source: sasview/src/sas/sascalc/realspace/VolumeCanvas.py @ 9e0dd49

magnetic_scattrelease-4.2.2ticket-1009ticket-1094-headlessticket-1242-2d-resolutionticket-1243ticket-1249unittest-saveload
Last change on this file since 9e0dd49 was 235f514, checked in by andyfaff, 8 years ago

MAINT: replace '== None' by 'is None'

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1#!/usr/bin/env python
2""" Volume Canvas
3
4    Simulation canvas for real-space simulation of SAS scattering intensity.
5    The user can create an arrangement of basic shapes and estimate I(q) and
6    I(q_x, q_y). Error estimates on the simulation are also available.
7   
8    Example:
9   
10    import sas.sascalc.realspace.VolumeCanvas as VolumeCanvas
11    canvas = VolumeCanvas.VolumeCanvas()
12    canvas.setParam('lores_density', 0.01)
13   
14    sphere = SphereDescriptor()
15    handle = canvas.addObject(sphere)
16
17    output, error = canvas.getIqError(q=0.1)
18    output, error = canvas.getIq2DError(0.1, 0.1)
19   
20    or alternatively:
21    iq = canvas.run(0.1)
22    i2_2D = canvas.run([0.1, 1.57])
23   
24"""
25
26from sas.models.BaseComponent import BaseComponent
27from sas.sascalc.simulation.pointsmodelpy import pointsmodelpy
28from sas.sascalc.simulation.geoshapespy import geoshapespy
29
30
31import os.path, math
32
33class ShapeDescriptor:
34    """
35        Class to hold the information about a shape
36        The descriptor holds a dictionary of parameters.
37       
38        Note: if shape parameters are accessed directly
39        from outside VolumeCanvas. The getPr method
40        should be called before evaluating I(q).
41               
42    """
43    def __init__(self):
44        """
45            Initialization
46        """
47        ## Real space object
48        self.shapeObject = None
49        ## Parameters of the object
50        self.params = {}
51        self.params["center"] = [0, 0, 0]
52        # Orientation are angular offsets in degrees with respect to X, Y, Z
53        self.params["orientation"] = [0, 0, 0]
54        # Default to lores shape
55        self.params['is_lores'] = True
56        self.params['order'] = 0
57           
58    def create(self):
59        """
60            Create an instance of the shape
61        """
62        # Set center
63        x0 = self.params["center"][0]
64        y0 = self.params["center"][1]
65        z0 = self.params["center"][2]
66        geoshapespy.set_center(self.shapeObject, x0, y0, z0)
67       
68        # Set orientation
69        x0 = self.params["orientation"][0]
70        y0 = self.params["orientation"][1]
71        z0 = self.params["orientation"][2]
72        geoshapespy.set_orientation(self.shapeObject, x0, y0, z0)
73               
74class SphereDescriptor(ShapeDescriptor):
75    """
76        Descriptor for a sphere
77       
78        The parameters are:
79            - radius [Angstroem] [default = 20 A]
80            - Contrast [A-2] [default = 1 A-2]
81           
82    """
83    def __init__(self):
84        """
85            Initialization
86        """ 
87        ShapeDescriptor.__init__(self)
88        # Default parameters
89        self.params["type"]   = "sphere"
90        # Radius of the sphere
91        self.params["radius"] = 20.0
92        # Constrast parameter
93        self.params["contrast"] = 1.0
94
95    def create(self):
96        """
97            Create an instance of the shape
98            @return: instance of the shape
99        """
100        self.shapeObject = geoshapespy.new_sphere(\
101            self.params["radius"])
102       
103        ShapeDescriptor.create(self)   
104        return self.shapeObject
105   
106class CylinderDescriptor(ShapeDescriptor):
107    """
108        Descriptor for a cylinder
109        Orientation: Default cylinder is along Y
110       
111        Parameters:
112            - Length [default = 40 A]
113            - Radius [default = 10 A]
114            - Contrast [default = 1 A-2]
115    """
116    def __init__(self):
117        """
118            Initialization
119        """ 
120        ShapeDescriptor.__init__(self)
121        # Default parameters
122        self.params["type"]   = "cylinder"
123        # Length of the cylinder
124        self.params["length"] = 40.0
125        # Radius of the cylinder
126        self.params["radius"] = 10.0
127        # Constrast parameter
128        self.params["contrast"] = 1.0
