From dcf99bdf4afdf345e7ed67c98df5702390d6c4d5 Mon Sep 17 00:00:00 2001 From: "Penn, John M 047828115" Date: Tue, 17 Nov 2020 13:41:44 -0600 Subject: [PATCH] Editing, improvement of READMEs. #1082 --- .../trick_utils/SAIntegrator/README.md | 579 ++++++++++++++---- .../examples/CannonBall/README.md | 21 +- .../examples/CannonBall/images/Cannon.png | Bin 406833 -> 163624 bytes 3 files changed, 451 insertions(+), 149 deletions(-) diff --git a/trick_source/trick_utils/SAIntegrator/README.md b/trick_source/trick_utils/SAIntegrator/README.md index 23c59b07..3159a145 100644 --- a/trick_source/trick_utils/SAIntegrator/README.md +++ b/trick_source/trick_utils/SAIntegrator/README.md @@ -4,7 +4,7 @@ * [Introduction](#Introduction) * [class Integrator](#class-Integrator) -* [typedef derivsFunc](#typedef-derivsFunc) +* [typedef DerivsFunc](#typedef-DerivsFunc) * [class FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator) * [typedef RootErrorFunc](#typedef-RootErrorFunc) * [class FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableStepIntegrator) @@ -34,14 +34,15 @@ Some examples of using these integrators can be found in the **examples/** direc ## class Integrator ### Description -This class represents an **integrator**. +This base-class represents a numerical **integrator**. -|Member |Type |Description| -|----------|------------|--------------------| -|X_in |```double```|Independent variable value of the input state.| -|X_out|```double```|Independent variable value of the output state.| -|default_h |```double```|Default integration step-size| -|user_data |```void*``` | A pointer to user defined data that will be passed to user-defined functions when called by the Integrator. | +### Data Members +|Member |Type |Access |Description| +|----------|------------|---------|-----------| +|X_in |```double```|Protected|Independent variable value of the input state.| +|X_out |```double```|Protected|Independent variable value of the output state.| +|default_h |```double```|Protected|Default integration step-size| +|user_data |```void*``` |Protected|A pointer to user defined data that will be passed to user-defined functions when called by the Integrator. | ### Constructor @@ -56,41 +57,65 @@ This class represents an **integrator**. #### ```virtual ~Integrator() {}``` -### Member Functions +### Public Member Functions -#### ```virtual void step();``` + +#### ```virtual void step()``` +Derived classes should override this method to perform a numeric integration step, and then call [```advanceIndyVar()```](#method-Integrator::advanceIndyVar) to advance the independent variable. The default behavior of this member-function is to call ```advanceIndyVar()```. -Derived classes should override this method to perform a numeric integration step. The default behavior is to simply increment the independent variable by the default integration step-size. - -#### ```virtual void load();``` - -Derived classes should override this method to load/prepare the integrator for the next integration step. The default behavior is to set the input value of the independent value to its previous output value, i.e, ```X_out = X_out```. - -#### ```virtual void unload() = 0;``` - -Derived classes must override this method to disseminate the values of the output state to their respective destination variables. - -#### ```double getIndyVar();``` -Return the value of the independent variable (i.e, the variable over which you are integrating) If you are integrating over time, this value will be the accumulated time. - -#### ```double setIndyVar( double t);``` -Set the value of the independent variable. (i.e, the variable over which you are integrating) If you are integrating over time, this value will be the accumulated time. + +#### ```virtual void load()``` +Derived classes should override this method to load/prepare the integrator for the next integration step. The default behavior is to set the input value of the independent variable to its previous output value, i.e, ```X_in = X_out```. - -## typedef derivsFunc + +#### ```virtual void unload()``` +Derived classes should override this method to disseminate the values of the output state to their respective destinations. The default behavior is to do nothing. + + +#### ```virtual void integrate()``` +Call ```load()```, ```step()```, and ```unload()``` in order. + + + +#### ```virtual double undo_integrate()``` +Derived classes should override this member function to **undo** the effect of ```integrate()``` and return that last step-size. The behavior of this function is to set the output value of the independent variable to its previous input value, i.e, ```X_out = X_in```, and then return the default step-size ```default_h```. + + + +#### ```double getIndyVar()``` +Returns the value of the independent variable (i.e, the variable over which you are integrating) If you are integrating over time, this value will be the accumulated time. + + + +#### ```double setIndyVar( double t)``` +Sets the value of the independent variable. (i.e, the variable over which you are integrating) If you are integrating over time, this will be the accumulated time. + +### Protected Member Functions + + +#### ```void advanceIndyVar()``` +This member function advances the independent variable by the default integration step-size. + + + +## typedef DerivsFunc + +### Description +This typedef defines a type of C/C++ function whose purpose is to populate +a state derivative array. ``` -typedef void (*derivsFunc)( double x, double state[], double derivs[], void* udata); +typedef void (*DerivsFunc)( double x, double state[], double derivs[], void* udata); ``` where: -|Parameter|Type|Description| -|---|---|---| -|x|```double```| independent variable | -|state|```double*```| (input) an array of state variable values | -|derivs|```double*```| (output) an array into which derivatives are to be returned| -|udata|```void*```| a pointer to user_data.