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   1 ------------------------------------------------------------------------------
   2 --                                                                          --
   3 --                         GNAT RUN-TIME COMPONENTS                         --
   4 --                                                                          --
   5 --                   ADA.NUMERICS.GENERIC_COMPLEX_ARRAYS                    --
   6 --                                                                          --
   7 --                                 S p e c                                  --
   8 --                                                                          --
   9 -- This specification is derived from the Ada Reference Manual for use with --
  10 -- GNAT.  In accordance with the copyright of that document, you can freely --
  11 -- copy and modify this specification,  provided that if you redistribute a --
  12 -- modified version,  any changes that you have made are clearly indicated. --
  13 --                                                                          --
  14 ------------------------------------------------------------------------------
  15
  16 with Ada.Numerics.Generic_Real_Arrays, Ada.Numerics.Generic_Complex_Types;
  17
  18 generic
  19    with package Real_Arrays is new Ada.Numerics.Generic_Real_Arrays (<>);
  20    use Real_Arrays;
  21    with package Complex_Types is new Ada.Numerics.Generic_Complex_Types (Real);
  22    use Complex_Types;
  23 package Ada.Numerics.Generic_Complex_Arrays is
  24    pragma Pure (Generic_Complex_Arrays);
  25
  26    --  Types
  27
  28    type Complex_Vector is array (Integer range <>) of Complex;
  29    type Complex_Matrix is
  30      array (Integer range <>, Integer range <>) of Complex;
  31
  32    --  Subprograms for Complex_Vector types
  33    --  Complex_Vector selection, conversion and composition operations
  34
  35    function Re (X : Complex_Vector) return Real_Vector;
  36    function Im (X : Complex_Vector) return Real_Vector;
  37
  38    procedure Set_Re (X : in out Complex_Vector; Re : Real_Vector);
  39    procedure Set_Im (X : in out Complex_Vector; Im : Real_Vector);
  40
  41    function Compose_From_Cartesian
  42      (Re : Real_Vector) return Complex_Vector;
  43    function Compose_From_Cartesian
  44      (Re, Im : Real_Vector) return Complex_Vector;
  45
  46    function Modulus (X : Complex_Vector) return Real_Vector;
  47    function "abs" (Right : Complex_Vector) return Real_Vector renames Modulus;
  48    function Argument (X : Complex_Vector) return Real_Vector;
  49
  50    function Argument
  51      (X     : Complex_Vector;
  52       Cycle : Real'Base) return Real_Vector;
  53
  54    function Compose_From_Polar
  55      (Modulus, Argument : Real_Vector) return Complex_Vector;
  56
  57    function Compose_From_Polar
  58      (Modulus, Argument : Real_Vector;
  59       Cycle             : Real'Base) return Complex_Vector;
  60
  61    --  Complex_Vector arithmetic operations
  62
  63    function "+" (Right : Complex_Vector) return Complex_Vector;
  64    function "-" (Right : Complex_Vector) return Complex_Vector;
  65    function Conjugate (X : Complex_Vector) return Complex_Vector;
  66    function "+" (Left, Right : Complex_Vector) return Complex_Vector;
  67    function "-" (Left, Right : Complex_Vector) return Complex_Vector;
  68    function "*" (Left, Right : Complex_Vector) return Complex;
  69    function "abs" (Right : Complex_Vector) return Complex;
  70
  71    --  Mixed Real_Vector and Complex_Vector arithmetic operations
  72
  73    function "+"
  74      (Left  : Real_Vector;
  75       Right : Complex_Vector) return Complex_Vector;
  76
  77    function "+"
  78      (Left  : Complex_Vector;
  79       Right : Real_Vector) return Complex_Vector;
  80
  81    function "-"
  82      (Left  : Real_Vector;
  83       Right : Complex_Vector) return Complex_Vector;
  84
  85    function "-"
  86      (Left  : Complex_Vector;
  87       Right : Real_Vector) return Complex_Vector;
  88
  89    function "*" (Left : Real_Vector; Right : Complex_Vector) return Complex;
  90    function "*" (Left : Complex_Vector; Right : Real_Vector) return Complex;
  91
  92    --  Complex_Vector scaling operations
  93
  94    function "*"
  95      (Left  : Complex;
  96       Right : Complex_Vector) return Complex_Vector;
  97
  98    function "*"
  99      (Left  : Complex_Vector;
 100       Right : Complex) return Complex_Vector;
 101
 102    function "/"
 103      (Left  : Complex_Vector;
 104       Right : Complex) return Complex_Vector;
 105
 106    function "*"
 107      (Left  : Real'Base;
 108       Right : Complex_Vector) return Complex_Vector;
 109
 110    function "*"
 111      (Left  : Complex_Vector;
 112       Right : Real'Base) return Complex_Vector;
 113
 114    function "/"
 115      (Left  : Complex_Vector;
 116       Right : Real'Base) return Complex_Vector;
 117
 118    --  Other Complex_Vector operations
 119
 120    function Unit_Vector
 121      (Index : Integer;
 122       Order : Positive;
 123       First : Integer := 1) return Complex_Vector;
 124
