Data update
This commit is contained in:
Ingy döt Net
parent
5150844a7d
commit
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7735 changed files with 38060 additions and 199180 deletions
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generic
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type Scalar is digits <>;
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with function F (X : Scalar) return Scalar;
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package Integrate is
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function Left_Rectangular (A, B : Scalar; N : Positive) return Scalar;
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function Right_Rectangular (A, B : Scalar; N : Positive) return Scalar;
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function Midpoint_Rectangular (A, B : Scalar; N : Positive) return Scalar;
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function Trapezium (A, B : Scalar; N : Positive) return Scalar;
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function Simpsons (A, B : Scalar; N : Positive) return Scalar;
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end Integrate;
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package body Integrate is
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function Left_Rectangular (A, B : Scalar; N : Positive) return Scalar is
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H : constant Scalar := (B - A) / Scalar (N);
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Sum : Scalar := 0.0;
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X : Scalar;
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begin
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for I in 0 .. N - 1 loop
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X := A + Scalar (I) * H;
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Sum := Sum + H * F (X);
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end loop;
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return Sum;
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end Left_Rectangular;
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function Right_Rectangular (A, B : Scalar; N : Positive) return Scalar is
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H : constant Scalar := (B - A) / Scalar (N);
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Sum : Scalar := 0.0;
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X : Scalar;
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begin
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for I in 1 .. N loop
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X := A + Scalar (I) * H;
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Sum := Sum + H * F (X);
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end loop;
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return Sum;
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end Right_Rectangular;
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function Midpoint_Rectangular (A, B : Scalar; N : Positive) return Scalar is
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H : constant Scalar := (B - A) / Scalar (N);
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Sum : Scalar := 0.0;
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X : Scalar;
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begin
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for I in 1 .. N loop
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X := A + Scalar (I) * H - 0.5 * H;
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Sum := Sum + H * F (X);
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end loop;
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return Sum;
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end Midpoint_Rectangular;
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function Trapezium (A, B : Scalar; N : Positive) return Scalar is
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H : constant Scalar := (B - A) / Scalar (N);
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Sum : Scalar := F(A) + F(B);
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X : Scalar := 1.0;
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begin
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while X <= Scalar (N) - 1.0 loop
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Sum := Sum + 2.0 * F (A + X * (B - A) / Scalar (N));
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X := X + 1.0;
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end loop;
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return (B - A) / (2.0 * Scalar (N)) * Sum;
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end Trapezium;
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function Simpsons (A, B : Scalar; N : Positive) return Scalar is
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H : constant Scalar := (B - A) / Scalar (N);
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Sum_U : Scalar := 0.0;
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Sum_E : Scalar := 0.0;
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begin
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for I in 1 .. N - 1 loop
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if I mod 2 /= 0 then
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Sum_U := Sum_U + F (A + H * Scalar (I));
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else
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Sum_E := Sum_E + F (A + H * Scalar (I));
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end if;
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end loop;
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return (H / 3.0) * (F (A) + F (B) + 4.0 * Sum_U + 2.0 * Sum_E);
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end Simpsons;
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end Integrate;
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with Ada.Text_IO, Ada.Integer_Text_IO;
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with Integrate;
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procedure Numerical_Integration is
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type Scalar is digits 18;
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package Scalar_Text_IO is new Ada.Text_IO.Float_IO (Scalar);
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generic
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with function F (X : Scalar) return Scalar;
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Name : String;
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From, To : Scalar;
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Steps : Positive;
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procedure Test;
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procedure Test is
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package Integrate_Scalar_F is new Integrate (Scalar, F);
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use Ada.Text_IO, Ada.Integer_Text_IO, Integrate_Scalar_F, Scalar_Text_IO;
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begin
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Put (Name & " integrated from ");
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Put (From);
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Put (" to ");
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Put (To);
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Put (" in ");
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Put (Steps);
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Put_Line (" steps:");
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Put ("Rectangular (left): ");
