-- generic_complex_linear_equations.ads
--
--
--   package YOUR_NAME is new GENERIC_COMPLEX_LINEAR_EQUATIONS
--     ( REAL,  ) ;
--
--   all the rest are defaults

with Ada.Numerics.Generic_Complex_Types;
with Array_Exceptions;
with Integer_Arrays; use Integer_Arrays;
with Generic_Real_Arrays;
with Generic_Complex_Arrays;

generic
  type REAL is digits <> ;
  with package Real_Arrays is new Generic_Real_Arrays(REAL);
  with package Complex_Types is new Ada.Numerics.Generic_Complex_Types(REAL);
  with package Complex_Arrays is new Generic_Complex_Arrays(REAL,
                                         Complex_Types, Real_Arrays);

package GENERIC_COMPLEX_LINEAR_EQUATIONS is

  use Real_Arrays;
  use Complex_Types;
  use Complex_Arrays;

  function LINEAR_EQUATIONS ( A : COMPLEX_MATRIX ;
                              Y : COMPLEX_VECTOR ) return COMPLEX_VECTOR ;

  function CROUT_SOLUTION ( A : COMPLEX_MATRIX ;
                            Y : COMPLEX_VECTOR ) return COMPLEX_VECTOR ;

  function DETERMINANT ( A : COMPLEX_MATRIX ) return COMPLEX ;

  function INVERSE ( A : COMPLEX_MATRIX ) return COMPLEX_MATRIX ;

  ARRAY_INDEX_ERROR : exception renames ARRAY_EXCEPTIONS.ARRAY_INDEX_ERROR;

  --
  --  function LINEAR_EQUATIONS ( A : COMPLEX_MATRIX ;
  --                              Y : COMPLEX_VECTOR ) return COMPLEX_VECTOR ;
  --
  --  function CROUT_SOLUTION ( A : COMPLEX_MATRIX ;
  --                            Y : COMPLEX_VECTOR ) return COMPLEX_VECTOR ;
  --
  --      PURPOSE : SOLVE THE LINEAR SYSTEM OF EQUATIONS WITH COMPLEX
  --                COEFFICIENTS   [A] * |X| = |Y|
  --
  --      INPUT  : THE COMPLEX MATRIX  A
  --               THE COMPLEX VECTOR  Y
  --
  --      OUTPUT : THE COMPLEX VECTOR  X
  --
  --      METHOD1 : GUASS-JORDAN ELIMINATION USING MAXIMUM ELEMENT
  --                FOR PIVOT.
  --      METHOD2 : CROUT REDUCTION USING MAXIMIM ELEMENT FOR
  --                DIAGONAL
  --
  --      USAGE  :     X := LINEAR_EQUATIONS ( A , Y ) ;
  --                   X := CROUT_SOLUTION ( A , Y ) ;
  --
  --      EXCEPTION : ARRAY_INDEX_ERROR  RASIED IF RESULT CAN NOT BE COMPUTED
  --
  --  function DETERMINANT ( A : COMPLEX_MATRIX ) return COMPLEX ;
  --
  --      PURPOSE : COMPUTE THE DETERMINANT OF A COMPLEX MATRIX
  --                Z := |A|
  --
  --      INPUT  : THE COMPLEX MATRIX  A   ( UNCHANGED )
  --
  --      OUTPUT : THE COMPLEX NUMBER Z
  --
  --      METHOD : GUASS-JORDAN ELIMINATION USING MAXIMUM ELEMENT
  --                FOR PIVOT.
  --
  --      USAGE  :     Z := DETERMINANT ( A ) ;
  --
  --      EXCEPTION : ARRAY_INDEX_ERROR  RASIED IF RESULT CAN NOT BE COMPUTED
  --
  --  function INVERSE ( A : COMPLEX_MATRIX ) return COMPLEX_MATRIX ;
  --
  --      PURPOSE : INVERT AN N BY N  COMPLEX MATRIX
  --
  --      INPUT : THE COMPLEX MATRIX  A  ( NOT CHANGED )
  --
  --      OUTPUT : THE INVERSE OF MATRIX  A
  --
  --      METHOD : GUASS-JORDAN ELIMINATION USING MAXIMUM ELEMENT
  --               FOR PIVOT.
  --
  --      EXCEPTION : ARRAY_INDEX_ERROR RAISED IF INVERSE CAN NOT BE COMPUTED
  --
  --      SAMPLE USE :  NEW_MATRIX := INVERSE ( OLD_MATRIX ) ;
  --                    MATRIX := INVERSE ( MATRIX ) * ANOTHER_MATRIX ;
  --
end GENERIC_COMPLEX_LINEAR_EQUATIONS ;