Examples of EulerIntegrator

ca.nengo.dynamics.impl.EulerIntegrator
Euler's method of numerical integration: x(t+h) ~ x(t) + h*x'(t) TODO: test TODO: should there be some means for aborting early (aside from exceptions, e.g. if output converges to constant)? @author Bryan Tripp
org.apache.commons.math.ode.EulerIntegrator
This class implements a simple Euler integrator for Ordinary Differential Equations.
The Euler algorithm is the simplest one that can be used to integrate ordinary differential equations. It is a simple inversion of the forward difference expression : f'=(f(t+h)-f(t))/h which leads to f(t+h)=f(t)+hf'. The interpolation scheme used for dense output is the linear scheme already used for integration.

This algorithm looks cheap because it needs only one function evaluation per step. However, as it uses linear estimates, it needs very small steps to achieve high accuracy, and small steps lead to numerical errors and instabilities.

This algorithm is almost never used and has been included in this package only as a comparison reference for more useful integrators.
@see MidpointIntegrator @see ClassicalRungeKuttaIntegrator @see GillIntegrator @see ThreeEighthesIntegrator @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $ @since 1.2
org.apache.commons.math.ode.nonstiff.EulerIntegrator
This class implements a simple Euler integrator for Ordinary Differential Equations.
The Euler algorithm is the simplest one that can be used to integrate ordinary differential equations. It is a simple inversion of the forward difference expression : f'=(f(t+h)-f(t))/h which leads to f(t+h)=f(t)+hf'. The interpolation scheme used for dense output is the linear scheme already used for integration.

This algorithm looks cheap because it needs only one function evaluation per step. However, as it uses linear estimates, it needs very small steps to achieve high accuracy, and small steps lead to numerical errors and instabilities.

This algorithm is almost never used and has been included in this package only as a comparison reference for more useful integrators.
@see MidpointIntegrator @see ClassicalRungeKuttaIntegrator @see GillIntegrator @see ThreeEighthesIntegrator @version $Revision: 810196 $ $Date: 2009-09-01 21:47:46 +0200 (mar. 01 sept. 2009) $ @since 1.2

Examples of ca.nengo.dynamics.impl.EulerIntegrator

      public float[] f(float t, float[] u) {
        u[0] = Math.abs(u[0]);
        return super.f(t, u);
      }
    };
    return new BasicTermination(this, myEADynamics, new EulerIntegrator(.001f), SkeletalMuscle.EXCITATION_TERMINATION);
  }

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Examples of ca.nengo.dynamics.impl.EulerIntegrator

    //Plotter.plot(CEForceVelocity, vmax, .1f, -vmax, "CE Force-Velocity");
    //Plotter.plot(SEForceLength, 0f, rl*.001f, rl*.1f, "SE Force-Length");


    Dynamics d = new Dynamics(tauEA, 5000f, CEForceLength, CEForceVelocity, SEForceLength, false);
    d.setState(new float[]{.001f, rl});
    Integrator i = new EulerIntegrator(.0001f);


//    TimeSeries input = new TimeSeriesImpl(new float[]{0f, 1f},
//        new float[][]{new float[]{1, rl, 0f}, new float[]{1, rl, 0f}},
//        new Units[]{Units.UNK, Units.M, Units.M_PER_S});
    TimeSeries input = new TimeSeriesImpl(new float[]{0f, .001f, .5f},
        new float[][]{new float[]{1, rl, 0f}, new float[]{0, rl, 0f}, new float[]{0, rl, 0f}},
        new Units[]{Units.UNK, Units.M, Units.M_PER_S});


    long startTime = System.currentTimeMillis();
    TimeSeries output = i.integrate(d, input);
    ourLogger.info("Elapsed time: " + (System.currentTimeMillis() - startTime));


    Plotter.plot(output, "Force");
  }

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Examples of ca.nengo.dynamics.impl.EulerIntegrator

  public static TimeSeries filter(TimeSeries series, float tau) {
    float[] times = series.getTimes();
    float meanStepSize = (times[times.length-1] - times[1]) / times.length;
    float integrationStepSize = Math.min(meanStepSize/2f, tau/2f);
    