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Put (Left_Rectangular (From, To, Steps));
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New_Line;
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Put ("Rectangular (right): ");
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Put (Right_Rectangular (From, To, Steps));
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New_Line;
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Put ("Rectangular (midpoint): ");
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Put (Midpoint_Rectangular (From, To, Steps));
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New_Line;
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Put ("Trapezium: ");
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Put (Trapezium (From, To, Steps));
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New_Line;
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Put ("Simpson's: ");
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Put (Simpsons (From, To, Steps));
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New_Line;
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New_Line;
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end Test;
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begin
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Ada.Integer_Text_IO.Default_Width := 0;
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Scalar_Text_IO.Default_Fore := 0;
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Scalar_Text_IO.Default_Exp := 0;
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Cubed:
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declare
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function F (X : Scalar) return Scalar is
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begin
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return X ** 3;
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end F;
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procedure Run is new Test (F => F,
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Name => "x^3",
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From => 0.0,
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To => 1.0,
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Steps => 100);
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begin
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Run;
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end Cubed;
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One_Over_X:
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declare
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function F (X : Scalar) return Scalar is
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begin
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return 1.0 / X;
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end F;
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procedure Run is new Test (F => F,
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Name => "1/x",
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From => 1.0,
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To => 100.0,
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Steps => 1_000);
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begin
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Run;
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end One_Over_X;
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X:
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declare
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function F (X : Scalar) return Scalar is
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begin
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return X;
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end F;
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procedure Run_1 is new Test (F => F,
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Name => "x",
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From => 0.0,
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To => 5_000.0,
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Steps => 5_000_000);
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procedure Run_2 is new Test (F => F,
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Name => "x",
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From => 0.0,
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To => 6_000.0,
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Steps => 6_000_000);
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begin
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Run_1;
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Run_2;
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end X;
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end Numerical_Integration;
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proc f1(x:real):real {
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return x**3;
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}
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proc f2(x:real):real {
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return 1/x;
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}
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proc f3(x:real):real {
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return x;
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}
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proc leftRectangleIntegration(a: real, b: real, N: int, f): real{
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var h: real = (b - a)/N;
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var sum: real = 0.0;
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var x_n: real;
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for n in 0..N-1 {
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x_n = a + n * h;
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sum = sum + f(x_n);
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}
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return h * sum;
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}
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proc rightRectangleIntegration(a: real, b: real, N: int, f): real{
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var h: real = (b - a)/N;
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var sum: real = 0.0;
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var x_n: real;
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for n in 0..N-1 {
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x_n = a + (n + 1) * h;
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sum = sum + f(x_n);
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}
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return h * sum;
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}
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proc midpointRectangleIntegration(a: real, b: real, N: int, f): real{
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var h: real = (b - a)/N;
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var sum: real = 0.0;
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var x_n: real;
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for n in 0..N-1 {
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x_n = a + (n + 0.5) * h;
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sum = sum + f(x_n);
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}
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return h * sum;
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}
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proc trapezoidIntegration(a: real(64), b: real(64), N: int(64), f): real{
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var h: real(64) = (b - a)/N;
