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@ -67,45 +67,45 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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/// <summary>
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/// <summary>
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/// The default number of starting vectors.
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/// The default number of starting vectors.
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/// </summary>
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/// </summary>
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private const int DefaultNumberOfStartingVectors = 50; |
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const int DefaultNumberOfStartingVectors = 50; |
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/// <summary>
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/// <summary>
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/// The status used if there is no status, i.e. the solver hasn't run yet and there is no
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/// The status used if there is no status, i.e. the solver hasn't run yet and there is no
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/// iterator.
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/// iterator.
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/// </summary>
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/// </summary>
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private static readonly ICalculationStatus DefaultStatus = new CalculationIndetermined(); |
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static readonly ICalculationStatus DefaultStatus = new CalculationIndetermined(); |
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/// <summary>
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/// <summary>
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/// The preconditioner that will be used. Can be set to <see langword="null" />, in which case the default
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/// The preconditioner that will be used. Can be set to <see langword="null" />, in which case the default
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/// pre-conditioner will be used.
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/// pre-conditioner will be used.
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/// </summary>
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/// </summary>
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private IPreConditioner<double> _preconditioner; |
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IPreConditioner<double> _preconditioner; |
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/// <summary>
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/// <summary>
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/// The iterative process controller.
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/// The iterative process controller.
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/// </summary>
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/// </summary>
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private IIterator<double> _iterator; |
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Iterator<double> _iterator; |
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/// <summary>
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/// <summary>
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/// The collection of starting vectors which are used as the basis for the Krylov sub-space.
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/// The collection of starting vectors which are used as the basis for the Krylov sub-space.
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/// </summary>
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/// </summary>
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private IList<Vector<double>> _startingVectors; |
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IList<Vector<double>> _startingVectors; |
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/// <summary>
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/// <summary>
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/// The number of starting vectors used by the algorithm
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/// The number of starting vectors used by the algorithm
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/// </summary>
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/// </summary>
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private int _numberOfStartingVectors = DefaultNumberOfStartingVectors; |
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int _numberOfStartingVectors = DefaultNumberOfStartingVectors; |
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/// <summary>
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/// <summary>
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/// Indicates if the user has stopped the solver.
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/// Indicates if the user has stopped the solver.
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/// </summary>
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/// </summary>
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private bool _hasBeenStopped; |
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bool _hasBeenStopped; |
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/// <summary>
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/// <summary>
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/// Initializes a new instance of the <see cref="MlkBiCgStab"/> class.
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/// Initializes a new instance of the <see cref="MlkBiCgStab"/> class.
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/// </summary>
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/// </summary>
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/// <remarks>
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/// <remarks>
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/// When using this constructor the solver will use the <see cref="IIterator{T}"/> with
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/// When using this constructor the solver will use the <see cref="Iterator{T}"/> with
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/// the standard settings and a default preconditioner.
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/// the standard settings and a default preconditioner.
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/// </remarks>
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/// </remarks>
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public MlkBiCgStab() : this(null, null) |
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public MlkBiCgStab() : this(null, null) |
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@ -120,18 +120,18 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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/// When using this constructor the solver will use a default preconditioner.
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/// When using this constructor the solver will use a default preconditioner.
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/// </para>
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/// </para>
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/// <para>
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/// <para>
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/// The main advantages of using a user defined <see cref="IIterator{T}"/> are:
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/// The main advantages of using a user defined <see cref="Iterator{T}"/> are:
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/// <list type="number">
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/// <list type="number">
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/// <item>It is possible to set the desired convergence limits.</item>
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/// <item>It is possible to set the desired convergence limits.</item>
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/// <item>
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/// <item>
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/// It is possible to check the reason for which the solver finished
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/// It is possible to check the reason for which the solver finished
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/// the iterative procedure by calling the <see cref="IIterator{T}.Status"/> property.
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/// the iterative procedure by calling the <see cref="Iterator{T}.Status"/> property.
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/// </item>
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/// </item>
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/// </list>
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/// </list>
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/// </para>
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/// </para>
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/// </remarks>
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/// </remarks>
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/// <param name="iterator">The <see cref="IIterator{T}"/> that will be used to monitor the iterative process.</param>
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/// <param name="iterator">The <see cref="Iterator{T}"/> that will be used to monitor the iterative process.</param>
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public MlkBiCgStab(IIterator<double> iterator) |
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public MlkBiCgStab(Iterator<double> iterator) |
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: this(null, iterator) |
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: this(null, iterator) |
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{ |
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{ |
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} |
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} |
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@ -140,7 +140,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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/// Initializes a new instance of the <see cref="MlkBiCgStab"/> class.
