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|
------------------------------------------------------------------------------
-- --
-- GNAT COMPILER COMPONENTS --
-- --
-- ADA.NUMERICS.GENERIC_COMPLEX_ARRAYS --
-- --
-- B o d y --
-- --
-- Copyright (C) 2006-2012, Free Software Foundation, Inc. --
-- --
-- GNAT is free software; you can redistribute it and/or modify it under --
-- terms of the GNU General Public License as published by the Free Soft- --
-- ware Foundation; either version 3, or (at your option) any later ver- --
-- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
-- OUT 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/>. --
-- --
-- GNAT was originally developed by the GNAT team at New York University. --
-- Extensive contributions were provided by Ada Core Technologies Inc. --
-- --
------------------------------------------------------------------------------
with System.Generic_Array_Operations; use System.Generic_Array_Operations;
with Ada.Numerics; use Ada.Numerics;
package body Ada.Numerics.Generic_Complex_Arrays is
-- Operations that are defined in terms of operations on the type Real,
-- such as addition, subtraction and scaling, are computed in the canonical
-- way looping over all elements.
package Ops renames System.Generic_Array_Operations;
subtype Real is Real_Arrays.Real;
-- Work around visibility bug ???
function Is_Non_Zero (X : Complex) return Boolean is (X /= (0.0, 0.0));
-- Needed by Back_Substitute
procedure Back_Substitute is new Ops.Back_Substitute
(Scalar => Complex,
Matrix => Complex_Matrix,
Is_Non_Zero => Is_Non_Zero);
procedure Forward_Eliminate is new Ops.Forward_Eliminate
(Scalar => Complex,
Real => Real'Base,
Matrix => Complex_Matrix,
Zero => (0.0, 0.0),
One => (1.0, 0.0));
procedure Transpose is new Ops.Transpose
(Scalar => Complex,
Matrix => Complex_Matrix);
-- Helper function that raises a Constraint_Error is the argument is
-- not a square matrix, and otherwise returns its length.
function Length is new Square_Matrix_Length (Complex, Complex_Matrix);
-- Instant a generic square root implementation here, in order to avoid
-- instantiating a complete copy of Generic_Elementary_Functions.
-- Speed of the square root is not a big concern here.
function Sqrt is new Ops.Sqrt (Real'Base);
-- Instantiating the following subprograms directly would lead to
-- name clashes, so use a local package.
package Instantiations is
---------
-- "*" --
---------
function "*" is new Vector_Scalar_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Operation => "*");
function "*" is new Vector_Scalar_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Operation => "*");
function "*" is new Scalar_Vector_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Right_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Operation => "*");
function "*" is new Scalar_Vector_Elementwise_Operation
(Left_Scalar => Real'Base,
Right_Scalar => Complex,
Result_Scalar => Complex,
Right_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Operation => "*");
function "*" is new Inner_Product
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Right_Vector => Real_Vector,
Zero => (0.0, 0.0));
function "*" is new Inner_Product
(Left_Scalar => Real'Base,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Vector => Real_Vector,
Right_Vector => Complex_Vector,
Zero => (0.0, 0.0));
function "*" is new Inner_Product
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Right_Vector => Complex_Vector,
Zero => (0.0, 0.0));
function "*" is new Outer_Product
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Right_Vector => Complex_Vector,
Matrix => Complex_Matrix);
function "*" is new Outer_Product
(Left_Scalar => Real'Base,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Vector => Real_Vector,
Right_Vector => Complex_Vector,
Matrix => Complex_Matrix);
function "*" is new Outer_Product
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Right_Vector => Real_Vector,
Matrix => Complex_Matrix);
