| 1 | """ |
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| 2 | This software was developed by the University of Tennessee as part of the |
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| 3 | Distributed Data Analysis of Neutron Scattering Experiments (DANSE) |
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| 4 | project funded by the US National Science Foundation. |
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| 5 | |
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| 6 | See the license text in license.txt |
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| 7 | |
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| 8 | copyright 2008, University of Tennessee |
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| 9 | """ |
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| 10 | |
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| 11 | |
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| 12 | import numpy |
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| 13 | import math |
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| 14 | import scipy.special |
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| 15 | |
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| 16 | def smear_selection(data1D): |
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| 17 | """ |
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| 18 | Creates the right type of smearer according |
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| 19 | to the data. |
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| 20 | |
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| 21 | The canSAS format has a rule that either |
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| 22 | slit smearing data OR resolution smearing data |
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| 23 | is available. |
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| 24 | |
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| 25 | For the present purpose, we choose the one that |
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| 26 | has none-zero data. If both slit and resolution |
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| 27 | smearing arrays are filled with good data |
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| 28 | (which should not happen), then we choose the |
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| 29 | resolution smearing data. |
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| 30 | |
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| 31 | @param data1D: Data1D object |
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| 32 | """ |
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| 33 | # Sanity check. If we are not dealing with a SANS Data1D |
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| 34 | # object, just return None |
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| 35 | if data1D.__class__.__name__ != 'Data1D': |
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| 36 | return None |
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| 37 | |
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| 38 | if not hasattr(data1D, "dx") and not hasattr(data1D, "dxl") and not hasattr(data1D, "dxw"): |
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| 39 | return None |
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| 40 | |
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| 41 | # Look for resolution smearing data |
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| 42 | _found_resolution = False |
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| 43 | if data1D.dx is not None and len(data1D.dx)==len(data1D.x): |
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| 44 | |
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| 45 | # Check that we have non-zero data |
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| 46 | if data1D.dx[0]>0.0: |
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| 47 | _found_resolution = True |
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| 48 | #print "_found_resolution",_found_resolution |
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| 49 | #print "data1D.dx[0]",data1D.dx[0],data1D.dxl[0] |
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| 50 | # If we found resolution smearing data, return a QSmearer |
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| 51 | if _found_resolution == True: |
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| 52 | return QSmearer(data1D) |
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| 53 | |
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| 54 | # Look for slit smearing data |
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| 55 | _found_slit = False |
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| 56 | if data1D.dxl is not None and len(data1D.dxl)==len(data1D.x) \ |
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| 57 | and data1D.dxw is not None and len(data1D.dxw)==len(data1D.x): |
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| 58 | |
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| 59 | # Check that we have non-zero data |
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| 60 | if data1D.dxl[0]>0.0 or data1D.dxw[0]>0.0: |
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| 61 | _found_slit = True |
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| 62 | |
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| 63 | # Sanity check: all data should be the same as a function of Q |
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| 64 | for item in data1D.dxl: |
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| 65 | if data1D.dxl[0] != item: |
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| 66 | _found_resolution = False |
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| 67 | break |
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| 68 | |
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| 69 | for item in data1D.dxw: |
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| 70 | if data1D.dxw[0] != item: |
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| 71 | _found_resolution = False |
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| 72 | break |
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| 73 | #print "_found_slit",_found_slit |
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| 74 | #print "data1D.dx[0]",data1D.dx[0],data1D.dxl[0] |
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| 75 | # If we found slit smearing data, return a slit smearer |
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| 76 | if _found_slit == True: |
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| 77 | return SlitSmearer(data1D) |
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| 78 | |
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| 79 | return None |
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| 80 | |
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| 81 | |
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| 82 | class _BaseSmearer(object): |
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| 83 | |
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| 84 | def __init__(self): |
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| 85 | self.nbins = 0 |
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| 86 | self._weights = None |
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| 87 | |
