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   1 ------------------------------------------------------------------------------
   2 --                                                                          --
   3 --                         GNAT RUN-TIME COMPONENTS                         --
   4 --                                                                          --
   5 --                     ADA.NUMERICS.GENERIC_REAL_ARRAYS                     --
   6 --                                                                          --
   7 --                                 S p e c                                  --
   8 --                                                                          --
   9 --            Copyright (C) 2009, Free Software Foundation, Inc.            --
  10 --                                                                          --
  11 -- This specification is derived from the Ada Reference Manual for use with --
  12 -- GNAT. The copyright notice above, and the license provisions that follow --
  13 -- apply solely to the  contents of the part following the private keyword. --
  14 --                                                                          --
  15 -- GNAT is free software;  you can  redistribute it  and/or modify it under --
  16 -- terms of the  GNU General Public License as published  by the Free Soft- --
  17 -- ware  Foundation;  either version 3,  or (at your option) any later ver- --
  18 -- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
  19 -- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
  20 -- or FITNESS FOR A PARTICULAR PURPOSE.                                     --
  21 --                                                                          --
  22 -- As a special exception under Section 7 of GPL version 3, you are granted --
  23 -- additional permissions described in the GCC Runtime Library Exception,   --
  24 -- version 3.1, as published by the Free Software Foundation.               --
  25 --                                                                          --
  26 -- You should have received a copy of the GNU General Public License and    --
  27 -- a copy of the GCC Runtime Library Exception along with this program;     --
  28 -- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --
  29 -- <http://www.gnu.org/licenses/>.                                          --
  30 --                                                                          --
  31 -- GNAT was originally developed  by the GNAT team at  New York University. --
  32 -- Extensive contributions were provided by Ada Core Technologies Inc.      --
  33 --                                                                          --
  34 ------------------------------------------------------------------------------
  35
  36 generic
  37    type Real is digits <>;
  38 package Ada.Numerics.Generic_Real_Arrays is
  39    pragma Pure (Generic_Real_Arrays);
  40
  41    --  Types
  42
  43    type Real_Vector is array (Integer range <>) of Real'Base;
  44    type Real_Matrix is array (Integer range <>, Integer range <>) of Real'Base;
  45
  46    --  Subprograms for Real_Vector types
  47
  48    --  Real_Vector arithmetic operations
  49
  50    function "+"   (Right : Real_Vector)       return Real_Vector;
  51    function "-"   (Right : Real_Vector)       return Real_Vector;
  52    function "abs" (Right : Real_Vector)       return Real_Vector;
  53
  54    function "+"   (Left, Right : Real_Vector) return Real_Vector;
  55    function "-"   (Left, Right : Real_Vector) return Real_Vector;
  56
  57    function "*"   (Left, Right : Real_Vector) return Real'Base;
  58
  59    function "abs" (Right : Real_Vector)       return Real'Base;
  60
  61    --  Real_Vector scaling operations
  62
  63    function "*" (Left : Real'Base;   Right : Real_Vector) return Real_Vector;
  64    function "*" (Left : Real_Vector; Right : Real'Base)   return Real_Vector;
  65    function "/" (Left : Real_Vector; Right : Real'Base)   return Real_Vector;
  66
  67    --  Other Real_Vector operations
  68
  69    function Unit_Vector
  70      (Index : Integer;
  71       Order : Positive;
  72       First : Integer := 1) return Real_Vector;
  73
  74    --  Subprograms for Real_Matrix types
  75
  76    --  Real_Matrix arithmetic operations
  77
  78    function "+"       (Right : Real_Matrix) return Real_Matrix;
  79    function "-"       (Right : Real_Matrix) return Real_Matrix;
  80    function "abs"     (Right : Real_Matrix) return Real_Matrix;
  81    function Transpose (X     : Real_Matrix) return Real_Matrix;
  82
  83    function "+" (Left, Right : Real_Matrix) return Real_Matrix;
  84    function "-" (Left, Right : Real_Matrix) return Real_Matrix;
  85    function "*" (Left, Right : Real_Matrix) return Real_Matrix;
  86
  87    function "*" (Left, Right : Real_Vector) return Real_Matrix;
  88
  89    function "*" (Left : Real_Vector; Right : Real_Matrix) return Real_Vector;
  90    function "*" (Left : Real_Matrix; Right : Real_Vector) return Real_Vector;
  91
  92    --  Real_Matrix scaling operations
  93
  94    function "*" (Left : Real'Base;   Right : Real_Matrix) return Real_Matrix;
  95    function "*" (Left : Real_Matrix; Right : Real'Base)   return Real_Matrix;
  96    function "/" (Left : Real_Matrix; Right : Real'Base)   return Real_Matrix;
  97
  98    --  Real_Matrix inversion and related operations
  99
 100    function Solve (A : Real_Matrix; X : Real_Vector) return Real_Vector;
 101    function Solve (A, X : Real_Matrix) return Real_Matrix;
 102    function Inverse (A : Real_Matrix) return Real_Matrix;
 103    function Determinant (A : Real_Matrix) return Real'Base;
 104
 105    --  Eigenvalues and vectors of a real symmetric matrix
 106
 107    function Eigenvalues (A : Real_Matrix) return Real_Vector;
 108
 109    procedure Eigensystem
 110      (A       : Real_Matrix;
 111       Values  : out Real_Vector;
 112       Vectors : out Real_Matrix);
 113
 114    --  Other Real_Matrix operations
 115
 116    function Unit_Matrix
 117      (Order   : Positive;
 118       First_1 : Integer := 1;
 119       First_2 : Integer := 1) return Real_Matrix;
 120
 121 private
 122    --  The following operations are either relatively simple compared to the
 123    --  expense of returning unconstrained arrays, or are just function wrappers
 124    --  calling procedures implementing the actual operation. By having the
 125    --  front end always inline these, the expense of the unconstrained returns
 126    --  can be avoided.
 127
 128    pragma Inline_Always ("+");
 129    pragma Inline_Always ("-");
 130    pragma Inline_Always ("*");
 131    pragma Inline_Always ("/");
 132    pragma Inline_Always ("abs");
 133    pragma Inline_Always (Eigenvalues);
 134    pragma Inline_Always (Inverse);
 135    pragma Inline_Always (Solve);
 136    pragma Inline_Always (Transpose);
 137    pragma Inline_Always (Unit_Matrix);
 138    pragma Inline_Always (Unit_Vector);
 139 end Ada.Numerics.Generic_Real_Arrays;