ActiViz .NET
5.10.1
|
vtkPolynomialSolversUnivariate - polynomial solvers More...
Public Member Functions | |
vtkPolynomialSolversUnivariate (IntPtr rawCppThis, bool callDisposalMethod, bool strong) | |
Automatically generated constructor - called from generated code. DO NOT call directly. More... | |
vtkPolynomialSolversUnivariate () | |
Undocumented Block More... | |
override int | IsA (string type) |
Undocumented Block More... | |
new vtkPolynomialSolversUnivariate | NewInstance () |
Undocumented Block More... | |
![]() | |
vtkObject (IntPtr rawCppThis, bool callDisposalMethod, bool strong) | |
Automatically generated constructor - called from generated code. DO NOT call directly. More... | |
vtkObject () | |
Create an object with Debug turned off, modified time initialized to zero, and reference counting on. More... | |
uint | AddObserver (uint arg0, vtkCommand arg1, float priority) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
uint | AddObserver (string arg0, vtkCommand arg1, float priority) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
virtual void | DebugOff () |
Turn debugging output off. More... | |
virtual void | DebugOn () |
Turn debugging output on. More... | |
vtkCommand | GetCommand (uint tag) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
byte | GetDebug () |
Get the value of the debug flag. More... | |
virtual uint | GetMTime () |
Return this object's modified time. More... | |
int | HasObserver (uint arg0, vtkCommand arg1) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
int | HasObserver (string arg0, vtkCommand arg1) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
int | HasObserver (uint arg0) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
int | HasObserver (string arg0) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
int | InvokeEvent (uint arg0, IntPtr callData) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
int | InvokeEvent (string arg0, IntPtr callData) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
int | InvokeEvent (uint arg0) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
int | InvokeEvent (string arg0) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
virtual void | Modified () |
Update the modification time for this object. Many filters rely on the modification time to determine if they need to recompute their data. The modification time is a unique monotonically increasing unsigned long integer. More... | |
vtkObject | NewInstance () |
Undocumented Block More... | |
void | RemoveAllObservers () |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
void | RemoveObserver (vtkCommand arg0) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
void | RemoveObserver (uint tag) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
void | RemoveObservers (uint arg0, vtkCommand arg1) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
void | RemoveObservers (string arg0, vtkCommand arg1) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
void | RemoveObservers (uint arg0) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
void | RemoveObservers (string arg0) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
void | SetDebug (byte debugFlag) |
Set the value of the debug flag. A non-zero value turns debugging on. More... | |
override string | ToString () |
Returns the result of calling vtkObject::Print as a C# string. More... | |
delegate void | vtkObjectEventHandler (vtkObject sender, vtkObjectEventArgs e) |
Generic signature for all vtkObject events. More... | |
void | RemoveAllHandlersForAllEvents () |
Call RemoveAllHandlers on each non-null vtkObjectEventRelay. TODO: This method needs to get called by the generated Dispose. Make that happen... More... | |
![]() | |
vtkObjectBase (IntPtr rawCppThis, bool callDisposalMethod, bool strong) | |
Automatically generated constructor - called from generated code. DO NOT call directly. More... | |
vtkObjectBase () | |
Create an object with Debug turned off, modified time initialized to zero, and reference counting on. More... | |
virtual void | Register (vtkObjectBase o) |
Increase the reference count (mark as used by another object). More... | |
virtual void | FastDelete () |
Delete a reference to this object. This version will not invoke garbage collection and can potentially leak the object if it is part of a reference loop. Use this method only when it is known that the object has another reference and would not be collected if a full garbage collection check were done. More... | |
string | GetClassName () |
Return the class name as a string. This method is defined in all subclasses of vtkObjectBase with the vtkTypeMacro found in vtkSetGet.h. More... | |
int | GetReferenceCount () |
Return the current reference count of this object. More... | |
void | SetReferenceCount (int arg0) |
Sets the reference count. (This is very dangerous, use with care.) More... | |
Static Public Member Functions | |
static new vtkPolynomialSolversUnivariate | New () |
Undocumented Block More... | |
static int | FerrariSolve (IntPtr c, IntPtr r, IntPtr m, double tol) |
Algebraically extracts REAL roots of the quartic polynomial with REAL coefficients X^4 + c[0] X^3 + c[1] X^2 + c[2] X + c[3] and stores them (when they exist) and their respective multiplicities in the r and m arrays, based on Ferrari's method. Some numerical noise can be filtered by the use of a tolerance tol instead of equality with 0 (one can use, e.g., VTK_DBL_EPSILON). Returns the number of roots. Warning: it is the user's responsibility to pass a non-negative tol. More... | |
static int | FilterRoots (IntPtr P, int d, IntPtr upperBnds, int rootcount, double diameter) |
This uses the derivative sequence to filter possible roots of a polynomial. First it sorts the roots and removes any duplicates. If the number of sign changes of the derivative sequence at a root at upperBnds[i] == that at upperBnds[i] - diameter then the i^th value is removed from upperBnds. It returns the new number of roots. More... | |
static double | GetDivisionTolerance () |
Set/get the tolerance used when performing polynomial Euclidean division to find polynomial roots. This tolerance is used to decide whether the coefficient(s) of a polynomial remainder are close enough to zero to be neglected. More... | |
static int | HabichtBisectionSolve (IntPtr P, int d, IntPtr a, IntPtr upperBnds, double tol) |
