VTK  9.2.5
vtkPolynomialSolversUnivariate.h
Go to the documentation of this file.
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
58class VTKCOMMONMATH_EXPORT vtkPolynomialSolversUnivariate : public vtkObject
59{
60public:
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
283protected:
286
287 static double DivisionTolerance;
288
289private:
291 void operator=(const vtkPolynomialSolversUnivariate&) = delete;
292};
293
294#endif
a simple class to control print indentation
Definition: vtkIndent.h:40
abstract base class for most VTK objects
Definition: vtkObject.h:63
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, 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 + ... + c[d-1] X + c[d] = 0 equation Lin...
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 + ....
~vtkPolynomialSolversUnivariate() override=default
static void SetDivisionTolerance(double tol)
Set/get the tolerance used when performing polynomial Euclidean division to find polynomial roots.
static double * SolveLinear(double c0, double c1)
Solves a linear equation c0*t + c1 = 0 when c0 and c1 are REAL.
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 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 ostream & PrintPolynomial(ostream &os, double *P, int degP)
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 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 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 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.
static vtkPolynomialSolversUnivariate * New()