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Ingy döt Net 2026-02-01 16:33:20 -08:00
parent 5150844a7d
commit 4bb20c9b71
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9
Task/LU-decomposition/Ada/lu-decomposition-1.ada
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with Ada.Numerics.Generic_Real_Arrays;
generic
with package Matrix is new Ada.Numerics.Generic_Real_Arrays (<>);
package Decomposition is
-- decompose a square matrix A by PA = LU
procedure Decompose (A : Matrix.Real_Matrix; P, L, U : out Matrix.Real_Matrix);
end Decomposition;

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Task/LU-decomposition/Ada/lu-decomposition-2.ada
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package body Decomposition is
procedure Swap_Rows (M : in out Matrix.Real_Matrix; From, To : Natural) is
Temporary : Matrix.Real;
begin
if From = To then
return;
end if;
for I in M'Range (2) loop
Temporary := M (M'First (1) + From, I);
M (M'First (1) + From, I) := M (M'First (1) + To, I);
M (M'First (1) + To, I) := Temporary;
end loop;
end Swap_Rows;
function Pivoting_Matrix
(M : Matrix.Real_Matrix)
return Matrix.Real_Matrix
is
use type Matrix.Real;
Order : constant Positive := M'Length (1);
Result : Matrix.Real_Matrix := Matrix.Unit_Matrix (Order);
Max : Matrix.Real;
Row : Natural;
begin
for J in 0 .. Order - 1 loop
Max := M (M'First (1) + J, M'First (2) + J);
Row := J;
for I in J .. Order - 1 loop
if M (M'First (1) + I, M'First (2) + J) > Max then
Max := M (M'First (1) + I, M'First (2) + J);
Row := I;
end if;
end loop;
if J /= Row then
-- swap rows J and Row
Swap_Rows (Result, J, Row);
end if;
end loop;
return Result;
end Pivoting_Matrix;
procedure Decompose (A : Matrix.Real_Matrix; P, L, U : out Matrix.Real_Matrix) is
use type Matrix.Real_Matrix, Matrix.Real;
Order : constant Positive := A'Length (1);
A2 : Matrix.Real_Matrix (A'Range (1), A'Range (2));
S : Matrix.Real;
begin
L := (others => (others => 0.0));
U := (others => (others => 0.0));
P := Pivoting_Matrix (A);
A2 := P * A;
for J in 0 .. Order - 1 loop
L (L'First (1) + J, L'First (2) + J) := 1.0;
for I in 0 .. J loop
S := 0.0;
for K in 0 .. I - 1 loop
S := S + U (U'First (1) + K, U'First (2) + J) *
L (L'First (1) + I, L'First (2) + K);
end loop;
U (U'First (1) + I, U'First (2) + J) :=
A2 (A2'First (1) + I, A2'First (2) + J) - S;
end loop;
for I in J + 1 .. Order - 1 loop
S := 0.0;
for K in 0 .. J loop
S := S + U (U'First (1) + K, U'First (2) + J) *
L (L'First (1) + I, L'First (2) + K);
end loop;
L (L'First (1) + I, L'First (2) + J) :=
(A2 (A2'First (1) + I, A2'First (2) + J) - S) /
U (U'First (1) + J, U'First (2) + J);
end loop;
end loop;
end Decompose;
end Decomposition;

53
Task/LU-decomposition/Ada/lu-decomposition-3.ada
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with Ada.Numerics.Real_Arrays;
with Ada.Text_IO;
with Decomposition;
procedure Decompose_Example is
package Real_Decomposition is new Decomposition
(Matrix => Ada.Numerics.Real_Arrays);
package Real_IO is new Ada.Text_IO.Float_IO (Float);
procedure Print (M : Ada.Numerics.Real_Arrays.Real_Matrix) is
begin
for Row in M'Range (1) loop
for Col in M'Range (2) loop
Real_IO.Put (M (Row, Col), 3, 2, 0);
end loop;
Ada.Text_IO.New_Line;
end loop;
end Print;
Example_1 : constant Ada.Numerics.Real_Arrays.Real_Matrix :=
((1.0, 3.0, 5.0),
(2.0, 4.0, 7.0),
(1.0, 1.0, 0.0));
P_1, L_1, U_1 : Ada.Numerics.Real_Arrays.Real_Matrix (Example_1'Range (1),
Example_1'Range (2));
Example_2 : constant Ada.Numerics.Real_Arrays.Real_Matrix :=
((11.0, 9.0, 24.0, 2.0),
(1.0, 5.0, 2.0, 6.0),
(3.0, 17.0, 18.0, 1.0),
(2.0, 5.0, 7.0, 1.0));
P_2, L_2, U_2 : Ada.Numerics.Real_Arrays.Real_Matrix (Example_2'Range (1),
Example_2'Range (2));
begin
Real_Decomposition.Decompose (A => Example_1,
P => P_1,
L => L_1,
U => U_1);
Real_Decomposition.Decompose (A => Example_2,
P => P_2,
L => L_2,
U => U_2);
Ada.Text_IO.Put_Line ("Example 1:");
Ada.Text_IO.Put_Line ("A:"); Print (Example_1);
Ada.Text_IO.Put_Line ("L:"); Print (L_1);
Ada.Text_IO.Put_Line ("U:"); Print (U_1);
Ada.Text_IO.Put_Line ("P:"); Print (P_1);
Ada.Text_IO.New_Line;
Ada.Text_IO.Put_Line ("Example 2:");
Ada.Text_IO.Put_Line ("A:"); Print (Example_2);
Ada.Text_IO.Put_Line ("L:"); Print (L_2);
Ada.Text_IO.Put_Line ("U:"); Print (U_2);
Ada.Text_IO.Put_Line ("P:"); Print (P_2);
end Decompose_Example;