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//==============================================================================
//
// Copyright (c) 2002-
// Authors:
// * Dave Parker <david.parker@comlab.ox.ac.uk> (University of Oxford, formerly University of Birmingham)
// * Rashid Mehmood <rxm@cs.bham.ac.uk> (University of Birmingham)
// * Joachim Klein <klein@tcs.inf.tu-dresden.de> (TU Dresden)
//
//------------------------------------------------------------------------------
//
// This file is part of PRISM.
//
// PRISM is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2 of the License, or
// (at your option) any later version.
//
// PRISM is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with PRISM; if not, write to the Free Software Foundation,
// Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
//
//==============================================================================
// includes
#include "PrismHybrid.h"
#include <cmath>
#include <util.h>
#include <cudd.h>
#include <dd.h>
#include <odd.h>
#include <dv.h>
#include "sparse.h"
#include "hybrid.h"
#include "PrismHybridGlob.h"
#include "jnipointer.h"
#include "prism.h"
#include "Measures.h"
#include "ExportIterations.h"
#include "IntervalIteration.h"
#include <memory>
#include <new>
// local prototypes
static void sor_rec(HDDNode *hdd, int level, int row_offset, int col_offset, int r, int c, bool transpose);
static void sor_rm(RMSparseMatrix *rmsm, int row_offset, int col_offset, int r, int c, bool is_diag);
static void sor_cmsr(CMSRSparseMatrix *cmsrsm, int row_offset, int col_offset, int r, int c, bool is_diag);
// globals (used by local functions)
static HDDNode *zero;
static int num_levels;
static bool compact_d, compact_sm;
static double *sm_dist;
static int sm_dist_shift;
static int sm_dist_mask;
static double *diags_vec = NULL;
static DistVector *diags_dist = NULL;
static double *soln = NULL, *soln2 = NULL;
static double omega;
static bool forwards;
static IntervalIteration* _helper = NULL;
static bool from_below;
//------------------------------------------------------------------------------
// solve the linear equation system Ax=b with Gauss-Seidel/SOR, interval variant
JNIEXPORT jlong __jlongpointer JNICALL Java_hybrid_PrismHybrid_PH_1SORInterval
(
JNIEnv *env,
jclass cls,
jlong __jlongpointer _odd, // odd
jlong __jlongpointer rv, // row vars
jint num_rvars,
jlong __jlongpointer cv, // col vars
jint num_cvars,
jlong __jlongpointer _a, // matrix A
jlong __jlongpointer _b, // vector b (if null, assume all zero)
jlong __jlongpointer _lower, // lower bound values
jlong __jlongpointer _upper, // upper bound values
jboolean transpose, // transpose A? (i.e. solve xA=b not Ax=b?)
jboolean row_sums, // use row sums for diags instead? (strictly speaking: negative sum of non-diagonal row elements)
jdouble om, // omega (over-relaxation parameter)
jboolean fwds, // forwards or backwards?
jint flags
)
{
// cast function parameters
ODDNode *odd = jlong_to_ODDNode(_odd); // odd
DdNode **rvars = jlong_to_DdNode_array(rv); // row vars
DdNode **cvars = jlong_to_DdNode_array(cv); // col vars
DdNode *a = jlong_to_DdNode(_a); // matrix A
DdNode *b = jlong_to_DdNode(_b); // vector b
DdNode *lower = jlong_to_DdNode(_lower); // lower bound values
DdNode *upper = jlong_to_DdNode(_upper); // upper bound values
omega = om;
forwards = fwds;
// mtbdds
