int matinv(double **A, double **Ainv, int n)
{
register int i, j;
double *b, temp;
/* Decompose matrix into L and U triangular matrices */
if (lu_decompose(A, n) == 0)
return (0); /* Singular */
/* Invert matrix by solving n simultaneous equations n times */
b = N_NEW(n, double);
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++)
b[j] = 0.0;
b[i] = 1.0;
lu_solve(Ainv[i], b, n); /* Into a row of Ainv: fix later */
}
free(b);
/* Transpose matrix */
for (i = 0; i < n; i++) {
for (j = 0; j < i; j++) {
temp = Ainv[i][j];
Ainv[i][j] = Ainv[j][i];
Ainv[j][i] = temp;
}
}
return (1);
}
int main(int, char**)
{
typedef mtl::dense2D<double> Matrix;
typedef mtl::dense_vector<double> Vector;
Matrix A(4, 4), L(4, 4), U(4, 4), AA(4, 4);
Vector v(4);
double c=1.0;
for (unsigned i= 0; i < 4; i++)
for(unsigned j= 0; j < 4; j++) {
U[i][j]= i <= j ? c * (i+j+2) : (0);
L[i][j]= i > j ? c * (i+j+1) : (i == j ? (1) : (0));
}
std::cout << "L is:\n" << L << "U is:\n" << U;
A= L * U;
std::cout << "A is:\n" << A;
AA= adjoint(A);
for (unsigned i= 0; i < 4; i++)
v[i]= double(i);
Vector b( A*v ), b2( adjoint(A)*v );
Matrix LU(A);
lu(LU);
std::cout << "LU decomposition of A is:\n" << LU;
Matrix B( lu_f(A) );
std::cout << "LU decomposition of A (as function result) is:\n" << B;
Vector v1( lu_solve_straight(A, b) );
std::cout << "v1 is " << v1 << "\n";
Vector v2( lu_solve(A, b) );
std::cout << "v2 is " << v2 << "\n";
mtl::dense_vector<unsigned> P;
lu(A, P);
std::cout << "LU with pivoting is \n" << with_format(A, 5, 2) << "Permutation is " << P << "\n";
Vector v3( lu_apply(A, P, b) );
std::cout << "v3 is " << v3 << "\n";
Vector v4(lu_adjoint_apply(A, P, b2));
std::cout << "v4 is " << v4 << "\n";
Vector v5(lu_adjoint_solve(AA, b));
std::cout << "v5 is " << v5 << "\n";
return 0;
}
double MatrixInversion(double** a,const int n,const double diagonal_increment)
{ // return the determined of matrix 'a'
double** lu;
int i,j;
double* col;
int* ps;
if(diagonal_increment!=0) for(int i=0;i<n;i++) a[i][i] += diagonal_increment;
lu = new double*[n]; assert(lu!=NULL);
for(i=0;i<n;i++) { lu[i] = new double[n]; assert(lu[i]!=NULL); }
ps = new int[n]; assert(ps!=NULL);
double det;
if((det=lu_decompose(a,n,lu,ps))==0) std::cerr<<"Singular Matrix!"<<std::endl;
for(i=0;i<n;i++) det *= lu[i][i];
col = new double[n]; assert(col!=NULL);
for(i=0;i<n;i++)
{
for(j=0;j<n;j++) col[j]=0.0;
col[i]=1.0;
lu_solve(a[i],col,n,lu,ps);
}
for(i=0;i<n;i++)
{
for(j=0;j<n;j++)
{
double temp;
temp=a[i][j];
a[i][j]=a[j][i];
a[j][i]=temp;
}
}
for(i=0;i<n;i++) { delete[] lu[i]; lu[i]=NULL; }
delete[] lu; lu=NULL;
delete[] ps; ps=NULL;
delete[] col; col=NULL;
return det;
}
myResult* simulate_implicit(Model_t *m, myResult *result, mySpecies *sp[], myParameter *param[], myCompartment *comp[], myReaction *re[], myRule *rule[], myEvent *event[], myInitialAssignment *initAssign[], myAlgebraicEquations *algEq, timeVariantAssignments *timeVarAssign, double sim_time, double dt, int print_interval, double *time, int order, int use_lazy_method, int print_amount, allocated_memory *mem){
unsigned int i, j;
int cycle;
int error;
int end_cycle = get_end_cycle(sim_time, dt);
double reverse_time;
double *value_time_p = result->values_time;
double *value_sp_p = result->values_sp;
double *value_param_p = result->values_param;
double *value_comp_p = result->values_comp;
double **coefficient_matrix = NULL;
double *constant_vector = NULL;
int *alg_pivot = NULL;
double reactants_numerator, products_numerator;
double min_value;
double *init_val;
/* for implicit */
double **jacobian;
int is_convergence = 0;
double *b;
double *pre_b;
int *p; /* for pivot selection */
boolean flag;
double delta = 1.0e-8;
double tolerance = 1.0e-4; /* error tolerance of neuton method */
unsigned int loop;
double *delta_value;
double k_next; /* speculated k value : k(t+1) */
double *k_t; /* k(t) */
/* num of SBase objects */
unsigned int num_of_species = Model_getNumSpecies(m);
unsigned int num_of_parameters = Model_getNumParameters(m);
unsigned int num_of_compartments = Model_getNumCompartments(m);
unsigned int num_of_reactions = Model_getNumReactions(m);
unsigned int num_of_rules = Model_getNumRules(m);
unsigned int num_of_events = Model_getNumEvents(m);
unsigned int num_of_initialAssignments = Model_getNumInitialAssignments(m);
/* num of variables whose quantity is not a constant */
unsigned int num_of_all_var_species = 0;
unsigned int num_of_all_var_parameters = 0;
unsigned int num_of_all_var_compartments = 0;
unsigned int num_of_all_var_species_reference = 0;
/* num of variables (which is NOT changed by assignment nor algebraic rule) */
unsigned int num_of_var_species = 0;
unsigned int num_of_var_parameters = 0;
unsigned int num_of_var_compartments = 0;
unsigned int num_of_var_species_reference = 0;
unsigned int sum_num_of_vars;
/* All variables (whose quantity is not a constant) */
mySpecies **all_var_sp; /* all variable species */
myParameter **all_var_param; /* all variable parameters */
myCompartment **all_var_comp; /* all variable compartments */