129       
130    def create(self):
131        """
132            Create an instance of the shape
133            @return: instance of the shape
134        """
135        self.shapeObject = geoshapespy.new_cylinder(\
136            self.params["radius"], self.params["length"])
137
138        ShapeDescriptor.create(self)
139        return self.shapeObject
140       
141
142class EllipsoidDescriptor(ShapeDescriptor):
143    """
144        Descriptor for an ellipsoid
145       
146        Parameters:
147            - Radius_x along the x-axis [default = 30 A]
148            - Radius_y along the y-axis [default = 20 A]
149            - Radius_z along the z-axis [default = 10 A]
150            - contrast [default = 1 A-2]
151    """
152    def __init__(self):
153        """
154            Initialization
155        """ 
156        ShapeDescriptor.__init__(self)
157        # Default parameters
158        self.params["type"]   = "ellipsoid"
159        self.params["radius_x"] = 30.0
160        self.params["radius_y"] = 20.0
161        self.params["radius_z"] = 10.0
162        self.params["contrast"] = 1.0
163       
164    def create(self):
165        """
166            Create an instance of the shape
167            @return: instance of the shape
168        """
169        self.shapeObject = geoshapespy.new_ellipsoid(\
170            self.params["radius_x"], self.params["radius_y"], 
171            self.params["radius_z"])
172       
173        ShapeDescriptor.create(self)   
174        return self.shapeObject
175       
176class HelixDescriptor(ShapeDescriptor):
177    """
178        Descriptor for an helix
179       
180        Parameters:
181            -radius_helix: the radius of the helix [default = 10 A]
182            -radius_tube: radius of the "tube" that forms the helix [default = 3 A]
183            -pitch: distance between two consecutive turns of the helix [default = 34 A]
184            -turns: number of turns of the helix [default = 3]
185            -contrast: contrast parameter [default = 1 A-2]
186    """
187    def __init__(self):
188        """
189            Initialization
190        """ 
191        ShapeDescriptor.__init__(self)
192        # Default parameters
193        self.params["type"]   = "singlehelix"
194        self.params["radius_helix"] = 10.0
195        self.params["radius_tube"] = 3.0
196        self.params["pitch"] = 34.0
197        self.params["turns"] = 3.0
198        self.params["contrast"] = 1.0
199
200    def create(self):
201        """
202            Create an instance of the shape
203            @return: instance of the shape
204        """
205        self.shapeObject = geoshapespy.new_singlehelix(\
206            self.params["radius_helix"], self.params["radius_tube"], 
207            self.params["pitch"], self.params["turns"])
208       
209        ShapeDescriptor.create(self)   
210        return self.shapeObject
211       
212class PDBDescriptor(ShapeDescriptor):
213    """
214        Descriptor for a PDB set of points
215       
216        Parameter:
217            - file = name of the PDB file
218    """
219    def __init__(self, filename):
220        """
221            Initialization
222            @param filename: name of the PDB file to load
223        """ 
224        ShapeDescriptor.__init__(self)
225        # Default parameters
226        self.params["type"]   = "pdb"
227        self.params["file"] = filename
228        self.params['is_lores'] = False
229
230    def create(self):
231        """
232            Create an instance of the shape
233            @return: instance of the shape
234        """
235        self.shapeObject = pointsmodelpy.new_pdbmodel()
236        pointsmodelpy.pdbmodel_add(self.shapeObject, self.params['file'])       
237       
238        #ShapeDescriptor.create(self)   
239        return self.shapeObject
240       
241# Define a dictionary for the shape until we find
242# a better way to create them
243shape_dict = {'sphere':SphereDescriptor,
244              'cylinder':CylinderDescriptor,
245              'ellipsoid':EllipsoidDescriptor,
246              'singlehelix':HelixDescriptor}
247       
248class VolumeCanvas(BaseComponent):
249    """
250        Class representing an empty space volume to add
251        geometrical object to.
252       
253        For 1D I(q) simulation, getPr() is called internally for the
254        first call to getIq().