function "*" is new Matrix_Scalar_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "*");
function "*" is new Matrix_Scalar_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "*");
function "*" is new Scalar_Matrix_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Right_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "*");
function "*" is new Scalar_Matrix_Elementwise_Operation
(Left_Scalar => Real'Base,
Right_Scalar => Complex,
Result_Scalar => Complex,
Right_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "*");
function "*" is new Matrix_Vector_Product
(Left_Scalar => Real'Base,
Right_Scalar => Complex,
Result_Scalar => Complex,
Matrix => Real_Matrix,
Right_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Zero => (0.0, 0.0));
function "*" is new Matrix_Vector_Product
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Matrix => Complex_Matrix,
Right_Vector => Real_Vector,
Result_Vector => Complex_Vector,
Zero => (0.0, 0.0));
function "*" is new Matrix_Vector_Product
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Matrix => Complex_Matrix,
Right_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Zero => (0.0, 0.0));
function "*" is new Vector_Matrix_Product
(Left_Scalar => Real'Base,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Vector => Real_Vector,
Matrix => Complex_Matrix,
Result_Vector => Complex_Vector,
Zero => (0.0, 0.0));
function "*" is new Vector_Matrix_Product
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Matrix => Real_Matrix,
Result_Vector => Complex_Vector,
Zero => (0.0, 0.0));
function "*" is new Vector_Matrix_Product
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Matrix => Complex_Matrix,
Result_Vector => Complex_Vector,
Zero => (0.0, 0.0));
function "*" is new Matrix_Matrix_Product
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Matrix => Complex_Matrix,
Right_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Zero => (0.0, 0.0));
function "*" is new Matrix_Matrix_Product
(Left_Scalar => Real'Base,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Matrix => Real_Matrix,
Right_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Zero => (0.0, 0.0));
function "*" is new Matrix_Matrix_Product
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Matrix => Complex_Matrix,
Right_Matrix => Real_Matrix,
Result_Matrix => Complex_Matrix,
Zero => (0.0, 0.0));
---------
-- "+" --
---------
function "+" is new Vector_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Complex,
X_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Operation => "+");
function "+" is new Vector_Vector_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Right_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Operation => "+");
function "+" is new Vector_Vector_Elementwise_Operation
(Left_Scalar => Real'Base,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Vector => Real_Vector,
Right_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Operation => "+");
function "+" is new Vector_Vector_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Right_Vector => Real_Vector,
Result_Vector => Complex_Vector,
Operation => "+");
function "+" is new Matrix_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Complex,
X_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "+");
function "+" is new Matrix_Matrix_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Matrix => Complex_Matrix,
Right_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "+");
function "+" is new Matrix_Matrix_Elementwise_Operation
(Left_Scalar => Real'Base,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Matrix => Real_Matrix,
Right_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "+");
function "+" is new Matrix_Matrix_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Matrix => Complex_Matrix,
Right_Matrix => Real_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "+");
---------
-- "-" --
---------
function "-" is new Vector_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Complex,
