Package edu.jas.root
Class ComplexRootsSturm<C extends RingElem<C> & Rational>
java.lang.Object
edu.jas.root.ComplexRootsAbstract<C>
edu.jas.root.ComplexRootsSturm<C>
- Type Parameters:
C
- coefficient type.
- All Implemented Interfaces:
ComplexRoots<C>
,Serializable
Complex roots implemented by Sturm sequences. Algorithms use exact method
derived from Wilf's numeric Routh-Hurwitz method.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate static final boolean
private static final org.apache.logging.log4j.Logger
Fields inherited from class edu.jas.root.ComplexRootsAbstract
engine
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Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionlong
complexRootCount
(Rectangle<C> rect, GenPolynomial<Complex<C>> a) Complex root count of complex polynomial on rectangle.complexRoots
(Rectangle<C> rect, GenPolynomial<Complex<C>> a) List of complex roots of complex polynomial a on rectangle.excludeZero
(Rectangle<C> rect, GenPolynomial<Complex<C>> f) Exclude zero.long
indexOfCauchy
(C a, C b, GenPolynomial<C> f, GenPolynomial<C> g) Cauchy index of rational function f/g on interval.long[]
indexOfRouth
(C a, C b, GenPolynomial<C> f, GenPolynomial<C> g) Routh index of complex function f + i g on interval.invariantRectangle
(Rectangle<C> rect, GenPolynomial<Complex<C>> f, GenPolynomial<Complex<C>> g) Invariant rectangle for algebraic number.sturmSequence
(GenPolynomial<C> f, GenPolynomial<C> g) Sturm sequence.long
windingNumber
(Rectangle<C> rect, GenPolynomial<Complex<C>> A) Winding number of complex function A on rectangle.Methods inherited from class edu.jas.root.ComplexRootsAbstract
approximateRoot, approximateRoots, complexMagnitude, complexRectangleMagnitude, complexRootRefinement, complexRoots, complexRoots, copyOfComplex, invariantMagnitudeRectangle, magnitudeBound, rootBound, toDecimal
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Field Details
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logger
private static final org.apache.logging.log4j.Logger logger -
debug
private static final boolean debug
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Constructor Details
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ComplexRootsSturm
Constructor.- Parameters:
cf
- coefficient factory.
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Method Details
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indexOfCauchy
Cauchy index of rational function f/g on interval.- Parameters:
a
- interval bound for I = [a,b].b
- interval bound for I = [a,b].f
- univariate polynomial.g
- univariate polynomial.- Returns:
- winding number of f/g in I.
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indexOfRouth
Routh index of complex function f + i g on interval.- Parameters:
a
- interval bound for I = [a,b].b
- interval bound for I = [a,b].f
- univariate polynomial.g
- univariate polynomial != 0.- Returns:
- index number of f + i g.
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sturmSequence
Sturm sequence.- Parameters:
f
- univariate polynomial.g
- univariate polynomial.- Returns:
- a Sturm sequence for f and g.
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complexRootCount
public long complexRootCount(Rectangle<C> rect, GenPolynomial<Complex<C>> a) throws InvalidBoundaryException Complex root count of complex polynomial on rectangle.- Specified by:
complexRootCount
in interfaceComplexRoots<C extends RingElem<C> & Rational>
- Specified by:
complexRootCount
in classComplexRootsAbstract<C extends RingElem<C> & Rational>
- Parameters:
rect
- rectangle.a
- univariate complex polynomial.- Returns:
- root count of a in rectangle.
- Throws:
InvalidBoundaryException
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windingNumber
public long windingNumber(Rectangle<C> rect, GenPolynomial<Complex<C>> A) throws InvalidBoundaryException Winding number of complex function A on rectangle.- Parameters:
rect
- rectangle.A
- univariate complex polynomial.- Returns:
- winding number of A around rect.
- Throws:
InvalidBoundaryException
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complexRoots
public List<Rectangle<C>> complexRoots(Rectangle<C> rect, GenPolynomial<Complex<C>> a) throws InvalidBoundaryException List of complex roots of complex polynomial a on rectangle.- Specified by:
complexRoots
in interfaceComplexRoots<C extends RingElem<C> & Rational>
- Specified by:
complexRoots
in classComplexRootsAbstract<C extends RingElem<C> & Rational>
- Parameters:
rect
- rectangle.a
- univariate squarefree complex polynomial.- Returns:
- list of complex roots.
- Throws:
InvalidBoundaryException
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invariantRectangle
public Rectangle<C> invariantRectangle(Rectangle<C> rect, GenPolynomial<Complex<C>> f, GenPolynomial<Complex<C>> g) throws InvalidBoundaryException Invariant rectangle for algebraic number.- Specified by:
invariantRectangle
in classComplexRootsAbstract<C extends RingElem<C> & Rational>
- Parameters:
rect
- root isolating rectangle for f which contains exactly one root.f
- univariate polynomial, non-zero.g
- univariate polynomial, gcd(f,g) == 1.- Returns:
- v a new rectangle contained in rect such that g(w) != 0 for w in v.
- Throws:
InvalidBoundaryException
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excludeZero
public Rectangle<C> excludeZero(Rectangle<C> rect, GenPolynomial<Complex<C>> f) throws InvalidBoundaryException Exclude zero. If an axis intersects with the rectangle, it is shrunk to exclude the axis. Not used.- Parameters:
rect
- root isolating rectangle for f which contains exactly one root.- Returns:
- a new rectangle r such that re(r) < 0 or (re)r > 0 and im(r) < 0 or (im)r > 0.
- Throws:
InvalidBoundaryException
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