source: trunk/python/sbseparator.py @ 2711

Last change on this file since 2711 was 2711, checked in by Kana Sugimoto, 11 years ago

New Development: No

JIRA Issue: Yes (CAS-4141/CSV-1526)

Ready for Test: Yes

Interface Changes: Yes

What Interface Changed: Added asap.sbseparator.set_lo1root() = SBSeparator::set_lo1root(),

and STSideBandSep::setLO1Root()

Test Programs:

Put in Release Notes: No

Module(s): sbseparator and STSideBandSep

Description:

Added a new python method asap.sbseparator.set_lo1root() to set MS
name to search for LO1 frequency.
Underlying c++ functions are SBSeparator::set_lo1root (interface) and STSideBandSep::setLO1Root().
Also developed a capability to get relevant table names from scantable header and
fill frequencies of image side band.


File size: 24.5 KB
Line 
1import os, shutil
2import numpy
3import numpy.fft as FFT
4import math
5
6from asap.scantable import scantable
7from asap.parameters import rcParams
8from asap.logging import asaplog, asaplog_post_dec
9from asap.selector import selector
10from asap.asapgrid import asapgrid2
11from asap._asap import SBSeparator
12
13class sbseparator:
14    """
15    The sbseparator class is defined to separate SIGNAL and IMAGE
16    sideband spectra observed by frequency-switching technique.
17    It also helps supressing emmission of IMAGE sideband.
18    *** WARNING *** THIS MODULE IS EXPERIMENTAL
19    Known issues:
20    - Frequencies of IMAGE sideband cannot be reconstructed from
21      information in scantable in sideband sparation. Frequency
22      setting of SIGNAL sideband is stored in output table for now.
23    - Flag information (stored in FLAGTRA) is ignored.
24
25    Example:
26        # Create sideband separator instance whith 3 input data
27        sbsep = sbseparator(['test1.asap', 'test2.asap', 'test3.asap'])
28        # Set reference IFNO and tolerance to select data
29        sbsep.set_frequency(5, 30, frame='TOPO')
30        # Set direction tolerance to select data in unit of radian
31        sbsep.set_dirtol(1.e-5)
32        # Set rejection limit of solution
33        sbsep.set_limit(0.2)
34        # Solve image sideband as well
35        sbsep.set_both(True)
36        # Invoke sideband separation
37        sbsep.separate('testout.asap', overwrite = True)
38    """
39    def __init__(self, infiles):
40        self.intables = None
41        self.signalShift = []
42        self.imageShift = []
43        self.dsbmode = True
44        self.getboth = False
45        self.rejlimit = 0.2
46        self.baseif = -1
47        self.freqtol = 10.
48        self.freqframe = ""
49        self.solveother = False
50        self.dirtol = [1.e-5, 1.e-5] # direction tolerance in rad (2 arcsec)
51        #self.lo1 = 0.
52
53        self.tables = []
54        self.nshift = -1
55        self.nchan = -1
56
57        self.set_data(infiles)
58       
59        self.separator = SBSeparator()
60
61    @asaplog_post_dec
62    def set_data(self, infiles):
63        """
64        Set data to be processed.
65
66        infiles  : a list of filenames or scantables
67        """
68        if not (type(infiles) in (list, tuple, numpy.ndarray)):
69            infiles = [infiles]
70        if isinstance(infiles[0], scantable):
71            # a list of scantable
72            for stab in infiles:
73                if not isinstance(stab, scantable):
74                    asaplog.post()
75                    raise TypeError, "Input data is not a list of scantables."
76
77            #self.separator._setdata(infiles)
78            self._reset_data()
79            self.intables = infiles
80        else:
81            # a list of filenames
82            for name in infiles:
83                if not os.path.exists(name):
84                    asaplog.post()
85                    raise ValueError, "Could not find input file '%s'" % name
86           
87            #self.separator._setdataname(infiles)
88            self._reset_data()
89            self.intables = infiles
90
91        asaplog.push("%d files are set to process" % len(self.intables))
92
93
94    def _reset_data(self):
95        del self.intables
96        self.intables = None
97        self.signalShift = []
98        #self.imageShift = []
99        self.tables = []
100        self.nshift = -1
101        self.nchan = -1
102
103    @asaplog_post_dec
104    def set_frequency(self, baseif, freqtol, frame=""):
105        """
106        Set IFNO and frequency tolerance to select data to process.
107
108        Parameters:
109          - reference IFNO to process in the first table in the list
110          - frequency tolerance from reference IF to select data
