import itertools import numpy import pytest from numpy.testing import assert_equal from thinc.api import Adam, fix_random_seed from spacy import registry, util from spacy.attrs import DEP, NORM from spacy.lang.en import English from spacy.pipeline import DependencyParser from spacy.pipeline.dep_parser import DEFAULT_PARSER_MODEL from spacy.pipeline.tok2vec import DEFAULT_TOK2VEC_MODEL from spacy.tokens import Doc from spacy.training import Example from spacy.vocab import Vocab from ..util import apply_transition_sequence, make_tempdir TRAIN_DATA = [ ( "They trade mortgage-backed securities.", { "heads": [1, 1, 4, 4, 5, 1, 1], "deps": ["nsubj", "ROOT", "compound", "punct", "nmod", "dobj", "punct"], }, ), ( "I like London and Berlin.", { "heads": [1, 1, 1, 2, 2, 1], "deps": ["nsubj", "ROOT", "dobj", "cc", "conj", "punct"], }, ), ] CONFLICTING_DATA = [ ( "I like London and Berlin.", { "heads": [1, 1, 1, 2, 2, 1], "deps": ["nsubj", "ROOT", "dobj", "cc", "conj", "punct"], }, ), ( "I like London and Berlin.", { "heads": [0, 0, 0, 0, 0, 0], "deps": ["ROOT", "nsubj", "nsubj", "cc", "conj", "punct"], }, ), ] PARTIAL_DATA = [ ( "I like London.", { "heads": [1, 1, 1, None], "deps": ["nsubj", "ROOT", "dobj", None], }, ), ] PARSERS = ["parser"] # TODO: Test beam_parser when ready eps = 0.1 @pytest.fixture def vocab(): return Vocab(lex_attr_getters={NORM: lambda s: s}) @pytest.fixture def parser(vocab): vocab.strings.add("ROOT") cfg = {"model": DEFAULT_PARSER_MODEL} model = registry.resolve(cfg, validate=True)["model"] parser = DependencyParser(vocab, model) parser.cfg["token_vector_width"] = 4 parser.cfg["hidden_width"] = 32 # parser.add_label('right') parser.add_label("left") parser.initialize(lambda: [_parser_example(parser)]) sgd = Adam(0.001) for i in range(10): losses = {} doc = Doc(vocab, words=["a", "b", "c", "d"]) example = Example.from_dict( doc, {"heads": [1, 1, 3, 3], "deps": ["left", "ROOT", "left", "ROOT"]} ) parser.update([example], sgd=sgd, losses=losses) return parser def _parser_example(parser): doc = Doc(parser.vocab, words=["a", "b", "c", "d"]) gold = {"heads": [1, 1, 3, 3], "deps": ["right", "ROOT", "left", "ROOT"]} return Example.from_dict(doc, gold) @pytest.mark.issue(2772) def test_issue2772(en_vocab): """Test that deprojectivization doesn't mess up sentence boundaries.""" # fmt: off words = ["When", "we", "write", "or", "communicate", "virtually", ",", "we", "can", "hide", "our", "true", "feelings", "."] # fmt: on # A tree with a non-projective (i.e. crossing) arc # The arcs (0, 4) and (2, 9) cross. heads = [4, 2, 9, 2, 2, 4, 9, 9, 9, 9, 12, 12, 9, 9] deps = ["dep"] * len(heads) doc = Doc(en_vocab, words=words, heads=heads, deps=deps) assert doc[1].is_sent_start is False @pytest.mark.issue(3830) def test_issue3830_no_subtok(): """Test that the parser doesn't have subtok label if not learn_tokens""" config = { "learn_tokens": False, } model = registry.resolve({"model": DEFAULT_PARSER_MODEL}, validate=True)["model"] parser = DependencyParser(Vocab(), model, **config) parser.add_label("nsubj") assert "subtok" not in parser.labels parser.initialize(lambda: [_parser_example(parser)]) assert "subtok" not in parser.labels @pytest.mark.issue(3830) def test_issue3830_with_subtok(): """Test that the parser does have subtok label if learn_tokens=True.""" config = { "learn_tokens": True, } model = registry.resolve({"model": DEFAULT_PARSER_MODEL}, validate=True)["model"] parser = DependencyParser(Vocab(), model, **config) parser.add_label("nsubj") assert "subtok" not in parser.labels parser.initialize(lambda: [_parser_example(parser)]) assert "subtok" in parser.labels @pytest.mark.issue(7716) @pytest.mark.xfail(reason="Not fixed yet") def test_partial_annotation(parser): doc = Doc(parser.vocab, words=["a", "b", "c", "d"]) doc[2].is_sent_start = False # Note that if the following line is used, then doc[2].is_sent_start == False # doc[3].is_sent_start = False doc = parser(doc) assert doc[2].is_sent_start == False def test_parser_root(en_vocab): words = ["i", "do", "n't", "have", "other", "assistance"] heads = [3, 3, 3, 3, 5, 3] deps = ["nsubj", "aux", "neg", "ROOT", "amod", "dobj"] doc = Doc(en_vocab, words=words, heads=heads, deps=deps) for t in doc: assert t.dep != 0, t.text @pytest.mark.skip( reason="The step_through API was removed (but should be brought back)" ) @pytest.mark.parametrize("words", [["Hello"]]) def test_parser_parse_one_word_sentence(en_vocab, en_parser, words): doc = Doc(en_vocab, words=words, heads=[0], deps=["ROOT"]) assert len(doc) == 1 with en_parser.step_through(doc) as _: # noqa: F841 pass assert doc[0].dep != 0 def test_parser_apply_actions(en_vocab, en_parser): words = ["I", "ate", "pizza"] words2 = ["Eat", "more", "pizza", "!"] doc1 = Doc(en_vocab, words=words) doc2 = Doc(en_vocab, words=words2) docs = [doc1, doc2] moves = en_parser.moves moves.add_action(0, "") moves.add_action(1, "") moves.add_action(2, "nsubj") moves.add_action(3, "obj") moves.add_action(2, "amod") actions = [ numpy.array([0, 0], dtype="i"), numpy.array([2, 0], dtype="i"), numpy.array([0, 4], dtype="i"), numpy.array([3, 3], dtype="i"), numpy.array([1, 1], dtype="i"), numpy.array([1, 1], dtype="i"), numpy.array([0], dtype="i"), numpy.array([1], dtype="i"), ] states = moves.init_batch(docs) active_states = states for step_actions in actions: active_states = moves.apply_actions(active_states, step_actions) assert len(active_states) == 0 for state, doc in zip(states, docs): moves.set_annotations(state, doc) assert docs[0][0].head.i == 1 assert docs[0][0].dep_ == "nsubj" assert docs[0][1].head.i == 1 assert docs[0][1].dep_ == "ROOT" assert docs[0][2].head.i == 1 assert docs[0][2].dep_ == "obj" assert docs[1][0].head.i == 0 assert docs[1][0].dep_ == "ROOT" assert docs[1][1].head.i == 2 assert docs[1][1].dep_ == "amod" assert docs[1][2].head.i == 0 assert docs[1][2].dep_ == "obj" @pytest.mark.skip( reason="The step_through API was removed (but should be brought back)" ) def test_parser_initial(en_vocab, en_parser): words = ["I", "ate", "the", "pizza", "with", "anchovies", "."] transition = ["L-nsubj", "S", "L-det"] doc = Doc(en_vocab, words=words) apply_transition_sequence(en_parser, doc, transition) assert doc[0].head.i == 1 assert doc[1].head.i == 1 assert doc[2].head.i == 3 assert doc[3].head.i == 3 def test_parser_parse_subtrees(en_vocab, en_parser): words = ["The", "four", "wheels", "on", "the", "bus", "turned", "quickly"] heads = [2, 2, 6, 2, 5, 3, 6, 6] deps = ["dep"] * len(heads) doc = Doc(en_vocab, words=words, heads=heads, deps=deps) assert len(list(doc[2].lefts)) == 2 assert len(list(doc[2].rights)) == 1 assert len(list(doc[2].children)) == 3 assert len(list(doc[5].lefts)) == 1 assert len(list(doc[5].rights)) == 0 assert len(list(doc[5].children)) == 1 assert len(list(doc[2].subtree)) == 6 def test_parser_merge_pp(en_vocab): words = ["A", "phrase", "with", "another", "phrase", "occurs"] heads = [1, 5, 1, 4, 2, 5] deps = ["det", "nsubj", "prep", "det", "pobj", "ROOT"] pos = ["DET", "NOUN", "ADP", "DET", "NOUN", "VERB"] doc = Doc(en_vocab, words=words, deps=deps, heads=heads, pos=pos) with doc.retokenize() as retokenizer: for np in doc.noun_chunks: retokenizer.merge(np, attrs={"lemma": np.lemma_}) assert doc[0].text == "A phrase" assert doc[1].text == "with" assert doc[2].text == "another phrase" assert doc[3].text == "occurs" @pytest.mark.skip( reason="The step_through API was removed (but should be brought back)" ) def test_parser_arc_eager_finalize_state(en_vocab, en_parser): words = ["a", "b", "c", "d", "e"] # right branching transition = ["R-nsubj", "D", "R-nsubj", "R-nsubj", "D", "R-ROOT"] tokens = Doc(en_vocab, words=words) apply_transition_sequence(en_parser, tokens, transition) assert tokens[0].n_lefts == 0 assert tokens[0].n_rights == 2 assert tokens[0].left_edge.i == 0 assert tokens[0].right_edge.i == 4 assert tokens[0].head.i == 0 assert tokens[1].n_lefts == 0 assert tokens[1].n_rights == 0 assert tokens[1].left_edge.i == 1 assert tokens[1].right_edge.i == 1 assert tokens[1].head.i == 0 assert tokens[2].n_lefts == 0 assert tokens[2].n_rights == 2 assert tokens[2].left_edge.i == 2 assert tokens[2].right_edge.i == 4 assert tokens[2].head.i == 0 assert tokens[3].n_lefts == 0 assert tokens[3].n_rights == 0 assert tokens[3].left_edge.i == 3 assert tokens[3].right_edge.i == 3 assert tokens[3].head.i == 2 assert tokens[4].n_lefts == 0 assert tokens[4].n_rights == 0 assert tokens[4].left_edge.i == 4 assert tokens[4].right_edge.i == 4 assert tokens[4].head.i == 2 # left branching transition = ["S", "S", "S", "L-nsubj", "L-nsubj", "L-nsubj", "L-nsubj"] tokens = Doc(en_vocab, words=words) apply_transition_sequence(en_parser, tokens, transition) assert tokens[0].n_lefts == 0 assert tokens[0].n_rights == 0 assert tokens[0].left_edge.i == 0 assert tokens[0].right_edge.i == 0 assert tokens[0].head.i == 4 assert tokens[1].n_lefts == 0 assert tokens[1].n_rights == 0 assert tokens[1].left_edge.i == 1 assert tokens[1].right_edge.i == 1 assert tokens[1].head.i == 4 assert tokens[2].n_lefts == 0 assert tokens[2].n_rights == 0 assert tokens[2].left_edge.i == 2 assert tokens[2].right_edge.i == 2 assert tokens[2].head.i == 4 assert tokens[3].n_lefts == 0 assert tokens[3].n_rights == 0 assert tokens[3].left_edge.i == 3 assert tokens[3].right_edge.i == 3 assert tokens[3].head.i == 4 assert tokens[4].n_lefts == 4 assert tokens[4].n_rights == 0 assert tokens[4].left_edge.i == 0 assert tokens[4].right_edge.i == 4 assert tokens[4].head.i == 4 def test_parser_set_sent_starts(en_vocab): # fmt: off words = ['Ein', 'Satz', '.', 'Außerdem', 'ist', 'Zimmer', 'davon', 'überzeugt', ',', 'dass', 'auch', 'epige-', '\n', 'netische', 'Mechanismen', 'eine', 'Rolle', 'spielen', ',', 'also', 'Vorgänge', ',', 'die', '\n', 'sich', 'darauf', 'auswirken', ',', 'welche', 'Gene', 'abgelesen', 'werden', 'und', '\n', 'welche', 'nicht', '.', '\n'] heads = [1, 1, 1, 30, 4, 4, 7, 4, 7, 17, 14, 14, 11, 14, 17, 16, 17, 6, 17, 20, 11, 20, 26, 22, 26, 26, 20, 26, 29, 31, 31, 25, 31, 32, 17, 4, 4, 36] deps = ['nk', 'ROOT', 'punct', 'mo', 'ROOT', 'sb', 'op', 'pd', 'punct', 'cp', 'mo', 'nk', '', 'nk', 'sb', 'nk', 'oa', 're', 'punct', 'mo', 'app', 'punct', 'sb', '', 'oa', 'op', 'rc', 'punct', 'nk', 'sb', 'oc', 're', 'cd', '', 'oa', 'ng', 'punct', ''] # fmt: on doc = Doc(en_vocab, words=words, deps=deps, heads=heads) for i in range(len(words)): if i == 0 or i == 3: assert doc[i].is_sent_start is True else: assert doc[i].is_sent_start is False for sent in doc.sents: for token in sent: assert