255       
256    """
257   
258    def __init__(self):
259        """
260            Initialization
261        """
262        BaseComponent.__init__(self)
263       
264        ## Maximum value of q reachable
265        self.params['q_max'] = 0.1
266        self.params['lores_density'] = 0.1
267        self.params['scale'] = 1.0
268        self.params['background'] = 0.0
269       
270        self.lores_model = pointsmodelpy.new_loresmodel(self.params['lores_density'])
271        self.complex_model = pointsmodelpy.new_complexmodel()
272        self.shapes = {}
273        self.shapecount = 0       
274        self.points = None
275        self.npts = 0
276        self.hasPr = False       
277       
278    def _model_changed(self):
279        """
280            Reset internal data members to reflect the fact that the
281            real-space model has changed
282        """
283        self.hasPr  = False
284        self.points = None
285       
286    def addObject(self, shapeDesc, id = None):
287        """
288            Adds a real-space object to the canvas.
289       
290            @param shapeDesc: object to add to the canvas [ShapeDescriptor]
291            @param id: string handle for the object [string] [optional]
292            @return: string handle for the object
293        """
294        # If the handle is not provided, create one
295        if id is None:
296            id = shapeDesc.params["type"]+str(self.shapecount)
297         
298        # Self the order number
299        shapeDesc.params['order'] = self.shapecount
300        # Store the shape in a dictionary entry associated
301        # with the handle
302        self.shapes[id] = shapeDesc
303        self.shapecount += 1
304
305        # model changed, need to recalculate P(r)
306        self._model_changed()
307
308        return id
309           
310   
311    def add(self, shape, id = None):
312        """
313            The intend of this method is to eventually be able to use it
314            as a factory for the canvas and unify the simulation with the
315            analytical solutions. For instance, if one adds a cylinder and
316            it is the only shape on the canvas, the analytical solution
317            could be called. If multiple shapes are involved, then
318            simulation has to be performed.
319           
320            This function is deprecated, use addObject().
321       
322            @param shape: name of the object to add to the canvas [string]
323            @param id: string handle for the object [string] [optional]
324            @return: string handle for the object
325        """
326        # If the handle is not provided, create one
327        if id is None:
328            id = "shape"+str(self.shapecount)
329 
330        # shapeDesc = ShapeDescriptor(shape.lower())
331        if shape.lower() in shape_dict:
332            shapeDesc = shape_dict[shape.lower()]()
333        elif os.path.isfile(shape):
334            # A valid filename was supplier, create a PDB object
335            shapeDesc = PDBDescriptor(shape)
336        else:
337            raise ValueError("VolumeCanvas.add: Unknown shape %s" % shape)
338       
339        return self.addObject(shapeDesc, id)
340
341    def delete(self, id):
342        """
343            Delete a shape. The ID for the shape is required.
344            @param id: string handle for the object [string] [optional]
345        """
346
347        if id in self.shapes:
348            del self.shapes[id]
349        else:
350            raise KeyError("VolumeCanvas.delete: could not find shape ID")
351
352        # model changed, need to recalculate P(r)
353        self._model_changed()
354
355
356    def setParam(self, name, value):   
357        """
358            Function to set the value of a parameter.
359            Both VolumeCanvas parameters and shape parameters
360            are accessible.
361           
362            Note: if shape parameters are accessed directly
363            from outside VolumeCanvas. The getPr method
364            should be called before evaluating I(q).
365       
366            TODO: implemented a check method to protect
367            against that.
368       
369            @param name: name of the parameter to change
370            @param value: value to give the parameter
371        """
372       
373        # Lowercase for case insensitivity
374        name = name.lower()
375       
376        # Look for shape access
377        toks = name.split('.')
378       
379        # If a shape identifier was given, look the shape up
380        # in the dictionary
381        if len(toks):
382            if toks[0] in self.shapes:
383                # The shape was found, now look for the parameter
384                if toks[1] in self.shapes[toks[0]].params:
385                    # The parameter was found, now change it
386                    self.shapes[toks[0]].params[toks[1]] = value
387                    self._model_changed()
388                else:
389                    raise ValueError("Could not find parameter %s" % name)
390            else:
391                raise ValueError("Could not find shape %s" % toks[0])
392       
393        else:
394            # If we are not accessing the parameters of a
395            # shape, see if the parameter is part of this object
396            BaseComponent.setParam(self, name, value)
397            self._model_changed()
398
399    def getParam(self, name):   
400        """
401            @param name: name of the parameter to change
402        """
403        #TODO: clean this up
404       
405        # Lowercase for case insensitivity
406        name = name.lower()
407       
408        # Look for sub-model access
409        toks = name.split('.')
