Index InitializeAlgorithmGrid::IndexReversal(Number number_of_initial_bins,
		Potential v_min,
		const parameters::PopulationParameter& parameter_population

		) const {
	return static_cast<Index>((parameter_population._V_reversal - v_min)
			/ DeltaV(number_of_initial_bins, v_min, parameter_population));
}
Beispiel #2
0
int TGnuPlot::AddErrBar(const TFltTrV& XYDValV, const TStr& Label) {
  TFltKdV XYFltValV(XYDValV.Len(), 0);
  TFltV DeltaV(XYDValV.Len(), 0);
  for (int i = 0; i < XYDValV.Len(); i++) {
    XYFltValV.Add(TFltKd(XYDValV[i].Val1, XYDValV[i].Val2));
    DeltaV.Add(XYDValV[i].Val3);
  }
  return AddErrBar(XYFltValV, DeltaV, Label);
}
Beispiel #3
0
int TGnuPlot::AddErrBar(const TFltTrV& XYDValV, const TStr& DatLabel, const TStr& ErrLabel) {
  TFltKdV XYFltValV(XYDValV.Len(), 0);
  TFltV DeltaV(XYDValV.Len(), 0);
  for (int i = 0; i < XYDValV.Len(); i++) {
    XYFltValV.Add(TFltKd(XYDValV[i].Val1, XYDValV[i].Val2));
    DeltaV.Add(XYDValV[i].Val3);
  }
  const int PlotId = AddPlot(XYFltValV, gpwLinesPoints, DatLabel);
  AddErrBar(XYFltValV, DeltaV, ErrLabel);
  return PlotId;
}
Beispiel #4
0
vector
Foam::centreOfVolume::calculate_acceleration(const volScalarField &p,
                                             const volSymmTensorField &R) {
    const Time& t = mesh_.time();

    dimensionedVector xcurrent(
        "xd",
        fvc::domainIntegrate(alpha_ * mesh_.C()) // centre of mass
            /
            fvc::domainIntegrate(alpha_));

    // Velocity difference (Rusche approach)
    dimensionedVector DeltaV("DeltaV",
                             (lambdaF_ * (xinit_ - xcurrent)) / t.deltaT() -
                                 lambdad_ * (xcurrent - xold_) / t.deltaT());

    xold_.value() = xcurrent.value();

    return -(DeltaV / t.deltaT()).value();
}
void CAI_BlendedMotor::BuildVelocityScript( const AILocalMoveGoal_t &move )
{
	int i;
	float a;

	float idealVelocity = GetIdealSpeed();
	if (idealVelocity == 0)
	{
		idealVelocity = 50;
	}

	float idealAccel = GetIdealAccel();
	if (idealAccel == 0)
	{
		idealAccel = 100;
	}

	AI_Movementscript_t script;

	// set current location as start of script
	script.vecLocation = GetAbsOrigin();
	script.flMaxVelocity = GetCurSpeed();
	m_scriptMove.AddToTail( script );

	//-------------------------

	extern ConVar *npc_height_adjust;
	if (npc_height_adjust->GetBool() && move.bHasTraced && move.directTrace.flTotalDist != move.thinkTrace.flTotalDist)
	{
		float flDist = (move.directTrace.vEndPosition - m_scriptMove[0].vecLocation).Length2D();
		float flHeight = move.directTrace.vEndPosition.z - m_scriptMove[0].vecLocation.z;
		float flDelta;

		if (flDist > 0)
		{
			flDelta = flHeight / flDist;
		}
		else
		{
			flDelta = 0;
		}

		m_flPredictiveSpeedAdjust = 1.1 - fabs( flDelta );
		m_flPredictiveSpeedAdjust = clamp( m_flPredictiveSpeedAdjust, (flHeight > 0.0) ? 0.5 : 0.8, 1.0 );

