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286 | -- This package is free software; you can redistribute it and/or
-- modify it under terms of the GNU General Public License as
-- published by the Free Software Foundation; either version 3, or
-- (at your option) any later version. It is distributed in the
-- hope that it will be useful, but WITHOUT ANY WARRANTY; without
-- even the implied warranty of MERCHANTABILITY or FITNESS FOR A
-- PARTICULAR PURPOSE.
--
-- As a special exception under Section 7 of GPL version 3, you are
-- granted additional permissions described in the GCC Runtime
-- Library Exception, version 3.1, as published by the Free Software
-- Foundation.
--
-- You should have received a copy of the GNU General Public License
-- and a copy of the GCC Runtime Library Exception along with this
-- program; see the files COPYING3 and COPYING.RUNTIME respectively.
-- If not, see <http://www.gnu.org/licenses/>.
--
-- Copyright Simon Wright <simon@pushface.org>
with Ada.Exceptions;
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
with Ada.Text_IO; use Ada.Text_IO;
with Ada.Text_IO.Complex_IO;
with Ada.Numerics.Float_Random;
with Ada.Numerics.Generic_Real_Arrays;
with Ada.Numerics.Generic_Complex_Types;
with Ada.Numerics.Generic_Complex_Arrays;
with Ada_Numerics.Generic_Arrays;
procedure Demo_Extensions is
subtype My_Float is Float;
package My_Float_IO is new Float_IO (My_Float);
package Real_Arrays
is new Ada.Numerics.Generic_Real_Arrays (My_Float);
package Complex_Types
is new Ada.Numerics.Generic_Complex_Types (My_Float);
package Complex_Arrays
is new Ada.Numerics.Generic_Complex_Arrays (Real_Arrays, Complex_Types);
package Extensions
is new Ada_Numerics.Generic_Arrays (Complex_Arrays);
package My_Complex_IO is new Complex_IO (Complex_Types);
use Real_Arrays;
use Complex_Types;
use Complex_Arrays;
use My_Float_IO;
use My_Complex_IO;
begin
Put_Line ("--------------------------------");
Put_Line ("Values from <143ef70b-7e74-426b-a621-a5fd157849be"
& "@x21g2000yqa.googlegroups.com>");
-- (posting by yc on comp.lang.ada)
New_Line;
declare
Input : constant Complex_Matrix
:= (42 => ((8.0, 0.0), (-1.0, 0.0), (-5.0, 0.0)),
43 => ((-4.0, 0.0), (4.0, 0.0), (-2.0, 0.0)),
44 => ((18.0, 0.0), (-5.0, 0.0), (-7.0, 0.0)));
Result : constant Complex_Vector := Extensions.Eigenvalues (Input);
begin
for J in Result'Range loop
Put (J, Width => 2);
Put (" => ");
Put (Result (J), Exp => 0);
New_Line;
end loop;
New_Line;
end;
Put_Line ("--------------------------------");
Put_Line ("Values in Test16 of "
& "http://people.sc.fsu.edu/~jburkardt/f_src/lapack"
& "/lapack_OSX_prb_output.txt");
New_Line;
declare
Z : constant Complex := (0.0, 0.0);
A : constant Complex := (2.44949, 0.0);
B : constant Complex := (3.16228, 0.0);
C : constant Complex := (3.46410, 0.0);
Input : constant Complex_Matrix
:= (
1 => (Z, A, Z, Z, Z, Z, Z),
2 => (A, Z, B, Z, Z, Z, Z),
3 => (Z, B, Z, C, Z, Z, Z),
4 => (Z, Z, C, Z, C, Z, Z),
5 => (Z, Z, Z, C, Z, B, Z),
6 => (Z, Z, Z, Z, B, Z, A),
7 => (Z, Z, Z, Z, Z, A, Z)
);
begin
-- GNAT: Eigenvalues of symmetrix complex matrix are real
Put_Line ("using Complex_Arrays.Eigenvalues");
declare
Result : constant Real_Vector := Complex_Arrays.Eigenvalues (Input);
begin
for J in Result'Range loop
Put (Result (J), Exp => 0);
New_Line;
end loop;
end;
New_Line;
-- Extension: Eigenvalues of general complex matrix are complex.
