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rkmethods.c
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rkmethods.c
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#include "rkmethods.h"
extern VEC* dump;
//Builds a dense output RK method of order 4 at each step (order 3 for dense output)
RKMethod* TheRKDense4_3()
{
RKMethod* method = (RKMethod*) malloc(sizeof(RKMethod));
method->s = 4;
method->unique_c = 4;
method->exp_imp = 0;
method->A = m_get(method->s,method->s);
method->b = v_get(method->s);
method->b_theta = v_get(method->s);
method->b_theta_deriv = NULL;
method->c = v_get(method->s);
method->dense_b = &TheRKDense4_3_b;
method->dense_bderiv = NULL;
method->e = v_get(method->s);
method->d = v_get(method->s);
method->e_order = 4;
method->e_order_ratio = 4.0/2.0;
//method->e_order_ratio = 1.0/2.0;
method->d_order = 3;
method->d_order_ratio = 3.0/2.0;
//method->d_order_ratio = 1.0/2.0;
// method->d_max_error = 1.0/3.0;
method->localorder = 4;
//Build the parameters for the method
method->A->me[1][0] = .5;
method->A->me[2][1] = .5;
method->A->me[3][2] = 1;
method->b->ve[0] = 1.0/6.0;
method->b->ve[1] = 2.0/6.0;
method->b->ve[2] = 2.0/6.0;
method->b->ve[3] = 1.0/6.0;
method->dense_b(1.0,method->b_theta);
method->c->ve[0] = 0;
method->c->ve[1] = .5;
method->c->ve[2] = .5;
method->c->ve[3] = 1;
method->e->ve[0] = 2.0/3.0;
method->e->ve[1] = 0.0;
method->e->ve[2] = -4.0/3.0;
method->e->ve[3] = 2.0/3.0;
method->d->ve[0] = 2.0/9.0;
method->d->ve[1] = 0.0;
method->d->ve[2] = -4.0/9.0;
method->d->ve[3] = 2.0/9.0;
method->w = NULL;
return method;
}
//The b(theta) coefficients for TheRKDense4_3()
void TheRKDense4_3_b(double theta,VEC* b)
{
b->ve[0] = theta - 3.0/2.0*theta*theta + 2.0/3.0*theta*theta*theta;
b->ve[1] = theta*theta - 2.0/3.0*theta*theta*theta;
b->ve[2] = b->ve[1];
b->ve[3] = -1.0/2.0*theta*theta + 2.0/3.0*theta*theta*theta;
}
//Builds a dense output version of Dormand-Prince 5(4) with dense order 4
RKMethod* DOPRI5_dense()
{
RKMethod* method = (RKMethod*) malloc(sizeof(RKMethod));
method->s = 7;
method->unique_c = 6;
method->exp_imp = 0;
method->A = m_get(method->s,method->s);
method->b = v_get(method->s);
method->b_theta = v_get(method->s);
method->b_theta_deriv = v_get(method->s);
method->c = v_get(method->s);
method->dense_b = &DOPRI5_b;
method->dense_bderiv = &DOPRI5_bderiv;
method->e = v_get(method->s);
method->d = v_get(method->s);
method->e_order = 5;
//method->e_order = 6;
method->e_order_ratio = 6.0/5.0;
//method->e_order_ratio = 1.0/5.0;
method->d_order = 4;
//method->d_order = 5;
method->d_order_ratio = 5.0/4.0;
//method->d_order_ratio = 1.0/4.0;
// method->d_max_error = .6510416666666667;
method->localorder = 5;
//Build the parameters for the method
method->A->me[1][0] = 1.0/5.0;
method->A->me[2][0] = 3.0/40.0;
method->A->me[2][1] = 9.0/40.0;
method->A->me[3][0] = 44.0/45.0;
method->A->me[3][1] = -56.0/15.0;
method->A->me[3][2] = 32.0/9.0;
method->A->me[4][0] = 19372.0/6561.0;
method->A->me[4][1] = -25360.0/2187.0;
method->A->me[4][2] = 64448.0/6561.0;
method->A->me[4][3] = -212.0/729.0;
method->A->me[5][0] = 9017.0/3168.0;
method->A->me[5][1] = -355.0/33.0;
method->A->me[5][2] = 46732.0/5247.0;
method->A->me[5][3] = 49.0/176.0;
method->A->me[5][4] = -5103.0/18656.0;
method->A->me[6][0] = 35.0/384.0;
method->A->me[6][1] = 0.0;
method->A->me[6][2] = 500.0/1113.0;
method->A->me[6][3] = 125.0/192.0;
method->A->me[6][4] = -2187.0/6784.0;
method->A->me[6][5] = 11.0/84.0;
method->dense_b(1.0,method->b);
method->dense_b(1.0,method->b_theta);
method->dense_bderiv(1.0,method->b_theta_deriv);
method->c->ve[0] = 0.0;
method->c->ve[1] = .2;
method->c->ve[2] = .3;
method->c->ve[3] = .8;
method->c->ve[4] = 8.0/9.0;
method->c->ve[5] = 1.0;
method->c->ve[6] = 1.0;
method->e->ve[0] = 71.0/57600.0;
method->e->ve[1] = 0.0;
method->e->ve[2] = -71.0/16695.0;
method->e->ve[3] = 71.0/1920.0;
method->e->ve[4] = -17253.0/339200.0;
method->e->ve[5] = 22.0/525.0;
method->e->ve[6] = -1.0/40.0;
method->d->ve[0] = .610351562499951;
method->d->ve[1] = 0.0;
method->d->ve[2] = -2.105795148247852;
method->d->ve[3] = 18.310546874999346;
method->d->ve[4] = -25.185639003536881;
method->d->ve[5] = 20.749496981890658;
method->d->ve[6] = -12.378961267605213;
method->w = lagrange_weights(method->unique_c,method->c);
return method;