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/// Initializes a new instance of the <see cref="MlkBiCgStab"/> class.
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/// </summary>
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/// </summary>
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/// <remarks>
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/// <remarks>
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/// When using this constructor the solver will use the <see cref="IIterator{T}"/> with
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/// When using this constructor the solver will use the <see cref="Iterator{T}"/> with
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/// the standard settings.
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/// the standard settings.
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/// </remarks>
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/// </remarks>
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/// <param name="preconditioner">The <see cref="IPreConditioner{T}"/> that will be used to precondition the matrix equation.</param>
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/// <param name="preconditioner">The <see cref="IPreConditioner{T}"/> that will be used to precondition the matrix equation.</param>
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@ -154,19 +154,19 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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/// </summary>
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/// </summary>
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/// <remarks>
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/// <remarks>
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/// <para>
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/// <para>
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/// The main advantages of using a user defined <see cref="IIterator{T}"/> are:
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/// The main advantages of using a user defined <see cref="Iterator{T}"/> are:
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/// <list type="number">
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/// <list type="number">
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/// <item>It is possible to set the desired convergence limits.</item>
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/// <item>It is possible to set the desired convergence limits.</item>
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/// <item>
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/// <item>
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/// It is possible to check the reason for which the solver finished
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/// It is possible to check the reason for which the solver finished
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/// the iterative procedure by calling the <see cref="IIterator{T}.Status"/> property.
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/// the iterative procedure by calling the <see cref="Iterator{T}.Status"/> property.
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/// </item>
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/// </item>
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/// </list>
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/// </list>
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/// </para>
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/// </para>
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/// </remarks>
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/// </remarks>
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/// <param name="preconditioner">The <see cref="IPreConditioner{T}"/> that will be used to precondition the matrix equation.</param>
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/// <param name="preconditioner">The <see cref="IPreConditioner{T}"/> that will be used to precondition the matrix equation.</param>
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/// <param name="iterator">The <see cref="IIterator{T}"/> that will be used to monitor the iterative process.</param>
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/// <param name="iterator">The <see cref="Iterator{T}"/> that will be used to monitor the iterative process.</param>
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public MlkBiCgStab(IPreConditioner<double> preconditioner, IIterator<double> iterator) |
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public MlkBiCgStab(IPreConditioner<double> preconditioner, Iterator<double> iterator) |
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{ |
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{ |
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_iterator = iterator; |
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_iterator = iterator; |
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_preconditioner = preconditioner; |
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_preconditioner = preconditioner; |
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@ -217,10 +217,10 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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} |
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} |
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/// <summary>
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/// <summary>
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/// Sets the <see cref="IIterator{T}"/> that will be used to track the iterative process.
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/// Sets the <see cref="Iterator{T}"/> that will be used to track the iterative process.
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/// </summary>
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/// </summary>
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/// <param name="iterator">The iterator.</param>
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/// <param name="iterator">The iterator.</param>
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public void SetIterator(IIterator<double> iterator) |
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public void SetIterator(Iterator<double> iterator) |
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{ |
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{ |
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_iterator = iterator; |
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_iterator = iterator; |
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} |
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} |
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@ -349,7 +349,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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{ |
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{ |
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_preconditioner = new UnitPreconditioner<double>(); |
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_preconditioner = new UnitPreconditioner<double>(); |
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} |
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} |
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_preconditioner.Initialize(matrix); |
