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Changed TPolynomialRoots.BisectIsolation return type to array

This commit is contained in:
Stefan Müller 2024-05-26 17:34:18 +02:00
parent 8d4a5c2ed8
commit 7db8f948c5
2 changed files with 22 additions and 19 deletions
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19
UPolynomialRoots.pas
View File

@ -37,6 +37,8 @@ type
TIsolatingIntervals = specialize TList<TIsolatingInterval>;
TIsolatingIntervalArray = array of TIsolatingInterval;
{ TPolynomialRoots }
TPolynomialRoots = class
@ -48,10 +50,10 @@ type
TIsolatingInterval;
public
// Returns root-isolating intervals for non-negative, non-multiple roots.
class function BisectIsolation(constref APolynomial: TBigIntPolynomial): TIsolatingIntervals;
class function BisectIsolation(constref APolynomial: TBigIntPolynomial): TIsolatingIntervalArray;
// Returns root-isolating intervals for non-multiple roots in the interval [0, 2^boundexp].
class function BisectIsolation(constref APolynomial: TBigIntPolynomial; constref ABoundExp: Cardinal):
TIsolatingIntervals;
TIsolatingIntervalArray;
end;
implementation
@ -100,7 +102,7 @@ begin
end;
end;
class function TPolynomialRoots.BisectIsolation(constref APolynomial: TBigIntPolynomial): TIsolatingIntervals;
class function TPolynomialRoots.BisectIsolation(constref APolynomial: TBigIntPolynomial): TIsolatingIntervalArray;
var
boundExp: Cardinal;
begin
@ -111,7 +113,7 @@ end;
// This is adapted from
// https://en.wikipedia.org/wiki/Real-root_isolation#Bisection_method
class function TPolynomialRoots.BisectIsolation(constref APolynomial: TBigIntPolynomial; constref ABoundExp: Cardinal):
TIsolatingIntervals;
TIsolatingIntervalArray;
type
TWorkItem = record
C, K: Cardinal;
@ -123,8 +125,9 @@ var
stack: TWorkStack;
n, v: Integer;
varq: TBigIntPolynomial;
iso: TIsolatingIntervals;
begin
Result := TIsolatingIntervals.Create;
iso := TIsolatingIntervals.Create;
stack := TWorkStack.Create;
item.C := 0;
@ -141,7 +144,7 @@ begin
// Found an integer root at 0.
item.P := item.P.DivideByVariable;
Dec(n);
Result.Add(CreateIsolatingInterval(item.C, item.K, 0, ABoundExp));
iso.Add(CreateIsolatingInterval(item.C, item.K, 0, ABoundExp));
end;
varq := item.P.RevertOrderOfCoefficients.TranslateVariableByOne;
@ -149,7 +152,7 @@ begin
if v = 1 then
begin
// Found isolating interval.
Result.Add(CreateIsolatingInterval(item.C, item.K, 1, ABoundExp));
iso.Add(CreateIsolatingInterval(item.C, item.K, 1, ABoundExp));
end
else if v > 1 then
begin
@ -164,6 +167,8 @@ begin
stack.Push(item);
end;
end;
Result := iso.ToArray;
iso.Free;
stack.Free;
end;

22
tests/UPolynomialRootsTestCases.pas
View File

@ -30,7 +30,7 @@ type
TPolynomialRootsTestCase = class(TTestCase)
private
procedure AssertBisectResult(constref AIsolatingIntervals: TIsolatingIntervals; constref AExpectedRoots:
procedure AssertBisectIntervals(AIsolatingIntervals: TIsolatingIntervalArray; constref AExpectedRoots:
array of Cardinal);
published
procedure TestBisectNoBound;
@ -41,18 +41,18 @@ implementation
{ TPolynomialRootsTestCase }
procedure TPolynomialRootsTestCase.AssertBisectResult(constref AIsolatingIntervals: TIsolatingIntervals; constref
AExpectedRoots: array of Cardinal);
procedure TPolynomialRootsTestCase.AssertBisectIntervals(AIsolatingIntervals: TIsolatingIntervalArray;
constref AExpectedRoots: array of Cardinal);
var
exp: Cardinal;
found: Boolean;
i, foundIndex: Integer;
begin
AssertEquals('Unexpected number of isolating intervals.', Length(AExpectedRoots), AIsolatingIntervals.Count);
AssertEquals('Unexpected number of isolating intervals.', Length(AExpectedRoots), Length(AIsolatingIntervals));
for exp in AExpectedRoots do
begin
found := False;
for i := 0 to AIsolatingIntervals.Count - 1 do
for i := 0 to Length(AIsolatingIntervals) - 1 do
if (AIsolatingIntervals[i].A <= exp) and (exp <= AIsolatingIntervals[i].B) then
begin
found := True;
@ -60,7 +60,7 @@ begin
Break;
end;
AssertTrue('No isolating interval for expected root ' + IntToStr(exp) + ' found.', found);
AIsolatingIntervals.Delete(foundIndex);
Delete(AIsolatingIntervals, foundIndex, 1);
end;
end;
@ -69,14 +69,13 @@ const
expRoots: array of Cardinal = (34000, 23017, 5);
var
a: TBigIntPolynomial;
r: TIsolatingIntervals;
r: TIsolatingIntervalArray;
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 := TPolynomialRoots.BisectIsolation(a);
AssertBisectResult(r, expRoots);
r.Free;
AssertBisectIntervals(r, expRoots);
end;
procedure TPolynomialRootsTestCase.TestBisectWithBound;
@ -84,14 +83,13 @@ const
expRoots: array of Cardinal = (23017, 5);
var
a: TBigIntPolynomial;
r: TIsolatingIntervals;
r: TIsolatingIntervalArray;
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 := TPolynomialRoots.BisectIsolation(a, 15);
AssertBisectResult(r, expRoots);
r.Free;
AssertBisectIntervals(r, expRoots);
end;
initialization