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------------------------------------------------------------------------------
-- --
-- GNAT RUN-TIME COMPONENTS --
-- --
-- ADA.NUMERICS.GENERIC_COMPLEX_ARRAYS --
-- --
-- S p e c --
-- --
-- This specification is derived from the Ada Reference Manual for use with --
-- GNAT. In accordance with the copyright of that document, you can freely --
-- copy and modify this specification, provided that if you redistribute a --
-- modified version, any changes that you have made are clearly indicated. --
-- --
------------------------------------------------------------------------------
with Ada.Numerics.Generic_Real_Arrays, Ada.Numerics.Generic_Complex_Types;
generic
with package Real_Arrays is new Ada.Numerics.Generic_Real_Arrays (<>);
use Real_Arrays;
with package Complex_Types is new Ada.Numerics.Generic_Complex_Types (Real);
use Complex_Types;
package Ada.Numerics.Generic_Complex_Arrays is
pragma Pure (Generic_Complex_Arrays);
-- Types
type Complex_Vector is array (Integer range <>) of Complex;
type Complex_Matrix is
array (Integer range <>, Integer range <>) of Complex;
-- Subprograms for Complex_Vector types
-- Complex_Vector selection, conversion and composition operations
function Re (X : Complex_Vector) return Real_Vector;
function Im (X : Complex_Vector) return Real_Vector;
procedure Set_Re (X : in out Complex_Vector; Re : Real_Vector);
procedure Set_Im (X : in out Complex_Vector; Im : Real_Vector);
function Compose_From_Cartesian
(Re : Real_Vector) return Complex_Vector;
function Compose_From_Cartesian
(Re, Im : Real_Vector) return Complex_Vector;
function Modulus (X : Complex_Vector) return Real_Vector;
function "abs" (Right : Complex_Vector) return Real_Vector renames Modulus;
function Argument (X : Complex_Vector) return Real_Vector;
function Argument
(X : Complex_Vector;
Cycle : Real'Base) return Real_Vector;
function Compose_From_Polar
(Modulus, Argument : Real_Vector) return Complex_Vector;
function Compose_From_Polar
(Modulus, Argument : Real_Vector;
Cycle : Real'Base) return Complex_Vector;
-- Complex_Vector arithmetic operations
function "+" (Right : Complex_Vector) return Complex_Vector;
function "-" (Right : Complex_Vector) return Complex_Vector;
function Conjugate (X : Complex_Vector) return Complex_Vector;
function "+" (Left, Right : Complex_Vector) return Complex_Vector;
function "-" (Left, Right : Complex_Vector) return Complex_Vector;
function "*" (Left, Right : Complex_Vector) return Complex;
function "abs" (Right : Complex_Vector) return Complex;
-- Mixed Real_Vector and Complex_Vector arithmetic operations
function "+"
(Left : Real_Vector;
Right : Complex_Vector) return Complex_Vector;
function "+"
(Left : Complex_Vector;
Right : Real_Vector) return Complex_Vector;
function "-"
(Left : Real_Vector;
Right : Complex_Vector) return Complex_Vector;
function "-"
(Left : Complex_Vector;
Right : Real_Vector) return Complex_Vector;
function "*" (Left : Real_Vector; Right : Complex_Vector) return Complex;
function "*" (Left : Complex_Vector; Right : Real_Vector) return Complex;
-- Complex_Vector scaling operations
function "*"
(Left : Complex;
Right : Complex_Vector) return Complex_Vector;
function "*"
(Left : Complex_Vector;
Right : Complex) return Complex_Vector;
function "/"
(Left : Complex_Vector;
Right : Complex) return Complex_Vector;
function "*"
(Left : Real'Base;
Right : Complex_Vector) return Complex_Vector;
function "*"
(Left : Complex_Vector;
Right : Real'Base) return Complex_Vector;
function "/"
(Left : Complex_Vector;
Right : Real'Base) return Complex_Vector;
-- Other Complex_Vector operations
function Unit_Vector
(Index : Integer;
Order : Positive;
First : Integer := 1) return Complex_Vector;
-- Subprograms for Complex_Matrix types
-- Complex_Matrix selection, conversion and composition operations
