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@@ -3,10 +3,14 @@ |
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namespace rack { |
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typedef void (*stepCallback)(float x, const float y[], float dydt[]); |
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/** The callback function `f` in each of these stepping functions must have the signature |
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void f(float x, const float y[], float dydt[]) |
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A capturing lambda is ideal for this. |
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*/ |
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/** Solve an ODE system using the 1st order Euler method */ |
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inline void stepEuler(stepCallback f, float x, float dx, float y[], int len) { |
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/** Solves an ODE system using the 1st order Euler method */ |
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template<typename F> |
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void stepEuler(float x, float dx, float y[], int len, F f) { |
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float k[len]; |
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f(x, y, k); |
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@@ -15,8 +19,28 @@ inline void stepEuler(stepCallback f, float x, float dx, float y[], int len) { |
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} |
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} |
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/** Solve an ODE system using the 4th order Runge-Kutta method */ |
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inline void stepRK4(stepCallback f, float x, float dx, float y[], int len) { |
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/** Solves an ODE system using the 2nd order Runge-Kutta method */ |
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template<typename F> |
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void stepRK2(float x, float dx, float y[], int len, F f) { |
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float k1[len]; |
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float k2[len]; |
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float yi[len]; |
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f(x, y, k1); |
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for (int i = 0; i < len; i++) { |
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yi[i] = y[i] + k1[i] * dx / 2.f; |
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} |
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f(x + dx / 2.f, yi, k2); |
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for (int i = 0; i < len; i++) { |
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y[i] += dx * k2[i]; |
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} |
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} |
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/** Solves an ODE system using the 4th order Runge-Kutta method */ |
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template<typename F> |
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void stepRK4(float x, float dx, float y[], int len, F f) { |
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float k1[len]; |
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float k2[len]; |
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float k3[len]; |
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@@ -26,14 +50,14 @@ inline void stepRK4(stepCallback f, float x, float dx, float y[], int len) { |
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f(x, y, k1); |
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for (int i = 0; i < len; i++) { |
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yi[i] = y[i] + k1[i] * dx / 2.0; |
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yi[i] = y[i] + k1[i] * dx / 2.f; |
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} |
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f(x + dx / 2.0, yi, k2); |
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f(x + dx / 2.f, yi, k2); |
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for (int i = 0; i < len; i++) { |
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yi[i] = y[i] + k2[i] * dx / 2.0; |
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yi[i] = y[i] + k2[i] * dx / 2.f; |
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} |
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f(x + dx / 2.0, yi, k3); |
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f(x + dx / 2.f, yi, k3); |
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for (int i = 0; i < len; i++) { |
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yi[i] = y[i] + k3[i] * dx; |
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@@ -41,7 +65,7 @@ inline void stepRK4(stepCallback f, float x, float dx, float y[], int len) { |
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f(x + dx, yi, k4); |
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for (int i = 0; i < len; i++) { |
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y[i] += dx * (k1[i] + 2.0 * k2[i] + 2.0 * k3[i] + k4[i]) / 6.0; |
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y[i] += dx * (k1[i] + 2.f * k2[i] + 2.f * k3[i] + k4[i]) / 6.f; |
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} |
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} |
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