| +|Parameter|Type |Direction|Description| +|---------|-------------|---------|-----------| +|x |```double``` |IN |Independent variable.| +|state |```double*```|IN |Array of state variable values.| +|derivs |```double*```|OUT |Array into which derivatives are to be returned.| +|udata |```void*``` |IN |Pointer to user_data.| #### Example ``` @@ -99,20 +124,30 @@ void my_derivs( double t, double state[], double deriv[], void* udata) { ... } ## class FirstOrderODEIntegrator -Derived from [Integrator](#class-Integrator). - -|Member |Type |Description| -|-----------|------------------|-------------------------| -|state_size |```unsigned int```|Size of the state vector.| -|inState |```double*``` |Input state vector to the integrator.| -|outState |```double*``` |Output state vector from the integrator.| -|inVars |```double**``` |Array of pointers to the variables from which input state vector values are copied.| -|outVars |```double**``` |Array of pointers to the variables to which output state vector values are copied.| -|derivs_func|[```DerivsFunc```](#typedef-derivsFunc)|Function thats generates the function (an array of state derivatives) to be integrated.| -|last_h |```double``` |the **last** integration step-size.| +Derived from [```Integrator```](#class-Integrator). ### Description -This class represents an integrator for a first order [Ordinary Differential Equation (ODE)]([https://en.wikipedia.org/wiki/Ordinary_differential_equation). + +This class represents an integrator for a first order [Ordinary Differential Equation]([https://en.wikipedia.org/wiki/Ordinary_differential_equation). + +### Data Members +Those inherited from [Integrator](#class-Integrator) plus: + +|Member |Type |Access |Description| +|-----------|------------------|---------|-----------| +|state_size |```unsigned int```|Protected|Size of the state vector.| +|inState |```double*``` |Protected|Input state vector to the integrator.| +|outState |```double*``` |Protected|Output state vector from the integrator.| +|inVars |```double**``` |Protected|Array of pointers to the variables from which input state vector values are copied.| +|outVars |```double**``` |Protected|Array of pointers to the variables to which output state vector values are copied.| +|derivs_func|[```DerivsFunc```](#typedef-DerivsFunc)|Protected|Function thats generates the function (an array of state derivatives) to be integrated.| + +This class introduces: + +* Input and output state arrays. +* A function that calculates state-derivatives for the integration algorithm. +* Array of pointers to variables from which to load the input state array, and array of pointers to variables to which to unload the output state array. + ### Constructor @@ -121,7 +156,7 @@ FirstOrderODEIntegrator( double h, int N, double* in_vars[], double* out_vars[], - derivsFunc func, + DerivsFunc func, void* user_data); ``` where: @@ -134,114 +169,216 @@ where: |N |```int``` |Number of state variables to be integrated| |in_vars |```double*```|Array of pointers to the state variables from which we ```load()``` the integrator state (```in_vars``` and ```out_vars``` will generally point to the same array of pointers.)| |out_vars |```double*```|Array of pointers to the state variables to which we ```unload()``` the integrator state (```in_vars``` and ```out_vars``` will generally point to the same array of pointers.)| -| derivs_func |[```derivsFunc```](#typedef-derivsFunc)| Function thats generates the function (the derivatives) to be integrated. | -|user_data |```void*``` | A pointer to user defined data that will be passed to a derivsFunc when called by the Integrator. | +| derivs_func |[```DerivsFunc```](#typedef-DerivsFunc)| Function thats generates the function (the derivatives) to be integrated. | +|user_data |```void*``` | A pointer to user defined data that will be passed to a DerivsFunc when called by the Integrator. | -### Member Functions +### Public Member Functions + #### ```void load()``` +**Overrides** [Integrator::load()](#method-Integrator::load) + Load the integrator's initial state from the variables specified by **in_vars**. Set the initial value of the independent variable for the next step to the final value of the previous step. ![load](images/load.png) + + #### ```void unload()``` +**Overrides** [Integrator::unload()](#method-Integrator::unload) + Unload the integrator's result state to the variables specified by **out_vars**. ![unload](images/unload.png) -#### ```virtual void undo_step()``` -Undo