def tc(): test = _Test() # Predict the reflections in place and put in a reflection manager ref_predictor = StillsExperimentsPredictor(test.stills_experiments) ref_predictor(test.reflections) test.refman = ReflectionManagerFactory.from_parameters_reflections_experiments( refman_phil_scope.extract(), test.reflections, test.stills_experiments, do_stills=True, ) test.refman.finalise() # Build a prediction parameterisation for the stills experiment test.pred_param = StillsPredictionParameterisation( test.stills_experiments, detector_parameterisations=[test.det_param], beam_parameterisations=[test.s0_param], xl_orientation_parameterisations=[test.xlo_param], xl_unit_cell_parameterisations=[test.xluc_param], ) return test
def test_stills_pred_param(tc): print("Testing derivatives for StillsPredictionParameterisation") print("========================================================") # Build a prediction parameterisation for the stills experiment pred_param = StillsPredictionParameterisation( tc.stills_experiments, detector_parameterisations=[tc.det_param], beam_parameterisations=[tc.s0_param], xl_orientation_parameterisations=[tc.xlo_param], xl_unit_cell_parameterisations=[tc.xluc_param], ) # Predict the reflections in place. Must do this ahead of calculating # the analytical gradients so quantities like s1 are correct ref_predictor = StillsExperimentsPredictor(tc.stills_experiments) ref_predictor(tc.reflections) # get analytical gradients an_grads = pred_param.get_gradients(tc.reflections) fd_grads = tc.get_fd_gradients(pred_param, ref_predictor) for i, (an_grad, fd_grad) in enumerate(zip(an_grads, fd_grads)): # compare FD with analytical calculations print(f"\nParameter {i}: {fd_grad['name']}") for name in ["dX_dp", "dY_dp", "dDeltaPsi_dp"]: print(name) a = fd_grad[name] b = an_grad[name] abs_error = a - b fns = five_number_summary(abs_error) print((" summary of absolute errors: %9.6f %9.6f %9.6f " + "%9.6f %9.6f") % fns) assert flex.max(flex.abs(abs_error)) < 0.0003 # largest absolute error found to be about 0.00025 for dY/dp of # Crystal0g_param_3. Reject outlying absolute errors and test again. iqr = fns[3] - fns[1] # skip further stats on errors with an iqr of near zero, e.g. dDeltaPsi_dp # for detector parameters, which are all equal to zero if iqr < 1.0e-10: continue sel1 = abs_error < fns[3] + 1.5 * iqr sel2 = abs_error > fns[1] - 1.5 * iqr sel = sel1 & sel2 tst = flex.max_index(flex.abs(abs_error.select(sel))) tst_val = abs_error.select(sel)[tst] n_outliers = sel.count(False) print((" {0} outliers rejected, leaving greatest " + "absolute error: {1:9.6f}").format(n_outliers, tst_val)) # largest absolute error now 0.000086 for dX/dp of Beam0Mu2 assert abs(tst_val) < 0.00009 # Completely skip parameters with FD gradients all zero (e.g. gradients of # DeltaPsi for detector parameters) sel1 = flex.abs(a) < 1.0e-10 if sel1.all_eq(True): continue # otherwise calculate normalised errors, by dividing absolute errors by # the IQR (more stable than relative error calculation) norm_error = abs_error / iqr fns = five_number_summary(norm_error) print((" summary of normalised errors: %9.6f %9.6f %9.6f " + "%9.6f %9.6f") % fns) # largest normalised error found to be about 25.7 for dY/dp of # Crystal0g_param_3. try: assert flex.max(flex.abs(norm_error)) < 30 except AssertionError as e: e.args += ( f"extreme normalised error value: {flex.max(flex.abs(norm_error))}", ) raise e # Reject outlying normalised errors and test again iqr = fns[3] - fns[1] if iqr > 0.0: sel1 = norm_error < fns[3] + 1.5 * iqr sel2 = norm_error > fns[1] - 1.5 * iqr sel = sel1 & sel2 tst = flex.max_index(flex.abs(norm_error.select(sel))) tst_val = norm_error.select(sel)[tst] n_outliers = sel.count(False) # most outliers found for for dY/dp of Crystal0g_param_3 (which had # largest errors, so no surprise there). try: assert n_outliers < 250 except AssertionError as e: e.args += (f"too many outliers rejected: {n_outliers}", ) raise e print( (" {0} outliers rejected, leaving greatest " + "normalised error: {1:9.6f}").format(n_outliers, tst_val)) # largest normalied error now about -4. for dX/dp of Detector0Tau1 assert abs(tst_val) < 6, f"should be < 6, not {tst_val}"
