From 3ec69af3bf455dd6b32fe7be7ce53ac024d33575 Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Wed, 2 Oct 2019 11:17:55 +0200 Subject: [PATCH 01/51] [Issue203] Created tf.data._spectrafit2d.py and tf.geom._core_Optics.py --- tofu/data/_spectrafit2d.py | 475 +++++++++++++++++++++++++++++++++++++ tofu/geom/_core.py | 3 +- tofu/geom/_core_Optics.py | 179 ++++++++++++++ tofu/version.py | 2 +- 4 files changed, 656 insertions(+), 3 deletions(-) create mode 100644 tofu/data/_spectrafit2d.py create mode 100644 tofu/geom/_core_Optics.py diff --git a/tofu/data/_spectrafit2d.py b/tofu/data/_spectrafit2d.py new file mode 100644 index 000000000..36506a2b5 --- /dev/null +++ b/tofu/data/_spectrafit2d.py @@ -0,0 +1,475 @@ + + + +# Built-in +import os +import warnings + +# Common +import numpy as np +import scipy.optimize as scpopt +import scipy.constants as scpct +import matplotlib.pyplot as plt + + + +_indymod = {0: np.arange(0,195), + 1: np.arange(212,407), + 2: np.arange(424,619), + 3: np.arange(636,831), + 4: np.arange(848,1043), + 5: np.arange(1060,1255), + 6: np.arange(1272,1467)} + +def get_binnedspectra(imp='FeXXV', mod=3, path='./', + dshots=_dshots, indymod=_indymod, save=True): + + # Prepare + indy = indymod[mod] + dimp = dict(dshots[imp]) + + # Loop on shots + lextra = ['Te0','ne0','dg16'] + ls = sorted(dimp.keys()) + for shot in ls: + + # Load data + if 'tlim' in dimp[shot].keys(): + tlim = dimp[shot]['tlim'] + else: + tlim = None + try: + xics, kh = tfw.SpectroX2D.load_data(shot, + tlim=tlim, plot=False) + except Exception as err: + dimp[shot]['err'] = str(err) + continue + + # Bin data + data, t = xics._Ref['data'], xics._Ref['t'] + dimp[shot]['nt'] = t.size + spectra = np.empty((dimp[shot]['nt'], 487), dtype=float) + for ii in range(0,dimp[shot]['nt']): + spectra[ii,:] = np.nanmean(data[ii,:].reshape(1467,487)[indy,:], + axis=0) + dimp[shot]['spectra'] = spectra + dimp[shot]['t'] = t + #dimp[shot]['date'] = IRFMtb. + + # Dextra + for ss in lextra: + try: + indt = np.digitize(xics.dextra[ss]['t'], 0.5*(t[1:]+t[:-1])) + val = np.empty((dimp[shot]['nt'],),dtype=float) + std = np.empty((dimp[shot]['nt'],),dtype=float) + ssum = np.empty((dimp[shot]['nt'],),dtype=float) + for ii in range(0,dimp[shot]['nt']): + val[ii] = np.nanmean(xics.dextra[ss]['data'][indt==ii]) + std[ii] = np.nanstd(xics.dextra[ss]['data'][indt==ii]) + ssum[ii] = np.nansum(xics.dextra[ss]['data'][indt==ii]) + dimp[shot][ss] = {'mean':val, 'std':std, 'sum':ssum} + except Exception as err: + dimp[shot][ss] = {'mean':np.nan, 'std':np.nan, 'sum':np.nan} + + # Reshape dict for np.savez and pandas DataFrame + nt = np.array([dimp[shot]['nt'] for shot in ls]) + nttot = np.sum(nt) + ntcum = np.cumsum(nt) + lk = ['shot','angle','spectra','t', + 'Te0-mean','Te0-std','ne0-mean','ne0-std', + 'dg16-sum'] + dk = {} + for k in lk: + shape = (nttot,487) if k=='spectra' else (nttot,) + dk[k] = np.full(shape, np.nan) + + i0 = 0 + for ii in range(0,len(ls)): + ind = np.arange(i0,i0+nt[ii]) + dk['shot'][ind] = ls[ii] + dk['angle'][ind] = dimp[ls[ii]]['ang'] + dk['spectra'][ind,:] = dimp[ls[ii]]['spectra'] + dk['t'][ind] = dimp[ls[ii]]['t'] + dk['Te0-mean'][ind] = dimp[ls[ii]]['Te0']['mean'] + dk['Te0-std'][ind] = dimp[ls[ii]]['Te0']['std'] + dk['ne0-mean'][ind] = dimp[ls[ii]]['ne0']['mean'] + dk['ne0-std'][ind] = dimp[ls[ii]]['ne0']['std'] + dk['dg16-sum'][ind] = dimp[ls[ii]]['dg16']['sum'] + i0 = ntcum[ii] + + # Saving + if save: + name = '%s_spectra'%imp + path = os.path.abspath(path) + pfe = os.path.join(path,name+'.npz') + try: + np.savez(pfe, **dk) + print("Saved in :", pfe) + except: + import ipdb + ipdb.set_trace() + pass + return dk + + + +#################################################################### +# spectral fit +#################################################################### + + +def remove_bck(x, y): + #opt = np.polyfit(x, y, deg=0) + opt = [np.nanmin(y)] + ybis = y - opt[0] + return ybis, opt[0] + + +def get_peaks(x, y, nmax=10): + + # Prepare + ybis = np.copy(y) + A = np.empty((nmax,),dtype=y.dtype) + x0 = np.empty((nmax,),dtype=x.dtype) + sigma = np.empty((nmax,),dtype=y.dtype) + gauss = lambda xx, A, x0, sigma: A*np.exp(-(xx-x0)**2/sigma**2) + def gauss_jac(xx, A, x0, sigma): + jac = np.empty((xx.size,3),dtype=float) + jac[:,0] = np.exp(-(xx-x0)**2/sigma**2) + jac[:,1] = A*2*(xx-x0)/sigma**2 * np.exp(-(xx-x0)**2/sigma**2) + jac[:,2] = A*2*(xx-x0)**2/sigma**3 * np.exp(-(xx-x0)**2/sigma**2) + return jac + + dx = np.nanmin(np.diff(x)) + + # Loop + nn = 0 + while nn=0.): + wp = min(x.size-1, + ind + np.nonzero(np.diff(ybis[ind:],n=2)>=0.)[0][0] + 1) + else: + wp = ybis.size-1 + if np.any(np.diff(ybis[:ind+1],n=2)>=0.): + wn = max(0, np.nonzero(np.diff(ybis[:ind+1],n=2)>=0.)[0][-1] - 1) + else: + wn = 0 + width = x[wp]-x[wn] + assert width>0. + indl = np.arange(wn,wp+1) + sig = np.ones((indl.size,)) + if (np.abs(np.mean(np.diff(ybis[ind:wp+1]))) + > np.abs(np.mean(np.diff(ybis[wn:ind+1])))): + sig[indlind] = 0.5 + else: + sig[indlind] = 1.5 + p0 = (ybis[ind],x00,width)#,0.) + bounds = (np.r_[0.,x[wn],dx/2.], + np.r_[5.*ybis[ind],x[wp],5.