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jeremybenn |
------------------------------------------------------------------------------
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-- --
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-- GNAT COMPILER COMPONENTS --
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-- --
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-- ADA.NUMERICS.GENERIC_COMPLEX_ARRAYS --
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-- --
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-- B o d y --
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-- --
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-- Copyright (C) 2006-2011, Free Software Foundation, Inc. --
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-- --
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-- GNAT is free software; you can redistribute it and/or modify it under --
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-- terms of the GNU General Public License as published by the Free Soft- --
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-- ware Foundation; either version 3, or (at your option) any later ver- --
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-- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
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-- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
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-- or FITNESS FOR A PARTICULAR PURPOSE. --
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-- --
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-- As a special exception under Section 7 of GPL version 3, you are granted --
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-- additional permissions described in the GCC Runtime Library Exception, --
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-- version 3.1, as published by the Free Software Foundation. --
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-- --
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-- You should have received a copy of the GNU General Public License and --
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-- a copy of the GCC Runtime Library Exception along with this program; --
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-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
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-- <http://www.gnu.org/licenses/>. --
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-- --
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-- GNAT was originally developed by the GNAT team at New York University. --
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-- Extensive contributions were provided by Ada Core Technologies Inc. --
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-- --
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------------------------------------------------------------------------------
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with System.Generic_Array_Operations; use System.Generic_Array_Operations;
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with Ada.Numerics; use Ada.Numerics;
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package body Ada.Numerics.Generic_Complex_Arrays is
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-- Operations that are defined in terms of operations on the type Real,
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-- such as addition, subtraction and scaling, are computed in the canonical
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-- way looping over all elements.
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package Ops renames System.Generic_Array_Operations;
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subtype Real is Real_Arrays.Real;
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-- Work around visibility bug ???
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function Is_Non_Zero (X : Complex) return Boolean is (X /= (0.0, 0.0));
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-- Needed by Back_Substitute
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procedure Back_Substitute is new Ops.Back_Substitute
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(Scalar => Complex,
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Matrix => Complex_Matrix,
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Is_Non_Zero => Is_Non_Zero);
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procedure Forward_Eliminate is new Ops.Forward_Eliminate
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(Scalar => Complex,
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Real => Real'Base,
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Matrix => Complex_Matrix,
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Zero => (0.0, 0.0),
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One => (1.0, 0.0));
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procedure Transpose is new Ops.Transpose
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(Scalar => Complex,
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Matrix => Complex_Matrix);
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-- Helper function that raises a Constraint_Error is the argument is
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-- not a square matrix, and otherwise returns its length.
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function Length is new Square_Matrix_Length (Complex, Complex_Matrix);
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-- Instant a generic square root implementation here, in order to avoid
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-- instantiating a complete copy of Generic_Elementary_Functions.
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-- Speed of the square root is not a big concern here.
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function Sqrt is new Ops.Sqrt (Real'Base);
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-- Instantiating the following subprograms directly would lead to
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-- name clashes, so use a local package.
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package Instantiations is
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---------
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-- "*" --
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---------
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function "*" is new Vector_Scalar_Elementwise_Operation
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(Left_Scalar => Complex,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Left_Vector => Complex_Vector,
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Result_Vector => Complex_Vector,
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Operation => "*");
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function "*" is new Vector_Scalar_Elementwise_Operation
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(Left_Scalar => Complex,
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Right_Scalar => Real'Base,
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Result_Scalar => Complex,
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Left_Vector => Complex_Vector,
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Result_Vector => Complex_Vector,
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Operation => "*");
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function "*" is new Scalar_Vector_Elementwise_Operation
