Package gov.nih.mipav.model.algorithms

Class QuarticEquation

java.lang.Object

gov.nih.mipav.model.algorithms.QuarticEquation

public class QuarticEquation
extends Object

Copyright Yair Chuchem 2011. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. Neither the name of Yair Chuchem nor the names of other contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. The equation is a*x**4 + b*x**3 + c*x**2 + d*x + e = 0 /* Solve Polynomials of up to the fourth degree. (over complex numbers) Algorithms by Ferrari, Tartaglia, Cardano, et al. (16th century Italy)

Author:

ilb

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
(package private) class	QuarticEquation.complex_t

Field Summary

Fields

Modifier and Type	Field	Description
private double	aimag
private double	areal
private double	bimag
private double	breal
private double	cimag
(package private) final int	COMPLEX_ROOTS
private double	creal
private int	degree
private double	dimag
private double	dreal
private double	eimag
private double	ereal
(package private) int	inputType
private final int	MAX_DEGREE
private int[]	num_sols
(package private) final int	ONLY_REAL_ROOTS
private double[]	solsimag
private double[]	solsreal

Constructor Summary

Constructors

Constructor	Description
QuarticEquation()
QuarticEquation(int degree, double areal, double aimag, double breal, double bimag, double creal, double cimag, double dreal, double dimag, double ereal, double eimag, int[] num_sols, double[] solsreal, double[] solsimag)
QuarticEquation(int degree, double areal, double breal, double creal, double dreal, double ereal, int[] num_sols, double[] sols)

Method Summary

Modifier and Type	Method	Description
private void	calc_binomials(int num_binoms, int stride, double[][] dst)
private void	calc_powers(double x, int max_power, double[] dst)
private void	calc_powers(QuarticEquation.complex_t x, int max_power, QuarticEquation.complex_t[] dst)
private void	calc_shifted_coefs(double shift, int degree, double[] src, double[] dst)
private void	calc_shifted_coefs(QuarticEquation.complex_t shift, int degree, QuarticEquation.complex_t[] src, QuarticEquation.complex_t[] dst)
private QuarticEquation.complex_t	complex_add(QuarticEquation.complex_t a, QuarticEquation.complex_t b)
private QuarticEquation.complex_t	complex_div(QuarticEquation.complex_t a, QuarticEquation.complex_t b)
private static boolean	complex_eq(QuarticEquation.complex_t a, QuarticEquation.complex_t b)
private QuarticEquation.complex_t	complex_from_real(double x)
private QuarticEquation.complex_t	complex_inverse(QuarticEquation.complex_t x)
private QuarticEquation.complex_t	complex_mult(QuarticEquation.complex_t a, QuarticEquation.complex_t b)
private QuarticEquation.complex_t	complex_mult_real(double c, QuarticEquation.complex_t x)
private QuarticEquation.complex_t	complex_negate(QuarticEquation.complex_t x)
private QuarticEquation.complex_t	complex_pow_real(QuarticEquation.complex_t x, double power)
private static double	complex_sqr_norm(QuarticEquation.complex_t x)
private QuarticEquation.complex_t	complex_sqrt(QuarticEquation.complex_t x)
private double	cubic_root(double x)
void	run()
void	runComplex()
void	runReal()
void	selfTest()
private int	solve_depressed_cubic(double[] poly, double[] results)
private int	solve_depressed_cubic(QuarticEquation.complex_t[] poly, QuarticEquation.complex_t[] results)
private int	solve_depressed_poly(int degree, double[] poly, double[] results)
private int	solve_depressed_poly(int degree, QuarticEquation.complex_t[] poly, QuarticEquation.complex_t[] results)
private int	solve_depressed_quadratic(double[] poly, double[] results)
private int	solve_depressed_quadratic(QuarticEquation.complex_t[] poly, QuarticEquation.complex_t[] results)
private int	solve_depressed_quartic(double[] poly, double[] results)
private int	solve_depressed_quartic(QuarticEquation.complex_t[] poly, QuarticEquation.complex_t[] results)
private int	solve_normalized_poly(int degree, double[] poly, double[] results)
private int	solve_normalized_poly(int degree, QuarticEquation.complex_t[] poly, QuarticEquation.complex_t[] results)
private int	solve_poly(int degree, QuarticEquation.complex_t[] poly, QuarticEquation.complex_t[] results)
(package private) int	solve_real_poly(int degree, double[] poly, double[] results)
private double	stableness_score(double a, double b)
private static double	stableness_score(QuarticEquation.complex_t a, QuarticEquation.complex_t b)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

degree

private int degree

areal

private double areal

aimag

private double aimag

breal

private double breal

bimag

private double bimag

creal

private double creal

cimag

private double cimag

dreal

private double dreal

dimag

private double dimag

ereal

private double ereal

eimag

private double eimag

num_sols

private int[] num_sols

solsreal

private double[] solsreal

solsimag

private double[] solsimag

MAX_DEGREE

private final int MAX_DEGREE

See Also:

• Constant Field Values

ONLY_REAL_ROOTS

final int ONLY_REAL_ROOTS

See Also:

• Constant Field Values

COMPLEX_ROOTS

final int COMPLEX_ROOTS

See Also:

• Constant Field Values

inputType

int inputType

Constructor Details

QuarticEquation

public QuarticEquation()

QuarticEquation

public QuarticEquation(int degree,
 double areal,
 double aimag,
 double breal,
 double bimag,
 double creal,
 double cimag,
 double dreal,
 double dimag,
 double ereal,
 double eimag,
 int[] num_sols,
 double[] solsreal,
 double[] solsimag)

QuarticEquation

public QuarticEquation(int degree,
 double areal,
 double breal,
 double creal,
 double dreal,
 double ereal,
 int[] num_sols,
 double[] sols)

Method Details

selfTest

public void selfTest()

run

public void run()

runReal

public void runReal()

solve_real_poly

int solve_real_poly(int degree,
 double[] poly,
 double[] results)

stableness_score

private double stableness_score(double a,
 double b)

solve_normalized_poly

private int solve_normalized_poly(int degree,
 double[] poly,
 double[] results)

calc_shifted_coefs

private void calc_shifted_coefs(double shift,
 int degree,
 double[] src,
 double[] dst)

calc_powers

private void calc_powers(double x,
 int max_power,
 double[] dst)

solve_depressed_poly

private int solve_depressed_poly(int degree,
 double[] poly,
 double[] results)

solve_depressed_quartic

private int solve_depressed_quartic(double[] poly,
 double[] results)

solve_depressed_cubic

private int solve_depressed_cubic(double[] poly,
 double[] results)

cubic_root

private double cubic_root(double x)

solve_depressed_quadratic

private int solve_depressed_quadratic(double[] poly,
 double[] results)

runComplex

public void runComplex()

solve_poly

private int solve_poly(int degree,
 QuarticEquation.complex_t[] poly,
 QuarticEquation.complex_t[] results)

solve_normalized_poly

private int solve_normalized_poly(int degree,
 QuarticEquation.complex_t[] poly,
 QuarticEquation.complex_t[] results)

calc_shifted_coefs

private void calc_shifted_coefs(QuarticEquation.complex_t shift,
 int degree,
 QuarticEquation.complex_t[] src,
 QuarticEquation.complex_t[] dst)

calc_binomials

private void calc_binomials(int num_binoms,
 int stride,
 double[][] dst)

solve_depressed_poly

private int solve_depressed_poly(int degree,
 QuarticEquation.complex_t[] poly,
 QuarticEquation.complex_t[] results)

solve_depressed_quartic

private int solve_depressed_quartic(QuarticEquation.complex_t[] poly,
 QuarticEquation.complex_t[] results)

solve_depressed_cubic

private int solve_depressed_cubic(QuarticEquation.complex_t[] poly,
 QuarticEquation.complex_t[] results)

solve_depressed_quadratic

private int solve_depressed_quadratic(QuarticEquation.complex_t[] poly,
 QuarticEquation.complex_t[] results)

calc_powers

private void calc_powers(QuarticEquation.complex_t x,
 int max_power,
 QuarticEquation.complex_t[] dst)

complex_eq

private static boolean complex_eq(QuarticEquation.complex_t a,
 QuarticEquation.complex_t b)

complex_from_real

private QuarticEquation.complex_t complex_from_real(double x)

stableness_score

private static double stableness_score(QuarticEquation.complex_t a,
 QuarticEquation.complex_t b)

complex_sqr_norm

private static double complex_sqr_norm(QuarticEquation.complex_t x)

complex_inverse

private QuarticEquation.complex_t complex_inverse(QuarticEquation.complex_t x)

complex_div

private QuarticEquation.complex_t complex_div(QuarticEquation.complex_t a,
 QuarticEquation.complex_t b)

complex_add

private QuarticEquation.complex_t complex_add(QuarticEquation.complex_t a,
 QuarticEquation.complex_t b)

complex_mult

private QuarticEquation.complex_t complex_mult(QuarticEquation.complex_t a,
 QuarticEquation.complex_t b)

complex_mult_real

private QuarticEquation.complex_t complex_mult_real(double c,
 QuarticEquation.complex_t x)

complex_negate

private QuarticEquation.complex_t complex_negate(QuarticEquation.complex_t x)

complex_sqrt

private QuarticEquation.complex_t complex_sqrt(QuarticEquation.complex_t x)

complex_pow_real

private QuarticEquation.complex_t complex_pow_real(QuarticEquation.complex_t x,
 double power)