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@ -68,39 +68,39 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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 _preconditioner; |
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IPreConditioner _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 _iterator; |
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IIterator _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> _startingVectors; |
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IList<Vector> _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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@ -109,7 +109,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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/// When using this constructor the solver will use the <see cref="IIterator"/> with
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/// When using this constructor the solver will use the <see cref="IIterator"/> 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() |
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: this(null, null) |
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{ |
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{ |
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} |
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} |
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@ -132,7 +133,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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"/> that will be used to monitor the iterative process.</param>
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/// <param name="iterator">The <see cref="IIterator"/> that will be used to monitor the iterative process.</param>
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public MlkBiCgStab(IIterator iterator) : this(null, iterator) |
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public MlkBiCgStab(IIterator 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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@ -144,7 +146,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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"/> that will be used to precondition the matrix equation.</param>
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/// <param name="preconditioner">The <see cref="IPreConditioner"/> that will be used to precondition the matrix equation.</param>
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public MlkBiCgStab(IPreConditioner preconditioner) : this(preconditioner, null) |
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public MlkBiCgStab(IPreConditioner preconditioner) |
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: this(preconditioner, null) |
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{ |
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{ |
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} |
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} |
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@ -181,10 +184,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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public int NumberOfStartingVectors |
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public int NumberOfStartingVectors |
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{ |
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{ |
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[DebuggerStepThrough] |
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[DebuggerStepThrough] |
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get |
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get { return _numberOfStartingVectors; } |
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{ |
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return _numberOfStartingVectors; |
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} |
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[DebuggerStepThrough] |
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[DebuggerStepThrough] |
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set |
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set |
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@ -231,10 +231,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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public IList<Vector> StartingVectors |
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public IList<Vector> StartingVectors |
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{ |
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{ |
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[DebuggerStepThrough] |
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[DebuggerStepThrough] |
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get |
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get { return _startingVectors; } |
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{ |
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return _startingVectors; |
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} |
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[DebuggerStepThrough] |
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[DebuggerStepThrough] |
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set |
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set |
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@ -256,10 +253,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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public ICalculationStatus IterationResult |
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public ICalculationStatus IterationResult |
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{ |
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{ |
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[DebuggerStepThrough] |
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[DebuggerStepThrough] |
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get |
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get { return (_iterator != null) ? _iterator.Status : DefaultStatus; } |
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{ |
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return (_iterator != null) ? _iterator.Status : DefaultStatus; |
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} |
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} |
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} |
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/// <summary>
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/// <summary>
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@ -348,7 +342,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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{ |
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{ |
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_preconditioner = new UnitPreconditioner(); |
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_preconditioner = new UnitPreconditioner(); |
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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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@ -402,7 +396,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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Vector zw = new DenseVector(residuals.Count); |
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Vector 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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@ -420,14 +414,14 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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matrix.Multiply(gtemp, w[k - 1]); |
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matrix.Multiply(gtemp, w[k - 1]); |
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// c_((j-1)k+k) = q^T_1 w_((j-1)k+k)
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// c_((j-1)k+k) = q^T_1 w_((j-1)k+k)
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c[k - 1] = _startingVectors[0].DotProduct(w[k - 1]); |
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c[k - 1] = _startingVectors[0].ConjugateDotProduct(w[k - 1]); |
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if (c[k - 1].Real.AlmostEqual(0, 1) && c[k - 1].Imaginary.AlmostEqual(0, 1)) |
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if (c[k - 1].Real.AlmostEqual(0, 1) && c[k - 1].Imaginary.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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} |
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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].ConjugateDotProduct(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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@ -439,7 +433,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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// rho_(j+1) = -u^t_(jk+1) A u~_(jk+1) / ||A u~_(jk+1)||^2
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// rho_(j+1) = -u^t_(jk+1) A u~_(jk+1) / ||A u~_(jk+1)||^2
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matrix.Multiply(temp1, temp); |
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matrix.Multiply(temp1, temp); |
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var rho = temp.DotProduct(temp); |
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var rho = temp.ConjugateDotProduct(temp); |
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// If rho is zero then temp is a zero vector and we're probably
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// If rho is zero then temp is a zero vector and we're probably
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// about to have zero residuals (i.e. an exact solution).
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// about to have zero residuals (i.e. an exact solution).