token.head in sent def test_parser_constructor(en_vocab): config = { "learn_tokens": False, "min_action_freq": 30, "update_with_oracle_cut_size": 100, } cfg = {"model": DEFAULT_PARSER_MODEL} model = registry.resolve(cfg, validate=True)["model"] DependencyParser(en_vocab, model, **config) DependencyParser(en_vocab, model) @pytest.mark.parametrize("pipe_name", PARSERS) def test_incomplete_data(pipe_name): # Test that the parser works with incomplete information nlp = English() parser = nlp.add_pipe(pipe_name) train_examples = [] for text, annotations in PARTIAL_DATA: train_examples.append(Example.from_dict(nlp.make_doc(text), annotations)) for dep in annotations.get("deps", []): if dep is not None: parser.add_label(dep) optimizer = nlp.initialize(get_examples=lambda: train_examples) for i in range(150): losses = {} nlp.update(train_examples, sgd=optimizer, losses=losses) assert losses[pipe_name] < 0.0001 # test the trained model test_text = "I like securities." doc = nlp(test_text) assert doc[0].dep_ == "nsubj" assert doc[2].dep_ == "dobj" assert doc[0].head.i == 1 assert doc[2].head.i == 1 @pytest.mark.parametrize( "pipe_name,max_moves", itertools.product(PARSERS, [0, 1, 5, 100]) ) def test_overfitting_IO(pipe_name, max_moves): fix_random_seed(0) # Simple test to try and quickly overfit the dependency parser (normal or beam) nlp = English() parser = nlp.add_pipe(pipe_name) parser.cfg["update_with_oracle_cut_size"] = max_moves train_examples = [] for text, annotations in TRAIN_DATA: train_examples.append(Example.from_dict(nlp.make_doc(text), annotations)) for dep in annotations.get("deps", []): parser.add_label(dep) optimizer = nlp.initialize() # run overfitting for i in range(200): losses = {} nlp.update(train_examples, sgd=optimizer, losses=losses) assert losses[pipe_name] < 0.0001 # test the trained model test_text = "I like securities." doc = nlp(test_text) assert doc[0].dep_ == "nsubj" assert doc[2].dep_ == "dobj" assert doc[3].dep_ == "punct" assert doc[0].head.i == 1 assert doc[2].head.i == 1 assert doc[3].head.i == 1 # Also test the results are still the same after IO with make_tempdir() as tmp_dir: nlp.to_disk(tmp_dir) nlp2 = util.load_model_from_path(tmp_dir) doc2 = nlp2(test_text) assert doc2[0].dep_ == "nsubj" assert doc2[2].dep_ == "dobj" assert doc2[3].dep_ == "punct" assert doc2[0].head.i == 1 assert doc2[2].head.i == 1 assert doc2[3].head.i == 1 # Make sure that running pipe twice, or comparing to call, always amounts to the same predictions texts = [ "Just a sentence.", "Then one more sentence about London.", "Here is another one.", "I like London.", ] batch_deps_1 = [doc.to_array([DEP]) for doc in nlp.pipe(texts)] batch_deps_2 = [doc.to_array([DEP]) for doc in nlp.pipe(texts)] no_batch_deps = [doc.to_array([DEP]) for doc in [nlp(text) for text in texts]] assert_equal(batch_deps_1, batch_deps_2) assert_equal(batch_deps_1, no_batch_deps) def test_is_distillable(): nlp = English() parser = nlp.add_pipe("parser") assert parser.is_distillable @pytest.mark.slow @pytest.mark.parametrize("max_moves", [0, 1, 5, 100]) def test_distill(max_moves): teacher = English() teacher_parser = teacher.add_pipe("parser") train_examples = [] for text, annotations in TRAIN_DATA: train_examples.append(Example.from_dict(teacher.make_doc(text), annotations)) for dep in annotations.get("deps", []): teacher_parser.add_label(dep) optimizer = teacher.initialize(get_examples=lambda: train_examples) for i in range(200): losses = {} teacher.update(train_examples, sgd=optimizer, losses=losses) assert