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(Left_Scalar => Complex,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Right_Vector => Complex_Vector,
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Result_Vector => Complex_Vector,
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Operation => "*");
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function "*" is new Scalar_Vector_Elementwise_Operation
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(Left_Scalar => Real'Base,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Right_Vector => Complex_Vector,
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Result_Vector => Complex_Vector,
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Operation => "*");
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function "*" is new Inner_Product
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(Left_Scalar => Complex,
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Right_Scalar => Real'Base,
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Result_Scalar => Complex,
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Left_Vector => Complex_Vector,
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Right_Vector => Real_Vector,
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Zero => (0.0, 0.0));
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function "*" is new Inner_Product
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(Left_Scalar => Real'Base,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Left_Vector => Real_Vector,
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Right_Vector => Complex_Vector,
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Zero => (0.0, 0.0));
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function "*" is new Inner_Product
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(Left_Scalar => Complex,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Left_Vector => Complex_Vector,
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Right_Vector => Complex_Vector,
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Zero => (0.0, 0.0));
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function "*" is new Outer_Product
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(Left_Scalar => Complex,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Left_Vector => Complex_Vector,
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Right_Vector => Complex_Vector,
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Matrix => Complex_Matrix);
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function "*" is new Outer_Product
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(Left_Scalar => Real'Base,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Left_Vector => Real_Vector,
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Right_Vector => Complex_Vector,
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Matrix => Complex_Matrix);
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function "*" is new Outer_Product
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(Left_Scalar => Complex,
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Right_Scalar => Real'Base,
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Result_Scalar => Complex,
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Left_Vector => Complex_Vector,
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Right_Vector => Real_Vector,
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Matrix => Complex_Matrix);
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function "*" is new Matrix_Scalar_Elementwise_Operation
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(Left_Scalar => Complex,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Left_Matrix => Complex_Matrix,
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Result_Matrix => Complex_Matrix,
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Operation => "*");
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function "*" is new Matrix_Scalar_Elementwise_Operation
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(Left_Scalar => Complex,
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Right_Scalar => Real'Base,
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Result_Scalar => Complex,
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Left_Matrix => Complex_Matrix,
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Result_Matrix => Complex_Matrix,
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Operation => "*");
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function "*" is new Scalar_Matrix_Elementwise_Operation
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(Left_Scalar => Complex,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Right_Matrix => Complex_Matrix,
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Result_Matrix => Complex_Matrix,
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Operation => "*");
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function "*" is new Scalar_Matrix_Elementwise_Operation
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(Left_Scalar => Real'Base,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Right_Matrix => Complex_Matrix,
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Result_Matrix => Complex_Matrix,
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Operation => "*");
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function "*" is new Matrix_Vector_Product
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(Left_Scalar => Real'Base,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Matrix => Real_Matrix,
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Right_Vector => Complex_Vector,
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Result_Vector => Complex_Vector,
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Zero => (0.0, 0.0));
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function "*" is new Matrix_Vector_Product
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(Left_Scalar => Complex,
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Right_Scalar => Real'Base,
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Result_Scalar => Complex,
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Matrix => Complex_Matrix,
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Right_Vector => Real_Vector,
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Result_Vector => Complex_Vector,
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Zero => (0.0, 0.0));
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function "*" is new Matrix_Vector_Product
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(Left_Scalar => Complex,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Matrix => Complex_Matrix,
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Right_Vector => Complex_Vector,
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Result_Vector => Complex_Vector,
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Zero => (0.0, 0.0));
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function "*" is new Vector_Matrix_Product
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(Left_Scalar => Real'Base,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Left_Vector => Real_Vector,
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Matrix => Complex_Matrix,
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Result_Vector => Complex_Vector,
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Zero => (0.0, 0.0));
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function "*" is new Vector_Matrix_Product
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(Left_Scalar => Complex,
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Right_Scalar => Real'Base,
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Result_Scalar => Complex,
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Left_Vector => Complex_Vector,
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Matrix => Real_Matrix,
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Result_Vector => Complex_Vector,
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Zero => (0.0, 0.0));
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function "*" is new Vector_Matrix_Product
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(Left_Scalar => Complex,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Left_Vector => Complex_Vector,
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Matrix => Complex_Matrix,
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Result_Vector => Complex_Vector,
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Zero => (0.0, 0.0));
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| 251 |
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function "*" is new Matrix_Matrix_Product
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(Left_Scalar => Complex,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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| 255 |
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Left_Matrix => Complex_Matrix,
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| 256 |
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Right_Matrix => Complex_Matrix,
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| 257 |
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Result_Matrix => Complex_Matrix,
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| 258 |
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Zero => (0.0, 0.0));
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function "*" is new Matrix_Matrix_Product
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(Left_Scalar => Real'Base,
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Right_Scalar => Complex,
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Result_Scalar => Complex,
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Left_Matrix => Real_Matrix,
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Right_Matrix => Complex_Matrix,
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| 266 |
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Result_Matrix => Complex_Matrix,
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| 267 |
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Zero => (0.0, 0.0));
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| 269 |
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function "*" is new Matrix_Matrix_Product
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(Left_Scalar => Complex,
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| 271 |
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Right_Scalar => Real'Base,
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| 272 |
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Result_Scalar => Complex,
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| 273 |
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Left_Matrix => Complex_Matrix,
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| 274 |
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Right_Matrix => Real_Matrix,
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| 275 |
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Result_Matrix => Complex_Matrix,
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| 276 |
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Zero => (0.0, 0.0));
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---------
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-- "+" --
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---------
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function "+" is new Vector_Elementwise_Operation
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(X_Scalar => Complex,
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| 284 |
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Result_Scalar => Complex,
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| 285 |
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X_Vector => Complex_Vector,
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| 286 |
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Result_Vector => Complex_Vector,
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| 287 |
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Operation => "+");
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| 288 |
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| 289 |
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function "+" is new Vector_Vector_Elementwise_Operation
|
| 290 |
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(Left_Scalar => Complex,
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| 291 |
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Right_Scalar => Complex,
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| 292 |
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Result_Scalar => Complex,
|
| 293 |
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Left_Vector => Complex_Vector,
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| 294 |
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Right_Vector => Complex_Vector,
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| 295 |
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Result_Vector => Complex_Vector,
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| 296 |
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Operation => "+");
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| 297 |
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| 298 |
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function "+" is new Vector_Vector_Elementwise_Operation
|
| 299 |
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(Left_Scalar => Real'Base,
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| 300 |
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Right_Scalar => Complex,
|
| 301 |
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Result_Scalar => Complex,
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| 302 |
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Left_Vector => Real_Vector,
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| 303 |
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Right_Vector => Complex_Vector,
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| 304 |
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Result_Vector => Complex_Vector,
|
| 305 |
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Operation => "+");
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| 306 |
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| 307 |
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function "+" is new Vector_Vector_Elementwise_Operation
|
| 308 |
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(Left_Scalar => Complex,
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| 309 |
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Right_Scalar => Real'Base,
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| 310 |