mySpeciesReference **all_var_spr; /* all varialbe SpeciesReferences */
/* variables (which is NOT changed by assignment nor algebraic rule) */
mySpecies **var_sp;
myParameter **var_param;
myCompartment **var_comp;
mySpeciesReference **var_spr;
set_seed();
check_num(num_of_species, num_of_parameters, num_of_compartments, num_of_reactions, &num_of_all_var_species, &num_of_all_var_parameters, &num_of_all_var_compartments, &num_of_all_var_species_reference, &num_of_var_species, &num_of_var_parameters, &num_of_var_compartments, &num_of_var_species_reference, sp, param, comp, re);
/* create objects */
all_var_sp = (mySpecies **)malloc(sizeof(mySpecies *) * num_of_all_var_species);
all_var_param = (myParameter **)malloc(sizeof(myParameter *) * num_of_all_var_parameters);
all_var_comp = (myCompartment **)malloc(sizeof(myCompartment *) * num_of_all_var_compartments);
all_var_spr = (mySpeciesReference **)malloc(sizeof(mySpeciesReference *) * num_of_all_var_species_reference);
var_sp = (mySpecies **)malloc(sizeof(mySpecies *) * num_of_var_species);
var_param = (myParameter **)malloc(sizeof(myParameter *) * num_of_var_parameters);
var_comp = (myCompartment **)malloc(sizeof(myCompartment *) * num_of_var_compartments);
var_spr = (mySpeciesReference **)malloc(sizeof(mySpeciesReference *) * num_of_var_species_reference);
/* mySpecies *all_var_sp[num_of_all_var_species]; */
/* myParameter *all_var_param[num_of_all_var_parameters]; */
/* myCompartment *all_var_comp[num_of_all_var_compartments]; */
/* mySpeciesReference *all_var_spr[num_of_all_var_species_reference]; */
/* mySpecies *var_sp[num_of_var_species]; */
/* myParameter *var_param[num_of_var_parameters]; */
/* myCompartment *var_comp[num_of_var_compartments]; */
/* mySpeciesReference *var_spr[num_of_var_species_reference]; */
create_calc_object_list(num_of_species, num_of_parameters, num_of_compartments, num_of_reactions, all_var_sp, all_var_param, all_var_comp, all_var_spr, var_sp, var_param, var_comp, var_spr, sp, param, comp, re);
sum_num_of_vars = num_of_var_species + num_of_var_parameters +
num_of_var_compartments + num_of_var_species_reference;
jacobian = (double**)malloc(sizeof(double*)*(sum_num_of_vars));
for(i=0; i<sum_num_of_vars; i++){
jacobian[i] = (double*)malloc(sizeof(double)*(sum_num_of_vars));
}
b = (double *)malloc(sizeof(double) * (sum_num_of_vars));
pre_b = (double *)malloc(sizeof(double) * (sum_num_of_vars));
p = (int *)malloc(sizeof(int) * (sum_num_of_vars));
delta_value = (double *)malloc(sizeof(double) * (sum_num_of_vars));
k_t = (double *)malloc(sizeof(double) * (sum_num_of_vars));
/*
double b[sum_num_of_vars];
double pre_b[sum_num_of_vars];
int p[sum_num_of_vars];
double delta_value[sum_num_of_vars];
double k_t[sum_num_of_vars];
*/
if(algEq != NULL){
coefficient_matrix = (double**)malloc(sizeof(double*)*(algEq->num_of_algebraic_variables));
for(i=0; i<algEq->num_of_algebraic_variables; i++){
coefficient_matrix[i] = (double*)malloc(sizeof(double)*(algEq->num_of_algebraic_variables));
}
constant_vector = (double*)malloc(sizeof(double)*(algEq->num_of_algebraic_variables));
alg_pivot = (int*)malloc(sizeof(int)*(algEq->num_of_algebraic_variables));
}
PRG_TRACE(("Simulation for [%s] Starts!\n", Model_getId(m)));
cycle = 0;
/* initialize delay_val */
initialize_delay_val(sp, num_of_species, param, num_of_parameters, comp, num_of_compartments, re, num_of_reactions, sim_time, dt, 0);
/* calc temp value by assignment */
for(i=0; i<num_of_all_var_species; i++){
if(all_var_sp[i]->depending_rule != NULL && all_var_sp[i]->depending_rule->is_assignment){
all_var_sp[i]->temp_value = calc(all_var_sp[i]->depending_rule->eq, dt, cycle, &reverse_time, 0);
}
}
for(i=0; i<num_of_all_var_parameters; i++){
if(all_var_param[i]->depending_rule != NULL && all_var_param[i]->depending_rule->is_assignment){
all_var_param[i]->temp_value = calc(all_var_param[i]->depending_rule->eq, dt, cycle, &reverse_time, 0);
}
}
for(i=0; i<num_of_all_var_compartments; i++){
if(all_var_comp[i]->depending_rule != NULL && all_var_comp[i]->depending_rule->is_assignment){
all_var_comp[i]->temp_value = calc(all_var_comp[i]->depending_rule->eq, dt, cycle, &reverse_time, 0);
}
}
for(i=0; i<num_of_all_var_species_reference; i++){
if(all_var_spr[i]->depending_rule != NULL && all_var_spr[i]->depending_rule->is_assignment){
all_var_spr[i]->temp_value = calc(all_var_spr[i]->depending_rule->eq, dt, cycle, &reverse_time, 0);
}
}
/* forwarding value */
forwarding_value(all_var_sp, num_of_all_var_species, all_var_param, num_of_all_var_parameters, all_var_comp, num_of_all_var_compartments, all_var_spr, num_of_all_var_species_reference);
/* initialize delay_val */
initialize_delay_val(sp, num_of_species, param, num_of_parameters, comp, num_of_compartments, re, num_of_reactions, sim_time, dt, 0);
/* calc InitialAssignment */
calc_initial_assignment(initAssign, num_of_initialAssignments, dt, cycle, &reverse_time);
/* initialize delay_val */
initialize_delay_val(sp, num_of_species, param, num_of_parameters, comp, num_of_compartments, re, num_of_reactions, sim_time, dt, 0);
