-- real_arrays.ads  package specification
  
package Real_Arrays is

-- Types --

  subtype Real is Long_float;
  type REAL_VECTOR is array (INTEGER range <>) of REAL;
  type REAL_MATRIX is array (INTEGER range <>, 
                             INTEGER range <>) of REAL;
-- SUBPROGRAMS for REAL_VECTOR TYPES --

  -- VECTOR arithmetic operations --

  function "+" (RIGHT : REAL_VECTOR) return REAL_VECTOR;
  function "-" (RIGHT : REAL_VECTOR) return REAL_VECTOR;
  function "abs" (RIGHT : REAL_VECTOR) return REAL_VECTOR; 

  function "+" (LEFT, RIGHT : REAL_VECTOR) return REAL_VECTOR;
  function "-" (LEFT, RIGHT : REAL_VECTOR) return REAL_VECTOR;
  function "*" (LEFT, RIGHT : REAL_VECTOR) return REAL_VECTOR; 
  function "/" (LEFT, RIGHT : REAL_VECTOR) return REAL_VECTOR;
  function "**" (LEFT : REAL_VECTOR; 
                 RIGHT : INTEGER) return REAL_VECTOR; 

  function "*" (LEFT, RIGHT : REAL_VECTOR) return REAL; 

  -- VECTOR scaling operations --

  function "*" (LEFT : REAL;
                RIGHT : REAL_VECTOR) return REAL_VECTOR;
  function "*" (LEFT : REAL_VECTOR;
                RIGHT : REAL) return REAL_VECTOR;
  function "/" (LEFT : REAL_VECTOR;
                RIGHT : REAL) return REAL_VECTOR;

  -- other operations --

  function UNIT_VECTOR (INDEX : INTEGER;
                        ORDER : POSITIVE;
                        FIRST : INTEGER := 1) return REAL_VECTOR;  

-- SUBPROGRAMS for REAL_MATRIX TYPES --

  -- MATRIX arithmetic operations --

  function "+" (RIGHT : REAL_MATRIX) return REAL_MATRIX;
  function "-" (RIGHT : REAL_MATRIX) return REAL_MATRIX;
  function "abs" (RIGHT : REAL_MATRIX) return REAL_MATRIX; 
  function TRANSPOSE (A : REAL_MATRIX) return REAL_MATRIX; 

  function "+" (LEFT, RIGHT : REAL_MATRIX) return REAL_MATRIX;
  function "-" (LEFT, RIGHT : REAL_MATRIX) return REAL_MATRIX;
  function "*" (LEFT, RIGHT : REAL_MATRIX) return REAL_MATRIX;

  function "*" (LEFT, RIGHT : REAL_VECTOR) return REAL_MATRIX; 
  function "*" (LEFT : REAL_VECTOR;
                RIGHT : REAL_MATRIX) return REAL_VECTOR;
  function "*" (LEFT : REAL_MATRIX;
                RIGHT : REAL_VECTOR) return REAL_VECTOR;

  -- MATRIX scaling operations --

  function "*" (LEFT : REAL;
                RIGHT : REAL_MATRIX) return REAL_MATRIX;
  function "*" (LEFT : REAL_MATRIX;
                RIGHT : REAL) return REAL_MATRIX;
  function "/" (LEFT : REAL_MATRIX;
                RIGHT : REAL) return REAL_MATRIX;

  -- other operations --

  function IDENTITY_MATRIX (ORDER : POSITIVE;
                            FIRST_1, FIRST_2 : INTEGER := 1) return REAL_MATRIX;

-- EXCEPTIONS --

  Array_Index_Error: exception;

end Real_Arrays;