DdNode *reach = NULL, *diags = NULL, *id = NULL;
// model stats
int n;
// flags
bool compact_b, l_b_max;
// matrix mtbdd
HDDMatrix *hddm = NULL;
HDDNode *hdd = NULL;
// vectors
double *b_vec = NULL;
DistVector *b_dist = NULL;
double *soln_below = NULL, *soln_above = NULL;
// timing stuff
long start1, start2, start3, stop;
double time_taken, time_for_setup, time_for_iters;
// misc
int i, j, fb, l, h, i2, h2, iters;
double kb, kbt;
bool done, diag_done;
// measure for convergence termination check
MeasureSupNormInterval measure(term_crit == TERM_CRIT_RELATIVE);
if (omega <= 0.0 || omega > 1.0) {
PH_SetErrorMessage("Interval iteration requires 0 < omega <= 1.0, have omega = %g", omega);
return ptr_to_jlong(NULL);
}
IntervalIteration helper(flags);
_helper = &helper; // store globally for recursion
// exception handling around whole function
try {
// start clocks
start1 = start2 = util_cpu_time();
// get number of states
n = odd->eoff + odd->toff;
// get reachable states
reach = odd->dd;
// make local copy of a
Cudd_Ref(a);
// remove and keep diagonal entries of matrix A
id = DD_Identity(ddman, rvars, cvars, num_rvars);
Cudd_Ref(reach);
id = DD_And(ddman, id, reach);
Cudd_Ref(id);
Cudd_Ref(a);
diags = DD_Apply(ddman, APPLY_TIMES, id, a);
Cudd_Ref(id);
a = DD_ITE(ddman, id, DD_Constant(ddman, 0), a);
// build hdd for matrix
PH_PrintToMainLog(env, "\nBuilding hybrid MTBDD matrix... ");
hddm = build_hdd_matrix(a, rvars, cvars, num_rvars, odd, true, transpose);
hdd = hddm->top;
zero = hddm->zero;
num_levels = hddm->num_levels;
kb = hddm->mem_nodes;
kbt = kb;
PH_PrintToMainLog(env, "[levels=%d, nodes=%d] ", hddm->num_levels, hddm->num_nodes);
PH_PrintMemoryToMainLog(env, "[", kb, "]\n");
// split hdd matrix into blocks
// nb: in terms of memory, this gets precedence over sparse matrices
PH_PrintToMainLog(env, "Splitting into blocks... ");
split_hdd_matrix(hddm, compact, false, transpose);
compact_b = hddm->compact_b;
rearrange_hdd_blocks(hddm, false);
kb = hddm->mem_b;
kbt += kb;
PH_PrintToMainLog(env, "[levels=%d, n=%d, nnz=%d%s] ", hddm->l_b, hddm->blocks->n, hddm->blocks->nnz, compact_b?", compact":"");
PH_PrintMemoryToMainLog(env, "[", kb, "]\n");
// add sparse matrices
PH_PrintToMainLog(env, "Adding explicit sparse matrices... ");
add_sparse_matrices(hddm, compact, true, transpose);
compact_sm = hddm->compact_sm;
if (compact_sm) {
sm_dist = hddm->dist;
sm_dist_shift = hddm->dist_shift;
sm_dist_mask = hddm->dist_mask;
}
l_b_max = (hddm->l_b == hddm->num_levels);
kb = hddm->mem_sm;
kbt += kb;
PH_PrintToMainLog(env, "[levels=%d, num=%d%s] ", hddm->l_sm, hddm->num_sm, compact_sm?", compact":"");
PH_PrintMemoryToMainLog(env, "[", kb, "]\n");
// get vector of diags, either by extracting from mtbdd or
// by doing (negative, non-diagonal) row sums of original A matrix (and then setting to 1 if sum is 0)
PH_PrintToMainLog(env, "Creating vector for diagonals... ");
if (!row_sums) {
diags = DD_MaxAbstract(ddman, diags, cvars, num_cvars);
diags_vec = mtbdd_to_double_vector(ddman, diags, rvars, num_rvars, odd);
} else {
diags_vec = hdd_negative_row_sums(hddm, n, transpose);
}
// if any of the diagonals are zero, set them to one - avoids division by zero errors later
// strictly speaking, such matrices shouldn't work for this iterative method
// but they do occur, e.g. for steady-state computation of a bscc, this fixes it