*width]) + try: + (Ai, x0i, sigi) = scpopt.curve_fit(gauss, x[indl], ybis[indl], + p0=p0, bounds=bounds, jac=gauss_jac, + sigma=sig, x_scale='jac')[0] + except Exception as err: + print(str(err)) + import ipdb + ipdb.set_trace() + pass + + ybis = ybis - gauss(x, Ai, x0i, sigi) + A[nn] = Ai + x0[nn] = x0i + sigma[nn] = sigi + + + nn += 1 + return A, x0, sigma + +def get_p0bounds(x, y, nmax=10): + + yflat, bck = remove_bck(x,y) + A, x0, sigma = get_peaks(x, yflat, nmax=nmax) + + p0 = A.tolist() + x0.tolist() + sigma.tolist() + [bck] + + lx = [np.nanmin(x), np.nanmax(x)] + Dx = np.diff(lx) + dx = np.nanmin(np.diff(x)) + + bA = (np.zeros(nmax,), np.full((nmax,),3.*np.nanmax(y))) + bx0 = (np.full((nmax,),lx[0]-Dx/2.), np.full((nmax,),lx[1]+Dx/2.)) + bsigma = (np.full((nmax,),dx/2.), np.full((nmax,),Dx/2.)) + bbck0 = (0., np.nanmax(y)) + + bounds = (np.r_[bA[0],bx0[0],bsigma[0], bbck0[0]], + np.r_[bA[1],bx0[1],bsigma[1], bbck0[1]]) + if not np.all(bounds[0] spectrum {0} / {1}".format(ii,nspect)) + + try: + popt, pcov = scpopt.curve_fit(func_sca, x, spectra[ii,:], + jac=func_sca_jac, + p0=p0, bounds=bounds, + max_nfev=max_nfev, xtol=xtol, + x_scale='jac', + verbose=verbose) + except Exception as err: + msg = " Convergence issue for {0} / {1}\n".format(ii,nspect) + msg += " => %s\n"%str(err) + msg += " => Resetting initial guess and bounds..." + print(msg) + try: + p0, bounds = get_p0bounds(x, spectra[ii,:], nmax=nmax) + popt, pcov = scpopt.curve_fit(func_sca, x, spectra[ii,:], + jac=func_sca_jac, + p0=p0, bounds=bounds, + max_nfev=max_nfev, xtol=xtol, + x_scale='jac', + verbose=verbose) + p0 = popt + popt, pcov = scpopt.curve_fit(func_sca, x, spectra[ii,:], + jac=func_sca_jac, + p0=p0, bounds=bounds, + max_nfev=max_nfev, xtol=xtol, + x_scale='jac', + verbose=verbose) + lch.append(ii) + except Exception as err: + print(str(err)) + import ipdb + ipdb.set_trace() + continue + + + A[ii,:] = popt[:nmax] + x0[ii,:] = popt[nmax:2*nmax] + sigma[ii,:] = popt[2*nmax:3*nmax] + bck0[ii] = popt[3*nmax] + + stdi = np.sqrt(np.diag(pcov)) + Astd[ii,:] = stdi[:nmax] + x0std[ii,:] = stdi[nmax:2*nmax] + sigmastd[ii,:] = stdi[2*nmax:3*nmax] + bck0std[ii] = stdi[3*nmax] + std[ii] = np.sqrt(np.sum((spectra[ii,:]-func_sca(x,*popt))**2)) + + p0[:] = popt[:] + + if plot_debug and ii in [0,1]: + fit = func_vect(x, A[ii,:], x0[ii,:], sigma[ii,:], bck0[ii]) + + plt.figure() + ax0 = plt.subplot(2,1,1) + ax1 = plt.subplot(2,1,2, sharex=ax0, sharey=ax0) + ax0.plot(x,spectra[ii,:], '.k', + x, np.sum(fit,axis=0), '-r') + ax1.plot(x, fit.T) + + import ipdb # DB + ipdb.set_trace() # DB + + return (A,Astd), (x0,x0std), (sigma,sigmastd), (bck0,bck0std), std, lch + + + +def add_gaussianfits(dimp, nmax=10, verbose=0, percent=20, + path='./', save=False): + assert type(dimp) in [str,dict] + + # Prepare + if type(dimp) is str: + imp = str(dimp) + if '_' in imp: + imp = imp.split('_')[0] + dimp = dict(np.load(dimp+'_spectra.npz')) + inds = np.argsort(dimp['angle']) + for k in dimp.keys(): + if inds.size in dimp[k].shape: + dimp[k] = dimp[k][inds] if dimp[k].ndim==1 else dimp[k][inds,:] + else: + imp = None + save = False + + + # Compute + ind = np.arange(3,437) + x = np.arange(0,dimp['spectra'].shape[1]) + spectra = dimp['spectra'][:,ind] + A, x0, sigma, bck0, std, lch = multiplegaussianfit(x[ind], spectra, + nmax=nmax, percent=percent, + verbose=verbose) + # Store + dimp['nmax'] = nmax + dimp['indch'] = np.r_[lch] + dimp['x'] = x + dimp['ind'] = ind + dimp['A'] = A[0] + dimp['A-std'] = A[1] + dimp['x0'] = x0[0] + dimp['x0-std'] = x0[1] + dimp['sigma'] = sigma[0] + dimp['sigma-std'] = sigma[1] + dimp['bck0'] = bck0[0] + dimp['bck0-std'] = bck0[1] + dimp['std'] = std + if imp is not None: + dimp['imp'] = imp + + if save: + name = '{0}_fitted{1}'.format(imp,nmax) + path = os.path.abspath(path) + pfe = os.path.join(path,name+'.npz') + np.savez(pfe, **dimp) + print("Saved in :", pfe) + + return dimp + + + +def plot_gaussianfits(dimp, ind): + + # Prepare + x = dimp['x'] + spectra = dimp['spectra'][ind,:] + func_vect, func_sca, func_sca_jac = get_func(dimp['nmax']) + fit = func_vect(x, dimp['A'][ind,:], dimp['x0'][ind,:], + dimp['sigma'][ind,:], dimp['bck0'][ind]) + + # Plot + plt.figure(); + ax0 = plt.subplot(2,1,1) + ax1 = plt.subplot(2,1,2, sharex=ax0, sharey=ax0) + + ax0.plot(x, spectra, '.k', label='spectrum') + ax0.plot(x, np.sum(fit,axis=0), '-r', label='fit') + ax1.plot(x, fit.T) + + ax1.set_xlabel(r'x') + ax0.set_ylabel(r'data') + ax1.set_ylabel(r'data') + + +def plot_allraw(dimp): + + # Prepare + x = dimp['x'] + spectra = dimp['spectra'] + nspect = spectra.shape[0] + spectranorm = spectra / np.nanmax(spectra,axis=1)[:,np.newaxis] + + # Plot + plt.figure(); + ax0 = plt.subplot(2,1,1) + ax1 = plt.subplot(2,1,2, sharex=ax0) + + ax0.imshow(spectranorm, cmap=plt.cm.viridis, + extent=(x.min(),x.max(),0,nspect), + origin='lower', + interpolation='bilinear') + + +def extract_lines(dimp): + + nspect, nx = dimp['spectra'].shape + if dimp['imp'] == 'ArXVII': + dlines = {'w': {'range':np.arange(280,nx)}, + 'z': {'range':np.arange(0,200)}} + for k in dlines.keys(): + spect = np.copy(dimp['spectra']) + spect[:,dlines[k]['range']] = 0. + dlines[k].update({'x':np.full((nspect,),np.nan), + 'x0':np.full((nspect,),np.nan), + 