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var sum: real(64) = f(a) + f(b);
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var x_n: real(64);
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for n in 1..N-1 {
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x_n = a + n * h;
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sum = sum + 2.0 * f(x_n);
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}
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return (h/2.0) * sum;
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}
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proc simpsonsIntegration(a: real(64), b: real(64), N: int(64), f): real{
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var h: real(64) = (b - a)/N;
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var sum: real(64) = f(a) + f(b);
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var x_n: real(64);
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for n in 1..N-1 by 2 {
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x_n = a + n * h;
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sum = sum + 4.0 * f(x_n);
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}
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for n in 2..N-2 by 2 {
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x_n = a + n * h;
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sum = sum + 2.0 * f(x_n);
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}
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return (h/3.0) * sum;
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}
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var exact:real;
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var calculated:real;
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writeln("f(x) = x**3 with 100 steps from 0 to 1");
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exact = 0.25;
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calculated = leftRectangleIntegration(a = 0.0, b = 1.0, N = 100, f = f1);
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writeln("leftRectangleIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = rightRectangleIntegration(a = 0.0, b = 1.0, N = 100, f = f1);
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writeln("rightRectangleIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = midpointRectangleIntegration(a = 0.0, b = 1.0, N = 100, f = f1);
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writeln("midpointRectangleIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = trapezoidIntegration(a = 0.0, b = 1.0, N = 100, f = f1);
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writeln("trapezoidIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = simpsonsIntegration(a = 0.0, b = 1.0, N = 100, f = f1);
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writeln("simpsonsIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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writeln();
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writeln("f(x) = 1/x with 1000 steps from 1 to 100");
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exact = 4.605170;
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calculated = leftRectangleIntegration(a = 1.0, b = 100.0, N = 1000, f = f2);
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writeln("leftRectangleIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = rightRectangleIntegration(a = 1.0, b = 100.0, N = 1000, f = f2);
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writeln("rightRectangleIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = midpointRectangleIntegration(a = 1.0, b = 100.0, N = 1000, f = f2);
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writeln("midpointRectangleIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = trapezoidIntegration(a = 1.0, b = 100.0, N = 1000, f = f2);
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writeln("trapezoidIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = simpsonsIntegration(a = 1.0, b = 100.0, N = 1000, f = f2);
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writeln("simpsonsIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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writeln();
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writeln("f(x) = x with 5000000 steps from 0 to 5000");
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exact = 12500000;
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calculated = leftRectangleIntegration(a = 0.0, b = 5000.0, N = 5000000, f = f3);
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writeln("leftRectangleIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = rightRectangleIntegration(a = 0.0, b = 5000.0, N = 5000000, f = f3);
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writeln("rightRectangleIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = midpointRectangleIntegration(a = 0.0, b = 5000.0, N = 5000000, f = f3);
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writeln("midpointRectangleIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = trapezoidIntegration(a = 0.0, b = 5000.0, N = 5000000, f = f3);
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writeln("trapezoidIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = simpsonsIntegration(a = 0.0, b = 5000.0, N = 5000000, f = f3);
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writeln("simpsonsIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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writeln();
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writeln("f(x) = x with 6000000 steps from 0 to 6000");
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exact = 18000000;
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calculated = leftRectangleIntegration(a = 0.0, b = 6000.0, N = 6000000, f = f3);
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writeln("leftRectangleIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = rightRectangleIntegration(a = 0.0, b = 6000.0, N = 6000000, f = f3);
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writeln("rightRectangleIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = midpointRectangleIntegration(a = 0.0, b = 6000.0, N = 6000000, f = f3);
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writeln("midpointRectangleIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = trapezoidIntegration(a = 0.0, b = 6000.0, N = 6000000, f = f3);
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writeln("trapezoidIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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calculated = simpsonsIntegration(a = 0.0, b = 6000.0, N = 6000000, f = f3);
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writeln("simpsonsIntegration: calculated = ", calculated, "; exact = ", exact, "; difference = ", abs(calculated - exact));
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writeln();
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f(x) = x**3 with 100 steps from 0 to 1
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leftRectangleIntegration: calculated = 0.245025; exact = 0.25; difference = 0.004975
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rightRectangleIntegration: calculated = 0.255025; exact = 0.25; difference = 0.005025
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midpointRectangleIntegration: calculated = 0.249988; exact = 0.25; difference = 1.25e-05
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trapezoidIntegration: calculated = 0.250025; exact = 0.25; difference = 2.5e-05
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simpsonsIntegration: calculated = 0.25; exact = 0.25; difference = 5.55112e-17
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f(x) = 1/x with 1000 steps from 1 to 100