/* rewriting for explicit delay */
for(i=0; i<num_of_initialAssignments; i++){
for(j=0; j<initAssign[i]->eq->math_length; j++){
if(initAssign[i]->eq->number[j] == time){
TRACE(("time is replaced with reverse time\n"));
initAssign[i]->eq->number[j] = &reverse_time;
}else if(initAssign[i]->eq->number[j] != NULL){
init_val = (double*)malloc(sizeof(double));
*init_val = *initAssign[i]->eq->number[j];
mem->memory[mem->num_of_allocated_memory++] = init_val;
initAssign[i]->eq->number[j] = init_val;
}
}
}
for(i=0; i<timeVarAssign->num_of_time_variant_assignments; i++){
for(j=0; j<timeVarAssign->eq[i]->math_length; j++){
if(timeVarAssign->eq[i]->number[j] == time){
TRACE(("time is replaced with reverse time\n"));
timeVarAssign->eq[i]->number[j] = &reverse_time;
}else if(timeVarAssign->eq[i]->number[j] != NULL){
init_val = (double*)malloc(sizeof(double));
*init_val = *timeVarAssign->eq[i]->number[j];
mem->memory[mem->num_of_allocated_memory++] = init_val;
timeVarAssign->eq[i]->number[j] = init_val;
}
}
}
/* initialize delay_val */
initialize_delay_val(sp, num_of_species, param, num_of_parameters, comp, num_of_compartments, re, num_of_reactions, sim_time, dt, 0);
/* calc temp value by assignment */
for(i=0; i<num_of_all_var_species; i++){
if(all_var_sp[i]->depending_rule != NULL && all_var_sp[i]->depending_rule->is_assignment){
all_var_sp[i]->temp_value = calc(all_var_sp[i]->depending_rule->eq, dt, cycle, &reverse_time, 0);
}
}
for(i=0; i<num_of_all_var_parameters; i++){
if(all_var_param[i]->depending_rule != NULL && all_var_param[i]->depending_rule->is_assignment){
all_var_param[i]->temp_value = calc(all_var_param[i]->depending_rule->eq, dt, cycle, &reverse_time, 0);
}
}
for(i=0; i<num_of_all_var_compartments; i++){
if(all_var_comp[i]->depending_rule != NULL && all_var_comp[i]->depending_rule->is_assignment){
all_var_comp[i]->temp_value = calc(all_var_comp[i]->depending_rule->eq, dt, cycle, &reverse_time, 0);
}
}
for(i=0; i<num_of_all_var_species_reference; i++){
if(all_var_spr[i]->depending_rule != NULL && all_var_spr[i]->depending_rule->is_assignment){
all_var_spr[i]->temp_value = calc(all_var_spr[i]->depending_rule->eq, dt, cycle, &reverse_time, 0);
}
}
/* forwarding value */
forwarding_value(all_var_sp, num_of_all_var_species, all_var_param, num_of_all_var_parameters, all_var_comp, num_of_all_var_compartments, all_var_spr, num_of_all_var_species_reference);
/* initialize delay_val */
initialize_delay_val(sp, num_of_species, param, num_of_parameters, comp, num_of_compartments, re, num_of_reactions, sim_time, dt, 0);
/* calc temp value algebraic by algebraic */
if(algEq != NULL){
if(algEq->num_of_algebraic_variables > 1){
/* initialize pivot */
for(i=0; i<algEq->num_of_algebraic_variables; i++){
alg_pivot[i] = i;
}
for(i=0; i<algEq->num_of_algebraic_variables; i++){
for(j=0; j<algEq->num_of_algebraic_variables; j++){
coefficient_matrix[i][j] = calc(algEq->coefficient_matrix[i][j], dt, cycle, &reverse_time, 0);
/* TRACE(("coefficient matrix[%d][%d] = %lf\n", i, j, coefficient_matrix[i][j])); */
}
}
for(i=0; i<algEq->num_of_algebraic_variables; i++){
constant_vector[i] = -calc(algEq->constant_vector[i], dt, cycle, &reverse_time, 0);
/* TRACE(("constant vector[%d] = %lf\n", i, constant_vector[i])); */
}
/* LU decompostion */
error = lu_decomposition(coefficient_matrix, alg_pivot, algEq->num_of_algebraic_variables);
if(error == 0){/* failure in LU decomposition */
return NULL;
}
/* forward substitution & backward substitution */
lu_solve(coefficient_matrix, alg_pivot, algEq->num_of_algebraic_variables, constant_vector);
/* for(i=0; i<algEq->num_of_algebraic_variables; i++){ */
/* TRACE(("ans[%d] = %lf\n", i, constant_vector[i])); */
/* } */
for(i=0; i<algEq->num_of_alg_target_sp; i++){
algEq->alg_target_species[i]->target_species->temp_value = constant_vector[algEq->alg_target_species[i]->order];
}
for(i=0; i<algEq->num_of_alg_target_param; i++){
algEq->alg_target_parameter[i]->target_parameter->temp_value = constant_vector[algEq->alg_target_parameter[i]->order];
}
for(i=0; i<algEq->num_of_alg_target_comp; i++){
/* new code */
for(j=0; j<algEq->alg_target_compartment[i]->target_compartment->num_of_including_species; j++){
if(algEq->alg_target_compartment[i]->target_compartment->including_species[j]->is_concentration){
algEq->alg_target_compartment[i]->target_compartment->including_species[j]->temp_value = algEq->alg_target_compartment[i]->target_compartment->including_species[j]->temp_value*algEq->alg_target_compartment[i]->target_compartment->temp_value/constant_vector[algEq->alg_target_compartment[i]->order];
}
}
/* new code end */
algEq->alg_target_compartment[i]->target_compartment->temp_value = constant_vector[algEq->alg_target_compartment[i]->order];
}
}else{
if(algEq->target_species != NULL){
algEq->target_species->temp_value = -calc(algEq->constant, dt, cycle, &reverse_time, 0)/calc(algEq->coefficient, dt, cycle, &reverse_time, 0);
}
if(algEq->target_parameter != NULL){
algEq->target_parameter->temp_value = -calc(algEq->constant, dt, cycle, &reverse_time, 0)/calc(algEq->coefficient, dt, cycle, &reverse_time, 0);
}
if(algEq->target_compartment != NULL){
/* new code */
for(i=0; i<algEq->target_compartment->num_of_including_species; i++){
if(algEq->target_compartment->including_species[i]->is_concentration){
algEq->target_compartment->including_species[i]->temp_value = algEq->target_compartment->including_species[i]->temp_value*algEq->target_compartment->temp_value/(-calc(algEq->constant, dt, cycle, &reverse_time, 0)/calc(algEq->coefficient, dt, cycle, &reverse_time, 0));
}
}
/* new code end */
algEq->target_compartment->temp_value = -calc(algEq->constant, dt, cycle, &reverse_time, 0)/calc(algEq->coefficient, dt, cycle, &reverse_time, 0);
}
}
/* forwarding value */
forwarding_value(all_var_sp, num_of_all_var_species, all_var_param, num_of_all_var_parameters, all_var_comp, num_of_all_var_compartments, all_var_spr, num_of_all_var_species_reference);
}
/* initialize delay_val */
initialize_delay_val(sp, num_of_species, param, num_of_parameters, comp, num_of_compartments, re, num_of_reactions, sim_time, dt, 1);
/* cycle start */
for(cycle=0; cycle<=end_cycle; cycle++){
/* calculate unreversible fast reaction */
for(i=0; i<num_of_reactions; i++){
if(re[i]->is_fast && !re[i]->is_reversible){
if(calc(re[i]->eq, dt, cycle, &reverse_time, 0) > 0){
min_value = DBL_MAX;
for(j=0; j<re[i]->num_of_reactants; j++){
if(min_value > re[i]->reactants[j]->mySp->value/calc(re[i]->reactants[j]->eq, dt, cycle, &reverse_time, 0)){
min_value = re[i]->reactants[j]->mySp->value/calc(re[i]->reactants[j]->eq, dt, cycle, &reverse_time, 0);
}
}
for(j=0; j<re[i]->num_of_products; j++){
if(!Species_getBoundaryCondition(re[i]->products[j]->mySp->origin)){
re[i]->products[j]->mySp->value += calc(re[i]->products[j]->eq, dt, cycle, &reverse_time, 0)*min_value;
re[i]->products[j]->mySp->temp_value = re[i]->products[j]->mySp->value;
}
}
for(j=0; j<re[i]->num_of_reactants; j++){
if(!Species_getBoundaryCondition(re[i]->reactants[j]->mySp->origin)){
re[i]->reactants[j]->mySp->value -= calc(re[i]->reactants[j]->eq, dt, cycle, &reverse_time, 0)*min_value;
re[i]->reactants[j]->mySp->temp_value = re[i]->reactants[j]->mySp->value;
}
}
}
}
}
/* calculate reversible fast reactioin */
for(i=0; i<num_of_reactions; i++){
if(re[i]->is_fast && re[i]->is_reversible){
if(!(Species_getBoundaryCondition(re[i]->products[0]->mySp->origin)
&& Species_getBoundaryCondition(re[i]->reactants[0]->mySp->origin))){
products_numerator = calc(re[i]->products_equili_numerator, dt, cycle, &reverse_time, 0);
reactants_numerator = calc(re[i]->reactants_equili_numerator, dt, cycle, &reverse_time, 0);
if(products_numerator > 0 || reactants_numerator > 0){
if(Species_getBoundaryCondition(re[i]->products[0]->mySp->origin)){
re[i]->reactants[0]->mySp->value = (reactants_numerator/products_numerator)*re[i]->products[0]->mySp->value;
re[i]->reactants[0]->mySp->temp_value = re[i]->reactants[0]->mySp->value;
}else if(Species_getBoundaryCondition(re[i]->reactants[0]->mySp->origin)){
re[i]->products[0]->mySp->value = (products_numerator/reactants_numerator)*re[i]->reactants[0]->mySp->value;
re[i]->products[0]->mySp->temp_value = re[i]->products[0]->mySp->value;
}else{
re[i]->products[0]->mySp->value = (products_numerator/(products_numerator+reactants_numerator))*(re[i]->products[0]->mySp->temp_value+re[i]->reactants[0]->mySp->temp_value);
re[i]->reactants[0]->mySp->value = (reactants_numerator/(products_numerator+reactants_numerator))*(re[i]->products[0]->mySp->temp_value+re[i]->reactants[0]->mySp->temp_value);
re[i]->products[0]->mySp->temp_value = re[i]->products[0]->mySp->value;
re[i]->reactants[0]->mySp->temp_value = re[i]->reactants[0]->mySp->value;
}
}
}
}
}
/* event */
calc_event(event, num_of_events, dt, *time, cycle, &reverse_time);
/* substitute delay val */
substitute_delay_val(sp, num_of_species, param, num_of_parameters, comp, num_of_compartments, re, num_of_reactions, cycle);
/* progress */
if(cycle%(int)(end_cycle/10) == 0){
PRG_TRACE(("%3d %%\n", (int)(100*((double)cycle/(double)end_cycle))));
PRG_TRACE(("\x1b[1A"));
PRG_TRACE(("\x1b[5D"));
}
/* print result */
if(cycle%print_interval == 0){
/* Time */
*value_time_p = *time;
value_time_p++;
/* Species */
for(i=0; i<num_of_species; i++){
/* if(!(Species_getConstant(sp[i]->origin) && Species_getBoundaryCondition(sp[i]->origin))){ // XXX must remove this */
if(print_amount){
if(sp[i]->is_concentration){
*value_sp_p = sp[i]->value*sp[i]->locating_compartment->value;
}else{
*value_sp_p = sp[i]->value;
}
}else{
if(sp[i]->is_amount){
*value_sp_p = sp[i]->value/sp[i]->locating_compartment->value;
}else{
*value_sp_p = sp[i]->value;
}
}
value_sp_p++;
/* } */
}
/* Parameter */
for(i=0; i<num_of_parameters; i++){
/* if(!Parameter_getConstant(param[i]->origin)){ // XXX must remove this */
*value_param_p = param[i]->value;
/* } */
value_param_p++;
}
/* Compartment */
for(i=0; i<num_of_compartments; i++){
/* if(!Compartment_getConstant(comp[i]->origin)){ // XXX must remove this */
*value_comp_p = comp[i]->value;
/* } */
value_comp_p++;
}
}
/* time increase */
*time = (cycle+1)*dt;
/* implicit method */
/* define init value by Euler start */
calc_k(all_var_sp, num_of_all_var_species, all_var_param, num_of_all_var_parameters, all_var_comp, num_of_all_var_compartments, all_var_spr, num_of_all_var_species_reference, re, num_of_reactions, rule, num_of_rules, cycle, dt, &reverse_time, 0, 1);
/* preserve k(t) value */
for(i=0; i<sum_num_of_vars; i++){
if(i < num_of_var_species){
k_t[i] = var_sp[i]->k[0];
}else if(i < num_of_var_species+num_of_var_parameters){
k_t[i] = var_param[i-num_of_var_species]->k[0];
}else if(i < num_of_var_species+num_of_var_parameters+num_of_var_compartments){
k_t[i] = var_comp[i-num_of_var_species-num_of_var_parameters]->k[0];
}else{
k_t[i] = var_spr[i-num_of_var_species-num_of_var_parameters-num_of_var_compartments]->k[0];
}
}
calc_temp_value(all_var_sp, num_of_all_var_species, all_var_param, num_of_all_var_parameters, all_var_comp, num_of_all_var_compartments, all_var_spr, num_of_all_var_species_reference, dt, 0);
/* define init value by Euler end */
/* newton method */
if(use_lazy_method){
is_convergence = 0;
for(i=0; i<sum_num_of_vars; i++){
pre_b[i] = 0;
}
}
flag = 1;
while(flag){
/* calc b */
calc_k(var_sp, num_of_var_species, var_param, num_of_var_parameters, var_comp, num_of_var_compartments, var_spr, num_of_var_species_reference, re, num_of_reactions, rule, num_of_rules, cycle, dt, &reverse_time, 0, 0);
for(i=0; i<num_of_var_species; i++){
k_next = var_sp[i]->k[0];
b[i] = calc_implicit_formula(order, var_sp[i]->temp_value, var_sp[i]->value, var_sp[i]->prev_val[0], var_sp[i]->prev_val[1], var_sp[i]->prev_val[2], k_next, k_t[i], var_sp[i]->prev_k[0], var_sp[i]->prev_k[1], dt);
}
for(i=0; i<num_of_var_parameters; i++){
b[num_of_var_species+i] = calc_implicit_formula(order, var_param[i]->temp_value, var_param[i]->value, var_param[i]->prev_val[0], var_param[i]->prev_val[1], var_param[i]->prev_val[2], var_param[i]->k[0], k_t[num_of_var_species+i], var_param[i]->prev_k[0], var_param[i]->prev_k[1], dt);
}
for(i=0; i<num_of_var_compartments; i++){
b[num_of_var_species+num_of_var_parameters+i] = calc_implicit_formula(order, var_comp[i]->temp_value, var_comp[i]->value, var_comp[i]->prev_val[0], var_comp[i]->prev_val[1], var_comp[i]->prev_val[2], var_comp[i]->k[0], k_t[num_of_var_species+num_of_var_parameters+i], var_comp[i]->prev_k[0], var_comp[i]->prev_k[1], dt);
}
for(i=0; i<num_of_var_species_reference; i++){
b[num_of_var_species+num_of_var_parameters+num_of_var_compartments+i] = calc_implicit_formula(order, var_spr[i]->temp_value, var_spr[i]->value, var_spr[i]->prev_val[0], var_spr[i]->prev_val[1], var_spr[i]->prev_val[2], var_spr[i]->k[0], k_t[num_of_var_species+num_of_var_parameters+num_of_var_compartments+i], var_spr[i]->prev_k[0], var_spr[i]->prev_k[1], dt);
}
if(!use_lazy_method || !is_convergence){
/* calc jacobian by numerical differentiation */
for(loop=0; loop<sum_num_of_vars; loop++){
if(loop < num_of_var_species){
var_sp[loop]->temp_value += delta;
}else if(loop < num_of_var_species+num_of_var_parameters){
var_param[loop-num_of_var_species]->temp_value += delta;
}else if(loop < num_of_var_species+num_of_var_parameters+num_of_var_compartments){
var_comp[loop-num_of_var_species-num_of_var_parameters]->temp_value += delta;
}else{
var_spr[loop-num_of_var_species-num_of_var_parameters-num_of_var_compartments]->temp_value += delta;
}
calc_k(var_sp, num_of_var_species, var_param, num_of_var_parameters, var_comp, num_of_var_compartments, var_spr, num_of_var_species_reference, re, num_of_reactions, rule, num_of_rules, cycle, dt, &reverse_time, 0, 0);
for(i=0; i<num_of_var_species; i++){
k_next = var_sp[i]->k[0];
delta_value[i] = calc_implicit_formula(order, var_sp[i]->temp_value, var_sp[i]->value, var_sp[i]->prev_val[0], var_sp[i]->prev_val[1], var_sp[i]->prev_val[2], k_next, k_t[i], var_sp[i]->prev_k[0], var_sp[i]->prev_k[1], dt);
/* numerical differentiation */
jacobian[i][loop] = (delta_value[i]-b[i])/delta;
}
for(i=0; i<num_of_var_parameters; i++){
delta_value[num_of_var_species+i] = calc_implicit_formula(order, var_param[i]->temp_value, var_param[i]->value, var_param[i]->prev_val[0], var_param[i]->prev_val[1], var_param[i]->prev_val[2], var_param[i]->k[0], k_t[num_of_var_species+i], var_param[i]->prev_k[0], var_param[i]->prev_k[1], dt);
/* numerical differentiation */
jacobian[num_of_var_species+i][loop] = (delta_value[num_of_var_species+i]-b[num_of_var_species+i])/delta;
}
for(i=0; i<num_of_var_compartments; i++){
delta_value[num_of_var_species+num_of_var_parameters+i] = calc_implicit_formula(order, var_comp[i]->temp_value, var_comp[i]->value, var_comp[i]->prev_val[0], var_comp[i]->prev_val[1], var_comp[i]->prev_val[2], var_comp[i]->k[0], k_t[num_of_var_species+num_of_var_parameters+i], var_comp[i]->prev_k[0], var_comp[i]->prev_k[1], dt);
/* numerical differentiation */
jacobian[num_of_var_species+num_of_var_parameters+i][loop] = (delta_value[num_of_var_species+num_of_var_parameters+i]-b[num_of_var_species+num_of_var_parameters+i])/delta;