'A':np.full((nspect,),np.nan), + 'sigma':np.full((nspect,),np.nan)}) + for ii in range(0,dimp['spectra'].shape[0]): + xl = dimp['x'][np.argmax(spect[ii,:])] + ind = np.argmin(np.abs(dimp['x0'][ii,:]-xl)) + dlines[k]['x'][ii] = xl + dlines[k]['x0'][ii] = dimp['x0'][ii,ind] + dlines[k]['A'][ii] = dimp['A'][ii,ind] + dlines[k]['sigma'][ii] = dimp['sigma'][ii,ind] + + dimp.update(**dlines) + return dimp diff --git a/tofu/geom/_core.py b/tofu/geom/_core.py index b4758261a..626ce63b0 100644 --- a/tofu/geom/_core.py +++ b/tofu/geom/_core.py @@ -44,7 +44,6 @@ _arrayorder = 'C' _Clock = False _Type = 'Tor' -_NUM_THREADS = 10 _PHITHETAPROJ_NPHI = 2000 _PHITHETAPROJ_NTHETA = 1000 _RES = 0.005 @@ -4518,7 +4517,7 @@ def _get_plotL(self, reflections=True, Lplot='Tot', return out def get_sample(self, res=None, resMode='abs', DL=None, method='sum', ind=None, - pts=False, compact=True, num_threads=_NUM_THREADS, Test=True): + pts=False, compact=True, num_threads=_NTHREADS, Test=True): """ Return a linear sampling of the LOS The LOS is sampled into a series a points and segments lengths diff --git a/tofu/geom/_core_Optics.py b/tofu/geom/_core_Optics.py new file mode 100644 index 000000000..a05bbfe49 --- /dev/null +++ b/tofu/geom/_core_Optics.py @@ -0,0 +1,179 @@ + +""" +This module is the geometrical part of the ToFu general package +It includes all functions and object classes necessary for tomography on Tokamaks +""" + +# Built-in +import os +import warnings +#import copy + + +# Common +import numpy as np +import datetime as dtm + +# ToFu-specific +from tofu import __version__ as __version__ +import tofu.pathfile as tfpf +import tofu.utils as utils +try: + import tofu.geom._def as _def + import tofu.geom._GG as _GG + import tofu.geom._comp as _comp + import tofu.geom._plot as _plot +except Exception: + from . import _def as _def + from . import _GG as _GG + from . import _comp as _comp + from . import _plot as _plot + +__all__ = ['Crystal'] + + + +_Type = 'Tor' +_NTHREADS = 16 + +""" +############################################################################### +############################################################################### + Ves class and functions +############################################################################### +""" + + + +class CrystalBragg(utils.ToFuObject): + """ A class defining crystals for Bragg diffraction + + A crystal can be of Type flat, cylindrical, spherical or elliptical + It is characterized by its: + - geometry (Type, dimensions, curvature radii and position/orientation) + - Material and lattice + - Bragg parameters (angle vs lambda) + + + Parameters + ---------- + Id : str / tfpf.ID + A name string or a pre-built tfpf.ID class to be used to identify this + particular instance, if a string is provided, it is fed to tfpf.ID() + dgeom : dict + An array (2,N) or (N,2) defining the contour of the vacuum vessel in a + cross-section, if not closed, will be closed automatically + dspectral: str + Flag indicating whether the vessel will be a torus ('Tor') or a linear + device ('Lin') + SavePath : None / str + If provided, forces the default saving path of the object to the + provided value + + """ + + # Fixed (class-wise) dictionary of default properties + _ddef = {'Id':{'shot':0, + 'include':['Mod','Cls','Exp','Diag', + 'Name','shot','version']}, + 'dgeom':{'Type':'Tor', 'Lim':[], 'arrayorder':'C'}, + 'dsino':{}, + 'dphys':{}, + 'dreflect':{'Type':'specular'}, + 'dmisc':{'color':'k'}} + _dplot = {'cross':{'Elt':'P', + 'dP':{'color':'k','lw':2}, + 'dI':{'color':'k','ls':'--','marker':'x','ms':8,'mew':2}, + 'dBs':{'color':'b','ls':'--','marker':'x','ms':8,'mew':2}, + 'dBv':{'color':'g','ls':'--','marker':'x','ms':8,'mew':2}, + 'dVect':{'color':'r','scale':10}}, + 'hor':{'Elt':'P', + 'dP':{'color':'k','lw':2}, + 'dI':{'color':'k','ls':'--'}, + 'dBs':{'color':'b','ls':'--'}, + 'dBv':{'color':'g','ls':'--'}, + 'Nstep':50}, + '3d':{'Elt':'P', + 'dP':{'color':(0.8,0.8,0.8,1.), + 'rstride':1,'cstride':1, + 'linewidth':0., 'antialiased':False}, + 'Lim':None, + 'Nstep':50}} + _DREFLECT_DTYPES = {'specular':0, 'diffusive':1, 'ccube':2} + + # Does not exist beofre Python 3.6 !!! + def __init_subclass__(cls, color='k', **kwdargs): + # Python 2 + super(Struct,cls).__init_subclass__(**kwdargs) + # Python 3 + #super().__init_subclass__(**kwdargs) + cls._ddef = copy.deepcopy(Struct._ddef) + cls._dplot = copy.deepcopy(Struct._dplot) + cls._set_color_ddef(cls._color) + + @classmethod + def _set_color_ddef(cls, color): + cls._ddef['dmisc']['color'] = mpl.colors.to_rgba(color) + + def __init__(self, Poly=None, Type=None, + Lim=None, pos=None, extent=None, mobile=False, + Id=None, Name=None, Exp=None, shot=None, + sino_RefPt=None, sino_nP=_def.TorNP, + Clock=False, arrayorder='C', fromdict=None, + SavePath=os.path.abspath('./'), + SavePath_Include=tfpf.defInclude, color=None): + + # To replace __init_subclass__ for Python 2 + if sys.version[0]=='2': + self._dstrip = utils.ToFuObjectBase._dstrip.copy() + self.__class__._strip_init() + + # Create a dplot at instance level + self._dplot = copy.deepcopy(self.__class__._dplot) + + kwdargs = locals() + del kwdargs['self'] + # super() + super(Struct,self).