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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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95
Task/QR-decomposition/Ada/qr-decomposition.ada
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with Ada.Text_IO; use Ada.Text_IO;
with Ada.Numerics.Real_Arrays; use Ada.Numerics.Real_Arrays;
with Ada.Numerics.Generic_Elementary_Functions;
procedure QR is
procedure Show (mat : Real_Matrix) is
package FIO is new Ada.Text_IO.Float_IO (Float);
begin
for row in mat'Range (1) loop
for col in mat'Range (2) loop
FIO.Put (mat (row, col), Exp => 0, Aft => 4, Fore => 5);
end loop;
New_Line;
end loop;
end Show;
function GetCol (mat : Real_Matrix; n : Integer) return Real_Matrix is
column : Real_Matrix (mat'Range (1), 1 .. 1);
begin
for row in mat'Range (1) loop
column (row, 1) := mat (row, n);
end loop;
return column;
end GetCol;
function Mag (mat : Real_Matrix) return Float is
sum : Real_Matrix := Transpose (mat) * mat;
package Math is new Ada.Numerics.Generic_Elementary_Functions
(Float);
begin
return Math.Sqrt (sum (1, 1));
end Mag;
function eVect (col : Real_Matrix; n : Integer) return Real_Matrix is
vect : Real_Matrix (col'Range (1), 1 .. 1);
begin
for row in col'Range (1) loop
if row /= n then vect (row, 1) := 0.0;
else vect (row, 1) := 1.0; end if;
end loop;
return vect;
end eVect;
function Identity (n : Integer) return Real_Matrix is
mat : Real_Matrix (1 .. n, 1 .. n) := (1 .. n => (others => 0.0));
begin
for i in Integer range 1 .. n loop mat (i, i) := 1.0; end loop;
return mat;
end Identity;
function Chop (mat : Real_Matrix; n : Integer) return Real_Matrix is
small : Real_Matrix (n .. mat'Length (1), n .. mat'Length (2));
begin
for row in small'Range (1) loop
for col in small'Range (2) loop
small (row, col) := mat (row, col);
end loop;
end loop;
return small;
end Chop;
function H_n (inmat : Real_Matrix; n : Integer)
return Real_Matrix is
mat : Real_Matrix := Chop (inmat, n);
col : Real_Matrix := GetCol (mat, n);
colT : Real_Matrix (1 .. 1, mat'Range (1));
H : Real_Matrix := Identity (mat'Length (1));
Hall : Real_Matrix := Identity (inmat'Length (1));
begin
col := col - Mag (col) * eVect (col, n);
col := col / Mag (col);
colT := Transpose (col);
H := H - 2.0 * (col * colT);
for row in H'Range (1) loop
for col in H'Range (2) loop
Hall (n - 1 + row, n - 1 + col) := H (row, col);
end loop;
end loop;
return Hall;
end H_n;
A : constant Real_Matrix (1 .. 3, 1 .. 3) := (
(12.0, -51.0, 4.0),
(6.0, 167.0, -68.0),
(-4.0, 24.0, -41.0));
Q1, Q2, Q3, Q, R: Real_Matrix (1 .. 3, 1 .. 3);
begin
Q1 := H_n (A, 1);
Q2 := H_n (Q1 * A, 2);
Q3 := H_n (Q2 * Q1* A, 3);
Q := Transpose (Q1) * Transpose (Q2) * TransPose(Q3);
R := Q3 * Q2 * Q1 * A;
Put_Line ("Q:"); Show (Q);
Put_Line ("R:"); Show (R);
end QR;