def test(): # Build models, with a larger crystal than default in order to get plenty of # reflections on the 'still' image overrides = """ geometry.parameters.crystal.a.length.range=40 50; geometry.parameters.crystal.b.length.range=40 50; geometry.parameters.crystal.c.length.range=40 50; geometry.parameters.random_seed = 42""" master_phil = parse( """ include scope dials.test.algorithms.refinement.geometry_phil """, process_includes=True, ) models = Extract(master_phil, overrides) mydetector = models.detector mygonio = models.goniometer mycrystal = models.crystal mybeam = models.beam # Build a mock scan for a 3 degree sweep from dxtbx.model import ScanFactory sf = ScanFactory() myscan = sf.make_scan( image_range=(1, 1), exposure_times=0.1, oscillation=(0, 3.0), epochs=list(range(1)), deg=True, ) sweep_range = myscan.get_oscillation_range(deg=False) # Create parameterisations of these models det_param = DetectorParameterisationSinglePanel(mydetector) s0_param = BeamParameterisation(mybeam, mygonio) xlo_param = CrystalOrientationParameterisation(mycrystal) xluc_param = CrystalUnitCellParameterisation(mycrystal) # Create a scans ExperimentList, only for generating reflections experiments = ExperimentList() experiments.append( Experiment( beam=mybeam, detector=mydetector, goniometer=mygonio, scan=myscan, crystal=mycrystal, imageset=None, )) # Create a stills ExperimentList stills_experiments = ExperimentList() stills_experiments.append( Experiment(beam=mybeam, detector=mydetector, crystal=mycrystal, imageset=None)) # Generate rays - only to work out which hkls are predicted ray_predictor = ScansRayPredictor(experiments, sweep_range) resolution = 2.0 index_generator = IndexGenerator( mycrystal.get_unit_cell(), space_group(space_group_symbols(1).hall()).type(), resolution, ) indices = index_generator.to_array() rays = ray_predictor(indices) # Make a standard reflection_table and copy in the ray data reflections = flex.reflection_table.empty_standard(len(rays)) reflections.update(rays) # Build a standard prediction parameterisation for the stills experiment to do # FD calculation (not used for its analytical gradients) pred_param = StillsPredictionParameterisation( stills_experiments, detector_parameterisations=[det_param], beam_parameterisations=[s0_param], xl_orientation_parameterisations=[xlo_param], xl_unit_cell_parameterisations=[xluc_param], ) # Make a managed SphericalRelpStillsReflectionPredictor reflection predictor # for the first (only) experiment ref_predictor = Predictor(stills_experiments) # Predict these reflections in place. Must do this ahead of calculating # the analytical gradients so quantities like s1 are correct ref_predictor.update() ref_predictor.predict(reflections) # calculate analytical gradients ag = AnalyticalGradients( stills_experiments, detector_parameterisation=det_param, beam_parameterisation=s0_param, xl_orientation_parameterisation=xlo_param, xl_unit_cell_parameterisation=xluc_param, ) an_grads = ag.get_beam_gradients(reflections) an_grads.update(ag.get_crystal_orientation_gradients(reflections)) an_grads.update(ag.get_crystal_unit_cell_gradients(reflections)) # get finite difference gradients p_vals = pred_param.get_param_vals() deltas = [1.0e-7] * len(p_vals) fd_grads = [] p_names = pred_param.get_param_names() for i, delta in enumerate(deltas): # save parameter value val = p_vals[i] # calc reverse state p_vals[i] -= delta / 2.0 pred_param.set_param_vals(p_vals) ref_predictor.update() ref_predictor.predict(reflections) x, y, _ = reflections["xyzcal.mm"].deep_copy().parts() s1 = reflections["s1"].deep_copy() rev_state = s1 # calc forward state p_vals[i] += delta pred_param.set_param_vals(p_vals) ref_predictor.update() ref_predictor.predict(reflections) x, y, _ = reflections["xyzcal.mm"].deep_copy().parts() s1 = reflections["s1"].deep_copy() fwd_state = s1 # reset parameter to saved value p_vals[i] = val # finite difference - currently