}
//The b(theta) coefficients for DOPRI5_dense()
void DOPRI5_b(double theta,VEC* b)
{
/*
double theta_sq = sq(theta);
double ntheta2m3 = 3.0 - 2.0*theta;
double thetam1_sq = sq(theta-1.0);
b->ve[0] = theta_sq*( ntheta2m3*(35.0/384.0) - thetam1_sq*(5.0/11282082432.0)*(2558722523.0-31403016.0*theta) ) + theta*thetam1_sq;
b->ve[1] = 0.0;
b->ve[2] = theta_sq*( ntheta2m3*(500.0/1113.0) + thetam1_sq*(100.0/32700410799.0)*(882725551.0-15701508.0*theta) );
b->ve[3] = theta_sq*( ntheta2m3*(125.0/192.0) - thetam1_sq*(25.0/1880347072.0)*(443332067.0-31403016.0*theta) );
b->ve[4] = theta_sq*( ntheta2m3*(-2187.0/6784.0) + thetam1_sq*(32805.0/199316789632.0)*(23143187.0-3489224.0*theta) );
b->ve[5] = theta_sq*( ntheta2m3*(11.0/84.0) - thetam1_sq*(55.0/822651844.0)*(29972135.0-7076736.0*theta) );
b->ve[6] = theta_sq*( (theta-1.0) + thetam1_sq*(10.0/29380423.0)*(7414447.0-829305.0*theta) );
*/
b->ve[0] = sq(theta)*( (3.0-2.0*theta)*(35.0/384.0) - sq(theta-1.0)*(5.0/11282082432.0)*(2558722523.0-31403016.0*theta) ) + theta*sq(theta-1.0);
b->ve[1] = 0.0;
b->ve[2] = sq(theta)*( (3.0-2.0*theta)*(500.0/1113.0) + sq(theta-1.0)*(100.0/32700410799.0)*(882725551.0-15701508.0*theta) );
b->ve[3] = sq(theta)*( (3.0-2.0*theta)*(125.0/192.0) - sq(theta-1.0)*(25.0/1880347072.0)*(443332067.0-31403016.0*theta) );
b->ve[4] = sq(theta)*( (3.0-2.0*theta)*(-2187.0/6784.0) + sq(theta-1.0)*(32805.0/199316789632.0)*(23143187.0-3489224.0*theta) );
b->ve[5] = sq(theta)*( (3.0-2.0*theta)*(11.0/84.0) - sq(theta-1.0)*(55.0/822651844.0)*(29972135.0-7076736.0*theta) );
b->ve[6] = sq(theta)*( (theta-1.0) + sq(theta-1.0)*(10.0/29380423.0)*(7414447.0-829305.0*theta) );
/*
b->ve[0] = sq(theta)*(3.0-2.0*theta)*35.0/384.0 + theta*sq(theta-1.0) - sq(theta)*sq(theta-1.0)*5.0*(2558722523.0-31403016.0*theta)/11282082432.0;
b->ve[1] = 0.0;
b->ve[2] = sq(theta)*(3.0-2.0*theta)*500.0/1113.0 + sq(theta)*sq(theta-1.0)*100.0*(882725551.0-15701508.0*theta)/32700410799.0;
b->ve[3] = sq(theta)*(3.0-2.0*theta)*125.0/192.0 - sq(theta)*sq(theta-1.0)*25.0*(443332067.0-31403016.0*theta)/1880347072.0;
b->ve[4] = sq(theta)*(3.0-2.0*theta)*-2187.0/6784.0 + sq(theta)*sq(theta-1.0)*32805.0*(23143187.0-3489224.0*theta)/199316789632.0;
b->ve[5] = sq(theta)*(3.0-2.0*theta)*11.0/84.0 - sq(theta)*sq(theta-1.0)*55.0*(29972135.0-7076736.0*theta)/822651844.0;
b->ve[6] = sq(theta)*(theta-1.0) + sq(theta)*sq(theta-1.0)*10.0*(7414447.0-829305.0*theta)/29380423.0;
*/
}
//The b'(theta) coefficients for DOPRI5_dense()
void DOPRI5_bderiv(double theta,VEC* b)
{
const double prod1 = 6.0*theta*(1.0-theta);
const double prod2 = 2.0*theta*(theta-1.0)*(2.0*theta-1.0);
const double prod3 = sq(theta)*sq(theta-1.0);
b->ve[0] = prod1*(35.0/384.0) + (theta-1.0)*(3.0*theta-1.0) - 2.0*theta*(theta-1.0)*(2.0*theta-1.0)*(5.0/11282082432.0)*(2558722523.0-31403016.0*theta) + prod3*(157015080.0/11282082432.0);
b->ve[1] = 0.0;
b->ve[2] = prod1*(500.0/1113.0) + prod2*(100.0/32700410799.0)*(882725551.0-15701508.0*theta) - prod3*(1570150800.0/32700410799.0);
b->ve[3] = prod1*(125.0/192.0) - prod2*(25.0/1880347072.0)*(443332067.0-31403016.0*theta) + prod3*(785075400.0/1880347072.0);
b->ve[4] = prod1*(-2187.0/6784.0) + prod2*(32805.0/199316789632.0)*(23143187.0-3489224.0*theta) - prod3*(1144640195640.0/199316789632.0);
b->ve[5] = prod1*(11.0/84.0) - prod2*(55.0/822651844.0)*(29972135.0-7076736.0*theta) + prod3*(389220480.0/822651844.0);
b->ve[6] = theta*(3.0*theta-2.0) + prod2*(10.0/29380423.0)*(7414447.0-829305.0*theta) - prod3*(8293050.0/29380423.0);
}
//Builds a dense output RK method of order 3 at each step (order 2 for dense output)
RKMethod* RKDense3_2()
{
RKMethod* method = (RKMethod*) malloc(sizeof(RKMethod));
method->s = 3;
method->unique_c = 3;
method->exp_imp = 0;
method->A = m_get(method->s,method->s);
method->b = v_get(method->s);
method->b_theta = v_get(method->s);
method->b_theta_deriv = v_get(method->s);
method->c = v_get(method->s);
method->dense_b = &RKDense3_2_b;
method->dense_bderiv = &RKDense3_2_bderiv;
method->e = v_get(method->s);
method->d = v_get(method->s);
method->e_order = 3;
method->e_order_ratio = 3.0/2.0;
//method->e_order_ratio = 1.0/2.0;
method->d_order = 2;
method->d_order_ratio = 2.0/2.0;
//method->d_order_ratio = 1.0/2.0;
// method->d_max_error = 2.0/3.0;
method->localorder = 3;
//Build the coefficients for the method