__init__(**kwdargs) + + def _reset(self): + # super() + super(Struct,self)._reset() + self._dgeom = dict.fromkeys(self._get_keys_dgeom()) + self._dsino = dict.fromkeys(self._get_keys_dsino()) + self._dphys = dict.fromkeys(self._get_keys_dphys()) + self._dreflect = dict.fromkeys(self._get_keys_dreflect()) + self._dmisc = dict.fromkeys(self._get_keys_dmisc()) + #self._dplot = copy.deepcopy(self.__class__._ddef['dplot']) + + @classmethod + def _checkformat_inputs_Id(cls, Id=None, Name=None, + Exp=None, shot=None, Type=None, + include=None, + **kwdargs): + if Id is not None: + assert isinstance(Id,utils.ID) + Name, Exp, shot, Type = Id.Name, Id.Exp, Id.shot, Id.Type + if shot is None: + shot = cls._ddef['Id']['shot'] + if Type is None: + Type = cls._ddef['dgeom']['Type'] + if include is None: + include = cls._ddef['Id']['include'] + + dins = {'Name':{'var':Name, 'cls':str}, + 'Exp': {'var':Exp, 'cls':str}, + 'shot': {'var':shot, 'cls':int}, + 'Type': {'var':Type, 'in':['Tor','Lin']}, + 'include':{'var':include, 'listof':str}} + dins, err, msg = cls._check_InputsGeneric(dins) + if err: + raise Exception(msg) + + kwdargs.update({'Name':Name, 'Exp':Exp, 'shot':shot, 'Type':Type, + 'include':include}) + return kwdargs + + ########### + # Get largs + ########### diff --git a/tofu/version.py b/tofu/version.py index cdbdcdf53..052393a80 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-52-g6f060e3' +__version__ = '1.4.1-117-gc65a988' From 872cb9484d873df9ff276c0696f1b5f04adcba37 Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Wed, 2 Oct 2019 15:33:00 +0200 Subject: [PATCH 02/51] tofu/data/_spectrafit2d.py added --- tofu/data/_spectrafit2d.py | 35 +++++++++++++++++++++++++++++++++++ tofu/version.py | 2 +- 2 files changed, 36 insertions(+), 1 deletion(-) diff --git a/tofu/data/_spectrafit2d.py b/tofu/data/_spectrafit2d.py index 36506a2b5..4be57c53a 100644 --- a/tofu/data/_spectrafit2d.py +++ b/tofu/data/_spectrafit2d.py @@ -13,6 +13,41 @@ + + +########################################################### +########################################################### +# +# From DataCam2D +# +########################################################### +########################################################### + + + + + + + + + + + + + + + + + + +########################################################### +########################################################### +# +# For inspiration +# +########################################################### +########################################################### + _indymod = {0: np.arange(0,195), 1: np.arange(212,407), 2: np.arange(424,619), diff --git a/tofu/version.py b/tofu/version.py index 052393a80..521c71bc8 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-117-gc65a988' +__version__ = '1.4.1-118-g3ec69af' From fd2f26d0bd5e8bf4683ac915f82b279bde50be8a Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Wed, 2 Oct 2019 18:02:02 +0200 Subject: [PATCH 03/51] [Issue203] Advanced tofu/data/_spectrafit2d.py --- tofu/data/_spectrafit2d.py | 377 +++++++++++++++++++++++++++++++++++++ tofu/version.py | 2 +- 2 files changed, 378 insertions(+), 1 deletion(-) diff --git a/tofu/data/_spectrafit2d.py b/tofu/data/_spectrafit2d.py index 4be57c53a..9544fcc87 100644 --- a/tofu/data/_spectrafit2d.py +++ b/tofu/data/_spectrafit2d.py @@ -14,6 +14,313 @@ +_NPEAKMAX = 10 + + + +########################################################### +########################################################### +# +# Preliminary +# utility tools for spectral fitting +# +########################################################### +########################################################### + + + +def remove_bck(x, y): + #opt = np.polyfit(x, y, deg=0) + opt = [np.nanmin(y)] + return y-opt[0], opt[0] + + +def get_peaks(x, y, nmax=None): + + if nmax is None: + nmax = _NPEAKMAX + + # Prepare + ybis = np.copy(y) + A = np.empty((nmax,),dtype=y.dtype) + x0 = np.empty((nmax,),dtype=x.dtype) + sigma = np.empty((nmax,),dtype=y.dtype) + gauss = lambda xx, A, x0, sigma: A*np.exp(-(xx-x0)**2/sigma**2) + def gauss_jac(xx, A, x0, sigma): + jac = np.empty((xx.size,3),dtype=float) + jac[:,0] = np.exp(-(xx-x0)**2/sigma**2) + jac[:,1] = A*2*(xx-x0)/sigma**2 * np.exp(-(xx-x0)**2/sigma**2) + jac[:,2] = A*2*(xx-x0)**2/sigma**3 * np.exp(-(xx-x0)**2/sigma**2) + return jac + + dx = np.nanmin(np.diff(x)) + + # Loop + nn = 0 + while nn < nmax: + ind = np.nanargmax(ybis) + x00 = x[ind] + if np.any(np.diff(ybis[ind:],n=2)>=0.): + wp = min(x.size-1, + ind + np.nonzero(np.diff(ybis[ind:],n=2)>=0.)[0][0] + 1) + else: + wp = ybis.size-1 + if np.any(np.diff(ybis[:ind+1],n=2)>=0.): + wn = max(0, np.nonzero(np.diff(ybis[:ind+1],n=2)>=0.)[0][-1] - 1) + else: + wn = 0 + width = x[wp]-x[wn] + assert width>0. + indl = np.arange(wn,wp+1) + sig = np.ones((indl.size,)) + if (np.abs(np.mean(np.diff(ybis[ind:wp+1]))) + > np.abs(np.mean(np.diff(ybis[wn:ind+1])))): + sig[indlind] = 0.5 + else: + sig[indlind] = 1.5 + p0 = (ybis[ind],x00,width)#,0.) + bounds = (np.r_[0.,x[wn],dx/2.], + np.r_[5.*ybis[ind],x[wp],5.