inline void output_value_on_line(const std::string& filename, //
Domain_<Float, Float, 2>& domain, //
Axes aix, Float v, st idx) {
//typedef Domain_<Float, Float, 2> Domain;
typedef Domain_<Float, Float, 2>::pNode pNode;
typedef Interpolate_<Float, Float, 2> Inter;
typedef Point_<Float, 2> Point;
typedef Expression_<Float, Float,2> Exp;
// build an array
st n = 300;
ArrayListV<Float> arr = Linspace( //
domain.grid().min(VerticalAxes2D(aix)), //
domain.grid().max(VerticalAxes2D(aix)), n);
// Interpolate
ArrayListV<Float> arrval(n);
std::fstream fss;
fss.open(filename, std::fstream::out);
for (st i = 0; i < n; ++i) {
Point p;
p[aix] = v;
p[VerticalAxes2D(aix)] = arr[i];
pNode pn = domain.grid().get_pnode(p.x(), p.y());
Exp exp = Inter::OnPlane(pn, _X_, _Y_, p.x(), p.y(), 1);
arrval[i] = exp.substitute(idx);
fss << arr[i] << " " << arrval[i] << "\n";
}
fss.close();
}
int main(){
int n = 6;
int m = n;
Matrix x = Linspace(-4.0, 4.0, m+1, 1);
Matrix y = Linspace(-4.0, 4.0, n+1, 1);
Matrix f(x.Size(), y.Size());
for(int i = 0; i < x.Size(); i++){
for(int j = 0; j < y.Size(); j++){
f(i, j) = 1/(1+(x(i)*x(i)) + (y(j)*y(j)));
}
}
Matrix a = Linspace(-4.0, 4.0, 201, 1);
a.Write("avals.txt");
Matrix b = Linspace(-4.0, 4.0, 101, 1);
b.Write("bvals.txt");
Matrix p6(a.Size(), b.Size());
for(int i = 0; i < a.Size(); i++){
for(int j = 0; j < b.Size(); j++){
p6(i, j) = Lagrange2D(x, y, f, a(i), b(j));
}
}
p6.Write("p6_uni.txt");
n = 24;
m = n;
x = Linspace(-4.0, 4.0, m+1, 1);
y = Linspace(-4.0, 4.0, n+1, 1);
f = Matrix(x.Size(), y.Size());
for(int i = 0; i < x.Size(); i++){
for(int j = 0; j < y.Size(); j++){
f(i, j) = 1/(1+(x(i)*x(i)) + (y(j)*y(j)));
}
}
Matrix p24(a.Size(), b.Size());
for(int i = 0; i < a.Size(); i++){
for(int j = 0; j < b.Size(); j++){
p24(i, j) = Lagrange2D(x, y, f, a(i), b(j));
}
}
p24.Write("p24_uni.txt");
Matrix runge(201, 101);
for(int i = 0; i < a.Size(); i++){
for(int j = 0; j < b.Size(); j++){
runge(i, j) = 1/(1+(a(i)*a(i)) + (b(j)*b(j)));
}
}
//create runge matrix
runge.Write("Runge.txt");
}
int main(int argc, char * argv[]){
double time_min = 0;
double time_max = 10;
F f;
FD fd;
f.solveE(2.0, 1.25);
fd.solveE(2.0, 1.25);
Matrix t = Linspace(time_min, time_max, 1, 10000);
Matrix x(t.Size() );
Matrix y(t.Size() );
double w = 0;
double rw = 0;
for(int i = 0; i < t.Size() ; i++){
f.setT( t(i) );
fd.setT( t(i) );
w = newton(f,fd, w, 6, 1e-5, false);
rw = radialPosition(2.0, 1.25, w);
x(i) = rw * cos(w);
y(i) = rw * sin(w);
}
t.Write("t.txt");
x.Write("x.txt");
y.Write("y.txt");
return 0;
}
int main(int argc, char** argv){
//Setup tolerances for experiments
double rtol, atol;
rtol = 1e-11;
atol = 1e-15;
// Create an array of 400 evenly-spaced T values over the
// interval[800,1200] K. Output this to disk as the file
// Temp.txt
Matrix T_values = Linspace(800, 1200, 400, 1);
T_values.Write("Temp.txt");
// Create an array of 600 evenly-spaced t values over the
// interval[1 sec,48 hours] K. Output this to disk as the file
// temp.txt
Matrix t_values = Linspace(1, 172800, 600, 1);
t_values.Write("time.txt");
// Create a 400 x 600 array that contains C(0.002,t,T).
// Output this to disk as the file C2mm.txt
//carbon(0.002, t_values(300), T_values(45), rtol, atol);
Matrix C2MM(400, 600);
for(int i = 0 ; i < T_values.Size(); i++){
for(int j = 0; j < t_values.Size(); j++){
C2MM(i, j) =
carbon( 0.002, t_values(j), T_values(i), rtol, atol);
}
}
C2MM.Write("C2mm.txt");
// Create a 400 x 600 array that contains C(0.004,t,T).
// Output this to disk as the file C4mm.txt
Matrix C4MM(400, 600);
for(int i = 0 ; i < T_values.Size(); i++){
for(int j = 0; j < t_values.Size(); j++){
C4MM(i, j) =
carbon( 0.004, t_values(j), T_values(i), rtol, atol);
}
}
C4MM.Write("C4mm.txt");
// Create an array of length 600 containing C(0.002,t,800)
// Output to disk as the file C2mm_800K.txt . Repeat this
// to output the carbon concentrations for 2mm depth at
// 900K (C2mm_900K.txt), 1000K (C2mm_1000K.txt),
// 1100K (C2mm_24hour.txt), 1200K (C2mm_1200K.txt)
Matrix C2mm_800K(600);
Matrix C2mm_900K(600);
Matrix C2mm_1000K(600);
Matrix C2mm_1100K(600);
Matrix C2mm_1200K(600);
for(int i =0 ; i < 600 ; i++){
C2mm_800K(i) = carbon(0.002, t_values(i), 800, rtol, atol);
C2mm_900K(i) = carbon(0.002, t_values(i), 900, rtol, atol);
C2mm_1000K(i) = carbon(0.002, t_values(i), 1000, rtol, atol);
C2mm_1100K(i) = carbon(0.002, t_values(i), 1100, rtol, atol);
C2mm_1200K(i) = carbon(0.002, t_values(i), 1200, rtol, atol);
}
C2mm_800K.Write("C2mm_800K.txt");
C2mm_900K.Write("C2mm_900K.txt");
C2mm_1000K.Write("C2mm_1000K.txt");
C2mm_1100K.Write("C2mm_24hour.txt");
C2mm_1200K.Write("C2mm_1200K.txt");
// Create an array of length 600 containing C(0.004,t,800)
// Output to disk as the file C4mm_800K.txt . Repeat this
// to output the carbon concentrations for 2mm depth at
// 900K (C4mm_900K.txt), 1000K (C4mm_1000K.txt),
// 1100K (C4mm_1100K.txt), 1200K (C4mm_1200K.txt)
Matrix C4mm_800K(600);
Matrix C4mm_900K(600);
Matrix C4mm_1000K(600);
Matrix C4mm_1100K(600);
Matrix C4mm_1200K(600);
for(int i =0 ; i < 600 ; i++){
C4mm_800K(i) = carbon(0.004, t_values(i), 800, rtol, atol);
C4mm_900K(i) = carbon(0.004, t_values(i), 900, rtol, atol);
C4mm_1000K(i) = carbon(0.004, t_values(i), 1000, rtol, atol);
C4mm_1100K(i) = carbon(0.004, t_values(i), 1100, rtol, atol);
C4mm_1200K(i) = carbon(0.004, t_values(i), 1200, rtol, atol);
}
C4mm_800K.Write("C4mm_800K.txt");
C4mm_900K.Write("C4mm_900K.txt");
C4mm_1000K.Write("C4mm_1000K.txt");
C4mm_1100K.Write("C4mm_1100K.txt");
C4mm_1200K.Write("C4mm_1200K.txt");
return 0;
}
int main(int argc, const char * argv[]) {
// insert code here...
double coeff[13];//array of coefficients for taylor polynomial of cos(x)
bool neg=false;//if coefficient is supposed to be negative, then true
for (int i=0.0; i<13; i++) {//assigns coefficients to array
if(i%2==0)
{if(!neg)
{
coeff[i]=(double)(1.0/factorial(i));
neg=true;
}
else
{ coeff[i]=(double)(-1.0/factorial(i));
neg=false;
}
}
else{
coeff[i]=0;
}
}
Matrix z=Linspace(-3, 3, 601);//creates matrix with 601 evenly div numbers between -3 and 3
Matrix p4coeff(1,5,coeff);//matrix with first 4 taylor coefficients
Matrix p4(1,601);//matrix with result for 4th degree polynomial evaluated at z
for (int i=0;i<601;i++)
{
p4(i)=nest(p4coeff,z(i));
}
p4.Write("p4.txt");//wriete results to text file
//same as above for 8th degree polynomial
Matrix p8coeff(1,9,coeff);
Matrix p8(1,601);
for (int i=0;i<601;i++)
{
p8(i)=nest(p8coeff,z(i));
}
p8.Write("p8.txt");
//same as above for 12th degree polynomial
Matrix p12coeff(1,13,coeff);
Matrix p12(1,601);
for (int i=0;i<601;i++)
{
p12(i)=nest(p12coeff,z(i));
}
p12.Write("p12.txt");
// all points are evaluated at cos(x)
Matrix f(1,601);
for (int i=0;i<601;i++)
{
f(i)=cos(z(i));
}
f.Write("f.txt");
//calculate relative error for the three taylor polynomials
Matrix err4(1,601);
for (int i=0;i<601;i++)
{
err4(i)=cos(z(i))-p4(i);
}
err4.Abs();
err4.Write("err4.txt");
Matrix err8(1,601);
for (int i=0;i<601;i++)
{
err8(i)=cos(z(i))-p8(i);
}
err8.Abs();
err8.Write("err8.txt");
Matrix err12(1,601);
for (int i=0;i<601;i++)
{
err12(i)=cos(z(i))-p12(i);
}
err12.Abs();
err12.Write("err12.txt");
z.Write("z.txt");
}
int main(){
Matrix a = Linspace(0.0, 5.0, 5, 1);
for(int i = 0; i < a.Size(); i++)
std::cout << a(i) << std::endl;
}