111          frame  : frequency frame to select IF
112        """
113        self._reset_if()
114        self.baseif = baseif
115        if isinstance(freqtol,dict) and freqtol["unit"] == "Hz":
116            if freqtol['value'] > 0.:
117                self.freqtol = freqtol
118            else:
119                asaplog.post()
120                asaplog.push("Frequency tolerance should be positive value.")
121                asaplog.post("ERROR")
122                return
123        else:
124            # torelance in channel unit
125            if freqtol > 0:
126                self.freqtol = float(freqtol)
127            else:
128                asaplog.post()
129                asaplog.push("Frequency tolerance should be positive value.")
130                asaplog.post("ERROR")
131                return
132        self.freqframe = frame
133
134    def _reset_if(self):
135        self.baseif = -1
136        self.freqtol = 0
137        self.freqframe = ""
138        self.signalShift = []
139        #self.imageShift = []
140        self.tables = []
141        self.nshift = 0
142        self.nchan = -1
143
144    @asaplog_post_dec
145    def set_dirtol(self, dirtol=[1.e-5,1.e-5]):
146        """
147        Set tolerance of direction to select data
148        """
149        # direction tolerance in rad
150        if not (type(dirtol) in [list, tuple, numpy.ndarray]):
151            dirtol = [dirtol, dirtol]
152        if len(dirtol) == 1:
153            dirtol = [dirtol[0], dirtol[0]]
154        if len(dirtol) > 1:
155            self.dirtol = dirtol[0:2]
156        else:
157            asaplog.post()
158            asaplog.push("Invalid direction tolerance. Should be a list of float in unit radian")
159            asaplog.post("ERROR")
160            return
161        asaplog.post("Set direction tolerance [%f, %f] (rad)" % \
162                     (self.dirtol[0], self.dirtol[1]))
163
164    @asaplog_post_dec
165    def set_shift(self, mode="DSB", imageshift=None):
166        """
167        Set shift mode and channel shift of image band.
168
169        mode       : shift mode ['DSB'|'SSB'(='2SB')]
170                     When mode='DSB', imageshift is assumed to be equal
171                     to the shift of signal sideband but in opposite direction.
172        imageshift : a list of number of channel shift in image band of
173                     each scantable. valid only mode='SSB'
174        """
175        if mode.upper().startswith("D"):
176            # DSB mode
177            self.dsbmode = True
178            self.imageShift = []
179        else:
180            if not imageshift:
181                raise ValueError, "Need to set shift value of image sideband"
182            self.dsbmode = False
183            self.imageShift = imageshift
184            asaplog.push("Image sideband shift is set manually: %s" % str(self.imageShift))
185
186    @asaplog_post_dec
187    def set_both(self, flag=False):
188        """
189        Resolve both image and signal sideband when True.
190        """
191        self.getboth = flag
192        if self.getboth:
193            asaplog.push("Both signal and image sidebands are solved and output as separate tables.")
194        else:
195            asaplog.push("Only signal sideband is solved and output as an table.")
196
197    @asaplog_post_dec
198    def set_limit(self, threshold=0.2):
199        """
200        Set rejection limit of solution.
201        """
202        #self.separator._setlimit(abs(threshold))
203        self.rejlimit = threshold
204        asaplog.push("The threshold of rejection is set to %f" % self.rejlimit)
205
206
207    @asaplog_post_dec
208    def set_solve_other(self, flag=False):
209        """
210        Calculate spectra by subtracting the solution of the other sideband
211        when True.
212        """
213        self.solveother = flag
214        if flag:
215            asaplog.push("Expert mode: solution are obtained by subtraction of the other sideband.")
216
217    def set_lo1(self,lo1):
218        """
219        Set LO1 frequency to calculate frequency of image sideband.
220
221        lo1 : LO1 frequency in float
222        """
223        lo1val = -1.
224        if isinstance(lo1, dict) and lo1["unit"] == "Hz":
225            lo1val = lo1["value"]
226        else:
227            lo1val = float(lo1)
228        if lo1val <= 0.:
229            asaplog.push("Got negative LO1 frequency. It will be ignored.")
230            asaplog.post("WARN")
231        else:
232            self.separator.set_lo1(lo1val)
233
234
235    def set_lo1root(self, name):
236        """