the effect of the last integration step. -![undo_step](images/undo_step.png) + +#### ```virtual void step()``` +**Overrides** [Integrator::step()](#method-Integrator::step) +![step](images/step.png) +Derived classes should override this method to calculate ```outState``` using some integration algorithm, using ```X_in```, ```inState```, and ```derivs_func```, and ```default_h```. The over-riding method should also pass the ```user_data``` when calling the ```DerivsFunc```. The default algorithm is Euler. + + +#### ```void integrate()``` +**Inherited** from [Integrator::integrate()](#method-Integrator::integrate) + + +#### ```virtual void undo_integrate()``` +**Overrides** [Integrator::undo_integrate()](#method-Integrator::undo_integrate) + +Undo the effect of the last integration step. +![undo_integrate](images/undo_step.png) + + + #### ```void load_from_outState()``` -Load the integrator's initial state from ```outState```, rather than from the variables referenced by ```in_vars```. + +Load ```inState``` from ```outState```, rather than from the variables referenced by ```in_vars```. ![load_from_outState](images/load_from_outState.png) + + #### ```double** set_in_vars( double* in_vars[])``` -Specify the variables from which ```inState``` values are to be copied when ```load()``` is called. The number of elements in this array must equal the number of state variables. -Return a pointer to the previous array so that it can be deleted if necessary. + +This function specifies the variables from which ```inState``` values are to be copied, when ```load()``` is called. The number of elements in this array must equal the number of state variables. Return a pointer to the previous array so that it can be deleted if necessary. ![set_in_vars](images/set_in_vars.png) + + #### ```double** set_out_vars( double* out_vars[])``` -Specify the variables to which ```outState``` values are to be copied when ```unload()``` is called. The number of elements in this array must equal the number of state variables. -Return a pointer to the previous array so that it can be deleted if necessary. +This function specifies the variables to which ```outState``` values are to be copied, when ```unload()``` is called. The number of elements in this array must equal the number of state variables. Return a pointer to the previous array so that it can be deleted if necessary. ![set_out_vars](images/set_out_vars.png) + + +#### ```double getIndyVar()``` +**Inherited** from [Integrator::getIndyVar()](#method-Integrator::getIndyVar) + + +#### ```double setIndyVar()``` +**Inherited** from [Integrator::setIndyVar()](#method-Integrator::setIndyVar) + +### Protected Member Functions + +#### ```advanceIndyVar()``` +**Inherited** from [Integrator::advanceIndyVar()](#method-Integrator::advanceIndyVar) + + ## typedef RootErrorFunc + +### Description + +This typedef defines a type of C/C++ function whose purpose is to specify the job of a [```RootFinder```](#class-RootFinder). + ``` typedef double (*RootErrorFunc)( double x, double state[], RootFinder* root_finder, void* udata); ``` where: -|Parameter |Type |Description| -|------------|-----------------|-----------| -|x |```double``` | Independent variable | -|state |```double*``` | Array of state variable values | -|root_finder |[```RootFinder*```](#class-RootFinder)| Class for finding the roots of a function.| -|udata |```void*``` | A pointer to user_data.| +|Parameter |Type |Direction|Description| +|------------|-----------------|---|--------| +|x |```double``` |In | Independent variable | +|state |```double*``` |In | Array of state variable values | +|root_finder |[```RootFinder*```](#class-RootFinder)|In | Class for finding the roots of a function.| +|udata |```void*``` |In | A pointer to user_data.| -This **user-supplied** function should: - -1. Call [```root_finder->find_roots()```](#member-find_roots). -2. Specify what happens when the root is found, i.e., when ```find_roots()``` returns 0.0. -3. Return the value returned by ```root_finder->find_roots()``` as in the example below. +A function of type **RootErrorFunc** should: + +1. Specify a (math) function f(x) whose roots [x : f(x)=0] the RootFinder is meant to find. + - f(x) is usually a function of the state variables. State variables are themselves functions of x. +2. Call [```root_finder->find_roots(x, y)```](#member-find_roots), where y = f(x). If it returns 0.0, it's found a root of f(x). +3. Specify what to do as a result of finding a root. +4. Return the value returned by ```root_finder->find_roots()```. ### Example RootErrorFunc from the Cannonball example ``` double impact( double t, double state[], RootFinder* root_finder, void* udata) { double root_error = root_finder->find_roots(t, state[1]); if (root_error == 0.0) { - printf("---------------------------------------------------------------\n"); - printf("Impact at t = %5.10f x = %5.10f y = %5.10f.