def test_synthesis_intermediate_steps_as_expected(self, dwt_depth, dwt_depth_ho): filter_params = tables.LIFTING_FILTERS[ tables.WaveletFilters.haar_with_shift] transform_coeffs = make_symbol_coeff_arrays(dwt_depth, dwt_depth_ho) _, intermediate_values = synthesis_transform( filter_params, filter_params, dwt_depth, dwt_depth_ho, transform_coeffs, ) # 2D stages have all expected values for level in range(dwt_depth_ho + 1, dwt_depth + dwt_depth_ho + 1): names = set(n for l, n in intermediate_values if l == level) assert names == set([ "LL", "LH", "HL", "HH", "L''", "L'", "L", "H''", "H'", "H", "DC''", "DC'", "DC", "Output", ]) # HO stages have all expected values for level in range(1, dwt_depth_ho + 1): names = set(n for l, n in intermediate_values if l == level) assert names == set([ "L", "H", "DC''", "DC'", "DC", "Output", ])
def test_find_synthesis_filter_bounds(): coeff_arrays = make_symbol_coeff_arrays(1, 0) expr = (1 * coeff_arrays[0]["LL"][0, 0] + 2 * coeff_arrays[0]["LL"][1, 0] + -4 * coeff_arrays[0]["LL"][2, 0] + 10 * coeff_arrays[1]["HH"][0, 0] + 20 * coeff_arrays[1]["HH"][1, 0] + -40 * coeff_arrays[1]["HH"][2, 0] + 100 * LinExp.new_affine_error_symbol() + 1) lower_bound, upper_bound = synthesis_filter_bounds(expr) assert lower_bound == (3 * LinExp("coeff_0_LL_min") + -4 * LinExp("coeff_0_LL_max") + 30 * LinExp("coeff_1_HH_min") + -40 * LinExp("coeff_1_HH_max") + -100 + 1) assert upper_bound == (-4 * LinExp("coeff_0_LL_min") + 3 * LinExp("coeff_0_LL_max") + -40 * LinExp("coeff_1_HH_min") + 30 * LinExp("coeff_1_HH_max") + +100 + 1)
def test_evaluate_synthesis_test_pattern_output(): # In this test we simply check that the decoded values match those # computed by the optimise_synthesis_maximising_test_pattern function wavelet_index = WaveletFilters.haar_with_shift wavelet_index_ho = WaveletFilters.le_gall_5_3 dwt_depth = 1 dwt_depth_ho = 0 picture_bit_width = 10 max_quantisation_index = 64 quantisation_matrix = { 0: { "LL": 0 }, 1: { "LH": 1, "HL": 2, "HH": 3 }, } h_filter_params = LIFTING_FILTERS[wavelet_index_ho] v_filter_params = LIFTING_FILTERS[wavelet_index] input_min, input_max = signed_integer_range(picture_bit_width) input_array = SymbolArray(2) analysis_transform_coeff_arrays, _ = analysis_transform( h_filter_params, v_filter_params, dwt_depth, dwt_depth_ho, input_array, ) symbolic_coeff_arrays = make_symbol_coeff_arrays(dwt_depth, dwt_depth_ho) symbolic_output_array, symbolic_intermediate_arrays = synthesis_transform( h_filter_params, v_filter_params, dwt_depth, dwt_depth_ho, symbolic_coeff_arrays, ) pyexp_coeff_arrays = make_variable_coeff_arrays(dwt_depth, dwt_depth_ho) _, pyexp_intermediate_arrays = synthesis_transform( h_filter_params, v_filter_params, dwt_depth, dwt_depth_ho, pyexp_coeff_arrays, ) for (level, array_name), target_array in symbolic_intermediate_arrays.items(): for x in range(target_array.period[0]): for y in range(target_array.period[1]): # Create a test pattern test_pattern = make_synthesis_maximising_pattern( input_array, analysis_transform_coeff_arrays, target_array, symbolic_output_array, x, y, ) synthesis_pyexp = pyexp_intermediate_arrays[(level, array_name)][x, y] # Run with no-optimisation iterations but, as a side effect, # compute the actual decoded value to compare with test_pattern = optimise_synthesis_maximising_test_pattern( h_filter_params, v_filter_params, dwt_depth, dwt_depth_ho, quantisation_matrix, synthesis_pyexp, test_pattern, input_min, input_max, max_quantisation_index, None, 1, None, 0.0, 0.0, 0, 0, ) # Find the actual values lower_value, upper_value = evaluate_synthesis_test_pattern_output( h_filter_params, v_filter_params, dwt_depth, dwt_depth_ho, quantisation_matrix, synthesis_pyexp, test_pattern, input_min, input_max, max_quantisation_index, ) assert upper_value[0] == test_pattern.decoded_value assert upper_value[1] == test_pattern.quantisation_index