237        Set MS name which stores LO1 frequency of signal side band.
238        It is used to calculate frequency of image sideband.
239
240        name : MS name which contains 'ASDM_SPECTRALWINDOW' and
241               'ASDM_RECEIVER' tables.
242        """
243        self.separator.set_lo1root(name)
244
245
246    @asaplog_post_dec
247    def separate(self, outname="", overwrite=False):
248        """
249        Invoke sideband separation.
250
251        outname   : a name of output scantable
252        overwrite : overwrite existing table
253        """
254        # List up valid scantables and IFNOs to convolve.
255        #self.separator._separate()
256        self._setup_shift()
257        #self._preprocess_tables()
258
259        nshift = len(self.tables)
260        signaltab = self._grid_outtable(self.tables[0])
261        if self.getboth:
262            imagetab = signaltab.copy()
263
264        rejrow = []
265        for irow in xrange(signaltab.nrow()):
266            currpol = signaltab.getpol(irow)
267            currbeam = signaltab.getbeam(irow)
268            currdir = signaltab.get_directionval(irow)
269            spec_array, tabidx = self._get_specarray(polid=currpol,\
270                                                     beamid=currbeam,\
271                                                     dir=currdir)
272            #if not spec_array:
273            if len(tabidx) == 0:
274                asaplog.post()
275                asaplog.push("skipping row %d" % irow)
276                rejrow.append(irow)
277                continue
278            signal = self._solve_signal(spec_array, tabidx)
279            signaltab.set_spectrum(signal, irow)
280
281            # Solve image side side band
282            if self.getboth:
283                image = self._solve_image(spec_array, tabidx)
284                imagetab.set_spectrum(image, irow)
285
286        # TODO: Need to remove rejrow form scantables here
287        signaltab.flag_row(rejrow)
288        if self.getboth:
289            imagetab.flag_row(rejrow)
290       
291        if outname == "":
292            outname = "sbsepareted.asap"
293        signalname = outname + ".signalband"
294        if os.path.exists(signalname):
295            if not overwrite:
296                raise Exception, "Output file '%s' exists." % signalname
297            else:
298                shutil.rmtree(signalname)
299        signaltab.save(signalname)
300
301        if self.getboth:
302            # Warnings
303            asaplog.post()
304            asaplog.push("Saving IMAGE sideband.")
305            #asaplog.push("Note, frequency information of IMAGE sideband cannot be properly filled so far. (future development)")
306            #asaplog.push("Storing frequency setting of SIGNAL sideband in FREQUENCIES table for now.")
307            #asaplog.post("WARN")
308
309            imagename = outname + ".imageband"
310            if os.path.exists(imagename):
311                if not overwrite:
312                    raise Exception, "Output file '%s' exists." % imagename
313                else:
314                    shutil.rmtree(imagename)
315            # Update frequency information
316            self.separator.set_imgtable(imagetab)
317            self.separator.solve_imgfreq()
318            imagetab.save(imagename)
319
320
321    def _solve_signal(self, data, tabidx=None):
322        if not tabidx:
323            tabidx = range(len(data))
324
325        tempshift = []
326        dshift = []
327        if self.solveother:
328            for idx in tabidx:
329                tempshift.append(-self.imageShift[idx])
330                dshift.append(self.signalShift[idx] - self.imageShift[idx])
331        else:
332            for idx in tabidx:
333                tempshift.append(-self.signalShift[idx])
334                dshift.append(self.imageShift[idx] - self.signalShift[idx])
335
336        shiftdata = numpy.zeros(data.shape, numpy.float)
337        for i in range(len(data)):
338            shiftdata[i] = self._shiftSpectrum(data[i], tempshift[i])
339        ifftdata = self._Deconvolution(shiftdata, dshift, self.rejlimit)
340        result_image = self._combineResult(ifftdata)
341        if not self.solveother:
342            return result_image
343        result_signal = self._subtractOtherSide(shiftdata, dshift, result_image)
344        return result_signal
345
346
347    def _solve_image(self, data, tabidx=None):
348        if not tabidx:
349            tabidx = range(len(data))
350
351        tempshift = []
352        dshift = []
353        if self.solveother:
354            for idx in tabidx:
355                tempshift.append(-self.signalShift[idx])
356                dshift.append(self.imageShift[idx] - self.signalShift[idx])
357        else:
358            for idx in tabidx:
359                tempshift.append(-self.imageShift[idx])
360                dshift.append(self.signalShift[idx] - self.imageShift[idx])
361
362        shiftdata = numpy.zeros(data.shape, numpy.float)
363        for i in range(len(data)):
364            shiftdata[i] = self._shiftSpectrum(data[i], tempshift[i])
365        ifftdata = self._Deconvolution(shiftdata, dshift, self.rejlimit)
366        result_image = self._combineResult(ifftdata)
367        if not self.solveother:
368            return result_image
369        result_signal = self._subtractOtherSide(shiftdata, dshift, result_image)
370        return result_signal
371
372    @asaplog_post_dec
373    def _grid_outtable(self, table):
374        # Generate gridded table for output (Just to get rows)
375        gridder = asapgrid2(table)
376        gridder.setIF(self.baseif)
377
378        cellx = str(self.dirtol[0])+"rad"
379        celly = str(self.dirtol[1])+"rad"
380        dirarr = numpy.array(table.get_directionval()).transpose()
381        mapx = dirarr[0].max() - dirarr[0].min()
382        mapy = dirarr[1].max() - dirarr[1].min()
383        centy = 0.5 * (dirarr[1].max() + dirarr[1].min())
384        nx = max(1, numpy.ceil(mapx*numpy.cos(centy)/self.dirtol[0]))
385        ny = max(1, numpy.ceil(mapy/self.dirtol[0]))
386
387        asaplog.push("Regrid output scantable with cell = [%s, %s]" % \
388                     (cellx, celly))
389        gridder.defineImage(nx=nx, ny=ny, cellx=cellx, celly=celly)
390        gridder.setFunc(func='box', convsupport=1)
391        gridder.setWeight(weightType='uniform')
392        gridder.grid()
393        return gridder.getResult()
394
395    @asaplog_post_dec
396    def _get_specarray(self, polid=None, beamid=None, dir=None):
397        ntable = len(self.tables)
398        spec_array = numpy.zeros((ntable, self.nchan), numpy.float)
399        nspec = 0
400        asaplog.push("Start data selection by POL=%d, BEAM=%d, direction=[%f, %f]" % (polid, beamid, dir[0], dir[1]))
401        tabidx = []
402        for itab in range(ntable):
403            tab = self.tables[itab]
404            # Select rows by POLNO and BEAMNO
405            try:
406                tab.set_selection(pols=[polid], beams=[beamid])
407                if tab.nrow() > 0: tabidx.append(itab)
408            except: # no selection
409                asaplog.post()
410                asaplog.push("table %d - No spectrum ....skipping the table" % (itab))
411                asaplog.post("WARN")
412                continue
413
414            # Select rows by direction
415            spec = numpy.zeros(self.nchan, numpy.float)
416            selrow = []
417            for irow in range(tab.nrow()):
418                currdir = tab.get_directionval(irow)
419                if (abs(currdir[0] - dir[0]) > self.dirtol[0]) or \
420                   (abs(currdir[1] - dir[1]) > self.dirtol[1]):
421                    continue
422                selrow.append(irow)
423            if len(selrow) == 0:
424                asaplog.post()
425                asaplog.push("table %d - No spectrum ....skipping the table" % (itab))
426                asaplog.post("WARN")
427                continue
428            else:
429                seltab = tab.copy()
430                seltab.set_selection(selector(rows=selrow))
431
432            if tab.nrow() > 1:
433                asaplog.push("table %d - More than a spectrum selected. averaging rows..." % (itab))
434                tab = seltab.average_time(scanav=False, weight="tintsys")
435            else:
436                tab = seltab
437
438            spec_array[nspec] = tab._getspectrum()
439            nspec += 1
440
441        if nspec != ntable:
442            asaplog.post()
443            #asaplog.push("Some tables has no spectrum with POL=%d BEAM=%d. averaging rows..." % (polid, beamid))
444            asaplog.push("Could not find corresponding rows in some tables.")
445            asaplog.push("Number of spectra selected = %d (table: %d)" % (nspec, ntable))
446            if nspec < 2:
447                asaplog.push("At least 2 spectra are necessary for convolution")
448                asaplog.post("ERROR")
449                return False, tabidx
450
451        return spec_array[0:nspec], tabidx
452
453
454    @asaplog_post_dec
455    def _setup_shift(self):
456        ### define self.tables, self.signalShift, and self.imageShift
457        if not self.intables:
458            asaplog.post()
459            raise RuntimeError, "Input data is not defined."
460        #if self.baseif < 0:
461        #    asaplog.post()
462        #    raise RuntimeError, "Reference IFNO is not defined."
463       
464        byname = False
465        #if not self.intables:
466        if isinstance(self.intables[0], str):
467            # A list of file name is given
468            if not os.path.exists(self.intables[0]):
469                asaplog.post()
470                raise RuntimeError, "Could not find '%s'" % self.intables[0]
471           
472            stab = scantable(self.intables[0],average=False)
473            ntab = len(self.intables)
474            byname = True
475        else:
476            stab = self.intables[0]
477            ntab = len(self.intables)
478
479        if len(stab.getbeamnos()) > 1:
480            asaplog.post()
481            asaplog.push("Mult-beam data is not supported by this module.")
482            asaplog.post("ERROR")
483            return
484
485        valid_ifs = stab.getifnos()
486        if self.baseif < 0:
487            self.baseif = valid_ifs[0]
488            asaplog.post()
489            asaplog.push("IFNO is not selected. Using the first IF in the first scantable. Reference IFNO = %d" % (self.baseif))
490
491        if not (self.baseif in valid_ifs):
492            asaplog.post()
493            errmsg = "IF%d does not exist in the first scantable" %  \
494                     self.baseif
495            raise RuntimeError, errmsg
496
497        asaplog.push("Start selecting tables and IFNOs to solve.")
498        asaplog.push("Checking frequency of the reference IF")
499        unit_org = stab.get_unit()
500        coord = stab._getcoordinfo()
501        frame_org = coord[1]
502        stab.set_unit("Hz")
503        if len(self.freqframe) > 0:
504            stab.set_freqframe(self.freqframe)
505        stab.set_selection(ifs=[self.baseif])
506        spx = stab._getabcissa()
507        stab.set_selection()
508        basech0 = spx[0]
509        baseinc = spx[1]-spx[0]
510        self.nchan = len(spx)
511        # frequency tolerance
512        if isinstance(self.freqtol, dict) and self.freqtol['unit'] == "Hz":
513            vftol = abs(self.freqtol['value'])
514        else:
515            vftol = abs(baseinc * float(self.freqtol))
516            self.freqtol = dict(value=vftol, unit="Hz")
517        # tolerance of frequency increment
518        inctol = abs(baseinc/float(self.nchan))
519        asaplog.push("Reference frequency setup (Table = 0, IFNO = %d):  nchan = %d, chan0 = %f Hz, incr = %f Hz" % (self.baseif, self.nchan, basech0, baseinc))
520        asaplog.push("Allowed frequency tolerance = %f Hz ( %f channels)" % (vftol, vftol/baseinc))
521        poltype0 = stab.poltype()
522
523        self.tables = []
524        self.signalShift = []
525        if self.dsbmode:
526            self.imageShift = []
527
528        for itab in range(ntab):
529            asaplog.push("Table %d:" % itab)
530            tab_selected = False
531            if itab > 0:
532                if byname:
533                    stab = scantable(self.intables[itab],average=False)
534                else:
535                    stab = self.intables[itab]
536                unit_org = stab.get_unit()
537                coord = stab._getcoordinfo()
538                frame_org = coord[1]
539                stab.set_unit("Hz")
540                if len(self.freqframe) > 0:
541                    stab.set_freqframe(self.freqframe)
542
543            # Check POLTYPE should be equal to the first table.
544            if stab.poltype() != poltype0:
545                asaplog.post()
546                raise Exception, "POLTYPE should be equal to the first table."
547            # Multiple beam data may not handled properly
548            if len(stab.getbeamnos()) > 1:
549                asaplog.post()
550                asaplog.push("table contains multiple beams. It may not be handled properly.")
551                asaplog.push("WARN")
552
553            for ifno in stab.getifnos():
554                stab.set_selection(ifs=[ifno])
555                spx = stab._getabcissa()
556                if (len(spx) != self.nchan) or \
557                   (abs(spx[0]-basech0) > vftol) or \
558                   (abs(spx[1]-spx[0]-baseinc) > inctol):
559                    continue
560                tab_selected = True
561                seltab = stab.copy()
562                seltab.set_unit(unit_org)
563                seltab.set_freqframe(frame_org)
564                self.tables.append(seltab)