Put_Line ("using Extensions.Eigenvalues");
declare
Result : constant Complex_Vector := Extensions.Eigenvalues (Input);
begin
for J in Result'Range loop
Put (Result (J), Exp => 0);
New_Line;
end loop;
end;
New_Line;
end;
Put_Line ("--------------------------------");
Put_Line
("Values from http://en.wikipedia.org/wiki/Skew-symmetric_matrix");
New_Line;
declare
Input : constant Complex_Matrix
:= (((0.0, 0.0), (2.0, 0.0), (-1.0, 0.0)),
((-2.0, 0.0), (0.0, 0.0), (-4.0, 0.0)),
((1.0, 0.0), (4.0, 0.0), (0.0, 0.0)));
Result : Complex_Vector (1 .. Input'Length (1));
begin
Result := Extensions.Eigenvalues (Input);
for J in Result'Range loop
Put (Result (J), Exp => 0);
New_Line;
end loop;
New_Line;
end;
Put_Line ("--------------------------------");
Put_Line
("Results from http://en.wikipedia.org/wiki/Orthogonal_matrix");
New_Line;
declare
Input : constant Complex_Matrix
:= (((0.0, 0.0), (-0.8, 0.0), (-0.6, 0.0)),
((0.8, 0.0), (-0.36, 0.0), (0.48, 0.0)),
((0.6, 0.0), (0.48, 0.0), (-0.64, 0.0)));
Result : Complex_Vector (Input'Range (1));
Values : Complex_Vector (Input'Range (1));
Vectors : Complex_Matrix (Input'Range (1), Input'Range (2));
begin
Result := Extensions.Eigenvalues (Input);
Put_Line ("Eigenvalues:");
for J in Result'Range loop
Put (Result (J), Exp => 0);
New_Line;
end loop;
New_Line;
Extensions.Eigensystem (Input, Values, Vectors);
Put_Line ("Eignesystem Values:");
for J in Values'Range loop
Put (Values (J), Exp => 0);
New_Line;
end loop;
New_Line;
Put_Line ("Eigensystem Vectors:");
for J in Vectors'Range (1) loop
for K in Vectors'Range loop
Put (Vectors (J, K), Exp => 0);
Put (" ");
end loop;
New_Line;
end loop;
New_Line;
end;
Put_Line ("--------------------------------");
Put_Line ("Generalized eigensystem of real non-symmetric matrix.");
Put_Line ("The solutions are such that beta*a - alpha*b is singular, ie");
Put_Line ("its determinant is zero. We'll show that it's small for");
Put_Line ("a selection of randomly-generated matrices.");
New_Line;
declare
Gen : Ada.Numerics.Float_Random.Generator;
A, B : Real_Arrays.Real_Matrix (1 .. 6, 1 .. 6);
Vectors : Complex_Arrays.Complex_Matrix (1 .. 6, 1 .. 6);
Values : Extensions.Generalized_Eigenvalue_Vector (A'Range (1));
A_Times_Beta, B_Times_Alpha, Difference :
Complex_Arrays.Complex_Matrix (A'Range (1), A'Range (2));
begin
Ada.Numerics.Float_Random.Reset (Gen, 1);
for T in 1 .. 6 loop
for J in A'Range (1) loop
for K in A'Range (2) loop
A (J, K) := My_Float (Ada.Numerics.Float_Random.Random (Gen));
end loop;
end loop;
for J in B'Range (1) loop
for K in B'Range (2) loop
B (J, K) := My_Float (Ada.Numerics.Float_Random.Random (Gen));
end loop;
end loop;
Extensions.Eigensystem (A, B, Values, Vectors);
for J in Values'Range loop
begin
A_Times_Beta := Compose_From_Cartesian (A) * Values (J).Beta;
B_Times_Alpha := Compose_From_Cartesian (B) * Values (J).Alpha;
Difference := A_Times_Beta - B_Times_Alpha;
Put ("j:" & J'Img);
Put (" determinant:");
Put (Modulus (Determinant (Difference)));
exception
when E : others =>
Put (" =====> " & Ada.Exceptions.Exception_Message (E));
end;
New_Line;
end loop;
New_Line;
end loop;
end;
Put_Line ("--------------------------------");
Put_Line ("ZGGEV example at http://www.nag.co.uk/lapack-ex/node122.html");
New_Line;
declare
A : constant Complex_Arrays.Complex_Matrix (1 .. 4, 1 .. 4) :=
(((-21.10,-22.50), ( 53.50,-50.50), (-34.50,127.50), ( 7.50, 0.50)),
(( -0.46, -7.78), ( -3.50,-37.50), (-15.50, 58.50), (-10.50, -1.50)),
(( 4.30, -5.50), ( 39.70,-17.10), (-68.50, 12.50), ( -7.50, -3.50)),
(( 5.50, 4.40), ( 14.40, 43.30), (-32.50,-46.00), (-19.00,-32.50)));
B : constant Complex_Arrays.Complex_Matrix (1 .. 4, 1 .. 4) :=
((( 1.00, -5.00), ( 1.60, 1.20), ( -3.00, 0.00), ( 0.00, -1.00)),
(( 0.80, -0.60), ( 3.00, -5.00), ( -4.00, 3.00), ( -2.40, -3.20)),
(( 1.00, 0.00), ( 2.40, 1.80), ( -4.00, -5.00), ( 0.00, -3.00)),
(( 0.00, 1.00), ( -1.80, 2.40), ( 0.00, -4.00), ( 4.00, -5.00)));
Values : Extensions.Generalized_Eigenvalue_Vector (1 .. 4);
Vectors : Complex_Arrays.Complex_Matrix (1 .. 4, 1 .. 4);
begin
Extensions.Eigensystem (A, B, Values, Vectors);
for J in 1 .. 4 loop
Put ("Eigenvalue(" & J'Img & ") = ");
Put (Values (J).Alpha / Values (J).Beta);
New_Line;
Put ("Eigenvector(" & J'Img & ") = ");
for K in 1 .. 4 loop
Put (Vectors (K, J));
end loop;
New_Line;
end loop;
end;
end Demo_Extensions;
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