for s1 only fd = fwd_state - rev_state inv_delta = 1.0 / delta s1_grads = fd * inv_delta # store gradients fd_grads.append({"name": p_names[i], "ds1": s1_grads}) # return to the initial state pred_param.set_param_vals(p_vals) for i, fd_grad in enumerate(fd_grads): ## compare FD with analytical calculations print("\n\nParameter {0}: {1}".format(i, fd_grad["name"])) print("d[s1]/dp for the first reflection") print("finite diff", fd_grad["ds1"][0]) try: an_grad = an_grads[fd_grad["name"]] except KeyError: continue print("checking analytical vs finite difference gradients for s1") for a, b in zip(fd_grad["ds1"], an_grad["ds1"]): assert a == pytest.approx(b, abs=1e-7)
def test_check_and_remove(): test = _Test() # Override the single panel model and parameterisation. This test function # exercises the code for non-hierarchical multi-panel detectors. The # hierarchical detector version is tested via test_cspad_refinement.py multi_panel_detector = Detector() for x in range(3): for y in range(3): new_panel = make_panel_in_array((x, y), test.detector[0]) multi_panel_detector.add_panel(new_panel) test.detector = multi_panel_detector test.stills_experiments[0].detector = multi_panel_detector test.det_param = DetectorParameterisationMultiPanel(multi_panel_detector, test.beam) # update the generated reflections test.generate_reflections() # Predict the reflections in place and put in a reflection manager ref_predictor = StillsExperimentsPredictor(test.stills_experiments) ref_predictor(test.reflections) test.refman = ReflectionManagerFactory.from_parameters_reflections_experiments( refman_phil_scope.extract(), test.reflections, test.stills_experiments, do_stills=True, ) test.refman.finalise() # Build a prediction parameterisation for the stills experiment test.pred_param = StillsPredictionParameterisation( test.stills_experiments, detector_parameterisations=[test.det_param], beam_parameterisations=[test.s0_param], xl_orientation_parameterisations=[test.xlo_param], xl_unit_cell_parameterisations=[test.xluc_param], ) # A non-hierarchical detector does not have panel groups, thus panels are # not treated independently wrt which reflections affect their parameters. # As before, setting 792 reflections as the minimum should leave all # parameters free, and should not remove any reflections options = ar_phil_scope.extract() options.min_nref_per_parameter = 792 ar = AutoReduce(options, pred_param=test.pred_param, reflection_manager=test.refman) ar.check_and_remove() det_params = test.pred_param.get_detector_parameterisations() beam_params = test.pred_param.get_beam_parameterisations() xl_ori_params = test.pred_param.get_crystal_orientation_parameterisations() xl_uc_params = test.pred_param.get_crystal_unit_cell_parameterisations() assert det_params[0].num_free() == 6 assert beam_params[0].num_free() == 3 assert xl_ori_params[0].num_free() == 3 assert xl_uc_params[0].num_free() == 6 assert len(test.refman.get_obs()) == 823 # Setting 793 reflections as the minimum fixes 3 unit cell parameters, # and removes all those reflections. There are then too few reflections # for any parameterisation and all will be fixed, leaving no free # parameters for refinement. This fails within PredictionParameterisation, # during update so the final 31 reflections are not removed. options = ar_phil_scope.extract() options.min_nref_per_parameter = 793 ar = AutoReduce(options, pred_param=test.pred_param, reflection_manager=test.refman) with pytest.raises( DialsRefineConfigError, match="There are no free parameters for refinement" ): ar.check_and_remove() det_params = test.pred_param.get_detector_parameterisations() beam_params = test.pred_param.get_beam_parameterisations() xl_ori_params = test.pred_param.get_crystal_orientation_parameterisations() xl_uc_params = test.pred_param.get_crystal_unit_cell_parameterisations() assert det_params[0].num_free() == 0 assert beam_params[0].num_free() == 0 assert xl_ori_params[0].num_free() == 0 assert xl_uc_params[0].num_free() == 0 assert len(test.refman.get_obs()) == 823 - 792
def run(verbose = False): # Build models, with a larger crystal than default in order to get plenty of # reflections on the 'still' image overrides = """ geometry.parameters.crystal.a.length.range=40 50; geometry.parameters.crystal.b.length.range=40 50; geometry.parameters.crystal.c.length.range=40 50; geometry.parameters.random_seed = 42""" master_phil = parse(""" include scope dials.test.algorithms.refinement.geometry_phil """, process_includes=True) models = Extract(master_phil, overrides) mydetector = models.detector mygonio = models.goniometer mycrystal = models.crystal mybeam = models.beam # Build a mock scan for a 3 degree sweep from dxtbx.model.scan import scan_factory sf = scan_factory() myscan = sf.make_scan(image_range = (1,1), exposure_times = 0.1, oscillation = (0, 3.0), epochs = range(1), deg = True) sweep_range = myscan.get_oscillation_range(deg=False) # Create parameterisations of these models det_param = DetectorParameterisationSinglePanel(mydetector) s0_param = BeamParameterisation(mybeam, mygonio) xlo_param = CrystalOrientationParameterisation(mycrystal) xluc_param = CrystalUnitCellParameterisation(mycrystal) # Create a scans ExperimentList, only for generating reflections experiments = ExperimentList() experiments.append(Experiment( beam=mybeam, detector=mydetector, goniometer=mygonio, scan=myscan, crystal=mycrystal, imageset=None)) # Create a stills ExperimentList stills_experiments = ExperimentList() stills_experiments.append(Experiment( beam=mybeam, detector=mydetector, crystal=mycrystal, imageset=None)) # Generate rays - only to work out which hkls are predicted ray_predictor = ScansRayPredictor(experiments, sweep_range) resolution = 2.0 index_generator = IndexGenerator(mycrystal.get_unit_cell(), space_group(space_group_symbols(1).hall()).type(), resolution) indices = index_generator.to_array() rays = ray_predictor.predict(indices) # Make a standard reflection_table and copy in the ray data reflections = flex.reflection_table.empty_standard(len(rays)) reflections.update(rays) # Build a standard prediction parameterisation for the stills experiment to do # FD calculation (not used for its analytical gradients) pred_param = StillsPredictionParameterisation(stills_experiments, detector_parameterisations = [det_param], beam_parameterisations = [s0_param], xl_orientation_parameterisations = [xlo_param], xl_unit_cell_parameterisations = [xluc_param]) # Make a managed SphericalRelpStillsReflectionPredictor reflection predictor # for the first (only) experiment ref_predictor = Predictor(stills_experiments) # Predict these reflections in place. Must do this ahead of calculating # the analytical gradients so quantities like s1 are correct ref_predictor.update() ref_predictor.predict(reflections) # calculate analytical gradients ag = AnalyticalGradients(stills_experiments, detector_parameterisation=det_param, beam_parameterisation=s0_param, xl_orientation_parameterisation=xlo_param, xl_unit_cell_parameterisation=xluc_param) an_grads = ag.get_beam_gradients(reflections) an_grads.update(ag.get_crystal_orientation_gradients(reflections)) an_grads.update(ag.get_crystal_unit_cell_gradients(reflections)) # get finite difference gradients p_vals = pred_param.get_param_vals() deltas = [1.e-7] * len(p_vals) fd_grads = [] p_names = pred_param.get_param_names() for i in range(len(deltas)): # save parameter value val = p_vals[i] # calc reverse state p_vals[i] -= deltas[i] / 2. pred_param.set_param_vals(p_vals) ref_predictor.update() ref_predictor.predict(reflections) x, y, _ = reflections['xyzcal.mm'].deep_copy().parts() delpsi = reflections['delpsical.rad'].deep_copy() s1 = reflections['s1'].deep_copy() rev_state = s1 # calc forward state p_vals[i] += deltas[i] pred_param.set_param_vals(p_vals) ref_predictor.update() ref_predictor.predict(reflections) x, y, _ = reflections['xyzcal.mm'].deep_copy().parts() delpsi = reflections['delpsical.rad'].deep_copy() s1 = reflections['s1'].deep_copy() fwd_state = s1 # reset parameter to saved value p_vals[i] = val # finite difference - currently for s1 only fd = (fwd_state - rev_state) inv_delta = 1. / deltas[i] s1_grads = fd * inv_delta # store gradients fd_grads.append({'name':p_names[i], 'ds1':s1_grads}) # return to the initial state pred_param.set_param_vals(p_vals) for i, fd_grad in enumerate(fd_grads): ## compare FD with analytical calculations if verbose: print "\n\nParameter {0}: {1}". format(i, fd_grad['name']) print "d[s1]/dp for the first reflection" print 'finite diff', fd_grad['ds1'][0] try: an_grad = an_grads[fd_grad['name']] except KeyError: continue print 'checking analytical vs finite difference gradients for s1' for a, b in zip(fd_grad['ds1'], an_grad['ds1']): assert approx_equal(a, b) print 'OK'
def run_stills_pred_param(self, verbose = False): if verbose: print 'Testing derivatives for StillsPredictionParameterisation' print '========================================================' # Build a prediction parameterisation for the stills experiment pred_param = StillsPredictionParameterisation(self.stills_experiments, detector_parameterisations = [self.det_param], beam_parameterisations = [self.s0_param], xl_orientation_parameterisations = [self.xlo_param], xl_unit_cell_parameterisations = [self.xluc_param]) # Predict the reflections in place. Must do this ahead of calculating # the analytical gradients so quantities like s1 are correct from dials.algorithms.refinement.prediction import ExperimentsPredictor ref_predictor = ExperimentsPredictor(self.stills_experiments) ref_predictor.update() ref_predictor.predict(self.reflections) # get analytical gradients an_grads = pred_param.get_gradients(self.reflections) fd_grads = self.get_fd_gradients(pred_param, ref_predictor) for i, (an_grad, fd_grad) in enumerate(zip(an_grads, fd_grads)): # compare FD with analytical calculations if verbose: print "\nParameter {0}: {1}". format(i, fd_grad['name']) for idx, name in enumerate(["dX_dp", "dY_dp", "dDeltaPsi_dp"]): if verbose: print name a = fd_grad[name] b = an_grad[name] abs_error = a - b denom = a + b fns = five_number_summary(abs_error) if verbose: print (" summary of absolute errors: %9.6f %9.6f %9.6f " + \ "%9.6f %9.6f") % fns assert flex.max(flex.abs(abs_error)) < 0.0003 # largest absolute error found to be about 0.00025 for dY/dp of # Crystal0g_param_3. Reject outlying absolute errors and test again. iqr = fns[3] - fns[1] # skip further stats on errors with an iqr of near zero, e.g. dDeltaPsi_dp # for detector parameters, which are all equal to zero if iqr < 1.e-10: continue sel1 = abs_error < fns[3] + 1.5 * iqr sel2 = abs_error > fns[1] - 1.5 * iqr sel = sel1 & sel2 tst = flex.max_index(flex.abs(abs_error.select(sel))) tst_val = abs_error.select(sel)[tst] n_outliers = sel.count(False) if verbose: print (" {0} outliers rejected, leaving greatest " + \ "absolute error: {1:9.6f}").format(n_outliers, tst_val) # largest absolute error now 0.000086 for dX/dp of Beam0Mu2 assert abs(tst_val) < 0.00009 # Completely skip parameters with FD gradients all zero (e.g. gradients of # DeltaPsi for detector parameters) sel1 = flex.abs(a) < 1.e-10 if sel1.all_eq(True): continue # otherwise calculate normalised errors, by dividing absolute errors by # the IQR (more stable than relative error calculation) norm_error = abs_error / iqr fns = five_number_summary(norm_error) if verbose: print (" summary of normalised errors: %9.6f %9.6f %9.6f " + \ "%9.6f %9.6f") % fns # largest normalised error found to be about 25.7 for dY/dp of # Crystal0g_param_3. try: assert flex.max(flex.abs(norm_error)) < 30 except AssertionError as e: e.args += ("extreme normalised error value: {0}".format( flex.max(flex.abs(norm_error))),) raise e # Reject outlying normalised errors and test again iqr = fns[3] - fns[1] if iqr > 0.: sel1 = norm_error < fns[3] + 1.5 * iqr sel2 = norm_error > fns[1] - 1.5 * iqr sel = sel1 & sel2 tst = flex.max_index(flex.abs(norm_error.select(sel))) tst_val = norm_error.select(sel)[tst] n_outliers = sel.count(False) # most outliers found for for dY/dp of Crystal0g_param_3 (which had # largest errors, so no surprise there). try: assert n_outliers < 250 except AssertionError as e: e.args += ("too many outliers rejected: {0}".format(n_outliers),) raise e if verbose: print (" {0} outliers rejected, leaving greatest " + \ "normalised error: {1:9.6f}").format(n_outliers, tst_val) # largest normalied error now about -4. for dX/dp of Detector0Tau1 assert abs(tst_val) < 4.5 if verbose: print return