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Result_Scalar => Complex,
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| 311 |
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Left_Vector => Complex_Vector,
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| 312 |
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Right_Vector => Real_Vector,
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| 313 |
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Result_Vector => Complex_Vector,
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| 314 |
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Operation => "+");
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| 315 |
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| 316 |
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function "+" is new Matrix_Elementwise_Operation
|
| 317 |
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(X_Scalar => Complex,
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| 318 |
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Result_Scalar => Complex,
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| 319 |
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X_Matrix => Complex_Matrix,
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| 320 |
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Result_Matrix => Complex_Matrix,
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| 321 |
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Operation => "+");
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| 322 |
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| 323 |
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function "+" is new Matrix_Matrix_Elementwise_Operation
|
| 324 |
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(Left_Scalar => Complex,
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| 325 |
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Right_Scalar => Complex,
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| 326 |
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Result_Scalar => Complex,
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| 327 |
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Left_Matrix => Complex_Matrix,
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| 328 |
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Right_Matrix => Complex_Matrix,
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| 329 |
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Result_Matrix => Complex_Matrix,
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| 330 |
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Operation => "+");
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| 331 |
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| 332 |
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function "+" is new Matrix_Matrix_Elementwise_Operation
|
| 333 |
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(Left_Scalar => Real'Base,
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| 334 |
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Right_Scalar => Complex,
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| 335 |
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Result_Scalar => Complex,
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| 336 |
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Left_Matrix => Real_Matrix,
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| 337 |
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Right_Matrix => Complex_Matrix,
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| 338 |
|
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Result_Matrix => Complex_Matrix,
|
| 339 |
|
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Operation => "+");
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| 340 |
|
|
|
| 341 |
|
|
function "+" is new Matrix_Matrix_Elementwise_Operation
|
| 342 |
|
|
(Left_Scalar => Complex,
|
| 343 |
|
|
Right_Scalar => Real'Base,
|
| 344 |
|
|
Result_Scalar => Complex,
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| 345 |
|
|
Left_Matrix => Complex_Matrix,
|
| 346 |
|
|
Right_Matrix => Real_Matrix,
|
| 347 |
|
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Result_Matrix => Complex_Matrix,
|
| 348 |
|
|
Operation => "+");
|
| 349 |
|
|
|
| 350 |
|
|
---------
|
| 351 |
|
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-- "-" --
|
| 352 |
|
|
---------
|
| 353 |
|
|
|
| 354 |
|
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function "-" is new Vector_Elementwise_Operation
|
| 355 |
|
|
(X_Scalar => Complex,
|
| 356 |
|
|
Result_Scalar => Complex,
|
| 357 |
|
|
X_Vector => Complex_Vector,
|
| 358 |
|
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Result_Vector => Complex_Vector,
|
| 359 |
|
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Operation => "-");
|
| 360 |
|
|
|
| 361 |
|
|
function "-" is new Vector_Vector_Elementwise_Operation
|
| 362 |
|
|
(Left_Scalar => Complex,
|
| 363 |
|
|
Right_Scalar => Complex,
|
| 364 |
|
|
Result_Scalar => Complex,
|
| 365 |
|
|
Left_Vector => Complex_Vector,
|
| 366 |
|
|
Right_Vector => Complex_Vector,
|
| 367 |
|
|
Result_Vector => Complex_Vector,
|
| 368 |
|
|
Operation => "-");
|
| 369 |
|
|
|
| 370 |
|
|
function "-" is new Vector_Vector_Elementwise_Operation
|
| 371 |
|
|
(Left_Scalar => Real'Base,
|
| 372 |
|
|
Right_Scalar => Complex,
|
| 373 |
|
|
Result_Scalar => Complex,
|
| 374 |
|
|
Left_Vector => Real_Vector,
|
| 375 |
|
|
Right_Vector => Complex_Vector,
|
| 376 |
|
|
Result_Vector => Complex_Vector,
|
| 377 |
|
|
Operation => "-");
|
| 378 |
|
|
|
| 379 |
|
|
function "-" is new Vector_Vector_Elementwise_Operation
|
| 380 |
|
|
(Left_Scalar => Complex,
|
| 381 |
|
|
Right_Scalar => Real'Base,
|
| 382 |
|
|
Result_Scalar => Complex,
|
| 383 |
|
|
Left_Vector => Complex_Vector,
|
| 384 |
|
|
Right_Vector => Real_Vector,
|
| 385 |
|
|
Result_Vector => Complex_Vector,
|
| 386 |
|
|
Operation => "-");
|
| 387 |
|
|
|
| 388 |
|
|
function "-" is new Matrix_Elementwise_Operation
|
| 389 |
|
|
(X_Scalar => Complex,
|
| 390 |
|
|
Result_Scalar => Complex,
|
| 391 |
|
|
X_Matrix => Complex_Matrix,
|
| 392 |
|
|
Result_Matrix => Complex_Matrix,
|
| 393 |
|
|
Operation => "-");
|
| 394 |
|
|
|
| 395 |
|
|
function "-" is new Matrix_Matrix_Elementwise_Operation
|
| 396 |
|
|
(Left_Scalar => Complex,
|
| 397 |
|
|
Right_Scalar => Complex,
|
| 398 |
|
|
Result_Scalar => Complex,
|
| 399 |
|
|
Left_Matrix => Complex_Matrix,
|
| 400 |
|
|
Right_Matrix => Complex_Matrix,
|
| 401 |
|
|
Result_Matrix => Complex_Matrix,
|
| 402 |
|
|
Operation => "-");
|
| 403 |
|
|
|
| 404 |
|
|
function "-" is new Matrix_Matrix_Elementwise_Operation
|
| 405 |
|
|
(Left_Scalar => Real'Base,
|
| 406 |
|
|
Right_Scalar => Complex,
|
| 407 |
|
|
Result_Scalar => Complex,
|
| 408 |
|
|
Left_Matrix => Real_Matrix,
|
| 409 |
|
|
Right_Matrix => Complex_Matrix,
|
| 410 |
|
|
Result_Matrix => Complex_Matrix,
|
| 411 |
|
|
Operation => "-");
|
| 412 |
|
|
|
| 413 |
|
|
function "-" is new Matrix_Matrix_Elementwise_Operation
|
| 414 |
|
|
(Left_Scalar => Complex,
|
| 415 |
|
|
Right_Scalar => Real'Base,
|
| 416 |
|
|
Result_Scalar => Complex,
|
| 417 |
|
|
Left_Matrix => Complex_Matrix,
|
| 418 |
|
|
Right_Matrix => Real_Matrix,
|
| 419 |
|
|
Result_Matrix => Complex_Matrix,
|
| 420 |
|
|
Operation => "-");
|
| 421 |
|
|
|
| 422 |
|
|
---------
|
| 423 |
|
|
-- "/" --
|
| 424 |
|
|
---------
|
| 425 |
|
|
|
| 426 |
|
|
function "/" is new Vector_Scalar_Elementwise_Operation
|
