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