/**
* Computes the change in U (stochasti version)
*
* @param[in] u,v1,v2,v3 Concentration matries
* @param[in] i,j Position in grid
* @param[in] hsq Spatial discretisation step squared \f$ h^2 = {\Delta x}^2 = \frac{L}{N}^2 \f$ used by the Laplacian
* @param[in] M,N Size (height = rows, length = columns) of the grid
* @param[in] r Reaction rates matrix
* @param[in] F Fuel feed rates
* @param[in] Du Diffusion coefficient of U
*/
inline double react_u(double** u, double** v1, double** v2, double** v3,
int i, int j, float hsq, int M, int N,
float r[][3], float F, float Du,
float cell_cap_1D, float noise_stddev, float noise_level, gsl_rng* rgen) {
double u_new;
// diffusion
u_new = Du * laplacian5_per_grid(u, i, j, M, N, hsq);
// reaction
u_new += -u[i][j] * (r[0][0]*v1[i][j]*v1[i][j] + r[1][1]*v2[i][j]*v2[i][j] + r[2][2]*v3[i][j]*v3[i][j] +
(r[0][1] + r[1][0])*v1[i][j]*v2[i][j] +
(r[1][2] + r[2][1])*v2[i][j]*v3[i][j] +
(r[0][2] + r[2][0])*v1[i][j]*v3[i][j]
);
// feed
u_new += F * (1.0 - u[i][j]);
// noise
u_new += gauss_noise(u[i][j], cell_cap_1D, noise_stddev, noise_level, rgen);
return u_new;
}
/**
* Computes the change in V3 (stochastic version)
*
* @param[in] u,v1,v2,v3 Concentration matries
* @param[in] i,j Position in grid
* @param[in] hsq Spatial discretisation step squared \f$ h^2 = {\Delta x}^2 = \frac{L}{N}^2 \f$ used by the Laplacian
* @param[in] M,N Size (height = rows, length = columns) of the grid
* @param[in] r Reaction rates matrix
* @param[in] F Fuel feed rates
* @param[in] k3 V1 degradation rate
* @param[in] Dc Diffusion coefficient of V3
*/
inline double react_v3(double** u, double** v1, double** v2, double** v3,
int i, int j, float hsq, int M, int N,
float r[][3], float F, float k3, float Dc,
float cell_cap_1D, float noise_stddev, float noise_level, gsl_rng* rgen) {
double v3_new;
// diffusion
v3_new = Dc * laplacian5_per_grid(v3, i, j, M, N, hsq);
// reaction
v3_new += u[i][j] * (r[2][2]*v3[i][j]*v3[i][j] + r[1][2]*v2[i][j]*v3[i][j] + r[0][2]*v1[i][j]*v3[i][j]);
// feed
v3_new += -(F + k3) * v3[i][j];
// noise
v3_new += gauss_noise(v3[i][j], cell_cap_1D, noise_stddev, noise_level, rgen);
return v3_new;
}
/**
* Loads initial conditions or fail with a non-null return value.
*
* Notes:
* 1. Replaces all previous data.
* 2. Any unkown catalyst type numbers (>=4) are ignored.
*
* @param[in] cond_file The file describing the inital conditions
* @param[in] u,v1,v2,v3 Concentration matrices
* @param[in] nrows,ncols Size of matrices
* @return 0 = success, 1 = failure to open file
*/
int load_initial_conditions(char* cond_file, double** u, double** v1, double** v2, double** v3, int nrows, int ncols,
bool initial_randomization, float cell_cap_1D, float noise_stddev, float noise_level, gsl_rng* rgen) {
#pragma omp parallel for collapse(2) schedule(static)
for (int i=0; i<nrows; ++i)
for (int j=0; j<ncols; ++j) {
u[i][j] = 1.0;
v1[i][j] = 0.0;
v2[i][j] = 0.0;
v3[i][j] = 0.0;
}
FILE *conds = fopen(cond_file, "r");
if (!conds)
return 1;
char c;
char buff[256];
int read;
double conc; // concentration
int cid; // catalyst id
int xlo, ylo, xhi, yhi;
double** species;
while (!feof(conds)) {
// set defaults to account for malformed inputs
species = NULL;
cid = 1;
conc = 0.0;
read = 0;
c = fgetc(conds);
switch(c) {
// catalyst
case 'C':
if (!fscanf(conds, "%d", &cid))
fprintf(stderr, "load_initial_conditions(): No catalyst type found. Defaulting to type %d\n", cid);
switch(cid) {
case 1: species = v1; break;
case 2: species = v2; break;
case 3: species = v3; break;
default: perror("load_initial_conditions(): Unknown chemical species found! Ignoring.\n"); break;
}
break;
// fuel
case 'F':
species = u;
break;
// comment line
case '#':
char* foo = fgets(buff, 256, conds); // stops at 256 chars or newline
if (foo[0] == '#') // getting the compiler to shut up
break;
break;
}
// read coordinates and concentration values
if (species) { // allow for ignoring unkown species
read += fscanf(conds, "%lf", &conc);
read += fscanf(conds, "%d %d", &xlo, &ylo);
read += fscanf(conds, "%d %d", &xhi, &yhi);
if (read < 5)
perror("load_initial_conditions(): Not all values correctly read. Used default concentration.\n");
// silently limit out of bounds coordinates to system size
if (xhi >= nrows) xhi = nrows-1;
if (yhi >= ncols) yhi = ncols-1;
// assign area with chemical species + noise
for (int i=xlo; i<=xhi; ++i)
for (int j=ylo; j<=yhi; ++j) {
species[i][j] = conc;
if (initial_randomization)
species[i][j] += gauss_noise(1, cell_cap_1D, noise_stddev, noise_level, rgen);
if (species[i][j] < 0.0)
species[i][j] = 0.0;
if (species[i][j] > 1.0)
species[i][j] = 1.0;
}
}
}
return 0;
}
Fonc_Num fonc_noise(INT sz,int aK,bool unif)
{
if (unif)
return unif_noise(sz,aK);
return gauss_noise(sz,aK);
}