}
for(i=0; i<num_of_var_species_reference; i++){
delta_value[num_of_var_species+num_of_var_parameters+num_of_var_compartments+i] = calc_implicit_formula(order, var_spr[i]->temp_value, var_spr[i]->value, var_spr[i]->prev_val[0], var_spr[i]->prev_val[1], var_spr[i]->prev_val[2], var_spr[i]->k[0], k_t[num_of_var_species+num_of_var_parameters+num_of_var_compartments+i], var_spr[i]->prev_k[0], var_spr[i]->prev_k[1], dt);
/* numerical differentiation */
jacobian[num_of_var_species+num_of_var_parameters+num_of_var_compartments+i][loop] = (delta_value[num_of_var_species+num_of_var_parameters+num_of_var_compartments+i]-b[num_of_var_species+num_of_var_parameters+num_of_var_compartments+i])/delta;
}
if(loop < num_of_var_species){
var_sp[loop]->temp_value -= delta;
}else if(loop < num_of_var_species+num_of_var_parameters){
var_param[loop-num_of_var_species]->temp_value -= delta;
}else if(loop < num_of_var_species+num_of_var_parameters+num_of_var_compartments){
var_comp[loop-num_of_var_species-num_of_var_parameters]->temp_value -= delta;
}else{
var_spr[loop-num_of_var_species-num_of_var_parameters-num_of_var_compartments]->temp_value -= delta;
}
}
}
/* initialize p */
for(i=0; i<sum_num_of_vars; i++){
p[i] = i;
}
/* LU decomposition */
error = lu_decomposition(jacobian, p, sum_num_of_vars);
if(error == 0){/* failure in LU decomposition */
return NULL;
}
/* forward substitution & backward substitution */
lu_solve(jacobian, p, sum_num_of_vars, b);
/* calculate next temp value */
for(i=0; i<sum_num_of_vars; i++){
if(i < num_of_var_species){
var_sp[i]->temp_value -= b[i];
}else if(i < num_of_var_species+num_of_var_parameters){
var_param[i-num_of_var_species]->temp_value -= b[i];
}else if(i < num_of_var_species+num_of_var_parameters+num_of_var_compartments){
var_comp[i-num_of_var_species-num_of_var_parameters]->temp_value -= b[i];
}else{
var_spr[i-num_of_var_species-num_of_var_parameters-num_of_var_compartments]->temp_value -= b[i];
}
}
/* convergence judgement */
if(use_lazy_method){
is_convergence = 1;
for(i=0; i<sum_num_of_vars; i++){
if(fabs(b[i]) > fabs(pre_b[i])){
is_convergence = 0;
}
}
for(i=0; i<sum_num_of_vars; i++){
pre_b[i] = b[i];
}
}
/* error judgement */
flag = 0;
for(i=0; i<sum_num_of_vars; i++){
if(fabs(b[i]) > tolerance){
flag = 1;
}
}
}
/* calc temp value by assignment */
for(i=0; i<num_of_all_var_species; i++){
if(all_var_sp[i]->depending_rule != NULL && all_var_sp[i]->depending_rule->is_assignment){
all_var_sp[i]->temp_value = calc(all_var_sp[i]->depending_rule->eq, dt, cycle, &reverse_time, 0);
}
}
for(i=0; i<num_of_all_var_parameters; i++){
if(all_var_param[i]->depending_rule != NULL && all_var_param[i]->depending_rule->is_assignment){
all_var_param[i]->temp_value = calc(all_var_param[i]->depending_rule->eq, dt, cycle, &reverse_time, 0);
}
}
for(i=0; i<num_of_all_var_compartments; i++){
if(all_var_comp[i]->depending_rule != NULL && all_var_comp[i]->depending_rule->is_assignment){
all_var_comp[i]->temp_value = calc(all_var_comp[i]->depending_rule->eq, dt, cycle, &reverse_time, 0);
}
}
for(i=0; i<num_of_all_var_species_reference; i++){
if(all_var_spr[i]->depending_rule != NULL && all_var_spr[i]->depending_rule->is_assignment){
all_var_spr[i]->temp_value = calc(all_var_spr[i]->depending_rule->eq, dt, cycle, &reverse_time, 0);
}
}
/* calc temp value algebraic by algebraic */
if(algEq != NULL){
if(algEq->num_of_algebraic_variables > 1){
/* initialize pivot */
for(i=0; i<algEq->num_of_algebraic_variables; i++){
alg_pivot[i] = i;
}
for(i=0; i<algEq->num_of_algebraic_variables; i++){
for(j=0; j<algEq->num_of_algebraic_variables; j++){
coefficient_matrix[i][j] = calc(algEq->coefficient_matrix[i][j], dt, cycle, &reverse_time, 0);
}
}
for(i=0; i<algEq->num_of_algebraic_variables; i++){
constant_vector[i] = -calc(algEq->constant_vector[i], dt, cycle, &reverse_time, 0);
}
/* LU decompostion */
error = lu_decomposition(coefficient_matrix, alg_pivot, algEq->num_of_algebraic_variables);
if(error == 0){/* failure in LU decomposition */
return NULL;
}
/* forward substitution & backward substitution */
lu_solve(coefficient_matrix, alg_pivot, algEq->num_of_algebraic_variables, constant_vector);
for(i=0; i<algEq->num_of_alg_target_sp; i++){
algEq->alg_target_species[i]->target_species->temp_value = constant_vector[algEq->alg_target_species[i]->order];
}
for(i=0; i<algEq->num_of_alg_target_param; i++){
algEq->alg_target_parameter[i]->target_parameter->temp_value = constant_vector[algEq->alg_target_parameter[i]->order];
}
for(i=0; i<algEq->num_of_alg_target_comp; i++){
/* new code */
for(j=0; j<algEq->alg_target_compartment[i]->target_compartment->num_of_including_species; j++){
if(algEq->alg_target_compartment[i]->target_compartment->including_species[j]->is_concentration){
algEq->alg_target_compartment[i]->target_compartment->including_species[j]->temp_value = algEq->alg_target_compartment[i]->target_compartment->including_species[j]->temp_value*algEq->alg_target_compartment[i]->target_compartment->temp_value/constant_vector[algEq->alg_target_compartment[i]->order];