function Re (X : Complex_Matrix) return Real_Matrix;
function Im (X : Complex_Matrix) return Real_Matrix;
procedure Set_Re (X : in out Complex_Matrix; Re : Real_Matrix);
procedure Set_Im (X : in out Complex_Matrix; Im : Real_Matrix);
function Compose_From_Cartesian (Re : Real_Matrix) return Complex_Matrix;
function Compose_From_Cartesian
(Re, Im : Real_Matrix) return Complex_Matrix;
function Modulus (X : Complex_Matrix) return Real_Matrix;
function "abs" (Right : Complex_Matrix) return Real_Matrix renames Modulus;
function Argument (X : Complex_Matrix) return Real_Matrix;
function Argument
(X : Complex_Matrix;
Cycle : Real'Base) return Real_Matrix;
function Compose_From_Polar
(Modulus, Argument : Real_Matrix) return Complex_Matrix;
function Compose_From_Polar
(Modulus : Real_Matrix;
Argument : Real_Matrix;
Cycle : Real'Base) return Complex_Matrix;
-- Complex_Matrix arithmetic operations
function "+" (Right : Complex_Matrix) return Complex_Matrix;
function "-" (Right : Complex_Matrix) return Complex_Matrix;
function Conjugate (X : Complex_Matrix) return Complex_Matrix;
function Transpose (X : Complex_Matrix) return Complex_Matrix;
function "+" (Left, Right : Complex_Matrix) return Complex_Matrix;
function "-" (Left, Right : Complex_Matrix) return Complex_Matrix;
function "*" (Left, Right : Complex_Matrix) return Complex_Matrix;
function "*" (Left, Right : Complex_Vector) return Complex_Matrix;
function "*"
(Left : Complex_Vector;
Right : Complex_Matrix) return Complex_Vector;
function "*"
(Left : Complex_Matrix;
Right : Complex_Vector) return Complex_Vector;
-- Mixed Real_Matrix and Complex_Matrix arithmetic operations
function "+"
(Left : Real_Matrix;
Right : Complex_Matrix) return Complex_Matrix;
function "+"
(Left : Complex_Matrix;
Right : Real_Matrix) return Complex_Matrix;
function "-"
(Left : Real_Matrix;
Right : Complex_Matrix) return Complex_Matrix;
function "-"
(Left : Complex_Matrix;
Right : Real_Matrix) return Complex_Matrix;
function "*"
(Left : Real_Matrix;
Right : Complex_Matrix) return Complex_Matrix;
function "*"
(Left : Complex_Matrix;
Right : Real_Matrix) return Complex_Matrix;
function "*"
(Left : Real_Vector;
Right : Complex_Vector) return Complex_Matrix;
function "*"
(Left : Complex_Vector;
Right : Real_Vector) return Complex_Matrix;
function "*"
(Left : Real_Vector;
Right : Complex_Matrix) return Complex_Vector;
function "*"
(Left : Complex_Vector;
Right : Real_Matrix) return Complex_Vector;
function "*"
(Left : Real_Matrix;
Right : Complex_Vector) return Complex_Vector;
function "*"
(Left : Complex_Matrix;
Right : Real_Vector) return Complex_Vector;
-- Complex_Matrix scaling operations
function "*"
(Left : Complex;
Right : Complex_Matrix) return Complex_Matrix;
function "*"
(Left : Complex_Matrix;
Right : Complex) return Complex_Matrix;
function "/"
(Left : Complex_Matrix;
Right : Complex) return Complex_Matrix;
function "*"
(Left : Real'Base;
Right : Complex_Matrix) return Complex_Matrix;
function "*"
(Left : Complex_Matrix;
Right : Real'Base) return Complex_Matrix;
function "/"
(Left : Complex_Matrix;
Right : Real'Base) return Complex_Matrix;
-- Complex_Matrix inversion and related operations
function Solve
(A : Complex_Matrix;
X : Complex_Vector) return Complex_Vector;
function Solve (A, X : Complex_Matrix) return Complex_Matrix;
function Inverse (A : Complex_Matrix) return Complex_Matrix;
function Determinant (A : Complex_Matrix) return Complex;
-- Eigenvalues and vectors of a Hermitian matrix
function Eigenvalues (A : Complex_Matrix) return Real_Vector;
procedure Eigensystem
(A : Complex_Matrix;
Values : out Real_Vector;
Vectors : out Complex_Matrix);
-- Other Complex_Matrix operations
function Unit_Matrix
(Order : Positive;
First_1, First_2 : Integer := 1) return Complex_Matrix;
end Ada.Numerics.Generic_Complex_Arrays;
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