for (i = 0; i < n; i++) diags_vec[i] = (diags_vec[i] == 0) ? 1.0 : diags_vec[i];
// try and convert to compact form if required
compact_d = false;
if (compact) {
if ((diags_dist = double_vector_to_dist(diags_vec, n))) {
compact_d = true;
delete[] diags_vec; diags_vec = NULL;
}
}
kb = (!compact_d) ? n*8.0/1024.0 : (diags_dist->num_dist*8.0+n*2.0)/1024.0;
kbt += kb;
if (compact_d) PH_PrintToMainLog(env, "[dist=%d, compact] ", diags_dist->num_dist);
PH_PrintMemoryToMainLog(env, "[", kb, "]\n");
// invert diagonal
if (!compact_d) {
for (i = 0; i < n; i++) diags_vec[i] = 1.0 / diags_vec[i];
} else {
for (i = 0; i < diags_dist->num_dist; i++) diags_dist->dist[i] = 1.0 / diags_dist->dist[i];
}
// build b vector (if present)
if (b != NULL) {
PH_PrintToMainLog(env, "Creating vector for RHS... ");
b_vec = mtbdd_to_double_vector(ddman, b, rvars, num_rvars, odd);
// try and convert to compact form if required
compact_b = false;
if (compact) {
if ((b_dist = double_vector_to_dist(b_vec, n))) {
compact_b = true;
delete[] b_vec; b_vec = NULL;
}
}
kb = (!compact_b) ? n*8.0/1024.0 : (b_dist->num_dist*8.0+n*2.0)/1024.0;
kbt += kb;
if (compact_b) PH_PrintToMainLog(env, "[dist=%d, compact] ", b_dist->num_dist);
PH_PrintMemoryToMainLog(env, "[", kb, "]\n");
}
// create solution/iteration vectors
PH_PrintToMainLog(env, "Allocating iteration vectors... ");
soln_below = mtbdd_to_double_vector(ddman, lower, rvars, num_rvars, odd);
soln_above = mtbdd_to_double_vector(ddman, upper, rvars, num_rvars, odd);
soln2 = new double[hddm->blocks->max];
for (i = 0; i < hddm->blocks->max; i++) soln2[i] = 0;
kb = 2*(n*8.0/1024.0)+(hddm->blocks->max*8.0/1024.0);
kbt += kb;
PH_PrintMemoryToMainLog(env, "[2 x ", (n*8.0/1024.0), "");
PH_PrintMemoryToMainLog(env, " + ", (hddm->blocks->max*8.0/1024.0), "");
PH_PrintMemoryToMainLog(env, " = ", kb, "]\n");
// print total memory usage
PH_PrintMemoryToMainLog(env, "TOTAL: [", kbt, "]\n");
std::unique_ptr<ExportIterations> iterationExport;
if (PH_GetFlagExportIterations()) {
std::string title("PH_SORInterval (");
title += (omega == 1.0)?"Gauss-Seidel": ("SOR omega=" + std::to_string(omega));
title += ")";
iterationExport.reset(new ExportIterations(title.c_str()));
PH_PrintToMainLog(env, "Exporting iterations to %s\n", iterationExport->getFileName().c_str());
iterationExport->exportVector(soln_below, n, 0);
iterationExport->exportVector(soln_above, n, 1);
}
// get setup time
stop = util_cpu_time();
time_for_setup = (double)(stop - start2)/1000;
start2 = stop;
start3 = stop;
// start iterations
iters = 0;
done = false;
PH_PrintToMainLog(env, "\nStarting iterations...\n");
while (!done && iters < max_iters) {
iters++;
// stuff for block storage
int b_n = hddm->blocks->n;
int b_nnz = hddm->blocks->nnz;
HDDNode **b_blocks = hddm->blocks->blocks;
unsigned int *b_rowscols = hddm->blocks->rowscols;
unsigned char *b_counts = hddm->blocks->counts;
int *b_starts = (int *)hddm->blocks->counts;
bool b_use_counts = hddm->blocks->use_counts;
int *b_offsets = hddm->blocks->offsets;
HDDNode **b_nodes = hddm->row_tables[hddm->l_b];
int b_dist_shift = hddm->blocks->dist_shift;
int b_dist_mask = hddm->blocks->dist_mask;
int row_offset, col_offset;
HDDNode *node;
int it;
for (it = 0; it <= 1; it++) {
if (it == 0) {
// from below
from_below = true;
soln = soln_below;
} else {
// from above
from_below = false;
soln = soln_above;
}