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_preconditioner.Initialize(matrix); |
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// Choose an initial guess x_0
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// Choose an initial guess x_0
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@ -403,7 +403,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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var zw = new DenseVector(residuals.Count); |
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var zw = new DenseVector(residuals.Count); |
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var d = CreateVectorArray(_startingVectors.Count, residuals.Count); |
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var d = CreateVectorArray(_startingVectors.Count, residuals.Count); |
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// g_0 = r_0
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// g_0 = r_0
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var g = CreateVectorArray(_startingVectors.Count, residuals.Count); |
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var g = CreateVectorArray(_startingVectors.Count, residuals.Count); |
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residuals.CopyTo(g[k - 1]); |
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residuals.CopyTo(g[k - 1]); |
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@ -428,7 +428,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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} |
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} |
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// alpha_(jk+1) = q^T_1 r_((j-1)k+k) / c_((j-1)k+k)
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// alpha_(jk+1) = q^T_1 r_((j-1)k+k) / c_((j-1)k+k)
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var alpha = _startingVectors[0].DotProduct(residuals) / c[k - 1]; |
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var alpha = _startingVectors[0].DotProduct(residuals)/c[k - 1]; |
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// u_(jk+1) = r_((j-1)k+k) - alpha_(jk+1) w_((j-1)k+k)
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// u_(jk+1) = r_((j-1)k+k) - alpha_(jk+1) w_((j-1)k+k)
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w[k - 1].Multiply(-alpha, temp); |
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w[k - 1].Multiply(-alpha, temp); |
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@ -450,7 +450,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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rho = 1.0; |
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rho = 1.0; |
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} |
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} |
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rho = -u.DotProduct(temp) / rho; |
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rho = -u.DotProduct(temp)/rho; |
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// r_(jk+1) = rho_(j+1) A u~_(jk+1) + u_(jk+1)
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// r_(jk+1) = rho_(j+1) A u~_(jk+1) + u_(jk+1)
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u.CopyTo(residuals); |
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u.CopyTo(residuals); |
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@ -468,7 +468,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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gtemp.Multiply(alpha, gtemp); |
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gtemp.Multiply(alpha, gtemp); |
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xtemp.Add(gtemp, temp2); |
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xtemp.Add(gtemp, temp2); |
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temp2.CopyTo(xtemp); |
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temp2.CopyTo(xtemp); |
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// Check convergence and stop if we are converged.
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// Check convergence and stop if we are converged.
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if (!ShouldContinue(iterationNumber, xtemp, input, residuals)) |
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if (!ShouldContinue(iterationNumber, xtemp, input, residuals)) |
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{ |
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{ |
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@ -503,7 +503,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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for (var s = i; s < k - 1; s++) |
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for (var s = i; s < k - 1; s++) |
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{ |
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{ |
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// beta^(jk+i)_((j-1)k+s) = -q^t_(s+1) z_d / c_((j-1)k+s)
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// beta^(jk+i)_((j-1)k+s) = -q^t_(s+1) z_d / c_((j-1)k+s)
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beta = -_startingVectors[s + 1].DotProduct(zd) / c[s]; |
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beta = -_startingVectors[s + 1].DotProduct(zd)/c[s]; |
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// z_d = z_d + beta^(jk+i)_((j-1)k+s) d_((j-1)k+s)
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// z_d = z_d + beta^(jk+i)_((j-1)k+s) d_((j-1)k+s)
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d[s].Multiply(beta, temp); |
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d[s].Multiply(beta, temp); |
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@ -522,7 +522,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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} |
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} |
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} |
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} |
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beta = rho * c[k - 1]; |
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beta = rho*c[k - 1]; |
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if (beta.AlmostEqual(0, 1)) |
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if (beta.AlmostEqual(0, 1)) |
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{ |
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{ |
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throw new Exception("Iterative solver experience a numerical break down"); |
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throw new Exception("Iterative solver experience a numerical break down"); |
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@ -531,7 +531,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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// beta^(jk+i)_((j-1)k+k) = -(q^T_1 (r_(jk+1) + rho_(j+1) z_w)) / (rho_(j+1) c_((j-1)k+k))
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// beta^(jk+i)_((j-1)k+k) = -(q^T_1 (r_(jk+1) + rho_(j+1) z_w)) / (rho_(j+1) c_((j-1)k+k))
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zw.Multiply(rho, temp2); |
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zw.Multiply(rho, temp2); |