*width]) + try: + (Ai, x0i, sigi) = scpopt.curve_fit(gauss, x[indl], ybis[indl], + p0=p0, bounds=bounds, jac=gauss_jac, + sigma=sig, x_scale='jac')[0] + except Exception as err: + print(str(err)) + import ipdb + ipdb.set_trace() + pass + + ybis = ybis - gauss(x, Ai, x0i, sigi) + A[nn] = Ai + x0[nn] = x0i + sigma[nn] = sigi + + + nn += 1 + return A, x0, sigma + +def get_p0bounds(x, y, nmax=None): + + yflat, bck = remove_bck(x,y) + A, x0, sigma = get_peaks(x, yflat, nmax=nmax) + + p0 = A.tolist() + x0.tolist() + sigma.tolist() + [bck] + + lx = [np.nanmin(x), np.nanmax(x)] + Dx = np.diff(lx) + dx = np.nanmin(np.diff(x)) + + bA = (np.zeros(nmax,), np.full((nmax,),3.*np.nanmax(y))) + bx0 = (np.full((nmax,),lx[0]-Dx/2.), np.full((nmax,),lx[1]+Dx/2.)) + bsigma = (np.full((nmax,),dx/2.), np.full((nmax,),Dx/2.)) + bbck0 = (0., np.nanmax(y)) + + bounds = (np.r_[bA[0],bx0[0],bsigma[0], bbck0[0]], + np.r_[bA[1],bx0[1],bsigma[1], bbck0[1]]) + if not np.all(bounds[0] spectrum {0} / {1}".format(ii,nspect)) + + try: + popt, pcov = scpopt.curve_fit(func_sca, x, spectra[ii,:], + jac=func_sca_jac, + p0=p0, bounds=bounds, + max_nfev=max_nfev, xtol=xtol, + x_scale='jac', + verbose=verbose) + except Exception as err: + msg = " Convergence issue for {0} / {1}\n".format(ii,nspect) + msg += " => %s\n"%str(err) + msg += " => Resetting initial guess and bounds..." + print(msg) + try: + p0, bounds = get_p0bounds(x, spectra[ii,:], nmax=nmax) + popt, pcov = scpopt.curve_fit(func_sca, x, spectra[ii,:], + jac=func_sca_jac, + p0=p0, bounds=bounds, + max_nfev=max_nfev, xtol=xtol, + x_scale='jac', + verbose=verbose) + p0 = popt + popt, pcov = scpopt.curve_fit(func_sca, x, spectra[ii,:], + jac=func_sca_jac, + p0=p0, bounds=bounds, + max_nfev=max_nfev, xtol=xtol, + x_scale='jac', + verbose=verbose) + lch.append(ii) + except Exception as err: + print(str(err)) + import ipdb + ipdb.set_trace() + continue + + + A[ii,:] = popt[:nmax] + x0[ii,:] = popt[nmax:2*nmax] + sigma[ii,:] = popt[2*nmax:3*nmax] + bck0[ii] = popt[3*nmax] + + stdi = np.sqrt(np.diag(pcov)) + Astd[ii,:] = stdi[:nmax] + x0std[ii,:] = stdi[nmax:2*nmax] + sigmastd[ii,:] = stdi[2*nmax:3*nmax] + bck0std[ii] = stdi[3*nmax] + std[ii] = np.sqrt(np.sum((spectra[ii,:]-func_sca(x,*popt))**2)) + + p0[:] = popt[:] + + if plot_debug and ii in [0,1]: + fit = func_vect(x, A[ii,:], x0[ii,:], sigma[ii,:], bck0[ii]) + + plt.figure() + ax0 = plt.subplot(2,1,1) + ax1 = plt.subplot(2,1,2, sharex=ax0, sharey=ax0) + ax0.plot(x,spectra[ii,:], '.k', + x, np.sum(fit,axis=0), '-r') + ax1.plot(x, fit.T) + + import ipdb # DB + ipdb.set_trace() # DB + + return (A,Astd), (x0,x0std), (sigma,sigmastd), (bck0,bck0std), std, lch + + + +def add_gaussianfits(dimp, nmax=None, verbose=0, percent=20, + path='./', save=False): + assert type(dimp) in [str,dict] + + # Prepare + if type(dimp) is str: + imp = str(dimp) + if '_' in imp: + imp = imp.split('_')[0] + dimp = dict(np.load(dimp+'_spectra.npz')) + inds = np.argsort(dimp['angle']) + for k in dimp.keys(): + if inds.size in dimp[k].shape: + dimp[k] = dimp[k][inds] if dimp[k].ndim==1 else dimp[k][inds,:] + else: + imp = None + save = False + + + # Compute + ind = np.arange(3,437) + x = np.arange(0,dimp['spectra'].shape[1]) + spectra = dimp['spectra'][:,ind] + A, x0, sigma, bck0, std, lch = multiplegaussianfit(x[ind], spectra, + nmax=nmax, percent=percent, + verbose=verbose) + # Store + dimp['nmax'] = nmax + dimp['indch'] = np.r_[lch] + dimp['x'] = x + dimp['ind'] = ind + dimp['A'] = A[0] + dimp['A-std'] = A[1] + dimp['x0'] = x0[0] + dimp['x0-std'] = x0[1] + dimp['sigma'] = sigma[0] + dimp['sigma-std'] = sigma[1] + dimp['bck0'] = bck0[0] + dimp['bck0-std'] = bck0[1] + dimp['std'] = std + if imp is not None: + dimp['imp'] = imp + + if save: + name = '{0}_fitted{1}'.format(imp,nmax) + path = os.path.abspath(path) + pfe = os.path.join(path,name+'.npz') + np.savez(pfe, **dimp) + print("Saved in :", pfe) + + return dimp + + + ########################################################### ########################################################### @@ -26,13 +333,83 @@ +def fit_spectra_2d_straight(data2d, nbin_init=None, nmax=None): + """ Return fitted spectra + + Can handle unique or multiple time + Takes already formatted 2d data: + - (nx, ny) + - (nt, nx, ny) + x being the horizontal / spectral direction (lambda) + + """ + ##################### + # Check / format input + ##################### + + # Check data + assert isinstance(data, np.ndarray) + assert data.ndim in [2,3] + if data.ndim == 2: + data = np.reshape((1,data.shape[0],data.shape[1])) + + # Extract shape + nt = data.shape[0] + nlamb, ny = data.shape[1:] + + # Check nbin_init vs ny + if ny % 2 != nbin_init % 2: + nbin_init += 1 + + # get indybin + indybin = np.arange(0, nbin_init) + if ny % 2 == 0: + indybin += ny/2 - nbin_init/2 + else: + indybin += (ny-1)/2 - (nbin_init-1)/2 + # get indybis + indybis = np.arange() + ##################### + # initialize output + ##################### + # results + amp = np.full((nt, ny, nmax), np.nan) + x0 = np.full((nt, ny, nmax), np.nan) + sigma = np.full((nt, ny, nmax), np.nan) + bck0 = np.full((nt, ny), np.nan) + # results std + amp_std = np.full((nt, ny, nmax), np.nan) + x0_std = np.full((nt, ny, nmax), np.nan) + sigma_std = np.full((nt, ny, nmax), np.nan) + bck0_std = np.full((nt, ny), np.nan) + std = np.full((nt, ny), np.nan) + + + ##################### + # compute fits + ##################### + + # data.shape = (nx, ny), where nx = lamb + + # Get binned spectra to deduce initial guess + databin = None + + # loop over y to fit spectra, start from middle, extent to edges + for ii in range(nt): + + # get initial guess from center or previous result + if init == 'center': + pass + else: + pass + for jj in range(nybis): diff --git a/tofu/version.py b/tofu/version.py index 521c71bc8..b8effa90d 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-118-g3ec69af' +__version__ = '1.4.1-119-g872cb94' From 1edd1a88b9279d7a32c2005dc2a6926f7a66bffb Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Wed, 2 Oct 2019 18:18:01 +0200 Subject: [PATCH 04/51] [Issue203] Advanced tofu/data/_spectrafit2d.py --- tofu/data/_spectrafit2d.py | 15 +++++++++++---- tofu/version.py | 2 +- 2 files changed, 12 insertions(+), 5 deletions(-) diff --git a/tofu/data/_spectrafit2d.py b/tofu/data/_spectrafit2d.py index 9544fcc87..e1baeca73 100644 --- a/tofu/data/_spectrafit2d.py +++ b/tofu/data/_spectrafit2d.py @@ -370,7 +370,12 @@ def fit_spectra_2d_straight(data2d, nbin_init=None, nmax=None): indybin += (ny-1)/2 - (nbin_init-1)/2 # get indybis - indybis = np.arange() + if ny % 2 ==0: + indy1 = np.arange(ny/2-1, -1, -1) + indy2 = np.arange(ny/2, ny, 1) + else: + indy1 = np.arange((ny-1)/2-1, -1, -1) + indy2 = np.arange((ny-1)/2, ny, 1) ##################### @@ -395,8 +400,6 @@ def fit_spectra_2d_straight(data2d, nbin_init=None, nmax=None): # compute fits ##################### - # data.shape = (nx, ny), where nx = lamb - # Get binned spectra to deduce initial guess databin = None @@ -404,13 +407,17 @@ def fit_spectra_2d_straight(data2d, nbin_init=None, nmax=None): for ii in range(nt): # get initial guess from center or previous result - if init == 'center': + if ii == 0 or init == 'center': pass else: pass for jj in range(nybis): + pass + # Upper half + + # Lower half diff --git a/tofu/version.py b/tofu/version.py index b8effa90d..a505f583f 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-119-g872cb94' +__version__ = '1.4.1-120-gfd2f26d' From 376ce6992b2dc80c244ecaf589dcce736846caaf Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Fri, 4 Oct 2019 18:19:29 +0200 Subject: [PATCH 05/51] [Issue203] Advanced tofu/data/_spectrafit2d.py: included simultaneous multi ellipse fitting before re-sampled 2d fitting with known x0(y) and bsplines for y --- tofu/data/_spectrafit2d.py | 221 ++++++++++++++++++++++++------------- tofu/version.py | 2 +- 2 files changed, 147 insertions(+), 76 deletions(-) diff --git a/tofu/data/_spectrafit2d.py b/tofu/data/_spectrafit2d.py index e1baeca73..5cc74df2e 100644 --- a/tofu/data/_spectrafit2d.py +++ b/tofu/data/_spectrafit2d.py @@ -128,7 +128,7 @@ def get_p0bounds(x, y, nmax=None): return p0, bounds -def get_func(n=5): +def get_func1d_all(n=5): def func_vect(x, A, x0, sigma, bck0): y = np.full((A.size+1, x.size), np.nan) for ii in range(A.size): @@ -267,57 +267,6 @@ def multiplegaussianfit(x, spectra, nmax=None, p0=None, bounds=None, -def add_gaussianfits(dimp, nmax=None, verbose=0, percent=20, - path='./', save=False): - assert type(dimp) in [str,dict] - - # Prepare - if type(dimp) is str: - imp = str(dimp) - if '_' in imp: - imp = imp.split('_')[0] - dimp = dict(np.load(dimp+'_spectra.npz')) - inds = np.argsort(dimp['angle']) - for k in dimp.keys(): - if inds.size in dimp[k].shape: - dimp[k] = dimp[k][inds] if dimp[k].ndim==1 else dimp[k][inds,:] - else: - imp = None - save = False - - - # Compute - ind = np.arange(3,437) - x = np.arange(0,dimp['spectra'].shape[1]) - spectra = dimp['spectra'][:,ind] - A, x0, sigma, bck0, std, lch = multiplegaussianfit(x[ind], spectra, - nmax=nmax, percent=percent, - verbose=verbose) - # Store - dimp['nmax'] = nmax - dimp['indch'] = np.r_[lch] - dimp['x'] = x - dimp['ind'] = ind - dimp['A'] = A[0] - dimp['A-std'] = A[1] - dimp['x0'] = x0[0] - dimp['x0-std'] = x0[1] - dimp['sigma'] = sigma[0] - dimp['sigma-std'] = sigma[1] - dimp['bck0'] = bck0[0] - dimp['bck0-std'] = bck0[1] - dimp['std'] = std - if imp is not None: - dimp['imp'] = imp - - if save: - name = '{0}_fitted{1}'.format(imp,nmax) - path = os.path.abspath(path) - pfe = os.path.join(path,name+'.npz') - np.savez(pfe, **dimp) - print("Saved in :", pfe) - - return dimp @@ -331,9 +280,81 @@ def add_gaussianfits(dimp, nmax=None, verbose=0, percent=20, ########################################################### +def fit_spectra2d_x0_per_row(): + + # Loop from centre to edges + for jj in range(ny): + out = multiplegaussianfit(x, datat[jj,:], nmax=nmax, p0=p0u, bounds=None, + max_nfev=None, xtol=1.e-8, verbose=0, + percent=20, plot_debug=False) + x0[jj,:], x0_std[jj,:] = out[:2] + for jj in range(nybis): + # Upper half + ju = indy1[jj] + out = multiplegaussianfit(x, spect, nmax=nmax, p0=p0u, bounds=None, + max_nfev=None, xtol=1.e-8, verbose=0, + percent=20, plot_debug=False) + x0[ju,:], x0_std[ju,:] = out[:2] + p0u[:nmax], p0u[nmax:2*nmax], = amp[ii,ju,:], x0[ii,ju,:] + p0u[2*nmax:3*nmax], p0u[3*nmax:] = sigma[ii,ju,:], bck0 -def