		/*
		if ((GetOuter()->m_debugOverlays & OVERLAY_NPC_SELECTED_BIT))
		{
			Msg("m_flPredictiveSpeedAdjust %.3f  %.1f %.1f\n", m_flPredictiveSpeedAdjust, flHeight, flDist );
			NDebugOverlay::Box( move.directTrace.vEndPosition, Vector( -2, -2, -2 ), Vector( 2, 2, 2 ), 0,255,255, 0, 0.12 );
		}
		*/
	}
	if (npc_height_adjust->GetBool())
	{
		float flDist = (move.thinkTrace.vEndPosition - m_vecPrevOrigin2).Length2D();
		float flHeight = move.thinkTrace.vEndPosition.z - m_vecPrevOrigin2.z;
		float flDelta;

		if (flDist > 0)
		{
			flDelta = flHeight / flDist;
		}
		else
		{
			flDelta = 0;
		}

		float newSpeedAdjust = 1.1 - fabs( flDelta );
		newSpeedAdjust = clamp( newSpeedAdjust, (flHeight > 0.0) ? 0.5 : 0.8, 1.0 );

		// debounce speed adjust
		if (newSpeedAdjust < m_flReactiveSpeedAdjust)
		{
			m_flReactiveSpeedAdjust = m_flReactiveSpeedAdjust * 0.2 + newSpeedAdjust * 0.8;
		}
		else
		{
			m_flReactiveSpeedAdjust = m_flReactiveSpeedAdjust * 0.5 + newSpeedAdjust * 0.5;
		}

		// filter through origins
		m_vecPrevOrigin2 = m_vecPrevOrigin1;
		m_vecPrevOrigin1 = GetAbsOrigin();

		/*
		if ((GetOuter()->m_debugOverlays & OVERLAY_NPC_SELECTED_BIT))
		{
			NDebugOverlay::Box( m_vecPrevOrigin2, Vector( -2, -2, -2 ), Vector( 2, 2, 2 ), 255,0,255, 0, 0.12 );
			NDebugOverlay::Box( move.thinkTrace.vEndPosition, Vector( -2, -2, -2 ), Vector( 2, 2, 2 ), 255,0,255, 0, 0.12 );
			Msg("m_flReactiveSpeedAdjust %.3f  %.1f %.1f\n", m_flReactiveSpeedAdjust, flHeight, flDist );
		}
		*/
	}

	idealVelocity = idealVelocity * min( m_flReactiveSpeedAdjust, m_flPredictiveSpeedAdjust );

	//-------------------------

	bool bAddedExpected = false;

	// add all waypoint locations and velocities
	AI_Waypoint_t *pCurWaypoint = GetNavigator()->GetPath()->GetCurWaypoint();

	// there has to be at least one waypoint
	Assert( pCurWaypoint );

	while (pCurWaypoint && (pCurWaypoint->NavType() == NAV_GROUND || pCurWaypoint->NavType() == NAV_FLY) /*&& flTotalDist / idealVelocity < 3.0*/) // limit lookahead to 3 seconds
	{
		script.Init();
		AI_Waypoint_t *pNext = pCurWaypoint->GetNext();

		if (ai_path_adjust_speed_on_immediate_turns->GetBool() && !bAddedExpected)
		{
			// hack in next expected immediate location for move
			script.vecLocation = GetAbsOrigin() + move.dir * move.curExpectedDist;
			bAddedExpected = true;
			pNext = pCurWaypoint;
		}
		else
		{
			script.vecLocation = pCurWaypoint->vecLocation;
			script.pWaypoint = pCurWaypoint;
		}

		//DevMsg("waypoint %.1f %.1f %.1f\n", script.vecLocation.x, script.vecLocation.y, script.vecLocation.z );

		if (pNext)
		{
			switch( pNext->NavType())
			{
			case NAV_GROUND:
			case NAV_FLY:
				{
					Vector d1 = pNext->vecLocation - script.vecLocation;
					Vector d2 = script.vecLocation - m_scriptMove[m_scriptMove.Count()-1].vecLocation;
					
					// remove very short, non terminal ground links
					// FIXME: is this safe?  Maybe just check for co-located ground points?
					if (d1.Length2D() < 1.0)
					{
						/*
						if (m_scriptMove.Count() > 1)
						{
							int i = m_scriptMove.Count() - 1;
							m_scriptMove[i].vecLocation = pCurWaypoint->vecLocation;
							m_scriptMove[i].pWaypoint = pCurWaypoint;
						}
						*/
						pCurWaypoint = pNext;
						continue;
					}

					d1.z = 0;
					VectorNormalize( d1 );
					d2.z = 0;
					VectorNormalize( d2 );

					// figure velocity
					float dot = (DotProduct( d1, d2 ) + 0.2);
					if (dot > 0)
					{
						dot = clamp( dot, 0.0f, 1.0f );
						script.flMaxVelocity = idealVelocity * dot;
					}
					else
					{
						script.flMaxVelocity = 0;
					}
				}
				break;
			case NAV_JUMP:

				// FIXME: information about what the jump should look like isn't stored in the waypoints
				// this'll need to call 
				//    GetMoveProbe()->MoveLimit( NAV_JUMP, GetLocalOrigin(), GetPath()->CurWaypointPos(), MASK_NPCSOLID, GetNavTargetEntity(), &moveTrace );
				// to get how far/fast the jump will be, but this is also stateless, so it'd call it per frame.
				// So far it's not clear that the moveprobe doesn't also call this.....

				{
					float minJumpHeight = 0;
					float maxHorzVel = max( GetCurSpeed(), 100 );
					float gravity = sv_gravity->GetFloat() * GetOuter()->GetGravity();
					Vector vecApex;
					Vector rawJumpVel = GetMoveProbe()->CalcJumpLaunchVelocity(script.vecLocation, pNext->vecLocation, gravity, &minJumpHeight, maxHorzVel, &vecApex );

					script.flMaxVelocity = rawJumpVel.Length2D();
					// Msg("%.1f\n", script.flMaxVelocity );
				}
				break;
			case NAV_CLIMB:
				{
					/*
					CAI_Node *pClimbNode = GetNavigator()->GetNetwork()->GetNode(pNext->iNodeID);

					check: pClimbNode->m_eNodeInfo
						bits_NODE_CLIMB_BOTTOM, 
						bits_NODE_CLIMB_ON, 
						bits_NODE_CLIMB_OFF_FORWARD, 
						bits_NODE_CLIMB_OFF_LEFT, 
						bits_NODE_CLIMB_OFF_RIGHT
					*/

					script.flMaxVelocity = 0;
				}
				break;
			/*
			case NAV_FLY:
				// FIXME: can there be a NAV_GROUND -> NAV_FLY transition?
				script.flMaxVelocity = 0;
				break;
			*/
			default:
				break;
			}
		}
		else
		{
			script.flMaxVelocity = GetNavigator()->GetArrivalSpeed();
			// Assert( script.flMaxVelocity == 0 );
		}

		m_scriptMove.AddToTail( script );
		pCurWaypoint = pNext;
	}


	//-------------------------

	// update distances
	float flTotalDist = 0;
	for (i = 0; i < m_scriptMove.Count() - 1; i++ )
	{
		flTotalDist += m_scriptMove[i].flDist = (m_scriptMove[i+1].vecLocation - m_scriptMove[i].vecLocation).Length2D();
	}

	//-------------------------

	if ( !m_bDeceleratingToGoal && m_scriptMove.Count() && flTotalDist > 0 )
	{
		float flNeededAccel = DeltaV( m_scriptMove[0].flMaxVelocity, m_scriptMove[m_scriptMove.Count() - 1].flMaxVelocity, flTotalDist );
		m_bDeceleratingToGoal =  (flNeededAccel < -idealAccel);
		//Assert( flNeededAccel != idealAccel);
	}

	//-------------------------

	// insert slowdown points due to blocking
	if (ai_path_insert_pause_at_obstruction->GetBool() && move.directTrace.pObstruction)
	{
		float distToObstruction = (move.directTrace.vEndPosition - m_scriptMove[0].vecLocation).Length2D();

		// HACK move obstruction out "stepsize" to account for it being based on stand position and not a trace
		distToObstruction = distToObstruction + 16;

		InsertSlowdown( distToObstruction, idealAccel, false );
	}

	if (ai_path_insert_pause_at_est_end->GetBool() && GetNavigator()->GetArrivalDistance() > 0.0)
	{
		InsertSlowdown( flTotalDist - GetNavigator()->GetArrivalDistance(), idealAccel, true );
	}

	// calc initial velocity based on immediate direction changes
	if ( ai_path_adjust_speed_on_immediate_turns->GetBool() && m_scriptMove.Count() > 1)
	{
		/*
		if ((GetOuter()->m_debugOverlays & OVERLAY_NPC_SELECTED_BIT))
		{
			Vector tmp = m_scriptMove[1].vecLocation - m_scriptMove[0].vecLocation;
			VectorNormalize( tmp );
			NDebugOverlay::Line( m_scriptMove[0].vecLocation + Vector( 0, 0, 10 ), m_scriptMove[0].vecLocation + tmp * 32 + Vector( 0, 0, 10 ), 255,255,255, true, 0.1 );
			
			NDebugOverlay::Line( m_scriptMove[0].vecLocation + Vector( 0, 0, 10 ), m_scriptMove[1].vecLocation + Vector( 0, 0, 10 ), 255,0,0, true, 0.1 );

			tmp = GetCurVel();
			VectorNormalize( tmp );
			NDebugOverlay::Line( m_scriptMove[0].vecLocation + Vector( 0, 0, 10 ), m_scriptMove[0].vecLocation + tmp * 32 + Vector( 0, 0, 10 ), 0,0,255, true, 0.1 );
		}
		*/

		Vector d1 = m_scriptMove[1].vecLocation - m_scriptMove[0].vecLocation;
		d1.z = 0;
		VectorNormalize( d1 );

		Vector d2 = GetCurVel();
		d2.z = 0;
		VectorNormalize( d2 );

		float dot = (DotProduct( d1, d2 ) + MIN_STEER_DOT);
		dot = clamp( dot, 0.0f, 1.0f );
		m_scriptMove[0].flMaxVelocity = m_scriptMove[0].flMaxVelocity * dot;
	}

	// clamp forward velocities
	for (i = 0; i < m_scriptMove.Count() - 1; i++ )
	{
		// find needed acceleration
		float dv = m_scriptMove[i+1].flMaxVelocity - m_scriptMove[i].flMaxVelocity;

		if (dv > 0.0)
		{
			// find time, distance to accel to next max vel
			float t1 = dv / idealAccel;
			float d1 = m_scriptMove[i].flMaxVelocity * t1 + 0.5 * (idealAccel) * t1 * t1;

			// is there enough distance
			if (d1 > m_scriptMove[i].flDist)
			{
				float r1, r2;

				// clamp the next velocity to the possible accel in the given distance
				if (SolveQuadratic( 0.5 * idealAccel, m_scriptMove[i].flMaxVelocity, -m_scriptMove[i].flDist, r1, r2 ))
				{
					m_scriptMove[i+1].flMaxVelocity = m_scriptMove[i].flMaxVelocity + idealAccel * r1;
				}
			}
		}
	}

	// clamp decel velocities
	for (i = m_scriptMove.Count() - 1; i > 0; i-- )
	{
		// find needed deceleration
		float dv = m_scriptMove[i].flMaxVelocity - m_scriptMove[i-1].flMaxVelocity;

		if (dv < 0.0)
		{
			// find time, distance to decal to next max vel
			float t1 = -dv / idealAccel;
			float d1 = m_scriptMove[i].flMaxVelocity * t1 + 0.5 * (idealAccel) * t1 * t1;

			// is there enough distance
			if (d1 > m_scriptMove[i-1].flDist)
			{
				float r1, r2;
				
				// clamp the next velocity to the possible decal in the given distance
				if (SolveQuadratic( 0.5 * idealAccel, m_scriptMove[i].flMaxVelocity, -m_scriptMove[i-1].flDist, r1, r2 ))
				{
					m_scriptMove[i-1].flMaxVelocity = m_scriptMove[i].flMaxVelocity + idealAccel * r1;
				}
			}
		}
	}

	/*
	for (i = 0; i < m_scriptMove.Count(); i++)
	{
		NDebugOverlay::Text( m_scriptMove[i].vecLocation, (const char *)CFmtStr( "%.2f ", m_scriptMove[i].flMaxVelocity  ), false, 0.1 );
		// DevMsg("%.2f ", m_scriptMove[i].flMaxVelocity );
	}
	// DevMsg("\n");
	*/

	// insert intermediate ideal velocities
	for (i = 0; i < m_scriptMove.Count() - 1;)
	{
		// accel to ideal
		float t1 = (idealVelocity - m_scriptMove[i].flMaxVelocity) / idealAccel;
		float d1 = m_scriptMove[i].flMaxVelocity * t1 + 0.5 * (idealAccel) * t1 * t1;

		// decel from ideal
		float t2 = (idealVelocity - m_scriptMove[i+1].flMaxVelocity) / idealAccel;
		float d2 = m_scriptMove[i+1].flMaxVelocity * t2 + 0.5 * (idealAccel) * t2 * t2;

		m_scriptMove[i].flDist = (m_scriptMove[i+1].vecLocation - m_scriptMove[i].vecLocation).Length2D();

		// is it possible to accel and decal to idealVelocity between next two nodes
		if (d1 + d2 < m_scriptMove[i].flDist)
		{
			Vector start =  m_scriptMove[i].vecLocation;
			Vector end = m_scriptMove[i+1].vecLocation;
			float dist = m_scriptMove[i].flDist;

			// insert the two points needed to end accel and start decel
			if (d1 > 1.0 && t1 > 0.1)
			{
				a = d1 / dist;

				script.Init();
				script.vecLocation = end * a + start * (1 - a);
				script.flMaxVelocity = idealVelocity;
				m_scriptMove.InsertAfter( i, script );
				i++;
			}

			if (dist - d2 > 1.0 && t2 > 0.1)
			{
				// DevMsg("%.2f : ", a );

				a = (dist - d2) / dist;

				script.Init();
				script.vecLocation = end * a + start * (1 - a);
				script.flMaxVelocity = idealVelocity;
				m_scriptMove.InsertAfter( i, script );
				i++;
			}

			i++;
		}
		else
		{
			// check to see if the amount of change needed to reach target is less than the ideal acceleration
			float flNeededAccel = fabs( DeltaV( m_scriptMove[i].flMaxVelocity, m_scriptMove[i+1].flMaxVelocity, m_scriptMove[i].flDist ) );
			if (flNeededAccel < idealAccel)
			{
				// if so, they it's possible to get a bit towards the ideal velocity
				float v1 = m_scriptMove[i].flMaxVelocity;
				float v2 = m_scriptMove[i+1].flMaxVelocity;
				float dist = m_scriptMove[i].flDist;

				// based on solving:
				//		v1+A*t1-v2-A*t2=0
				//		v1*t1+0.5*A*t1*t1+v2*t2+0.5*A*t2*t2-D=0

				float tmp = idealAccel*dist+0.5*v1*v1+0.5*v2*v2;
				Assert( tmp >= 0 );
				t1 = (-v1+sqrt( tmp )) / idealAccel;
				t2 = (v1+idealAccel*t1-v2)/idealAccel;

				// if this assert hits, write down the v1, v2, dist, and idealAccel numbers and send them to me (Ken).
				// go ahead the comment it out, it's safe, but I'd like to know a test case where it's happening
				//Assert( t1 > 0 && t2 > 0 );

				// check to make sure it's really worth it
				if (t1 > 0.0 && t2 > 0.0)
				{
					d1 = v1 * t1 + 0.5 * idealAccel * t1 * t1;
					
					/*
					d2 = v2 * t2 + 0.5 * idealAccel * t2 * t2;
					Assert( fabs( d1 + d2 - dist ) < 0.001 );
					*/

					float a = d1 / m_scriptMove[i].flDist;
					script.Init();
					script.vecLocation = m_scriptMove[i+1].vecLocation * a + m_scriptMove[i].vecLocation * (1 - a);
					script.flMaxVelocity = m_scriptMove[i].flMaxVelocity + idealAccel * t1;

					if (script.flMaxVelocity < idealVelocity)
					{
						// DevMsg("insert %.2f %.2f %.2f\n", m_scriptMove[i].flMaxVelocity, script.flMaxVelocity, m_scriptMove[i+1].flMaxVelocity ); 
						m_scriptMove.InsertAfter( i, script );
						i += 1;
					}
				}
			}
			i += 1;
		}
	}

	// clamp min velocities
	for (i = 0; i < m_scriptMove.Count(); i++)
	{
		m_scriptMove[i].flMaxVelocity = max( m_scriptMove[i].flMaxVelocity, MIN_VELOCITY );
	}

	// rebuild fields
	m_scriptMove[0].flElapsedTime = 0;
	for (i = 0; i < m_scriptMove.Count() - 1; )
	{
		m_scriptMove[i].flDist = (m_scriptMove[i+1].vecLocation - m_scriptMove[i].vecLocation).Length2D();

		if (m_scriptMove[i].flMaxVelocity == 0 && m_scriptMove[i+1].flMaxVelocity == 0)
		{
			// force a minimum velocity 
			//CE_assert
			//Assert( 0 );
			m_scriptMove[i+1].flMaxVelocity = 1.0;
		}

		float t = m_scriptMove[i].flDist / (0.5 * (m_scriptMove[i].flMaxVelocity + m_scriptMove[i+1].flMaxVelocity));
		m_scriptMove[i].flTime = t;