// loop through rows of blocks
l = b_nnz; h = 0;
for(fb = 0; fb < b_n; fb++)
{
// loop actually over i (can do forwards or backwards sor/gs)
i = (forwards) ? fb : b_n-1-fb;
// store block row offset
row_offset = b_offsets[i];
// initialise (partial) solution vector
h2 = b_offsets[i+1] - b_offsets[i];
// initialise vector
if (b == NULL) {
for (i2 = 0; i2 < h2; i2++) { soln2[i2] = 0.0; }
} else if (!compact_b) {
for (i2 = 0; i2 < h2; i2++) { soln2[i2] = b_vec[row_offset + i2]; }
} else {
for (i2 = 0; i2 < h2; i2++) { soln2[i2] = b_dist->dist[b_dist->ptrs[row_offset + i2]]; }
}
// loop through blocks in this row of blocks
if (!b_use_counts) { l = b_starts[i]; h = b_starts[i+1]; }
else if (forwards) { l = h; h += b_counts[i]; }
else { h = l; l -= b_counts[i]; }
diag_done = false;
for(j = l; j < h; j++)
{
// get node for block and its col offset
if (!compact_b) {
node = b_blocks[j];
col_offset = b_offsets[b_rowscols[j]];
} else {
node = b_nodes[(int)(b_rowscols[j] & b_dist_mask)];
col_offset = b_offsets[(int)(b_rowscols[j] >> b_dist_shift)];
}
// trivial case where we are the bottom of the mtbdd already
if (l_b_max) {
soln2[0] -= soln[col_offset] * node->type.val;
//printf("(%d,%d)=%f\n", row_offset, col_offset, node->type.val);
continue;
}
// non-diagonal blocks treated normally
// (diagonal should be the last block, unless it is absent because empty)
if ((j != h-1) || (j == h-1 && row_offset !=col_offset)) {
sor_rec(node, hddm->l_b, row_offset, col_offset, 0, 0, transpose);
}
// diagonal blocks (last blocks in row/col) are different
// call sparse matrix traversal directly with "is_diag" flag = true
else {
diag_done = true;
if (!compact_sm) {
sor_rm((RMSparseMatrix *)node->sm.ptr, row_offset, col_offset, 0, 0, true);
} else {
sor_cmsr((CMSRSparseMatrix *)node->sm.ptr, row_offset, col_offset, 0, 0, true);
}
}
}
// if we never found a diagonal block (because it is empty and so not there),
// then we do the stuff that should have been done after the processing of the diagonal block
if (!l_b_max && !diag_done) for (i2 = 0; i2 < h2; i2++) {
// divide by diagonal
if (!compact_d) {
soln2[i2] *= diags_vec[row_offset + i2];
} else {
soln2[i2] *= (diags_dist->dist[(int)diags_dist->ptrs[row_offset + i2]]);
}
// do over-relaxation if necessary
if (omega != 1) {
soln2[i2] = ((1-omega) * soln[row_offset + i2]) + (omega * soln2[i2]);
}
// set vector element
helper.updateValue(soln[row_offset + i2], soln[row_offset + i2], soln2[i2], from_below);
}
// trivial case where we are the bottom of the mtbdd already
if (l_b_max) {
soln2[0] *= ((!compact_d)?(diags_vec[row_offset]):(diags_dist->dist[(int)diags_dist->ptrs[row_offset]]));
if (omega != 1) soln2[0] = ((1-omega) * soln[row_offset]) + (omega * soln2[0]);
// set vector element
helper.updateValue(soln[row_offset], soln[row_offset], soln2[0], from_below);
}
}
}
if (iterationExport) {
iterationExport->exportVector(soln_below, n, 0);
iterationExport->exportVector(soln_above, n, 1);
}
// check convergence
measure.reset();
measure.measure(soln_below, soln_above, n);
if (measure.value() < term_crit_param) {
PH_PrintToMainLog(env, "Max %sdiff between upper and lower bound on convergence: %G", measure.isRelative()?"relative ":"", measure.value());
done = true;
}
// print occasional status update
if ((util_cpu_time() - start3) > UPDATE_DELAY) {
PH_PrintToMainLog(env, "Iteration %d: max %sdiff=%f", iters, measure.isRelative()?"relative ":"", measure.value());