X_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Operation => "-");
function "-" is new Vector_Vector_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Right_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Operation => "-");
function "-" is new Vector_Vector_Elementwise_Operation
(Left_Scalar => Real'Base,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Vector => Real_Vector,
Right_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Operation => "-");
function "-" is new Vector_Vector_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Right_Vector => Real_Vector,
Result_Vector => Complex_Vector,
Operation => "-");
function "-" is new Matrix_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Complex,
X_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "-");
function "-" is new Matrix_Matrix_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Matrix => Complex_Matrix,
Right_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "-");
function "-" is new Matrix_Matrix_Elementwise_Operation
(Left_Scalar => Real'Base,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Matrix => Real_Matrix,
Right_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "-");
function "-" is new Matrix_Matrix_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Matrix => Complex_Matrix,
Right_Matrix => Real_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "-");
---------
-- "/" --
---------
function "/" is new Vector_Scalar_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Operation => "/");
function "/" is new Vector_Scalar_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Operation => "/");
function "/" is new Matrix_Scalar_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Complex,
Result_Scalar => Complex,
Left_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "/");
function "/" is new Matrix_Scalar_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Operation => "/");
-----------
-- "abs" --
-----------
function "abs" is new L2_Norm
(X_Scalar => Complex,
Result_Real => Real'Base,
X_Vector => Complex_Vector);
--------------
-- Argument --
--------------
function Argument is new Vector_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Real'Base,
X_Vector => Complex_Vector,
Result_Vector => Real_Vector,
Operation => Argument);
function Argument is new Vector_Scalar_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Real'Base,
Left_Vector => Complex_Vector,
Result_Vector => Real_Vector,
Operation => Argument);
function Argument is new Matrix_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Real'Base,
X_Matrix => Complex_Matrix,
Result_Matrix => Real_Matrix,
Operation => Argument);
function Argument is new Matrix_Scalar_Elementwise_Operation
(Left_Scalar => Complex,
Right_Scalar => Real'Base,
Result_Scalar => Real'Base,
Left_Matrix => Complex_Matrix,
Result_Matrix => Real_Matrix,
Operation => Argument);
----------------------------
-- Compose_From_Cartesian --
----------------------------
function Compose_From_Cartesian is new Vector_Elementwise_Operation
(X_Scalar => Real'Base,
Result_Scalar => Complex,
X_Vector => Real_Vector,
Result_Vector => Complex_Vector,
Operation => Compose_From_Cartesian);
function Compose_From_Cartesian is
new Vector_Vector_Elementwise_Operation
(Left_Scalar => Real'Base,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Vector => Real_Vector,
Right_Vector => Real_Vector,
Result_Vector => Complex_Vector,
Operation => Compose_From_Cartesian);
function Compose_From_Cartesian is new Matrix_Elementwise_Operation
(X_Scalar => Real'Base,
Result_Scalar => Complex,
X_Matrix => Real_Matrix,
Result_Matrix => Complex_Matrix,
Operation => Compose_From_Cartesian);
function Compose_From_Cartesian is
new Matrix_Matrix_Elementwise_Operation
(Left_Scalar => Real'Base,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Matrix => Real_Matrix,
Right_Matrix => Real_Matrix,
Result_Matrix => Complex_Matrix,
Operation => Compose_From_Cartesian);
