FUNCTION derive_function_domain

(* SCHEMA FUNCTIONAL_DATA_AND_SCHEMATIC_REPRESENTATION_MIM_LF; *)

 
FUNCTION derive_function_domain(func : maths_function) : tuple_space;
LOCAL
  typenames : SET OF STRING := stripped_typeof(func);
  tspace : tuple_space := make_listed_product_space([]);
  shape : LIST OF positive_integer;
  sidxs : LIST OF INTEGER := [0];
  itvl : finite_integer_interval;
  factors : LIST OF finite_integer_interval := [];
  is_uniform : BOOLEAN := TRUE;
END_LOCAL;
  IF 'FINITE_FUNCTION' IN typenames THEN
    RETURN (derive_finite_function_domain(func\finite_function.pairs));
  END_IF;
  IF 'CONSTANT_FUNCTION' IN typenames THEN
    RETURN (domain_from(func\constant_function.source_of_domain));
  END_IF;
  IF 'SELECTOR_FUNCTION' IN typenames THEN
    RETURN (domain_from(func\selector_function.source_of_domain));
  END_IF;
  IF 'ELEMENTARY_FUNCTION' IN typenames THEN
    RETURN (derive_elementary_function_domain(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
    IF func\repackaging_function.input_repack = ro_nochange THEN
      RETURN (func\repackaging_function.operand.domain);
    END_IF;
    IF func\repackaging_function.input_repack = ro_wrap_as_tuple THEN
      RETURN (factor1(func\repackaging_function.operand.domain));
    END_IF;
    IF func\repackaging_function.input_repack = ro_unwrap_tuple THEN
      RETURN (one_tuples_of(func\repackaging_function.operand.domain));
    END_IF;
    RETURN (?);
  END_IF;
  IF 'REINDEXED_ARRAY_FUNCTION' IN typenames THEN
    shape := shape_of_array(func\unary_generic_expression.operand);
    sidxs := func\reindexed_array_function.starting_indices;
    REPEAT i := 1 TO SIZEOF(shape);
      itvl := make_finite_integer_interval(sidxs[i], sidxs[i] + shape[i] - 1);
      INSERT(factors, itvl, i - 1);
      IF shape[i] <> shape[1] THEN
        is_uniform := FALSE;
      END_IF;
    END_REPEAT;
    IF is_uniform THEN
      RETURN (make_uniform_product_space(factors[1], SIZEOF(shape)));
    END_IF;
    RETURN (make_listed_product_space(factors));
  END_IF;
  IF 'SERIES_COMPOSED_FUNCTION' IN typenames THEN
    RETURN (func\series_composed_function.operands[1].domain);
  END_IF;
  IF 'PARALLEL_COMPOSED_FUNCTION' IN typenames THEN
    RETURN (domain_from(func\parallel_composed_function.source_of_domain));
  END_IF;
  IF 'EXPLICIT_TABLE_FUNCTION' IN typenames THEN
    shape := func\explicit_table_function.shape;
    sidxs[1] := func\explicit_table_function.index_base;
    REPEAT i := 1 TO SIZEOF(shape);
      itvl := make_finite_integer_interval(sidxs[1], sidxs[1] + shape[i] - 1);
      INSERT(factors, itvl, i - 1);
      IF shape[i] <> shape[1] THEN
        is_uniform := FALSE;
      END_IF;
    END_REPEAT;
    IF is_uniform THEN
      RETURN (make_uniform_product_space(factors[1], SIZEOF(shape)));
    END_IF;
    RETURN (make_listed_product_space(factors));
  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[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[func\general_linear_function.sum_index] - 1))
    );
  END_IF;
  IF 'B_SPLINE_BASIS' IN typenames THEN
    RETURN (one_tuples_of(make_finite_real_interval(func\b_spline_basis.
    repeated_knots[func\b_spline_basis.order], closed, func\b_spline_basis.
    repeated_knots[func\b_spline_basis.num_basis + 1], closed)));
  END_IF;
  IF 'B_SPLINE_FUNCTION' IN typenames THEN
    REPEAT i := 1 TO SIZEOF(func\b_spline_function.basis);
      tspace := assoc_product_space(tspace, func\b_spline_function.basis[i].
      domain);
    END_REPEAT;
    RETURN (one_tuples_of(tspace));
  END_IF;
  IF 'RATIONALIZE_FUNCTION' IN typenames THEN
    RETURN (func\rationalize_function.fun.domain);
  END_IF;
  IF 'PARTIAL_DERIVATIVE_FUNCTION' IN typenames THEN
    RETURN (func\partial_derivative_function.derivand.domain);
  END_IF;
  IF 'DEFINITE_INTEGRAL_FUNCTION' IN typenames THEN
    RETURN (derive_definite_integral_domain(func));
  END_IF;
  IF 'ABSTRACTED_EXPRESSION_FUNCTION' IN typenames THEN
    REPEAT i := 1 TO SIZEOF(func\abstracted_expression_function.variables);
      tspace := assoc_product_space(tspace, one_tuples_of(values_space_of(func\
      abstracted_expression_function.variables[i])));
    END_REPEAT;
    RETURN (tspace);
  END_IF;
  IF 'EXPRESSION_DENOTED_FUNCTION' IN typenames THEN
    RETURN (values_space_of(func\expression_denoted_function.expr)\
    function_space.domain_argument);
  END_IF;
  IF 'IMPORTED_POINT_FUNCTION' IN typenames THEN
    RETURN (one_tuples_of(make_listed_product_space([])));
  END_IF;
  IF 'IMPORTED_CURVE_FUNCTION' IN typenames THEN
    RETURN (func\imported_curve_function.parametric_domain);
  END_IF;
  IF 'IMPORTED_SURFACE_FUNCTION' IN typenames THEN
    RETURN (func\imported_surface_function.parametric_domain);
  END_IF;
  IF 'IMPORTED_VOLUME_FUNCTION' IN typenames THEN
    RETURN (func\imported_volume_function.parametric_domain);
  END_IF;
  IF 'APPLICATION_DEFINED_FUNCTION' IN typenames THEN
    RETURN (func\application_defined_function.explicit_domain);
  END_IF;
  RETURN (?);
END_FUNCTION;

Referenced By

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