PH_PrintToMainLog(env, ", %.2f sec so far\n", ((double)(util_cpu_time() - start2)/1000));
start3 = util_cpu_time();
}
}
// stop clocks
stop = util_cpu_time();
time_for_iters = (double)(stop - start2)/1000;
time_taken = (double)(stop - start1)/1000;
// print iters/timing info
PH_PrintToMainLog(env, "\n%s%s (interval iteration): %d iterations in %.2f seconds (average %.6f, setup %.2f)\n", forwards?"":"Backwards ", (omega == 1.0)?"Gauss-Seidel":"SOR", iters, time_taken, time_for_iters/iters, time_for_setup);
// if the iterative method didn't terminate, this is an error
if (!done) {
delete[] soln_below;
soln_below = NULL;
PH_SetErrorMessage("Iterative method (interval iteration) did not converge within %d iterations.\nConsider using a different numerical method or increasing the maximum number of iterations", iters);
PH_PrintToMainLog(env, "Max remaining %sdiff between upper and lower bound on convergence: %G", measure.isRelative()?"relative ":"", measure.value());
}
if (helper.flag_select_midpoint() && soln_below) { // we did converge, select midpoint
helper.selectMidpoint(soln_below, soln_above, n);
if (iterationExport) {
// export result vector as below and above
iterationExport->exportVector(soln_below, n, 0);
iterationExport->exportVector(soln_below, n, 1);
}
}
// catch exceptions: register error, free memory
} catch (std::bad_alloc e) {
PH_SetErrorMessage("Out of memory");
if (soln_below) delete[] soln_below;
soln_below = 0;
}
// free memory
if (a) Cudd_RecursiveDeref(ddman, a);
if (id) Cudd_RecursiveDeref(ddman, id);
if (diags) Cudd_RecursiveDeref(ddman, diags);
if (hddm) delete hddm;
if (diags_vec) delete[] diags_vec;
if (diags_dist) delete diags_dist;
if (b_vec) delete[] b_vec;
if (b_dist) delete b_dist;
if (soln2) delete[] soln2;
if (soln_above) delete[] soln_above;
return ptr_to_jlong(soln_below);
}
//------------------------------------------------------------------------------
static void sor_rec(HDDNode *hdd, int level, int row_offset, int col_offset, int r, int c, bool transpose)
{
HDDNode *e, *t;
// if it's the zero node
if (hdd == zero) {
return;
}
// or if we've reached a submatrix
// (check for non-null ptr but, equivalently, we could just check if level==l_sm)
else if (hdd->sm.ptr) {
if (!compact_sm) {
sor_rm((RMSparseMatrix *)hdd->sm.ptr, row_offset, col_offset, r, c, false);
} else {
sor_cmsr((CMSRSparseMatrix *)hdd->sm.ptr, row_offset, col_offset, r, c, false);
}
return;
}
// or if we've reached the bottom
else if (level == num_levels) {
//printf("(%d,%d)=%f\n", row_offset, col_offset, hdd->type.val);
soln2[r] -= soln[col_offset+c] * hdd->type.val;
return;
}
// otherwise recurse
e = hdd->type.kids.e;
if (e != zero) {
if (!transpose) {
sor_rec(e->type.kids.e, level+1, row_offset, col_offset, r, c, transpose);
sor_rec(e->type.kids.t, level+1, row_offset, col_offset, r, c+e->off.val, transpose);
} else {
sor_rec(e->type.kids.e, level+1, row_offset, col_offset, r, c, transpose);
sor_rec(e->type.kids.t, level+1, row_offset, col_offset, r+e->off.val, c, transpose);
}
}
t = hdd->type.kids.t;
if (t != zero) {
if (!transpose) {
sor_rec(t->type.kids.e, level+1, row_offset, col_offset, r+hdd->off.val, c, transpose);
sor_rec(t->type.kids.t, level+1, row_offset, col_offset, r+hdd->off.val, c+t->off.val, transpose);
} else {
sor_rec(t->type.kids.e, level+1, row_offset, col_offset, r, c+hdd->off.val, transpose);
sor_rec(t->type.kids.t, level+1, row_offset, col_offset, r+t->off.val, c+hdd->off.val, transpose);
}
}
}
//-----------------------------------------------------------------------------------
static void sor_rm(RMSparseMatrix *rmsm, int row_offset, int col_offset, int r, int c, bool is_diag)
{
int fb2, i2, j2, l2, h2;
int sm_n = rmsm->n;
int sm_nnz = rmsm->nnz;
double *sm_non_zeros = rmsm->non_zeros;
unsigned char *sm_row_counts = rmsm->row_counts;
int *sm_row_starts = (int *)rmsm->row_counts;
bool sm_use_counts = rmsm->use_counts;
unsigned int *sm_cols = rmsm->cols;
// loop through rows of submatrix
l2 = sm_nnz; h2 = 0;
for (fb2 = 0; fb2 < sm_n; fb2++) {
// loop actually over i2 (can do forwards or backwards sor/gs)
i2 = (forwards) ? fb2 : sm_n-1-fb2;
// loop through entries in this row
if (!sm_use_counts) { l2 = sm_row_starts[i2]; h2 = sm_row_starts[i2+1]; }
else if (forwards) { l2 = h2; h2 += sm_row_counts[i2]; }
else { h2 = l2; l2 -= sm_row_counts[i2]; }
for (j2 = l2; j2 < h2; j2++) {
soln2[r + i2] -= soln[col_offset + c + sm_cols[j2]] * sm_non_zeros[j2];
//printf("(%d,%d)=%f\n", r + i2, col_offset + c + sm_cols[j2], sm_non_zeros[j2]);
}
if (is_diag) {
// divide by diagonal
if (!compact_d) {
soln2[r + i2] *= diags_vec[row_offset + r + i2];
} else {
soln2[r + i2] *= (diags_dist->dist[(int)diags_dist->ptrs[row_offset + r + i2]]);
}
// do over-relaxation if necessary
if (omega != 1) {
soln2[r + i2] = ((1-omega) * soln[row_offset + r + i2]) + (omega * soln2[r + i2]);
}
// set vector element
_helper->updateValue(soln[row_offset + r + i2], soln[row_offset + r + i2], soln2[r + i2], from_below);
}
}
}
//-----------------------------------------------------------------------------------
static void sor_cmsr(CMSRSparseMatrix *cmsrsm, int row_offset, int col_offset, int r, int c, bool is_diag)
{
int fb2, i2, j2, l2, h2;
int sm_n = cmsrsm->n;
int sm_nnz = cmsrsm->nnz;
unsigned char *sm_row_counts = cmsrsm->row_counts;
int *sm_row_starts = (int *)cmsrsm->row_counts;
bool sm_use_counts = cmsrsm->use_counts;
unsigned int *sm_cols = cmsrsm->cols;
// loop through rows of submatrix
l2 = sm_nnz; h2 = 0;
for (fb2 = 0; fb2 < sm_n; fb2++) {
// loop actually over i2 (can do forwards or backwards sor/gs)
i2 = (forwards) ? fb2 : sm_n-1-fb2;
// loop through entries in this row
if (!sm_use_counts) { l2 = sm_row_starts[i2]; h2 = sm_row_starts[i2+1]; }
else if (forwards) { l2 = h2; h2 += sm_row_counts[i2]; }
else { h2 = l2; l2 -= sm_row_counts[i2]; }
for (j2 = l2; j2 < h2; j2++) {
soln2[r + i2] -= soln[col_offset + c + (int)(sm_cols[j2] >> sm_dist_shift)] * sm_dist[(int)(sm_cols[j2] & sm_dist_mask)];
//printf("(%d,%d)=%f\n", row_offset + r + i2, col_offset + c + (int)(sm_cols[j2] >> sm_dist_shift), sm_dist[(int)(sm_cols[j2] & sm_dist_mask)]);
}
if (is_diag) {
// divide by diagonal
if (!compact_d) {
soln2[r + i2] *= diags_vec[row_offset + r + i2];
} else {
soln2[r + i2] *= (diags_dist->dist[(int)diags_dist->ptrs[row_offset + r + i2]]);
}
// do over-relaxation if necessary
if (omega != 1) {
soln2[r + i2] = ((1-omega) * soln[row_offset + r + i2]) + (omega * soln2[r + i2]);
}
// set vector element
_helper->updateValue(soln[row_offset + r + i2], soln[row_offset + r + i2], soln2[r + i2], from_below);
}
}
}
//------------------------------------------------------------------------------