fit_spectra_2d_straight(data2d, nbin_init=None, nmax=None): + # Lower half + jl = indy2[jj] + return x0 + +def fit_spectra2d_fit_ellipses(x0): + # Each lamb is associated to a cone + # All cones have the same axis, but + # - different summits + # - different opening + # All cones are intersected by the same unique plane (detector) + # => all have the same center and rotation, but + # - different minor and major radius + ellip_C = [None, None] + ellip_rot = None + ellip_radii = np.full((2, x0.shape[1]), np.nan) + + return ellip_C, ellip_rot, ellip_radii + +def get_func_x0_from_y(): + + # General ellipse equation in cartesian coordinates + ((x-x0)cos(theta) + (y-y0)*sin(theta))**2 / rx**2 + + ((x-x0)sin(theta) - (y-y0)*cos(theta))**2 / ry**2 + + # Hence x = f(y) for x > x0 + + + return + + + +def fit_spectra2d_single_from_center(): + + + return + + + + + + +def get_func2d(y0, y1, x0_y, bspl_n, bspl_deg): + knots = np.linspace(y0,y1, 6) + bspliney = scpinterp.LSQUnivariateSpline() + def func(x, y, ampy_coefs, sigy_coefs, bcky_coefs): + amp_bs = scpinterp.BSpline(knots, ampy_coefs, k=bspl_deg, + extrapolate=False, axis=0) + amp = amp_bs(y) + x0y = x0_y(y) + return np.sum(amp*np.exp((x-xoy)**2/sig**2) + bck0, axis=-1) + return func + + + +def fit_spectra_2d(data2d, indt=None, nbin_init=None, + nmax=None, bck=None, nbsplines=None): """ Return fitted spectra Can handle unique or multiple time @@ -353,30 +374,49 @@ def fit_spectra_2d_straight(data2d, nbin_init=None, nmax=None): assert data.ndim in [2,3] if data.ndim == 2: data = np.reshape((1,data.shape[0],data.shape[1])) + if indt is not None: + data = data[indt,...] + + # Set bck type + if bck is None: + bck = 0 + assert type(bck) in [int, str] + if type(bck) is int: + nbck = bck + 1 + elif bck == 'exp': + nbck = 3 # Extract shape nt = data.shape[0] nlamb, ny = data.shape[1:] + x = np.arange(0,nlamb) + + # max number of spectral lines (gaussians) + if nmax is None: + nmax = 10 # Check nbin_init vs ny + if nbin_init is None: + nbin_init = 100 if ny % 2 != nbin_init % 2: nbin_init += 1 # get indybin indybin = np.arange(0, nbin_init) if ny % 2 == 0: - indybin += ny/2 - nbin_init/2 + indybin += int(ny/2 - nbin_init/2) else: - indybin += (ny-1)/2 - (nbin_init-1)/2 + indybin += int((ny-1)/2 - (nbin_init-1)/2) # get indybis - if ny % 2 ==0: + if ny % 2 == 0: indy1 = np.arange(ny/2-1, -1, -1) indy2 = np.arange(ny/2, ny, 1) else: indy1 = np.arange((ny-1)/2-1, -1, -1) - indy2 = np.arange((ny-1)/2, ny, 1) - + indy2 = np.arange((ny-1)/2+1, ny, 1) + nybis = indy1.size + assert nybis == indy2.size ##################### # initialize output @@ -384,20 +424,53 @@ def fit_spectra_2d_straight(data2d, nbin_init=None, nmax=None): # results amp = np.full((nt, ny, nmax), np.nan) - x0 = np.full((nt, ny, nmax), np.nan) + x0 = np.full((ny, nmax), np.nan) sigma = np.full((nt, ny, nmax), np.nan) - bck0 = np.full((nt, ny), np.nan) + bck0 = np.full((nt, ny, nbck), np.nan) + p0u = np.full((nmax*3 + nbck,), np.nan) + p0l = np.full((nmax*3 + nbck,), np.nan) # results std amp_std = np.full((nt, ny, nmax), np.nan) x0_std = np.full((nt, ny, nmax), np.nan) sigma_std = np.full((nt, ny, nmax), np.nan) - bck0_std = np.full((nt, ny), np.nan) - std = np.full((nt, ny), np.nan) + bck0_std = np.full((nt, ny, nbck), np.nan) + std = np.full((nt,), np.nan) + + + ##################### + # Determine x0 for each row + ##################### + + datat = np.sum(data, axis=0) + + # Start with central binned (initial guess) + + # if ny is odd => use binned result for central line + + + x0 = None + + # Deduce ellipses + + # Derive x0_func(y, x0) ##################### - # compute fits + # Define 2d multi-gaussian + ##################### + + # Define x0(y) law + import ipdb # DB + ipdb.set_trace() # DB + + func = get_func2d() + + + + + ##################### + # compute fits, with fixed x0 ##################### # Get binned spectra to deduce initial guess @@ -406,22 +479,20 @@ def fit_spectra_2d_straight(data2d, nbin_init=None, nmax=None): # loop over y to fit spectra, start from middle, extent to edges for ii in range(nt): - # get initial guess from center or previous result - if ii == 0 or init == 'center': - pass - else: - pass - - for jj in range(nybis): - pass - # Upper half - - - # Lower half + out = fit2dspectra(x, y, data[ii,:,:]) + p0u[:nmax] = amp[ii-1,indy1[0],:] + p0u[nmax:2*nmax] = x0[ii-1,indy1[0],:] + p0u[2*nmax:3*nmax] = sigma[ii,indy1[0],:] + p0u[3*nmax:] = bck0[ii,indy1[0]] + p0l[:nmax] = amp[ii-1,indy2[0],:] + p0l[nmax:2*nmax] = x0[ii-1,indy2[0],:] + p0l[2*nmax:3*nmax] = sigma[ii,indy2[0],:] + p0l[3*nmax:] = bck0[ii,indy2[0]] + return (x0, x0_std), ( ) ########################################################### diff --git a/tofu/version.py b/tofu/version.py index a505f583f..d6d46c941 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-120-gfd2f26d' +__version__ = '1.4.1-121-g1edd1a8' From ee04449e1d337f5b65ab3697ca89ade543ef1428 Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Tue, 15 Oct 2019 18:16:31 +0200 Subject: [PATCH 06/51] [Issue203] Advanced a bit herratically spectral fits... --- tofu/data/_spectrafit2d.py | 12 ++++++++++-- tofu/version.py | 2 +- 2 files changed, 11 insertions(+), 3 