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Added bisection root finding algorithm with custom upper bound

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This commit is contained in:
Stefan Müller
2024-05-24 20:47:52 +02:00
parent 53e3922654
commit baa1f8f31f
2 changed files with 57 additions and 24 deletions
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61
tests/UPolynomialRootsTestCases.pas
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@@ -29,18 +29,43 @@ type
{ TPolynomialRootsTestCase }
TPolynomialRootsTestCase = class(TTestCase)
private
procedure AssertBisectResult(constref AIsolatingIntervals: TIsolatingIntervals; constref AExpectedRoots:
array of Cardinal);
protected
FRootIsolation: TRootIsolation;
procedure SetUp; override;
procedure TearDown; override;
published
procedure TestBisectionRootIsolation;
procedure TestBisectNoBound;
procedure TestBisectWithBound;
end;
implementation
{ TPolynomialRootsTestCase }
procedure TPolynomialRootsTestCase.AssertBisectResult(constref AIsolatingIntervals: TIsolatingIntervals; constref
AExpectedRoots: array of Cardinal);
var
exp: Cardinal;
ri: TIsolatingInterval;
found: Boolean;
begin
AssertEquals('Unexpected number of isolating intervals.', Length(AExpectedRoots), AIsolatingIntervals.Count);
for exp in AExpectedRoots do
begin
found := False;
for ri in AIsolatingIntervals do
if (ri.A <= exp) and (exp <= ri.B) then
begin
found := True;
Break;
end;
AssertTrue('No isolating interval for expected root ' + IntToStr(exp) + ' found.', found);
end;
end;
procedure TPolynomialRootsTestCase.SetUp;
begin
inherited SetUp;
@@ -53,32 +78,34 @@ begin
inherited TearDown;
end;
procedure TPolynomialRootsTestCase.TestBisectionRootIsolation;
procedure TPolynomialRootsTestCase.TestBisectNoBound;
const
expRoots: array of Cardinal = (34000, 23017, 5);
var
exp: Cardinal;
a: TBigIntPolynomial;
r: TIsolatingIntervals;
ri: TIsolatingInterval;
found: Boolean;
begin
// 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
a := TBigIntPolynomial.Create([-24979889760000, 4774763204640, -1270471872603, 251300082690, 2329429920, -170730, 3]);
r := FRootIsolation.Bisect(a);
AssertEquals(Length(expRoots), r.Count);
for exp in expRoots do
begin
found := False;
for ri in r do
if (ri.A <= exp) and (exp <= ri.B) then
begin
found := True;
Break;
end;
AssertTrue('No isolating interval for expected root ' + IntToStr(exp) + ' found.', found);
end;
AssertBisectResult(r, expRoots);
r.Free;
end;
procedure TPolynomialRootsTestCase.TestBisectWithBound;
const
expRoots: array of Cardinal = (23017, 5);
var
a: TBigIntPolynomial;
r: TIsolatingIntervals;
begin
// 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
a := TBigIntPolynomial.Create([-24979889760000, 4774763204640, -1270471872603, 251300082690, 2329429920, -170730, 3]);
r := FRootIsolation.Bisect(a, TBigInt.One << 15);
AssertBisectResult(r, expRoots);
r.Free;
end;
initialization