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Feature/allow mixture of bounded and unbounded fit parameters #932

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Feature/allow mixture of bounded and unbounded fit parameters #932

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c804e80
Remove checks for parameter bounds finiteness
Jul 4, 2022
deffc53
Handle non-finite bounds in parameter projection
Jul 4, 2022
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155 changes: 6 additions & 149 deletions src/Numerics/Optimization/NonlinearMinimizerBase.cs
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Original file line number Diff line number Diff line change
@@ -1,5 +1,6 @@
using MathNet.Numerics.LinearAlgebra;
using System;
using System.Collections.Generic;
using System.Linq;

namespace MathNet.Numerics.Optimization
Expand Down Expand Up @@ -58,20 +59,12 @@ protected void ValidateBounds(Vector<double> parameters, Vector<double> lowerBou
throw new ArgumentNullException(nameof(parameters));
}

if (lowerBound != null && lowerBound.Count(x => double.IsInfinity(x) || double.IsNaN(x)) > 0)
{
throw new ArgumentException("The lower bounds must be finite.");
}
if (lowerBound != null && lowerBound.Count != parameters.Count)
{
throw new ArgumentException("The lower bounds can't have different size from the parameters.");
}
LowerBound = lowerBound;

if (upperBound != null && upperBound.Count(x => double.IsInfinity(x) || double.IsNaN(x)) > 0)
{
throw new ArgumentException("The upper bounds must be finite.");
}
if (upperBound != null && upperBound.Count != parameters.Count)
{
throw new ArgumentException("The upper bounds can't have different size from the parameters.");
Expand Down Expand Up @@ -161,150 +154,14 @@ protected double EvaluateFunction(IObjectiveModel objective, Vector<double> Pint
// Except when it is initial guess, the parameters argument is always internal parameter.
// So, first map the parameters argument to the external parameters in order to calculate function values.

protected Vector<double> ProjectToInternalParameters(Vector<double> Pext)
{
var Pint = Pext.Clone();

if (LowerBound != null && UpperBound != null)
{
for (int i = 0; i < Pext.Count; i++)
{
Pint[i] = Math.Asin((2.0 * (Pext[i] - LowerBound[i]) / (UpperBound[i] - LowerBound[i])) - 1.0);
}

return Pint;
}

if (LowerBound != null && UpperBound == null)
{
for (int i = 0; i < Pext.Count; i++)
{
Pint[i] = (Scales == null)
? Math.Sqrt(Math.Pow(Pext[i] - LowerBound[i] + 1.0, 2) - 1.0)
: Math.Sqrt(Math.Pow((Pext[i] - LowerBound[i]) / Scales[i] + 1.0, 2) - 1.0);
}

return Pint;
}

if (LowerBound == null && UpperBound != null)
{
for (int i = 0; i < Pext.Count; i++)
{
Pint[i] = (Scales == null)
? Math.Sqrt(Math.Pow(UpperBound[i] - Pext[i] + 1.0, 2) - 1.0)
: Math.Sqrt(Math.Pow((UpperBound[i] - Pext[i]) / Scales[i] + 1.0, 2) - 1.0);
}

return Pint;
}

if (Scales != null)
{
for (int i = 0; i < Pext.Count; i++)
{
Pint[i] = Pext[i] / Scales[i];
}

return Pint;
}

return Pint;
}

protected Vector<double> ProjectToExternalParameters(Vector<double> Pint)
{
var Pext = Pint.Clone();

if (LowerBound != null && UpperBound != null)
{
for (int i = 0; i < Pint.Count; i++)
{
Pext[i] = LowerBound[i] + (UpperBound[i] / 2.0 - LowerBound[i] / 2.0) * (Math.Sin(Pint[i]) + 1.0);
}

return Pext;
}

if (LowerBound != null && UpperBound == null)
{
for (int i = 0; i < Pint.Count; i++)
{
Pext[i] = (Scales == null)
? LowerBound[i] + Math.Sqrt(Pint[i] * Pint[i] + 1.0) - 1.0
: LowerBound[i] + Scales[i] * (Math.Sqrt(Pint[i] * Pint[i] + 1.0) - 1.0);
}

return Pext;
}

if (LowerBound == null && UpperBound != null)
{
for (int i = 0; i < Pint.Count; i++)
{
Pext[i] = (Scales == null)
? UpperBound[i] - Math.Sqrt(Pint[i] * Pint[i] + 1.0) + 1.0
: UpperBound[i] - Scales[i] * (Math.Sqrt(Pint[i] * Pint[i] + 1.0) - 1.0);
}

return Pext;
}

if (Scales != null)
{
for (int i = 0; i < Pint.Count; i++)
{
Pext[i] = Pint[i] * Scales[i];
}

return Pext;
}
private ProjectableParameters Projectable(IEnumerable<double> parameterValues) =>
new ProjectableParameters(parameterValues, LowerBound, UpperBound, Scales);

