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

22
tests/UPolynomialRootsTestCases.pas
View File

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