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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;