\n", t, state[0], state[1]); - printf("---------------------------------------------------------------\n"); root_finder->init(); - state[1] = 0.0000000001; // pos_y - state[2] = 0.0; // vel_x - state[3] = 0.0; // vel_y - state[4] = 0.0; // acc_x - state[5] = 0.0; // acc_y + state[2] = 0.9 * state[2]; + state[3] = -0.9 * state[3]; } return (root_error); } ``` +In this example : + +* the independent variable is t. +* y = f(t) = state[1], that is the y (vertical) component of the cannonball position. +* When ```root_finder->find_roots``` returns 0.0, then the result of finding the root (i.e, [t:state[1]=0]) is to "bounce" the cannon ball, by negating the y component of the velocity, and reducing the magnitude of the velocity by 10%. ## class FirstOrderODEVariableStepIntegrator Derived from [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator). -|Member |Type |Description| -|-------------------|--------------------|-----------| -| root_finder |[```RootFinder*```](#class-RootFinder) |Pointer to a RootFinder object.| -| root\_error\_func |[```RootErrorFunc```](#typedef-RootErrorFunc)|Function that specifies what happens when a function-root is found.| - - ### Description + This class represents a first order ODE integrator whose step-size can be varied. -### Constructor -### Member Functions +### Data Members +Those inherited from [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator) plus: +|Member |Type |Access |Description| +|--------------------|--------------------|---------|-----------| +| root_finder |[```RootFinder*```](#class-RootFinder)|Private|Pointer to a RootFinder object.| +| root\_error\_func |[```RootErrorFunc```](#typedef-RootErrorFunc)|Private|Function that specifies what happens when a function-root is found.| +|last_h| ```double```|Protected| Value of h used in the last integration step. | + +### Constructor + + +### Public Member Functions + + +#### ```void load()``` +**Inherited** from [FirstOrderODEIntegrator::load()](#method-FirstOrderODEIntegrator::load) + + + +#### ```void unload()``` +**Inherited** from [FirstOrderODEIntegrator::unload()](#method-FirstOrderODEIntegrator::unload) + + + +#### ```void step()``` +**Overrides** [FirstOrderODEIntegrator::step()](#method-FirstOrderODEIntegrator::step) + +This function calls the virtual function ```variable_step()``` (below) with the default step-size. Then, if a RootFinder has been specified using ```add_Rootfinder()``` (below), search that interval for roots . + + +#### ```void integrate()``` +**Inherited** from [Integrator::integrate()](#method-Integrator::integrate) + + +#### ```double undo_integrate()``` +**Overrides** [FirstOrderODEIntegrator::undo_integrate()](#method-FirstOrderODEIntegrator::undo_integrate) +Call ```FirstOrderODEIntegrator::undo_integrate()```, and then return ```last_h```. + + +#### ```load_from_outState()``` +**Inherited** from [FirstOrderODEIntegrator::load\_from\_outState()](#method-FirstOrderODEIntegrator::load_from_outState) + + +#### ```set_in_vars()``` +**Inherited** from [FirstOrderODEIntegrator::set\_in\_vars()](#method-FirstOrderODEIntegrator::set_in_vars) + + +#### ```set_out_vars()``` +**Inherited** from [FirstOrderODEIntegrator::set\_out\_vars()](#method-FirstOrderODEIntegrator::set_out_vars) + + #### ```virtual void variable_step( double h)``` -Derived classes should override this method to calculate ```outState``` using some integration algorithm, given ```X_in```, ```inState```, and ```derivs_func```. The over-riding method should also pass the ```user_data``` when calling the ```derivsFunc```. The default behavior is to simply add the integration step-size (```h```) to ```X_in```. + +|Parameter |Type |Description| +|------------|-------------|-----------------------| +| h |```double``` | Integration step-size that overrides the default step-size.| + +Derived classes should override this method to calculate ```outState``` using some integration algorithm, given ```h```, ```X_in```, ```inState```, and ```derivs_func```. The over-riding method should also pass the ```user_data``` when calling the ```DerivsFunc```. ![step](images/step.png) -#### ```void step()``` -Call the virtual function (```variable_step()```) with the default step-size. -Then, if a RootFinder has been specified (using ```add_Rootfinder()``` below), search that interval for roots . - - + #### ```void add_Rootfinder( RootFinder* root_finder, RootErrorFunc rfunc)``` |Parameter |Type |Description| |------------|-------------|-----------------------| -| root_finder|[```RootFinder*```](#class-RootFinder)| Error tolerance. | -| rfunc |[```RootErrorFunc```](#typedef-RootErrorFunc)| User supplied function that ??? | +| root_finder|[```RootFinder*```](#class-RootFinder)| RootFinder object. | +| rfunc |[```RootErrorFunc```](#typedef-RootErrorFunc)| User supplied function whose purpose is to specify the job of a RootFinder. | Configure the integrator to find roots of state-element vs. independent-variable functions. + +#### ```double getIndyVar()``` +**Inherited** from [Integrator::getIndyVar()](#method-Integrator::getIndyVar) + +#### ```double setIndyVar()``` +**Inherited** from [Integrator::setIndyVar()](#method-Integrator::setIndyVar) +### Protected Member Functions +#### ```advanceIndyVar()``` +**Inherited** from [Integrator::advanceIndyVar()](#method-Integrator::advanceIndyVar) ## class EulerIntegrator @@ -249,11 +386,32 @@ Derived from [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableS ### Description The Euler method is a first