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial
in ]a[0] ; a[1]] using the Habicht sequence (polynomial coefficients are REAL) and returns the count nr. All roots are bracketed in the first ]upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.). More... | |
static int | HabichtBisectionSolve (IntPtr P, int d, IntPtr a, IntPtr upperBnds, double tol, int intervalType) |
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial
in ]a[0] ; a[1]] using the Habicht sequence (polynomial coefficients are REAL) and returns the count nr. All roots are bracketed in the first ]upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.). More... | |
static int | HabichtBisectionSolve (IntPtr P, int d, IntPtr a, IntPtr upperBnds, double tol, int intervalType, bool divideGCD) |
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial
in ]a[0] ; a[1]] using the Habicht sequence (polynomial coefficients are REAL) and returns the count nr. All roots are bracketed in the first ]upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.). More... | |
static new int | IsTypeOf (string type) |
Undocumented Block More... | |
static int | LinBairstowSolve (IntPtr c, int d, IntPtr r, ref double tolerance) |
Seeks all REAL roots of the d -th degree polynomial c[0] X^d + ... + c[d-1] X + c[d] = 0 equation Lin-Bairstow's method ( polynomial coefficients are REAL ) and stores the nr roots found ( multiple roots are multiply stored ) in r. tolerance is the user-defined solver tolerance; this variable may be relaxed by the iterative solver if needed. Returns nr. Warning: it is the user's responsibility to make sure the r array is large enough to contain the maximal number of expected roots. More... | |
static new vtkPolynomialSolversUnivariate | SafeDownCast (vtkObjectBase o) |
Undocumented Block More... | |
static void | SetDivisionTolerance (double tol) |
Set/get the tolerance used when performing polynomial Euclidean division to find polynomial roots. This tolerance is used to decide whether the coefficient(s) of a polynomial remainder are close enough to zero to be neglected. More... | |
static IntPtr | SolveCubic (double c0, double c1, double c2, double c3) |
Solves a cubic equation c0*t^3 + c1*t^2 + c2*t + c3 = 0 when c0, c1, c2, and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Return array contains number of (real) roots (counting multiple roots as one) followed by roots themselves. The value in roots[4] is a integer giving further information about the roots (see return codes for int SolveCubic() ). More... | |
static int | SolveCubic (double c0, double c1, double c2, double c3, IntPtr r1, IntPtr r2, IntPtr r3, IntPtr num_roots) |
Solves a cubic equation when c0, c1, c2, And c3 Are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Roots and number of real roots are stored in user provided variables r1, r2, r3, and num_roots. Note that the function can return the following integer values describing the roots: (0)-no solution; (-1)-infinite number of solutions; (1)-one distinct real root of multiplicity 3 (stored in r1); (2)-two distinct real roots, one of multiplicity 2 (stored in r1 & r2); (3)-three distinct real roots; (-2)-quadratic equation with complex conjugate solution (real part of root returned in r1, imaginary in r2); (-3)-one real root and a complex conjugate pair (real root in r1 and real part of pair in r2 and imaginary in r3). More... | |
static IntPtr | SolveLinear (double c0, double c1) |
Solves a linear equation c2*t + c3 = 0 when c2 and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Return array contains number of roots followed by roots themselves. More... | |
static int | SolveLinear (double c0, double c1, IntPtr r1, IntPtr num_roots) |
Solves a linear equation c2*t + c3 = 0 when c2 and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Root and number of (real) roots are stored in user provided variables r2 and num_roots. More... | |
static IntPtr | SolveQuadratic (double c0, double c1, double c2) |
Solves a quadratic equation c1*t^2 + c2*t + c3 = 0 when c1, c2, and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Return array contains number of (real) roots (counting multiple roots as one) followed by roots themselves. Note that roots[3] contains a return code further describing solution - see documentation for SolveCubic() for meaning of return codes. More... | |
static int | SolveQuadratic (double c0, double c1, double c2, IntPtr r1, IntPtr r2, IntPtr num_roots) |
Solves a quadratic equation c1*t^2 + c2*t + c3 = 0 when c1, c2, and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Roots and number of roots are stored in user provided variables r1, r2, num_roots More... | |
static int | SolveQuadratic (IntPtr c, IntPtr r, IntPtr m) |
Algebraically extracts REAL roots of the quadratic polynomial with REAL coefficients c[0] X^2 + c[1] X + c[2] and stores them (when they exist) and their respective multiplicities in the r and m arrays. Returns either the number of roots, or -1 if ininite number of roots. More... | |
static int | SturmBisectionSolve (IntPtr P, int d, IntPtr a, IntPtr upperBnds, double tol) |
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial P[0] X^d + ... + P[d-1] X + P[d] in ]a[0] ; a[1]] using Sturm's theorem ( polynomial coefficients are REAL ) and returns the count nr. All roots are bracketed in the first ]upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.). More... | |
static int | SturmBisectionSolve (IntPtr P, int d, IntPtr a, IntPtr upperBnds, double tol, int intervalType) |
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial P[0] X^d + ... + P[d-1] X + P[d] in ]a[0] ; a[1]] using Sturm's theorem ( polynomial coefficients are REAL ) and returns the count nr. All roots are bracketed in the first ]upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.). More... | |
static int | SturmBisectionSolve (IntPtr P, int d, IntPtr a, IntPtr upperBnds, double tol, int intervalType, bool divideGCD) |
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial P[0] X^d + ... + P[d-1] X + P[d] in ]a[0] ; a[1]] using Sturm's theorem ( polynomial coefficients are REAL ) and returns the count nr. All roots are bracketed in the first ]upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.). More... | |
static int | TartagliaCardanSolve (IntPtr c, IntPtr r, IntPtr m, double tol) |