 125    --  Subprograms for Complex_Matrix types
 126
 127    --  Complex_Matrix selection, conversion and composition operations
 128
 129    function Re (X : Complex_Matrix) return Real_Matrix;
 130    function Im (X : Complex_Matrix) return Real_Matrix;
 131
 132    procedure Set_Re (X : in out Complex_Matrix; Re : Real_Matrix);
 133    procedure Set_Im (X : in out Complex_Matrix; Im : Real_Matrix);
 134
 135    function Compose_From_Cartesian (Re : Real_Matrix) return Complex_Matrix;
 136
 137    function Compose_From_Cartesian
 138      (Re, Im : Real_Matrix) return  Complex_Matrix;
 139
 140    function Modulus (X : Complex_Matrix) return Real_Matrix;
 141    function "abs" (Right : Complex_Matrix) return Real_Matrix renames Modulus;
 142
 143    function Argument (X : Complex_Matrix) return Real_Matrix;
 144
 145    function Argument
 146      (X     : Complex_Matrix;
 147       Cycle : Real'Base) return Real_Matrix;
 148
 149    function Compose_From_Polar
 150      (Modulus, Argument : Real_Matrix) return Complex_Matrix;
 151
 152    function Compose_From_Polar
 153      (Modulus  : Real_Matrix;
 154       Argument : Real_Matrix;
 155       Cycle    : Real'Base) return Complex_Matrix;
 156
 157    --  Complex_Matrix arithmetic operations
 158
 159    function "+" (Right : Complex_Matrix) return Complex_Matrix;
 160    function "-" (Right : Complex_Matrix) return Complex_Matrix;
 161
 162    function Conjugate (X : Complex_Matrix) return Complex_Matrix;
 163    function Transpose (X : Complex_Matrix) return Complex_Matrix;
 164
 165    function "+" (Left, Right : Complex_Matrix) return Complex_Matrix;
 166    function "-" (Left, Right : Complex_Matrix) return Complex_Matrix;
 167    function "*" (Left, Right : Complex_Matrix) return Complex_Matrix;
 168    function "*" (Left, Right : Complex_Vector) return Complex_Matrix;
 169
 170    function "*"
 171      (Left  : Complex_Vector;
 172       Right : Complex_Matrix) return Complex_Vector;
 173
 174    function "*"
 175      (Left  : Complex_Matrix;
 176       Right : Complex_Vector) return Complex_Vector;
 177
 178    --  Mixed Real_Matrix and Complex_Matrix arithmetic operations
 179
 180    function "+"
 181      (Left  : Real_Matrix;
 182       Right : Complex_Matrix) return Complex_Matrix;
 183
 184    function "+"
 185      (Left  : Complex_Matrix;
 186       Right : Real_Matrix) return Complex_Matrix;
 187
 188    function "-"
 189      (Left  : Real_Matrix;
 190       Right : Complex_Matrix) return Complex_Matrix;
 191
 192    function "-"
 193      (Left  : Complex_Matrix;
 194       Right : Real_Matrix) return Complex_Matrix;
 195
 196    function "*"
 197      (Left  : Real_Matrix;
 198       Right : Complex_Matrix) return Complex_Matrix;
 199
 200    function "*"
 201      (Left  : Complex_Matrix;
 202       Right : Real_Matrix) return Complex_Matrix;
 203
 204    function "*"
 205      (Left  : Real_Vector;
 206       Right : Complex_Vector) return Complex_Matrix;
 207
 208    function "*"
 209      (Left  : Complex_Vector;
 210       Right : Real_Vector) return Complex_Matrix;
 211
 212    function "*"
 213      (Left  : Real_Vector;
 214       Right : Complex_Matrix) return Complex_Vector;
 215
 216    function "*"
 217      (Left  : Complex_Vector;
 218       Right : Real_Matrix) return Complex_Vector;
 219
 220    function "*"
 221      (Left  : Real_Matrix;
 222       Right : Complex_Vector) return Complex_Vector;
 223
 224    function "*"
 225      (Left  : Complex_Matrix;
 226       Right : Real_Vector) return Complex_Vector;
 227
 228    --  Complex_Matrix scaling operations
 229
 230    function "*"
 231      (Left  : Complex;
 232       Right : Complex_Matrix) return  Complex_Matrix;
 233
 234    function "*"
 235      (Left  : Complex_Matrix;
 236       Right : Complex) return Complex_Matrix;
 237
 238    function "/"
 239      (Left  : Complex_Matrix;
 240       Right : Complex) return Complex_Matrix;
 241
 242    function "*"
 243      (Left  : Real'Base;
 244       Right : Complex_Matrix) return Complex_Matrix;
 245
 246    function "*"
 247      (Left  : Complex_Matrix;
 248       Right : Real'Base) return Complex_Matrix;
 249
 250    function "/"
 251      (Left  : Complex_Matrix;
 252       Right : Real'Base) return Complex_Matrix;
 253
 254    --  Complex_Matrix inversion and related operations
 255
 256    function Solve
 257      (A : Complex_Matrix;
 258       X : Complex_Vector) return Complex_Vector;
 259
 260    function Solve (A, X : Complex_Matrix) return Complex_Matrix;
 261
 262    function Inverse (A : Complex_Matrix) return Complex_Matrix;
 263
 264    function Determinant (A : Complex_Matrix) return Complex;
 265
 266    --  Eigenvalues and vectors of a Hermitian matrix
 267
 268    function Eigenvalues (A : Complex_Matrix) return Real_Vector;
 269
 270    procedure Eigensystem
 271      (A       : Complex_Matrix;
 272       Values  : out Real_Vector;
 273       Vectors : out Complex_Matrix);
 274
 275    --  Other Complex_Matrix operations
 276
 277    function Unit_Matrix
 278      (Order            : Positive;
 279       First_1, First_2 : Integer := 1) return Complex_Matrix;
 280
 281 end Ada.Numerics.Generic_Complex_Arrays;