410        if len(toks) == 1:
411            try:
412                value = self.params[toks[0]]
413            except KeyError:
414                raise ValueError("VolumeCanvas.getParam: Could not find"
415                                 " %s" % name)
416            if isinstance(value, ShapeDescriptor):
417                raise ValueError("VolumeCanvas.getParam: Cannot get parameter"
418                                 " value.")
419            else:
420                return value
421
422        elif len(toks) == 2:
423            try:
424                shapeinstance = self.shapes[toks[0]]
425            except KeyError:
426                raise ValueError("VolumeCanvas.getParam: Could not find "
427                                 "%s" % name)
428
429            if not toks[1] in shapeinstance.params:
430                raise ValueError("VolumeCanvas.getParam: Could not find "
431                                 "%s" % name)
432
433            return shapeinstance.params[toks[1]]
434
435        else:
436            raise ValueError("VolumeCanvas.getParam: Could not find %s" % name)
437           
438    def getParamList(self, shapeid=None):
439        """
440               return a full list of all available parameters from
441           self.params.keys(). If a key in self.params is a instance
442           of ShapeDescriptor, extend the return list to:
443           [param1,param2,shapeid.param1,shapeid.param2.......]
444
445           If shapeid is provided, return the list of parameters that
446           belongs to that shape id only : [shapeid.param1, shapeid.param2...]
447        """
448
449        param_list = []
450        if shapeid is None:
451            for key1 in self.params:
452                #value1 = self.params[key1]
453                param_list.append(key1)
454            for key2 in self.shapes:
455                value2 = self.shapes[key2]
456                header = key2 + '.'
457                for key3 in value2.params:
458                    fullname = header + key3                 
459                    param_list.append(fullname)
460     
461        else:
462            if not shapeid in self.shapes:
463                raise ValueError("VolumeCanvas: getParamList: Could not find "
464                                 "%s" % shapeid)
465
466            header = shapeid + '.'
467            param_list = [header + param for param in self.shapes[shapeid].params]
468        return param_list
469
470    def getShapeList(self):
471        """
472            Return a list of the shapes
473        """
474        return self.shapes.keys()
475
476    def _addSingleShape(self, shapeDesc):
477        """
478            create shapeobject based on shapeDesc
479            @param shapeDesc: shape description
480        """
481        # Create the object model
482        shapeDesc.create()
483                   
484        if shapeDesc.params['is_lores']:
485            # Add the shape to the lores_model
486            pointsmodelpy.lores_add(self.lores_model, 
487                shapeDesc.shapeObject, shapeDesc.params['contrast']) 
488
489    def _createVolumeFromList(self):
490        """
491            Create a new lores model with all the shapes in our internal list
492            Whenever we change a parameter of a shape, we have to re-create
493            the whole thing.
494           
495            Items with higher 'order' number take precedence for regions
496            of space that are shared with other objects. Points in the
497            overlapping region belonging to objects with lower 'order'
498            will be ignored.
499           
500            Items are added in decreasing 'order' number.
501            The item with the highest 'order' will be added *first*.
502            [That conventions is prescribed by the realSpaceModeling module]
503        """
504       
505        # Create empty model
506        self.lores_model = \
507            pointsmodelpy.new_loresmodel(self.params['lores_density'])
508
509        # Create empty complex model
510        self.complex_model = pointsmodelpy.new_complexmodel()
511       
512        # Order the object first
513        obj_list = []
514   
515        for shape in self.shapes:
516            order = self.shapes[shape].params['order']
517            # find where to place it in the list
518            stored = False
519           
520            for i in range(len(obj_list)):
521                if obj_list[i][0] > order:
522                    obj_list.insert(i, [order, shape])
523                    stored = True
524                    break
525           
526            if not stored:
527                obj_list.append([order, shape])
528               
529        # Add each shape
530        len_list = len(obj_list)
531        for i in range(len_list-1, -1, -1):
532            shapedesc = self.shapes[obj_list[i][1]]
533            self._addSingleShape(shapedesc)
534
535        return 0     
536   
537    def getPr(self):
538        """
539            Calculate P(r) from the objects on the canvas.
540            This method should always be called after the shapes
541            on the VolumeCanvas have changed.