}
}
/* new code end */
algEq->alg_target_compartment[i]->target_compartment->temp_value = constant_vector[algEq->alg_target_compartment[i]->order];
}
}else{
if(algEq->target_species != NULL){
algEq->target_species->temp_value = -calc(algEq->constant, dt, cycle, &reverse_time, 0)/calc(algEq->coefficient, dt, cycle, &reverse_time, 0);
}
if(algEq->target_parameter != NULL){
algEq->target_parameter->temp_value = -calc(algEq->constant, dt, cycle, &reverse_time, 0)/calc(algEq->coefficient, dt, cycle, &reverse_time, 0);
}
if(algEq->target_compartment != NULL){
/* new code */
for(i=0; i<algEq->target_compartment->num_of_including_species; i++){
if(algEq->target_compartment->including_species[i]->is_concentration){
algEq->target_compartment->including_species[i]->temp_value = algEq->target_compartment->including_species[i]->temp_value*algEq->target_compartment->temp_value/(-calc(algEq->constant, dt, cycle, &reverse_time, 0)/calc(algEq->coefficient, dt, cycle, &reverse_time, 0));
}
}
/* new code end */
algEq->target_compartment->temp_value = -calc(algEq->constant, dt, cycle, &reverse_time, 0)/calc(algEq->coefficient, dt, cycle, &reverse_time, 0);
}
}
}
/* preserve prev_value and prev_k for multistep solution */
for(i=0; i<num_of_var_species; i++){
var_sp[i]->prev_val[2] = var_sp[i]->prev_val[1];
var_sp[i]->prev_val[1] = var_sp[i]->prev_val[0];
var_sp[i]->prev_val[0] = var_sp[i]->value;
var_sp[i]->prev_k[2] = var_sp[i]->prev_k[1];
var_sp[i]->prev_k[1] = var_sp[i]->prev_k[0];
var_sp[i]->prev_k[0] = k_t[i];
}
for(i=0; i<num_of_var_parameters; i++){
var_param[i]->prev_val[2] = var_param[i]->prev_val[1];
var_param[i]->prev_val[1] = var_param[i]->prev_val[0];
var_param[i]->prev_val[0] = var_param[i]->value;
var_param[i]->prev_k[2] = var_param[i]->prev_k[1];
var_param[i]->prev_k[1] = var_param[i]->prev_k[0];
var_param[i]->prev_k[0] = k_t[num_of_var_species+i];
}
for(i=0; i<num_of_var_compartments; i++){
var_comp[i]->prev_val[2] = var_comp[i]->prev_val[1];
var_comp[i]->prev_val[1] = var_comp[i]->prev_val[0];
var_comp[i]->prev_val[0] = var_comp[i]->value;
var_comp[i]->prev_k[2] = var_comp[i]->prev_k[1];
var_comp[i]->prev_k[1] = var_comp[i]->prev_k[0];
var_comp[i]->prev_k[0] = k_t[num_of_var_species+num_of_var_parameters+i];
}
for(i=0; i<num_of_var_species_reference; i++){
var_spr[i]->prev_val[2] = var_spr[i]->prev_val[1];
var_spr[i]->prev_val[1] = var_spr[i]->prev_val[0];
var_spr[i]->prev_val[0] = var_spr[i]->value;
var_spr[i]->prev_k[2] = var_spr[i]->prev_k[1];
var_spr[i]->prev_k[1] = var_spr[i]->prev_k[0];
var_spr[i]->prev_k[0] = k_t[num_of_var_species+num_of_var_parameters+i];
}
/* forwarding value */
forwarding_value(all_var_sp, num_of_all_var_species, all_var_param, num_of_all_var_parameters, all_var_comp, num_of_all_var_compartments, all_var_spr, num_of_all_var_species_reference);
}
PRG_TRACE(("Simulation for [%s] Ends!\n", Model_getId(m)));
if(algEq != NULL){
for(i=0; i<algEq->num_of_algebraic_variables; i++){
free(coefficient_matrix[i]);
}
free(coefficient_matrix);
free(constant_vector);
free(alg_pivot);
}
for(i=0; i<sum_num_of_vars; i++){
free(jacobian[i]);
}
free(all_var_sp);
free(all_var_param);
free(all_var_comp);
free(all_var_spr);
free(var_sp);
free(var_param);
free(var_comp);
free(var_spr);
/* for implicit */
free(jacobian);
return result;
}
DLLEXPORT lapack_int z_lu_solve(lapack_int n, lapack_int nrhs, lapack_complex_double a[], lapack_complex_double b[])
{
return lu_solve(n, nrhs, a, b, LAPACK_zgetrf, LAPACK_zgetrs);
}
DLLEXPORT lapack_int c_lu_solve(lapack_int n, lapack_int nrhs, lapack_complex_float a[], lapack_complex_float b[])
{
return lu_solve(n, nrhs, a, b, LAPACK_cgetrf, LAPACK_cgetrs);
}
DLLEXPORT lapack_int d_lu_solve(lapack_int n, lapack_int nrhs, double a[], double b[])
{
return lu_solve(n, nrhs, a, b, LAPACK_dgetrf, LAPACK_dgetrs);
}
DLLEXPORT lapack_int s_lu_solve(lapack_int n, lapack_int nrhs, float a[], float b[])
{
return lu_solve(n, nrhs, a, b, LAPACK_sgetrf, LAPACK_sgetrs);
}
// overload to allow Region1D as rhs arg
//---------------------------------------------------------
DVec& lu_solve(DMat& LU, Region1D<DVec> R)
//---------------------------------------------------------
{
DVec rhs(R);
return lu_solve(LU,rhs);
}
Vector inline solve(const Matrix& A, const Vector& b, tag::dense)
{
vampir_trace<3034> tracer;
return lu_solve(A, b);
}
int zgesv_idrs(
const size_t n,
// A is a function which multiplies the matrix by the first argument
// and returns the result in the second. The second argument must
// be manually cleared. The third parameter is user data, passed in
// through Adata.
void (*A)(const std::complex<double>*, std::complex<double>*, void*),
std::complex<double>* b,
std::complex<double>* x,
// Optional parameters
void *Adata = NULL,
size_t maxit = 0, // default is min(2*n,1000)
const size_t s = 4,
const double tol = 1e-8,
bool x_initialized = false,
// P is a precondition which simply solves P*x' = x,
// where x i the first argument. The second parameter is user data,
// which is passed in through Pdata.
void (*P)(std::complex<double>*, void*) = NULL,
void *Pdata = NULL,
double angle = 0.7
){
double normb = vecnorm(n, b);
if(0 == normb){
for(size_t i = 0; i < n; ++i){ x[i] = 0; }
return 0;
}
const double tolb = tol*normb; // compute tolerance
// Set initial x
if(!x_initialized){
for(size_t i = 0; i < n; ++i){ x[i] = 0; }
}
std::complex<double> *r = new std::complex<double>[n];
A(x,r,Adata);
for(size_t i = 0; i < n; ++i){ r[i] = b[i]-r[i]; }
double normr = vecnorm(n, r);
// Now, r = b-A*x
std::complex<double> *Q = new std::complex<double>[n*s];
{ // set up shadow space
for(size_t j = 0; j < s; ++j){
for(size_t i = 0; i < n; ++i){
Q[i+j*n] = (double)rand()/(double)RAND_MAX - 0.5;
}
}
// Orthogonalize Q
orth(n, s, Q);
}
std::complex<double> *G = new std::complex<double>[n*s];
std::complex<double> *U = new std::complex<double>[n*s];
std::complex<double> *M = new std::complex<double>[s*s];
std::complex<double> *Mcopy = new std::complex<double>[s*s];
size_t *pivots = new size_t[s];
for(size_t j = 0; j < s; ++j){
for(size_t i = 0; i < n; ++i){
G[i+j*n] = 0;
U[i+j*n] = 0;
}
for(size_t i = 0; i < s; ++i){
if(i == j){
M[i+j*s] = 1;
}else{
M[i+j*s] = 0;
}
}
}
std::complex<double> *f = new std::complex<double>[s];
std::complex<double> *c = new std::complex<double>[s];
std::complex<double> *v = new std::complex<double>[n];
std::complex<double> *t = new std::complex<double>[n];
size_t iter = 0;
std::complex<double> om = 1;
if(0 == maxit){
maxit = 2*n;
if(1000 < maxit){ maxit = 1000; }
}
int ret = 0;
while(normr > tolb && iter < maxit){
std::cout << "iter = " << iter << std::endl;
// generate RHS for small system
for(size_t j = 0; j < s; ++j){
std::complex<double> sum = 0;
for(size_t i = 0; i < n; ++i){
sum += r[i] * std::conj(Q[i+j*n]);
}
f[j] = sum;
}
for(size_t k = 0; k < s; ++k){
// solve small systems of M(k:s,k:s)*c(k:s) = f(k:s)
{
// Copy over stuff for a destructive LU solve in Mcopy
for(size_t j = k; j < s; ++j){
for(size_t i = k; i < s; ++i){
Mcopy[i+j*s] = M[i+j*s];
}
c[j] = f[j];
}
// Perform LU solve...
lu(s-k, s-k, s, &Mcopy[k+k*s], pivots);
lu_solve(s-k, s-k, s, &Mcopy[k+k*s], pivots, &c[k]);
}
// v = r - G(:,k:s)*c;
for(size_t i = 0; i < n; ++i){
std::complex<double> sum = 0;
for(size_t j = k; j < s; ++j){
sum += G[i+j*n]*c[j];
}
v[i] = r[i] - sum;
}
if(NULL != P){
P(v, Pdata);
}
//U(:,k) = U(:,k:s)*c + om*v;
for(size_t i = 0; i < n; ++i){
std::complex<double> sum = 0;
for(size_t j = k; j < s; ++j){
sum += U[i+j*n]*c[j];
}
U[i+k*n] = sum + om*v[i];
}
//G(:,k) = A*U(:,k);
A(&U[0+k*n], &G[0+k*n], Adata);
// Bi-Orthogonalise the new basis vectors
for(size_t j = 0; j < k; ++j){
std::complex<double> alpha = 0;
for(size_t i = 0; i < n; ++i){
alpha += std::conj(Q[i+j*n])*G[i+k*n];
}
alpha /= M[j+j*s];
for(size_t i = 0; i < n; ++i){
G[i+k*n] -= alpha*G[i+j*n];
}
for(size_t i = 0; i < n; ++i){
U[i+k*n] -= alpha*U[i+j*n];
}
}
// New column of M = (Q'*G)' (first k-1 entries are zero)
for(size_t j = k; j < s; ++j){
std::complex<double> sum = 0;
for(size_t i = 0; i < n; ++i){
sum += G[i+k*n]*std::conj(Q[i+j*n]);
}
M[j+k*s] = sum;
}
// Make r orthogonal to p_i, i = 1..k
std::complex<double> beta = f[k]/M[k+k*s];
for(size_t i = 0; i < n; ++i){
r[i] -= beta*G[i+k*n];
}
for(size_t i = 0; i < n; ++i){
x[i] += beta*U[i+k*n];
}
++iter;
normr = vecnorm(n, r);
if(normr < tolb || iter == maxit){ break; }
// New f = Q'*r (first k components are zero)
for(size_t j = k+1; j < s; ++j){
f[j] -= beta*M[j+k*s];
}
} // end k loop
// If we break'd out of the inner loop, do so again
if(normr < tolb){ break; }
// Now we have sufficient vectors in G_j to compute residual in G_j+1
// Note: r is already perpendicular to Q so v = r
for(size_t i = 0; i < n; ++i){ v[i] = r[i]; }
if(NULL != P){
P(v, Pdata);
}
A(v, t, Adata);
{ // compute new omega
double norms = vecnorm(n, r), normt = vecnorm(n, t);
std::complex<double> ts = 0;
for(size_t i = 0; i < n; ++i){
ts += std::conj(t[i])*r[i];
}
double rho = std::abs(ts/(normt*norms));
om = ts/(normt*normt);
if(rho < angle){
om *= angle/rho;
}
}
for(size_t i = 0; i < n; ++i){ r[i] -= om*t[i]; }
for(size_t i = 0; i < n; ++i){ x[i] += om*v[i]; }
normr = vecnorm(n, r);
++iter;
}
delete [] r;
delete [] G;
delete [] U;
delete [] M;
delete [] Mcopy;
delete [] f;
delete [] c;
delete [] v;
delete [] t;
return ret;
}
DLLEXPORT MKL_INT z_lu_solve(MKL_INT n, MKL_INT nrhs, MKL_Complex16 a[], MKL_Complex16 b[])
{
return lu_solve(n, nrhs, a, b, zgetrf, zgetrs);
}
DLLEXPORT MKL_INT c_lu_solve(MKL_INT n, MKL_INT nrhs, MKL_Complex8 a[], MKL_Complex8 b[])
{
return lu_solve(n, nrhs, a, b, cgetrf, cgetrs);
}
DLLEXPORT MKL_INT d_lu_solve(MKL_INT n, MKL_INT nrhs, double a[], double b[])
{
return lu_solve(n, nrhs, a, b, dgetrf, dgetrs);
}
DLLEXPORT MKL_INT s_lu_solve(MKL_INT n, MKL_INT nrhs, float a[], float b[])
{
return lu_solve(n, nrhs, a, b, sgetrf, sgetrs);
}
