FUNCTION derive_function_range

(* SCHEMA FUNCTIONAL_DATA_AND_SCHEMATIC_REPRESENTATION_MIM_LF; *)

 
FUNCTION derive_function_range(func : maths_function) : tuple_space;
LOCAL
  typenames : SET OF STRING := stripped_typeof(func);
  tspace : tuple_space := make_listed_product_space([]);
  m : nonnegative_integer := 0;
  n : nonnegative_integer := 0;
END_LOCAL;
  IF 'FINITE_FUNCTION' IN typenames THEN
    RETURN (derive_finite_function_range(func\finite_function.pairs));
  END_IF;
  IF 'CONSTANT_FUNCTION' IN typenames THEN
    RETURN (one_tuples_of(make_finite_space([func\constant_function.sole_output
    ])));
  END_IF;
  IF 'SELECTOR_FUNCTION' IN typenames THEN
    tspace := func.domain;
    IF (space_dimension(tspace) = 1) AND (schema_prefix + 'TUPLE_SPACE' IN 
    TYPEOF(tspace)) THEN
      tspace := factor1(tspace);
    END_IF;
    RETURN (one_tuples_of(factor_space(tspace, func\selector_function.selector)
    ));
  END_IF;
  IF 'ELEMENTARY_FUNCTION' IN typenames THEN
    RETURN (derive_elementary_function_range(func\elementary_function.func_id))
    ;
  END_IF;
  IF 'RESTRICTION_FUNCTION' IN typenames THEN
    RETURN (one_tuples_of(func\restriction_function.operand));
  END_IF;
  IF 'REPACKAGING_FUNCTION' IN typenames THEN
    tspace := func\repackaging_function.operand.range;
    IF func\repackaging_function.output_repack = ro_wrap_as_tuple THEN
      tspace := one_tuples_of(tspace);
    END_IF;
    IF func\repackaging_function.output_repack = ro_unwrap_tuple THEN
      tspace := factor1(tspace);
    END_IF;
    IF func\repackaging_function.selected_output > 0 THEN
      tspace := one_tuples_of(factor_space(tspace, func\repackaging_function.
      selected_output));
    END_IF;
    RETURN (tspace);
  END_IF;
  IF 'REINDEXED_ARRAY_FUNCTION' IN typenames THEN
    RETURN (func\unary_generic_expression.operand\maths_function.range);
  END_IF;
  IF 'SERIES_COMPOSED_FUNCTION' IN typenames THEN
    RETURN (func\series_composed_function.operands[SIZEOF(func\
    series_composed_function.operands)].range);
  END_IF;
  IF 'PARALLEL_COMPOSED_FUNCTION' IN typenames THEN
    RETURN (func\parallel_composed_function.final_function.range);
  END_IF;
  IF 'EXPLICIT_TABLE_FUNCTION' IN typenames THEN
    IF 'LISTED_REAL_DATA' IN typenames THEN
      RETURN (one_tuples_of(the_reals));
    END_IF;
    IF 'LISTED_INTEGER_DATA' IN typenames THEN
      RETURN (one_tuples_of(the_integers));
    END_IF;
    IF 'LISTED_LOGICAL_DATA' IN typenames THEN
      RETURN (one_tuples_of(the_logicals));
    END_IF;
    IF 'LISTED_STRING_DATA' IN typenames THEN
      RETURN (one_tuples_of(the_strings));
    END_IF;
    IF 'LISTED_COMPLEX_NUMBER_DATA' IN typenames THEN
      RETURN (one_tuples_of(the_complex_numbers));
    END_IF;
    IF 'LISTED_DATA' IN typenames THEN
      RETURN (one_tuples_of(func\listed_data.value_range));
    END_IF;
    IF 'EXTERNALLY_LISTED_DATA' IN typenames THEN
      RETURN (one_tuples_of(func\externally_listed_data.value_range));
    END_IF;
    IF 'LINEARIZED_TABLE_FUNCTION' IN typenames THEN
      RETURN (func\linearized_table_function.source.range);
    END_IF;
    IF 'BASIC_SPARSE_MATRIX' IN typenames THEN
      RETURN (func\basic_sparse_matrix.val.range);
    END_IF;
    RETURN (?);
  END_IF;
