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Cleaned up the c_Y functions for GERG to make use of the beta functions relationship beta_ij = 1/beta_ji

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Signed-off-by: Ian Bell <ian.h.bell@gmail.com>
This commit is contained in:
Ian Bell
2014-09-06 21:43:53 +02:00
parent 7466ffd6d5
commit e92ed95a98
2 changed files with 15 additions and 20 deletions
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34
src/Backends/Helmholtz/ReducingFunctions.cpp
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@@ -17,9 +17,9 @@ long double ReducingFunction::d_ndTrdni_dxj__constxi(const std::vector<long doub
long double s = 0;
for (std::size_t k = 0; k < N-1; k++)
{
s += x[k]*d2Trdxidxj(x,j,k, xN_flag);
s += x[k]*d2Trdxidxj(x,k,j, xN_flag);
}
long double val = d2Trdxidxj(x,i,j, xN_flag)-dTrdxi__constxj(x,j, xN_flag)-s;
long double val = d2Trdxidxj(x,j,i,xN_flag)-dTrdxi__constxj(x,j, xN_flag)-s;
return val;
}
else{
@@ -158,7 +158,7 @@ long double GERG2008ReducingFunction::dYrdxi__constxj(const std::vector<long dou
long double dYr_dxi = 2*xi*Yc[i];
for (std::size_t k = 0; k < i; k++)
{
dYr_dxi += c_Y_ji(k,i,beta,gamma,Y_c_ij)*dfYkidxi__constxk(x,k,i,beta);
dYr_dxi += c_Y_ij(k,i,beta,gamma,Y_c_ij)*dfYkidxi__constxk(x,k,i,beta);
}
for (std::size_t k = i+1; k < N; k++)
{
@@ -172,18 +172,18 @@ long double GERG2008ReducingFunction::dYrdxi__constxj(const std::vector<long dou
long double dYr_dxi = 2*x[i]*Yc[i] - 2*x[N-1]*Yc[N-1];
for (std::size_t k = 0; k < i; k++)
{
dYr_dxi += c_Y_ji(k, i, beta, gamma, Y_c_ij)*dfYkidxi__constxk(x,k,i,beta);
dYr_dxi += c_Y_ij(k, i, beta, gamma, Y_c_ij)*dfYkidxi__constxk(x,k,i,beta);
}
for (std::size_t k = i+1; k < N-1; k++)
{
dYr_dxi += c_Y_ji(i, k, beta, gamma, Y_c_ij)*dfYkidxi__constxk(x,i,k,beta);
dYr_dxi += c_Y_ij(i, k, beta, gamma, Y_c_ij)*dfYkidxi__constxk(x,i,k,beta);
}
double beta_Y_iN = beta[i][N-1], xN = x[N-1];
dYr_dxi += c_Y_ji(i, N-1, beta, gamma, Y_c_ij)*(xN*(x[i]+xN)/(pow(beta_Y_iN,2)*x[i]+xN)+(1-beta_Y_iN*beta_Y_iN)*x[i]*xN*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 2));
dYr_dxi += c_Y_ij(i, N-1, beta, gamma, Y_c_ij)*(xN*(x[i]+xN)/(pow(beta_Y_iN,2)*x[i]+xN)+(1-beta_Y_iN*beta_Y_iN)*x[i]*xN*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 2));
for (std::size_t k = 0; k < N-1; ++k)
{
double beta_Y_kN = beta[k][N-1];
dYr_dxi += c_Y_ji(k, N-1, beta, gamma, Y_c_ij)*(-x[k]*(x[k]+xN)/(pow(beta_Y_kN,2)*x[k]+xN)+(1-beta_Y_kN*beta_Y_kN)*xN*x[k]*x[k]/pow(beta_Y_kN*beta_Y_kN*x[k]+xN, 2));
dYr_dxi += c_Y_ij(k, N-1, beta, gamma, Y_c_ij)*(-x[k]*(x[k]+xN)/(pow(beta_Y_kN,2)*x[k]+xN)+(1-beta_Y_kN*beta_Y_kN)*xN*x[k]*x[k]/pow(beta_Y_kN*beta_Y_kN*x[k]+xN, 2));
}
return dYr_dxi;
}
@@ -212,18 +212,18 @@ long double GERG2008ReducingFunction::d2Yrdxi2__constxj(const std::vector<long d
long double d2Yr_dxi2 = 2*Yc[i] + 2*Yc[N-1];
for (std::size_t k = 0; k < i; k++)
{
d2Yr_dxi2 += c_Y_ji(k, i, beta, gamma, Y_c_ij)*d2fYkidxi2__constxk(x,k,i,beta);
d2Yr_dxi2 += c_Y_ij(k, i, beta, gamma, Y_c_ij)*d2fYkidxi2__constxk(x,k,i,beta);
}
for (std::size_t k = i+1; k < N-1; k++)
{
d2Yr_dxi2 += c_Y_ji(i, k, beta, gamma, Y_c_ij)*d2fYkidxi2__constxk(x,i,k,beta);
d2Yr_dxi2 += c_Y_ij(i, k, beta, gamma, Y_c_ij)*d2fYkidxi2__constxk(x,i,k,beta);
}
double beta_Y_iN = beta[i][N-1], xN = x[N-1];
d2Yr_dxi2 += 2*c_Y_ji(i, N-1, beta, gamma, Y_c_ij)*(-(x[i]+xN)/(pow(beta_Y_iN,2)*x[i]+xN)+(1-beta_Y_iN*beta_Y_iN)*(xN*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 2)+((1-beta_Y_iN*beta_Y_iN)*x[i]*xN*xN-beta_Y_iN*beta_Y_iN*x[i]*x[i]*xN)/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 3)));
d2Yr_dxi2 += 2*c_Y_ij(i, N-1, beta, gamma, Y_c_ij)*(-(x[i]+xN)/(pow(beta_Y_iN,2)*x[i]+xN)+(1-beta_Y_iN*beta_Y_iN)*(xN*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 2)+((1-beta_Y_iN*beta_Y_iN)*x[i]*xN*xN-beta_Y_iN*beta_Y_iN*x[i]*x[i]*xN)/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 3)));
for (std::size_t k = 0; k < N-1; ++k)
{
double beta_Y_kN = beta[k][N-1];
d2Yr_dxi2 += 2*c_Y_ji(k, N-1, beta, gamma, Y_c_ij)*x[k]*x[k]*(1-beta_Y_kN*beta_Y_kN)/pow(pow(beta_Y_kN,2)*x[k]+xN, 2)*(xN/(beta_Y_kN*beta_Y_kN*x[k]+xN)-1);
d2Yr_dxi2 += 2*c_Y_ij(k, N-1, beta, gamma, Y_c_ij)*x[k]*x[k]*(1-beta_Y_kN*beta_Y_kN)/pow(pow(beta_Y_kN,2)*x[k]+xN, 2)*(xN/(beta_Y_kN*beta_Y_kN*x[k]+xN)-1);
}
return d2Yr_dxi2;
}
@@ -251,17 +251,17 @@ long double GERG2008ReducingFunction::d2Yrdxidxj__constxj(const std::vector<long
if (i == j){ return d2Yrdxi2__constxj(x, i, beta, gamma, Y_c_ij, Yc, xN_flag); }
long double xN = x[N-1];
long double d2Yr_dxidxj = 2*Yc[N-1];
d2Yr_dxidxj += c_Y_ji(i, j, beta, gamma, Y_c_ij)*d2fYijdxidxj(x,i,j,beta);
d2Yr_dxidxj += c_Y_ij(i, j, beta, gamma, Y_c_ij)*d2fYijdxidxj(x,i,j,beta);
for (std::size_t k = 0; k < N-1; k++)
{
double beta_Y_kN = beta[k][N-1];
d2Yr_dxidxj += 2*c_Y_ji(k, N-1, beta, gamma, Y_c_ij)*x[k]*x[k]*(1-beta_Y_kN*beta_Y_kN)/pow(beta_Y_kN*beta_Y_kN*x[k]+xN,2)*(xN/(beta_Y_kN*beta_Y_kN*x[k]+xN)-1);
d2Yr_dxidxj += 2*c_Y_ij(k, N-1, beta, gamma, Y_c_ij)*x[k]*x[k]*(1-beta_Y_kN*beta_Y_kN)/pow(beta_Y_kN*beta_Y_kN*x[k]+xN,2)*(xN/(beta_Y_kN*beta_Y_kN*x[k]+xN)-1);
}
double beta_Y_iN = beta[i][N-1], beta_Y_jN = beta[j][N-1];
d2Yr_dxidxj += c_Y_ji(i, N-1, beta, gamma, Y_c_ij)*((1-beta_Y_iN*beta_Y_iN)*(2*x[i]*xN*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 3)-x[i]*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 2)) - (x[i]+xN)/(beta_Y_iN*beta_Y_iN*x[i]+xN));
d2Yr_dxidxj += -c_Y_ji(j, N-1, beta, gamma, Y_c_ij)*((1-beta_Y_jN*beta_Y_jN)*(2*x[j]*x[j]*xN*beta_Y_jN*beta_Y_jN/pow(beta_Y_jN*beta_Y_jN*x[j]+xN, 3)-x[j]*xN/pow(beta_Y_jN*beta_Y_jN*x[j]+xN, 2)) - (x[j]+xN)/(beta_Y_jN*beta_Y_jN*x[j]+xN));
d2Yr_dxidxj += c_Y_ij(i, N-1, beta, gamma, Y_c_ij)*((1-beta_Y_iN*beta_Y_iN)*(2*x[i]*xN*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 3)-x[i]*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 2)) - (x[i]+xN)/(beta_Y_iN*beta_Y_iN*x[i]+xN));
d2Yr_dxidxj += -c_Y_ij(j, N-1, beta, gamma, Y_c_ij)*((1-beta_Y_jN*beta_Y_jN)*(2*x[j]*x[j]*xN*beta_Y_jN*beta_Y_jN/pow(beta_Y_jN*beta_Y_jN*x[j]+xN, 3)-x[j]*xN/pow(beta_Y_jN*beta_Y_jN*x[j]+xN, 2)) - (x[j]+xN)/(beta_Y_jN*beta_Y_jN*x[j]+xN));
return d2Yr_dxidxj;
}
@@ -284,10 +284,6 @@ long double GERG2008ReducingFunction::c_Y_ij(std::size_t i, std::size_t j, const
{
return 2*beta[i][j]*gamma[i][j]*Y_c[i][j];
}
long double GERG2008ReducingFunction::c_Y_ji(std::size_t j, std::size_t i, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c)
{
return 2/beta[i][j]*gamma[i][j]*Y_c[i][j];
}
long double GERG2008ReducingFunction::f_Y_ij(const std::vector<long double> &x, std::size_t i, std::size_t j, const STLMatrix &beta)
{
double xi = x[i], xj = x[j], beta_Y = beta[i][j];

1
src/Backends/Helmholtz/ReducingFunctions.h
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@@ -139,7 +139,6 @@ public:
long double d2Yrdxi2__constxj(const std::vector<long double> &x, std::size_t i, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector<long double> &Yc, x_N_dependency_flag xN_flag);
long double d2Yrdxidxj__constxj(const std::vector<long double> &x, std::size_t i, std::size_t j, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector<long double> &Yc, x_N_dependency_flag xN_flag);
long double c_Y_ij(std::size_t i, std::size_t j, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c);
long double c_Y_ji(std::size_t j, std::size_t i, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c);
long double f_Y_ij(const std::vector<long double> &x, std::size_t i, std::size_t j, const STLMatrix &beta);
long double dfYkidxi__constxk(const std::vector<long double> &x, std::size_t k, std::size_t i, const STLMatrix &beta);