| 427 |
|
|
(Left_Scalar => Complex,
|
| 428 |
|
|
Right_Scalar => Complex,
|
| 429 |
|
|
Result_Scalar => Complex,
|
| 430 |
|
|
Left_Vector => Complex_Vector,
|
| 431 |
|
|
Result_Vector => Complex_Vector,
|
| 432 |
|
|
Operation => "/");
|
| 433 |
|
|
|
| 434 |
|
|
function "/" is new Vector_Scalar_Elementwise_Operation
|
| 435 |
|
|
(Left_Scalar => Complex,
|
| 436 |
|
|
Right_Scalar => Real'Base,
|
| 437 |
|
|
Result_Scalar => Complex,
|
| 438 |
|
|
Left_Vector => Complex_Vector,
|
| 439 |
|
|
Result_Vector => Complex_Vector,
|
| 440 |
|
|
Operation => "/");
|
| 441 |
|
|
|
| 442 |
|
|
function "/" is new Matrix_Scalar_Elementwise_Operation
|
| 443 |
|
|
(Left_Scalar => Complex,
|
| 444 |
|
|
Right_Scalar => Complex,
|
| 445 |
|
|
Result_Scalar => Complex,
|
| 446 |
|
|
Left_Matrix => Complex_Matrix,
|
| 447 |
|
|
Result_Matrix => Complex_Matrix,
|
| 448 |
|
|
Operation => "/");
|
| 449 |
|
|
|
| 450 |
|
|
function "/" is new Matrix_Scalar_Elementwise_Operation
|
| 451 |
|
|
(Left_Scalar => Complex,
|
| 452 |
|
|
Right_Scalar => Real'Base,
|
| 453 |
|
|
Result_Scalar => Complex,
|
| 454 |
|
|
Left_Matrix => Complex_Matrix,
|
| 455 |
|
|
Result_Matrix => Complex_Matrix,
|
| 456 |
|
|
Operation => "/");
|
| 457 |
|
|
|
| 458 |
|
|
-----------
|
| 459 |
|
|
-- "abs" --
|
| 460 |
|
|
-----------
|
| 461 |
|
|
|
| 462 |
|
|
function "abs" is new L2_Norm
|
| 463 |
|
|
(X_Scalar => Complex,
|
| 464 |
|
|
Result_Real => Real'Base,
|
| 465 |
|
|
X_Vector => Complex_Vector);
|
| 466 |
|
|
|
| 467 |
|
|
--------------
|
| 468 |
|
|
-- Argument --
|
| 469 |
|
|
--------------
|
| 470 |
|
|
|
| 471 |
|
|
function Argument is new Vector_Elementwise_Operation
|
| 472 |
|
|
(X_Scalar => Complex,
|
| 473 |
|
|
Result_Scalar => Real'Base,
|
| 474 |
|
|
X_Vector => Complex_Vector,
|
| 475 |
|
|
Result_Vector => Real_Vector,
|
| 476 |
|
|
Operation => Argument);
|
| 477 |
|
|
|
| 478 |
|
|
function Argument is new Vector_Scalar_Elementwise_Operation
|
| 479 |
|
|
(Left_Scalar => Complex,
|
| 480 |
|
|
Right_Scalar => Real'Base,
|
| 481 |
|
|
Result_Scalar => Real'Base,
|
| 482 |
|
|
Left_Vector => Complex_Vector,
|
| 483 |
|
|
Result_Vector => Real_Vector,
|
| 484 |
|
|
Operation => Argument);
|
| 485 |
|
|
|
| 486 |
|
|
function Argument is new Matrix_Elementwise_Operation
|
| 487 |
|
|
(X_Scalar => Complex,
|
| 488 |
|
|
Result_Scalar => Real'Base,
|
| 489 |
|
|
X_Matrix => Complex_Matrix,
|
| 490 |
|
|
Result_Matrix => Real_Matrix,
|
| 491 |
|
|
Operation => Argument);
|
| 492 |
|
|
|
| 493 |
|
|
function Argument is new Matrix_Scalar_Elementwise_Operation
|
| 494 |
|
|
(Left_Scalar => Complex,
|
| 495 |
|
|
Right_Scalar => Real'Base,
|
| 496 |
|
|
Result_Scalar => Real'Base,
|
| 497 |
|
|
Left_Matrix => Complex_Matrix,
|
| 498 |
|
|
Result_Matrix => Real_Matrix,
|
| 499 |
|
|
Operation => Argument);
|
| 500 |
|
|
|
| 501 |
|
|
----------------------------
|
| 502 |
|
|
-- Compose_From_Cartesian --
|
| 503 |
|
|
----------------------------
|
| 504 |
|
|
|
| 505 |
|
|
function Compose_From_Cartesian is new Vector_Elementwise_Operation
|
| 506 |
|
|
(X_Scalar => Real'Base,
|
| 507 |
|
|
Result_Scalar => Complex,
|
| 508 |
|
|
X_Vector => Real_Vector,
|
| 509 |
|
|
Result_Vector => Complex_Vector,
|
| 510 |
|
|
Operation => Compose_From_Cartesian);
|
| 511 |
|
|
|
| 512 |
|
|
function Compose_From_Cartesian is
|
| 513 |
|
|
new Vector_Vector_Elementwise_Operation
|
| 514 |
|
|
(Left_Scalar => Real'Base,
|
| 515 |
|
|
Right_Scalar => Real'Base,
|
| 516 |
|
|
Result_Scalar => Complex,
|
| 517 |
|
|
Left_Vector => Real_Vector,
|
| 518 |
|
|
Right_Vector => Real_Vector,
|
| 519 |
|
|
Result_Vector => Complex_Vector,
|
| 520 |
|
|
Operation => Compose_From_Cartesian);
|
| 521 |
|
|
|
| 522 |
|
|
function Compose_From_Cartesian is new Matrix_Elementwise_Operation
|
| 523 |
|
|
(X_Scalar => Real'Base,
|
| 524 |
|
|
Result_Scalar => Complex,
|
| 525 |
|
|
X_Matrix => Real_Matrix,
|
| 526 |
|
|
Result_Matrix => Complex_Matrix,
|
| 527 |
|
|
Operation => Compose_From_Cartesian);
|
| 528 |
|
|
|
| 529 |
|
|
function Compose_From_Cartesian is
|
| 530 |
|
|
new Matrix_Matrix_Elementwise_Operation
|
| 531 |
|
|
(Left_Scalar => Real'Base,
|
| 532 |
|
|
Right_Scalar => Real'Base,
|
| 533 |
|
|
Result_Scalar => Complex,
|
| 534 |
|
|
Left_Matrix => Real_Matrix,
|
| 535 |
|
|
Right_Matrix => Real_Matrix,
|
| 536 |
|
|
Result_Matrix => Complex_Matrix,
|
| 537 |
|
|
Operation => Compose_From_Cartesian);
|
| 538 |
|
|
|
| 539 |
|
|
------------------------
|
| 540 |
|
|
-- Compose_From_Polar --
|
| 541 |
|
|
------------------------
|
| 542 |
|
|
|
| 543 |
|
|
function Compose_From_Polar is
|
| 544 |
|
|
new Vector_Vector_Elementwise_Operation
|
| 545 |
|
|
(Left_Scalar => Real'Base,
|
| 546 |
|
|
Right_Scalar => Real'Base,
|
| 547 |
|
|
Result_Scalar => Complex,
|
| 548 |
|
|
Left_Vector => Real_Vector,
|
| 549 |
|
|
Right_Vector => Real_Vector,
|
| 550 |
|
|
Result_Vector => Complex_Vector,
|
| 551 |
|
|
Operation => Compose_From_Polar);
|
| 552 |
|
|
|
| 553 |
|
|
function Compose_From_Polar is
|
| 554 |
|
|
new Vector_Vector_Scalar_Elementwise_Operation
|
| 555 |
|
|
(X_Scalar => Real'Base,
|
| 556 |
|
|
Y_Scalar => Real'Base,
|
| 557 |
|
|
Z_Scalar => Real'Base,
|
| 558 |
|
|
Result_Scalar => Complex,
|
| 559 |
|
|
X_Vector => Real_Vector,
|
| 560 |
|
|
Y_Vector => Real_Vector,
|
| 561 |
|
|
Result_Vector => Complex_Vector,
|
| 562 |
|
|
Operation => Compose_From_Polar);
|
| 563 |
|
|
|
| 564 |
|
|
function Compose_From_Polar is
|
| 565 |
|
|
new Matrix_Matrix_Elementwise_Operation
|
| 566 |
|
|
(Left_Scalar => Real'Base,
|
| 567 |
|
|
Right_Scalar => Real'Base,
|
| 568 |
|
|
Result_Scalar => Complex,
|
| 569 |
|
|
Left_Matrix => Real_Matrix,
|
| 570 |
|
|
Right_Matrix => Real_Matrix,
|
| 571 |
|
|
Result_Matrix => Complex_Matrix,
|
| 572 |
|
|
Operation => Compose_From_Polar);
|
| 573 |
|
|
|
| 574 |
|
|
function Compose_From_Polar is
|
| 575 |
|
|
new Matrix_Matrix_Scalar_Elementwise_Operation
|
| 576 |
|
|
(X_Scalar => Real'Base,
|
| 577 |
|
|
Y_Scalar => Real'Base,
|
| 578 |
|
|
Z_Scalar => Real'Base,
|
| 579 |
|
|
Result_Scalar => Complex,
|
| 580 |
|
|
X_Matrix => Real_Matrix,
|
| 581 |
|
|
Y_Matrix => Real_Matrix,
|
| 582 |
|
|
Result_Matrix => Complex_Matrix,
|
| 583 |
|
|
Operation => Compose_From_Polar);
|
| 584 |
|
|
|
| 585 |
|
|
---------------
|
| 586 |
|
|
-- Conjugate --
|
| 587 |
|
|
---------------
|
| 588 |
|
|
|
| 589 |
|
|
function Conjugate is new Vector_Elementwise_Operation
|
| 590 |
|
|
(X_Scalar => Complex,
|
| 591 |
|
|
Result_Scalar => Complex,
|
| 592 |
|
|
X_Vector => Complex_Vector,
|
| 593 |
|
|
Result_Vector => Complex_Vector,
|
| 594 |
|
|
Operation => Conjugate);
|
| 595 |
|
|
|
| 596 |
|
|
function Conjugate is new Matrix_Elementwise_Operation
|
| 597 |
|
|
(X_Scalar => Complex,
|
| 598 |
|
|
Result_Scalar => Complex,
|
| 599 |
|
|
X_Matrix => Complex_Matrix,
|
| 600 |
|
|
Result_Matrix => Complex_Matrix,
|
| 601 |
|
|
Operation => Conjugate);
|
| 602 |
|
|
|
| 603 |
|
|
--------
|
| 604 |
|
|
-- Im --
|
| 605 |
|
|
--------
|
| 606 |
|
|
|
| 607 |
|
|
function Im is new Vector_Elementwise_Operation
|
| 608 |
|
|
(X_Scalar => Complex,
|
| 609 |
|
|
Result_Scalar => Real'Base,
|
| 610 |
|
|
X_Vector => Complex_Vector,
|
| 611 |
|
|
Result_Vector => Real_Vector,
|
| 612 |
|
|
Operation => Im);
|
| 613 |
|
|
|
| 614 |
|
|
function Im is new Matrix_Elementwise_Operation
|
| 615 |
|
|
(X_Scalar => Complex,
|
| 616 |
|
|
Result_Scalar => Real'Base,
|
| 617 |
|
|
X_Matrix => Complex_Matrix,
|
| 618 |
|
|