------------------------
-- Compose_From_Polar --
------------------------
function Compose_From_Polar is
new Vector_Vector_Elementwise_Operation
(Left_Scalar => Real'Base,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Vector => Real_Vector,
Right_Vector => Real_Vector,
Result_Vector => Complex_Vector,
Operation => Compose_From_Polar);
function Compose_From_Polar is
new Vector_Vector_Scalar_Elementwise_Operation
(X_Scalar => Real'Base,
Y_Scalar => Real'Base,
Z_Scalar => Real'Base,
Result_Scalar => Complex,
X_Vector => Real_Vector,
Y_Vector => Real_Vector,
Result_Vector => Complex_Vector,
Operation => Compose_From_Polar);
function Compose_From_Polar is
new Matrix_Matrix_Elementwise_Operation
(Left_Scalar => Real'Base,
Right_Scalar => Real'Base,
Result_Scalar => Complex,
Left_Matrix => Real_Matrix,
Right_Matrix => Real_Matrix,
Result_Matrix => Complex_Matrix,
Operation => Compose_From_Polar);
function Compose_From_Polar is
new Matrix_Matrix_Scalar_Elementwise_Operation
(X_Scalar => Real'Base,
Y_Scalar => Real'Base,
Z_Scalar => Real'Base,
Result_Scalar => Complex,
X_Matrix => Real_Matrix,
Y_Matrix => Real_Matrix,
Result_Matrix => Complex_Matrix,
Operation => Compose_From_Polar);
---------------
-- Conjugate --
---------------
function Conjugate is new Vector_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Complex,
X_Vector => Complex_Vector,
Result_Vector => Complex_Vector,
Operation => Conjugate);
function Conjugate is new Matrix_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Complex,
X_Matrix => Complex_Matrix,
Result_Matrix => Complex_Matrix,
Operation => Conjugate);
--------
-- Im --
--------
function Im is new Vector_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Real'Base,
X_Vector => Complex_Vector,
Result_Vector => Real_Vector,
Operation => Im);
function Im is new Matrix_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Real'Base,
X_Matrix => Complex_Matrix,
Result_Matrix => Real_Matrix,
Operation => Im);
-------------
-- Modulus --
-------------
function Modulus is new Vector_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Real'Base,
X_Vector => Complex_Vector,
Result_Vector => Real_Vector,
Operation => Modulus);
function Modulus is new Matrix_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Real'Base,
X_Matrix => Complex_Matrix,
Result_Matrix => Real_Matrix,
Operation => Modulus);
--------
-- Re --
--------
function Re is new Vector_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Real'Base,
X_Vector => Complex_Vector,
Result_Vector => Real_Vector,
Operation => Re);
function Re is new Matrix_Elementwise_Operation
(X_Scalar => Complex,
Result_Scalar => Real'Base,
X_Matrix => Complex_Matrix,
Result_Matrix => Real_Matrix,
Operation => Re);
------------
-- Set_Im --
------------
procedure Set_Im is new Update_Vector_With_Vector
(X_Scalar => Complex,
Y_Scalar => Real'Base,
X_Vector => Complex_Vector,
Y_Vector => Real_Vector,
Update => Set_Im);
procedure Set_Im is new Update_Matrix_With_Matrix
(X_Scalar => Complex,
Y_Scalar => Real'Base,
X_Matrix => Complex_Matrix,
Y_Matrix => Real_Matrix,
Update => Set_Im);
------------
-- Set_Re --
------------
procedure Set_Re is new Update_Vector_With_Vector
(X_Scalar => Complex,
Y_Scalar => Real'Base,
X_Vector => Complex_Vector,
Y_Vector => Real_Vector,
Update => Set_Re);
procedure Set_Re is new Update_Matrix_With_Matrix
(X_Scalar => Complex,
Y_Scalar => Real'Base,
X_Matrix => Complex_Matrix,
Y_Matrix => Real_Matrix,
Update => Set_Re);
-----------
-- Solve --
-----------
function Solve is
new Matrix_Vector_Solution (Complex, Complex_Vector, Complex_Matrix);
function Solve is
new Matrix_Matrix_Solution (Complex, Complex_Matrix);
-----------------
-- Unit_Matrix --
-----------------
function Unit_Matrix is new System.Generic_Array_Operations.Unit_Matrix
(Scalar => Complex,
Matrix => Complex_Matrix,
Zero => (0.0, 0.0),
One => (1.0, 0.0));
function Unit_Vector is new System.Generic_Array_Operations.Unit_Vector
(Scalar => Complex,
