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-rw-r--r--Master/texmf/asymptote/ode.asy73
1 files changed, 55 insertions, 18 deletions
diff --git a/Master/texmf/asymptote/ode.asy b/Master/texmf/asymptote/ode.asy
index 77ab8d6e589..0b88060e081 100644
--- a/Master/texmf/asymptote/ode.asy
+++ b/Master/texmf/asymptote/ode.asy
@@ -244,17 +244,31 @@ real adjust(real h, real error, real tolmin, real tolmax, RKTableau tableau)
return h;
}
+struct solution
+{
+ real[] t;
+ real[] y;
+}
+
+void write(solution S)
+{
+ for(int i=0; i < S.t.length; ++i)
+ write(S.t[i],S.y[i]);
+}
+
// Integrate dy/dt+cy=f(t,y) from a to b using initial conditions y,
// specifying either the step size h or the number of steps n.
-real[] integrate(real y, real c=0, real g(real t, real y), real a, real b=a,
- real h=0, int n=0, bool dynamic=false, real tolmin=0,
- real tolmax=0, real dtmin=0, real dtmax=realMax,
- RKTableau tableau, bool verbose=false)
+solution integrate(real y, real c=0, real g(real t, real y), real a, real b=a,
+ real h=0, int n=0, bool dynamic=false, real tolmin=0,
+ real tolmax=0, real dtmin=0, real dtmax=realMax,
+ RKTableau tableau, bool verbose=false)
{
- real[] Y={y};
+ solution S;
+ S.t=new real[] {a};
+ S.y=new real[]{y};
if(h == 0) {
- if(b == a) return Y;
+ if(b == a) return S;
if(n == 0) abort("Either n or h must be specified");
else h=(b-a)/n;
}
@@ -302,30 +316,49 @@ real[] integrate(real y, real c=0, real g(real t, real y), real a, real b=a,
if(h >= dt) {
t += dt;
y=y0+highOrder;
- Y.push(y);
+ S.t.push(t);
+ S.y.push(y);
f0=f1;
}
h=min(max(h,dtmin),dtmax);
} else {
t += h;
y=y0+highOrder;
- Y.push(y);
+ S.y.push(y);
}
}
- return Y;
+ return S;
+}
+
+struct Solution
+{
+ real[] t;
+ real[][] y;
+}
+
+void write(Solution S)
+{
+ for(int i=0; i < S.t.length; ++i) {
+ write(S.t[i],tab);
+ for(real y : S.y[i])
+ write(y,tab);
+ write();
+ }
}
// Integrate a set of equations, dy/dt=f(t,y), from a to b using initial
// conditions y, specifying either the step size h or the number of steps n.
-real[][] integrate(real[] y, real[] f(real t, real[] y), real a, real b=a,
+Solution integrate(real[] y, real[] f(real t, real[] y), real a, real b=a,
real h=0, int n=0, bool dynamic=false,
real tolmin=0, real tolmax=0, real dtmin=0,
real dtmax=realMax, RKTableau tableau, bool verbose=false)
{
- real[][] Y={copy(y)};
+ Solution S;
+ S.t=new real[] {a};
+ S.y=new real[][] {copy(y)};
if(h == 0) {
- if(b == a) return Y;
+ if(b == a) return S;
if(n == 0) abort("Either n or h must be specified");
else h=(b-a)/n;
}
@@ -366,17 +399,19 @@ real[][] integrate(real[] y, real[] f(real t, real[] y), real a, real b=a,
if(h >= dt) {
t += dt;
y += highOrder;
- Y.push(y);
+ S.t.push(t);
+ S.y.push(y);
f0=f1;
}
h=min(max(h,dtmin),dtmax);
} else {
t += h;
y += highOrder;
- Y.push(y);
+ S.t.push(t);
+ S.y.push(y);
}
}
- return Y;
+ return S;
}
real[][] finiteDifferenceJacobian(real[] f(real[]), real[] t,
@@ -408,12 +443,14 @@ real[] newton(int iterations=100, real[] f(real[]), real[][] jacobian(real[]),
}
real[] solveBVP(real[] f(real, real[]), real a, real b=a, real h=0, int n=0,
+ bool dynamic=false, real tolmin=0, real tolmax=0, real dtmin=0,
+ real dtmax=realMax, RKTableau tableau, bool verbose=false,
real[] initial(real[]), real[] discrepancy(real[]),
- real[] guess, RKTableau tableau, int iterations=100)
+ real[] guess, int iterations=100)
{
real[] g(real[] t) {
- real[][] y=integrate(initial(t),f,a,b,h,n,tableau);
- return discrepancy(y[y.length-1]);
+ real[][] y=integrate(initial(t),f,a,b,h,n,dynamic,tolmin,tolmax,dtmin,dtmax,
+ tableau,verbose).y;return discrepancy(y[y.length-1]);
}
real[][] jacobian(real[] t) {return finiteDifferenceJacobian(g,t);}
return initial(newton(iterations,g,jacobian,guess));