542           
543            @return: calculation output flag
544        """
545        # To find a complete example of the correct call order:
546        # In LORES2, in actionclass.py, method CalculateAction._get_iq()
547       
548        # If there are not shapes, do nothing
549        if len(self.shapes) == 0:
550            self._model_changed()
551            return 0
552       
553        # generate space filling points from shape list
554        self._createVolumeFromList()
555
556        self.points = pointsmodelpy.new_point3dvec()
557
558        pointsmodelpy.complexmodel_add(self.complex_model, 
559                                        self.lores_model, "LORES")
560        for shape in self.shapes:
561            if self.shapes[shape].params['is_lores'] == False:
562                pointsmodelpy.complexmodel_add(self.complex_model, 
563                    self.shapes[shape].shapeObject, "PDB")
564       
565        #pointsmodelpy.get_lorespoints(self.lores_model, self.points)
566        self.npts = pointsmodelpy.get_complexpoints(self.complex_model, self.points)
567       
568        # expecting the rmax is a positive float or 0. The maximum distance.
569        #rmax = pointsmodelpy.get_lores_pr(self.lores_model, self.points)   
570         
571        rmax = pointsmodelpy.get_complex_pr(self.complex_model, self.points) 
572        self.hasPr = True   
573
574        return rmax
575       
576    def run(self, q = 0):
577        """
578            Returns the value of I(q) for a given q-value
579            @param q: q-value ([float] or [list]) ([A-1] or [[A-1], [rad]])
580            @return: I(q) [float] [cm-1]
581        """
582        # Check for 1D q length
583        if q.__class__.__name__ == 'int' \
584            or q.__class__.__name__ == 'float':
585            return self.getIq(q)
586        # Check for 2D q-value
587        elif q.__class__.__name__ == 'list':
588            # Compute (Qx, Qy) from (Q, phi)
589            # Phi is in radian and Q-values are in A-1
590            qx = q[0]*math.cos(q[1])
591            qy = q[0]*math.sin(q[1])
592            return self.getIq2D(qx, qy)
593        # Through an exception if it's not a
594        # type we recognize
595        else:
596            raise ValueError("run(q): bad type for q")
597   
598    def runXY(self, q = 0):
599        """
600            Standard run command for the canvas.
601            Redirects to the correct method
602            according to the input type.
603            @param q: q-value [float] or [list] [A-1]
604            @return: I(q) [float] [cm-1]
605        """
606        # Check for 1D q length
607        if q.__class__.__name__ == 'int' \
608            or q.__class__.__name__ == 'float':
609            return self.getIq(q)
610        # Check for 2D q-value
611        elif q.__class__.__name__ == 'list':
612            return self.getIq2D(q[0], q[1])
613        # Through an exception if it's not a
614        # type we recognize
615        else:
616            raise ValueError("runXY(q): bad type for q")
617   
618    def _create_modelObject(self):
619        """
620            Create the simulation model obejct from the list
621            of shapes.
622           
623            This method needs to be called each time a parameter
624            changes because of the way the underlying library
625            was (badly) written. It is impossible to change a
626            parameter, or remove a shape without having to
627            refill the space points.
628           
629            TODO: improve that.
630        """
631        # To find a complete example of the correct call order:
632        # In LORES2, in actionclass.py, method CalculateAction._get_iq()
633       
634        # If there are not shapes, do nothing
635        if len(self.shapes) == 0:
636            self._model_changed()
637            return 0
638       
639        # generate space filling points from shape list
640        self._createVolumeFromList()
641
642        self.points = pointsmodelpy.new_point3dvec()
643
644        pointsmodelpy.complexmodel_add(self.complex_model, 
645                                        self.lores_model, "LORES")
646        for shape in self.shapes:
647            if self.shapes[shape].params['is_lores'] == False:
648                pointsmodelpy.complexmodel_add(self.complex_model, 
649                    self.shapes[shape].shapeObject, "PDB")
650       
651        #pointsmodelpy.get_lorespoints(self.lores_model, self.points)
652        self.npts = pointsmodelpy.get_complexpoints(self.complex_model, self.points)
653       
654       
655    def getIq2D(self, qx, qy):
656        """