return Pext;
}
protected Vector<double> ProjectToInternalParameters(Vector<double> Pext) => Projectable(Pext).ToInternal();

protected Vector<double> ScaleFactorsOfJacobian(Vector<double> Pint)
{
var scale = Vector<double>.Build.Dense(Pint.Count, 1.0);
protected Vector<double> ProjectToExternalParameters(Vector<double> Pint) => Projectable(Pint).ToExternal();

if (LowerBound != null && UpperBound != null)
{
for (int i = 0; i < Pint.Count; i++)
{
scale[i] = (UpperBound[i] - LowerBound[i]) / 2.0 * Math.Cos(Pint[i]);
}
return scale;
}

if (LowerBound != null && UpperBound == null)
{
for (int i = 0; i < Pint.Count; i++)
{
scale[i] = (Scales == null)
? Pint[i] / Math.Sqrt(Pint[i] * Pint[i] + 1.0)
: Scales[i] * Pint[i] / Math.Sqrt(Pint[i] * Pint[i] + 1.0);
}
return scale;
}

if (LowerBound == null && UpperBound != null)
{
for (int i = 0; i < Pint.Count; i++)
{
scale[i] = (Scales == null)
? -Pint[i] / Math.Sqrt(Pint[i] * Pint[i] + 1.0)
: -Scales[i] * Pint[i] / Math.Sqrt(Pint[i] * Pint[i] + 1.0);
}
return scale;
}

if (Scales != null)
{
return Scales;
}

return scale;
}
protected Vector<double> ScaleFactorsOfJacobian(Vector<double> Pint) => Projectable(Pint).JacobianScaleFactors();

#endregion Projection of Parameters
}
Expand Down
88 changes: 88 additions & 0 deletions src/Numerics/Optimization/ProjectableParameters.cs
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Original file line number Diff line number Diff line change
@@ -0,0 +1,88 @@
using System;
using System.Collections.Generic;
using System.Linq;
using MathNet.Numerics.LinearAlgebra;
using MathNet.Numerics.LinearAlgebra.Double;

namespace MathNet.Numerics.Optimization
{
internal class ProjectableParameters
{
private readonly IEnumerable<ProjectableParameter> _parameters;

internal ProjectableParameters(IEnumerable<double> values, IList<double> lowerBounds, IList<double> upperBounds,
IList<double> scales)
{
_parameters = values.Select((value, index) =>
new ProjectableParameter(value, lowerBounds?[index], upperBounds?[index], scales?[index]));
}

internal Vector<double> ToInternal() =>
DenseVector.OfEnumerable(_parameters.Select(p => p.ToInternal()));

internal Vector<double> ToExternal() =>
DenseVector.OfEnumerable(_parameters.Select(p => p.ToExternal()));

internal Vector<double> JacobianScaleFactors() =>
DenseVector.OfEnumerable(_parameters.Select(p => p.JacobianScaleFactor()));
}


internal class ProjectableParameter
{
private readonly double _value;
private readonly double _lowerBound;
private readonly double _upperBound;
private readonly double _scaleFactor;

internal ProjectableParameter(double value, double? lowerBound, double? upperBound, double? scaleFactor)
{
_value = value;
_lowerBound = lowerBound ?? double.NegativeInfinity;
_upperBound = upperBound ?? double.PositiveInfinity;
_scaleFactor = scaleFactor ?? 1;
}

internal double ToInternal()
{
if (_lowerBound.IsFinite() && _upperBound.IsFinite())
return Math.Asin(2 * (_value - _lowerBound) / (_upperBound - _lowerBound) - 1);

if (_lowerBound.IsFinite())
return Math.Sqrt(Math.Pow((_value - _lowerBound) / _scaleFactor + 1, 2) - 1);

if (_upperBound.IsFinite())
return Math.Sqrt(Math.Pow((_upperBound - _value) / _scaleFactor + 1, 2) - 1);

return _value / _scaleFactor;
}

internal double ToExternal()
{
if (_lowerBound.IsFinite() && _upperBound.IsFinite())
return _lowerBound + (_upperBound / 2 - _lowerBound / 2) * (Math.Sin(_value) + 1);

if (_lowerBound.IsFinite())
return _lowerBound + _scaleFactor * (Math.Sqrt(_value * _value + 1) - 1);

if (_upperBound.IsFinite())
return _upperBound - _scaleFactor * (Math.Sqrt(_value * _value + 1) - 1);

return _value * _scaleFactor;
}

internal double JacobianScaleFactor()
{
if (_lowerBound.IsFinite() && _upperBound.IsFinite())
return (_upperBound - _lowerBound) / 2 * Math.Cos(_value);

if (_lowerBound.IsFinite())
return _scaleFactor * _value / Math.Sqrt(_value * _value + 1);

if (_upperBound.IsFinite())
return -_scaleFactor * _value / Math.Sqrt(_value * _value + 1);

return _scaleFactor;
}
}
}