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@ -449,7 +443,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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rho = 1.0f; |
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rho = 1.0f; |
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} |
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} |
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rho = -u.DotProduct(temp) / rho; |
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rho = -u.ConjugateDotProduct(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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@ -502,7 +496,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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].ConjugateDotProduct(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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@ -521,7 +515,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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.Real.AlmostEqual(0, 1) && beta.Imaginary.AlmostEqual(0, 1)) |
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if (beta.Real.AlmostEqual(0, 1) && beta.Imaginary.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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@ -530,7 +524,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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].ConjugateDotProduct(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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@ -550,7 +544,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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].ConjugateDotProduct(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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@ -573,14 +567,14 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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if (i < k - 1) |
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if (i < k - 1) |
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{ |
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{ |
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// c_(jk+1) = q^T_i+1 d_(jk+i)
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// c_(jk+1) = q^T_i+1 d_(jk+i)
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c[i] = _startingVectors[i + 1].DotProduct(d[i]); |
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c[i] = _startingVectors[i + 1].ConjugateDotProduct(d[i]); |
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if (c[i].Real.AlmostEqual(0, 1) && c[i].Imaginary.AlmostEqual(0, 1)) |
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if (c[i].Real.AlmostEqual(0, 1) && c[i].Imaginary.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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} |
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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].ConjugateDotProduct(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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@ -591,7 +585,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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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@ -599,7 +593,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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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@ -626,7 +620,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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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@ -643,7 +637,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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> CreateStartingVectors(int maximumNumberOfStartingVectors, int numberOfVariables) |
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static IList<Vector> 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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@ -662,7 +656,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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var samplesIm = distribution.Samples().Take(matrix.RowCount).ToArray(); |
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var samplesIm = distribution.Samples().Take(matrix.RowCount).ToArray(); |
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for (int j = 0; j < matrix.RowCount; j++) |
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for (int j = 0; j < matrix.RowCount; j++) |
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{ |
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{ |
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samples[j] = new Complex32((float)samplesRe[j], (float)samplesIm[j]); |
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samples[j] = new Complex32((float) samplesRe[j], (float) samplesIm[j]); |
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} |
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} |
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// Set the column
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// Set the column
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@ -677,10 +671,10 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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var result = new List<Vector>(); |
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var result = new List<Vector>(); |
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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((Vector)orthogonalMatrix.Column(i)); |
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result.Add((Vector) 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().Real, result[i]); |
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result[i].Multiply(1/result[i].L2Norm().Real, 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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@ -692,7 +686,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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[] CreateVectorArray(int arraySize, int vectorSize) |
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static Vector[] CreateVectorArray(int arraySize, int vectorSize) |
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{ |
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{ |
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var result = new Vector[arraySize]; |
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var result = new Vector[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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@ -710,7 +704,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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 matrix, Vector residual, Vector x, Vector b) |
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static void CalculateTrueResidual(Matrix matrix, Vector residual, Vector x, Vector b) |
|
|
{ |
|
|
{ |
|
|
// -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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@ -728,7 +722,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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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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|
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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>
|
|
|
private bool ShouldContinue(int iterationNumber, Vector result, Vector source, Vector residuals) |
|
|
bool ShouldContinue(int iterationNumber, Vector result, Vector source, Vector residuals) |
|
|
{ |
|
|
{ |
|
|
if (_hasBeenStopped) |
|
|
if (_hasBeenStopped) |
|
|
{ |
|
|
{ |
|
|
@ -764,7 +758,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
|
|
throw new ArgumentNullException("input"); |
|
|
throw new ArgumentNullException("input"); |
|
|
} |
|
|
} |
|
|
|
|
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|
|
var result = (Matrix)matrix.CreateMatrix(input.RowCount, input.ColumnCount); |
|
|
var result = (Matrix) matrix.CreateMatrix(input.RowCount, input.ColumnCount); |
|
|
Solve(matrix, input, result); |
|
|
Solve(matrix, input, result); |
|
|
return result; |
|
|
return result; |
|
|
} |
|
|
} |
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|
@ -800,7 +794,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers.Iterative |
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|
|
for (var column = 0; column < input.ColumnCount; column++) |
|
|
for (var column = 0; column < input.ColumnCount; column++) |
|
|
{ |
|
|
{ |
|
|
var solution = Solve(matrix, (Vector)input.Column(column)); |
|
|
var solution = Solve(matrix, (Vector) input.Column(column)); |
|
|
foreach (var element in solution.GetIndexedEnumerator()) |
|
|
foreach (var element in solution.GetIndexedEnumerator()) |
|
|
{ |
|
|
{ |
|
|
result.At(element.Item1, column, element.Item2); |
|
|
result.At(element.Item1, column, element.Item2); |
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Christoph Ruegg
13 years ago