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Renamed root finding class and methods, now class methods

This commit is contained in:
Stefan Müller 2024-05-26 14:23:31 +02:00
parent ae30889bbb
commit ab453b347d
2 changed files with 20 additions and 33 deletions
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33
UPolynomialRoots.pas
View File

@ -37,22 +37,23 @@ type
TIsolatingIntervals = specialize TList<TIsolatingInterval>; TIsolatingIntervals = specialize TList<TIsolatingInterval>;
{ TRootIsolation } { TPolynomialRoots }
TRootIsolation = class TPolynomialRoots = class
private private
function CalcSimpleRootBound(constref APolynomial: TBigIntPolynomial): TBigInt; class function CalcUpperRootBound(constref APolynomial: TBigIntPolynomial): TBigInt;
function GetIsolatingInterval(const AC, AK, AH: Cardinal; constref ABound: TBigInt): TIsolatingInterval; class function CreateIsolatingInterval(const AC, AK, AH: Cardinal; constref ABound: TBigInt): TIsolatingInterval;
public public
function Bisect(constref APolynomial: TBigIntPolynomial): TIsolatingIntervals; class function BisectIsolation(constref APolynomial: TBigIntPolynomial): TIsolatingIntervals;
function Bisect(constref APolynomial: TBigIntPolynomial; constref ABound: TBigInt): TIsolatingIntervals; class function BisectIsolation(constref APolynomial: TBigIntPolynomial; constref ABound: TBigInt):
TIsolatingIntervals;
end; end;
implementation implementation
{ TRootIsolation } { TPolynomialRoots }
function TRootIsolation.CalcSimpleRootBound(constref APolynomial: TBigIntPolynomial): TBigInt; class function TPolynomialRoots.CalcUpperRootBound(constref APolynomial: TBigIntPolynomial): TBigInt;
var var
i, sign: Integer; i, sign: Integer;
an, ai, max: TBigInt; an, ai, max: TBigInt;
@ -76,7 +77,8 @@ begin
Result := TBigInt.One << (numeratorBit - denominatorBit); Result := TBigInt.One << (numeratorBit - denominatorBit);
end; end;
function TRootIsolation.GetIsolatingInterval(const AC, AK, AH: Cardinal; constref ABound: TBigInt): TIsolatingInterval; class function TPolynomialRoots.CreateIsolatingInterval(const AC, AK, AH: Cardinal; constref ABound: TBigInt):
TIsolatingInterval;
begin begin
Result.C := AC; Result.C := AC;
Result.K := AK; Result.K := AK;
@ -86,17 +88,18 @@ begin
Result.B := ((AC + AH) * ABound) >> AK; Result.B := ((AC + AH) * ABound) >> AK;
end; end;
function TRootIsolation.Bisect(constref APolynomial: TBigIntPolynomial): TIsolatingIntervals; class function TPolynomialRoots.BisectIsolation(constref APolynomial: TBigIntPolynomial): TIsolatingIntervals;
var var
bound: TBigInt; bound: TBigInt;
begin begin
bound := CalcSimpleRootBound(APolynomial); bound := CalcUpperRootBound(APolynomial);
Result := Bisect(APolynomial, bound); Result := BisectIsolation(APolynomial, bound);
end; end;
// This is adapted from // This is adapted from
// https://en.wikipedia.org/wiki/Real-root_isolation#Bisection_method // https://en.wikipedia.org/wiki/Real-root_isolation#Bisection_method
function TRootIsolation.Bisect(constref APolynomial: TBigIntPolynomial; constref ABound: TBigInt): TIsolatingIntervals; class function TPolynomialRoots.BisectIsolation(constref APolynomial: TBigIntPolynomial; constref ABound: TBigInt):
TIsolatingIntervals;
type type
TWorkItem = record TWorkItem = record
C, K: Cardinal; C, K: Cardinal;
@ -126,7 +129,7 @@ begin
// Found an integer root at 0. // Found an integer root at 0.
item.P := item.P.DivideByVariable; item.P := item.P.DivideByVariable;
Dec(n); Dec(n);
Result.Add(GetIsolatingInterval(item.C, item.K, 0, ABound)); Result.Add(CreateIsolatingInterval(item.C, item.K, 0, ABound));
end; end;
varq := item.P.RevertOrderOfCoefficients.TranslateVariableByOne; varq := item.P.RevertOrderOfCoefficients.TranslateVariableByOne;
@ -134,7 +137,7 @@ begin
if v = 1 then if v = 1 then
begin begin
// Found isolating interval. // Found isolating interval.
Result.Add(GetIsolatingInterval(item.C, item.K, 1, ABound)); Result.Add(CreateIsolatingInterval(item.C, item.K, 1, ABound));
end end
else if v > 1 then else if v > 1 then
begin begin