method->A->me[1][0] = .5;
method->A->me[2][0] = -1;
method->A->me[2][1] = 2;
method->dense_b(1.0,method->b);
method->dense_b(1.0,method->b_theta);
method->c->ve[0] = 0.0;
method->c->ve[1] = .5;
method->c->ve[2] = 1.0;
method->e->ve[0] = 2.0/3.0;
method->e->ve[1] = -4.0/3.0;
method->e->ve[2] = 2.0/3.0;
method->d->ve[0] = 1.0/3.0;
method->d->ve[1] = -2.0/3.0;
method->d->ve[2] = 1.0/3.0;
method->w = NULL;
return method;
}
//The b(theta) coefficients for RKDense3_2()
void RKDense3_2_b(double theta,VEC* b)
{
b->ve[0] = theta*(1+theta*(-3.0/2.0+2.0/3.0*theta));
b->ve[1] = 2*theta*theta*(1-2.0/3.0*theta);
b->ve[2] = theta*theta*(2.0/3.0*theta-.5);
}
//The b'(theta) coefficients for RKDense3_2()
void RKDense3_2_bderiv(double theta,VEC* b)
{
b->ve[0] = 1.0 - 3.0*theta + 2.0*theta*theta;
b->ve[1] = 4.0*theta - 4.0*theta*theta;
b->ve[2] = 2.0*theta*theta - theta;
}
//Builds a dense output version of the 3 stage RadauIIA method with dense output
RKMethod* RadauIIA3_dense()
{
RKMethod* method = (RKMethod*) malloc(sizeof(RKMethod));
method->s = 3;
method->unique_c = 3;
method->exp_imp = 1;
method->A = m_get(method->s,method->s);
method->b = v_get(method->s);
method->b_theta = v_get(method->s);
method->b_theta_deriv = NULL;
method->dense_bderiv = NULL;
method->c = v_get(method->s);
method->dense_b = &RadauIIA3_b;
method->e = v_get(method->s + 1);
method->d = v_get(method->s + 1);
method->e_order = 4;
method->e_order_ratio = 4.0/3.0;
method->d_order = 3;
method->d_order_ratio = 3.0/2.0;
method->localorder = 5;
//Build the parameters for the method
method->A->me[0][0] = 0.1968154772236604;
method->A->me[0][1] = -0.06553542585019839;
method->A->me[0][2] = 0.02377097434822015;
method->A->me[1][0] = 0.3944243147390873;
method->A->me[1][1] = 0.2920734116652285;
method->A->me[1][2] = -0.04154875212599793;
method->A->me[2][0] = 0.3764030627004673;
method->A->me[2][1] = 0.5124858261884216;
method->A->me[2][2] = 0.1111111111111111;
method->dense_b(1.0,method->b);
method->dense_b(1.0,method->b_theta);
method->c->ve[0] = 0.1550510257216822;
method->c->ve[1] = 0.6449489742783178;
method->c->ve[2] = 1.0;
method->e->ve[0] = -2.762305454748599;
method->e->ve[1] = 0.379935598252729;
method->e->ve[2] = -0.091629609865226;
method->e->ve[3] = 0.2748888295956774;
/*
//Two trees 0
method->d->ve[0] = 0.8097732865210982;
method->d->ve[1] = -2.701318593546288;
method->d->ve[2] = 1.616656477429513;
method->d->ve[3] = 0.2748888295956774;
*/
//Three trees 0 (Original)
method->d->ve[0] = -0.428298294115368;
method->d->ve[1] = 0.245039074384917;
method->d->ve[2] = -0.091629609865226;
method->d->ve[3] = 0.2748888295956774;
/*
//No d_0, two tree 0
method->d->ve[0] = 1.238071580636466;
method->d->ve[1] = -2.946357667931205;
method->d->ve[2] = 1.708286087294739;
*/
method->w = lagrange_weights(method->s,method->c);
return method;
}
//The b(theta) coefficients for RadauIIA2_dense()
void RadauIIA3_b(double theta,VEC* b)
{
double t2 = theta * theta;
double t3 = t2 * theta;
b->ve[0] = 1.558078204724922 * theta - 1.986947221348443 * t2 + 0.805272079323988 * t3;
b->ve[1] = -0.891411538058256 * theta + 3.320280554681776 * t2 - 1.916383190435099 * t3;
b->ve[2] = 0.3333333333333333 * theta - 1.333333333333333 * t2 + 1.111111111111111 * t3;
}
double InitialStepSize(double t,Link* link_i,UnivVars* GlobalVars,TempStorage* workspace)
{
unsigned int start = link_i->diff_start;
VEC* y0 = link_i->list->tail->y_approx;
double t_0 = link_i->list->tail->t;
VEC*** temp_parent_approx = workspace->temp_parent_approx;
VEC* fy0 = workspace->temp;
VEC* fy1 = workspace->sum;
VEC* y1 = workspace->temp2;
VEC* SC = workspace->temp3;
unsigned int p = link_i->method->localorder;
Link* currentp;
RKSolutionNode* curr_node;
double d0,d1,d2,h0,h1,largest,timediff,current_theta;
unsigned int i,l,m,idx;
unsigned int dim = link_i->dim;
unsigned int num_dense = link_i->num_dense;
unsigned int* dense_indices = link_i->dense_indices;
ErrorData* error = link_i->errorinfo;
//Build SC for this link
for(i=0;i<dim;i++) SC->ve[i] = max(fabs(y0->ve[i]),fabs(y0->ve[i])) * error->reltol->ve[i] + error->abstol->ve[i];
//Grab parents data
for(i=0;i<link_i->numparents;i++)
{
currentp = link_i->parents[i];
curr_node = currentp->list->head;
if( fabs(currentp->list->tail->t - t) < 1e-10 ) //!!!! Ugh... !!!!