def static_filter_analysis( wavelet_index, wavelet_index_ho, dwt_depth, dwt_depth_ho, num_batches=1, batch_num=0, ): r""" Performs a complete static analysis of a VC-2 filter configuration, computing theoretical upper- and lower-bounds for signal values (see :ref:`theory-affine-arithmetic`) and heuristic test patterns (see :ref:`theory-test-patterns`) for all intermediate and final analysis and synthesis filter values. Parameters ========== wavelet_index : :py:class:`vc2_data_tables.WaveletFilters` or int wavelet_index_ho : :py:class:`vc2_data_tables.WaveletFilters` or int dwt_depth : int dwt_depth_ho : int The filter parameters. num_batches : int batch_num : int Though for most filters this function runs either instantaneously or at worst in the space of a couple of hours, unusually large filters can take an extremely long time to run. For example, a 4-level Fidelity transform may take around a month to evaluate. These arguments may be used to split this job into separate batches which may be computed separately (and in parallel) and later combined. For example, setting ``num_batches`` to 3 results in only analysing every third filter phase. The ``batch_num`` parameter should then be set to either 0, 1 or 2 to specify which third. The skipped phases are simply omitted from the returned dictionaries. The dictionaries returned for each batch should be unified to produce the complete analysis. Returns ======= analysis_signal_bounds : {(level, array_name, x, y): (lower_bound_exp, upper_bound_exp), ...} synthesis_signal_bounds : {(level, array_name, x, y): (lower_bound_exp, upper_bound_exp), ...} Expressions defining the upper and lower bounds for all intermediate and final analysis and synthesis filter values. The keys of the returned dictionaries give the level, array name and filter phase for which each pair of bounds corresponds (see :ref:`terminology`). The naming conventions used are those defined by :py:func:`vc2_bit_widths.vc2_filters.analysis_transform` and :py:func:`vc2_bit_widths.vc2_filters.synthesis_transform`. Arrays which are just interleavings, subsamplings or renamings of other arrays are omitted. The lower and upper bounds are given algebraically as :py:class:`~vc2_bit_widths.linexp.LinExp`\ s. For the analysis filter bounds, the expressions are defined in terms of the variables ``LinExp("signal_min")`` and ``LinExp("signal_max")``. These should be substituted for the minimum and maximum picture signal level to find the upper and lower bounds for a particular picture bit width. For the synthesis filter bounds, the expressions are defined in terms of variables of the form ``LinExp("coeff_LEVEL_ORIENT_min")`` and ``LinExp("coeff_LEVEL_ORIENT_max")`` which give lower and upper bounds for the transform coefficients with the named level and orientation. The :py:func:`~vc2_bit_widths.helpers.evaluate_filter_bounds` function may be used to substitute concrete values into these expressions for a particular picture bit width. analysis_test_patterns: {(level, array_name, x, y): :py:class:`~vc2_bit_widths.patterns.TestPatternSpecification`, ...} synthesis_test_patterns: {(level, array_name, x, y): :py:class:`~vc2_bit_widths.patterns.TestPatternSpecification`, ...} Heuristic test patterns which are designed to maximise a particular intermediate or final filter value. For a minimising test pattern, invert the polarities of the pixels. The keys of the returned dictionaries give the level, array name and filter phase for which each set of bounds corresponds (see :ref:`terminology`). Arrays which are just interleavings, subsamplings or renamings of other arrays are omitted. """ v_filter_params = LIFTING_FILTERS[wavelet_index] h_filter_params = LIFTING_FILTERS[wavelet_index_ho] # Create the algebraic representation of the analysis transform picture_array = SymbolArray(2) analysis_coeff_arrays, intermediate_analysis_arrays = analysis_transform( h_filter_params, v_filter_params, dwt_depth, dwt_depth_ho, picture_array, ) # Count the total number of arrays for use in logging messages num_arrays = sum(array.period[0] * array.period[1] for array in intermediate_analysis_arrays.values() if not array.nop) array_num = 0 # Compute bounds/test pattern for every intermediate/output analysis value analysis_signal_bounds = OrderedDict() analysis_test_patterns = OrderedDict() for (level, array_name), target_array in intermediate_analysis_arrays.items(): # Skip arrays which are just views of other arrays if target_array.nop: continue for x in range(target_array.period[0]): for y in range(target_array.period[1]): array_num += 1 if (array_num - 1) % num_batches != batch_num: continue logger.info( "Analysing analysis filter %d of %d (level %d, %s[%d, %d])", array_num, num_arrays, level, array_name, x, y, ) # Compute signal bounds