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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 Real'Base;
+
+   --  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;