20
tests/UPolynomialRootsTestCases.pas
View File

@ -32,10 +32,6 @@ type
private private
procedure AssertBisectResult(constref AIsolatingIntervals: TIsolatingIntervals; constref AExpectedRoots: procedure AssertBisectResult(constref AIsolatingIntervals: TIsolatingIntervals; constref AExpectedRoots:
array of Cardinal); array of Cardinal);
protected
FRootIsolation: TRootIsolation;
procedure SetUp; override;
procedure TearDown; override;
published published
procedure TestBisectNoBound; procedure TestBisectNoBound;
procedure TestBisectWithBound; procedure TestBisectWithBound;
@ -68,18 +64,6 @@ begin
end; end;
end; end;
procedure TPolynomialRootsTestCase.SetUp;
begin
inherited SetUp;
FRootIsolation := TRootIsolation.Create;
end;
procedure TPolynomialRootsTestCase.TearDown;
begin
FRootIsolation.Free;
inherited TearDown;
end;
procedure TPolynomialRootsTestCase.TestBisectNoBound; procedure TPolynomialRootsTestCase.TestBisectNoBound;
const const
expRoots: array of Cardinal = (34000, 23017, 5); expRoots: array of Cardinal = (34000, 23017, 5);
@ -90,7 +74,7 @@ begin
// y = 3 * (x - 34000) * (x - 23017) * (x - 5) * (x^2 - 19) * (x + 112) // y = 3 * (x - 34000) * (x - 23017) * (x - 5) * (x^2 - 19) * (x + 112)
// = 3 * x^6 - 170730 * x^5 + 2329429920 * x^4 + 251300082690 * x^3 - 1270471872603 * x^2 + 4774763204640 * x - 24979889760000 // = 3 * x^6 - 170730 * x^5 + 2329429920 * x^4 + 251300082690 * x^3 - 1270471872603 * x^2 + 4774763204640 * x - 24979889760000
a := TBigIntPolynomial.Create([-24979889760000, 4774763204640, -1270471872603, 251300082690, 2329429920, -170730, 3]); a := TBigIntPolynomial.Create([-24979889760000, 4774763204640, -1270471872603, 251300082690, 2329429920, -170730, 3]);
r := FRootIsolation.Bisect(a); r := TPolynomialRoots.BisectIsolation(a);
AssertBisectResult(r, expRoots); AssertBisectResult(r, expRoots);
r.Free; r.Free;
end; end;
@ -105,7 +89,7 @@ begin
// y = 3 * (x - 34000) * (x - 23017) * (x - 5) * (x^2 - 19) * (x + 112) // y = 3 * (x - 34000) * (x - 23017) * (x - 5) * (x^2 - 19) * (x + 112)
// = 3 * x^6 - 170730 * x^5 + 2329429920 * x^4 + 251300082690 * x^3 - 1270471872603 * x^2 + 4774763204640 * x - 24979889760000 // = 3 * x^6 - 170730 * x^5 + 2329429920 * x^4 + 251300082690 * x^3 - 1270471872603 * x^2 + 4774763204640 * x - 24979889760000
a := TBigIntPolynomial.Create([-24979889760000, 4774763204640, -1270471872603, 251300082690, 2329429920, -170730, 3]); a := TBigIntPolynomial.Create([-24979889760000, 4774763204640, -1270471872603, 251300082690, 2329429920, -170730, 3]);
r := FRootIsolation.Bisect(a, TBigInt.One << 15); r := TPolynomialRoots.BisectIsolation(a, TBigInt.One << 15);
AssertBisectResult(r, expRoots); AssertBisectResult(r, expRoots);
r.Free; r.Free;
end; end;