Result_Matrix => Real_Matrix,
|
| 619 |
|
|
Operation => Im);
|
| 620 |
|
|
|
| 621 |
|
|
-------------
|
| 622 |
|
|
-- Modulus --
|
| 623 |
|
|
-------------
|
| 624 |
|
|
|
| 625 |
|
|
function Modulus is new Vector_Elementwise_Operation
|
| 626 |
|
|
(X_Scalar => Complex,
|
| 627 |
|
|
Result_Scalar => Real'Base,
|
| 628 |
|
|
X_Vector => Complex_Vector,
|
| 629 |
|
|
Result_Vector => Real_Vector,
|
| 630 |
|
|
Operation => Modulus);
|
| 631 |
|
|
|
| 632 |
|
|
function Modulus is new Matrix_Elementwise_Operation
|
| 633 |
|
|
(X_Scalar => Complex,
|
| 634 |
|
|
Result_Scalar => Real'Base,
|
| 635 |
|
|
X_Matrix => Complex_Matrix,
|
| 636 |
|
|
Result_Matrix => Real_Matrix,
|
| 637 |
|
|
Operation => Modulus);
|
| 638 |
|
|
|
| 639 |
|
|
--------
|
| 640 |
|
|
-- Re --
|
| 641 |
|
|
--------
|
| 642 |
|
|
|
| 643 |
|
|
function Re is new Vector_Elementwise_Operation
|
| 644 |
|
|
(X_Scalar => Complex,
|
| 645 |
|
|
Result_Scalar => Real'Base,
|
| 646 |
|
|
X_Vector => Complex_Vector,
|
| 647 |
|
|
Result_Vector => Real_Vector,
|
| 648 |
|
|
Operation => Re);
|
| 649 |
|
|
|
| 650 |
|
|
function Re is new Matrix_Elementwise_Operation
|
| 651 |
|
|
(X_Scalar => Complex,
|
| 652 |
|
|
Result_Scalar => Real'Base,
|
| 653 |
|
|
X_Matrix => Complex_Matrix,
|
| 654 |
|
|
Result_Matrix => Real_Matrix,
|
| 655 |
|
|
Operation => Re);
|
| 656 |
|
|
|
| 657 |
|
|
------------
|
| 658 |
|
|
-- Set_Im --
|
| 659 |
|
|
------------
|
| 660 |
|
|
|
| 661 |
|
|
procedure Set_Im is new Update_Vector_With_Vector
|
| 662 |
|
|
(X_Scalar => Complex,
|
| 663 |
|
|
Y_Scalar => Real'Base,
|
| 664 |
|
|
X_Vector => Complex_Vector,
|
| 665 |
|
|
Y_Vector => Real_Vector,
|
| 666 |
|
|
Update => Set_Im);
|
| 667 |
|
|
|
| 668 |
|
|
procedure Set_Im is new Update_Matrix_With_Matrix
|
| 669 |
|
|
(X_Scalar => Complex,
|
| 670 |
|
|
Y_Scalar => Real'Base,
|
| 671 |
|
|
X_Matrix => Complex_Matrix,
|
| 672 |
|
|
Y_Matrix => Real_Matrix,
|
| 673 |
|
|
Update => Set_Im);
|
| 674 |
|
|
|
| 675 |
|
|
------------
|
| 676 |
|
|
-- Set_Re --
|
| 677 |
|
|
------------
|
| 678 |
|
|
|
| 679 |
|
|
procedure Set_Re is new Update_Vector_With_Vector
|
| 680 |
|
|
(X_Scalar => Complex,
|
| 681 |
|
|
Y_Scalar => Real'Base,
|
| 682 |
|
|
X_Vector => Complex_Vector,
|
| 683 |
|
|
Y_Vector => Real_Vector,
|
| 684 |
|
|
Update => Set_Re);
|
| 685 |
|
|
|
| 686 |
|
|
procedure Set_Re is new Update_Matrix_With_Matrix
|
| 687 |
|
|
(X_Scalar => Complex,
|
| 688 |
|
|
Y_Scalar => Real'Base,
|
| 689 |
|
|
X_Matrix => Complex_Matrix,
|
| 690 |
|
|
Y_Matrix => Real_Matrix,
|
| 691 |
|
|
Update => Set_Re);
|
| 692 |
|
|
|
| 693 |
|
|
-----------
|
| 694 |
|
|
-- Solve --
|
| 695 |
|
|
-----------
|
| 696 |
|
|
|
| 697 |
|
|
function Solve is
|
| 698 |
|
|
new Matrix_Vector_Solution (Complex, Complex_Vector, Complex_Matrix);
|
| 699 |
|
|
|
| 700 |
|
|
function Solve is
|
| 701 |
|
|
new Matrix_Matrix_Solution (Complex, Complex_Matrix);
|
| 702 |
|
|
|
| 703 |
|
|
-----------------
|
| 704 |
|
|
-- Unit_Matrix --
|
| 705 |
|
|
-----------------
|
| 706 |
|
|
|
| 707 |
|
|
function Unit_Matrix is new System.Generic_Array_Operations.Unit_Matrix
|
| 708 |
|
|
(Scalar => Complex,
|
| 709 |
|
|
Matrix => Complex_Matrix,
|
| 710 |
|
|
Zero => (0.0, 0.0),
|
| 711 |
|
|
One => (1.0, 0.0));
|
| 712 |
|
|
|
| 713 |
|
|
function Unit_Vector is new System.Generic_Array_Operations.Unit_Vector
|
| 714 |
|
|
(Scalar => Complex,
|
| 715 |
|
|
Vector => Complex_Vector,
|
| 716 |
|
|
Zero => (0.0, 0.0),
|
| 717 |
|
|
One => (1.0, 0.0));
|
| 718 |
|
|
end Instantiations;
|
| 719 |
|
|
|
| 720 |
|
|
---------
|
| 721 |
|
|
-- "*" --
|
| 722 |
|
|
---------
|
| 723 |
|
|
|
| 724 |
|
|
function "*"
|
| 725 |
|
|
(Left : Complex_Vector;
|
| 726 |
|
|
Right : Complex_Vector) return Complex
|
| 727 |
|
|
renames Instantiations."*";
|
| 728 |
|
|
|
| 729 |
|
|
function "*"
|
| 730 |
|
|
(Left : Real_Vector;
|
| 731 |
|
|
Right : Complex_Vector) return Complex
|
| 732 |
|
|
renames Instantiations."*";
|
| 733 |
|
|
|
| 734 |
|
|
function "*"
|
| 735 |
|
|
(Left : Complex_Vector;
|
| 736 |
|
|
Right : Real_Vector) return Complex
|
| 737 |
|
|
renames Instantiations."*";
|
| 738 |
|
|
|
| 739 |
|
|
function "*"
|
| 740 |
|
|
(Left : Complex;
|
| 741 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 742 |
|
|
renames Instantiations."*";
|
| 743 |
|
|
|
| 744 |
|
|
function "*"
|
| 745 |
|
|
(Left : Complex_Vector;
|
| 746 |
|
|
Right : Complex) return Complex_Vector
|
| 747 |
|
|
renames Instantiations."*";
|
| 748 |
|
|
|
| 749 |
|
|
function "*"
|
| 750 |
|
|
(Left : Real'Base;
|
| 751 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 752 |
|
|
renames Instantiations."*";
|
| 753 |
|
|
|
| 754 |
|
|
function "*"
|
| 755 |
|
|
(Left : Complex_Vector;
|
| 756 |
|
|
Right : Real'Base) return Complex_Vector
|
| 757 |
|
|
renames Instantiations."*";
|
| 758 |
|
|
|
| 759 |
|
|
function "*"
|
| 760 |
|
|
(Left : Complex_Matrix;
|
| 761 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 762 |
|
|
renames Instantiations."*";
|
| 763 |
|
|
|
| 764 |
|
|
function "*"
|
| 765 |
|
|
(Left : Complex_Vector;
|
| 766 |
|
|
Right : Complex_Vector) return Complex_Matrix
|
| 767 |
|
|
renames Instantiations."*";
|
| 768 |
|
|
|
| 769 |
|
|
function "*"
|
| 770 |
|
|
(Left : Complex_Vector;
|
| 771 |
|
|
Right : Complex_Matrix) return Complex_Vector
|
| 772 |
|
|
renames Instantiations."*";
|
| 773 |
|
|
|
| 774 |
|
|
function "*"
|
| 775 |
|
|
(Left : Complex_Matrix;
|
| 776 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 777 |
|
|
renames Instantiations."*";
|
| 778 |
|
|
|
| 779 |
|
|
function "*"
|
| 780 |
|
|
(Left : Real_Matrix;
|
| 781 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 782 |
|
|
renames Instantiations."*";
|
| 783 |
|
|
|
| 784 |
|
|
function "*"
|
| 785 |
|
|
(Left : Complex_Matrix;
|
| 786 |
|
|
Right : Real_Matrix) return Complex_Matrix
|
| 787 |
|
|
renames Instantiations."*";
|
| 788 |
|
|
|
| 789 |
|
|
function "*"
|
| 790 |
|
|
(Left : Real_Vector;
|
| 791 |
|
|
Right : Complex_Vector) return Complex_Matrix
|
| 792 |
|
|
renames Instantiations."*";
|
| 793 |
|
|
|
| 794 |
|
|
function "*"
|
| 795 |
|
|
(Left : Complex_Vector;
|
| 796 |
|
|
Right : Real_Vector) return Complex_Matrix
|
| 797 |
|
|
renames Instantiations."*";
|
| 798 |
|
|
|
| 799 |
|
|
function "*"
|
| 800 |
|
|
(Left : Real_Vector;
|
| 801 |
|
|
Right : Complex_Matrix) return Complex_Vector
|
| 802 |
|
|
renames Instantiations."*";
|
| 803 |
|
|
|
| 804 |
|
|
function "*"
|
| 805 |
|
|
(Left : Complex_Vector;
|
| 806 |
|
|
Right : Real_Matrix) return Complex_Vector
|
| 807 |
|
|
renames Instantiations."*";
|
| 808 |
|
|
|
| 809 |
|
|
function "*"
|
| 810 |
|
|
(Left : Real_Matrix;
|
| 811 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 812 |
|
|
renames Instantiations."*";
|
| 813 |
|
|
|
| 814 |
|
|
function "*"
|
| 815 |
|
|
(Left : Complex_Matrix;
|
| 816 |
|
|
Right : Real_Vector) return Complex_Vector
|
| 817 |
|
|
renames Instantiations."*";
|
| 818 |
|
|
|
| 819 |
|
|
function "*"
|
| 820 |
|
|
(Left : Complex;
|
| 821 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 822 |
|
|
renames Instantiations."*";
|
| 823 |
|
|
|
| 824 |
|
|
function "*"
|
| 825 |
|
|
(Left : Complex_Matrix;
|
| 826 |
|
|
Right : Complex) return Complex_Matrix
|
| 827 |
|
|
renames Instantiations."*";
|
| 828 |
|
|
|
| 829 |
|
|
function "*"
|
| 830 |
|
|
(Left : Real'Base;
|
| 831 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 832 |
|
|
renames Instantiations."*";
|
| 833 |
|
|
|
| 834 |
|
|
function "*"