    Integrator integrator = new EulerIntegrator(integrationStepSize);
    
    int dim = series.getDimension();
    float[] A = new float[dim];
    float[][] B = new float[dim][];
    float[][] C = new float[dim][];
    for (int i = 0; i < dim; i++) {
      A[i] = -1f / tau;
      B[i] = new float[dim];
      B[i][i] = 1f;
      C[i] = new float[dim];
      C[i][i] = 1f / tau;
    }    
    LTISystem filter = new SimpleLTISystem(A, B, C, new float[dim], series.getUnits());
    
    return integrator.integrate(filter, series);    
  }

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Examples of ca.nengo.dynamics.impl.EulerIntegrator


    //functional test ...
    public static void main(String[] args) {
        float tau = .01f;
        DynamicalSystem dynamics = new SimpleLTISystem(new float[]{-1f/tau}, new float[][]{new float[]{1f/tau}}, MU.I(1), new float[1], new Units[]{Units.UNK});
        Integrator integrator = new EulerIntegrator(.0001f);
//      Noise noise = NoiseFactory.makeRandomNoise(1000, new GaussianPDF(0, 1));
        Noise noise = NoiseFactory.makeRandomNoise(1000, new GaussianPDF(0, 1), dynamics, integrator);
//      Noise noise = NoiseFactory.makeNullNoise(1);
//      Noise noise = NoiseFactory.makeExplicitNoise(new Function[]{new FourierFunction(1, 10, 1, -1)});

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Examples of ca.nengo.dynamics.impl.EulerIntegrator


  /**
   * Uses default parameters to allow later configuration.
   */
  public DynamicalSystemSpikeGenerator() {
    this(getDefaultDynamics(), new EulerIntegrator(.001f), 0, 0.99f, .002f, new float[]{0, 1}, .5f);
  }

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Examples of ca.nengo.dynamics.impl.EulerIntegrator

    myReuseApproximators = true;
    myUnscaledEvalPoints = evalPoints;
    setRadii(radii);
    myFixedModes = null;


    myDirectModeIntegrator = new EulerIntegrator(.001f);


    myUseGPU = true;
  }

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Examples of ca.nengo.dynamics.impl.EulerIntegrator

      }
      biasEncoders[j] = max;
    }


    float baseTauPSC = baseTermination.getTau();
    EulerIntegrator integrator = new EulerIntegrator(Math.min(interneuronTauPSC, baseTauPSC) / 10f);


    float scale = 1 / interneuronTauPSC; //output scaling to make impulse integral = 1
    LinearSystem interneuronDynamics = new SimpleLTISystem(
        new float[]{-1f/interneuronTauPSC},
        new float[][]{new float[]{1f}},

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Examples of ca.nengo.dynamics.impl.EulerIntegrator

                new float[][]{new float[]{scale}},
                new float[]{0f},
                new Units[]{Units.UNK}
        );


        EulerIntegrator integrator = new EulerIntegrator(tauPSC / 10f);


        DecodedTermination result = new DecodedTermination(this, name, matrix, dynamics, integrator);
        if (isModulatory) {
            result.setModulatory(isModulatory);
        }

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Examples of ca.nengo.dynamics.impl.EulerIntegrator

            if (Math.abs(eigenvalues[i]) > fastest) {
                fastest = Math.abs(eigenvalues[i]);
            }
        }


        EulerIntegrator integrator = new EulerIntegrator(1f / (10f * (float) fastest));


        DecodedTermination result = new DecodedTermination(this, name, matrix, dynamics, integrator);
        if (isModulatory) {
            result.setModulatory(isModulatory);
        }

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Examples of ca.nengo.dynamics.impl.EulerIntegrator

    myNodes = nodes;
    myNodeOrigin = nodeOrigin;
    myFunctions = functions;
    myDecoders = findDecoders(nodes, functions, approximator);
    myMode = SimulationMode.DEFAULT;
    myIntegrator = new EulerIntegrator(.001f);


    reset(false);
  }

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