565                self.signalShift.append((spx[0]-basech0)/baseinc)
566                if self.dsbmode:
567                    self.imageShift.append(-self.signalShift[-1])
568                asaplog.push("- IF%d selected: sideband shift = %16.12e channels" % (ifno, self.signalShift[-1]))
569            stab.set_selection()
570            stab.set_unit(unit_org)
571            stab.set_freqframe(frame_org)
572            if not tab_selected:
573                asaplog.post()
574                asaplog.push("No data selected in Table %d" % itab)
575                asaplog.post("WARN")
576
577        asaplog.push("Total number of IFs selected = %d" % len(self.tables))
578        if len(self.tables) < 2:
579            asaplog.post()
580            raise RuntimeError, "At least 2 IFs are necessary for convolution!"
581
582        if not self.dsbmode and len(self.imageShift) != len(self.signalShift):
583            asaplog.post()
584            errmsg = "User defined channel shift of image sideband has %d elements, while selected IFNOs are %d" % (len(self.imageShift), len(self.signalShift))
585            errmsg += "\nThe frequency tolerance (freqtol) you set may be too small."
586            raise RuntimeError, errmsg
587
588        self.signalShift = numpy.array(self.signalShift)
589        self.imageShift = numpy.array(self.imageShift)
590        self.nshift = len(self.tables)
591
592    @asaplog_post_dec
593    def _preprocess_tables(self):
594        ### temporary method to preprocess data
595        ### Do time averaging for now.
596        for itab in range(len(self.tables)):
597            self.tables[itab] = self.tables[itab].average_time(scanav=False, weight="tintsys")
598
599#     @asaplog_post_dec
600#     def _setup_image_freq(self, table):
601#         # User defined coordinate
602#         # Get from associated MS
603#         # Get from ASDM
604#         lo1 = -1.
605#         if self.lo1 > 0.:
606#             asaplog.push("Using user defined LO1 frequency %e16.12 [Hz]" % self.lo1)
607#             lo1 = self.lo1
608#         else:
609#             print "NOT IMPLEMENTED YET!!!"
610
611#     def save(self, outfile, outform="ASAP", overwrite=False):
612#         if not overwrite and os.path.exists(outfile):
613#             raise RuntimeError, "Output file '%s' already exists" % outfile
614#
615#         #self.separator._save(outfile, outform)
616
617#     def done(self):
618#         self.close()
619
620#     def close(self):
621#         pass
622#         #del self.separator
623   
624
625
626########################################################################
627    def _Deconvolution(self, data_array, shift, threshold=0.00000001):
628        FObs = []
629        Reject = 0
630        nshift, nchan = data_array.shape
631        nspec = nshift*(nshift-1)/2
632        ifftObs  = numpy.zeros((nspec, nchan), numpy.float)
633        for i in range(nshift):
634           F = FFT.fft(data_array[i])
635           FObs.append(F)
636        z = 0
637        for i in range(nshift):
638            for j in range(i+1, nshift):
639                Fobs = (FObs[i]+FObs[j])/2.0
640                dX = (shift[j]-shift[i])*2.0*math.pi/float(self.nchan)
641                #print 'dX,i,j=',dX,i,j
642                for k in range(1,self.nchan):
643                    if math.fabs(math.sin(dX*k)) > threshold:
644                        Fobs[k] += ((FObs[i][k]-FObs[j][k])/2.0/(1.0-math.cos(dX*k))*math.sin(dX*k))*1.0j
645                    else: Reject += 1
646                ifftObs[z] = FFT.ifft(Fobs)
647                z += 1
648        print 'Threshold=%s Reject=%d' % (threshold, Reject)
649        return ifftObs
650
651    def _combineResult(self, ifftObs):
652        nspec = len(ifftObs)
653        sum = ifftObs[0]
654        for i in range(1,nspec):
655            sum += ifftObs[i]
656        return(sum/float(nspec))
657
658    def _subtractOtherSide(self, data_array, shift, Data):
659        sum = numpy.zeros(len(Data), numpy.float)
660        numSP = len(data_array)
661        for i in range(numSP):
662            SPsub = data_array[i] - Data
663            sum += self._shiftSpectrum(SPsub, -shift[i])
664        return(sum/float(numSP))
665
666    def _shiftSpectrum(self, data, Shift):
667        Out = numpy.zeros(self.nchan, numpy.float)
668        w2 = Shift % 1
669        w1 = 1.0 - w2
670        for i in range(self.nchan):
671            c1 = int((Shift + i) % self.nchan)
672            c2 = (c1 + 1) % self.nchan
673            Out[c1] += data[i] * w1
674            Out[c2] += data[i] * w2
675        return Out.copy()
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