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| 88 | def _compute_matrix(self): return NotImplemented |
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| 89 | |
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| 90 | def __call__(self, iq): |
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| 91 | """ |
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| 92 | Return the smeared I(q) value at the given q. |
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| 93 | The smeared I(q) is computed using a predetermined |
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| 94 | smearing matrix for a particular binning. |
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| 95 | |
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| 96 | @param q: I(q) array |
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| 97 | @return: smeared I(q) |
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| 98 | """ |
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| 99 | # Sanity check |
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| 100 | if len(iq) != self.nbins: |
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| 101 | raise RuntimeError, "Invalid I(q) vector: inconsistent array length %s <> %s" % (len(iq), self.nbins) |
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| 102 | |
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| 103 | if self._weights == None: |
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| 104 | self._compute_matrix() |
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| 105 | |
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| 106 | iq_smeared = numpy.zeros(self.nbins) |
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| 107 | # Loop over q-values |
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| 108 | idwb=[] |
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| 109 | |
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| 110 | for q_i in range(self.nbins): |
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| 111 | sum = 0.0 |
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| 112 | counts = 0.0 |
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| 113 | |
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| 114 | for i in range(self.nbins): |
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| 115 | if iq[i]==0 or self._weights[q_i][i]==0: |
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| 116 | continue |
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| 117 | else: |
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| 118 | sum += iq[i] * self._weights[q_i][i] |
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| 119 | counts += self._weights[q_i][i] |
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| 120 | #print "i,iq[i],self._weights[q_i][i] ",i,iq[i],self._weights[q_i][i] |
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| 121 | if counts == 0: |
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| 122 | iq_smeared[q_i] = 0 |
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| 123 | else: |
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| 124 | iq_smeared[q_i] = sum/counts |
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| 125 | #print "q_i,iq_smeared[q_i]",q_i,iq[i],iq_smeared[q_i] |
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| 126 | #print "iq[i],iq_smeared[q_i],sum,counts,self.nbins",iq[i], iq_smeared[q_i],sum,counts,self.nbins |
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| 127 | return iq_smeared |
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| 128 | |
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| 129 | class _SlitSmearer(_BaseSmearer): |
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| 130 | """ |
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| 131 | Slit smearing for I(q) array |
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| 132 | """ |
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| 133 | |
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| 134 | def __init__(self, nbins=None, width=None, height=None, min=None, max=None): |
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| 135 | """ |
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| 136 | Initialization |
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| 137 | |
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| 138 | @param iq: I(q) array [cm-1] |
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| 139 | @param width: slit width [A-1] |
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| 140 | @param height: slit height [A-1] |
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| 141 | @param min: Q_min [A-1] |
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| 142 | @param max: Q_max [A-1] |
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| 143 | """ |
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| 144 | ## Slit width in Q units |
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| 145 | self.width = width |
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| 146 | ## Slit height in Q units |
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| 147 | self.height = height |
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| 148 | ## Q_min (Min Q-value for I(q)) |
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| 149 | self.min = min |
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| 150 | ## Q_max (Max Q_value for I(q)) |
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| 151 | self.max = max |
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| 152 | ## Number of Q bins |
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| 153 | self.nbins = nbins |
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| 154 | ## Number of points used in the smearing computation |
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| 155 | self.npts = 10000 |
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| 156 | ## Smearing matrix |
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| 157 | self._weights = None |
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| 158 | |
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| 159 | def _compute_matrix(self): |
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| 160 | """ |
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| 161 | Compute the smearing matrix for the current I(q) array |
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| 162 | """ |
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| 163 | weights = numpy.zeros([self.nbins, self.nbins]) |
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| 164 | |
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| 165 | # Loop over all q-values |
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| 166 | for i in range(self.nbins): |
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| 167 | q = self.min + i*(self.max-self.min)/float(self.nbins-1.0) |
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| 168 | |
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| 169 | # For each q-value, compute the weight of each other q-bin |
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| 170 | # in the I(q) array |
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| 171 | npts_h = self.npts if self.height>0 else 1 |
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| 172 | npts_w = self.npts if self.width>0 else 1 |
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| 173 | |
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| 174 | # If both height and width are great than zero, |
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| 175 | # modify the number of points in each direction so |
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| 176 | # that the total number of points is still what |
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| 177 | # the user would expect (downgrade resolution) |
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| 178 | if npts_h>1 and npts_w>1: |
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| 179 | npts_h = int(math.ceil(math.sqrt(self.npts))) |
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| 180 | npts_w = npts_h |
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| 181 | |
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| 182 | for k in range(npts_h): |
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| 183 | if npts_h==1: |
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| 184 | shift_h = 0 |
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| 185 | else: |
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| 186 | shift_h = self.height/(float(npts_h-1.0)) * k |
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| 187 | for j in range(npts_w): |
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| 188 | if npts_w==1: |
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| 189 | shift_w = 0 |
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| 190 | else: |
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| 191 | shift_w = self.width/(float(npts_w-1.0)) * j |
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| 192 | q_shifted = math.sqrt( ((q-shift_w)*(q-shift_w) + shift_h*shift_h) ) |
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| 193 | q_i = int(math.floor( (q_shifted-self.min)/((self.max-self.min)/(self.nbins -1.0)) )) |
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| 194 | |
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| 195 | # Skip the entries outside our I(q) range |
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| 196 | #TODO: be careful with edge effect |
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| 197 | if q_i<self.nbins: |
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| 198 | weights[i][q_i] = weights[i][q_i]+1.0 |
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| 199 | |
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| 200 | self._weights = weights |
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| 201 | return self._weights |
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| 202 | |
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| 203 | class SlitSmearer(_SlitSmearer): |
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| 204 | """ |
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| 205 | Adaptor for slit smearing class and SANS data |
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| 206 | """ |
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| 207 | def __init__(self, data1D): |
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| 208 | """ |
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| 209 | Assumption: equally spaced bins of increasing q-values. |
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| 210 | |
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| 211 | @param data1D: data used to set the smearing parameters |
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| 212 | """ |
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| 213 | # Initialization from parent class |
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| 214 | super(SlitSmearer, self).__init__() |
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| 215 | |
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| 216 | ## Slit width |
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| 217 | self.width = 0 |
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| 218 | if data1D.dxw is not None and len(data1D.dxw)==len(data1D.x): |
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| 219 | self.width = data1D.dxw[0] |
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| 220 | # Sanity check |
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| 221 | for value in data1D.dxw: |
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| 222 | if value != self.width: |
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| 223 | raise RuntimeError, "Slit smearing parameters must be the same for all data" |
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| 224 | |
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| 225 | ## Slit height |
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| 226 | self.height = 0 |
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| 227 | if data1D.dxl is not None and len(data1D.dxl)==len(data1D.x): |
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| 228 | self.height = data1D.dxl[0] |
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| 229 | # Sanity check |
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| 230 | for value in data1D.dxl: |
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| 231 | if value != self.height: |
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| 232 | raise RuntimeError, "Slit smearing parameters must be the same for all data" |
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| 233 | |
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| 234 | ## Number of Q bins |
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| 235 | self.nbins = len(data1D.x) |
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| 236 | ## Minimum Q |
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| 237 | self.min = data1D.x[0] |
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| 238 | ## Maximum |
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| 239 | self.max = data1D.x[len(data1D.x)-1] |
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| 240 | |
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| 241 | #print "nbin,npts",self.nbins,self.npts |
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| 242 | |
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| 243 | class _QSmearer(_BaseSmearer): |
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| 244 | """ |
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| 245 | Perform Gaussian Q smearing |
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| 246 | """ |
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| 247 | |
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| 248 | def __init__(self, nbins=None, width=None, min=None, max=None): |
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| 249 | """ |
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| 250 | Initialization |
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| 251 | |
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| 252 | @param nbins: number of Q bins |
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| 253 | @param width: array standard deviation in Q [A-1] |
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| 254 | @param min: Q_min [A-1] |
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| 255 | @param max: Q_max [A-1] |
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| 256 | """ |
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| 257 | ## Standard deviation in Q [A-1] |
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| 258 | self.width = width |
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| 259 | ## Q_min (Min Q-value for I(q)) |
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| 260 | self.min = min |
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| 261 | ## Q_max (Max Q_value for I(q)) |
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| 262 | self.max = max |
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| 263 | ## Number of Q bins |
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| 264 | self.nbins = nbins |
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| 265 | ## Smearing matrix |
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| 266 | self._weights = None |
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| 267 | |
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| 268 | def _compute_matrix(self): |
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| 269 | """ |
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| 270 | Compute the smearing matrix for the current I(q) array |
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| 271 | """ |
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| 272 | weights = numpy.zeros([self.nbins, self.nbins]) |
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| 273 | |
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| 274 | # Loop over all q-values |
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| 275 | step = (self.max-self.min)/float(self.nbins-1.0) |
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| 276 | for i in range(self.nbins): |
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| 277 | q = self.min + i*step |
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| 278 | q_min = q - 0.5*step |
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| 279 | q_max = q + 0.5*step |
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| 280 | for j in range(self.nbins): |
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| 281 | q_j = self.min + j*step |
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| 282 | |
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| 283 | # Compute the fraction of the Gaussian contributing |
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| 284 | # to the q bin between q_min and q_max |
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| 285 | #value = math.exp(-math.pow((q_max-q_j),2)/(2*math.pow(self.width[j],2) )) |
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| 286 | #value += math.exp(-math.pow((q_max-q_j),2)/(2*math.pow(self.width[j],2) )) |
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| 287 | value = scipy.special.erf( (q_max-q_j)/(math.sqrt(2.0)*self.width[j]) ) |
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| 288 | value -=scipy.special.erf( (q_min-q_j)/(math.sqrt(2.0)*self.width[j]) ) |
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| 289 | weights[i][j] += value |
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| 290 | |
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| 291 | self._weights = weights |
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| 292 | return self._weights |
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| 293 | |
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| 294 | class QSmearer(_QSmearer): |
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| 295 | """ |
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| 296 | Adaptor for Gaussian Q smearing class and SANS data |
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| 297 | """ |
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| 298 | def __init__(self, data1D): |
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| 299 | """ |
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| 300 | Assumption: equally spaced bins of increasing q-values. |
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| 301 | |
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| 302 | @param data1D: data used to set the smearing parameters |
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| 303 | """ |
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| 304 | # Initialization from parent class |
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| 305 | super(QSmearer, self).__init__() |
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| 306 | |
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| 307 | ## Resolution |
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| 308 | self.width = numpy.zeros(len(data1D.x)) |
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| 309 | if data1D.dx is not None and len(data1D.dx)==len(data1D.x): |
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| 310 | self.width = data1D.dx |
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| 311 | |
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| 312 | ## Number of Q bins |
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| 313 | self.nbins = len(data1D.x) |
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| 314 | ## Minimum Q |
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| 315 | self.min = data1D.x[0] |
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| 316 | ## Maximum |
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| 317 | self.max = data1D.x[len(data1D.x)-1] |
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| 318 | |
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| 319 | |
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| 320 | if __name__ == '__main__': |
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| 321 | x = 0.001*numpy.arange(1,11) |
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| 322 | y = 12.0-numpy.arange(1,11) |
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| 323 | print x |
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| 324 | #for i in range(10): print i, 0.001 + i*0.008/9.0 |
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| 325 | #for i in range(100): print i, int(math.floor( (i/ (100/9.0)) )) |
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| 326 | |
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| 327 | |
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| 328 | s = _SlitSmearer(nbins=10, width=0.0, height=0.005, min=0.001, max=0.010) |
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| 329 | #s = _QSmearer(nbins=10, width=0.001, min=0.001, max=0.010) |
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| 330 | s._compute_matrix() |
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| 331 | |
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| 332 | sy = s(y) |
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| 333 | print sy |
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| 334 | |
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| 335 | if True: |
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| 336 | for i in range(10): |
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| 337 | print x[i],y[i], sy[i] |
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| 338 | #print q, ' : ', s.weight(q), s._compute_iq(q) |
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| 339 | #print q, ' : ', s(q), s._compute_iq(q) |
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| 340 | #s._compute_iq(q) |
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| 341 | |
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| 342 | |
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| 343 | |
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| 344 | |
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