v_copy_u(currentp->list->tail->y_approx,temp_parent_approx[0][i],currentp->dim);
else
{
//Find the corresponding theta value and approximate solution
while(t > curr_node->t)
curr_node = curr_node->next;
if(curr_node != currentp->list->head) curr_node = curr_node->prev;
timediff = curr_node->next->t - curr_node->t;
current_theta = (t - curr_node->t)/timediff;
currentp->method->dense_b(current_theta,currentp->method->b_theta);
// !!!! Note: this varies with num_print. Consider doing a linear interpolation. !!!!
for(m=0;m<currentp->num_dense;m++)
{
idx = currentp->dense_indices[m];
temp_parent_approx[0][i]->ve[idx] = curr_node->y_approx->ve[idx];
for(l=0;l<currentp->method->s;l++)
temp_parent_approx[0][i]->ve[idx] += timediff*currentp->method->b_theta->ve[l] * curr_node->next->k[l]->ve[m];
}
link_i->CheckConsistency(temp_parent_approx[0][i],currentp->params,GlobalVars->global_params);
//if(link_i->alg != NULL) link_i->alg(temp_parent_approx[0][i],GlobalVars->global_params,currentp->params,currentp->qvs,curr_node->next->state,temp_parent_approx[0][i]);
if(currentp->alg) currentp->alg(temp_parent_approx[0][i],GlobalVars->global_params,currentp->params,currentp->qvs,curr_node->state,currentp->user,temp_parent_approx[0][i]);
}
}
//Step a
//d0 = vector_norminf(y0,start);
d0 = norm_inf_u(y0,SC,start,link_i->dim);
link_i->f(t_0,y0,temp_parent_approx[0],link_i->numparents,GlobalVars->global_params,link_i->forcing_values,link_i->qvs,link_i->params,link_i->state,link_i->user,fy0);
d1 = norm_inf_u(fy0,SC,start,link_i->dim);
//Step b
if(d0 < 1e-5 || d1 < 1e-5) h0 = 1e-6;
else h0 = 0.01*(d0/d1);
//Step c
//Note: This assumes the parents discharge is the same. It also assume no change in rain or state
v_copy_u(y0,y1,link_i->dim);
daxpy_u(h0,fy0,y1,start,link_i->dim);
link_i->CheckConsistency(y1,link_i->params,GlobalVars->global_params);
link_i->f(t_0 + h0,y1,temp_parent_approx[0],link_i->numparents,GlobalVars->global_params,link_i->forcing_values,link_i->qvs,link_i->params,link_i->state,link_i->user,fy1);
//Step d
v_sub(fy1,fy0,fy1,start);
d2 = norm_inf_u(fy1,SC,start,link_i->dim);
//Step e
largest = max(d1,d2);
h1 = (largest < 1e-1) ? max(1e-6,h0*1e-3) : pow(1e-2/largest,1.0/(p+1.0));
//Step f
h1 = min(100.0*h0,h1);
//Make sure returned value is not too small. This can create roundoff problems when time gets larger
//return h1;
//frexp(h1,&exponent);
//if(exponent < -29) return 1e-10;
if(y0->ve[0] < 1e-6) return 1e-2;
else return h1;
}
//Computes one step of a method to solve the ODE at a link. Assumes parents have enough computed solutions.
//Link* link_i: the link to apply a numerical method to.
//Returns 1 if the step was successfully taken, 0 if the step was rejected.
int ExplicitRKSolver(Link* link_i,UnivVars* GlobalVars,int* assignments,short int print_flag,FILE* outputfile,ConnData* conninfo,Forcing** forcings,TempStorage* workspace)
{
unsigned int i,j,l,m,idx;
//VEC** k;
VEC* new_y;
RKSolutionNode *curr_node[link_i->numparents],*node,*new_node;
Link* currentp;
double t_needed,timediff,current_theta;
//Some variables to make things easier to read
VEC* y_0 = link_i->list->tail->y_approx;
double h = link_i->h;
double t = link_i->list->tail->t;
MAT* A = link_i->method->A;
VEC* b = link_i->method->b;
VEC* c = link_i->method->c;
unsigned int s = link_i->method->s;
VEC* params = link_i->params;
VEC* e = link_i->method->e;
VEC* d = link_i->method->d;
RKMethod* meth = link_i->method;
ErrorData* error = link_i->errorinfo;
unsigned int dim = link_i->dim;
unsigned int num_dense = link_i->num_dense;
unsigned int* dense_indices = link_i->dense_indices;
unsigned int num_print = GlobalVars->num_print;
VEC* temp = workspace->temp;
VEC* sum = workspace->sum;
VEC*** temp_parent_approx = workspace->temp_parent_approx;
VEC** temp_k = workspace->temp_k;
//Get the approximate solutions from each parent
for(i=0;i<link_i->numparents;i++)
{
currentp = link_i->parents[i];
curr_node[i] = currentp->list->head;
for(j=0;j<s;j++)
{
//Find the needed value of t and corresponding node for y_p
//Assuming everything needed is already calculated
//This assumes c_s is the biggest. If not, one extra step may not get freed.
