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Ingy döt Net 2026-02-01 16:33:20 -08:00
parent 5150844a7d
commit 4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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9
Task/Cholesky-decomposition/Ada/cholesky-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 A = L * Transpose (L)
procedure Decompose (A : Matrix.Real_Matrix; L : out Matrix.Real_Matrix);
end Decomposition;

33
Task/Cholesky-decomposition/Ada/cholesky-decomposition-2.ada
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with Ada.Numerics.Generic_Elementary_Functions;
package body Decomposition is
package Math is new Ada.Numerics.Generic_Elementary_Functions
(Matrix.Real);
procedure Decompose (A : Matrix.Real_Matrix; L : out Matrix.Real_Matrix) is
use type Matrix.Real_Matrix, Matrix.Real;
Order : constant Positive := A'Length (1);
S : Matrix.Real;
begin
L := (others => (others => 0.0));
for I in 0 .. Order - 1 loop
for K in 0 .. I loop
S := 0.0;
for J in 0 .. K - 1 loop
S := S +
L (L'First (1) + I, L'First (2) + J) *
L (L'First (1) + K, L'First (2) + J);
end loop;
-- diagonals
if K = I then
L (L'First (1) + K, L'First (2) + K) :=
Math.Sqrt (A (A'First (1) + K, A'First (2) + K) - S);
else
L (L'First (1) + I, L'First (2) + K) :=
1.0 / L (L'First (1) + K, L'First (2) + K) *
(A (A'First (1) + I, A'First (2) + K) - S);
end if;
end loop;
end loop;
end Decompose;
end Decomposition;

45
Task/Cholesky-decomposition/Ada/cholesky-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), 4, 3, 0);
end loop;
Ada.Text_IO.New_Line;
end loop;
end Print;
Example_1 : constant Ada.Numerics.Real_Arrays.Real_Matrix :=
((25.0, 15.0, -5.0),
(15.0, 18.0, 0.0),
(-5.0, 0.0, 11.0));
L_1 : Ada.Numerics.Real_Arrays.Real_Matrix (Example_1'Range (1),
Example_1'Range (2));
Example_2 : constant Ada.Numerics.Real_Arrays.Real_Matrix :=
((18.0, 22.0, 54.0, 42.0),
(22.0, 70.0, 86.0, 62.0),
(54.0, 86.0, 174.0, 134.0),
(42.0, 62.0, 134.0, 106.0));
L_2 : Ada.Numerics.Real_Arrays.Real_Matrix (Example_2'Range (1),
Example_2'Range (2));
begin
Real_Decomposition.Decompose (A => Example_1,
L => L_1);
Real_Decomposition.Decompose (A => Example_2,
L => L_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.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);
end Decompose_Example;

51
Task/Cholesky-decomposition/PowerShell/cholesky-decomposition.psh
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function cholesky ($a) {
$l = @()
if ($a) {
$n = $a.count
$end = $n - 1
$l = 1..$n | foreach {$row = @(0) * $n; ,$row}
foreach ($k in 0..$end) {
$m = $k - 1
$sum = 0
if(0 -lt $k) {
foreach ($j in 0..$m) {$sum += $l[$k][$j]*$l[$k][$j]}
}
$l[$k][$k] = [Math]::Sqrt($a[$k][$k] - $sum)
if ($k -lt $end) {
foreach ($i in ($k+1)..$end) {
$sum = 0
if (0 -lt $k) {
foreach ($j in 0..$m) {$sum += $l[$i][$j]*$l[$k][$j]}
}
$l[$i][$k] = ($a[$i][$k] - $sum)/$l[$k][$k]
}
}
}
}
$l
}
function show($a) {$a | foreach {"$_"}}
$a1 = @(
@(25, 15, -5),
@(15, 18, 0),
@(-5, 0, 11)
)
"a1 ="
show $a1
""
"l1 ="
show (cholesky $a1)
""
$a2 = @(
@(18, 22, 54, 42),
@(22, 70, 86, 62),
@(54, 86, 174, 134),
@(42, 62, 134, 106)
)
"a2 ="
show $a2
""
"l2 ="
show (cholesky $a2)