		/*
		if (m_scriptMove[i].flDist < 0.01)
		{
			// Assert( m_scriptMove[i+1].pWaypoint == NULL );

			m_scriptMove.Remove( i + 1 );
			continue;
		}
		*/

		m_scriptMove[i+1].flElapsedTime = m_scriptMove[i].flElapsedTime + m_scriptMove[i].flTime;

		i++;
	}

	/*
	for (i = 0; i < m_scriptMove.Count(); i++)
	{
		DevMsg("(%.2f : %.2f : %.2f)", m_scriptMove[i].flMaxVelocity, m_scriptMove[i].flDist, m_scriptMove[i].flTime );
		// DevMsg("(%.2f:%.2f)", m_scriptMove[i].flTime, m_scriptMove[i].flElapsedTime );
	}
	DevMsg("\n");
	*/
}
algorithm::AlgorithmGrid InitializeAlgorithmGrid::InitializeGrid(
		Number number_of_initial_bins, Potential v_min,
		const parameters::PopulationParameter& parameter_population,
		const parameters::InitialDensityParameter& parameter_density) const {
	parameters::InitialDensityParameter parameter_initial = parameter_density;

	std::vector<double> vector_potential(number_of_initial_bins, 0);
	std::vector<double> vector_state(number_of_initial_bins, 0);

	// first calculate which bin is closest to V = V_reversal
	double delta_v = DeltaV(number_of_initial_bins, v_min,
			parameter_population);

	int index_reversal = static_cast<int>(IndexReversal(number_of_initial_bins,
			v_min, parameter_population));

	// if index_reversal == n initial bins - 1, delta_v is undefined
	if (!(index_reversal >= 0
			&& index_reversal <= static_cast<int>(number_of_initial_bins) - 1))
		throw utilities::Exception(
				"Reversal potential is too close to threshold");

	vector_potential[index_reversal] = parameter_population._V_reversal;

	// So, we have one bin which exactly matches the reversal potential
	// this is important in determining the zero leak parameters

	// we now recalculate delta_v
	int number_positive_potential_bins = number_of_initial_bins
			- index_reversal;
	delta_v = (parameter_population._theta - parameter_population._V_reversal)
			/ (number_positive_potential_bins - 1);

	// realign the potential if sigma == 0, so that one and only one bin corresponds to approximately the desired initial potential
	if (parameter_density._sigma == 0) {
		int index_mu_relative_to_reversal =
				static_cast<int>((parameter_density._mu
						- parameter_population._V_reversal) / delta_v);
		parameter_initial._mu = parameter_population._V_reversal
				+ index_mu_relative_to_reversal * delta_v;
	}

	// fill in the potential bins that are larger than V_reversal
	for (int index_positive = index_reversal + 1;
			index_positive < static_cast<int>(number_of_initial_bins);
			index_positive++) {
		vector_potential[index_positive] = parameter_population._V_reversal
				+ delta_v * (index_positive - index_reversal);

		// renormalize the density later
		vector_state[index_positive] = gaussian(
				vector_potential[index_positive], parameter_initial);
	}

	// fill in the negative bins
	for (int index_negative = index_reversal - 1; index_negative >= 0;
			index_negative--) {
		vector_potential[index_negative] = parameter_population._V_reversal
				- delta_v * (index_reversal - index_negative);

		// renormalize the density later
		vector_state[index_negative] = gaussian(
				vector_potential[index_negative], parameter_initial);
	}

	// the reversal bin already has correct potential, but the initial value must still be set
	vector_state[index_reversal] = gaussian(vector_potential[index_reversal],
			parameter_initial);

	double sum = std::accumulate(vector_state.begin(), vector_state.end(), 0.0)
			/ number_of_initial_bins;

	assert( sum > 0);

	std::transform(vector_state.begin(), vector_state.end(),
			vector_state.begin(), std::bind2nd(std::divides<double>(), sum));

	return algorithm::AlgorithmGrid(vector_state, vector_potential);
}