t_needed = min(t + c->ve[j]*h,currentp->last_t);
//t_needed = t + c->ve[j]*h;
//Find the corresponding theta value and approximate solution
//while(t_needed > curr_node[i]->t && ( fabs(curr_node[i]->t) < 1e-12 || fabs(t_needed - curr_node[i]->t)/curr_node[i]->t > 1e-12) )
while(t_needed > curr_node[i]->t)
curr_node[i] = curr_node[i]->next;
if(curr_node[i] != currentp->list->head) curr_node[i] = curr_node[i]->prev;
timediff = curr_node[i]->next->t - curr_node[i]->t;
current_theta = (t_needed-curr_node[i]->t)/timediff;
currentp->method->dense_b(current_theta,currentp->method->b_theta);
for(m=0;m<currentp->num_dense;m++)
{
idx = currentp->dense_indices[m];
temp_parent_approx[j][i]->ve[idx] = curr_node[i]->y_approx->ve[idx];
for(l=0;l<currentp->method->s;l++)
temp_parent_approx[j][i]->ve[idx] += timediff*currentp->method->b_theta->ve[l] * curr_node[i]->next->k[l]->ve[m];
}
link_i->CheckConsistency(temp_parent_approx[j][i],params,GlobalVars->global_params);
}
}
//Do the RK method to get the next approximation
//Setup variables for the new data
new_node = New_Step(link_i->list);
new_node->t = t + h;
//k = new_node->k;
new_y = new_node->y_approx;
/*
int stopper = 0;
if(link_i->ID == 0 && link_i->dim > 7)
{
printf("************\n");
printf("t = %e\n",t);
Print_Vector(y_0);
stopper = 1;
//Print_Vector(new_y);
printf("************\n");
}
*/
//Compute the k's
for(i=0;i<s;i++)
{
v_copy_u(y_0,sum,link_i->dim);
for(j=0;j<i;j++)
daxpy_u(h*A->me[i][j],temp_k[j],sum,0,link_i->dim);
link_i->CheckConsistency(sum,params,GlobalVars->global_params);
link_i->f(t + c->ve[i] * h,sum,temp_parent_approx[i],link_i->numparents,GlobalVars->global_params,link_i->forcing_values,link_i->qvs,params,link_i->state,link_i->user,temp_k[i]);
/*
if(stopper)
{
Print_Vector(sum);
Print_Vector(temp_k[i]);
printf("+++++\n");
getchar();
}
*/
}
//Build the solution
v_copy_u(y_0,new_y,link_i->dim);
for(i=0;i<s;i++) daxpy_u(h*b->ve[i],temp_k[i],new_y,0,link_i->dim);
link_i->CheckConsistency(new_y,params,GlobalVars->global_params);
new_node->state = link_i->state;
/*
if(stopper)
{
printf("************\n");
printf("t = %e\n",t);
//Print_Vector(y_0);
Print_Vector(new_y);
printf("************\n");
getchar();
}
*/
//Error estimation and step size selection
//Check the error of y_1 (in inf norm) to determine if the step can be accepted
double err_1;
v_copy_u(temp_k[0],sum,link_i->dim);
sv_mlt_u(h * e->ve[0],sum,0,link_i->dim);
for(i=1;i<s;i++) daxpy_u(h*e->ve[i],temp_k[i],sum,0,link_i->dim);
//Build SC_i
for(i=0;i<dim;i++)
temp->ve[i] = max(fabs(new_y->ve[i]),fabs(y_0->ve[i])) * error->reltol->ve[i] + error->abstol->ve[i];
//err_1 = norm_inf(sum,temp,meth->e_order_ratio,0);
err_1 = norm_inf_u(sum,temp,0,link_i->dim);
double value_1 = pow(1.0/err_1,1.0/meth->e_order);
//Check the dense error (in inf norm) to determine if the step can be accepted
double err_d;
v_copy_u(temp_k[0],sum,link_i->dim);
sv_mlt_u(h * d->ve[0],sum,0,link_i->dim);
for(i=1;i<s;i++) daxpy_u(h*d->ve[i],temp_k[i],sum,0,link_i->dim);
for(i=0;i<dim;i++)
temp->ve[i] = max(fabs(new_y->ve[i]),fabs(y_0->ve[i])) * error->reltol_dense->ve[i] + error->abstol_dense->ve[i];
//err_d = norm_inf(sum,temp,meth->d_order_ratio,0);
err_d = norm_inf_u(sum,temp,0,link_i->dim);
double value_d = pow(1.0/err_d,1.0/meth->d_order);
//Determine a new step size for the next step
double step_1 = h*min(error->facmax,max(error->facmin,error->fac * value_1));
double step_d = h*min(error->facmax,max(error->facmin,error->fac * value_d));
link_i->h = min(step_1,step_d);
/*
if(err_1 < 1.0 && err_d < 1.0)
{
printf("Accepted time = %e new h = %e %e %e\n",t+h,link_i->h,err_1,err_d);
Print_Vector(new_y);
}
else
{
printf("Rejected time = %e new h = %e %e %e\n",t+h,link_i->h,err_1,err_d);
Print_Vector(new_y);
}
*/
/*
//Try new error control
//This uses new idea to modify step size of the parents, not link_i
Link* child = link_i->c;
//Link* p;
double err_new = 0.0;
double step_new = step_1;
double sum_of_errors;
if(child != NULL)
{
//Works ok
//!!!! Assumes 1d problem !!!!