Vector => Complex_Vector,
Zero => (0.0, 0.0),
One => (1.0, 0.0));
end Instantiations;
---------
-- "*" --
---------
function "*"
(Left : Complex_Vector;
Right : Complex_Vector) return Complex
renames Instantiations."*";
function "*"
(Left : Real_Vector;
Right : Complex_Vector) return Complex
renames Instantiations."*";
function "*"
(Left : Complex_Vector;
Right : Real_Vector) return Complex
renames Instantiations."*";
function "*"
(Left : Complex;
Right : Complex_Vector) return Complex_Vector
renames Instantiations."*";
function "*"
(Left : Complex_Vector;
Right : Complex) return Complex_Vector
renames Instantiations."*";
function "*"
(Left : Real'Base;
Right : Complex_Vector) return Complex_Vector
renames Instantiations."*";
function "*"
(Left : Complex_Vector;
Right : Real'Base) return Complex_Vector
renames Instantiations."*";
function "*"
(Left : Complex_Matrix;
Right : Complex_Matrix) return Complex_Matrix
renames Instantiations."*";
function "*"
(Left : Complex_Vector;
Right : Complex_Vector) return Complex_Matrix
renames Instantiations."*";
function "*"
(Left : Complex_Vector;
Right : Complex_Matrix) return Complex_Vector
renames Instantiations."*";
function "*"
(Left : Complex_Matrix;
Right : Complex_Vector) return Complex_Vector
renames Instantiations."*";
function "*"
(Left : Real_Matrix;
Right : Complex_Matrix) return Complex_Matrix
renames Instantiations."*";
function "*"
(Left : Complex_Matrix;
Right : Real_Matrix) return Complex_Matrix
renames Instantiations."*";
function "*"
(Left : Real_Vector;
Right : Complex_Vector) return Complex_Matrix
renames Instantiations."*";
function "*"
(Left : Complex_Vector;
Right : Real_Vector) return Complex_Matrix
renames Instantiations."*";
function "*"
(Left : Real_Vector;
Right : Complex_Matrix) return Complex_Vector
renames Instantiations."*";
function "*"
(Left : Complex_Vector;
Right : Real_Matrix) return Complex_Vector
renames Instantiations."*";
function "*"
(Left : Real_Matrix;
Right : Complex_Vector) return Complex_Vector
renames Instantiations."*";
function "*"
(Left : Complex_Matrix;
Right : Real_Vector) return Complex_Vector
renames Instantiations."*";
function "*"
(Left : Complex;
Right : Complex_Matrix) return Complex_Matrix
renames Instantiations."*";
function "*"
(Left : Complex_Matrix;
Right : Complex) return Complex_Matrix
renames Instantiations."*";
function "*"
(Left : Real'Base;
Right : Complex_Matrix) return Complex_Matrix
renames Instantiations."*";
function "*"
(Left : Complex_Matrix;
Right : Real'Base) return Complex_Matrix
renames Instantiations."*";
---------
-- "+" --
---------
function "+" (Right : Complex_Vector) return Complex_Vector
renames Instantiations."+";
function "+"
(Left : Complex_Vector;
Right : Complex_Vector) return Complex_Vector
renames Instantiations."+";
function "+"
(Left : Real_Vector;
Right : Complex_Vector) return Complex_Vector
renames Instantiations."+";
function "+"
(Left : Complex_Vector;
Right : Real_Vector) return Complex_Vector
renames Instantiations."+";
function "+" (Right : Complex_Matrix) return Complex_Matrix
renames Instantiations."+";
function "+"
(Left : Complex_Matrix;
Right : Complex_Matrix) return Complex_Matrix
renames Instantiations."+";
function "+"
(Left : Real_Matrix;
Right : Complex_Matrix) return Complex_Matrix
renames Instantiations."+";
function "+"
(Left : Complex_Matrix;
Right : Real_Matrix) return Complex_Matrix
renames Instantiations."+";
---------
-- "-" --
---------
function "-"
(Right : Complex_Vector) return Complex_Vector
renames Instantiations."-";
function "-"
(Left : Complex_Vector;
Right : Complex_Vector) return Complex_Vector
renames Instantiations."-";
function "-"
(Left : Real_Vector;
Right : Complex_Vector) return Complex_Vector
renames Instantiations."-";
function "-"
(Left : Complex_Vector;
Right : Real_Vector) return Complex_Vector
renames Instantiations."-";
function "-" (Right : Complex_Matrix) return Complex_Matrix
renames Instantiations."-";
function "-"