Algebraically extracts REAL roots of the cubic polynomial with REAL coefficients X^3 + c[0] X^2 + c[1] X + c[2] and stores them (when they exist) and their respective multiplicities in the r and m arrays. Some numerical noise can be filtered by the use of a tolerance tol instead of equality with 0 (one can use, e.g., VTK_DBL_EPSILON). The main differences with SolveCubic are that (1) the polynomial must have unit leading coefficient, (2) complex roots are discarded upfront, (3) non-simple roots are stored only once, along with their respective multiplicities, and (4) some numerical noise is filtered by the use of relative tolerance instead of equality with 0. Returns the number of roots. <i> In memoriam </i> Niccolo Tartaglia (1500 - 1559), unfairly forgotten. More... | |
![]() | |
static new vtkObject | New () |
Create an object with Debug turned off, modified time initialized to zero, and reference counting on. More... | |
static void | BreakOnError () |
This method is called when vtkErrorMacro executes. It allows the debugger to break on error. More... | |
static int | GetGlobalWarningDisplay () |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
static void | GlobalWarningDisplayOff () |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
static void | GlobalWarningDisplayOn () |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
static new int | IsTypeOf (string type) |
Undocumented Block More... | |
static vtkObject | SafeDownCast (vtkObjectBase o) |
Undocumented Block More... | |
static void | SetGlobalWarningDisplay (int val) |
This is a global flag that controls whether any debug, warning or error messages are displayed. More... | |
![]() | |
static vtkObjectBase | New () |
Create an object with Debug turned off, modified time initialized to zero, and reference counting on. More... | |
static int | IsTypeOf (string name) |
Return 1 if this class type is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeMacro found in vtkSetGet.h. More... | |
Public Attributes | |
new const string | MRFullTypeName = "Kitware.VTK.vtkPolynomialSolversUnivariate" |
Automatically generated type registration mechanics. More... | |
![]() | |
new const string | MRFullTypeName = "Kitware.VTK.vtkObject" |
Automatically generated type registration mechanics. More... | |
![]() | |
new const string | MRFullTypeName = "Kitware.VTK.vtkObjectBase" |
Automatically generated type registration mechanics. More... | |
![]() | |
const string | vtkChartsEL_dll = "libKitware.VTK.vtkCharts.Unmanaged.so" |
Export layer functions for 'vtkCharts' are exported from the DLL named by the value of this variable. More... | |
const string | vtkCommonEL_dll = "libKitware.VTK.vtkCommon.Unmanaged.so" |
Export layer functions for 'vtkCommon' are exported from the DLL named by the value of this variable. More... | |
const string | vtkFilteringEL_dll = "libKitware.VTK.vtkFiltering.Unmanaged.so" |
Export layer functions for 'vtkFiltering' are exported from the DLL named by the value of this variable. More... | |
const string | vtkGenericFilteringEL_dll = "libKitware.VTK.vtkGenericFiltering.Unmanaged.so" |
Export layer functions for 'vtkGenericFiltering' are exported from the DLL named by the value of this variable. More... | |
const string | vtkGeovisEL_dll = "libKitware.VTK.vtkGeovis.Unmanaged.so" |
Export layer functions for 'vtkGeovis' are exported from the DLL named by the value of this variable. More... | |
const string | vtkGraphicsEL_dll = "libKitware.VTK.vtkGraphics.Unmanaged.so" |
Export layer functions for 'vtkGraphics' are exported from the DLL named by the value of this variable. More... | |
const string | vtkHybridEL_dll = "libKitware.VTK.vtkHybrid.Unmanaged.so" |
Export layer functions for 'vtkHybrid' are exported from the DLL named by the value of this variable. More... | |
const string | vtkIOEL_dll = "libKitware.VTK.vtkIO.Unmanaged.so" |
Export layer functions for 'vtkIO' are exported from the DLL named by the value of this variable. More... | |
const string | vtkImagingEL_dll = "libKitware.VTK.vtkImaging.Unmanaged.so" |
Export layer functions for 'vtkImaging' are exported from the DLL named by the value of this variable. More... | |
const string | vtkInfovisEL_dll = "libKitware.VTK.vtkInfovis.Unmanaged.so" |
Export layer functions for 'vtkInfovis' are exported from the DLL named by the value of this variable. More... | |
const string | vtkParallelEL_dll = "libKitware.VTK.vtkParallel.Unmanaged.so" |
Export layer functions for 'vtkParallel' are exported from the DLL named by the value of this variable. More... | |
const string | vtkRenderingEL_dll = "libKitware.VTK.vtkRendering.Unmanaged.so" |
Export layer functions for 'vtkRendering' are exported from the DLL named by the value of this variable. More... | |
const string | vtkViewsEL_dll = "libKitware.VTK.vtkViews.Unmanaged.so" |
Export layer functions for 'vtkViews' are exported from the DLL named by the value of this variable. More... | |
const string | vtkVolumeRenderingEL_dll = "libKitware.VTK.vtkVolumeRendering.Unmanaged.so" |
Export layer functions for 'vtkVolumeRendering' are exported from the DLL named by the value of this variable. More... | |
const string | vtkWidgetsEL_dll = "libKitware.VTK.vtkWidgets.Unmanaged.so" |
Export layer functions for 'vtkWidgets' are exported from the DLL named by the value of this variable. More... | |
Static Public Attributes | |
static new readonly string | MRClassNameKey = "30vtkPolynomialSolversUnivariate" |
Automatically generated type registration mechanics. More... | |
![]() | |
static new readonly string | MRClassNameKey = "9vtkObject" |
Automatically generated type registration mechanics. More... | |
![]() | |
static new readonly string | MRClassNameKey = "13vtkObjectBase" |
Automatically generated type registration mechanics. More... | |
Protected Member Functions | |
override void | Dispose (bool disposing) |
Automatically generated protected Dispose method - called from public Dispose or the C# destructor. DO NOT call directly. More... | |
![]() | |
override void | Dispose (bool disposing) |
Automatically generated protected Dispose method - called from public Dispose or the C# destructor. DO NOT call directly. More... | |
![]() | |
override void | Dispose (bool disposing) |