|
| 835 |
|
|
(Left : Complex_Matrix;
|
| 836 |
|
|
Right : Real'Base) return Complex_Matrix
|
| 837 |
|
|
renames Instantiations."*";
|
| 838 |
|
|
|
| 839 |
|
|
---------
|
| 840 |
|
|
-- "+" --
|
| 841 |
|
|
---------
|
| 842 |
|
|
|
| 843 |
|
|
function "+" (Right : Complex_Vector) return Complex_Vector
|
| 844 |
|
|
renames Instantiations."+";
|
| 845 |
|
|
|
| 846 |
|
|
function "+"
|
| 847 |
|
|
(Left : Complex_Vector;
|
| 848 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 849 |
|
|
renames Instantiations."+";
|
| 850 |
|
|
|
| 851 |
|
|
function "+"
|
| 852 |
|
|
(Left : Real_Vector;
|
| 853 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 854 |
|
|
renames Instantiations."+";
|
| 855 |
|
|
|
| 856 |
|
|
function "+"
|
| 857 |
|
|
(Left : Complex_Vector;
|
| 858 |
|
|
Right : Real_Vector) return Complex_Vector
|
| 859 |
|
|
renames Instantiations."+";
|
| 860 |
|
|
|
| 861 |
|
|
function "+" (Right : Complex_Matrix) return Complex_Matrix
|
| 862 |
|
|
renames Instantiations."+";
|
| 863 |
|
|
|
| 864 |
|
|
function "+"
|
| 865 |
|
|
(Left : Complex_Matrix;
|
| 866 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 867 |
|
|
renames Instantiations."+";
|
| 868 |
|
|
|
| 869 |
|
|
function "+"
|
| 870 |
|
|
(Left : Real_Matrix;
|
| 871 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 872 |
|
|
renames Instantiations."+";
|
| 873 |
|
|
|
| 874 |
|
|
function "+"
|
| 875 |
|
|
(Left : Complex_Matrix;
|
| 876 |
|
|
Right : Real_Matrix) return Complex_Matrix
|
| 877 |
|
|
renames Instantiations."+";
|
| 878 |
|
|
|
| 879 |
|
|
---------
|
| 880 |
|
|
-- "-" --
|
| 881 |
|
|
---------
|
| 882 |
|
|
|
| 883 |
|
|
function "-"
|
| 884 |
|
|
(Right : Complex_Vector) return Complex_Vector
|
| 885 |
|
|
renames Instantiations."-";
|
| 886 |
|
|
|
| 887 |
|
|
function "-"
|
| 888 |
|
|
(Left : Complex_Vector;
|
| 889 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 890 |
|
|
renames Instantiations."-";
|
| 891 |
|
|
|
| 892 |
|
|
function "-"
|
| 893 |
|
|
(Left : Real_Vector;
|
| 894 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 895 |
|
|
renames Instantiations."-";
|
| 896 |
|
|
|
| 897 |
|
|
function "-"
|
| 898 |
|
|
(Left : Complex_Vector;
|
| 899 |
|
|
Right : Real_Vector) return Complex_Vector
|
| 900 |
|
|
renames Instantiations."-";
|
| 901 |
|
|
|
| 902 |
|
|
function "-" (Right : Complex_Matrix) return Complex_Matrix
|
| 903 |
|
|
renames Instantiations."-";
|
| 904 |
|
|
|
| 905 |
|
|
function "-"
|
| 906 |
|
|
(Left : Complex_Matrix;
|
| 907 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 908 |
|
|
renames Instantiations."-";
|
| 909 |
|
|
|
| 910 |
|
|
function "-"
|
| 911 |
|
|
(Left : Real_Matrix;
|
| 912 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 913 |
|
|
renames Instantiations."-";
|
| 914 |
|
|
|
| 915 |
|
|
function "-"
|
| 916 |
|
|
(Left : Complex_Matrix;
|
| 917 |
|
|
Right : Real_Matrix) return Complex_Matrix
|
| 918 |
|
|
renames Instantiations."-";
|
| 919 |
|
|
|
| 920 |
|
|
---------
|
| 921 |
|
|
-- "/" --
|
| 922 |
|
|
---------
|
| 923 |
|
|
|
| 924 |
|
|
function "/"
|
| 925 |
|
|
(Left : Complex_Vector;
|
| 926 |
|
|
Right : Complex) return Complex_Vector
|
| 927 |
|
|
renames Instantiations."/";
|
| 928 |
|
|
|
| 929 |
|
|
function "/"
|
| 930 |
|
|
(Left : Complex_Vector;
|
| 931 |
|
|
Right : Real'Base) return Complex_Vector
|
| 932 |
|
|
renames Instantiations."/";
|
| 933 |
|
|
|
| 934 |
|
|
function "/"
|
| 935 |
|
|
(Left : Complex_Matrix;
|
| 936 |
|
|
Right : Complex) return Complex_Matrix
|
| 937 |
|
|
renames Instantiations."/";
|
| 938 |
|
|
|
| 939 |
|
|
function "/"
|
| 940 |
|
|
(Left : Complex_Matrix;
|
| 941 |
|
|
Right : Real'Base) return Complex_Matrix
|
| 942 |
|
|
renames Instantiations."/";
|
| 943 |
|
|
|
| 944 |
|
|
-----------
|
| 945 |
|
|
-- "abs" --
|
| 946 |
|
|
-----------
|
| 947 |
|
|
|
| 948 |
|
|
function "abs" (Right : Complex_Vector) return Real'Base
|
| 949 |
|
|
renames Instantiations."abs";
|
| 950 |
|
|
|
| 951 |
|
|
--------------
|
| 952 |
|
|
-- Argument --
|
| 953 |
|
|
--------------
|
| 954 |
|
|
|
| 955 |
|
|
function Argument (X : Complex_Vector) return Real_Vector
|
| 956 |
|
|
renames Instantiations.Argument;
|
| 957 |
|
|
|
| 958 |
|
|
function Argument
|
| 959 |
|
|
(X : Complex_Vector;
|
| 960 |
|
|
Cycle : Real'Base) return Real_Vector
|
| 961 |
|
|
renames Instantiations.Argument;
|
| 962 |
|
|
|
| 963 |
|
|
function Argument (X : Complex_Matrix) return Real_Matrix
|
| 964 |
|
|
renames Instantiations.Argument;
|
| 965 |
|
|
|
| 966 |
|
|
function Argument
|
| 967 |
|
|
(X : Complex_Matrix;
|
| 968 |
|
|
Cycle : Real'Base) return Real_Matrix
|
| 969 |
|
|
renames Instantiations.Argument;
|
| 970 |
|
|
|
| 971 |
|
|
----------------------------
|
| 972 |
|
|
-- Compose_From_Cartesian --
|
| 973 |
|
|
----------------------------
|
| 974 |
|
|
|
| 975 |
|
|
function Compose_From_Cartesian (Re : Real_Vector) return Complex_Vector
|
| 976 |
|
|
renames Instantiations.Compose_From_Cartesian;
|
| 977 |
|
|
|
| 978 |
|
|
function Compose_From_Cartesian
|
| 979 |
|
|
(Re : Real_Vector;
|
| 980 |
|
|
Im : Real_Vector) return Complex_Vector
|
| 981 |
|
|
renames Instantiations.Compose_From_Cartesian;
|
| 982 |
|
|
|
| 983 |
|
|
function Compose_From_Cartesian (Re : Real_Matrix) return Complex_Matrix
|
| 984 |
|
|
renames Instantiations.Compose_From_Cartesian;
|
| 985 |
|
|
|
| 986 |
|
|
function Compose_From_Cartesian
|
| 987 |
|
|
(Re : Real_Matrix;
|
| 988 |
|
|
Im : Real_Matrix) return Complex_Matrix
|
| 989 |
|
|
renames Instantiations.Compose_From_Cartesian;
|
| 990 |
|
|
|
| 991 |
|
|
------------------------
|
| 992 |
|
|
-- Compose_From_Polar --
|
| 993 |
|
|
------------------------
|
| 994 |
|
|
|
| 995 |
|
|
function Compose_From_Polar
|
| 996 |
|
|
(Modulus : Real_Vector;
|
| 997 |
|
|
Argument : Real_Vector) return Complex_Vector
|
| 998 |
|
|
renames Instantiations.Compose_From_Polar;
|
| 999 |
|
|
|
| 1000 |
|
|
function Compose_From_Polar
|
| 1001 |
|
|
(Modulus : Real_Vector;
|
| 1002 |
|
|
Argument : Real_Vector;
|
| 1003 |
|
|
Cycle : Real'Base) return Complex_Vector
|
| 1004 |
|
|
renames Instantiations.Compose_From_Polar;
|
| 1005 |
|
|
|
| 1006 |
|
|
function Compose_From_Polar
|
| 1007 |
|
|
(Modulus : Real_Matrix;
|
| 1008 |
|
|
Argument : Real_Matrix) return Complex_Matrix
|
| 1009 |
|
|
renames Instantiations.Compose_From_Polar;
|
| 1010 |
|
|
|
| 1011 |
|
|
function Compose_From_Polar
|
| 1012 |
|
|
(Modulus : Real_Matrix;
|
| 1013 |
|
|
Argument : Real_Matrix;
|
| 1014 |
|
|
Cycle : Real'Base) return Complex_Matrix
|
| 1015 |
|
|
renames Instantiations.Compose_From_Polar;
|
| 1016 |
|
|
|
| 1017 |
|
|
---------------
|
| 1018 |
|
|
-- Conjugate --
|
| 1019 |
|
|
---------------
|
| 1020 |
|
|
|
| 1021 |
|
|
function Conjugate (X : Complex_Vector) return Complex_Vector
|
| 1022 |
|
|
renames Instantiations.Conjugate;
|
| 1023 |
|
|
|
| 1024 |
|
|
function Conjugate (X : Complex_Matrix) return Complex_Matrix
|
| 1025 |
|
|
renames Instantiations.Conjugate;
|
| 1026 |
|
|
|
| 1027 |
|
|
-----------------
|
| 1028 |
|
|
-- Determinant --
|
| 1029 |
|
|
-----------------
|
| 1030 |
|
|
|
| 1031 |
|
|
function Determinant (A : Complex_Matrix) return Complex is
|
| 1032 |
|
|
M : Complex_Matrix := A;
|
| 1033 |
|
|
B : Complex_Matrix (A'Range (1), 1 .. 0);
|
| 1034 |
|
|
R : Complex;
|
| 1035 |
|
|
begin
|
| 1036 |
|
|
Forward_Eliminate (M, B, R);
|
| 1037 |
|
|
return R;
|
| 1038 |
|
|
end Determinant;
|
| 1039 |
|
|
|
| 1040 |
|
|
-----------------
|
| 1041 |
|
|