analysis_signal_bounds[(level, array_name, x, y)] = analysis_filter_bounds( target_array[x, y]) # Generate test pattern analysis_test_patterns[(level, array_name, x, y)] = make_analysis_maximising_pattern( picture_array, target_array, x, y, ) # Create the algebraic representation of the synthesis transform coeff_arrays = make_symbol_coeff_arrays(dwt_depth, dwt_depth_ho) synthesis_output_array, intermediate_synthesis_arrays = synthesis_transform( h_filter_params, v_filter_params, dwt_depth, dwt_depth_ho, coeff_arrays, ) # Create a view of the analysis coefficient arrays which avoids recomputing # already-known analysis filter phases cached_analysis_coeff_arrays = { level: { orient: SymbolicPeriodicCachingArray(array, picture_array) for orient, array in orients.items() } for level, orients in analysis_coeff_arrays.items() } # Count the total number of arrays for use in logging messages num_arrays = sum(array.period[0] * array.period[1] for array in intermediate_synthesis_arrays.values() if not array.nop) array_num = 0 # Compute bounds/test pattern for every intermediate/output analysis value synthesis_signal_bounds = OrderedDict() synthesis_test_patterns = OrderedDict() for (level, array_name), target_array in intermediate_synthesis_arrays.items(): # Skip arrays which are just views of other arrays if target_array.nop: continue for x in range(target_array.period[0]): for y in range(target_array.period[1]): array_num += 1 if (array_num - 1) % num_batches != batch_num: continue logger.info( "Analysing synthesis filter %d of %d (level %d, %s[%d, %d])", array_num, num_arrays, level, array_name, x, y, ) # Compute signal bounds synthesis_signal_bounds[(level, array_name, x, y)] = synthesis_filter_bounds( target_array[x, y]) # Compute test pattern synthesis_test_patterns[( level, array_name, x, y)] = make_synthesis_maximising_pattern( picture_array, cached_analysis_coeff_arrays, target_array, synthesis_output_array, x, y, ) # For extremely large filters, a noteworthy amount of overall # RAM can be saved by not caching synthesis filters. These # filters generally don't benefit much in terms of runtime from # caching so this has essentially no impact on runtime. for a in intermediate_synthesis_arrays.values(): a.clear_cache() return ( analysis_signal_bounds, synthesis_signal_bounds, analysis_test_patterns, synthesis_test_patterns, )
def test_integration(): # A simple integration test which computes signal bounds for a small # transform operation filter_params = LIFTING_FILTERS[WaveletFilters.haar_with_shift] dwt_depth = 1 dwt_depth_ho = 1 input_picture_array = SymbolArray(2) analysis_coeff_arrays, analysis_intermediate_values = analysis_transform( filter_params, filter_params, dwt_depth, dwt_depth_ho, input_picture_array, ) input_coeff_arrays = make_symbol_coeff_arrays(dwt_depth, dwt_depth_ho) synthesis_output, synthesis_intermediate_values = synthesis_transform( filter_params, filter_params, dwt_depth, dwt_depth_ho, input_coeff_arrays, ) signal_min = LinExp("signal_min") signal_max = LinExp("signal_max") example_range = {signal_min: -512, signal_max: 511} # Input signal bounds should be as specified assert analysis_filter_bounds( analysis_intermediate_values[(2, "Input")][0, 0], ) == (signal_min, signal_max) # Output of final analysis filter should require a greater depth (NB: for # the Haar transform it is the high-pass bands which gain the largest # signal range) analysis_output_lower, analysis_output_upper = analysis_filter_bounds( analysis_intermediate_values[(1, "H")][0, 0], ) assert analysis_output_lower.subs(example_range) < signal_min.subs( example_range) assert analysis_output_upper.subs(example_range) > signal_max.subs( example_range) example_coeff_range = { "coeff_{}_{}_{}".format(level, orient, minmax): maximum_dequantised_magnitude( int(round(value.subs(example_range).constant))) for level, orients in analysis_coeff_arrays.items() for orient, expr in orients.items() for minmax, value in zip(["min", "max"], analysis_filter_bounds(expr)) } # Signal range should shrink down by end of synthesis process but should # still be larger than the original signal final_output_lower, final_output_upper = synthesis_filter_bounds( synthesis_output[0, 0]) assert final_output_upper.subs( example_coeff_range) < analysis_output_upper.subs(example_range) assert final_output_lower.subs( example_coeff_range) > analysis_output_lower.subs(example_range) assert final_output_upper.subs(example_coeff_range) > signal_max.subs( example_range) assert final_output_lower.subs(example_coeff_range) < signal_min.subs( example_range)