657            Returns simulate I(q) for given q_x and q_y values.
658            @param qx: q_x [A-1]
659            @param qy: q_y [A-1]
660            @return: I(q) [cm-1]
661        """
662       
663        # If this is the first simulation call, we need to generate the
664        # space points
665        if self.points is None:
666            self._create_modelObject()
667           
668            # Protect against empty model
669            if self.points is None:
670                return 0
671               
672        # Evalute I(q)
673        norm =  1.0e8/self.params['lores_density']*self.params['scale']
674        return norm*pointsmodelpy.get_complex_iq_2D(self.complex_model, self.points, qx, qy)\
675            + self.params['background']
676               
677    def write_pr(self, filename):
678        """
679            Write P(r) to an output file
680            @param filename: file name for P(r) output
681        """   
682        if self.hasPr == False:
683            self.getPr()
684     
685        pointsmodelpy.outputPR(self.complex_model, filename)
686     
687    def getPrData(self):
688        """
689            Write P(r) to an output file
690            @param filename: file name for P(r) output
691        """   
692        if self.hasPr == False:
693            self.getPr()
694     
695        return pointsmodelpy.get_pr(self.complex_model)
696     
697    def getIq(self, q):
698        """
699            Returns the value of I(q) for a given q-value
700           
701            This method should remain internal to the class
702            and the run() method should be used instead.
703           
704            @param q: q-value [float]
705            @return: I(q) [float]
706        """
707       
708        if self.hasPr == False:
709            self.getPr()
710
711        # By dividing by the density instead of the actuall V/N,
712        # we have an uncertainty of +-1 on N because the number
713        # of points chosen for the simulation is int(density*volume).
714        # Propagation of error gives:
715        #   delta(1/density^2) = 2*(1/density^2)/N
716        # where N is stored in self.npts
717
718        norm =  1.0e8/self.params['lores_density']*self.params['scale']
719        #return norm*pointsmodelpy.get_lores_i(self.lores_model, q)
720        return norm*pointsmodelpy.get_complex_i(self.complex_model, q)\
721            + self.params['background']
722   
723    def getError(self, q):
724        """
725            Returns the error of I(q) for a given q-value
726            @param q: q-value [float]
727            @return: I(q) [float]
728        """
729       
730        if self.hasPr == False:
731            self.getPr()
732
733        # By dividing by the density instead of the actual V/N,
734        # we have an uncertainty of +-1 on N because the number
735        # of points chosen for the simulation is int(density*volume).
736        # Propagation of error gives:
737        #   delta(1/density^2) = 2*(1/density^2)/N
738        # where N is stored in self.npts
739
740        norm =  1.0e8/self.params['lores_density']*self.params['scale']
741        #return norm*pointsmodelpy.get_lores_i(self.lores_model, q)
742        return norm*pointsmodelpy.get_complex_i_error(self.complex_model, q)\
743            + self.params['background']
744   
745    def getIqError(self, q):
746        """
747            Return the simulated value along with its estimated
748            error for a given q-value
749           
750            Propagation of errors is used to evaluate the
751            uncertainty.
752           
753            @param q: q-value [float]
754            @return: mean, error [float, float]
755        """
756        val = self.getIq(q)
757        # Simulation error (statistical)
758        err = self.getError(q)
759        # Error on V/N
760        simerr = 2*val/self.npts
761        return val, err+simerr
762
763    def getIq2DError(self, qx, qy):
764        """
765            Return the simulated value along with its estimated
766            error for a given q-value
767           
768            Propagation of errors is used to evaluate the
769            uncertainty.
770           
771            @param qx: qx-value [float]
772            @param qy: qy-value [float]
773            @return: mean, error [float, float]
774        """
775        self._create_modelObject()
776               
777        norm =  1.0e8/self.params['lores_density']*self.params['scale']
778        val = norm*pointsmodelpy.get_complex_iq_2D(self.complex_model, self.points, qx, qy)\
779            + self.params['background']
780       
781        # Simulation error (statistical)
782        norm =  1.0e8/self.params['lores_density']*self.params['scale'] \
783                * math.pow(self.npts/self.params['lores_density'], 1.0/3.0)/self.npts
784        err = norm*pointsmodelpy.get_complex_iq_2D_err(self.complex_model, self.points, qx, qy)
785        # Error on V/N
786        simerr = 2*val/self.npts
787       
788        # The error used for the position is over-simplified.
789        # The actual error was empirically found to be about
790        # an order of magnitude larger.
791        return val, 10.0*err+simerr
792       
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