public static WrappedGaussian AngleAverageLogarithm([SkipIfUniform] VectorGaussian rotate, double x, double y)
{
if (rotate.Dimension != 2)
{
throw new ArgumentException("rotate.Dimension (" + rotate.Dimension + ") != 2");
}
double rPrec = rotate.Precision[0, 0];
if (rotate.Precision[0, 1] != 0)
{
throw new ArgumentException("rotate.Precision is not diagonal");
}
if (rotate.Precision[1, 1] != rPrec)
{
throw new ArgumentException("rotate.Precision is not spherical");
}
#if false
Vector rotateMean = rotate.GetMean();
double a = x * rotateMean[0] + y * rotateMean[1];
double b = x * rotateMean[1] - y * rotateMean[0];
#else
double rotateMean0 = rotate.MeanTimesPrecision[0] / rotate.Precision[0, 0];
double rotateMean1 = rotate.MeanTimesPrecision[1] / rotate.Precision[1, 1];
double a = x * rotateMean0 + y * rotateMean1;
double b = x * rotateMean1 - y * rotateMean0;
#endif
double c = Math.Sqrt(a * a + b * b) * rPrec;
double angle0 = Math.Atan2(b, a);
// the exact conditional is exp(c*cos(angle - angle0)) which is a von Mises distribution.
// we will approximate this with a Gaussian lower bound that makes contact at the mode.
WrappedGaussian result = WrappedGaussian.Uniform();
result.Gaussian = Gaussian.FromMeanAndPrecision(angle0, c);
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="DoublePlusOp"]/message_doc[@name="AAverageConditional(WrappedGaussian, double)"]/*'/>
public static WrappedGaussian AAverageConditional([SkipIfUniform] WrappedGaussian sum, double b)
{
WrappedGaussian result = WrappedGaussian.Uniform(sum.Period);
result.Gaussian = AAverageConditional(sum.Gaussian, b);
result.Normalize();
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="DoublePlusOp"]/message_doc[@name="SumAverageConditional(WrappedGaussian, double)"]/*'/>
public static WrappedGaussian SumAverageConditional([SkipIfUniform] WrappedGaussian a, double b)
{
WrappedGaussian result = WrappedGaussian.Uniform(a.Period);
result.Gaussian = SumAverageConditional(a.Gaussian, b);
result.Normalize();
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PlusWrappedGaussianOp"]/message_doc[@name="AAverageLogarithm(WrappedGaussian, double)"]/*'/>
public static WrappedGaussian AAverageLogarithm([SkipIfUniform] WrappedGaussian sum, double b)
{
WrappedGaussian result = WrappedGaussian.Uniform(sum.Period);
result.Gaussian = DoublePlusVmpOp.AAverageLogarithm(sum.Gaussian, b);
result.Normalize();
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="DoublePlusOp"]/message_doc[@name="AAverageConditional(WrappedGaussian, WrappedGaussian)"]/*'/>
public static WrappedGaussian AAverageConditional([SkipIfUniform] WrappedGaussian sum, [SkipIfUniform] WrappedGaussian b)
{
if (sum.Period != b.Period)
{
throw new ArgumentException("sum.Period (" + sum.Period + ") != b.Period (" + b.Period + ")");
}
WrappedGaussian result = WrappedGaussian.Uniform(sum.Period);
result.Gaussian = AAverageConditional(sum.Gaussian, b.Gaussian);
result.Normalize();
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PlusWrappedGaussianOp"]/message_doc[@name="SumAverageConditional(WrappedGaussian, WrappedGaussian)"]/*'/>
public static WrappedGaussian SumAverageConditional([SkipIfUniform] WrappedGaussian a, [SkipIfUniform] WrappedGaussian b)
{
if (a.Period != b.Period)
{
throw new ArgumentException("a.Period (" + a.Period + ") != b.Period (" + b.Period + ")");
}
WrappedGaussian result = WrappedGaussian.Uniform(a.Period);
result.Gaussian = DoublePlusOp.SumAverageConditional(a.Gaussian, b.Gaussian);
result.Normalize();
return(result);
}
public static WrappedGaussian AngleAverageLogarithm([SkipIfUniform] VectorGaussian rotate, double x, double y, [Proper] WrappedGaussian angle)
{
if (rotate.Dimension != 2)
{
throw new ArgumentException("rotate.Dimension (" + rotate.Dimension + ") != 2");
}
double rPrec = rotate.Precision[0, 0];
if (rotate.Precision[0, 1] != 0)
{
throw new ArgumentException("rotate.Precision is not diagonal");
}
if (rotate.Precision[1, 1] != rPrec)
{
throw new ArgumentException("rotate.Precision is not spherical");
}
Vector rotateMean = rotate.GetMean();
double a = x * rotateMean[0] + y * rotateMean[1];
double b = x * rotateMean[1] - y * rotateMean[0];
double c = Math.Sqrt(a * a + b * b) * rPrec;
double angle0 = Math.Atan2(b, a);
// the exact conditional is exp(c*cos(angle - angle0)) which is a von Mises distribution.
// we will approximate this with a Gaussian lower bound that makes contact at the current angleMean.
if (angle.Period != 2 * Math.PI)
{
throw new ArgumentException("angle.Period (" + angle.Period + ") != 2*PI (" + 2 * Math.PI + ")");
}
double angleMean = angle.Gaussian.GetMean();
double angleDiff = angleMean - angle0;
double df = -c *Math.Sin(angleDiff);
double precision = c * Math.Abs(Math.Cos(angleDiff * 0.5)); // ensures a lower bound
double meanTimesPrecision = angleMean * precision + df;
if (double.IsNaN(meanTimesPrecision))
{
throw new ApplicationException("result is nan");
}
WrappedGaussian result = WrappedGaussian.Uniform(angle.Period);
result.Gaussian = Gaussian.FromNatural(meanTimesPrecision, precision);
return(result);
}