DOP |
Specialized core implementation for DOP853, optimized by skipping multiplications with zero coefficients.
Inheritance HierarchyNamespace: Altaxo.Calc.Ode
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3448.0 (4.8.3448.0)
SyntaxC#
protected class CoreDOP853 : RungeKuttaExplicitBaseCore
The DOP853CoreDOP853 type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | DOP853CoreDOP853 | Initializes a new instance of the DOP853CoreDOP853 class. |
Properties| Name | Description | |
|---|---|---|
 | AbsoluteTolerance |
Gets or sets the absolute tolerance.
(Inherited from RungeKuttaExplicitBaseCore) |
| AbsoluteTolerances |
Gets or sets the absolute tolerances.
It must be ensured that this array is not altered.
(Inherited from RungeKuttaExplicitBaseCore) |
| BHML |
Sets the coefficients for the error evaluation.
These coefficients are the difference of the high-order and low-order bottom side
coefficients of the Runge-Kutta scheme.
If set to , local error calculation (and thus automatic step size control) is not possible.
(Inherited from RungeKuttaExplicitBaseCore) |
| ErrorNorm |
Gets the vector norm used to reduce the vector of relative errors (dimension N) to a scalar relative error.
(Inherited from RungeKuttaExplicitBaseCore) |
| InterpolationCoefficients |
Gets or sets the interpolation coefficients for dense output.
(Inherited from RungeKuttaExplicitBaseCore) |
| RelativeTolerance |
Gets or sets the relative tolerance.
(Inherited from RungeKuttaExplicitBaseCore) |
| RelativeTolerances |
Gets or sets the relative tolerances.
It must be ensured that this array is not altered.
(Inherited from RungeKuttaExplicitBaseCore) |
| StepSizeFilter |
Gets or sets the step size filter.
For the values see StepSizeFilter.
(Inherited from RungeKuttaExplicitBaseCore) |
| StiffnessDetectionEveryNumberOfSteps |
Gets or sets the number of successful steps between tests for stiffness.
Setting this value to 0 disables stiffness detection. The default value is 0.
(Inherited from RungeKuttaExplicitBaseCore) |
| StiffnessDetectionThresholdValue |
Sets the stiffness detection threshold value.
(Inherited from RungeKuttaExplicitBaseCore) |
| X |
Gets the current value of x.
(Inherited from RungeKuttaExplicitBaseCore) |
| X_previous |
Gets the value of x before the last step.
(Inherited from RungeKuttaExplicitBaseCore) |
| Y_volatile |
Gets the current values of the variables.
Attention: the returned array will change the next time you call EvaluateNextSolutionPoint(Double).
Therefore, if you do not intend to use the values immediately, make a copy of this array! (Inherited from RungeKuttaExplicitBaseCore) |
Methods| Name | Description | |
|---|---|---|
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object) |
| EvaluateNextSolutionPoint |
Evaluates the next solution point in one step.
To get the results, see X and Y_volatile.
(Overrides RungeKuttaExplicitBaseCoreEvaluateNextSolutionPoint(Double)) |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
| GetHashCode | Serves as the default hash function. (Inherited from Object) |
| GetInitialStepSize |
Gets the initial step size.
The absolute and relative tolerances must be set before the call to this function.
(Inherited from RungeKuttaExplicitBaseCore) |
| GetInterpolatedY_volatile |
Gets an interpolated point in the last evaluated interval.
Please use the result immediately, or else make a copy of the result, since an internal array
is returned, which is overwritten at the next operation.
(Overrides RungeKuttaExplicitBaseCoreGetInterpolatedY_volatile(Double)) |
| GetRecommendedStepSize |
Gets the recommended step size.
(Overrides RungeKuttaExplicitBaseCoreGetRecommendedStepSize(Double, Double)) |
| GetRelativeError_InfinityNorm |
Gets the relative error by the infinity norm, which should be in the order of 1 if the step size is optimally chosen.
(Inherited from RungeKuttaExplicitBaseCore) |
| GetRelativeError_L2Norm |
Gets the relative error calculated by the L2-norm, which should be in the order of 1 if the step size is optimally chosen.
(Inherited from RungeKuttaExplicitBaseCore) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| Revert |
Reverts the state of the instance to the former solution point by setting X to X_previous
and reverting Y_volatile.
(Inherited from RungeKuttaExplicitBaseCore) |
| SetCoefficientsForAdditionalStages |
Sets the coefficients for additional stages that are necessary for dense output (interpolation).
(Inherited from RungeKuttaExplicitBaseCore) |
| ThrowIfStiffnessDetected |
Called after every successful step.
Detects a stiffness condition. If one is found, an exception is thrown.
(Inherited from RungeKuttaExplicitBaseCore) |
| ToString | Returns a string that represents the current object. (Inherited from Object) |
Fields| Name | Description | |
|---|---|---|
 | _a | Central coefficients of the Runge-Kutta scheme. See [1], page 135. (Inherited from RungeKuttaExplicitBaseCore) |
| _a_interpolation | Additional central coefficients of the Runge-Kutta scheme optionally needed for interpolation. (Inherited from RungeKuttaExplicitBaseCore) |
 | _absoluteTolerances |
The absolute tolerances.
This is either an array of length 1 (in this case, the absolute tolerances of all y values are equal),
or an array of the same size as y.
(Inherited from RungeKuttaExplicitBaseCore) |
| _b | High order bottom side coefficients of the Runge-Kutta scheme. (Inherited from RungeKuttaExplicitBaseCore) |
| _bhml | Differences between high order and low order bottom side coefficients of the Runge-Kutta scheme (for error estimation). (Inherited from RungeKuttaExplicitBaseCore) |
| _c | Left side coefficients of the Runge-Kutta scheme (partitions of the step). (Inherited from RungeKuttaExplicitBaseCore) |
| _c_interpolation |
Additional left side coefficients of the Runge-Kutta scheme optionally needed for dense output (partitions of the step).
(Inherited from RungeKuttaExplicitBaseCore) |
| _f |
The ODE function.
(Inherited from RungeKuttaExplicitBaseCore) |
| _interpolationCoefficients |
The interpolation coefficients.
Note that zero to third order is calculated from the y values and slopes at the start and end of the step.
Thus, these coefficients only have to cover the orders 4..n of the interpolation.
(Inherited from RungeKuttaExplicitBaseCore) |
| _isDenseOutputPrepared | True if dense output was prepared, i.e. the array _rcont contains valid values. (Inherited from RungeKuttaExplicitBaseCore) |
| _isFirstSameAsLastMethod | if the method has the FSAL (first-same-as-last) property; otherwise, .
This is, for instance, true for the Dormand-Prince (RK547M) method.
(Inherited from RungeKuttaExplicitBaseCore) |
| _isKnextEvaluated |
Designates whether the slope at y_current was evaluated (for non-FSAL methods).
For FSAL methods, this value is meaningless, because the last stage always contains k_next after a step.
(Inherited from RungeKuttaExplicitBaseCore) |
| _k | Array of derivatives at the different stages. (Inherited from RungeKuttaExplicitBaseCore) |
| _numberOfAdditionalStagesForDenseOutput | The number of additional stages for dense output of high order. (Inherited from RungeKuttaExplicitBaseCore) |
| _numberOfNonstiffEvaluationResults |
The number of evaluation results in ThrowIfStiffnessDetected for which the result was false (non-stiff).
This counter is reset to zero if a stiff condition is detected.
(Inherited from RungeKuttaExplicitBaseCore) |
| _numberOfRejectedStiffnessDetectionCalls |
The number of rejected stiffness detection calls after the last stiffness evaluation.
(Inherited from RungeKuttaExplicitBaseCore) |
| _numberOfStages | The number of stages of this method. (Inherited from RungeKuttaExplicitBaseCore) |
| _numberOfStiffEvaluationResults |
The number of evaluation results in ThrowIfStiffnessDetected for which the result was true (stiff).
This counter is reset to zero if a non-stiff condition is detected.
(Inherited from RungeKuttaExplicitBaseCore) |
| _order | Order of the Runge-Kutta method (the highest order of the embedded pair). (Inherited from RungeKuttaExplicitBaseCore) |
| _rcont | Contains the precalculated polynomial coefficients for dense output. (Inherited from RungeKuttaExplicitBaseCore) |
| _relativeTolerances |
The relative tolerances.
This is either an array of length 1 (in this case, the relative tolerances of all y values are equal),
or an array of the same size as y.
(Inherited from RungeKuttaExplicitBaseCore) |
| _stepSize_current | Step size of the current step. (Inherited from RungeKuttaExplicitBaseCore) |
| _stepSize_previous | Step size of the previous step. (Inherited from RungeKuttaExplicitBaseCore) |
| _stepSizeFilter |
The step size filter.
(Inherited from RungeKuttaExplicitBaseCore) |
| _stiffnessDetectionEveryNumberOfSteps |
Number of successful steps between calls to stiffness detection.
If this value is 0, stiffness detection is disabled.
(Inherited from RungeKuttaExplicitBaseCore) |
| _stiffnessDetectionThresholdValueSquared |
Squared value of the stiffness detection threshold.
(Inherited from RungeKuttaExplicitBaseCore) |
| _wasSolutionPointEvaluated | True if at least one solution point was evaluated. (Inherited from RungeKuttaExplicitBaseCore) |
| _x_current | X value at the end of the current step. (Inherited from RungeKuttaExplicitBaseCore) |
| _x_previous | X value at the begin of the current step. (Inherited from RungeKuttaExplicitBaseCore) |
| _y_current | Y values at the end of the current step. (Inherited from RungeKuttaExplicitBaseCore) |
| _y_current_LocalError |
Contains the array of local errors.
(Inherited from RungeKuttaExplicitBaseCore) |
| _y_previous | Y values at the beginning of the current step. (Inherited from RungeKuttaExplicitBaseCore) |
| _y_stages |
Array to accommodate y for calculation of the stages.
At the end of EvaluateNextSolutionPoint(Double), this array usually contains the y
of the last stage (for non-FSAL methods), or the y of the stage before the last stage (FSAL methods).
(Inherited from RungeKuttaExplicitBaseCore) |
See Also