def run_stills_pred_param(self, verbose=False): if verbose: print 'Testing derivatives for StillsPredictionParameterisation' print '========================================================' # Build a prediction parameterisation for the stills experiment pred_param = StillsPredictionParameterisation( self.stills_experiments, detector_parameterisations=[self.det_param], beam_parameterisations=[self.s0_param], xl_orientation_parameterisations=[self.xlo_param], xl_unit_cell_parameterisations=[self.xluc_param]) # Predict the reflections in place. Must do this ahead of calculating # the analytical gradients so quantities like s1 are correct from dials.algorithms.refinement.prediction import ExperimentsPredictor ref_predictor = ExperimentsPredictor(self.stills_experiments) ref_predictor(self.reflections) # get analytical gradients an_grads = pred_param.get_gradients(self.reflections) fd_grads = self.get_fd_gradients(pred_param, ref_predictor) for i, (an_grad, fd_grad) in enumerate(zip(an_grads, fd_grads)): # compare FD with analytical calculations if verbose: print "\nParameter {0}: {1}".format(i, fd_grad['name']) for idx, name in enumerate(["dX_dp", "dY_dp", "dDeltaPsi_dp"]): if verbose: print name a = fd_grad[name] b = an_grad[name] abs_error = a - b denom = a + b fns = five_number_summary(abs_error) if verbose: print (" summary of absolute errors: %9.6f %9.6f %9.6f " + \ "%9.6f %9.6f") % fns assert flex.max(flex.abs(abs_error)) < 0.0003 # largest absolute error found to be about 0.00025 for dY/dp of # Crystal0g_param_3. Reject outlying absolute errors and test again. iqr = fns[3] - fns[1] # skip further stats on errors with an iqr of near zero, e.g. dDeltaPsi_dp # for detector parameters, which are all equal to zero if iqr < 1.e-10: continue sel1 = abs_error < fns[3] + 1.5 * iqr sel2 = abs_error > fns[1] - 1.5 * iqr sel = sel1 & sel2 tst = flex.max_index(flex.abs(abs_error.select(sel))) tst_val = abs_error.select(sel)[tst] n_outliers = sel.count(False) if verbose: print (" {0} outliers rejected, leaving greatest " + \ "absolute error: {1:9.6f}").format(n_outliers, tst_val) # largest absolute error now 0.000086 for dX/dp of Beam0Mu2 assert abs(tst_val) < 0.00009 # Completely skip parameters with FD gradients all zero (e.g. gradients of # DeltaPsi for detector parameters) sel1 = flex.abs(a) < 1.e-10 if sel1.all_eq(True): continue # otherwise calculate normalised errors, by dividing absolute errors by # the IQR (more stable than relative error calculation) norm_error = abs_error / iqr fns = five_number_summary(norm_error) if verbose: print (" summary of normalised errors: %9.6f %9.6f %9.6f " + \ "%9.6f %9.6f") % fns # largest normalised error found to be about 25.7 for dY/dp of # Crystal0g_param_3. try: assert flex.max(flex.abs(norm_error)) < 30 except AssertionError as e: e.args += ("extreme normalised error value: {0}".format( flex.max(flex.abs(norm_error))), ) raise e # Reject outlying normalised errors and test again iqr = fns[3] - fns[1] if iqr > 0.: sel1 = norm_error < fns[3] + 1.5 * iqr sel2 = norm_error > fns[1] - 1.5 * iqr sel = sel1 & sel2 tst = flex.max_index(flex.abs(norm_error.select(sel))) tst_val = norm_error.select(sel)[tst] n_outliers = sel.count(False) # most outliers found for for dY/dp of Crystal0g_param_3 (which had # largest errors, so no surprise there). try: assert n_outliers < 250 except AssertionError as e: e.args += ("too many outliers rejected: {0}".format( n_outliers), ) raise e if verbose: print (" {0} outliers rejected, leaving greatest " + \ "normalised error: {1:9.6f}").format(n_outliers, tst_val) # largest normalied error now about -4. for dX/dp of Detector0Tau1 assert abs( tst_val) < 4.5, 'should be about 4 not %s' % tst_val if verbose: print return