 0.25 noborder, \\\n", i, j);
+       }
+}
+#endif
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