//for(i=0;i<dim;i++) temp2->ve[i] = 0.0;
sum_of_errors = 0.0;
for(i=0;i<child->numparents;i++) //Assumes one state is passed link to link
sum_of_errors += child->parents[i]->errorinfo->abstol_dense->ve[0];
Jx_simple_river(child->list->tail->y_approx,GlobalVars->global_params,child->params,temp);
sv_mlt((t+h - child->last_t)*sum_of_errors,temp,GlobalVars->diff_start);
//temp2->ve[0] *= (t+h - child->last_t) * Jx;
err_new = norm_inf(temp,error->abstol_dense,1.0,0);
double value_new = pow(1.0/(link_i->h * err_new),1.0/4.0); //!!!! For Dormand & Prince !!!!
unsigned int maxorder = 4; // !!!! Need loop !!!!
double largest = child->parents[0]->h;
for(i=1;i<child->numparents;i++)
largest = max(largest,child->parents[i]->h);
step_new = largest * value_new;
//for(i=0;i<child->numparents;i++)
// child->parents[i]->h = min(child->parents[i]->h,step_new);
link_i->h = min(link_i->h,step_new);
}
*/
// if(err_1 < 1.0 && err_d < 1.0 && err_new < 1.0)
if(err_1 < 1.0 && err_d < 1.0)
// if(err_1 < 1.0)
{
/*
//Try new error control
//This uses new idea to modify step size of the parents, not link_i
if(link_i->numparents > 0)
{
double err_new = norm_inf(sum,error->abstol_dense,1.0,0);
double value_new = pow(1.0/(link_i->h * err_new),1.0/4.0); //!!!! For Dormand & Prince !!!!
unsigned int maxorder = 4; // !!!! Need loop !!!!
double smallest = link_i->parents[0]->h;
for(i=1;i<link_i->numparents;i++)
smallest = min(smallest,link_i->parents[i]->h);
double newh = smallest * value_new * .9;
for(i=0;i<link_i->numparents;i++)
link_i->parents[i]->h = min(link_i->parents[i]->h,newh);
}
*/
//Check if a discontinuity has been stepped on
if(link_i->discont_count > 0 && (t + h) >= link_i->discont[link_i->discont_start])
{
(link_i->discont_count)--;
link_i->discont_start = (link_i->discont_start + 1) % GlobalVars->discont_size;
link_i->h = InitialStepSize(link_i->last_t,link_i,GlobalVars,workspace);
}
//Save the new data
link_i->last_t = t + h;
link_i->current_iterations++;
store_k(temp_k,new_node->k,s,dense_indices,num_dense);
//Check if new data should be written to disk
if(print_flag)
{
//while(t <= link_i->next_save && link_i->next_save <= link_i->last_t)
while( t <= link_i->next_save && (link_i->next_save < link_i->last_t || fabs(link_i->next_save - link_i->last_t)/link_i->next_save < 1e-12) )
{
/*
//Don't write anything if using data assimilation and at a time when data is available
if(GlobalVars->assim_flag)
{
if( fabs(GlobalVars->maxtime - link_i->next_save) < 1e-13 ) break;
//double rounded = 1e-13*rint(1e13*(GlobalVars->maxtime - link_i->next_save));
//if(rounded < 1e-13 && -rounded < 1e-13) break;
}
*/
if(link_i->disk_iterations == link_i->expected_file_vals)
{
printf("[%i]: Warning: Too many steps computed for link id %u. Expected no more than %u. No more values will be stored for this link.\n",my_rank,link_i->ID,link_i->expected_file_vals);
break;
}
(link_i->disk_iterations)++;
node = link_i->list->tail->prev;
current_theta = (link_i->next_save - t)/h;
link_i->method->dense_b(current_theta,link_i->method->b_theta);
for(m=0;m<num_dense;m++)
{
idx = dense_indices[m];
sum->ve[idx] = node->y_approx->ve[idx];
for(l=0;l<link_i->method->s;l++)
sum->ve[idx] += h*link_i->method->b_theta->ve[l] * node->next->k[l]->ve[m];
}
link_i->CheckConsistency(sum,params,GlobalVars->global_params);
//printf("writing ID = %u t = %e, q = %e s_p = %e\n",link_i->ID,link_i->next_save,sum->ve[0],sum->ve[1]);
//Write to a file
//fsetpos(outputfile,&(link_i->pos));
//WriteStep(link_i->next_save,sum,GlobalVars,params,link_i->state,outputfile,link_i->output_user,&(link_i->pos));
WriteStep(link_i->next_save,sum,GlobalVars,params,link_i->state,outputfile,link_i->output_user,&(link_i->pos_offset));
//fgetpos(outputfile,&(link_i->pos));
/*
fsetpos(outputfile,&(link_i->pos));
fwrite(&(link_i->next_save),sizeof(double),1,outputfile);
for(j=0;j<num_print;j++)
fwrite(&(sum->ve[print_indices[j]]),sizeof(double),1,outputfile);
fgetpos(outputfile,&(link_i->pos));
*/
/*
#ifdef PRINT2DATABASE
sprintf(conninfo->query,"%i,%u,%.12e,%.12e\n",link_i->ID,(unsigned int)(link_i->next_save * 60.0) + conninfo->time_offset,sum->ve[0]/link_i->Q_TM,sum->ve[0]);
unsigned int length = strlen(conninfo->query);
(conninfo->submission_content) += length;
while(conninfo->submission_content > conninfo->submission_size)
{
//Allocate more space
(conninfo->submission_size) *= 2;
conninfo->submission = realloc(conninfo->submission,conninfo->submission_size);
}
strcat(conninfo->submission,conninfo->query);
#else //Write to a file
fsetpos(outputfile,&(link_i->pos));
fwrite(&(link_i->next_save),sizeof(double),1,outputfile);
for(j=0;j<num_print;j++)