  IF 'HOMOGENEOUS_LINEAR_FUNCTION' IN typenames THEN
    RETURN (one_tuples_of(make_uniform_product_space(factor1(func\
    homogeneous_linear_function.mat.range), func\homogeneous_linear_function.
    mat\explicit_table_function.shape[3 - func\homogeneous_linear_function.
    sum_index])));
  END_IF;
  IF 'GENERAL_LINEAR_FUNCTION' IN typenames THEN
    RETURN (one_tuples_of(make_uniform_product_space(factor1(func\
    general_linear_function.mat.range), func\general_linear_function.mat\
    explicit_table_function.shape[3 - func\general_linear_function.sum_index]))
    );
  END_IF;
  IF 'B_SPLINE_BASIS' IN typenames THEN
    RETURN (one_tuples_of(make_uniform_product_space(the_reals, func\
    b_spline_basis.num_basis)));
  END_IF;
  IF 'B_SPLINE_FUNCTION' IN typenames THEN
    tspace := factor1(func\b_spline_function.coef.domain);
    m := SIZEOF(func\b_spline_function.basis);
    n := space_dimension(tspace);
    IF m = n THEN
      RETURN (one_tuples_of(the_reals));
    END_IF;
    IF m = n - 1 THEN
      RETURN (one_tuples_of(make_uniform_product_space(the_reals, factor_space(
      tspace, n)\finite_integer_interval.size)));
    END_IF;
    tspace := extract_factors(tspace, m + 1, n);
    RETURN (one_tuples_of(make_function_space(sc_equal, tspace, sc_subspace, 
    number_superspace_of(func\b_spline_function.coef.range))));
  END_IF;
  IF 'RATIONALIZE_FUNCTION' IN typenames THEN
    tspace := factor1(func\rationalize_function.fun.range);
    n := space_dimension(tspace);
    RETURN (one_tuples_of(make_uniform_product_space(number_superspace_of(
    factor1(tspace)), n - 1)));
  END_IF;
  IF 'PARTIAL_DERIVATIVE_FUNCTION' IN typenames THEN
    RETURN (drop_numeric_constraints(func\partial_derivative_function.derivand.
    range));
  END_IF;
  IF 'DEFINITE_INTEGRAL_FUNCTION' IN typenames THEN
    RETURN (drop_numeric_constraints(func\definite_integral_function.integrand.
    range));
  END_IF;
  IF 'ABSTRACTED_EXPRESSION_FUNCTION' IN typenames THEN
    RETURN (one_tuples_of(values_space_of(func\abstracted_expression_function.
    expr)));
  END_IF;
  IF 'EXPRESSION_DENOTED_FUNCTION' IN typenames THEN
    RETURN (values_space_of(func\expression_denoted_function.expr)\
    function_space.range_argument);
  END_IF;
  IF 'IMPORTED_POINT_FUNCTION' IN typenames THEN
    RETURN (one_tuples_of(make_uniform_product_space(the_reals, dimension_of(
    func\imported_point_function.geometry))));
  END_IF;
  IF 'IMPORTED_CURVE_FUNCTION' IN typenames THEN
    RETURN (one_tuples_of(make_uniform_product_space(the_reals, dimension_of(
    func\imported_curve_function.geometry))));
  END_IF;
  IF 'IMPORTED_SURFACE_FUNCTION' IN typenames THEN
    RETURN (one_tuples_of(make_uniform_product_space(the_reals, dimension_of(
    func\imported_surface_function.geometry))));
  END_IF;
  IF 'IMPORTED_VOLUME_FUNCTION' IN typenames THEN
    RETURN (one_tuples_of(make_uniform_product_space(the_reals, dimension_of(
    func\imported_volume_function.geometry))));
  END_IF;
  IF 'APPLICATION_DEFINED_FUNCTION' IN typenames THEN
    RETURN (func\application_defined_function.explicit_range);
  END_IF;
  RETURN (?);
END_FUNCTION;

Referenced By

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2012-03-27T17:17:33-04:00