VTK  9.2.5
vtkPolynomialSolversUnivariate.h
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1 /*=========================================================================
2 
3  Program: Visualization Toolkit
4  Module: vtkPolynomialSolversUnivariate.h
5 
6  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
7  All rights reserved.
8  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
9 
10  This software is distributed WITHOUT ANY WARRANTY; without even
11  the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
12  PURPOSE. See the above copyright notice for more information.
13 
14 =========================================================================
15  Copyright 2011 Sandia Corporation.
16  Under the terms of Contract DE-AC04-94AL85000, there is a non-exclusive
17  license for use of this work by or on behalf of the
18  U.S. Government. Redistribution and use in source and binary forms, with
19  or without modification, are permitted provided that this Notice and any
20  statement of authorship are reproduced on all copies.
21 
22  Contact: pppebay@sandia.gov,dcthomp@sandia.gov
23 
24 =========================================================================*/
52 #ifndef vtkPolynomialSolversUnivariate_h
53 #define vtkPolynomialSolversUnivariate_h
54 
55 #include "vtkCommonMathModule.h" // For export macro
56 #include "vtkObject.h"
57 
58 class VTKCOMMONMATH_EXPORT vtkPolynomialSolversUnivariate : public vtkObject
59 {
60 public:
63  void PrintSelf(ostream& os, vtkIndent indent) override;
64  static ostream& PrintPolynomial(ostream& os, double* P, int degP);
65 
67 
106  static int HabichtBisectionSolve(double* P, int d, double* a, double* upperBnds, double tol);
108  double* P, int d, double* a, double* upperBnds, double tol, int intervalType);
110  double* P, int d, double* a, double* upperBnds, double tol, int intervalType, bool divideGCD);
112 
114 
144  static int SturmBisectionSolve(double* P, int d, double* a, double* upperBnds, double tol);
146  double* P, int d, double* a, double* upperBnds, double tol, int intervalType);
148  double* P, int d, double* a, double* upperBnds, double tol, int intervalType, bool divideGCD);
150 
158  static int FilterRoots(double* P, int d, double* upperBnds, int rootcount, double diameter);
159 
171  static int LinBairstowSolve(double* c, int d, double* r, double& tolerance);
172 
183  static int FerrariSolve(double* c, double* r, int* m, double tol);
184 
200  static int TartagliaCardanSolve(double* c, double* r, int* m, double tol);
201 
210  static double* SolveCubic(double c0, double c1, double c2, double c3);
211 
220  static double* SolveQuadratic(double c0, double c1, double c2);
221 
227  static double* SolveLinear(double c0, double c1);
228 
242  static int SolveCubic(
243  double c0, double c1, double c2, double c3, double* r1, double* r2, double* r3, int* num_roots);
244 
252  static int SolveQuadratic(
253  double c0, double c1, double c2, double* r1, double* r2, int* num_roots);
254 
262  static int SolveQuadratic(double* c, double* r, int* m);
263 
270  static int SolveLinear(double c0, double c1, double* r1, int* num_roots);
271 
273 
279  static void SetDivisionTolerance(double tol);
280  static double GetDivisionTolerance();
282 
283 protected:
285  ~vtkPolynomialSolversUnivariate() override = default;
286 
287  static double DivisionTolerance;
288 
289 private:
291  void operator=(const vtkPolynomialSolversUnivariate&) = delete;
292 };
293 
294 #endif
a simple class to control print indentation
Definition: vtkIndent.h:119
abstract base class for most VTK objects
Definition: vtkObject.h:82
static int HabichtBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol, int intervalType, bool divideGCD)
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial.
static int FilterRoots(double *P, int d, double *upperBnds, int rootcount, double diameter)
This uses the derivative sequence to filter possible roots of a polynomial.
static int LinBairstowSolve(double *c, int d, double *r, double &tolerance)
Seeks all REAL roots of the d -th degree polynomial c[0] X^d + ...
static int SolveCubic(double c0, double c1, double c2, double c3, double *r1, double *r2, double *r3, int *num_roots)
Solves a cubic equation when c0, c1, c2, And c3 Are REAL.
static int FerrariSolve(double *c, double *r, int *m, double tol)
Algebraically extracts REAL roots of the quartic polynomial with REAL coefficients X^4 + c[0] X^3 + c...
static int SturmBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol, int intervalType)
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial P[0] X^d + ....
static ostream & PrintPolynomial(ostream &os, double *P, int degP)
static vtkPolynomialSolversUnivariate * New()
~vtkPolynomialSolversUnivariate() override=default
static void SetDivisionTolerance(double tol)
Set/get the tolerance used when performing polynomial Euclidean division to find polynomial roots.
static int SolveLinear(double c0, double c1, double *r1, int *num_roots)
Solves a linear equation c0*t + c1 = 0 when c0 and c1 are REAL.
void PrintSelf(ostream &os, vtkIndent indent) override
Methods invoked by print to print information about the object including superclasses.
static double * SolveLinear(double c0, double c1)
Solves a linear equation c0*t + c1 = 0 when c0 and c1 are REAL.
static double * SolveQuadratic(double c0, double c1, double c2)
Solves a quadratic equation c0*t^2 + c1*t + c2 = 0 when c0, c1, and c2 are REAL.
static int SturmBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol, int intervalType, bool divideGCD)
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial P[0] X^d + ....
static int SolveQuadratic(double *c, double *r, int *m)
Algebraically extracts REAL roots of the quadratic polynomial with REAL coefficients c[0] X^2 + c[1] ...
static int TartagliaCardanSolve(double *c, double *r, int *m, double tol)
Algebraically extracts REAL roots of the cubic polynomial with REAL coefficients X^3 + c[0] X^2 + c[1...
static double GetDivisionTolerance()
Set/get the tolerance used when performing polynomial Euclidean division to find polynomial roots.
static int HabichtBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol)
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial.
static int SturmBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol)
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial P[0] X^d + ....
static double * 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.
static int HabichtBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol, int intervalType)
Finds all REAL roots (within tolerance tol) of the d -th degree polynomial.
static int SolveQuadratic(double c0, double c1, double c2, double *r1, double *r2, int *num_roots)
Solves a quadratic equation c0*t^2 + c1*t + c2 = 0 when c0, c1, and c2 are REAL.