VTK
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) VTK_OVERRIDE;
64  static ostream& PrintPolynomial( ostream& os, double* P, int degP );
65 
67 
107  double* P, int d, double* a, double* upperBnds, double tol );
109  double* P, int d, double* a, double* upperBnds, double tol,
110  int intervalType );
112  double* P, int d, double* a, double* upperBnds, double tol,
113  int intervalType, bool divideGCD );
115 
117 
148  double* P, int d, double* a, double* upperBnds, double tol );
150  double* P, int d, double* a, double* upperBnds, double tol,
151  int intervalType );
153  double* P, int d, double* a, double* upperBnds, double tol,
154  int intervalType, bool divideGCD );
156 
164  static int FilterRoots(
165  double* P, int d, double *upperBnds, int rootcount, double diameter );
166 
178  static int LinBairstowSolve( double* c, int d, double* r, double& tolerance );
179 
190  static int FerrariSolve( double* c, double* r, int* m, double tol );
191 
207  static int TartagliaCardanSolve( double* c, double* r, int* m, double tol );
208 
217  static double* SolveCubic(double c0, double c1, double c2, double c3);
218 
227  static double* SolveQuadratic(double c0, double c1, double c2);
228 
234  static double* SolveLinear(double c0, double c1);
235 
249  static int SolveCubic(double c0, double c1, double c2, double c3,
250  double *r1, double *r2, double *r3, int *num_roots);
251 
259  static int SolveQuadratic(double c0, double c1, double c2,
260  double *r1, double *r2, int *num_roots);
261 
269  static int SolveQuadratic( double* c, double* r, int* m );
270 
277  static int SolveLinear(double c0, double c1, double *r1, int *num_roots);
278 
280 
286  static void SetDivisionTolerance( double tol );
287  static double GetDivisionTolerance();
289 
290 protected:
293 
294  static double DivisionTolerance;
295 
296 private:
298  void operator=(const vtkPolynomialSolversUnivariate&) VTK_DELETE_FUNCTION;
299 };
300 
301 #endif
a simple class to control print indentation
Definition: vtkIndent.h:40
abstract base class for most VTK objects
Definition: vtkObject.h:60
static int HabichtBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol, int intervalType, bool divideGCD)
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)
static ostream & PrintPolynomial(ostream &os, double *P, int degP)
static vtkPolynomialSolversUnivariate * New()
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 c2*t + c3 = 0 when c2 and c3 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 c2*t + c3 = 0 when c2 and c3 are REAL.
static double * 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.
static int SturmBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol, int intervalType, bool divideGCD)
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()
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)
static int SolveQuadratic(double c0, double c1, double c2, double *r1, double *r2, int *num_roots)
Solves a quadratic equation c1*t^2 + c2*t + c3 = 0 when c1, c2, and c3 are REAL.