-- Eigensystem --
|
| 1042 |
|
|
-----------------
|
| 1043 |
|
|
|
| 1044 |
|
|
procedure Eigensystem
|
| 1045 |
|
|
(A : Complex_Matrix;
|
| 1046 |
|
|
Values : out Real_Vector;
|
| 1047 |
|
|
Vectors : out Complex_Matrix)
|
| 1048 |
|
|
is
|
| 1049 |
|
|
N : constant Natural := Length (A);
|
| 1050 |
|
|
|
| 1051 |
|
|
-- For a Hermitian matrix C, we convert the eigenvalue problem to a
|
| 1052 |
|
|
-- real symmetric one: if C = A + i * B, then the (N, N) complex
|
| 1053 |
|
|
-- eigenvalue problem:
|
| 1054 |
|
|
-- (A + i * B) * (u + i * v) = Lambda * (u + i * v)
|
| 1055 |
|
|
--
|
| 1056 |
|
|
-- is equivalent to the (2 * N, 2 * N) real eigenvalue problem:
|
| 1057 |
|
|
-- [ A, B ] [ u ] = Lambda * [ u ]
|
| 1058 |
|
|
-- [ -B, A ] [ v ] [ v ]
|
| 1059 |
|
|
--
|
| 1060 |
|
|
-- Note that the (2 * N, 2 * N) matrix above is symmetric, as
|
| 1061 |
|
|
-- Transpose (A) = A and Transpose (B) = -B if C is Hermitian.
|
| 1062 |
|
|
|
| 1063 |
|
|
-- We solve this eigensystem using the real-valued algorithms. The final
|
| 1064 |
|
|
-- result will have every eigenvalue twice, so in the sorted output we
|
| 1065 |
|
|
-- just pick every second value, with associated eigenvector u + i * v.
|
| 1066 |
|
|
|
| 1067 |
|
|
M : Real_Matrix (1 .. 2 * N, 1 .. 2 * N);
|
| 1068 |
|
|
Vals : Real_Vector (1 .. 2 * N);
|
| 1069 |
|
|
Vecs : Real_Matrix (1 .. 2 * N, 1 .. 2 * N);
|
| 1070 |
|
|
|
| 1071 |
|
|
begin
|
| 1072 |
|
|
for J in 1 .. N loop
|
| 1073 |
|
|
for K in 1 .. N loop
|
| 1074 |
|
|
declare
|
| 1075 |
|
|
C : constant Complex :=
|
| 1076 |
|
|
(A (A'First (1) + (J - 1), A'First (2) + (K - 1)));
|
| 1077 |
|
|
begin
|
| 1078 |
|
|
M (J, K) := Re (C);
|
| 1079 |
|
|
M (J + N, K + N) := Re (C);
|
| 1080 |
|
|
M (J + N, K) := Im (C);
|
| 1081 |
|
|
M (J, K + N) := -Im (C);
|
| 1082 |
|
|
end;
|
| 1083 |
|
|
end loop;
|
| 1084 |
|
|
end loop;
|
| 1085 |
|
|
|
| 1086 |
|
|
Eigensystem (M, Vals, Vecs);
|
| 1087 |
|
|
|
| 1088 |
|
|
for J in 1 .. N loop
|
| 1089 |
|
|
declare
|
| 1090 |
|
|
Col : constant Integer := Values'First + (J - 1);
|
| 1091 |
|
|
begin
|
| 1092 |
|
|
Values (Col) := Vals (2 * J);
|
| 1093 |
|
|
|
| 1094 |
|
|
for K in 1 .. N loop
|
| 1095 |
|
|
declare
|
| 1096 |
|
|
Row : constant Integer := Vectors'First (2) + (K - 1);
|
| 1097 |
|
|
begin
|
| 1098 |
|
|
Vectors (Row, Col)
|
| 1099 |
|
|
:= (Vecs (J * 2, Col), Vecs (J * 2, Col + N));
|
| 1100 |
|
|
end;
|
| 1101 |
|
|
end loop;
|
| 1102 |
|
|
end;
|
| 1103 |
|
|
end loop;
|
| 1104 |
|
|
end Eigensystem;
|
| 1105 |
|
|
|
| 1106 |
|
|
-----------------
|
| 1107 |
|
|
-- Eigenvalues --
|
| 1108 |
|
|
-----------------
|
| 1109 |
|
|
|
| 1110 |
|
|
function Eigenvalues (A : Complex_Matrix) return Real_Vector is
|
| 1111 |
|
|
-- See Eigensystem for a description of the algorithm
|
| 1112 |
|
|
|
| 1113 |
|
|
N : constant Natural := Length (A);
|
| 1114 |
|
|
R : Real_Vector (A'Range (1));
|
| 1115 |
|
|
|
| 1116 |
|
|
M : Real_Matrix (1 .. 2 * N, 1 .. 2 * N);
|
| 1117 |
|
|
Vals : Real_Vector (1 .. 2 * N);
|
| 1118 |
|
|
begin
|
| 1119 |
|
|
for J in 1 .. N loop
|
| 1120 |
|
|
for K in 1 .. N loop
|
| 1121 |
|
|
declare
|
| 1122 |
|
|
C : constant Complex :=
|
| 1123 |
|
|
(A (A'First (1) + (J - 1), A'First (2) + (K - 1)));
|
| 1124 |
|
|
begin
|
| 1125 |
|
|
M (J, K) := Re (C);
|
| 1126 |
|
|
M (J + N, K + N) := Re (C);
|
| 1127 |
|
|
M (J + N, K) := Im (C);
|
| 1128 |
|
|
M (J, K + N) := -Im (C);
|
| 1129 |
|
|
end;
|
| 1130 |
|
|
end loop;
|
| 1131 |
|
|
end loop;
|
| 1132 |
|
|
|
| 1133 |
|
|
Vals := Eigenvalues (M);
|
| 1134 |
|
|
|
| 1135 |
|
|
for J in 1 .. N loop
|
| 1136 |
|
|
R (A'First (1) + (J - 1)) := Vals (2 * J);
|
| 1137 |
|
|
end loop;
|
| 1138 |
|
|
|
| 1139 |
|
|
return R;
|
| 1140 |
|
|
end Eigenvalues;
|
| 1141 |
|
|
|
| 1142 |
|
|
--------
|
| 1143 |
|
|
-- Im --
|
| 1144 |
|
|
--------
|
| 1145 |
|
|
|
| 1146 |
|
|
function Im (X : Complex_Vector) return Real_Vector
|
| 1147 |
|
|
renames Instantiations.Im;
|
| 1148 |
|
|
|
| 1149 |
|
|
function Im (X : Complex_Matrix) return Real_Matrix
|
| 1150 |
|
|
renames Instantiations.Im;
|
| 1151 |
|
|
|
| 1152 |
|
|
-------------
|
| 1153 |
|
|
-- Inverse --
|
| 1154 |
|
|
-------------
|
| 1155 |
|
|
|
| 1156 |
|
|
function Inverse (A : Complex_Matrix) return Complex_Matrix is
|
| 1157 |
|
|
(Solve (A, Unit_Matrix (Length (A))));
|
| 1158 |
|
|
|
| 1159 |
|
|
-------------
|
| 1160 |
|
|
-- Modulus --
|
| 1161 |
|
|
-------------
|
| 1162 |
|
|
|
| 1163 |
|
|
function Modulus (X : Complex_Vector) return Real_Vector
|
| 1164 |
|
|
renames Instantiations.Modulus;
|
| 1165 |
|
|
|
| 1166 |
|
|
function Modulus (X : Complex_Matrix) return Real_Matrix
|
| 1167 |
|
|
renames Instantiations.Modulus;
|
| 1168 |
|
|
|
| 1169 |
|
|
--------
|
| 1170 |
|
|
-- Re --
|
| 1171 |
|
|
--------
|
| 1172 |
|
|
|
| 1173 |
|
|
function Re (X : Complex_Vector) return Real_Vector
|
| 1174 |
|
|
renames Instantiations.Re;
|
| 1175 |
|
|
|
| 1176 |
|
|
function Re (X : Complex_Matrix) return Real_Matrix
|
| 1177 |
|
|
renames Instantiations.Re;
|
| 1178 |
|
|
|
| 1179 |
|
|
------------
|
| 1180 |
|
|
-- Set_Im --
|
| 1181 |
|
|
------------
|
| 1182 |
|
|
|
| 1183 |
|
|
procedure Set_Im
|
| 1184 |
|
|
(X : in out Complex_Matrix;
|
| 1185 |
|
|
Im : Real_Matrix)
|
| 1186 |
|
|
renames Instantiations.Set_Im;
|
| 1187 |
|
|
|
| 1188 |
|
|
procedure Set_Im
|
| 1189 |
|
|
(X : in out Complex_Vector;
|
| 1190 |
|
|
Im : Real_Vector)
|
| 1191 |
|
|
renames Instantiations.Set_Im;
|
| 1192 |
|
|
|
| 1193 |
|
|
------------
|
| 1194 |
|
|
-- Set_Re --
|
| 1195 |
|
|
------------
|
| 1196 |
|
|
|
| 1197 |
|
|
procedure Set_Re
|
| 1198 |
|
|
(X : in out Complex_Matrix;
|
| 1199 |
|
|
Re : Real_Matrix)
|
| 1200 |
|
|
renames Instantiations.Set_Re;
|
| 1201 |
|
|
|
| 1202 |
|
|
procedure Set_Re
|
| 1203 |
|
|
(X : in out Complex_Vector;
|
| 1204 |
|
|
Re : Real_Vector)
|
| 1205 |
|
|
renames Instantiations.Set_Re;
|
| 1206 |
|
|
|
| 1207 |
|
|
-----------
|
| 1208 |
|
|
-- Solve --
|
| 1209 |
|
|
-----------
|
| 1210 |
|
|
|
| 1211 |
|
|
function Solve
|
| 1212 |
|
|
(A : Complex_Matrix;
|
| 1213 |
|
|
X : Complex_Vector) return Complex_Vector
|
| 1214 |
|
|
renames Instantiations.Solve;
|
| 1215 |
|
|
|
| 1216 |
|
|
function Solve
|
| 1217 |
|
|
(A : Complex_Matrix;
|
| 1218 |
|
|
X : Complex_Matrix) return Complex_Matrix
|
| 1219 |
|
|
renames Instantiations.Solve;
|
| 1220 |
|
|
|
| 1221 |
|
|
---------------
|
| 1222 |
|
|
-- Transpose --
|
| 1223 |
|
|
---------------
|
| 1224 |
|
|
|
| 1225 |
|
|
function Transpose
|
| 1226 |
|
|
(X : Complex_Matrix) return Complex_Matrix
|
| 1227 |
|
|
is
|
| 1228 |
|
|
R : Complex_Matrix (X'Range (2), X'Range (1));
|
| 1229 |
|
|
begin
|
| 1230 |
|
|
Transpose (X, R);
|
| 1231 |
|
|
return R;
|
| 1232 |
|
|
end Transpose;
|
| 1233 |
|
|
|
| 1234 |
|
|
-----------------
|
| 1235 |
|
|
-- Unit_Matrix --
|
| 1236 |
|
|
-----------------
|
| 1237 |
|
|
|
| 1238 |
|
|
function Unit_Matrix
|
| 1239 |
|
|
(Order : Positive;
|
| 1240 |
|
|
First_1 : Integer := 1;
|
| 1241 |
|
|
First_2 : Integer := 1) return Complex_Matrix
|
| 1242 |
|
|
renames Instantiations.Unit_Matrix;
|
| 1243 |
|
|
|
| 1244 |
|
|
-----------------
|
| 1245 |
|
|
-- Unit_Vector --
|
| 1246 |
|
|
-----------------
|
| 1247 |
|
|
|
| 1248 |
|
|
function Unit_Vector
|
| 1249 |
|
|
(Index : Integer;
|
| 1250 |
|
|
Order : Positive;
|
| 1251 |
|
|
First : Integer := 1) return Complex_Vector
|
| 1252 |
|
|
renames Instantiations.Unit_Vector;
|
| 1253 |
|
|
|
| 1254 |
|
|
end Ada.Numerics.Generic_Complex_Arrays;
|