losses["parser"] < 0.0001 student = English() student_parser = student.add_pipe("parser") student_parser.cfg["update_with_oracle_cut_size"] = max_moves student_parser.initialize( get_examples=lambda: train_examples, labels=teacher_parser.label_data ) distill_examples = [ Example.from_dict(teacher.make_doc(t[0]), {}) for t in TRAIN_DATA ] for i in range(200): losses = {} student_parser.distill( teacher_parser, distill_examples, sgd=optimizer, losses=losses ) assert losses["parser"] < 0.0001 test_text = "I like securities." doc = student(test_text) assert doc[0].dep_ == "nsubj" assert doc[2].dep_ == "dobj" assert doc[3].dep_ == "punct" assert doc[0].head.i == 1 assert doc[2].head.i == 1 assert doc[3].head.i == 1 # fmt: off @pytest.mark.slow @pytest.mark.parametrize("pipe_name", ["parser", "beam_parser"]) @pytest.mark.parametrize( "parser_config", [ # TODO: re-enable after we have a spacy-legacy release for v4. See # https://github.com/explosion/spacy-legacy/pull/36 #({"@architectures": "spacy.TransitionBasedParser.v1", "tok2vec": DEFAULT_TOK2VEC_MODEL, "state_type": "parser", "extra_state_tokens": False, "hidden_width": 64, "maxout_pieces": 2, "use_upper": True}), ({"@architectures": "spacy.TransitionBasedParser.v2", "tok2vec": DEFAULT_TOK2VEC_MODEL, "state_type": "parser", "extra_state_tokens": False, "hidden_width": 64, "maxout_pieces": 2, "use_upper": True}), ({"@architectures": "spacy.TransitionBasedParser.v2", "tok2vec": DEFAULT_TOK2VEC_MODEL, "state_type": "parser", "extra_state_tokens": False, "hidden_width": 64, "maxout_pieces": 2, "use_upper": False}), ({"@architectures": "spacy.TransitionBasedParser.v3", "tok2vec": DEFAULT_TOK2VEC_MODEL, "state_type": "parser", "extra_state_tokens": False, "hidden_width": 64, "maxout_pieces": 2}), ], ) # fmt: on def test_parser_configs(pipe_name, parser_config): pipe_config = {"model": parser_config} nlp = English() parser = nlp.add_pipe(pipe_name, config=pipe_config) train_examples = [] for text, annotations in TRAIN_DATA: train_examples.append(Example.from_dict(nlp.make_doc(text), annotations)) for dep in annotations.get("deps", []): parser.add_label(dep) optimizer = nlp.initialize() for i in range(5): losses = {} nlp.update(train_examples, sgd=optimizer, losses=losses) def test_beam_parser_scores(): # Test that we can get confidence values out of the beam_parser pipe beam_width = 16 beam_density = 0.0001 nlp = English() config = { "beam_width": beam_width, "beam_density": beam_density, } parser = nlp.add_pipe("beam_parser", config=config) train_examples = [] for text, annotations in CONFLICTING_DATA: train_examples.append(Example.from_dict(nlp.make_doc(text), annotations)) for dep in annotations.get("deps", []): parser.add_label(dep) optimizer = nlp.initialize() # update a bit with conflicting data for i in range(10): losses = {} nlp.update(train_examples, sgd=optimizer, losses=losses) # test the scores from the beam test_text = "I like securities." doc = nlp.make_doc(test_text) docs = [doc] beams = parser.predict(docs) head_scores, label_scores = parser.scored_parses(beams) for j in range(len(doc)): for label in parser.labels: label_score = label_scores[0][(j, label)] assert 0 - eps <= label_score <= 1 + eps for i in range(len(doc)): head_score = head_scores[0][(j, i)] assert 0 - eps <= head_score <= 1 + eps def test_beam_overfitting_IO(): # Simple test to try and quickly overfit the Beam dependency parser nlp = English() beam_width = 16 beam_density = 0.0001 config = { "beam_width": beam_width, "beam_density": beam_density, } parser = nlp.add_pipe("beam_parser", config=config) train_examples = [] for text, annotations in TRAIN_DATA: train_examples.append(Example.from_dict(nlp.make_doc(text), annotations)) for dep in annotations.get("deps", []): parser.add_label(dep) optimizer = nlp.initialize() # run overfitting for i in range(150): losses = {} nlp.update(train_examples, sgd=optimizer, losses=losses) assert losses["beam_parser"] < 0.0001 # test the scores from the beam test_text = "I like securities." docs = [nlp.make_doc(test_text)] beams = parser.predict(docs) head_scores, label_scores = parser.scored_parses(beams) # we only processed one document head_scores = head_scores[0] label_scores = label_scores[0] # test label annotations: 0=nsubj, 2=dobj, 3=punct assert label_scores[(0, "nsubj")] == pytest.approx(1.0, abs=eps) assert label_scores[(0, "dobj")] == pytest.approx(0.0, abs=eps) assert label_scores[(0, "punct")] == pytest.approx(0.0, abs=eps) assert label_scores[(2, "nsubj")] == pytest.approx(0.0, abs=eps) assert label_scores[(2, "dobj")] == pytest.approx(1.0, abs=eps) assert label_scores[(2, "punct")] == pytest.approx(0.0, abs=eps) assert label_scores[(3, "nsubj")] == pytest.approx(0.0, abs=eps) assert label_scores[(3, "dobj")] == pytest.approx(0.0, abs=eps) assert label_scores[(3, "punct")] == pytest.approx(1.0, abs=eps) # test head annotations: the root is token at index 1 assert head_scores[(0, 0)] == pytest.approx(0.0, abs=eps) assert head_scores[(0, 1)] == pytest.approx(1.0, abs=eps) assert head_scores[(0, 2)] == pytest.approx(0.0, abs=eps) assert head_scores[(2, 0)] == pytest.approx(0.0, abs=eps) assert head_scores[(2, 1)] == pytest.approx(1.0, abs=eps) assert head_scores[(2, 2)] == pytest.approx(0.0, abs=eps) assert head_scores[(3, 0)] == pytest.approx(0.0, abs=eps) assert head_scores[(3, 1)] == pytest.approx(1.0, abs=eps) assert head_scores[(3, 2)] == pytest.approx(0.0, abs=eps) # Also test the results are still the same after IO with make_tempdir() as tmp_dir: nlp.to_disk(tmp_dir) nlp2 = util.load_model_from_path(tmp_dir) docs2 = [nlp2.make_doc(test_text)] parser2 = nlp2.get_pipe("beam_parser") beams2 = parser2.predict(docs2) head_scores2, label_scores2 = parser2.scored_parses(beams2) # we only processed one document head_scores2 = head_scores2[0] label_scores2 = label_scores2[0] # check the results again assert label_scores2[(0, "nsubj")] == pytest.approx(1.0, abs=eps) assert label_scores2[(0, "dobj")] == pytest.approx(0.0, abs=eps) assert label_scores2[(0, "punct")] == pytest.approx(0.0, abs=eps) assert label_scores2[(2, "nsubj")] == pytest.approx(0.0, abs=eps) assert label_scores2[(2, "dobj")] == pytest.approx(1.0, abs=eps) assert label_scores2[(2, "punct")] == pytest.approx(0.0, abs=eps) assert label_scores2[(3, "nsubj")] == pytest.approx(0.0, abs=eps) assert label_scores2[(3, "dobj")] == pytest.approx(0.0, abs=eps) assert label_scores2[(3, "punct")] == pytest.approx(1.0, abs=eps) assert head_scores2[(0, 0)] == pytest.approx(0.0, abs=eps) assert head_scores2[(0, 1)] == pytest.approx(1.0, abs=eps) assert head_scores2[(0, 2)] == pytest.approx(0.0, abs=eps) assert head_scores2[(2, 0)] == pytest.approx(0.0, abs=eps) assert head_scores2[(2, 1)] == pytest.approx(1.0, abs=eps) assert head_scores2[(2, 2)] == pytest.approx(0.0, abs=eps) assert head_scores2[(3, 0)] == pytest.approx(0.0, abs=eps) assert head_scores2[(3, 1)] == pytest.approx(1.0, abs=eps) assert head_scores2[(3, 2)] == pytest.approx(0.0, abs=eps)