mat Scheme::implicitScheme(int nSteps, double tSteps, double(*u_s)(double))
{
//input: nSteps (# of interior points), time, tSteps, u_s(x)
double deltaX = 1.0 / (nSteps + 1);
double deltaT = 1.0 / tSteps;
double alpha = deltaT / pow(deltaX,2);
vec v(nSteps), vNext(nSteps), u(nSteps);
int printIndex = tSteps / 10;
mat M(printIndex, nSteps);
int index = 0;
for( int i = 0; i < nSteps; i++)
{
double x = (i + 1) * deltaX;
vNext[i] = v[i] = -u_s(x);
}
// Boundary conditions
v[0] = vNext[0] = v[nSteps] = vNext[nSteps] = 0;
double a = -alpha; // diagonal element
double b = 1 + 2*alpha; // off-diagonal element
Solver solv = Solver();
for(int t = 1; t <= tSteps; t++)
{
solv.tridiagonalSolver(a, b, v, vNext);
// Initial conditions
vNext[0] = vNext[nSteps] = 0;
v = vNext;
for (int i = 0; i < nSteps; i++)
{
double x = (i + 1) * deltaX;
u[i] = v[i] + u_s(x);
}
// Print to file !
if (t % 10 == 0)
{
for (int i = 0; i < nSteps; i++)
M(index, i) = u[i];
index++;
}
}
for (int i = 0; i < printIndex; i++)
{
for (int j = 0; j < nSteps; j++)
printf("%f \t", M(i, j));
}
return M;
}
//-----------------------------------------------------------------------------
// Purpose:
// Input : time -
// type -
// Output : float
//-----------------------------------------------------------------------------
float CSentence::GetIntensity( float time, float endtime )
{
float zeroValue = 0.5f;
int c = GetNumSamples();
if ( c <= 0 )
{
return zeroValue;
}
int i;
for ( i = -1 ; i < c; i++ )
{
CEmphasisSample *s = GetBoundedSample( i, endtime );
CEmphasisSample *n = GetBoundedSample( i + 1, endtime );
if ( !s || !n )
continue;
if ( time >= s->time && time <= n->time )
{
break;
}
}
int prev = i - 1;
int start = i;
int end = i + 1;
int next = i + 2;
prev = max( -1, prev );
start = max( -1, start );
end = min( end, GetNumSamples() );
next = min( next, GetNumSamples() );
CEmphasisSample *esPre = GetBoundedSample( prev, endtime );
CEmphasisSample *esStart = GetBoundedSample( start, endtime );
CEmphasisSample *esEnd = GetBoundedSample( end, endtime );
CEmphasisSample *esNext = GetBoundedSample( next, endtime );
float dt = esEnd->time - esStart->time;
dt = clamp( dt, 0.01f, 1.0f );
Vector vPre( esPre->time, esPre->value, 0 );
Vector vStart( esStart->time, esStart->value, 0 );
Vector vEnd( esEnd->time, esEnd->value, 0 );
Vector vNext( esNext->time, esNext->value, 0 );
float f2 = ( time - esStart->time ) / ( dt );
f2 = clamp( f2, 0.0f, 1.0f );
Vector vOut;
Catmull_Rom_Spline(
vPre,
vStart,
vEnd,
vNext,
f2,
vOut );
float retval = clamp( vOut.y, 0.0f, 1.0f );
return retval;
}
mat Scheme::explicitScheme(int nSteps, double tSteps, double(*u_s)(double))
{
//input: nSteps , time, u_s(x)
double deltaX = 1.0 / (float)(nSteps + 1);
double alpha = 0.4;
double deltaT = alpha * pow(deltaX, 2);
//double
tSteps = 1.0 / deltaT;
vec v(nSteps), vNext(nSteps), u(nSteps);
int printIndex = tSteps / 10;
mat M(printIndex, nSteps);
int index = 0;
//Initialization
for (int i = 1; i < nSteps; i++)
{
double x = (i + 1) * deltaX;
v(i) = -u_s(x);
}
// Boundary conditions
v[0] = vNext[0] = 0;
v[nSteps] = vNext[nSteps] = 0;
//
for(int t = 1; t <= tSteps; t ++)
{
if ((t - 1) % 204 == 0)
{
for (int i = 0; i < nSteps; i++)
printf("%f \t", v(i));
printf("\n");
}
for(int i = 1; i < nSteps; i++ )
{
vNext[i] = (1 - 2 * alpha) * v[i];
double truc = vNext[i]; // XX
if( i > 0 )
vNext[i] += alpha * v[i-1]; // else += 0
if( i < nSteps )
vNext[i] += alpha * v[i+1]; // else += 0
}
v = vNext;
/*if ((t - 1) % 204 == 0)
{
for (int i = 0; i < nSteps; i++)
printf("%f \t", v(i));
printf("\n");
}*/
for (int i = 0; i < nSteps; i++)
{
double x = (i + 1) * deltaX;
u[i] = v[i] + u_s(x);
}
// Print to file !
if (t % 10 == 0)
{
for (int i = 0; i < nSteps; i++)
M(index, i) = u[i];
index++;
}
}
for (int i = 0; i < printIndex; i++)
{
for (int j = 0; j < nSteps; j++)
printf("%f \t", M(i, j));
}
return M;
}