fwrite(&(sum->ve[print_indices[j]]),sizeof(double),1,outputfile);
fgetpos(outputfile,&(link_i->pos));
#endif
*/
link_i->next_save += link_i->print_time;
}
}
//Check if this is a max discharge
if( link_i->peak_flag && (new_y->ve[0] > link_i->peak_value->ve[0]) )
{
v_copy_u(new_y,link_i->peak_value,link_i->dim);
link_i->peak_time = link_i->last_t;
}
//Check if the newest step is on a change in rainfall
short int propagated = 0; //Set to 1 when last_t has been propagated
for(j=0;j<GlobalVars->num_forcings;j++)
{
if( forcings[j]->active && link_i->forcing_buff[j] && (fabs(link_i->last_t - link_i->forcing_change_times[j]) < 1e-8) )
{
//Propagate the discontinuity to downstream links
if(!propagated)
{
propagated = 1;
Link* next = link_i->c;
Link* prev = link_i;
for(i=0;i<GlobalVars->max_localorder && next != NULL;i++)
{
if(assignments[next->location] == my_rank && i < next->method->localorder)
{
//Insert the time into the discontinuity list
next->discont_end = Insert_Discontinuity(link_i->forcing_change_times[j],next->discont_start,next->discont_end,&(next->discont_count),GlobalVars->discont_size,next->discont,next->ID);
}
else if(next != NULL && assignments[next->location] != my_rank)
{
//Store the time to send to another process
Insert_SendDiscontinuity(link_i->forcing_change_times[j],i,&(prev->discont_send_count),GlobalVars->discont_size,prev->discont_send,prev->discont_order_send,prev->ID);
break;
}
prev = next;
next = next->c;
}
}
//Find the right index in rainfall
//for(l=1;l<link_i->forcing_buff[j]->n_times;l++)
for(l=link_i->forcing_indices[j]+1;l<link_i->forcing_buff[j]->n_times;l++)
if( fabs(link_i->forcing_change_times[j] - link_i->forcing_buff[j]->rainfall[l][0]) < 1e-8 ) break;
link_i->forcing_indices[j] = l;
double forcing_buffer = link_i->forcing_buff[j]->rainfall[l][1];
link_i->forcing_values[j] = forcing_buffer;
//Find and set the new change in rainfall
for(i=l+1;i<link_i->forcing_buff[j]->n_times;i++)
{
//if(link_i->forcing_buff[j]->rainfall[i][1] != forcing_buffer)
if( fabs(link_i->forcing_buff[j]->rainfall[i][1] - forcing_buffer) > 1e-8 )
{
link_i->forcing_change_times[j] = link_i->forcing_buff[j]->rainfall[i][0];
break;
}
}
if(i == link_i->forcing_buff[j]->n_times)
link_i->forcing_change_times[j] = link_i->forcing_buff[j]->rainfall[i-1][0];
}
}
//Select new step size, if forcings changed
if(propagated) link_i->h = InitialStepSize(link_i->last_t,link_i,GlobalVars,workspace);
//Free up parents' old data
for(i=0;i<link_i->numparents;i++)
{
currentp = link_i->parents[i];
while(currentp->list->head != curr_node[i])
{
Remove_Head_Node(currentp->list);
currentp->current_iterations--;
currentp->iters_removed++;
}
}
return 1;
}
else
{
//Trash the data from the failed step
Undo_Step(link_i->list);
return 0;
}
}
//Computes one step of a method to solve the ODE at a link. Assumes parents have enough computed solutions.
//Link* link_i: the link to apply a numerical method to.
//VEC* sum: some space for temporary calculations. Should have same dimension as number of equations.
//VEC* temp: same as sum.
//Returns 1 if the step was successfully taken, 0 if the step was rejected.
int ExplicitRKIndex1Solver(Link* link_i,UnivVars* GlobalVars,int* assignments,short int print_flag,FILE* outputfile,ConnData* conninfo,Forcing** forcings,TempStorage* workspace)
{
unsigned int i,j,l,m,idx;
//VEC** k;
VEC* new_y;
RKSolutionNode *curr_node[link_i->numparents],*node,*new_node;
Link* currentp;
double t_needed,timediff,theta;
//Some variables to make things easier to read
VEC* y_0 = link_i->list->tail->y_approx;
double h = link_i->h;
double t = link_i->list->tail->t;
MAT* A = link_i->method->A;
VEC* b = link_i->method->b;
VEC* c = link_i->method->c;
unsigned int s = link_i->method->s;
VEC* params = link_i->params;
VEC* e = link_i->method->e;
VEC* d = link_i->method->d;
RKMethod* meth = link_i->method;
ErrorData* error = link_i->errorinfo;
const unsigned int dim = link_i->dim;
unsigned int num_dense = link_i->num_dense;
unsigned int* dense_indices = link_i->dense_indices;
unsigned int num_print = GlobalVars->num_print;
unsigned int* print_indices = GlobalVars->print_indices;
VEC* temp = workspace->temp;
VEC* sum = workspace->sum;
VEC*** temp_parent_approx = workspace->temp_parent_approx;
VEC** temp_k = workspace->temp_k;
//Get the approximate solutions from each parent
for(i=0;i<link_i->numparents;i++)
{
currentp = link_i->parents[i];
curr_node[i] = currentp->list->head;
for(j=0;j<s;j++)
{
//Find the needed value of t and corresponding node for y_p
//Assuming everything needed is already calculated
//This assumes c_s is the biggest. If not, one extra step may not get freed.
t_needed = min(t + c->ve[j]*h,currentp->last_t);
//t_needed = t + c->ve[j]*h;
//Find the corresponding theta value and approximate solution
while(t_needed > curr_node[i]->t)
curr_node[i] = curr_node[i]->next;
if(curr_node[i] != currentp->list->head) curr_node[i] = curr_node[i]->prev;
timediff = curr_node[i]->next->t - curr_node[i]->t;
theta = (t_needed-curr_node[i]->t)/timediff;
currentp->method->dense_b(theta,currentp->method->b_theta);
for(m=0;m<currentp->num_dense;m++)
{
idx = currentp->dense_indices[m];
temp_parent_approx[j][i]->ve[idx] = curr_node[i]->y_approx->ve[idx];
for(l=0;l<currentp->method->s;l++)
temp_parent_approx[j][i]->ve[idx] += timediff*currentp->method->b_theta->ve[l] * curr_node[i]->next->k[l]->ve[m];
}
//Build the algebraic variable
currentp->CheckConsistency(temp_parent_approx[j][i],currentp->params,GlobalVars->global_params);
//link_i->alg(temp_parent_approx[j][i],GlobalVars->global_params,currentp->params,currentp->qvs,curr_node[i]->next->state,temp_parent_approx[j][i]);
if(currentp->alg) currentp->alg(temp_parent_approx[j][i],GlobalVars->global_params,currentp->params,currentp->qvs,curr_node[i]->state,currentp->user,temp_parent_approx[j][i]);
}
}
//Do the RK method to get the next approximation
//Setup variables for the new data
new_node = New_Step(link_i->list);
new_node->t = t + h;
//k = new_node->k;
new_y = new_node->y_approx;
//Compute the k's
for(i=0;i<s;i++)
{
v_copy_u(y_0,sum,link_i->dim);
for(j=0;j<i;j++)
daxpy_u(h*A->me[i][j],temp_k[j],sum,1,link_i->dim);
link_i->CheckConsistency(sum,params,GlobalVars->global_params);
link_i->f(t + c->ve[i] * h,sum,temp_parent_approx[i],link_i->numparents,GlobalVars->global_params,link_i->forcing_values,link_i->qvs,params,link_i->state,link_i->user,temp_k[i]);
}
//Build the solution
v_copy_u(y_0,new_y,link_i->dim);
for(i=0;i<s;i++) daxpy_u(h*b->ve[i],temp_k[i],new_y,1,link_i->dim);
//new_node->state = 0;
new_node->state = link_i->state_check(new_y,GlobalVars->global_params,params,link_i->qvs,link_i->dam);
link_i->CheckConsistency(new_y,params,GlobalVars->global_params);
link_i->alg(new_y,GlobalVars->global_params,params,link_i->qvs,new_node->state,link_i->user,new_y);
//Error estimation and step size selection
//Check the error of y_1 (in inf norm) to determine if the step can be accepted
double err_1;
v_copy_u(temp_k[0],sum,link_i->dim);
sv_mlt_u(h * e->ve[0],sum,1,link_i->dim);
for(i=1;i<s;i++) daxpy_u(h*e->ve[i],temp_k[i],sum,1,link_i->dim);
//Build SC_i
for(i=1;i<dim;i++)
temp->ve[i] = max(fabs(new_y->ve[i]),fabs(y_0->ve[i])) * error->reltol->ve[i] + error->abstol->ve[i];
//err_1 = norm_inf(sum,temp,meth->e_order_ratio,1);
err_1 = norm_inf_u(sum,temp,1,link_i->dim);
double value_1 = pow(1.0/err_1,1.0/meth->e_order);
//Check the dense error (in inf norm) to determine if the step can be accepted
double err_d;
v_copy_u(temp_k[0],sum,link_i->dim);
sv_mlt_u(h * d->ve[0],sum,1,link_i->dim);
for(i=1;i<s;i++) daxpy_u(h*d->ve[i],temp_k[i],sum,1,link_i->dim);
for(i=1;i<dim;i++)
temp->ve[i] = max(fabs(new_y->ve[i]),fabs(y_0->ve[i])) * error->reltol_dense->ve[i] + error->abstol_dense->ve[i];
err_d = norm_inf_u(sum,temp,1,link_i->dim);
double value_d = pow(1.0/err_d,1.0/meth->d_order);
//Determine a new step size for the next step
double step_1 = h*min(error->facmax,max(error->facmin,error->fac * value_1));
double step_d = h*min(error->facmax,max(error->facmin,error->fac * value_d));
link_i->h = min(step_1,step_d);
//link_i->h = step_1;
if(err_1 < 1.0 && err_d < 1.0)
//if(err_1 < 1.0)
{
//Check if a discontinuity has been stepped on
if(link_i->discont_count > 0 && (t + h) >= link_i->discont[link_i->discont_start])
{
(link_i->discont_count)--;
link_i->discont_start = (link_i->discont_start + 1) % GlobalVars->discont_size;
link_i->h = InitialStepSize(link_i->last_t,link_i,GlobalVars,workspace);
}
//Save the new data
link_i->last_t = t + h;
link_i->current_iterations++;
//new_node->state = 0;
store_k(temp_k,new_node->k,s,dense_indices,num_dense);
//Check if new data should be written to disk