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residuals.Add(temp2, temp); |
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residuals.Add(temp2, temp); |
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beta = -_startingVectors[0].DotProduct(temp) / beta; |
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beta = -_startingVectors[0].DotProduct(temp)/beta; |
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// z_g = z_g + beta^(jk+i)_((j-1)k+k) g_((j-1)k+k)
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// z_g = z_g + beta^(jk+i)_((j-1)k+k) g_((j-1)k+k)
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g[k - 1].Multiply(beta, temp); |
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g[k - 1].Multiply(beta, temp); |
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@ -551,7 +551,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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for (var s = 0; s < i - 1; s++) |
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for (var s = 0; s < i - 1; s++) |
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{ |
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{ |
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// beta^(jk+i)_(jk+s) = -q^T_s+1 z_d / c_(jk+s)
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// beta^(jk+i)_(jk+s) = -q^T_s+1 z_d / c_(jk+s)
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beta = -_startingVectors[s + 1].DotProduct(zd) / c[s]; |
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beta = -_startingVectors[s + 1].DotProduct(zd)/c[s]; |
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// z_d = z_d + beta^(jk+i)_(jk+s) * d_(jk+s)
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// z_d = z_d + beta^(jk+i)_(jk+s) * d_(jk+s)
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d[s].Multiply(beta, temp); |
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d[s].Multiply(beta, temp); |
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@ -581,7 +581,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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} |
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} |
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// alpha_(jk+i+1) = q^T_(i+1) u_(jk+i) / c_(jk+i)
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// alpha_(jk+i+1) = q^T_(i+1) u_(jk+i) / c_(jk+i)
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alpha = _startingVectors[i + 1].DotProduct(u) / c[i]; |
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alpha = _startingVectors[i + 1].DotProduct(u)/c[i]; |
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// u_(jk+i+1) = u_(jk+i) - alpha_(jk+i+1) d_(jk+i)
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// u_(jk+i+1) = u_(jk+i) - alpha_(jk+i+1) d_(jk+i)
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d[i].Multiply(-alpha, temp); |
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d[i].Multiply(-alpha, temp); |
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@ -592,7 +592,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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_preconditioner.Approximate(g[i], gtemp); |
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_preconditioner.Approximate(g[i], gtemp); |
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// x_(jk+i+1) = x_(jk+i) + rho_(j+1) alpha_(jk+i+1) g~_(jk+i)
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// x_(jk+i+1) = x_(jk+i) + rho_(j+1) alpha_(jk+i+1) g~_(jk+i)
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gtemp.Multiply(rho * alpha, temp); |
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gtemp.Multiply(rho*alpha, temp); |
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xtemp.Add(temp, temp2); |
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xtemp.Add(temp, temp2); |
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temp2.CopyTo(xtemp); |
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temp2.CopyTo(xtemp); |
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@ -600,7 +600,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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matrix.Multiply(gtemp, w[i]); |
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matrix.Multiply(gtemp, w[i]); |
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// r_(jk+i+1) = r_(jk+i) - rho_(j+1) alpha_(jk+i+1) w_(jk+i)
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// r_(jk+i+1) = r_(jk+i) - rho_(j+1) alpha_(jk+i+1) w_(jk+i)
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w[i].Multiply(-rho * alpha, temp); |
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w[i].Multiply(-rho*alpha, temp); |
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residuals.Add(temp, temp2); |
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residuals.Add(temp, temp2); |
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temp2.CopyTo(residuals); |
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temp2.CopyTo(residuals); |
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@ -627,7 +627,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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/// <param name="maximumNumberOfStartingVectors">Maximum number</param>
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/// <param name="maximumNumberOfStartingVectors">Maximum number</param>
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/// <param name="numberOfVariables">Number of variables</param>
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/// <param name="numberOfVariables">Number of variables</param>
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/// <returns>Number of starting vectors to create</returns>
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/// <returns>Number of starting vectors to create</returns>
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private static int NumberOfStartingVectorsToCreate(int maximumNumberOfStartingVectors, int numberOfVariables) |
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static int NumberOfStartingVectorsToCreate(int maximumNumberOfStartingVectors, int numberOfVariables) |
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{ |
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{ |
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// Create no more starting vectors than the size of the problem - 1
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// Create no more starting vectors than the size of the problem - 1
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return Math.Min(maximumNumberOfStartingVectors, (numberOfVariables - 1)); |
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return Math.Min(maximumNumberOfStartingVectors, (numberOfVariables - 1)); |
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@ -644,7 +644,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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/// the <paramref name="numberOfVariables"/> is smaller than
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/// the <paramref name="numberOfVariables"/> is smaller than
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/// the <paramref name="maximumNumberOfStartingVectors"/>.
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/// the <paramref name="maximumNumberOfStartingVectors"/>.