Decrease the reference count (release by another object). This has the same effect as invoking Delete() (i.e., it reduces the reference count by 1). More... | |
![]() | |
WrappedObject (IntPtr rawCppThis, bool callDisposalMethod, bool strong) | |
Constructor expected by the mummy Runtime. More... | |
Static Private Member Functions | |
static | vtkPolynomialSolversUnivariate () |
Automatically generated type registration mechanics. More... | |
Additional Inherited Members | |
![]() | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | AbortCheckEvt |
The AbortCheckEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.AbortCheckEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | AnimationCueTickEvt |
The AnimationCueTickEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.AnimationCueTickEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | AnyEvt |
The AnyEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.AnyEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | CharEvt |
The CharEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.CharEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | ConfigureEvt |
The ConfigureEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.ConfigureEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | ConnectionClosedEvt |
The ConnectionClosedEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.ConnectionClosedEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | ConnectionCreatedEvt |
The ConnectionCreatedEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.ConnectionCreatedEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | CreateTimerEvt |
The CreateTimerEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.CreateTimerEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | CursorChangedEvt |
The CursorChangedEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.CursorChangedEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | DeleteEvt |
The DeleteEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.DeleteEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | DestroyTimerEvt |
The DestroyTimerEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.DestroyTimerEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | DisableEvt |
The DisableEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.DisableEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | DomainModifiedEvt |
The DomainModifiedEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.DomainModifiedEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | EnableEvt |
The EnableEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.EnableEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | EndAnimationCueEvt |
The EndAnimationCueEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.EndAnimationCueEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | EndEvt |
The EndEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.EndEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | EndInteractionEvt |
The EndInteractionEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.EndInteractionEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | EndPickEvt |
The EndPickEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.EndPickEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | EndWindowLevelEvt |
The EndWindowLevelEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.EndWindowLevelEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | EnterEvt |
The EnterEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.EnterEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | ErrorEvt |
The ErrorEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.ErrorEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | ExecuteInformationEvt |
The ExecuteInformationEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.ExecuteInformationEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | ExitEvt |
The ExitEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.ExitEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | ExposeEvt |
The ExposeEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.ExposeEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | InteractionEvt |
The InteractionEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.InteractionEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | KeyPressEvt |
The KeyPressEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.KeyPressEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | KeyReleaseEvt |
The KeyReleaseEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.KeyReleaseEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | LeaveEvt |
The LeaveEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.LeaveEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | LeftButtonPressEvt |
The LeftButtonPressEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.LeftButtonPressEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | LeftButtonReleaseEvt |
The LeftButtonReleaseEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.LeftButtonReleaseEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | MiddleButtonPressEvt |
The MiddleButtonPressEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.MiddleButtonPressEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | MiddleButtonReleaseEvt |
The MiddleButtonReleaseEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.MiddleButtonReleaseEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | ModifiedEvt |
The ModifiedEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.ModifiedEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | MouseMoveEvt |
The MouseMoveEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.MouseMoveEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | MouseWheelBackwardEvt |
The MouseWheelBackwardEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.MouseWheelBackwardEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | MouseWheelForwardEvt |
The MouseWheelForwardEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.MouseWheelForwardEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | PickEvt |
The PickEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.PickEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | PlacePointEvt |
The PlacePointEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.PlacePointEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | PlaceWidgetEvt |
The PlaceWidgetEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.PlaceWidgetEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | ProgressEvt |
The ProgressEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.ProgressEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | PropertyModifiedEvt |
The PropertyModifiedEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.PropertyModifiedEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | RegisterEvt |
The RegisterEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.RegisterEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | RenderEvt |
The RenderEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.RenderEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | RenderWindowMessageEvt |
The RenderWindowMessageEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.RenderWindowMessageEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | ResetCameraClippingRangeEvt |
The ResetCameraClippingRangeEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.ResetCameraClippingRangeEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | ResetCameraEvt |
The ResetCameraEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.ResetCameraEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | ResetWindowLevelEvt |
The ResetWindowLevelEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.ResetWindowLevelEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | RightButtonPressEvt |
The RightButtonPressEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.RightButtonPressEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | RightButtonReleaseEvt |
The RightButtonReleaseEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.RightButtonReleaseEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | SelectionChangedEvt |
The SelectionChangedEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.SelectionChangedEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | SetOutputEvt |
The SetOutputEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.SetOutputEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | StartAnimationCueEvt |
The StartAnimationCueEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.StartAnimationCueEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | StartEvt |
The StartEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.StartEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | StartInteractionEvt |
The StartInteractionEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.StartInteractionEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | StartPickEvt |
The StartPickEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.StartPickEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | StartWindowLevelEvt |
The StartWindowLevelEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.StartWindowLevelEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | TimerEvt |
The TimerEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.TimerEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | UnRegisterEvt |
The UnRegisterEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.UnRegisterEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | UpdateEvt |
The UpdateEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.UpdateEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | UpdateInformationEvt |
The UpdateInformationEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.UpdateInformationEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | UpdatePropertyEvt |
The UpdatePropertyEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.UpdatePropertyEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | VolumeMapperComputeGradientsEndEvt |
The VolumeMapperComputeGradientsEndEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.VolumeMapperComputeGradientsEndEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | VolumeMapperComputeGradientsProgressEvt |
The VolumeMapperComputeGradientsProgressEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.VolumeMapperComputeGradientsProgressEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | VolumeMapperComputeGradientsStartEvt |
The VolumeMapperComputeGradientsStartEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.VolumeMapperComputeGradientsStartEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | VolumeMapperRenderEndEvt |
The VolumeMapperRenderEndEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.VolumeMapperRenderEndEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | VolumeMapperRenderProgressEvt |
The VolumeMapperRenderProgressEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.VolumeMapperRenderProgressEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | VolumeMapperRenderStartEvt |
The VolumeMapperRenderStartEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.VolumeMapperRenderStartEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | WarningEvt |
The WarningEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.WarningEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | WidgetActivateEvt |
The WidgetActivateEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.WidgetActivateEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | WidgetModifiedEvt |
The WidgetModifiedEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.WidgetModifiedEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | WidgetValueChangedEvt |
The WidgetValueChangedEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.WidgetValueChangedEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | WindowLevelEvt |
The WindowLevelEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.WindowLevelEvent as the eventId parameter. More... | |
Kitware.VTK.vtkObject.vtkObjectEventHandler | WrongTagEvt |
The WrongTagEvt event is invoked when the sender's InvokeEvent method is called with vtkCommand.EventIds.WrongTagEvent as the eventId parameter. More... | |
vtkPolynomialSolversUnivariate - polynomial solvers
Description vtkPolynomialSolversUnivariate provides solvers for univariate polynomial equations with real coefficients. The Tartaglia-Cardan and Ferrari solvers work on polynomials of fixed degree 3 and 4, respectively. The Lin-Bairstow and Sturm solvers work on polynomials of arbitrary degree. The Sturm solver is the most robust solver but only reports roots within an interval and does not report multiplicities. The Lin-Bairstow solver reports multiplicities.
