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/* Copyright (c) 2004 Tim Blechmann. */
/* For information on usage and redistribution, and for a DISCLAIMER OF ALL */
/* WARRANTIES, see the file, "COPYING" in this distribution. */
/* */
/* */
/* him~ is a semi-classicical simulation of an hydrogen atom in a magnetic field*/
/* */
/* him~ uses the flext C++ layer for Max/MSP and PD externals. */
/* get it at http://www.parasitaere-kapazitaeten.de/PD/ext */
/* thanks to Thomas Grill */
/* */
/* him~ is based on code provided in the lecture "physik auf dem computer 1" */
/* held by joerg main during the winter semester 2003/04 at the university */
/* stuttgart ... many thanks to him and his assistant ralf habel */
/* */
/* */
/* */
/* This program is free software; you can redistribute it and/or */
/* modify it under the terms of the GNU General Public License */
/* as published by the Free Software Foundation; either version 2 */
/* of the License, or (at your option) any later version. */
/* */
/* See file LICENSE for further informations on licensing terms. */
/* */
/* This program is distributed in the hope that it will be useful, */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the */
/* GNU General Public License for more details. */
/* */
/* You should have received a copy of the GNU General Public License */
/* along with this program; if not, write to the Free Software */
/* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */
/* */
/* Based on PureData by Miller Puckette and others. */
/* */
/* */
/* */
/* coded while listening to: Elliott Sharp: The Velocity Of Hue */
/* Fred Frith: Traffic Continues */
/* Nmperign: Twisted Village */
/* Frank Lowe: Black Beings */
/* */
#include <flext.h>
#include <cstdlib>
#include <cmath>
#if !defined(FLEXT_VERSION) || (FLEXT_VERSION < 401)
#error upgrade your flext version!!!!!!
#endif
#define NUMB_EQ 4
class him: public flext_dsp
{
FLEXT_HEADER(him,flext_dsp);
public:
him(int argc, t_atom *argv);
protected:
virtual void m_signal (int n, float *const *in, float *const *out);
virtual void m_dsp (int n, float *const *in, float *const *out);
void set_mu(t_float);
void set_muv(t_float);
void set_nu(t_float);
void set_nuv(t_float);
void set_etilde(t_float);
void set_dt(t_float);
void set_regtime(bool);
void state();
void reset();
private:
// contains DGL-System
t_float deriv(t_float x[],int eq);
// 4th order Runge Kutta update of the dynamical variables
void runge_kutta_4(t_float dt);
//these are our data
t_float data[4]; //mu, muv, nu, nuv (semi-parabolische koordinaten)
t_float E;
//and these our settings
t_float dt;
bool regtime; //if true "regularisierte zeit"
bool xfade;
t_float newE;
t_float newdt;
bool newsystem;
bool newregtime;
t_float * m_fader;
//Callbacks
FLEXT_CALLBACK_1(set_mu,t_float);
FLEXT_CALLBACK_1(set_muv,t_float);
FLEXT_CALLBACK_1(set_nu,t_float);
FLEXT_CALLBACK_1(set_nuv,t_float);
FLEXT_CALLBACK_1(set_etilde,t_float);
FLEXT_CALLBACK_1(set_dt,t_float);
FLEXT_CALLBACK_1(set_regtime,bool);
FLEXT_CALLBACK(state);
FLEXT_CALLBACK(reset);
//reset mus / nus
void reset_nuv()
{
data[3]= 0.5*sqrt( - (4*data[1]*data[1]) -
( data[0]*data[0]*data[1]*data[1]*data[1]*data[1])
+ (8*E*data[0]) - (8*E*data[2]) -
(data[0]*data[0]*data[0]*data[0]*data[1]*data[1])
+ 16);
if (fabs((data[3]))<1e-5)
data[3]=0;
}
void reset_muv()
{
data[1]= 0.5*sqrt( - (4*data[3]*data[3]) -
( data[0]*data[0]*data[1]*data[1]*data[1]*data[1])
+ (8*E*data[0]) - (8*E*data[2]) -
(data[0]*data[0]*data[0]*data[0]*data[1]*data[1])
+ 16);
if (fabs((data[1]))<1e-5)
data[1]=0;
}
};
FLEXT_LIB_DSP_V("him~",him)
him::him(int argc, t_atom *argv)
{
AddInAnything();
AddOutSignal();
AddOutSignal();
AddOutSignal();
AddOutSignal();
AddOutSignal();
AddOutSignal();
FLEXT_ADDMETHOD_F(0,"mu",set_mu);
FLEXT_ADDMETHOD_F(0,"muv",set_muv);
FLEXT_ADDMETHOD_F(0,"nu",set_nu);
FLEXT_ADDMETHOD_F(0,"nuv",set_nuv);
FLEXT_ADDMETHOD_F(0,"e",set_etilde);
FLEXT_ADDMETHOD_F(0,"dt",set_dt);
FLEXT_ADDMETHOD_B(0,"regtime",set_regtime);
FLEXT_ADDMETHOD_(0,"state",state);
FLEXT_ADDMETHOD_(0,"reset",reset);
//beginning values
if (argc==1)
E=atom_getfloat(argv);
else
E= -float(rand())/float(RAND_MAX);