(Left : Complex_Matrix;
Right : Complex_Matrix) return Complex_Matrix
renames Instantiations."-";
function "-"
(Left : Real_Matrix;
Right : Complex_Matrix) return Complex_Matrix
renames Instantiations."-";
function "-"
(Left : Complex_Matrix;
Right : Real_Matrix) return Complex_Matrix
renames Instantiations."-";
---------
-- "/" --
---------
function "/"
(Left : Complex_Vector;
Right : Complex) return Complex_Vector
renames Instantiations."/";
function "/"
(Left : Complex_Vector;
Right : Real'Base) return Complex_Vector
renames Instantiations."/";
function "/"
(Left : Complex_Matrix;
Right : Complex) return Complex_Matrix
renames Instantiations."/";
function "/"
(Left : Complex_Matrix;
Right : Real'Base) return Complex_Matrix
renames Instantiations."/";
-----------
-- "abs" --
-----------
function "abs" (Right : Complex_Vector) return Real'Base
renames Instantiations."abs";
--------------
-- Argument --
--------------
function Argument (X : Complex_Vector) return Real_Vector
renames Instantiations.Argument;
function Argument
(X : Complex_Vector;
Cycle : Real'Base) return Real_Vector
renames Instantiations.Argument;
function Argument (X : Complex_Matrix) return Real_Matrix
renames Instantiations.Argument;
function Argument
(X : Complex_Matrix;
Cycle : Real'Base) return Real_Matrix
renames Instantiations.Argument;
----------------------------
-- Compose_From_Cartesian --
----------------------------
function Compose_From_Cartesian (Re : Real_Vector) return Complex_Vector
renames Instantiations.Compose_From_Cartesian;
function Compose_From_Cartesian
(Re : Real_Vector;
Im : Real_Vector) return Complex_Vector
renames Instantiations.Compose_From_Cartesian;
function Compose_From_Cartesian (Re : Real_Matrix) return Complex_Matrix
renames Instantiations.Compose_From_Cartesian;
function Compose_From_Cartesian
(Re : Real_Matrix;
Im : Real_Matrix) return Complex_Matrix
renames Instantiations.Compose_From_Cartesian;
------------------------
-- Compose_From_Polar --
------------------------
function Compose_From_Polar
(Modulus : Real_Vector;
Argument : Real_Vector) return Complex_Vector
renames Instantiations.Compose_From_Polar;
function Compose_From_Polar
(Modulus : Real_Vector;
Argument : Real_Vector;
Cycle : Real'Base) return Complex_Vector
renames Instantiations.Compose_From_Polar;
function Compose_From_Polar
(Modulus : Real_Matrix;
Argument : Real_Matrix) return Complex_Matrix
renames Instantiations.Compose_From_Polar;
function Compose_From_Polar
(Modulus : Real_Matrix;
Argument : Real_Matrix;
Cycle : Real'Base) return Complex_Matrix
renames Instantiations.Compose_From_Polar;
---------------
-- Conjugate --
---------------
function Conjugate (X : Complex_Vector) return Complex_Vector
renames Instantiations.Conjugate;
function Conjugate (X : Complex_Matrix) return Complex_Matrix
renames Instantiations.Conjugate;
-----------------
-- Determinant --
-----------------
function Determinant (A : Complex_Matrix) return Complex is
M : Complex_Matrix := A;
B : Complex_Matrix (A'Range (1), 1 .. 0);
R : Complex;
begin
Forward_Eliminate (M, B, R);
return R;
end Determinant;
-----------------
-- Eigensystem --
-----------------
procedure Eigensystem
(A : Complex_Matrix;
Values : out Real_Vector;
Vectors : out Complex_Matrix)
is
N : constant Natural := Length (A);
-- For a Hermitian matrix C, we convert the eigenvalue problem to a
-- real symmetric one: if C = A + i * B, then the (N, N) complex
-- eigenvalue problem:
-- (A + i * B) * (u + i * v) = Lambda * (u + i * v)
--
-- is equivalent to the (2 * N, 2 * N) real eigenvalue problem:
-- [ A, B ] [ u ] = Lambda * [ u ]
-- [ -B, A ] [ v ] [ v ]
--
-- Note that the (2 * N, 2 * N) matrix above is symmetric, as
-- Transpose (A) = A and Transpose (B) = -B if C is Hermitian.
-- We solve this eigensystem using the real-valued algorithms. The final
-- result will have every eigenvalue twice, so in the sorted output we
-- just pick every second value, with associated eigenvector u + i * v.