For difficult polynomials, you may wish to use FilterRoots to eliminate some of the roots reported by the Sturm solver. FilterRoots evaluates the derivatives near each root to eliminate cases where a local minimum or maximum is close to zero.
Thanks Thanks to Philippe Pebay, Korben Rusek, David Thompson, and Maurice Rojas for implementing these solvers.
|
staticprivate |
Automatically generated type registration mechanics.
Kitware.VTK.vtkPolynomialSolversUnivariate.vtkPolynomialSolversUnivariate | ( | IntPtr | rawCppThis, |
bool | callDisposalMethod, | ||
bool | strong | ||
) |
Automatically generated constructor - called from generated code. DO NOT call directly.
Kitware.VTK.vtkPolynomialSolversUnivariate.vtkPolynomialSolversUnivariate | ( | ) |
Undocumented Block
|
protected |
Automatically generated protected Dispose method - called from public Dispose or the C# destructor. DO NOT call directly.
|
static |
Algebraically extracts REAL roots of the quartic polynomial with REAL coefficients X^4 + c[0] X^3 + c[1] X^2 + c[2] X + c[3] and stores them (when they exist) and their respective multiplicities in the r and m arrays, based on Ferrari's method. Some numerical noise can be filtered by the use of a tolerance tol instead of equality with 0 (one can use, e.g., VTK_DBL_EPSILON). Returns the number of roots. Warning: it is the user's responsibility to pass a non-negative tol.
|
static |
This uses the derivative sequence to filter possible roots of a polynomial. First it sorts the roots and removes any duplicates. If the number of sign changes of the derivative sequence at a root at upperBnds[i] == that at upperBnds[i] - diameter then the i^th value is removed from upperBnds. It returns the new number of roots.
|
static |
Set/get the tolerance used when performing polynomial Euclidean division to find polynomial roots. This tolerance is used to decide whether the coefficient(s) of a polynomial remainder are close enough to zero to be neglected.
|
static |
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial
in ]a[0] ; a[1]] using the Habicht sequence (polynomial coefficients are REAL) and returns the count nr. All roots are bracketed in the first ]upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.).
intervalType specifies the search interval as follows: 0 = 00 = ]a,b[ 1 = 10 = [a,b[ 2 = 01 = ]a,b] 3 = 11 = [a,b] This defaults to 0.
The last non-zero item in the Habicht sequence is the gcd of P and P'. The parameter divideGCD specifies whether the program should attempt to divide by the gcd and run again. It works better with polynomials known to have high multiplicities. When divideGCD != 0 then it attempts to divide by the GCD, if applicable. This defaults to 0.
Compared to the Sturm solver the Habicht solver is slower, although both are O(d^2). The Habicht solver has the added benefit that it has a built in mechanism to keep the leading coefficients of the result from polynomial division bounded above and below in absolute value. This will tend to keep the coefficients of the polynomials in the sequence from zeroing out prematurely or becoming infinite.
Constructing the Habicht sequence is O(d^2) in both time and space.
Warning: it is the user's responsibility to make sure the upperBnds array is large enough to contain the maximal number of expected roots. Note that nr is smaller or equal to the actual number of roots in ]a[0] ; a[1]] since roots within are lumped in the same bracket. array is large enough to contain the maximal number of expected upper bounds.
|
static |
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial
in ]a[0] ; a[1]] using the Habicht sequence (polynomial coefficients are REAL) and returns the count nr. All roots are bracketed in the first ]upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.).
intervalType specifies the search interval as follows: 0 = 00 = ]a,b[ 1 = 10 = [a,b[ 2 = 01 = ]a,b] 3 = 11 = [a,b] This defaults to 0.
The last non-zero item in the Habicht sequence is the gcd of P and P'. The parameter divideGCD specifies whether the program should attempt to divide by the gcd and run again. It works better with polynomials known to have high multiplicities. When divideGCD != 0 then it attempts to divide by the GCD, if applicable. This defaults to 0.