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/// </returns>
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/// </returns>
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private static IList<Vector<double>> CreateStartingVectors(int maximumNumberOfStartingVectors, int numberOfVariables) |
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static IList<Vector<double>> CreateStartingVectors(int maximumNumberOfStartingVectors, int numberOfVariables) |
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{ |
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{ |
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// Create no more starting vectors than the size of the problem - 1
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// Create no more starting vectors than the size of the problem - 1
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// Get random values and then orthogonalize them with
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// Get random values and then orthogonalize them with
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@ -659,7 +659,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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for (var i = 0; i < matrix.ColumnCount; i++) |
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for (var i = 0; i < matrix.ColumnCount; i++) |
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{ |
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{ |
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var samples = distribution.Samples().Take(matrix.RowCount).ToArray(); |
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var samples = distribution.Samples().Take(matrix.RowCount).ToArray(); |
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// Set the column
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// Set the column
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matrix.SetColumn(i, samples); |
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matrix.SetColumn(i, samples); |
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} |
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} |
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@ -673,9 +673,9 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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for (var i = 0; i < orthogonalMatrix.ColumnCount; i++) |
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for (var i = 0; i < orthogonalMatrix.ColumnCount; i++) |
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{ |
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{ |
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result.Add(orthogonalMatrix.Column(i)); |
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result.Add(orthogonalMatrix.Column(i)); |
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// Normalize the result vector
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// Normalize the result vector
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result[i].Multiply(1 / result[i].L2Norm(), result[i]); |
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result[i].Multiply(1/result[i].L2Norm(), result[i]); |
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} |
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} |
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return result; |
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return result; |
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@ -687,7 +687,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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/// <param name="arraySize">Number of vectors</param>
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/// <param name="arraySize">Number of vectors</param>
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/// <param name="vectorSize">Size of each vector</param>
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/// <param name="vectorSize">Size of each vector</param>
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/// <returns>Array of random vectors</returns>
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/// <returns>Array of random vectors</returns>
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private static Vector<double>[] CreateVectorArray(int arraySize, int vectorSize) |
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static Vector<double>[] CreateVectorArray(int arraySize, int vectorSize) |
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{ |
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{ |
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var result = new Vector<double>[arraySize]; |
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var result = new Vector<double>[arraySize]; |
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for (var i = 0; i < result.Length; i++) |
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for (var i = 0; i < result.Length; i++) |
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@ -705,7 +705,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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/// <param name="residual">Residual <see cref="Vector"/> data.</param>
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/// <param name="residual">Residual <see cref="Vector"/> data.</param>
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/// <param name="x">x <see cref="Vector"/> data.</param>
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/// <param name="x">x <see cref="Vector"/> data.</param>
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/// <param name="b">b <see cref="Vector"/> data.</param>
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/// <param name="b">b <see cref="Vector"/> data.</param>
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private static void CalculateTrueResidual(Matrix<double> matrix, Vector<double> residual, Vector<double> x, Vector<double> b) |
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static void CalculateTrueResidual(Matrix<double> matrix, Vector<double> residual, Vector<double> x, Vector<double> b) |
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|
{ |
|
|
{ |
|
|
// -Ax = residual
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// -Ax = residual
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matrix.Multiply(x, residual); |
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matrix.Multiply(x, residual); |
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@ -723,21 +723,19 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers |
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/// <param name="source">Source <see cref="Vector"/>.</param>
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/// <param name="source">Source <see cref="Vector"/>.</param>
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/// <param name="residuals">Residual <see cref="Vector"/>.</param>
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/// <param name="residuals">Residual <see cref="Vector"/>.</param>
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/// <returns><c>true</c> if continue, otherwise <c>false</c></returns>
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/// <returns><c>true</c> if continue, otherwise <c>false</c></returns>
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|
|
private bool ShouldContinue(int iterationNumber, Vector<double> result, Vector<double> source, Vector<double> residuals) |
|
|
bool ShouldContinue(int iterationNumber, Vector<double> result, Vector<double> source, Vector<double> residuals) |
|
|
{ |
|
|
{ |
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|
|
// We stop if either:
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|
|
// - the user has stopped the calculation
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// - the calculation needs to be stopped from a numerical point of view (divergence, convergence etc.)
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|
|
if (_hasBeenStopped) |
|
|
if (_hasBeenStopped) |
|
|
{ |
|
|
{ |
|
|
_iterator.IterationCancelled(); |
|
|
_iterator.Cancel(); |
|
|
return true; |
|
|
return true; |
|
|
} |
|
|
} |
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|
|
_iterator.DetermineStatus(iterationNumber, result, source, residuals); |
|
|
return !_iterator.DetermineStatus(iterationNumber, result, source, residuals).TerminatesCalculation; |
|
|
var status = _iterator.Status; |
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|
// We stop if either:
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|
|
// - the user has stopped the calculation
|
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|
|
// - the calculation needs to be stopped from a numerical point of view (divergence, convergence etc.)
|
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|
|
return (!status.TerminatesCalculation) && (!_hasBeenStopped); |
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|
|
} |
|
|
} |
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/// <summary>
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|
/// <summary>
|
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|
|
Christoph Ruegg
13 years ago