order numerical integration method. It is the simplest, explicit [Runge-Kutta](https://en.wikipedia.org/wiki/Runge–Kutta_methods) method. + +### Data Members +Those inherited from [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableStepIntegrator). + ### Constructor ``` -EulerIntegrator(double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data) +EulerIntegrator( double h, + int N, + double* in_vars[], + double* out_vars[], + DerivsFunc func, + void* user_data) ``` -[Constructor Parameters](#FOODEConstructorParameters) are those of [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator). +Constructor Parameters are those of [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableStepIntegrator). + +### Public Member Functions + +* All of the [Public Member Functions of FirstOrderODEVariableStepIntegrator](#FirstOrderODEVariableStepIntegrator::publicMemberFunctions), plus : + + +#### ```void variable_step( double h)``` +**Overrides** [FirstOrderODEVariableStepIntegrator::variable_step()](#method-FirstOrderODEVariableStepIntegrator::variable_step) + +Calculates ```outState``` from ```h```, ```X_in```, ```inState```, and +```derivs_func```, using the Euler method. + ## class HeunsMethod @@ -262,12 +420,31 @@ Derived from [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableS This integrator implements [Heun's Method](https://en.wikipedia.org/wiki/Heun%27s_method). +### Data Members +Those inherited from [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableStepIntegrator). + ### Constructor ``` -HeunsMethod( double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data) +HeunsMethod( double h, + int N, + double* in_vars[], + double* out_vars[], + DerivsFunc func, + void* user_data) ``` [Constructor Parameters](#FOODEConstructorParameters) are those of [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator). +### Public Member Functions + +* All of the [Public Member Functions of FirstOrderODEVariableStepIntegrator](#FirstOrderODEVariableStepIntegrator::publicMemberFunctions). + + +#### ```void variable_step( double h)``` +**Overrides** [FirstOrderODEVariableStepIntegrator::variable_step()](#method-FirstOrderODEVariableStepIntegrator::variable_step) + +Calculates ```outState``` from ```h```, ```X_in```, ```inState```, and +```derivs_func```, using the Heun's method. + ## class RK2Integrator Derived from [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableStepIntegrator). @@ -276,12 +453,32 @@ Derived from [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableS ![RK2_tableau](images/RK2_tableau.png) +### Data Members +Those inherited from [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableStepIntegrator). + ### Constructor ``` -RK2Integrator( double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data) +RK2Integrator( double h, + int N, + double* in_vars[], + double* out_vars[], + DerivsFunc func, + void* user_data) ``` [Constructor Parameters](#FOODEConstructorParameters) are those of [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator). +### Public Member Functions + +* All of the [Public Member Functions of FirstOrderODEVariableStepIntegrator](#FirstOrderODEVariableStepIntegrator::publicMemberFunctions). + + +#### ```void variable_step( double h)``` +**Overrides** [FirstOrderODEVariableStepIntegrator::variable_step()](#method-FirstOrderODEVariableStepIntegrator::variable_step) + +Calculates ```outState``` from ```h```, ```X_in```, ```inState```, and +```derivs_func```, using the Runge-Kutta 2 method. + + ## class RK4Integrator Derived from [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableStepIntegrator). @@ -290,12 +487,31 @@ Derived from [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableS ![RK4_tableau](images/RK4_tableau.png) +### Data Members +Those inherited from [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableStepIntegrator). + ### Constructor ``` -RK4Integrator( double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data) +RK4Integrator( double h, + int N, + double* in_vars[], + double* out_vars[], + DerivsFunc func, + void* user_data) ``` [Constructor Parameters](#FOODEConstructorParameters) are those of [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator). +### Public Member Functions + +* All of the [Public Member Functions of FirstOrderODEVariableStepIntegrator](#FirstOrderODEVariableStepIntegrator::publicMemberFunctions). + + +#### ```void variable_step( double h)``` +**Overrides** [FirstOrderODEVariableStepIntegrator::variable_step()](#method-FirstOrderODEVariableStepIntegrator::variable_step) + +Calculates ```outState``` from ```h```, ```X_in```, ```inState```, and +```derivs_func```, using the Runge-Kutta 4 method. + ## class RK3_8Integrator Derived from [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableStepIntegrator). @@ -303,13 +519,33 @@ Derived from [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableS ```RK3_8Integrator``` implements the fourth order, explicit, [Runge-Kutta](https://en.wikipedia.org/wiki/Runge–Kutta_methods) method whose Butcher tableau is as follows. ![RK38_tableau](images/RK38_tableau.png) + +### Data Members +Those inherited from [FirstOrderODEVariableStepIntegrator](#class-FirstOrderODEVariableStepIntegrator). + ### Constructor ``` -RK3_8Integrator( double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data) +RK3_8Integrator( double h, + int N, + double* in_vars[], + double* out_vars[], + DerivsFunc func, + void* user_data) ``` [Constructor Parameters](#FOODEConstructorParameters) are those of [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator). +### Public Member Functions + +* All of the [Public Member Functions of FirstOrderODEVariableStepIntegrator](#FirstOrderODEVariableStepIntegrator::publicMemberFunctions). + + +#### ```void variable_step( double h)``` +**Overrides** [FirstOrderODEVariableStepIntegrator::variable_step()](#method-FirstOrderODEVariableStepIntegrator::variable_step) + +Calculates ```outState``` from ```h```, ```X_in```, ```inState```, and +```derivs_func```, using the Runge-Kutta 3/8 method. + ## class ABM2Integrator Derived from [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator). @@ -317,9 +553,17 @@ Derived from [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator). The ABM2Integrator implements the second-order Adams-Bashforth-Moulton predictor/corrector method. Adams methods maintain a history of derivatives rather than calculating intermediate values like Runge-Kutta methods. +### Data Members +Those inherited from [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator). + ### Constructor ``` -ABM2Integrator ( double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data) +ABM2Integrator ( double h, + int N, + double* in_vars[], + double* out_vars[], + DerivsFunc func, + void* user_data) ``` [Constructor Parameters](#FOODEConstructorParameters) are those of [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator). @@ -330,9 +574,17 @@ Derived from [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator). ### Description The ABM2Integrator implements the second-order Adams-Bashforth-Moulton predictor/corrector method. Adams methods maintain a history of derivatives rather than calculating intermediate values like Runge-Kutta methods. +### Data Members +Those inherited from [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator). + ### Constructor ``` -ABM4Integrator ( double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data) +ABM4Integrator ( double h, + int N, + double* in_vars[], + double* out_vars[], + DerivsFunc func, + void* user_data) ``` [Constructor Parameters](#FOODEConstructorParameters) are those of [FirstOrderODEIntegrator](#class-FirstOrderODEIntegrator). @@ -344,52 +596,121 @@ Derived from [Integrator](#class-Integrator). ### Description EulerCromer is integration method that conserves energy in oscillatory systems better than Runge-Kutta. So, it's good for mass-spring-damper systems, and orbital systems. +### Data Members +Those inherited from [Integrator](#class-Integrator) plus: + +|Member |Type |Access |Description | +|-----------|------------------|---------|------------| +|nDimensions|```unsigned int```|Protected|Number of dimensions in position, velocity, and acceleration vectors. Typically 1,2, or 3.| +| pos_p |```double**``` |Protected|Array of pointers to variables from which we ```load()``` and to which we ```unload()``` the position values .| +| vel_p |```double**``` |Protected|Array of pointers to variables from which we ```load()``` and to which we ```unload()``` the velocity values .| +| pos_in |```double*``` |Protected|Position input array.| +| vel_in |```double*``` |Protected|Velocity input array.| +| pos_out |```double*``` |Protected|Position output array.| +| vel_out |```double*``` |Protected|Velocity output array.| +| g_out |```double*``` |Protected|Array of accelerations returned from gderivs.| +| f_out |```double*``` |Protected|Array of velocities returned from fderivs.| +| gderivs |[```DerivsFunc```](#typedef-DerivsFunc)|Protected|A function that returns accelerations.| +| fderivs |[```DerivsFunc```](#typedef-DerivsFunc)|Protected|A function that returns velocities.| + ### Constructor ``` -SemiImplicitEuler(double dt, int N, double* xp[], double* vp[], derivsFunc gfunc, derivsFunc ffunc, void* user_data) +EulerCromerIntegrator(double dt, + int N, + double* xp[], + double* vp[], + DerivsFunc gfunc, + DerivsFunc ffunc, + void* user_data) ``` |Parameter |Type |Description| |-----------|-------------|-----------------------| -| dt |```double``` |Default time step value| -| N |```int``` |Number of state variables to be integrated| -| xp |```double*```|Array of pointers to the variables from which we ```load()``` and to which we ```unload()``` the integrator's position values .| -| vp |```double*```|Array of pointers to the variables from which we ```load()``` and to which we ```unload()``` the integrator's velocity values .| -| gfunc |[```derivsFunc```](#typedef-derivsFunc)| A function that returns acceleration | -| ffunc |[```derivsFunc```](#typedef-derivsFunc)| A function that returns velocity | -|user_data |```void*```| A pointer to user defined data that will be passed to a derivsFunc when called by the Integrator. | +| dt |```double``` |Default time step value. Sets Integrator::default_h. | +| N |```int``` |Sets nDimensions above.| +| xp |```double*```|Sets pos_p above.| +| vp |```double*```|Sets vel_p above.| +| gfunc |[```DerivsFunc```](#typedef-DerivsFunc)| Sets gderivs above. | +| ffunc |[```DerivsFunc```](#typedef-DerivsFunc)| Sets fderivs above. | +|user_data |```void*``` | Sets Integrator::user_data. | + +### Public Member Functions + +#### ```void step( double dt)``` + +|Parameter |Type |Description| +|------------|-------------|-----------------------| +| dt |```double``` | Integration step-size that overrides the default step-size.| + +This function calculates ```pos_out``` and ```vel_out``` from ```dt```, ```X_in```, ```pos_in```, ```vel_in```, ```f_func```, and ```gfunc``` using the Euler-Cromer method. + +#### ```void step()``` + +This function calls ```step(dt)``` (above) with the default step-size. + +#### ```void load()``` +**Overrides** [Integrator::integrate()](#method-Integrator::integrate) +Load the integrator's initial state from the variables specified by **xp**, and **vp**. Set the initial value of the independent variable for the next step to the final value of the previous step. + +#### ```void unload()``` +**Overrides** [Integrator::integrate()](#method-Integrator::integrate) + +Unload the integrator's result state (**pos\_out**, and **vel\_out**) to the variables specified by **xp**, and **vp**. + +#### ```void integrate()``` +**Inherited** from [Integrator::integrate()](#method-Integrator::integrate) + +#### ```double undo_integrate()``` +**Overrides** [Integrator::undo_integrate()](#method-Integrator::undo_integrate) + +Undo the effect of the last integration step. + + +#### ```double getIndyVar()``` +**Inherited** from [Integrator::getIndyVar()](#method-Integrator::getIndyVar) + + +#### ```double setIndyVar()``` +**Inherited** from [Integrator::setIndyVar()](#method-Integrator::setIndyVar) + +### Protected Member Functions + +#### ```advanceIndyVar()``` +**Inherited** from [Integrator::advanceIndyVar()](#method-Integrator::advanceIndyVar) ## enum SlopeConstraint +### Description + | Value | Meaning | |-------------------|---------| -| Negative | Require slope of the function to be negative at the root. | -| Unconstrained | No slope constraint. | -| Positive | Require slope of the function to be positive at the root. | +| Negative | Require slope of the function to be negative at the root.| +| Unconstrained | No slope constraint.| +| Positive | Require slope of the function to be positive at the root.| ## class RootFinder -Derived from [RootFinder](#class-RootFinder). - -|Member |Type |Description | -|------------------|------------|------------| -| f_upper |```double```| | -| x_upper |```double```| | -| upper_set |```bool``` | | -| f_lower |```double```| | -| x_lower |```double```| | -| lower_set |```bool``` | | -| prev\_f_error |```double```| | -| f\_error\_tol |```double```| | -| iterations |```int``` | | -| slope_constraint |[```SlopeConstraint```](#enum-SlopeConstraint)| | -| f_slope |[```SlopeConstraint```](#enum-SlopeConstraint)| | - ### Description The RootFinder class uses the [Regula-Falsi](https://en.wikipedia.org/wiki/Regula_falsi) method to find roots of a math function. A root is a value of **x** such that **f(x)=0**. +### Data Members +|Member |Type |Access |Description | +|------------------|------------|-------|------------| +| f_upper |```double```|Private|Error-function value upper bound.| +| x_upper |```double```|Private|Independent variable value upper bound.| +| upper_set |```bool``` |Private|True = bound is valid. False = not valid.| +| f_lower |```double```|Private|Error-function value lower bound.| +| x_lower |```double```|Private|Independent variable value lower bound.| +| lower_set |```bool``` |Private|True = bound is valid. False = not valid.| +| prev\_f_error |```double```|Private|Absolute value of the previous root function value.| +| f\_error\_tol |```double```|Private|How close is close enough.| +| iterations |```int``` |Private|Number of Regula Falsi iterations.| +| slope_constraint |[```SlopeConstraint```](#enum-SlopeConstraint)|Private|Find roots with this slope sign.| +| f_slope |[```SlopeConstraint```](#enum-SlopeConstraint)|Private|Current root function slope.| + + ### Constructors #### ```RootFinder()``` @@ -402,7 +723,7 @@ Default constructor that calls ```void RootFinder::init()``` below. | tolerance |```double``` | Error tolerance. | | constraint |[```SlopeConstraint```](#enum-SlopeConstraint)| | -### Methods +### Public Member Functions #### ```void init( double tolerance, SlopeConstraint constraint)``` Initialize the RootFinder with the given tolerance, and SlopeConstraint. diff --git a/trick_source/trick_utils/SAIntegrator/examples/CannonBall/README.md b/trick_source/trick_utils/SAIntegrator/examples/CannonBall/README.md index 597c1103..cd86cb8b 100644 --- a/trick_source/trick_utils/SAIntegrator/examples/CannonBall/README.md +++ b/trick_source/trick_utils/SAIntegrator/examples/CannonBall/README.md @@ -1,6 +1,6 @@ # CannonBall -This is an example of using the RK2Integrator to create a simple cannon ball simulation. +This is an example of using the RK2Integrator to create a simple cannon ball simulation. We also use a rootfinder with out integrator to detect contact with the ground, and bounce the cannonball. ``` $ make @@ -9,22 +9,3 @@ $ python plot_trajectory.py ``` ![Cannon](images/Cannon.png) - -``` -$ make -$ ./Cannonball -``` - -Next edit, and uncomment the indicated lines, recompile, and run. You should see: - -``` -5.070, 219.5374398594, 0.6674655000, 43.3012701892, -24.7367000000, 0.0000000000, -9.8100000000 -5.080, 219.9704525612, 0.4196080000, 43.3012701892, -24.8348000000, 0.0000000000, -9.8100000000 -5.090, 220.4034652631, 0.1707695000, 43.3012701892, -24.9329000000, 0.0000000000, -9.8100000000 ---------------------------------------------------------------- -Impact at t = 5.0968399592 x = 220.6996441856 y = 0.0000000000. ---------------------------------------------------------------- -5.100, 220.6996441856, 0.0000000001, 0.0000000000, 0.0000000000, 0.0000000000, 0.0000000000 -5.110, 220.6996441856, 0.0000000001, 0.0000000000, 0.0000000000, 0.0000000000, 0.0000000000 -5.120, 220.6996441856, 0.0000000001, 0.0000000000, 0.0000000000, 0.0000000000, 0.0000000000 -``` diff --git a/trick_source/trick_utils/SAIntegrator/examples/CannonBall/images/Cannon.png b/trick_source/trick_utils/SAIntegrator/examples/CannonBall/images/Cannon.png index 866afeb24e35816f936d639c24f719fb0760ffd2..20d91876e03d05d659057b2e641e63327d34c09b 100644 GIT binary patch literal 163624 zcmeFZby!v1)&~kmY(S+&Q93218@6;K-QC^Y3MwL9(h4FX-OUE1Q=~QxlG5FAC+~aC zcaFa2e&>Amxqlv?M_7CAxz?I<%rVCNjo%oP&}RygcQA-B5D*aVNK1(+BOpLz5D;z& zKu|%8OyHOs0>W)6D^byB(xRed&zv31t!&K@5TrumHPAFwy6&axC`(%gL8QE*qCoaD288-b5gAeV!11cgjdnJg?4Vk9pmZxT&{bbA$v-Vw!Hpi#Fw zA}kE`8S3_R9JdByX1#&4lCz)iwSl-IS=>G%^aoi#cIT-V_BASkeoJCE1_Id`wBhgo zDHm7qIUI_L7p(cERm)m8v-N?sZf>dc+ZAX%9s*l*d2vw`CLa2DEtS>!0}n5%vEA#Wz0_d3iaX{ij6Yg$ zPjuq%c3;?$9pTAPhzwuA)Z7cXi4)4b*OM%OgO5)K;!P`&X0GkRS;EUiv%!IgejTnb*%XnE`J|t(qK%DPwCne{FMJ5TplW0vtn7eNl3V}e=|ULV zy(X00vQ2wr-sjU-_!*GXJdKugFAHzFZ>f{-W8>+uFEaUw>$oGUge?;cmX=6d*vP z|6<;;!_RTH*%k)JBf;T=9HVPM(t;nVv|*ag4u3^jfYQFjF3ja!SWkB1?_3LgHHR2Q z>bxK~g?%Gk;k?6A@t z0}rV*oAzf0yrS&0?JK?`R*3bIem0>@Ek{N<#U}6v8)T!%nsA)_2mF!5%0E7+9XzXe zgPPTrx7QUU@MHVOE(dFTT3p>oom-us>Hq;GEN)w}DTyYH9M2*YL(}$TnXt4Pw{abk zP?u8o5TSef^%>{ko7^)YvfeTS*HcNv9i|uE`7C_toCs(nh)tgR;ue>MX`5%Gv5aB7Ng!RCh?dvEzq|(n63Am zB&Kjksj$&SGowAJ2&5%TvC%W3=H!^s&ZgALA+{oGQ3lbsI$0NQe-E01Zjn!S$}Zk| z^MPX+fm3wzTl8nFZi%dKVya>>v^M83{ga|grjuo?CB}sE1lNSp z#GMHSzBGGDtWPJB_6Zrf?t6;?uh3f(K*vyQ|!SNQOWb%-nb@zadc zFw*?^2wlBhAJ@9qKGI9ydNgf4eXDlN_59$zch-UN;od>Q>gG58tYfi^j}AGcpIE-J z49?~U=w2h|pI1JA^h@#4KlzxtBTko0jf!-;` z7CGz6{*7v_NZugKAje(iAGl#5xdL>;rEowJ|NcXQK;P6A5B@QaP*p9$-g zZJVQXmr5p*O!r6F*0Sqj`DYs@E=$p-DW^;dCCfU(2K%!@vbf(iZguTES~<8e%U6TA9S| zl?pF1bwskKxNzWOhC`Sz?J$S1WHItE>K@t?q!Z|q&ODrdz{>u^l8T&--dTK+v+zOU zK*7RM#32d4&qgSnwyKD#+VG`ij-{4s50C2<+$pbpI-(>zx|O5txu*Tb7dXGuk<+OY zERr@N@}Ys?mD0uM6Rq7G-23P%cF9ZEKN*>B|3&On2{6cSFZ+wzsDN?DrnOoR% zF@j7IR!LoI|7hZ*2G(;s1>640)S#)jscEmp`h)sgxPH(~{R^mf^AN#*6TUj(3 zTqR%VYsJ~-J&IOL;3mA^bm!bFlhVKk9_-PsQ945POJKE;k zV7;vtdlr@brKy|&qYdL5<0;EzE^N!?{T1mtY*jY;t@WGxx%)25*ELOc&D|(Pgr68~ zAG0zfY3$9tdQG|}TOn(fJ?4LK?X*DQ8||qyX&l+MelLI-FD{MAgQ1A-x;hxPxS^Qk z|K-BU&}#X6rI~&Y7b7imA|tGp!m{ls-kTvzLr9a;UTwj8bgguxXiQGe<&&{%TYJTD z#hZ$>_`&$Tb=y%UgX0nzRkv)ukKP{PR((H`tJYE0S?nP*---uqO-|dfgu?#o^(~+-CaJVd&FD-EKxj4den{jjFm-ArElUye_oaU$9 zw4EiW&8un7HX5>D-r5s1j5Hn?G8hVIsO7eHSQpChy8|1)QZLIWf#u^^r4GU;sjSy* z73{Wno*Y4K!UB4(X7vJQ-M{S_9+H0*?YXOhmH3E+N7?t|_U8l3fs%X^EbW}i89t%; zlO?L->K1QRrUe8>8wJ5O_PRNbva5S6j zk>Xgl5wVr_rtXu6&Gphr(R7-A+N-UQ8U6s_`Kto73$y`}Zc_gZdM~j6)m``xr)j)n zTC}>ab(0wiz7vOXXZf(41C|DubvnPm_2%{*Y~Wa7b<>;Nhjqufi(x@yQa{pvdV+Aw z<5+$s<*LeT`|Ye$C7&^uoq~&pkD>!i_M1M}gU|xqQA*1N0pT9?&3{B`WvU$n1jKYJRZUk-c{x54 z2RmjXQwL)+W=}gu&>I0kz>^PL+L^f;k$KwL+Pm<13R3*hgAZKaG_z2U{n5qMMvy{N z{u!C5gR>bKCo>206AB>=GBPp&XH#=NWig4r-3~qpQdqjWI`XlwczAd)d$2P*I9sr= z^78VsJYi#DV`Bn6m|VQ|H4Te8}IQBWC7e;%w#UYUN;0cJo{#V+S`^K?;hS z7yZw_KgVh2Y4wjc*}MF0T3~`KH{Y_UC*=mYe*_qk9fOiP7 zv9hrV{BgryzWT>2|LIn(f85H$#`Dj2{?j*qyHkMWW(NN>qd&#8OLkah_GMy#wsoGhXf9_0Bs`6bUg|lGab6U1 zDE#@x`DF&X^GZ_9fM2@Lw#&d&4f}r57=zzdZz``#|M}ExL%{WZorU&NFAWzmHWUHz z-~J%Gg;XFF*V#ljB>r#v-aKvxSt@QWJP-j1LiTTeB;k-LQLu~3OXB<|BMB5kpSkrP zJQYF~^#Bo|9>U?cZK<{O8i$PesfCyRf+$q z#D7)dHwpazsS-@M)khOHZvDI~o@4qheVlyf8)Z7Gio=9=NCY$~CEo7Xv)fPc*p>Bh zh1(~^HF8*chGW&AZ`G|0j#R3uHDH+{1rI7hZ@e* zdwI`?5FTul4XiCC8jN<32INNyokbQ3m#r>2N+zQACKw#Y-Mjd>|Q?48<&3r zRgS^5j;AXbH&6MwSvBj<<%>q*`JTjg=c&bE&F9x*=!9>EgMNid*i{IjxK5D>$CAH* zGi9n`$9a)y@AZP(#TeOx)0K?GkuuVYIkeh~y&g`-IcSCT$d`N@I#p66Dw*JpAhFP5 zNx`kYBz8%?I`_lm(E=TAztg3}L%7^T@NX|H0WZY4r6TwXVv8aON@BNIEB<F0fMFE}IB&QKYDh?7E>37kY zuT|E9cFSidM{%r=dv=4g1YNw(ZuWA^!)?l`gHz+<@=8o&CUPh)XF!jm=r7RnJu`U7 z=N_XEO26n3v=rIA_uU6#clcA49EC$7dySVo>-lA_Kn*$-j_%pl=qflg945THOH9u{ z-spSkJTARlHXu}2On2_a2+b5Td%^C1;d!_|HUR5vN7S*qc}W4chv+YIUQ+`K;7$Bs zBIFk-QHdFL#ZXUp%=#T33@Q3B+0QmMkoat{0-4yG9UAT}cJW=EEV!M_zlx<(O3=K- zr%=i)Eg@6NWGkYRiKW8{p?9PBJ7V}_QeAie`g)m2g#7}2gKBY4dJL{I*#`uM9EKJm zg$o;wXC`M^R@$DUV45Z#%sTfl^*mNc;sd}rvoz@c!}D=8%PpgiEyI5f<@ng~9S*A; zR>3a&tj?GF)A9zhB-dxJud4L@4%OsSd6W!%cSHC*w(<{0brktG%VYfyvPi841dmnM zM+;IKj$h+Ya(M0-7WEGJAF*HlR1DbD7vAq>uf05)JlyMHS$}~g^ex$@Fqhb4N=cH` zul#7zL3ms;l%oQL7KSCT0~I`(d!avAV$!h>$L(1zxR@S5TQ;Iqj|k7TIWK?Sb87 zrQMfqiH?r94;DsjCaoqd@MO8B97VUCXe<4W406x<`L_l1+(y*&rz^uN3or?p57rvi z3+p(HT9Ervc~u&`55MdCY-Xz{@MfF-kSP&EpXAcH7CfF>7_*wR?pUc_h#2CUv>o~! 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