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leftRectangleIntegration: calculated = 4.65499; exact = 4.60517; difference = 0.0498211
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rightRectangleIntegration: calculated = 4.55698; exact = 4.60517; difference = 0.0481889
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midpointRectangleIntegration: calculated = 4.60476; exact = 4.60517; difference = 0.000407451
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trapezoidIntegration: calculated = 4.60599; exact = 4.60517; difference = 0.000816058
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simpsonsIntegration: calculated = 4.60517; exact = 4.60517; difference = 3.31627e-06
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f(x) = x with 5000000 steps from 0 to 5000
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leftRectangleIntegration: calculated = 1.25e+07; exact = 1.25e+07; difference = 2.5
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rightRectangleIntegration: calculated = 1.25e+07; exact = 1.25e+07; difference = 2.5
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midpointRectangleIntegration: calculated = 1.25e+07; exact = 1.25e+07; difference = 0.0
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trapezoidIntegration: calculated = 1.25e+07; exact = 1.25e+07; difference = 1.86265e-09
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simpsonsIntegration: calculated = 1.25e+07; exact = 1.25e+07; difference = 3.72529e-09
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f(x) = x with 6000000 steps from 0 to 6000
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leftRectangleIntegration: calculated = 1.8e+07; exact = 1.8e+07; difference = 3.0
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rightRectangleIntegration: calculated = 1.8e+07; exact = 1.8e+07; difference = 3.0
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midpointRectangleIntegration: calculated = 1.8e+07; exact = 1.8e+07; difference = 7.45058e-09
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trapezoidIntegration: calculated = 1.8e+07; exact = 1.8e+07; difference = 3.72529e-09
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simpsonsIntegration: calculated = 1.8e+07; exact = 1.8e+07; difference = 0.0
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@ -1,79 +0,0 @@
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function int_leftrect(sequence bounds, integer n, integer func_id)
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atom h, sum
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h = (bounds[2]-bounds[1])/n
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sum = 0
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for x = bounds[1] to bounds[2]-h by h do
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sum += call_func(func_id, {x})
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end for
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return h*sum
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end function
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function int_rightrect(sequence bounds, integer n, integer func_id)
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atom h, sum
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h = (bounds[2]-bounds[1])/n
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sum = 0
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for x = bounds[1] to bounds[2]-h by h do
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sum += call_func(func_id, {x+h})
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end for
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return h*sum
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end function
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function int_midrect(sequence bounds, integer n, integer func_id)
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atom h, sum
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h = (bounds[2]-bounds[1])/n
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sum = 0
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for x = bounds[1] to bounds[2]-h by h do
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sum += call_func(func_id, {x+h/2})
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end for
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return h*sum
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end function
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function int_trapezium(sequence bounds, integer n, integer func_id)
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atom h, sum
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h = (bounds[2]-bounds[1])/n
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sum = call_func(func_id, {bounds[1]}) + call_func(func_id, {bounds[2]})
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for x = bounds[1] to bounds[2]-h by h do
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sum += 2*call_func(func_id, {x})
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end for
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return h * sum / 2
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end function
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function int_simpson(sequence bounds, integer n, integer func_id)
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atom h, sum1, sum2
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h = (bounds[2]-bounds[1])/n
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sum1 = call_func(func_id, {bounds[1] + h/2})
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sum2 = 0
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for i = 1 to n-1 do
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sum1 += call_func(func_id, {bounds[1] + h * i + h / 2})
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sum2 += call_func(func_id, {bounds[1] + h * i})
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end for
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return h/6 * (call_func(func_id, {bounds[1]}) +
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call_func(func_id, {bounds[2]}) + 4*sum1 + 2*sum2)
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end function
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function xp2d2(atom x)
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return x*x/2
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end function
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function logx(atom x)
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return log(x)
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end function
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function x(atom x)
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return x
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end function
|
||||
|
||||
? int_leftrect({-1,1},1000,routine_id("xp2d2"))
|
||||
? int_rightrect({-1,1},1000,routine_id("xp2d2"))
|
||||
? int_midrect({-1,1},1000,routine_id("xp2d2"))
|
||||
? int_simpson({-1,1},1000,routine_id("xp2d2"))
|
||||
puts(1,'\n')
|
||||
? int_leftrect({1,2},1000,routine_id("logx"))
|
||||
? int_rightrect({1,2},1000,routine_id("logx"))
|
||||
? int_midrect({1,2},1000,routine_id("logx"))
|
||||
? int_simpson({1,2},1000,routine_id("logx"))
|
||||
puts(1,'\n')
|
||||
? int_leftrect({0,10},1000,routine_id("x"))
|
||||
? int_rightrect({0,10},1000,routine_id("x"))
|
||||
? int_midrect({0,10},1000,routine_id("x"))
|
||||
? int_simpson({0,10},1000,routine_id("x"))
|
||||
|
|
@ -1,5 +1,5 @@
|
|||
-- 28 Jul 2025
|
||||
include Settings
|
||||
-- 24 Aug 2025
|
||||
include Setting
|
||||
arg digs
|
||||
if digs = '' then
|
||||
digs=9
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue