bool CubicSpline::SetSpline( VectorView& X, VectorView& Y, bool logX, bool logY )
{
int i,k;
double p,sig;
// determine element count
N_ = X.size();
// test that X and Y same size
if( N_ < 2 || N_ > 100 || N_ != Y.size() )
goto initFailed;
// dimension structures for N elements
X_.resize( N_ );
Y_.resize( N_ );
Y2_.resize( N_ );
// put values into local X_ and Y_ vectors
if( X[N_-1] < X[0] )
{
// Case 1: X_ values descending
X_ = X.reverse();
Y_ = Y.reverse();
}
else
{
// Caes 2: X_ values ascending
X_ = X;
Y_ = Y;
}
// convert X axis to its log if required
if( logX )
{
logX_ = true;
if( !X_.setLog() )
goto initFailed;
}
// convert Y axis to its log if required
if( logY )
{
logY_ = true;
if( !Y_.setLog() )
goto initFailed;
}
// use natural spline at boundaries
Y2_[0] = u[0] = 0;
Y2_[N_-1] = u[N_-1] = 0;
// decomposition loop - tri-diagonal algorithm
for( i=1; i<(N_-1); i++ )
{
sig = ( X_[i] - X_[i-1] ) / ( X_[i+1] - X_[i-1] );
p = sig * Y2_[i-1] + 2.0;
Y2_[i] = ( sig - 1.0 ) / p;
u[i] = ( Y_[i+1] - Y_[i] ) / ( X_[i+1] - X_[i] )
- ( Y_[i] - Y_[i-1] ) / ( X_[i] - X_[i-1] );
u[i] = ( ( 6.0 * u[i] ) / ( X_[i+1] - X_[i-1] ) - sig * u[i-1] ) / p;
}
// backsubstitition loop - tri-diagonal algorithm
for( k = N_-2; k >= 0; k -- )
{
Y2_[k] = Y2_[k] * Y2_[k+1] + u[k];
}
// SetSpline succeeded
return true;
initFailed:
// Set empty state
SetEmpty( );
// SetSpline failed
return false;
}
double RioTintoTS::SPNV3
(
int N,
VectorView X,
VectorView Y,
VectorView& S,
double XX
)
{
double XIXI1 = 0.0;
double DX = 0.0;
double XXI = 0.0;
double YY = 0.0;
double T = 0.0;
// Reverse vectors if X descending order
if( X[N-1] < X[0] )
{
X.reset( X.reverse() );
Y.reset( Y.reverse() );
}
// Find interval containing XX
if( XX < X[0] )
{
// before X[0]
XIXI1 = X[0] - X[1];
DX = (Y[0]-Y[1])/(XIXI1+1e-30) + XIXI1*(S[1]+2*S[0])/6.0;
XXI = XX - X[0];
YY = Y[0] + XXI * ( DX + XXI*S[0] );
}
else if( XX > X[N-1] )
{
// after X[N-1]
XIXI1 = X[N-1] - X[N-2];
DX = (Y[N-1]-Y[N-2])/(XIXI1+1e-30) + XIXI1*(2*S[N-1]+S[N-2])/6.0;
XXI = XX - X[N-1];
YY = Y[N-1] + XXI * ( DX + XXI*S[N-1] );
}
else
{
int i = 0;
int left = 0;
int right = N-1;
int mid = 0;
while( XX>=X[left] && XX<=X[right] )
{
mid = left + (right-left)/2;
if( mid==left )
{
i = left;
break;
}
else if( XX < X[mid] )
{
right = mid;
}
else
{
left = mid;
}
}
// between X[i] and X[i+1]
double x1 = X[i];
double x2 = X[i+1];
double y1 = Y[i];
double y2 = Y[i+1];
XXI = XX - X[i];
XIXI1 = X[i] - X[i+1];
T = 2.0*S[i] + XXI*(S[i]-S[i+1])/(XIXI1+1e-30) + S[i+1];
YY = Y[i] + XXI*(Y[i]-Y[i+1])/(XIXI1+1e-30) + (XX-X[i+1])*T/6.0;
}
return YY;
}
void RioTintoTS::SPN3( int N, VectorView X, VectorView Y, VectorView& S )
{
double DI;
double AI;
double AI1;
double CI;
double PI;
double PI1;
double Z;
int i;
int j;
int NM1;
static double C[100];
if( N>2 && N<100 )
{
// Reverse vectors if X descending order
if( X[N-1] < X[0] )
{
X.reset( X.reverse() );
Y.reset( Y.reverse() );
}
// End points
NM1 = N-1;
S[0] = 0;
S[NM1] = 0;
// Initial values
DI = 0.0;
AI = X[1] - X[0];
CI = -AI * S[0];
PI = ( Y[1] - Y[0] ) / ( AI + 1e-30 );
// Form equations and reduce to triangular form
for( i=1; i<NM1; i++ )
{
// Segment width
AI1 = X[i+1] - X[i];
// Diagonal elements
Z = 2.0 * (AI1+AI) - DI;
// Constant term
PI1 = ( Y[i+1] - Y[i] ) / ( AI1 + 1e-30 );
C[i] = ( 6.0*(PI1-PI) - CI ) / ( Z + 1e-30 );
CI = C[i] * AI1;
// Upper daigonal
S[i] = AI1 / ( Z + 1e-30 );
DI = S[i] * AI1;
AI = AI1;
}
// Back substitute
for( j=(NM1-1); j>0; j-- )
{
S[j] = C[j] - S[j]*S[j+1];
}
}
}
