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------------------------------------------------------------------------------
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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) 2006-2009, 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 System.Generic_Complex_BLAS;
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with System.Generic_Complex_LAPACK;
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package body Ada.Numerics.Generic_Complex_Arrays is
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-- Operations involving inner products use BLAS library implementations.
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-- This allows larger matrices and vectors to be computed efficiently,
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-- taking into account memory hierarchy issues and vector instructions
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-- that vary widely between machines.
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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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-- Operations for solving linear systems and computing determinant,
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-- eigenvalues, eigensystem and inverse, are implemented using the
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-- LAPACK library.
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type BLAS_Real_Vector is array (Integer range <>) of Real;
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package BLAS is new System.Generic_Complex_BLAS
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(Real => Real,
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Complex_Types => Complex_Types,
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Complex_Vector => Complex_Vector,
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Complex_Matrix => Complex_Matrix);
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package LAPACK is new System.Generic_Complex_LAPACK
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(Real => Real,
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Real_Vector => BLAS_Real_Vector,
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Complex_Types => Complex_Types,
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Complex_Vector => Complex_Vector,
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Complex_Matrix => Complex_Matrix);
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subtype Real is Real_Arrays.Real;
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-- Work around visibility bug ???
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use BLAS, LAPACK;
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-- Procedure versions of functions returning unconstrained values.
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-- This allows for inlining the function wrapper.
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procedure Eigenvalues
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(A : Complex_Matrix;
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Values : out Real_Vector);
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procedure Inverse
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(A : Complex_Matrix;
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R : out Complex_Matrix);
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procedure Solve
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(A : Complex_Matrix;
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X : Complex_Vector;
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B : out Complex_Vector);
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procedure Solve
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(A : Complex_Matrix;
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X : Complex_Matrix;
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B : out Complex_Matrix);
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procedure Transpose is new System.Generic_Array_Operations.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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-- 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 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 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 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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Result_Matrix => Complex_Matrix,
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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 => 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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Right_Matrix => Real_Matrix,
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Result_Matrix => Complex_Matrix,
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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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Result_Scalar => Complex,
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X_Vector => Complex_Vector,
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Result_Vector => Complex_Vector,
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Operation => "+");
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function "+" is new Vector_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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Left_Vector => Complex_Vector,
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| 284 |
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Right_Vector => Complex_Vector,
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| 285 |
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Result_Vector => Complex_Vector,
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| 286 |
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Operation => "+");
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function "+" is new Vector_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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| 292 |
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Left_Vector => Real_Vector,
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| 293 |
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Right_Vector => Complex_Vector,
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| 294 |
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Result_Vector => Complex_Vector,
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| 295 |
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Operation => "+");
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| 296 |
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| 297 |
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function "+" is new Vector_Vector_Elementwise_Operation
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| 298 |
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(Left_Scalar => Complex,
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| 299 |
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Right_Scalar => Real'Base,
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| 300 |
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Result_Scalar => Complex,
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| 301 |