def synthesis_input_arrays(self, dwt_depth, dwt_depth_ho): return make_symbol_coeff_arrays(dwt_depth, dwt_depth_ho)
def test_add_missing_synthesis_values( wavelet_index, wavelet_index_ho, dwt_depth, dwt_depth_ho, ): h_filter_params = tables.LIFTING_FILTERS[wavelet_index_ho] v_filter_params = tables.LIFTING_FILTERS[wavelet_index] _, intermediate_values = synthesis_transform( h_filter_params, v_filter_params, dwt_depth, dwt_depth_ho, make_symbol_coeff_arrays(dwt_depth, dwt_depth_ho), ) all_expressions = { (level, array_name, x, y): array[x, y] for (level, array_name), array in intermediate_values.items() for x in range(array.period[0]) for y in range(array.period[1]) } non_nop_expressions = { (level, array_name, x, y): array[x, y] for (level, array_name), array in intermediate_values.items() for x in range(array.period[0]) for y in range(array.period[1]) if not array.nop } # Sanity check assert all_expressions != non_nop_expressions refilled_expressions_not_filled = add_missing_synthesis_values( h_filter_params, v_filter_params, dwt_depth, dwt_depth_ho, non_nop_expressions, fill_in_equivalent_phases=False, ) refilled_expressions_filled = add_missing_synthesis_values( h_filter_params, v_filter_params, dwt_depth, dwt_depth_ho, non_nop_expressions, fill_in_equivalent_phases=True, ) assert set(refilled_expressions_not_filled) == set(all_expressions) assert set(refilled_expressions_filled) == set(all_expressions) for key in all_expressions: if refilled_expressions_not_filled[key] is not None: # Where a phase hasn't been repeated, should have exactly the same # value. assert ( all_expressions[key] == refilled_expressions_not_filled[key]) assert (all_expressions[key] == refilled_expressions_filled[key]) else: # Where a phase has been filled in, without going to a lot of # effort, all we can do is check that the substituted phase is # 'similar' (i.e. likely to be the same expression just with # different coordinates) assert (sorted( coeff for sym, coeff in all_expressions[key]) == sorted( coeff for sym, coeff in refilled_expressions_filled[key]))
def test_make_symbol_coeff_arrays(): coeff_arrays = make_symbol_coeff_arrays(2, 0, "foobar") assert isinstance(coeff_arrays[1]["HL"][2, 3], LinExp) assert coeff_arrays[1]["HL"][2, 3].symbol == (("foobar", 1, "HL"), 2, 3)
def test_aggregation_flag(tmpdir, capsys, arg, exp_phases): # Check that aggregation of filter phases works f = str(tmpdir.join("file.json")) # vc2-static-filter-analysis assert sfa(shlex.split("-w haar_with_shift -d 1 -o") + [f]) == 0 # vc2-bit-widths-table assert bwt([f] + shlex.split("-b 10 {}".format(arg))) == 0 csv_rows = list(csv.reader(capsys.readouterr().out.splitlines())) columns = csv_rows[0][:-5] # Check all phase columns are present as expected if exp_phases: assert columns == ["type", "level", "array_name", "x", "y"] else: assert columns == ["type", "level", "array_name"] # Check the rows are as expected row_headers = [tuple(row[:-5]) for row in csv_rows[1:]] # ...by comparing with the intermediate arrays expected for this filter... h_filter_params = LIFTING_FILTERS[WaveletFilters.haar_with_shift] v_filter_params = LIFTING_FILTERS[WaveletFilters.haar_with_shift] dwt_depth = 1 dwt_depth_ho = 0 _, analysis_intermediate_arrays = analysis_transform( h_filter_params, v_filter_params, dwt_depth, dwt_depth_ho, SymbolArray(2), ) _, synthesis_intermediate_arrays = synthesis_transform( h_filter_params, v_filter_params, dwt_depth, dwt_depth_ho, make_symbol_coeff_arrays(dwt_depth, dwt_depth_ho), ) if exp_phases: assert row_headers == [ (type_name, str(level), array_name, str(x), str(y)) for type_name, intermediate_arrays in [ ("analysis", analysis_intermediate_arrays), ("synthesis", synthesis_intermediate_arrays), ] for (level, array_name), array in intermediate_arrays.items() for x in range(array.period[0]) for y in range(array.period[1]) ] else: assert row_headers == [(type_name, str(level), array_name) for type_name, intermediate_arrays in [ ("analysis", analysis_intermediate_arrays), ("synthesis", synthesis_intermediate_arrays), ] for level, array_name in intermediate_arrays]