Compared to the Sturm solver the Habicht solver is slower, although both are O(d^2). The Habicht solver has the added benefit that it has a built in mechanism to keep the leading coefficients of the result from polynomial division bounded above and below in absolute value. This will tend to keep the coefficients of the polynomials in the sequence from zeroing out prematurely or becoming infinite.
Constructing the Habicht sequence is O(d^2) in both time and space.
Warning: it is the user's responsibility to make sure the upperBnds array is large enough to contain the maximal number of expected roots. Note that nr is smaller or equal to the actual number of roots in ]a[0] ; a[1]] since roots within are lumped in the same bracket. array is large enough to contain the maximal number of expected upper bounds.
|
static |
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial
in ]a[0] ; a[1]] using the Habicht sequence (polynomial coefficients are REAL) and returns the count nr. All roots are bracketed in the first ]upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.).
intervalType specifies the search interval as follows: 0 = 00 = ]a,b[ 1 = 10 = [a,b[ 2 = 01 = ]a,b] 3 = 11 = [a,b] This defaults to 0.
The last non-zero item in the Habicht sequence is the gcd of P and P'. The parameter divideGCD specifies whether the program should attempt to divide by the gcd and run again. It works better with polynomials known to have high multiplicities. When divideGCD != 0 then it attempts to divide by the GCD, if applicable. This defaults to 0.
Compared to the Sturm solver the Habicht solver is slower, although both are O(d^2). The Habicht solver has the added benefit that it has a built in mechanism to keep the leading coefficients of the result from polynomial division bounded above and below in absolute value. This will tend to keep the coefficients of the polynomials in the sequence from zeroing out prematurely or becoming infinite.
Constructing the Habicht sequence is O(d^2) in both time and space.
Warning: it is the user's responsibility to make sure the upperBnds array is large enough to contain the maximal number of expected roots. Note that nr is smaller or equal to the actual number of roots in ]a[0] ; a[1]] since roots within are lumped in the same bracket. array is large enough to contain the maximal number of expected upper bounds.
|
virtual |
Undocumented Block
Reimplemented from Kitware.VTK.vtkObject.
|
static |
Undocumented Block
|
static |
Seeks all REAL roots of the d -th degree polynomial c[0] X^d + ... + c[d-1] X + c[d] = 0 equation Lin-Bairstow's method ( polynomial coefficients are REAL ) and stores the nr roots found ( multiple roots are multiply stored ) in r. tolerance is the user-defined solver tolerance; this variable may be relaxed by the iterative solver if needed. Returns nr. Warning: it is the user's responsibility to make sure the r array is large enough to contain the maximal number of expected roots.
|
static |
Undocumented Block
new vtkPolynomialSolversUnivariate Kitware.VTK.vtkPolynomialSolversUnivariate.NewInstance | ( | ) |
Undocumented Block
|
static |
Undocumented Block
|
static |
Set/get the tolerance used when performing polynomial Euclidean division to find polynomial roots. This tolerance is used to decide whether the coefficient(s) of a polynomial remainder are close enough to zero to be neglected.
|
static |
Solves a cubic equation c0*t^3 + c1*t^2 + c2*t + c3 = 0 when c0, c1, c2, and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Return array contains number of (real) roots (counting multiple roots as one) followed by roots themselves. The value in roots[4] is a integer giving further information about the roots (see return codes for int SolveCubic() ).
|
static |
Solves a cubic equation when c0, c1, c2, And c3 Are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Roots and number of real roots are stored in user provided variables r1, r2, r3, and num_roots. Note that the function can return the following integer values describing the roots: (0)-no solution; (-1)-infinite number of solutions; (1)-one distinct real root of multiplicity 3 (stored in r1); (2)-two distinct real roots, one of multiplicity 2 (stored in r1 & r2); (3)-three distinct real roots; (-2)-quadratic equation with complex conjugate solution (real part of root returned in r1, imaginary in r2); (-3)-one real root and a complex conjugate pair (real root in r1 and real part of pair in r2 and imaginary in r3).
|
static |
Solves a linear equation c2*t + c3 = 0 when c2 and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Return array contains number of roots followed by roots themselves.
|
static |
Solves a linear equation c2*t + c3 = 0 when c2 and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Root and number of (real) roots are stored in user provided variables r2 and num_roots.
|
static |
Solves a quadratic equation c1*t^2 + c2*t + c3 = 0 when c1, c2, and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Return array contains number of (real) roots (counting multiple roots as one) followed by roots themselves. Note that roots[3] contains a return code further describing solution - see documentation for SolveCubic() for meaning of return codes.