M : Real_Matrix (1 .. 2 * N, 1 .. 2 * N);
Vals : Real_Vector (1 .. 2 * N);
Vecs : Real_Matrix (1 .. 2 * N, 1 .. 2 * N);
begin
for J in 1 .. N loop
for K in 1 .. N loop
declare
C : constant Complex :=
(A (A'First (1) + (J - 1), A'First (2) + (K - 1)));
begin
M (J, K) := Re (C);
M (J + N, K + N) := Re (C);
M (J + N, K) := Im (C);
M (J, K + N) := -Im (C);
end;
end loop;
end loop;
Eigensystem (M, Vals, Vecs);
for J in 1 .. N loop
declare
Col : constant Integer := Values'First + (J - 1);
begin
Values (Col) := Vals (2 * J);
for K in 1 .. N loop
declare
Row : constant Integer := Vectors'First (2) + (K - 1);
begin
Vectors (Row, Col)
:= (Vecs (J * 2, Col), Vecs (J * 2, Col + N));
end;
end loop;
end;
end loop;
end Eigensystem;
-----------------
-- Eigenvalues --
-----------------
function Eigenvalues (A : Complex_Matrix) return Real_Vector is
-- See Eigensystem for a description of the algorithm
N : constant Natural := Length (A);
R : Real_Vector (A'Range (1));
M : Real_Matrix (1 .. 2 * N, 1 .. 2 * N);
Vals : Real_Vector (1 .. 2 * N);
begin
for J in 1 .. N loop
for K in 1 .. N loop
declare
C : constant Complex :=
(A (A'First (1) + (J - 1), A'First (2) + (K - 1)));
begin
M (J, K) := Re (C);
M (J + N, K + N) := Re (C);
M (J + N, K) := Im (C);
M (J, K + N) := -Im (C);
end;
end loop;
end loop;
Vals := Eigenvalues (M);
for J in 1 .. N loop
R (A'First (1) + (J - 1)) := Vals (2 * J);
end loop;
return R;
end Eigenvalues;
--------
-- Im --
--------
function Im (X : Complex_Vector) return Real_Vector
renames Instantiations.Im;
function Im (X : Complex_Matrix) return Real_Matrix
renames Instantiations.Im;
-------------
-- Inverse --
-------------
function Inverse (A : Complex_Matrix) return Complex_Matrix is
(Solve (A, Unit_Matrix (Length (A))));
-------------
-- Modulus --
-------------
function Modulus (X : Complex_Vector) return Real_Vector
renames Instantiations.Modulus;
function Modulus (X : Complex_Matrix) return Real_Matrix
renames Instantiations.Modulus;
--------
-- Re --
--------
function Re (X : Complex_Vector) return Real_Vector
renames Instantiations.Re;
function Re (X : Complex_Matrix) return Real_Matrix
renames Instantiations.Re;
------------
-- Set_Im --
------------
procedure Set_Im
(X : in out Complex_Matrix;
Im : Real_Matrix)
renames Instantiations.Set_Im;
procedure Set_Im
(X : in out Complex_Vector;
Im : Real_Vector)
renames Instantiations.Set_Im;
------------
-- Set_Re --
------------
procedure Set_Re
(X : in out Complex_Matrix;
Re : Real_Matrix)
renames Instantiations.Set_Re;
procedure Set_Re
(X : in out Complex_Vector;
Re : Real_Vector)
renames Instantiations.Set_Re;
-----------
-- Solve --
-----------
function Solve
(A : Complex_Matrix;
X : Complex_Vector) return Complex_Vector
renames Instantiations.Solve;
function Solve
(A : Complex_Matrix;
X : Complex_Matrix) return Complex_Matrix
renames Instantiations.Solve;
---------------
-- Transpose --
---------------
function Transpose
(X : Complex_Matrix) return Complex_Matrix
is
R : Complex_Matrix (X'Range (2), X'Range (1));
begin
Transpose (X, R);
return R;
end Transpose;
-----------------
-- Unit_Matrix --
-----------------
function Unit_Matrix
(Order : Positive;
First_1 : Integer := 1;
First_2 : Integer := 1) return Complex_Matrix
renames Instantiations.Unit_Matrix;
-----------------
-- Unit_Vector --
-----------------
function Unit_Vector
(Index : Integer;
Order : Positive;
First : Integer := 1) return Complex_Vector
renames Instantiations.Unit_Vector;
end Ada.Numerics.Generic_Complex_Arrays;
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