reset();
state();
//default mode
regtime=true;
dt=0.01;
}
inline t_float him::deriv(t_float * x, int eq)
{
t_float result;
// set DGL-System here
if (eq == 0) result = x[1];
if (eq == 1) result = 2*E*x[0]-0.25*x[0]*x[2]*x[2]*(2*x[0]*x[0]+x[2]*x[2]);
if (eq == 2) result = x[3];
if (eq == 3) result = 2*E*x[2]-0.25*x[2]*x[0]*x[0]*(2*x[2]*x[2]+x[0]*x[0]);
return result;
}
inline void him::runge_kutta_4(t_float dt)
{
t_float k1[NUMB_EQ],k2[NUMB_EQ],k3[NUMB_EQ],k4[NUMB_EQ];
t_float temp1[NUMB_EQ], temp2[NUMB_EQ], temp3[NUMB_EQ];
for(int i=0;i<=NUMB_EQ-1;i++) // iterate over equations
{
k1[i] = dt * deriv(data,i);
temp1[i] = data[i] + 0.5*k1[i];
}
for(int i=0;i<=NUMB_EQ-1;i++)
{
k2[i] = dt * deriv(temp1,i);
temp2[i] = data[i] + 0.5*k2[i];
}
for(int i=0;i<=NUMB_EQ-1;i++)
{
k3[i] = dt * deriv(temp2,i);
temp3[i] = data[i] + k3[i];
}
for(int i=0;i<=NUMB_EQ-1;i++)
{
k4[i] = dt * deriv(temp3,i);
data[i] = data[i] + (k1[i] + (2.*(k2[i]+k3[i])) + k4[i])/6.;
// we don't want to experience denormals in the next step */
if(fabs((data[i]))<1e-5)
data[i]=0;
}
/*
the system might become unstable ... in this case, we'll request a new system
*/
for(int i=0;i<=NUMB_EQ-1;i++)
{
if(data[i]>2)
{
xfade = newsystem = true;
data[i] = 2;
}
if(data[i]<-2)
{
xfade = newsystem = true;
data[i] = -2;
}
}
}
void him::m_signal(int n, t_float *const *in, t_float *const *out)
{
t_float * out0 = out[0];
t_float * out1 = out[1];
t_float * out2 = out[2];
t_float * out3 = out[3];
t_float * out4 = out[4];
t_float * out5 = out[5];
if (regtime)
{
for (int i=0;i!=n;++i)
{
runge_kutta_4(dt);
(*(out0)++)=data[0];
(*(out1)++)=data[1];
(*(out2)++)=data[2];
(*(out3)++)=data[3];
(*(out4)++)=data[0]*data[2];
(*(out5)++)=(data[0]*data[0]-data[2]*data[2])*0.5;
}
}
else
{
for (int i=0;i!=n;++i)
{
runge_kutta_4(dt/(2*sqrt(data[0]*data[0]+data[2]*data[2])));
(*(out0)++)=data[0];
(*(out1)++)=data[1];
(*(out2)++)=data[2];
(*(out3)++)=data[3];
(*(out4)++)=data[0]*data[2];
(*(out5)++)=(data[0]*data[0]-data[2]*data[2])*0.5;
}
}
if (xfade)
{
/* fading */
out0 = out[0];
out1 = out[1];
out2 = out[2];
out3 = out[3];
out4 = out[4];
out5 = out[5];
t_float * fader = m_fader + n - 1;
for (int i=0;i!=n;++i)
{
(*(out0)++) *= *fader;
(*(out1)++) *= *fader;
(*(out2)++) *= *fader;
(*(out3)++) *= *fader;
(*(out4)++) *= *fader;
(*(out5)++) *= *fader--;
}
if (newsystem)
{
reset();
newsystem = false;
}
E = newE;
dt = newdt;
regtime = newregtime;
out0 = out[0];
out1 = out[1];
out2 = out[2];
out3 = out[3];
out4 = out[4];
out5 = out[5];
fader = m_fader;
if (regtime)
{
for (int i=0;i!=n;++i)
{
runge_kutta_4(dt);
(*(out0)++)+= data[0]* *fader;
(*(out1)++)+= data[1]* *fader;
(*(out2)++)+= data[2]* *fader;
(*(out3)++)+= data[3]* *fader;
(*(out4)++)+= data[0]*data[2]* *fader;
(*(out5)++)+= (data[0]*data[0]-data[2]*data[2])*0.5* *fader++;
}
}
else
{
for (int i=0;i!=n;++i)
{
runge_kutta_4(dt/(2*sqrt(data[0]*data[0]+data[2]*data[2])));
(*(out0)++)+= data[0]* *fader;
(*(out1)++)+= data[1]* *fader;
(*(out2)++)+= data[2]* *fader;
(*(out3)++)+= data[3]* *fader;
(*(out4)++)+= data[0]*data[2]* *fader;
(*(out5)++)+= (data[0]*data[0]-data[2]*data[2])*0.5* *fader++;
}
}
xfade = false;
}
}
void him::m_dsp(int n, t_float *const *in, t_float *const *out)
{
m_fader = new t_float[n];
t_float on = 1.f/(n-1);
t_float value = 0;
t_float* localfader = m_fader;
while (n--)
{
*localfader = value;
value += on;
++localfader;
}
xfade = false;
}
void him::set_mu(t_float f)
{
data[0]=f;
reset_nuv();
}
void him::set_muv(t_float f)
{
data[1]=f;
reset_nuv();
}
void him::set_nu(t_float f)
{
data[3]=f;
reset_nuv();
}
void him::set_nuv(t_float f)
{
data[3]=f;
reset_muv();
}
void him::set_etilde(t_float f)
{
newE=f;
xfade = true;
//reset_nuv();
}
void him::set_dt(t_float f)
{
newdt=f;
xfade = true;
}
void him::set_regtime(bool b)
{
newregtime=b;
xfade = true;
}
void him::state()
{
post("mu %f",data[0]);
post("mus %f",data[1]);
post("nu %f",data[2]);
post("nus %f",data[3]);
post("etilde %f",E);
}
void him::reset()
{
data[0]=float(rand())/float(RAND_MAX);
data[1]=float(rand())/float(RAND_MAX);
data[2]=float(rand())/float(RAND_MAX);
reset_nuv();
}
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