|
static |
Solves a quadratic equation c1*t^2 + c2*t + c3 = 0 when c1, c2, and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Roots and number of roots are stored in user provided variables r1, r2, num_roots
|
static |
Algebraically extracts REAL roots of the quadratic polynomial with REAL coefficients c[0] X^2 + c[1] X + c[2] and stores them (when they exist) and their respective multiplicities in the r and m arrays. Returns either the number of roots, or -1 if ininite number of roots.
|
static |
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial P[0] X^d + ... + P[d-1] X + P[d] in ]a[0] ; a[1]] using Sturm's theorem ( polynomial coefficients are REAL ) and returns the count nr. All roots are bracketed in the first ]upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.).
intervalType specifies the search interval as follows: 0 = 00 = ]a,b[ 1 = 10 = [a,b[ 2 = 01 = ]a,b] 3 = 11 = [a,b] This defaults to 0.
The last non-zero item in the Sturm sequence is the gcd of P and P'. The parameter divideGCD specifies whether the program should attempt to divide by the gcd and run again. It works better with polynomials known to have high multiplicities. When divideGCD != 0 then it attempts to divide by the GCD, if applicable. This defaults to 0.
Constructing the Sturm sequence is O(d^2) in both time and space.
Warning: it is the user's responsibility to make sure the upperBnds array is large enough to contain the maximal number of expected roots. Note that nr is smaller or equal to the actual number of roots in ]a[0] ; a[1]] since roots within are lumped in the same bracket. array is large enough to contain the maximal number of expected upper bounds.
|
static |
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial P[0] X^d + ... + P[d-1] X + P[d] in ]a[0] ; a[1]] using Sturm's theorem ( polynomial coefficients are REAL ) and returns the count nr. All roots are bracketed in the first ]upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.).
intervalType specifies the search interval as follows: 0 = 00 = ]a,b[ 1 = 10 = [a,b[ 2 = 01 = ]a,b] 3 = 11 = [a,b] This defaults to 0.
The last non-zero item in the Sturm sequence is the gcd of P and P'. The parameter divideGCD specifies whether the program should attempt to divide by the gcd and run again. It works better with polynomials known to have high multiplicities. When divideGCD != 0 then it attempts to divide by the GCD, if applicable. This defaults to 0.
Constructing the Sturm sequence is O(d^2) in both time and space.
Warning: it is the user's responsibility to make sure the upperBnds array is large enough to contain the maximal number of expected roots. Note that nr is smaller or equal to the actual number of roots in ]a[0] ; a[1]] since roots within are lumped in the same bracket. array is large enough to contain the maximal number of expected upper bounds.
|
static |
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial P[0] X^d + ... + P[d-1] X + P[d] in ]a[0] ; a[1]] using Sturm's theorem ( polynomial coefficients are REAL ) and returns the count nr. All roots are bracketed in the first ]upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.).
intervalType specifies the search interval as follows: 0 = 00 = ]a,b[ 1 = 10 = [a,b[ 2 = 01 = ]a,b] 3 = 11 = [a,b] This defaults to 0.
The last non-zero item in the Sturm sequence is the gcd of P and P'. The parameter divideGCD specifies whether the program should attempt to divide by the gcd and run again. It works better with polynomials known to have high multiplicities. When divideGCD != 0 then it attempts to divide by the GCD, if applicable. This defaults to 0.
Constructing the Sturm sequence is O(d^2) in both time and space.
Warning: it is the user's responsibility to make sure the upperBnds array is large enough to contain the maximal number of expected roots. Note that nr is smaller or equal to the actual number of roots in ]a[0] ; a[1]] since roots within are lumped in the same bracket. array is large enough to contain the maximal number of expected upper bounds.
|
static |
Algebraically extracts REAL roots of the cubic polynomial with REAL coefficients X^3 + c[0] X^2 + c[1] X + c[2] and stores them (when they exist) and their respective multiplicities in the r and m arrays. Some numerical noise can be filtered by the use of a tolerance tol instead of equality with 0 (one can use, e.g., VTK_DBL_EPSILON). The main differences with SolveCubic are that (1) the polynomial must have unit leading coefficient, (2) complex roots are discarded upfront, (3) non-simple roots are stored only once, along with their respective multiplicities, and (4) some numerical noise is filtered by the use of relative tolerance instead of equality with 0. Returns the number of roots. <i> In memoriam </i> Niccolo Tartaglia (1500 - 1559), unfairly forgotten.
|
static |
Automatically generated type registration mechanics.
new const string Kitware.VTK.vtkPolynomialSolversUnivariate.MRFullTypeName = "Kitware.VTK.vtkPolynomialSolversUnivariate" |
Automatically generated type registration mechanics.