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Left_Vector => Complex_Vector,
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| 302 |
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Right_Vector => Real_Vector,
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| 303 |
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Result_Vector => Complex_Vector,
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| 304 |
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Operation => "+");
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| 306 |
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function "+" is new Matrix_Elementwise_Operation
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| 307 |
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(X_Scalar => Complex,
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| 308 |
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Result_Scalar => Complex,
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| 309 |
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X_Matrix => Complex_Matrix,
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| 310 |
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Result_Matrix => Complex_Matrix,
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| 311 |
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Operation => "+");
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| 313 |
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function "+" is new Matrix_Matrix_Elementwise_Operation
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| 314 |
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(Left_Scalar => Complex,
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| 315 |
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Right_Scalar => Complex,
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| 316 |
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Result_Scalar => Complex,
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| 317 |
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Left_Matrix => Complex_Matrix,
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| 318 |
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Right_Matrix => Complex_Matrix,
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| 319 |
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Result_Matrix => Complex_Matrix,
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| 320 |
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Operation => "+");
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function "+" is new Matrix_Matrix_Elementwise_Operation
|
| 323 |
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(Left_Scalar => Real'Base,
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| 324 |
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Right_Scalar => Complex,
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| 325 |
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Result_Scalar => Complex,
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| 326 |
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Left_Matrix => Real_Matrix,
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| 327 |
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Right_Matrix => Complex_Matrix,
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| 328 |
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Result_Matrix => Complex_Matrix,
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| 329 |
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Operation => "+");
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| 331 |
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function "+" is new Matrix_Matrix_Elementwise_Operation
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| 332 |
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(Left_Scalar => Complex,
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| 333 |
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Right_Scalar => Real'Base,
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Result_Scalar => Complex,
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| 335 |
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Left_Matrix => Complex_Matrix,
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| 336 |
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Right_Matrix => Real_Matrix,
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| 337 |
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Result_Matrix => Complex_Matrix,
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| 338 |
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Operation => "+");
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---------
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| 341 |
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-- "-" --
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| 342 |
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---------
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| 343 |
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| 344 |
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function "-" is new Vector_Elementwise_Operation
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| 345 |
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(X_Scalar => Complex,
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| 346 |
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Result_Scalar => Complex,
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| 347 |
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X_Vector => Complex_Vector,
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| 348 |
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Result_Vector => Complex_Vector,
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| 349 |
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Operation => "-");
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| 350 |
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| 351 |
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function "-" is new Vector_Vector_Elementwise_Operation
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| 352 |
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(Left_Scalar => Complex,
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| 353 |
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Right_Scalar => Complex,
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| 354 |
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Result_Scalar => Complex,
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| 355 |
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Left_Vector => Complex_Vector,
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| 356 |
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Right_Vector => Complex_Vector,
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| 357 |
|
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Result_Vector => Complex_Vector,
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| 358 |
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Operation => "-");
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| 359 |
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|
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| 360 |
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function "-" is new Vector_Vector_Elementwise_Operation
|
| 361 |
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(Left_Scalar => Real'Base,
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| 362 |
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Right_Scalar => Complex,
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| 363 |
|
|
Result_Scalar => Complex,
|
| 364 |
|
|
Left_Vector => Real_Vector,
|
| 365 |
|
|
Right_Vector => Complex_Vector,
|
| 366 |
|
|
Result_Vector => Complex_Vector,
|
| 367 |
|
|
Operation => "-");
|
| 368 |
|
|
|
| 369 |
|
|
function "-" is new Vector_Vector_Elementwise_Operation
|
| 370 |
|
|
(Left_Scalar => Complex,
|
| 371 |
|
|
Right_Scalar => Real'Base,
|
| 372 |
|
|
Result_Scalar => Complex,
|
| 373 |
|
|
Left_Vector => Complex_Vector,
|
| 374 |
|
|
Right_Vector => Real_Vector,
|
| 375 |
|
|
Result_Vector => Complex_Vector,
|
| 376 |
|
|
Operation => "-");
|
| 377 |
|
|
|
| 378 |
|
|
function "-" is new Matrix_Elementwise_Operation
|
| 379 |
|
|
(X_Scalar => Complex,
|
| 380 |
|
|
Result_Scalar => Complex,
|
| 381 |
|
|
X_Matrix => Complex_Matrix,
|
| 382 |
|
|
Result_Matrix => Complex_Matrix,
|
| 383 |
|
|
Operation => "-");
|
| 384 |
|
|
|
| 385 |
|
|
function "-" is new Matrix_Matrix_Elementwise_Operation
|
| 386 |
|
|
(Left_Scalar => Complex,
|
| 387 |
|
|
Right_Scalar => Complex,
|
| 388 |
|
|
Result_Scalar => Complex,
|
| 389 |
|
|
Left_Matrix => Complex_Matrix,
|
| 390 |
|
|
Right_Matrix => Complex_Matrix,
|
| 391 |
|
|
Result_Matrix => Complex_Matrix,
|
| 392 |
|
|
Operation => "-");
|
| 393 |
|
|
|
| 394 |
|
|
function "-" is new Matrix_Matrix_Elementwise_Operation
|
| 395 |
|
|
(Left_Scalar => Real'Base,
|
| 396 |
|
|
Right_Scalar => Complex,
|
| 397 |
|
|
Result_Scalar => Complex,
|
| 398 |
|
|
Left_Matrix => Real_Matrix,
|
| 399 |
|
|
Right_Matrix => Complex_Matrix,
|
| 400 |
|
|
Result_Matrix => Complex_Matrix,
|
| 401 |
|
|
Operation => "-");
|
| 402 |
|
|
|
| 403 |
|
|
function "-" is new Matrix_Matrix_Elementwise_Operation
|
| 404 |
|
|
(Left_Scalar => Complex,
|
| 405 |
|
|
Right_Scalar => Real'Base,
|
| 406 |
|
|
Result_Scalar => Complex,
|
| 407 |
|
|
Left_Matrix => Complex_Matrix,
|
| 408 |
|
|
Right_Matrix => Real_Matrix,
|
| 409 |
|
|
Result_Matrix => Complex_Matrix,
|
| 410 |
|
|
Operation => "-");
|
| 411 |
|
|
|
| 412 |
|
|
---------
|
| 413 |
|
|
-- "/" --
|
| 414 |
|
|
---------
|
| 415 |
|
|
|
| 416 |
|
|
function "/" is new Vector_Scalar_Elementwise_Operation
|
| 417 |
|
|
(Left_Scalar => Complex,
|
| 418 |
|
|
Right_Scalar => Complex,
|
| 419 |
|
|
Result_Scalar => Complex,
|
| 420 |
|
|
Left_Vector => Complex_Vector,
|
| 421 |
|
|
Result_Vector => Complex_Vector,
|
| 422 |
|
|
Operation => "/");
|
| 423 |
|
|
|
| 424 |
|
|
function "/" is new Vector_Scalar_Elementwise_Operation
|
| 425 |
|
|
(Left_Scalar => Complex,
|
| 426 |
|
|
Right_Scalar => Real'Base,
|
| 427 |
|
|
Result_Scalar => Complex,
|
| 428 |
|
|
Left_Vector => Complex_Vector,
|
| 429 |
|
|
Result_Vector => Complex_Vector,
|
| 430 |
|
|
Operation => "/");
|
| 431 |
|
|
|
| 432 |
|
|
function "/" is new Matrix_Scalar_Elementwise_Operation
|
| 433 |
|
|
(Left_Scalar => Complex,
|
| 434 |
|
|
Right_Scalar => Complex,
|
| 435 |
|
|
Result_Scalar => Complex,
|
| 436 |
|
|
Left_Matrix => Complex_Matrix,
|
| 437 |
|
|
Result_Matrix => Complex_Matrix,
|
| 438 |
|
|
Operation => "/");
|
| 439 |
|
|
|
| 440 |
|
|
function "/" is new Matrix_Scalar_Elementwise_Operation
|
| 441 |
|
|
(Left_Scalar => Complex,
|
| 442 |
|
|
Right_Scalar => Real'Base,
|
| 443 |
|
|
Result_Scalar => Complex,
|
| 444 |
|
|
Left_Matrix => Complex_Matrix,
|
| 445 |
|
|
Result_Matrix => Complex_Matrix,
|
| 446 |
|
|
Operation => "/");
|
| 447 |
|
|
|
| 448 |
|
|
--------------
|
| 449 |
|
|
-- Argument --
|
| 450 |
|
|
--------------
|
| 451 |
|
|
|
| 452 |
|
|
function Argument is new Vector_Elementwise_Operation
|
| 453 |
|
|
(X_Scalar => Complex,
|
| 454 |
|
|
Result_Scalar => Real'Base,
|
| 455 |
|
|
X_Vector => Complex_Vector,
|
| 456 |
|
|
Result_Vector => Real_Vector,
|
| 457 |
|
|
Operation => Argument);
|
| 458 |
|
|
|
| 459 |
|
|
function Argument is new Vector_Scalar_Elementwise_Operation
|
| 460 |
|
|
(Left_Scalar => Complex,
|
| 461 |
|
|
Right_Scalar => Real'Base,
|
| 462 |
|
|
Result_Scalar => Real'Base,
|
| 463 |
|
|
Left_Vector => Complex_Vector,
|
| 464 |
|
|
Result_Vector => Real_Vector,
|
| 465 |
|
|
Operation => Argument);
|
| 466 |
|
|
|
| 467 |
|
|
function Argument is new Matrix_Elementwise_Operation
|
| 468 |
|
|
(X_Scalar => Complex,
|
| 469 |
|
|
Result_Scalar => Real'Base,
|
| 470 |
|
|
X_Matrix => Complex_Matrix,
|
| 471 |
|
|
Result_Matrix => Real_Matrix,
|
| 472 |
|
|
Operation => Argument);
|
| 473 |
|
|
|
| 474 |
|
|
function Argument is new Matrix_Scalar_Elementwise_Operation
|
| 475 |
|
|
(Left_Scalar => Complex,
|
| 476 |
|
|
Right_Scalar => Real'Base,
|
| 477 |
|
|
Result_Scalar => Real'Base,
|
| 478 |
|
|
Left_Matrix => Complex_Matrix,
|
| 479 |
|
|
Result_Matrix => Real_Matrix,
|
| 480 |
|
|
Operation => Argument);
|
| 481 |
|
|
|
| 482 |
|
|
----------------------------
|
| 483 |
|
|
-- Compose_From_Cartesian --
|
| 484 |
|
|
----------------------------
|
| 485 |
|
|
|
| 486 |
|
|
function Compose_From_Cartesian is new Vector_Elementwise_Operation
|
| 487 |
|
|
(X_Scalar => Real'Base,
|
| 488 |
|
|
Result_Scalar => Complex,
|
| 489 |
|
|
X_Vector => Real_Vector,
|
| 490 |
|
|
Result_Vector => Complex_Vector,
|
| 491 |
|
|
Operation => Compose_From_Cartesian);
|
| 492 |
|
|
|
| 493 |
|
|
function Compose_From_Cartesian is
|
| 494 |
|
|
new Vector_Vector_Elementwise_Operation
|
| 495 |
|
|
(Left_Scalar => Real'Base,
|
| 496 |
|
|
Right_Scalar => Real'Base,
|
| 497 |
|
|
Result_Scalar => Complex,
|
| 498 |
|
|
Left_Vector => Real_Vector,
|
| 499 |
|
|
Right_Vector => Real_Vector,
|
| 500 |
|
|
Result_Vector => Complex_Vector,
|
| 501 |
|
|
Operation => Compose_From_Cartesian);
|
| 502 |
|
|
|
| 503 |
|
|
function Compose_From_Cartesian is new Matrix_Elementwise_Operation
|
| 504 |
|
|
(X_Scalar => Real'Base,
|
| 505 |
|
|
Result_Scalar => Complex,
|
| 506 |
|
|
X_Matrix => Real_Matrix,
|
| 507 |
|
|
Result_Matrix => Complex_Matrix,
|
| 508 |
|
|
Operation => Compose_From_Cartesian);
|
| 509 |
|
|
|
| 510 |
|
|
function Compose_From_Cartesian is
|
| 511 |
|
|
new Matrix_Matrix_Elementwise_Operation
|
| 512 |
|
|
(Left_Scalar => Real'Base,
|
| 513 |
|
|
Right_Scalar => Real'Base,
|
| 514 |
|
|
Result_Scalar => Complex,
|
| 515 |
|
|
Left_Matrix => Real_Matrix,
|
| 516 |
|
|
Right_Matrix => Real_Matrix,
|
| 517 |
|
|
Result_Matrix => Complex_Matrix,
|
| 518 |
|
|
Operation => Compose_From_Cartesian);
|
| 519 |
|
|
|
| 520 |
|
|
------------------------
|
| 521 |
|
|
-- Compose_From_Polar --
|
| 522 |
|
|
------------------------
|
| 523 |
|
|
|
| 524 |
|
|
function Compose_From_Polar is
|
| 525 |
|
|
new Vector_Vector_Elementwise_Operation
|
| 526 |
|
|
(Left_Scalar => Real'Base,
|
| 527 |
|
|
Right_Scalar => Real'Base,
|
| 528 |
|
|
Result_Scalar => Complex,
|
| 529 |
|
|
Left_Vector => Real_Vector,
|
| 530 |
|
|
Right_Vector => Real_Vector,
|
| 531 |
|
|
Result_Vector => Complex_Vector,
|
| 532 |
|
|
Operation => Compose_From_Polar);
|
| 533 |
|
|
|
| 534 |
|
|
function Compose_From_Polar is
|
| 535 |
|
|
new Vector_Vector_Scalar_Elementwise_Operation
|
| 536 |
|
|
(X_Scalar => Real'Base,
|
| 537 |
|
|
Y_Scalar => Real'Base,
|
| 538 |
|
|
Z_Scalar => Real'Base,
|
| 539 |
|
|
Result_Scalar => Complex,
|
| 540 |
|
|
X_Vector => Real_Vector,
|
| 541 |
|
|
Y_Vector => Real_Vector,
|
| 542 |
|
|
Result_Vector => Complex_Vector,
|
| 543 |
|
|
Operation => Compose_From_Polar);
|
| 544 |
|
|
|
| 545 |
|
|
function Compose_From_Polar is
|
| 546 |
|
|
new Matrix_Matrix_Elementwise_Operation
|
| 547 |
|
|
(Left_Scalar => Real'Base,
|
| 548 |
|
|
Right_Scalar => Real'Base,
|
| 549 |
|
|
Result_Scalar => Complex,
|
| 550 |
|
|
Left_Matrix => Real_Matrix,
|
| 551 |
|
|
Right_Matrix => Real_Matrix,
|
| 552 |
|
|
Result_Matrix => Complex_Matrix,
|
| 553 |
|
|
Operation => Compose_From_Polar);
|
| 554 |
|
|
|
| 555 |
|
|
function Compose_From_Polar is
|
| 556 |
|
|
new Matrix_Matrix_Scalar_Elementwise_Operation
|
| 557 |
|
|
(X_Scalar => Real'Base,
|
| 558 |
|
|
Y_Scalar => Real'Base,
|
| 559 |
|
|
Z_Scalar => Real'Base,
|
| 560 |
|
|
Result_Scalar => Complex,
|
| 561 |
|
|
X_Matrix => Real_Matrix,
|
| 562 |
|
|
Y_Matrix => Real_Matrix,
|
| 563 |
|
|
Result_Matrix => Complex_Matrix,
|
| 564 |
|
|
Operation => Compose_From_Polar);
|
| 565 |
|
|
|
| 566 |
|
|
---------------
|
| 567 |
|
|
-- Conjugate --
|
| 568 |
|
|
---------------
|
| 569 |
|
|
|
| 570 |
|
|
function Conjugate is new Vector_Elementwise_Operation
|
| 571 |
|
|
(X_Scalar => Complex,
|
| 572 |
|
|
Result_Scalar => Complex,
|
| 573 |
|
|
X_Vector => Complex_Vector,
|
| 574 |
|
|
Result_Vector => Complex_Vector,
|
| 575 |
|
|
Operation => Conjugate);
|
| 576 |
|
|
|
| 577 |
|
|
function Conjugate is new Matrix_Elementwise_Operation
|
| 578 |
|
|
(X_Scalar => Complex,
|
| 579 |
|
|
Result_Scalar => Complex,
|
| 580 |
|
|
X_Matrix => Complex_Matrix,
|
| 581 |
|
|
Result_Matrix => Complex_Matrix,
|
| 582 |
|
|
Operation => Conjugate);
|
| 583 |
|
|
|
| 584 |
|
|
--------
|
| 585 |
|
|
-- Im --
|
| 586 |
|
|
--------
|
| 587 |
|
|
|
| 588 |
|
|
function Im is new Vector_Elementwise_Operation
|
| 589 |
|
|
(X_Scalar => Complex,
|
| 590 |
|
|
Result_Scalar => Real'Base,
|
| 591 |
|
|
X_Vector => Complex_Vector,
|
| 592 |
|
|
Result_Vector => Real_Vector,
|
| 593 |
|
|
Operation => Im);
|
| 594 |
|
|
|
| 595 |
|
|
function Im is new Matrix_Elementwise_Operation
|
| 596 |
|
|
(X_Scalar => Complex,
|
| 597 |
|
|
Result_Scalar => Real'Base,
|
| 598 |
|
|
X_Matrix => Complex_Matrix,
|
| 599 |
|
|
Result_Matrix => Real_Matrix,
|
| 600 |
|
|
Operation => Im);
|
| 601 |
|
|
|
| 602 |
|
|
-------------
|
| 603 |
|
|
-- Modulus --
|
| 604 |
|
|
-------------
|
| 605 |
|
|
|
| 606 |
|
|
function Modulus is new Vector_Elementwise_Operation
|
| 607 |
|
|
(X_Scalar => Complex,
|
| 608 |
|
|
Result_Scalar => Real'Base,
|
| 609 |
|
|
X_Vector => Complex_Vector,
|
| 610 |
|
|
Result_Vector => Real_Vector,
|
| 611 |
|
|
Operation => Modulus);
|
| 612 |
|
|
|
| 613 |
|
|
function Modulus is new Matrix_Elementwise_Operation
|
| 614 |
|
|
(X_Scalar => Complex,
|
| 615 |
|
|
Result_Scalar => Real'Base,
|
| 616 |
|
|
X_Matrix => Complex_Matrix,
|
| 617 |
|
|
Result_Matrix => Real_Matrix,
|
| 618 |
|
|
Operation => Modulus);
|
| 619 |
|
|
|
| 620 |
|
|
--------
|
| 621 |
|
|
-- Re --
|
| 622 |
|
|
--------
|
| 623 |
|
|
|
| 624 |
|
|
function Re is new Vector_Elementwise_Operation
|
| 625 |
|
|
(X_Scalar => Complex,
|
| 626 |
|
|
Result_Scalar => Real'Base,
|
| 627 |
|
|
X_Vector => Complex_Vector,
|
| 628 |
|
|
Result_Vector => Real_Vector,
|
| 629 |
|
|
Operation => Re);
|
| 630 |
|
|
|
| 631 |
|
|
function Re is new Matrix_Elementwise_Operation
|
| 632 |
|
|
(X_Scalar => Complex,
|
| 633 |
|
|
Result_Scalar => Real'Base,
|
| 634 |
|
|
X_Matrix => Complex_Matrix,
|
| 635 |
|
|
Result_Matrix => Real_Matrix,
|
| 636 |
|
|
Operation => Re);
|
| 637 |
|
|
|
| 638 |
|
|
------------
|
| 639 |
|
|
-- Set_Im --
|
| 640 |
|
|
------------
|
| 641 |
|
|
|
| 642 |
|
|
procedure Set_Im is new Update_Vector_With_Vector
|
| 643 |
|
|
(X_Scalar => Complex,
|
| 644 |
|
|
Y_Scalar => Real'Base,
|
| 645 |
|
|
X_Vector => Complex_Vector,
|
| 646 |
|
|
Y_Vector => Real_Vector,
|
| 647 |
|
|
Update => Set_Im);
|
| 648 |
|
|
|
| 649 |
|
|
procedure Set_Im is new Update_Matrix_With_Matrix
|
| 650 |
|
|
(X_Scalar => Complex,
|
| 651 |
|
|
Y_Scalar => Real'Base,
|
| 652 |
|
|
X_Matrix => Complex_Matrix,
|
| 653 |
|
|
Y_Matrix => Real_Matrix,
|
| 654 |
|
|
Update => Set_Im);
|
| 655 |
|
|
|
| 656 |
|
|
------------
|
| 657 |
|
|
-- Set_Re --
|
| 658 |
|
|
------------
|
| 659 |
|
|
|
| 660 |
|
|
procedure Set_Re is new Update_Vector_With_Vector
|
| 661 |
|
|
(X_Scalar => Complex,
|
| 662 |
|
|
Y_Scalar => Real'Base,
|
| 663 |
|
|
X_Vector => Complex_Vector,
|
| 664 |
|
|
Y_Vector => Real_Vector,
|
| 665 |
|
|
Update => Set_Re);
|
| 666 |
|
|
|
| 667 |
|
|
procedure Set_Re is new Update_Matrix_With_Matrix
|
| 668 |
|
|
(X_Scalar => Complex,
|
| 669 |
|
|
Y_Scalar => Real'Base,
|
| 670 |
|
|
X_Matrix => Complex_Matrix,
|
| 671 |
|
|
Y_Matrix => Real_Matrix,
|
| 672 |
|
|
Update => Set_Re);
|
| 673 |
|
|
|
| 674 |
|
|
-----------------
|
| 675 |
|
|
-- Unit_Matrix --
|
| 676 |
|
|
-----------------
|
| 677 |
|
|
|
| 678 |
|
|
function Unit_Matrix is new System.Generic_Array_Operations.Unit_Matrix
|
| 679 |
|
|
(Scalar => Complex,
|
| 680 |
|
|
Matrix => Complex_Matrix,
|
| 681 |
|
|
Zero => (0.0, 0.0),
|
| 682 |
|
|
One => (1.0, 0.0));
|
| 683 |
|
|
|
| 684 |
|
|
function Unit_Vector is new System.Generic_Array_Operations.Unit_Vector
|
| 685 |
|
|
(Scalar => Complex,
|
| 686 |
|
|
Vector => Complex_Vector,
|
| 687 |
|
|
Zero => (0.0, 0.0),
|
| 688 |
|
|
One => (1.0, 0.0));
|
| 689 |
|
|
|
| 690 |
|
|
end Instantiations;
|
| 691 |
|
|
|
| 692 |
|
|
---------
|
| 693 |
|
|
-- "*" --
|
| 694 |
|
|
---------
|
| 695 |
|
|
|
| 696 |
|
|
function "*"
|
| 697 |
|
|
(Left : Complex_Vector;
|
| 698 |
|
|
Right : Complex_Vector) return Complex
|
| 699 |
|
|
is
|
| 700 |
|
|
begin
|
| 701 |
|
|
if Left'Length /= Right'Length then
|
| 702 |
|
|
raise Constraint_Error with
|
| 703 |
|
|
"vectors are of different length in inner product";
|
| 704 |
|
|
end if;
|
| 705 |
|
|
|
| 706 |
|
|
return dot (Left'Length, X => Left, Y => Right);
|
| 707 |
|
|
end "*";
|
| 708 |
|
|
|
| 709 |
|
|
function "*"
|
| 710 |
|
|
(Left : Real_Vector;
|
| 711 |
|
|
Right : Complex_Vector) return Complex
|
| 712 |
|
|
renames Instantiations."*";
|
| 713 |
|
|
|
| 714 |
|
|
function "*"
|
| 715 |
|
|
(Left : Complex_Vector;
|
| 716 |
|
|
Right : Real_Vector) return Complex
|
| 717 |
|
|
renames Instantiations."*";
|
| 718 |
|
|
|
| 719 |
|
|
function "*"
|
| 720 |
|
|
(Left : Complex;
|
| 721 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 722 |
|
|
renames Instantiations."*";
|
| 723 |
|
|
|
| 724 |
|
|
function "*"
|
| 725 |
|
|
(Left : Complex_Vector;
|
| 726 |
|
|
Right : Complex) return Complex_Vector
|
| 727 |
|
|
renames Instantiations."*";
|
| 728 |
|
|
|
| 729 |
|
|
function "*"
|
| 730 |
|
|
(Left : Real'Base;
|
| 731 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 732 |
|
|
renames Instantiations."*";
|
| 733 |
|
|
|
| 734 |
|
|
function "*"
|
| 735 |
|
|
(Left : Complex_Vector;
|
| 736 |
|
|
Right : Real'Base) return Complex_Vector
|
| 737 |
|
|
renames Instantiations."*";
|
| 738 |
|
|
|
| 739 |
|
|
function "*"
|
| 740 |
|
|
(Left : Complex_Matrix;
|
| 741 |
|
|
Right : Complex_Matrix)
|
| 742 |
|
|
return Complex_Matrix
|
| 743 |
|
|
is
|
| 744 |
|
|
R : Complex_Matrix (Left'Range (1), Right'Range (2));
|
| 745 |
|
|
|
| 746 |
|
|
begin
|
| 747 |
|
|
if Left'Length (2) /= Right'Length (1) then
|
| 748 |
|
|
raise Constraint_Error with
|
| 749 |
|
|
"incompatible dimensions in matrix-matrix multiplication";
|
| 750 |
|
|
end if;
|
| 751 |
|
|
|
| 752 |
|
|
gemm (Trans_A => No_Trans'Access,
|
| 753 |
|
|
Trans_B => No_Trans'Access,
|
| 754 |
|
|
M => Right'Length (2),
|
| 755 |
|
|
N => Left'Length (1),
|
| 756 |
|
|
K => Right'Length (1),
|
| 757 |
|
|
A => Right,
|
| 758 |
|
|
Ld_A => Right'Length (2),
|
| 759 |
|
|
B => Left,
|
| 760 |
|
|
Ld_B => Left'Length (2),
|
| 761 |
|
|
C => R,
|
| 762 |
|
|
Ld_C => R'Length (2));
|
| 763 |
|
|
|
| 764 |
|
|
return R;
|
| 765 |
|
|
end "*";
|
| 766 |
|
|
|
| 767 |
|
|
function "*"
|
| 768 |
|
|
(Left : Complex_Vector;
|
| 769 |
|
|
Right : Complex_Vector) return Complex_Matrix
|
| 770 |
|
|
renames Instantiations."*";
|
| 771 |
|
|
|
| 772 |
|
|
function "*"
|
| 773 |
|
|
(Left : Complex_Vector;
|
| 774 |
|
|
Right : Complex_Matrix) return Complex_Vector
|
| 775 |
|
|
is
|
| 776 |
|
|
R : Complex_Vector (Right'Range (2));
|
| 777 |
|
|
|
| 778 |
|
|
begin
|
| 779 |
|
|
if Left'Length /= Right'Length (1) then
|
| 780 |
|
|
raise Constraint_Error with
|
| 781 |
|
|
"incompatible dimensions in vector-matrix multiplication";
|
| 782 |
|
|
end if;
|
| 783 |
|
|
|
| 784 |
|
|
gemv (Trans => No_Trans'Access,
|
| 785 |
|
|
M => Right'Length (2),
|
| 786 |
|
|
N => Right'Length (1),
|
| 787 |
|
|
A => Right,
|
| 788 |
|
|
Ld_A => Right'Length (2),
|
| 789 |
|
|
X => Left,
|
| 790 |
|
|
Y => R);
|
| 791 |
|
|
|
| 792 |
|
|
return R;
|
| 793 |
|
|
end "*";
|
| 794 |
|
|
|
| 795 |
|
|
function "*"
|
| 796 |
|
|
(Left : Complex_Matrix;
|
| 797 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 798 |
|
|
is
|
| 799 |
|
|
R : Complex_Vector (Left'Range (1));
|
| 800 |
|
|
|
| 801 |
|
|
begin
|
| 802 |
|
|
if Left'Length (2) /= Right'Length then
|
| 803 |
|
|
raise Constraint_Error with
|
| 804 |
|
|
"incompatible dimensions in matrix-vector multiplication";
|
| 805 |
|
|
end if;
|
| 806 |
|
|
|
| 807 |
|
|
gemv (Trans => Trans'Access,
|
| 808 |
|
|
M => Left'Length (2),
|
| 809 |
|
|
N => Left'Length (1),
|
| 810 |
|
|
A => Left,
|
| 811 |
|
|
Ld_A => Left'Length (2),
|
| 812 |
|
|
X => Right,
|
| 813 |
|
|
Y => R);
|
| 814 |
|
|
|
| 815 |
|
|
return R;
|
| 816 |
|
|
end "*";
|
| 817 |
|
|
|
| 818 |
|
|
function "*"
|
| 819 |
|
|
(Left : Real_Matrix;
|
| 820 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 821 |
|
|
renames Instantiations."*";
|
| 822 |
|
|
|
| 823 |
|
|
function "*"
|
| 824 |
|
|
(Left : Complex_Matrix;
|
| 825 |
|
|
Right : Real_Matrix) return Complex_Matrix
|
| 826 |
|
|
renames Instantiations."*";
|
| 827 |
|
|
|
| 828 |
|
|
function "*"
|
| 829 |
|
|
(Left : Real_Vector;
|
| 830 |
|
|
Right : Complex_Vector) return Complex_Matrix
|
| 831 |
|
|
renames Instantiations."*";
|
| 832 |
|
|
|
| 833 |
|
|
function "*"
|
| 834 |
|
|
(Left : Complex_Vector;
|
| 835 |
|
|
Right : Real_Vector) return Complex_Matrix
|
| 836 |
|
|
renames Instantiations."*";
|
| 837 |
|
|
|
| 838 |
|
|
function "*"
|
| 839 |
|
|
(Left : Real_Vector;
|
| 840 |
|
|
Right : Complex_Matrix) return Complex_Vector
|
| 841 |
|
|
renames Instantiations."*";
|
| 842 |
|
|
|
| 843 |
|
|
function "*"
|
| 844 |
|
|
(Left : Complex_Vector;
|
| 845 |
|
|
Right : Real_Matrix) return Complex_Vector
|
| 846 |
|
|
renames Instantiations."*";
|
| 847 |
|
|
|
| 848 |
|
|
function "*"
|
| 849 |
|
|
(Left : Real_Matrix;
|
| 850 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 851 |
|
|
renames Instantiations."*";
|
| 852 |
|
|
|
| 853 |
|
|
function "*"
|
| 854 |
|
|
(Left : Complex_Matrix;
|
| 855 |
|
|
Right : Real_Vector) return Complex_Vector
|
| 856 |
|
|
renames Instantiations."*";
|
| 857 |
|
|
|
| 858 |
|
|
function "*"
|
| 859 |
|
|
(Left : Complex;
|
| 860 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 861 |
|
|
renames Instantiations."*";
|
| 862 |
|
|
|
| 863 |
|
|
function "*"
|
| 864 |
|
|
(Left : Complex_Matrix;
|
| 865 |
|
|
Right : Complex) return Complex_Matrix
|
| 866 |
|
|
renames Instantiations."*";
|
| 867 |
|
|
|
| 868 |
|
|
function "*"
|
| 869 |
|
|
(Left : Real'Base;
|
| 870 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 871 |
|
|
renames Instantiations."*";
|
| 872 |
|
|
|
| 873 |
|
|
function "*"
|
| 874 |
|
|
(Left : Complex_Matrix;
|
| 875 |
|
|
Right : Real'Base) return Complex_Matrix
|
| 876 |
|
|
renames Instantiations."*";
|
| 877 |
|
|
|
| 878 |
|
|
---------
|
| 879 |
|
|
-- "+" --
|
| 880 |
|
|
---------
|
| 881 |
|
|
|
| 882 |
|
|
function "+" (Right : Complex_Vector) return Complex_Vector
|
| 883 |
|
|
renames Instantiations."+";
|
| 884 |
|
|
|
| 885 |
|
|
function "+"
|
| 886 |
|
|
(Left : Complex_Vector;
|
| 887 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 888 |
|
|
renames Instantiations."+";
|
| 889 |
|
|
|
| 890 |
|
|
function "+"
|
| 891 |
|
|
(Left : Real_Vector;
|
| 892 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 893 |
|
|
renames Instantiations."+";
|
| 894 |
|
|
|
| 895 |
|
|
function "+"
|
| 896 |
|
|
(Left : Complex_Vector;
|
| 897 |
|
|
Right : Real_Vector) return Complex_Vector
|
| 898 |
|
|
renames Instantiations."+";
|
| 899 |
|
|
|
| 900 |
|
|
function "+" (Right : Complex_Matrix) return Complex_Matrix
|
| 901 |
|
|
renames Instantiations."+";
|
| 902 |
|
|
|
| 903 |
|
|
function "+"
|
| 904 |
|
|
(Left : Complex_Matrix;
|
| 905 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 906 |
|
|
renames Instantiations."+";
|
| 907 |
|
|
|
| 908 |
|
|
function "+"
|
| 909 |
|
|
(Left : Real_Matrix;
|
| 910 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 911 |
|
|
renames Instantiations."+";
|
| 912 |
|
|
|
| 913 |
|
|
function "+"
|
| 914 |
|
|
(Left : Complex_Matrix;
|
| 915 |
|
|
Right : Real_Matrix) return Complex_Matrix
|
| 916 |
|
|
renames Instantiations."+";
|
| 917 |
|
|
|
| 918 |
|
|
---------
|
| 919 |
|
|
-- "-" --
|
| 920 |
|
|
---------
|
| 921 |
|
|
|
| 922 |
|
|
function "-"
|
| 923 |
|
|
(Right : Complex_Vector) return Complex_Vector
|
| 924 |
|
|
renames Instantiations."-";
|
| 925 |
|
|
|
| 926 |
|
|
function "-"
|
| 927 |
|
|
(Left : Complex_Vector;
|
| 928 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 929 |
|
|
renames Instantiations."-";
|
| 930 |
|
|
|
| 931 |
|
|
function "-"
|
| 932 |
|
|
(Left : Real_Vector;
|
| 933 |
|
|
Right : Complex_Vector) return Complex_Vector
|
| 934 |
|
|
renames Instantiations."-";
|
| 935 |
|
|
|
| 936 |
|
|
function "-"
|
| 937 |
|
|
(Left : Complex_Vector;
|
| 938 |
|
|
Right : Real_Vector) return Complex_Vector
|
| 939 |
|
|
renames Instantiations."-";
|
| 940 |
|
|
|
| 941 |
|
|
function "-" (Right : Complex_Matrix) return Complex_Matrix
|
| 942 |
|
|
renames Instantiations."-";
|
| 943 |
|
|
|
| 944 |
|
|
function "-"
|
| 945 |
|
|
(Left : Complex_Matrix;
|
| 946 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 947 |
|
|
renames Instantiations."-";
|
| 948 |
|
|
|
| 949 |
|
|
function "-"
|
| 950 |
|
|
(Left : Real_Matrix;
|
| 951 |
|
|
Right : Complex_Matrix) return Complex_Matrix
|
| 952 |
|
|
renames Instantiations."-";
|
| 953 |
|
|
|
| 954 |
|
|
function "-"
|
| 955 |
|
|
(Left : Complex_Matrix;
|
| 956 |
|
|
Right : Real_Matrix) return Complex_Matrix
|
| 957 |
|
|
renames Instantiations."-";
|
| 958 |
|
|
|
| 959 |
|
|
---------
|
| 960 |
|
|
-- "/" --
|
| 961 |
|
|
---------
|
| 962 |
|
|
|
| 963 |
|
|
function "/"
|
| 964 |
|
|
(Left : Complex_Vector;
|
| 965 |
|
|
Right : Complex) return Complex_Vector
|
| 966 |
|
|
renames Instantiations."/";
|
| 967 |
|
|
|
| 968 |
|
|
function "/"
|
| 969 |
|
|
(Left : Complex_Vector;
|
| 970 |
|
|
Right : Real'Base) return Complex_Vector
|
| 971 |
|
|
renames Instantiations."/";
|
| 972 |
|
|
|
| 973 |
|
|
function "/"
|
| 974 |
|
|
(Left : Complex_Matrix;
|
| 975 |
|
|
Right : Complex) return Complex_Matrix
|
| 976 |
|
|
renames Instantiations."/";
|
| 977 |
|
|
|
| 978 |
|
|
function "/"
|
| 979 |
|
|
(Left : Complex_Matrix;
|
| 980 |
|
|
Right : Real'Base) return Complex_Matrix
|
| 981 |
|
|
renames Instantiations."/";
|
| 982 |
|
|
|
| 983 |
|
|
-----------
|
| 984 |
|
|
-- "abs" --
|
| 985 |
|
|
-----------
|
| 986 |
|
|
|
| 987 |
|
|
function "abs" (Right : Complex_Vector) return Complex is
|
| 988 |
|
|
begin
|
| 989 |
|
|
return (nrm2 (Right'Length, Right), 0.0);
|
| 990 |
|
|
end "abs";
|
| 991 |
|
|
|
| 992 |
|
|
--------------
|
| 993 |
|
|
-- Argument --
|
| 994 |
|
|
--------------
|
| 995 |
|
|
|
| 996 |
|
|
function Argument (X : Complex_Vector) return Real_Vector
|
| 997 |
|
|
renames Instantiations.Argument;
|
| 998 |
|
|
|
| 999 |
|
|
function Argument
|
| 1000 |
|
|
(X : Complex_Vector;
|
| 1001 |
|
|
Cycle : Real'Base) return Real_Vector
|
| 1002 |
|
|
renames Instantiations.Argument;
|
| 1003 |
|
|
|
| 1004 |
|
|
function Argument (X : Complex_Matrix) return Real_Matrix
|
| 1005 |
|
|
renames Instantiations.Argument;
|
| 1006 |
|
|
|
| 1007 |
|
|
function Argument
|
| 1008 |
|
|
(X : Complex_Matrix;
|
| 1009 |
|
|
Cycle : Real'Base) return Real_Matrix
|
| 1010 |
|
|
renames Instantiations.Argument;
|
| 1011 |
|
|
|
| 1012 |
|
|
----------------------------
|
| 1013 |
|
|
-- Compose_From_Cartesian --
|
| 1014 |
|
|
----------------------------
|
| 1015 |
|
|
|
| 1016 |
|
|
function Compose_From_Cartesian (Re : Real_Vector) return Complex_Vector
|
| 1017 |
|
|
renames Instantiations.Compose_From_Cartesian;
|
| 1018 |
|
|
|
| 1019 |
|
|
function Compose_From_Cartesian
|
| 1020 |
|
|
(Re : Real_Vector;
|
| 1021 |
|
|
Im : Real_Vector) return Complex_Vector
|
| 1022 |
|
|
renames Instantiations.Compose_From_Cartesian;
|
| 1023 |
|
|
|
| 1024 |
|
|
function Compose_From_Cartesian (Re : Real_Matrix) return Complex_Matrix
|
| 1025 |
|
|
renames Instantiations.Compose_From_Cartesian;
|
| 1026 |
|
|
|
| 1027 |
|
|
function Compose_From_Cartesian
|
| 1028 |
|
|
(Re : Real_Matrix;
|
| 1029 |
|
|
Im : Real_Matrix) return Complex_Matrix
|
| 1030 |
|
|
renames Instantiations.Compose_From_Cartesian;
|
| 1031 |
|
|
|
| 1032 |
|
|
------------------------
|
| 1033 |
|
|
-- Compose_From_Polar --
|
| 1034 |
|
|
------------------------
|
| 1035 |
|
|
|
| 1036 |
|
|
function Compose_From_Polar
|
| 1037 |
|
|
(Modulus : Real_Vector;
|
| 1038 |
|
|
Argument : Real_Vector) return Complex_Vector
|
| 1039 |
|
|
renames Instantiations.Compose_From_Polar;
|
| 1040 |
|
|
|
| 1041 |
|
|
function Compose_From_Polar
|
| 1042 |
|
|
(Modulus : Real_Vector;
|
| 1043 |
|
|
Argument : Real_Vector;
|
| 1044 |
|
|
Cycle : Real'Base) return Complex_Vector
|
| 1045 |
|
|
renames Instantiations.Compose_From_Polar;
|
| 1046 |
|
|
|
| 1047 |
|
|
function Compose_From_Polar
|
| 1048 |
|
|
(Modulus : Real_Matrix;
|
| 1049 |
|
|
Argument : Real_Matrix) return Complex_Matrix
|
| 1050 |
|
|
renames Instantiations.Compose_From_Polar;
|
| 1051 |
|
|
|
| 1052 |
|
|
function Compose_From_Polar
|
| 1053 |
|
|
(Modulus : Real_Matrix;
|
| 1054 |
|
|
Argument : Real_Matrix;
|
| 1055 |
|
|
Cycle : Real'Base) return Complex_Matrix
|
| 1056 |
|
|
renames Instantiations.Compose_From_Polar;
|
| 1057 |
|
|
|
| 1058 |
|
|
---------------
|
| 1059 |
|
|
-- Conjugate --
|
| 1060 |
|
|
---------------
|
| 1061 |
|
|
|
| 1062 |
|
|
function Conjugate (X : Complex_Vector) return Complex_Vector
|
| 1063 |
|
|
renames Instantiations.Conjugate;
|
| 1064 |
|
|
|
| 1065 |
|
|
function Conjugate (X : Complex_Matrix) return Complex_Matrix
|
| 1066 |
|
|
renames Instantiations.Conjugate;
|
| 1067 |
|
|
|
| 1068 |
|
|
-----------------
|
| 1069 |
|
|
-- Determinant --
|
| 1070 |
|
|
-----------------
|
| 1071 |
|
|
|
| 1072 |
|
|
function Determinant (A : Complex_Matrix) return Complex is
|
| 1073 |
|
|
N : constant Integer := Length (A);
|
| 1074 |
|
|
LU : Complex_Matrix (1 .. N, 1 .. N) := A;
|
| 1075 |
|
|
Piv : Integer_Vector (1 .. N);
|
| 1076 |
|
|
Info : aliased Integer := -1;
|
| 1077 |
|
|
Neg : Boolean;
|
| 1078 |
|
|
Det : Complex;
|
| 1079 |
|
|
|
| 1080 |
|
|
begin
|
| 1081 |
|
|
if N = 0 then
|
| 1082 |
|
|
return (0.0, 0.0);
|
| 1083 |
|
|
end if;
|
| 1084 |
|
|
|
| 1085 |
|
|
getrf (N, N, LU, N, Piv, Info'Access);
|
| 1086 |
|
|
|
| 1087 |
|
|
if Info /= 0 then
|
| 1088 |
|
|
raise Constraint_Error with "ill-conditioned matrix";
|
| 1089 |
|
|
end if;
|
| 1090 |
|
|
|
| 1091 |
|
|
Det := LU (1, 1);
|
| 1092 |
|
|
Neg := Piv (1) /= 1;
|
| 1093 |
|
|
|
| 1094 |
|
|
for J in 2 .. N loop
|
| 1095 |
|
|
Det := Det * LU (J, J);
|
| 1096 |
|
|
Neg := Neg xor (Piv (J) /= J);
|
| 1097 |
|
|
end loop;
|
| 1098 |
|
|
|
| 1099 |
|
|
if Neg then
|
| 1100 |
|
|
return -Det;
|
| 1101 |
|
|
|
| 1102 |
|
|
else
|
| 1103 |
|
|
return Det;
|
| 1104 |
|
|
end if;
|
| 1105 |
|
|
end Determinant;
|
| 1106 |
|
|
|
| 1107 |
|
|
-----------------
|
| 1108 |
|
|
-- Eigensystem --
|
| 1109 |
|
|
-----------------
|
| 1110 |
|
|
|
| 1111 |
|
|
procedure Eigensystem
|
| 1112 |
|
|
(A : Complex_Matrix;
|
| 1113 |
|
|
Values : out Real_Vector;
|
| 1114 |
|
|
Vectors : out Complex_Matrix)
|
| 1115 |
|
|
is
|
| 1116 |
|
|
Job_Z : aliased Character := 'V';
|
| 1117 |
|
|
Rng : aliased Character := 'A';
|
| 1118 |
|
|
Uplo : aliased Character := 'U';
|
| 1119 |
|
|
|
| 1120 |
|
|
N : constant Natural := Length (A);
|
| 1121 |
|
|
W : BLAS_Real_Vector (Values'Range);
|
| 1122 |
|
|
M : Integer;
|
| 1123 |
|
|
B : Complex_Matrix (1 .. N, 1 .. N);
|
| 1124 |
|
|
L_Work : Complex_Vector (1 .. 1);
|
| 1125 |
|
|
LR_Work : BLAS_Real_Vector (1 .. 1);
|
| 1126 |
|
|
LI_Work : Integer_Vector (1 .. 1);
|
| 1127 |
|
|
I_Supp_Z : Integer_Vector (1 .. 2 * N);
|
| 1128 |
|
|
Info : aliased Integer;
|
| 1129 |
|
|
|
| 1130 |
|
|
begin
|
| 1131 |
|
|
if Values'Length /= N then
|
| 1132 |
|
|
raise Constraint_Error with "wrong length for output vector";
|
| 1133 |
|
|
end if;
|
| 1134 |
|
|
|
| 1135 |
|
|
if Vectors'First (1) /= A'First (1)
|
| 1136 |
|
|
or else Vectors'Last (1) /= A'Last (1)
|
| 1137 |
|
|
or else Vectors'First (2) /= A'First (2)
|
| 1138 |
|
|
or else Vectors'Last (2) /= A'Last (2)
|
| 1139 |
|
|
then
|
| 1140 |
|
|
raise Constraint_Error with "wrong dimensions for output matrix";
|
| 1141 |
|
|
end if;
|
| 1142 |
|
|
|
| 1143 |
|
|
if N = 0 then
|
| 1144 |
|
|
return;
|
| 1145 |
|
|
end if;
|
| 1146 |
|
|
|
| 1147 |
|
|
-- Check for hermitian matrix ???
|
| 1148 |
|
|
-- Copy only required triangle ???
|
| 1149 |
|
|
|
| 1150 |
|
|
B := A;
|
| 1151 |
|
|
|
| 1152 |
|
|
-- Find size of work area
|
| 1153 |
|
|
|
| 1154 |
|
|
heevr
|
| 1155 |
|
|
(Job_Z'Access, Rng'Access, Uplo'Access, N, B, N,
|
| 1156 |
|
|
M => M,
|
| 1157 |
|
|
W => W,
|
| 1158 |
|
|
Z => Vectors,
|
| 1159 |
|
|
Ld_Z => N,
|
| 1160 |
|
|
I_Supp_Z => I_Supp_Z,
|
| 1161 |
|
|
Work => L_Work,
|
| 1162 |
|
|
L_Work => -1,
|
| 1163 |
|
|
R_Work => LR_Work,
|
| 1164 |
|
|
LR_Work => -1,
|
| 1165 |
|
|
I_Work => LI_Work,
|
| 1166 |
|
|
LI_Work => -1,
|
| 1167 |
|
|
Info => Info'Access);
|
| 1168 |
|
|
|
| 1169 |
|
|
if Info /= 0 then
|
| 1170 |
|
|
raise Constraint_Error;
|
| 1171 |
|
|
end if;
|
| 1172 |
|
|
|
| 1173 |
|
|
declare
|
| 1174 |
|
|
Work : Complex_Vector (1 .. Integer (L_Work (1).Re));
|
| 1175 |
|
|
R_Work : BLAS_Real_Vector (1 .. Integer (LR_Work (1)));
|
| 1176 |
|
|
I_Work : Integer_Vector (1 .. LI_Work (1));
|
| 1177 |
|
|
|
| 1178 |
|
|
begin
|
| 1179 |
|
|
heevr
|
| 1180 |
|
|
(Job_Z'Access, Rng'Access, Uplo'Access, N, B, N,
|
| 1181 |
|
|
M => M,
|
| 1182 |
|
|
W => W,
|
| 1183 |
|
|
Z => Vectors,
|
| 1184 |
|
|
Ld_Z => N,
|
| 1185 |
|
|
I_Supp_Z => I_Supp_Z,
|
| 1186 |
|
|
Work => Work,
|
| 1187 |
|
|
L_Work => Work'Length,
|
| 1188 |
|
|
R_Work => R_Work,
|
| 1189 |
|
|
LR_Work => LR_Work'Length,
|
| 1190 |
|
|
I_Work => I_Work,
|
| 1191 |
|
|
LI_Work => LI_Work'Length,
|
| 1192 |
|
|
Info => Info'Access);
|
| 1193 |
|
|
|
| 1194 |
|
|
if Info /= 0 then
|
| 1195 |
|
|
raise Constraint_Error with "inverting non-Hermitian matrix";
|
| 1196 |
|
|
end if;
|
| 1197 |
|
|
|
| 1198 |
|
|
for J in Values'Range loop
|
| 1199 |
|
|
Values (J) := W (J);
|
| 1200 |
|
|
end loop;
|
| 1201 |
|
|
end;
|
| 1202 |
|
|
end Eigensystem;
|
| 1203 |
|
|
|
| 1204 |
|
|
-----------------
|
| 1205 |
|
|
-- Eigenvalues --
|
| 1206 |
|
|
-----------------
|
| 1207 |
|
|
|
| 1208 |
|
|
procedure Eigenvalues
|
| 1209 |
|
|
(A : Complex_Matrix;
|
| 1210 |
|
|
Values : out Real_Vector)
|
| 1211 |
|
|
is
|
| 1212 |
|
|
Job_Z : aliased Character := 'N';
|
| 1213 |
|
|
Rng : aliased Character := 'A';
|
| 1214 |
|
|
Uplo : aliased Character := 'U';
|
| 1215 |
|
|
N : constant Natural := Length (A);
|
| 1216 |
|
|
B : Complex_Matrix (1 .. N, 1 .. N) := A;
|
| 1217 |
|
|
Z : Complex_Matrix (1 .. 1, 1 .. 1);
|
| 1218 |
|
|
W : BLAS_Real_Vector (Values'Range);
|
| 1219 |
|
|
L_Work : Complex_Vector (1 .. 1);
|
| 1220 |
|
|
LR_Work : BLAS_Real_Vector (1 .. 1);
|
| 1221 |
|
|
LI_Work : Integer_Vector (1 .. 1);
|
| 1222 |
|
|
I_Supp_Z : Integer_Vector (1 .. 2 * N);
|
| 1223 |
|
|
M : Integer;
|
| 1224 |
|
|
Info : aliased Integer;
|
| 1225 |
|
|
|
| 1226 |
|
|
begin
|
| 1227 |
|
|
if Values'Length /= N then
|
| 1228 |
|
|
raise Constraint_Error with "wrong length for output vector";
|
| 1229 |
|
|
end if;
|
| 1230 |
|
|
|
| 1231 |
|
|
if N = 0 then
|
| 1232 |
|
|
return;
|
| 1233 |
|
|
end if;
|
| 1234 |
|
|
|
| 1235 |
|
|
-- Check for hermitian matrix ???
|
| 1236 |
|
|
|
| 1237 |
|
|
-- Find size of work area
|
| 1238 |
|
|
|
| 1239 |
|
|
heevr (Job_Z'Access, Rng'Access, Uplo'Access, N, B, N,
|
| 1240 |
|
|
M => M,
|
| 1241 |
|
|
W => W,
|
| 1242 |
|
|
Z => Z,
|
| 1243 |
|
|
Ld_Z => 1,
|
| 1244 |
|
|
I_Supp_Z => I_Supp_Z,
|
| 1245 |
|
|
Work => L_Work, L_Work => -1,
|
| 1246 |
|
|
R_Work => LR_Work, LR_Work => -1,
|
| 1247 |
|
|
I_Work => LI_Work, LI_Work => -1,
|
| 1248 |
|
|
Info => Info'Access);
|
| 1249 |
|
|
|
| 1250 |
|
|
if Info /= 0 then
|
| 1251 |
|
|
raise Constraint_Error;
|
| 1252 |
|
|
end if;
|
| 1253 |
|
|
|
| 1254 |
|
|
declare
|
| 1255 |
|
|
Work : Complex_Vector (1 .. Integer (L_Work (1).Re));
|
| 1256 |
|
|
R_Work : BLAS_Real_Vector (1 .. Integer (LR_Work (1)));
|
| 1257 |
|
|
I_Work : Integer_Vector (1 .. LI_Work (1));
|
| 1258 |
|
|
begin
|
| 1259 |
|
|
heevr (Job_Z'Access, Rng'Access, Uplo'Access, N, B, N,
|
| 1260 |
|
|
M => M,
|
| 1261 |
|
|
W => W,
|
| 1262 |
|
|
Z => Z,
|
| 1263 |
|
|
Ld_Z => 1,
|
| 1264 |
|
|
I_Supp_Z => I_Supp_Z,
|
| 1265 |
|
|
Work => Work, L_Work => Work'Length,
|
| 1266 |
|
|
R_Work => R_Work, LR_Work => R_Work'Length,
|
| 1267 |
|
|
I_Work => I_Work, LI_Work => I_Work'Length,
|
| 1268 |
|
|
Info => Info'Access);
|
| 1269 |
|
|
|
| 1270 |
|
|
if Info /= 0 then
|
| 1271 |
|
|
raise Constraint_Error with "inverting singular matrix";
|
| 1272 |
|
|
end if;
|
| 1273 |
|
|
|
| 1274 |
|
|
for J in Values'Range loop
|
| 1275 |
|
|
Values (J) := W (J);
|
| 1276 |
|
|
end loop;
|
| 1277 |
|
|
end;
|
| 1278 |
|
|
end Eigenvalues;
|
| 1279 |
|
|
|
| 1280 |
|
|
function Eigenvalues (A : Complex_Matrix) return Real_Vector is
|
| 1281 |
|
|
R : Real_Vector (A'Range (1));
|
| 1282 |
|
|
begin
|
| 1283 |
|
|
Eigenvalues (A, R);
|
| 1284 |
|
|
return R;
|
| 1285 |
|
|
end Eigenvalues;
|
| 1286 |
|
|
|
| 1287 |
|
|
--------
|
| 1288 |
|
|
-- Im --
|
| 1289 |
|
|
--------
|
| 1290 |
|
|
|
| 1291 |
|
|
function Im (X : Complex_Vector) return Real_Vector
|
| 1292 |
|
|
renames Instantiations.Im;
|
| 1293 |
|
|
|
| 1294 |
|
|
function Im (X : Complex_Matrix) return Real_Matrix
|
| 1295 |
|
|
renames Instantiations.Im;
|
| 1296 |
|
|
|
| 1297 |
|
|
-------------
|
| 1298 |
|
|
-- Inverse --
|
| 1299 |
|
|
-------------
|
| 1300 |
|
|
|
| 1301 |
|
|
procedure Inverse (A : Complex_Matrix; R : out Complex_Matrix) is
|
| 1302 |
|
|
N : constant Integer := Length (A);
|
| 1303 |
|
|
Piv : Integer_Vector (1 .. N);
|
| 1304 |
|
|
L_Work : Complex_Vector (1 .. 1);
|
| 1305 |
|
|
Info : aliased Integer := -1;
|
| 1306 |
|
|
|
| 1307 |
|
|
begin
|
| 1308 |
|
|
-- All computations are done using column-major order, but this works
|
| 1309 |
|
|
-- out fine, because Transpose (Inverse (Transpose (A))) = Inverse (A).
|
| 1310 |
|
|
|
| 1311 |
|
|
R := A;
|
| 1312 |
|
|
|
| 1313 |
|
|
-- Compute LU decomposition
|
| 1314 |
|
|
|
| 1315 |
|
|
getrf (M => N,
|
| 1316 |
|
|
N => N,
|
| 1317 |
|
|
A => R,
|
| 1318 |
|
|
Ld_A => N,
|
| 1319 |
|
|
I_Piv => Piv,
|
| 1320 |
|
|
Info => Info'Access);
|
| 1321 |
|
|
|
| 1322 |
|
|
if Info /= 0 then
|
| 1323 |
|
|
raise Constraint_Error with "inverting singular matrix";
|
| 1324 |
|
|
end if;
|
| 1325 |
|
|
|
| 1326 |
|
|
-- Determine size of work area
|
| 1327 |
|
|
|
| 1328 |
|
|
getri (N => N,
|
| 1329 |
|
|
A => R,
|
| 1330 |
|
|
Ld_A => N,
|
| 1331 |
|
|
I_Piv => Piv,
|
| 1332 |
|
|
Work => L_Work,
|
| 1333 |
|
|
L_Work => -1,
|
| 1334 |
|
|
Info => Info'Access);
|
| 1335 |
|
|
|
| 1336 |
|
|
if Info /= 0 then
|
| 1337 |
|
|
raise Constraint_Error;
|
| 1338 |
|
|
end if;
|
| 1339 |
|
|
|
| 1340 |
|
|
declare
|
| 1341 |
|
|
Work : Complex_Vector (1 .. Integer (L_Work (1).Re));
|
| 1342 |
|
|
|
| 1343 |
|
|
begin
|
| 1344 |
|
|
-- Compute inverse from LU decomposition
|
| 1345 |
|
|
|
| 1346 |
|
|
getri (N => N,
|
| 1347 |
|
|
A => R,
|
| 1348 |
|
|
Ld_A => N,
|
| 1349 |
|
|
I_Piv => Piv,
|
| 1350 |
|
|
Work => Work,
|
| 1351 |
|
|
L_Work => Work'Length,
|
| 1352 |
|
|
Info => Info'Access);
|
| 1353 |
|
|
|
| 1354 |
|
|
if Info /= 0 then
|
| 1355 |
|
|
raise Constraint_Error with "inverting singular matrix";
|
| 1356 |
|
|
end if;
|
| 1357 |
|
|
|
| 1358 |
|
|
-- ??? Should iterate with gerfs, based on implementation advice
|
| 1359 |
|
|
end;
|
| 1360 |
|
|
end Inverse;
|
| 1361 |
|
|
|
| 1362 |
|
|
function Inverse (A : Complex_Matrix) return Complex_Matrix is
|
| 1363 |
|
|
R : Complex_Matrix (A'Range (2), A'Range (1));
|
| 1364 |
|
|
begin
|
| 1365 |
|
|
Inverse (A, R);
|
| 1366 |
|
|
return R;
|
| 1367 |
|
|
end Inverse;
|
| 1368 |
|
|
|
| 1369 |
|
|
-------------
|
| 1370 |
|
|
-- Modulus --
|
| 1371 |
|
|
-------------
|
| 1372 |
|
|
|
| 1373 |
|
|
function Modulus (X : Complex_Vector) return Real_Vector
|
| 1374 |
|
|
renames Instantiations.Modulus;
|
| 1375 |
|
|
|
| 1376 |
|
|
function Modulus (X : Complex_Matrix) return Real_Matrix
|
| 1377 |
|
|
renames Instantiations.Modulus;
|
| 1378 |
|
|
|
| 1379 |
|
|
--------
|
| 1380 |
|
|
-- Re --
|
| 1381 |
|
|
--------
|
| 1382 |
|
|
|
| 1383 |
|
|
function Re (X : Complex_Vector) return Real_Vector
|
| 1384 |
|
|
renames Instantiations.Re;
|
| 1385 |
|
|
|
| 1386 |
|
|
function Re (X : Complex_Matrix) return Real_Matrix
|
| 1387 |
|
|
renames Instantiations.Re;
|
| 1388 |
|
|
|
| 1389 |
|
|
------------
|
| 1390 |
|
|
-- Set_Im --
|
| 1391 |
|
|
------------
|
| 1392 |
|
|
|
| 1393 |
|
|
procedure Set_Im
|
| 1394 |
|
|
(X : in out Complex_Matrix;
|
| 1395 |
|
|
Im : Real_Matrix)
|
| 1396 |
|
|
renames Instantiations.Set_Im;
|
| 1397 |
|
|
|
| 1398 |
|
|
procedure Set_Im
|
| 1399 |
|
|
(X : in out Complex_Vector;
|
| 1400 |
|
|
Im : Real_Vector)
|
| 1401 |
|
|
renames Instantiations.Set_Im;
|
| 1402 |
|
|
|
| 1403 |
|
|
------------
|
| 1404 |
|
|
-- Set_Re --
|
| 1405 |
|
|
------------
|
| 1406 |
|
|
|
| 1407 |
|
|
procedure Set_Re
|
| 1408 |
|
|
(X : in out Complex_Matrix;
|
| 1409 |
|
|
Re : Real_Matrix)
|
| 1410 |
|
|
renames Instantiations.Set_Re;
|
| 1411 |
|
|
|
| 1412 |
|
|
procedure Set_Re
|
| 1413 |
|
|
(X : in out Complex_Vector;
|
| 1414 |
|
|
Re : Real_Vector)
|
| 1415 |
|
|
renames Instantiations.Set_Re;
|
| 1416 |
|
|
|
| 1417 |
|
|
-----------
|
| 1418 |
|
|
-- Solve --
|
| 1419 |
|
|
-----------
|
| 1420 |
|
|
|
| 1421 |
|
|
procedure Solve
|
| 1422 |
|
|
(A : Complex_Matrix;
|
| 1423 |
|
|
X : Complex_Vector;
|
| 1424 |
|
|
B : out Complex_Vector)
|
| 1425 |
|
|
is
|
| 1426 |
|
|
begin
|
| 1427 |
|
|
if Length (A) /= X'Length then
|
| 1428 |
|
|
raise Constraint_Error with
|
| 1429 |
|
|
"incompatible matrix and vector dimensions";
|
| 1430 |
|
|
end if;
|
| 1431 |
|
|
|
| 1432 |
|
|
-- ??? Should solve directly, is faster and more accurate
|
| 1433 |
|
|
|
| 1434 |
|
|
B := Inverse (A) * X;
|
| 1435 |
|
|
end Solve;
|
| 1436 |
|
|
|
| 1437 |
|
|
procedure Solve
|
| 1438 |
|
|
(A : Complex_Matrix;
|
| 1439 |
|
|
X : Complex_Matrix;
|
| 1440 |
|
|
B : out Complex_Matrix)
|
| 1441 |
|
|
is
|
| 1442 |
|
|
begin
|
| 1443 |
|
|
if Length (A) /= X'Length (1) then
|
| 1444 |
|
|
raise Constraint_Error with "incompatible matrix dimensions";
|
| 1445 |
|
|
end if;
|
| 1446 |
|
|
|
| 1447 |
|
|
-- ??? Should solve directly, is faster and more accurate
|
| 1448 |
|
|
|
| 1449 |
|
|
B := Inverse (A) * X;
|
| 1450 |
|
|
end Solve;
|
| 1451 |
|
|
|
| 1452 |
|
|
function Solve
|
| 1453 |
|
|
(A : Complex_Matrix;
|
| 1454 |
|
|
X : Complex_Vector) return Complex_Vector
|
| 1455 |
|
|
is
|
| 1456 |
|
|
B : Complex_Vector (A'Range (2));
|
| 1457 |
|
|
begin
|
| 1458 |
|
|
Solve (A, X, B);
|
| 1459 |
|
|
return B;
|
| 1460 |
|
|
end Solve;
|
| 1461 |
|
|
|
| 1462 |
|
|
function Solve (A, X : Complex_Matrix) return Complex_Matrix is
|
| 1463 |
|
|
B : Complex_Matrix (A'Range (2), X'Range (2));
|
| 1464 |
|
|
begin
|
| 1465 |
|
|
Solve (A, X, B);
|
| 1466 |
|
|
return B;
|
| 1467 |
|
|
end Solve;
|
| 1468 |
|
|
|
| 1469 |
|
|
---------------
|
| 1470 |
|
|
-- Transpose --
|
| 1471 |
|
|
---------------
|
| 1472 |
|
|
|
| 1473 |
|
|
function Transpose
|
| 1474 |
|
|
(X : Complex_Matrix) return Complex_Matrix
|
| 1475 |
|
|
is
|
| 1476 |
|
|
R : Complex_Matrix (X'Range (2), X'Range (1));
|
| 1477 |
|
|
begin
|
| 1478 |
|
|
Transpose (X, R);
|
| 1479 |
|
|
return R;
|
| 1480 |
|
|
end Transpose;
|
| 1481 |
|
|
|
| 1482 |
|
|
-----------------
|
| 1483 |
|
|
-- Unit_Matrix --
|
| 1484 |
|
|
-----------------
|
| 1485 |
|
|
|
| 1486 |
|
|
function Unit_Matrix
|
| 1487 |
|
|
(Order : Positive;
|
| 1488 |
|
|
First_1 : Integer := 1;
|
| 1489 |
|
|
First_2 : Integer := 1) return Complex_Matrix
|
| 1490 |
|
|
renames Instantiations.Unit_Matrix;
|
| 1491 |
|
|
|
| 1492 |
|
|
-----------------
|
| 1493 |
|
|
-- Unit_Vector --
|
| 1494 |
|
|
-----------------
|
| 1495 |
|
|
|
| 1496 |
|
|
function Unit_Vector
|
| 1497 |
|
|
(Index : Integer;
|
| 1498 |
|
|
Order : Positive;
|
| 1499 |
|
|
First : Integer := 1) return Complex_Vector
|
| 1500 |
|
|
renames Instantiations.Unit_Vector;
|
| 1501 |
|
|
|
| 1502 |
|
|
end Ada.Numerics.Generic_Complex_Arrays;
|