deletions(-) diff --git a/tofu/data/_spectrafit2d.py b/tofu/data/_spectrafit2d.py index 5cc74df2e..c9be9181c 100644 --- a/tofu/data/_spectrafit2d.py +++ b/tofu/data/_spectrafit2d.py @@ -329,10 +329,17 @@ def get_func_x0_from_y(): return - -def fit_spectra2d_single_from_center(): +def coord_transform(ang_in, ang_cone, xc, yc, rot, ang_plane, ang_rot, Z): + x1 = None + X2 = None + return +def coord_transform(x, y, xc, yc, ang_rot, ang_plane, Z): + """ Return the coordinates transform of (x,y) in (ang_cone, ang_in) """ + x1 = (x-xc)*np.cos(ang_rot) + X2 = None + X2 = None return @@ -340,6 +347,7 @@ def fit_spectra2d_single_from_center(): + def get_func2d(y0, y1, x0_y, bspl_n, bspl_deg): knots = np.linspace(y0,y1, 6) bspliney = scpinterp.LSQUnivariateSpline() diff --git a/tofu/version.py b/tofu/version.py index 130273100..ab0cc2b65 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-122-g376ce69' +__version__ = '1.4.1-147-gfaac425' From c4146ac74773ecd65ba9daccd4557e657a58fffe Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Tue, 15 Oct 2019 18:19:13 +0200 Subject: [PATCH 07/51] [Issue203] Started latex / pdf notes on ellipse intersection with plane for spectral fits (Notes_Upgrades) --- .../SpectroX2D_ConePlaneEllipse.out | 7 + .../SpectroX2D_ConePlaneEllipse.pdf | Bin 0 -> 97581 bytes .../SpectroX2D_ConePlaneEllipse.tex | 317 ++++++++++++++++++ .../SpectroX2D_ConePlaneEllipse.toc | 8 + tofu/version.py | 2 +- 5 files changed, 333 insertions(+), 1 deletion(-) create mode 100644 Notes_Upgrades/SpectroX2D_ConePlaneEllipse.out create mode 100644 Notes_Upgrades/SpectroX2D_ConePlaneEllipse.pdf create mode 100644 Notes_Upgrades/SpectroX2D_ConePlaneEllipse.tex create mode 100644 Notes_Upgrades/SpectroX2D_ConePlaneEllipse.toc diff --git a/Notes_Upgrades/SpectroX2D_ConePlaneEllipse.out b/Notes_Upgrades/SpectroX2D_ConePlaneEllipse.out new file mode 100644 index 000000000..895e632ad --- /dev/null +++ b/Notes_Upgrades/SpectroX2D_ConePlaneEllipse.out @@ -0,0 +1,7 @@ +\BOOKMARK [0][-]{chapter.1}{Geometry}{} +\BOOKMARK [1][-]{section.1.1}{Generic cone and plane}{chapter.1} +\BOOKMARK [1][-]{section.1.2}{Intersection}{chapter.1} +\BOOKMARK [1][-]{section.1.3}{Focal-centered polar coordinates}{chapter.1} +\BOOKMARK [0][-]{appendix.A}{Acceleration radiation from a unique point-like charge}{} +\BOOKMARK [1][-]{section.A.1}{Retarded time and potential}{appendix.A} +\BOOKMARK [2][-]{subsection.A.1.1}{Retarded time}{section.A.1} diff --git a/Notes_Upgrades/SpectroX2D_ConePlaneEllipse.pdf b/Notes_Upgrades/SpectroX2D_ConePlaneEllipse.pdf new file mode 100644 index 0000000000000000000000000000000000000000..aaddb986c9dd0396b5c726e01fc552e6fb0d7389 GIT binary patch literal 97581 zcmce;2|Sfe`#5eF5!sXFAY1mcpAtfp$ew-Qvaf|~*+LPeM52W3OQGzAP_~qP$x=y$ zLR1Ll+dN2%K}aLq zt(|CPWf4-k2q{%}J$HnZGD5`Wl$D2%otLDHC_+w-*3Qiq>V)6wETU@X?rP`bjg^apjU5El4y@AM#mWmT+TF|6(ap-o&ijuk 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b/Notes_Upgrades/SpectroX2D_ConePlaneEllipse.tex @@ -0,0 +1,317 @@ +\documentclass[a4paper,11pt,twoside,titlepage,openright]{book} + +\usepackage[english]{babel} +\usepackage{color} +\usepackage{graphicx} +\usepackage{amsmath} +\numberwithin{equation}{section} +\usepackage[margin=3cm]{geometry} +\usepackage{hyperref} +\usepackage{epsfig,amsfonts} +\usepackage{xcolor,import} + + +\pagestyle{plain} + +\newcommand{\ud}[1]{\underline{#1}} +\newcommand{\lt}{\left} +\newcommand{\rt}{\right} +\DeclareMathOperator{\e0}{\epsilon_0} +\DeclareMathOperator{\n}{\underline{n}} +\DeclareMathOperator{\ei}{\underline{e}_1} +\DeclareMathOperator{\et}{\underline{e}_2} +\DeclareMathOperator{\ex}{\underline{e}_x} +\DeclareMathOperator{\ey}{\underline{e}_y} +\DeclareMathOperator{\ez}{\underline{e}_z} +\DeclareMathOperator{\DD}{\cos(\theta)^2 - \sin(\psi)^2} +\newcommand{\wdg}{\wedge} +\newcommand{\hypot}[1]{\textbf{\textcolor{green}{#1}}} + + +\begin{document} + +\title{ToFu geometric tools\\ Intersection of a cone with a plane} +\author{Didier VEZINET} +\date{15.10.2019} +\maketitle + +\tableofcontents + +\chapter{Geometry} +\label{chap:Definitions} + +\section{Generic cone and plane} + +Let's consider a half-cone $C_1$ (defined only for $z > 0$), with summit on the cartesian frame's origin $(O, \ex, \ey, \ez)$. +The cone's axis is the $(O,\ez)$ axis. +It's angular opening is $\theta$. + +Let's consider plane $P_1$, of normal $\n$, intersection axis $(O,\ez)$ at point $F$ of coordinates $(0,0,Z_F)$. +Vector $\n$ is oriented by angles $\phi$ and $\psi$ such that one can define the local frame $(F, \ei, \et, \n)$: +$$ +\lt\{ + \begin{array}{ll} + \ei & = \cos(\phi)\ex + \sin(\phi)\ey\\ + \et & = \lt(-\sin(\phi)\ex + \cos(\phi)\ey\rt)\cos(\psi) + \sin(\psi)\ez\\ + \n & = \ei \wdg \et\\ + & = \lt( \sin(\phi)\ex - \cos(\phi)\ey \rt)\sin(\psi) + \cos(\psi)\ez + \end{array} +\rt. +$$ + +We want to find all points $M$ of coordinates $(x, y, z)$ and $(x_1, x_2)$ belonging both to the cone $C_1$ and the plane $P_1$. + +$$ +M \in F_1 \Leftrightarrow \underline{OM}.\ez = \cos(\theta) \|\underline{OM}\| +$$ + +$$ +M \in P_1 \Leftrightarrow \underline{FM}.\n = 0 +$$ + + +\section{Intersection} + +If $M$ belongs to both $P_1$ and $C_1$, then: +$$ +(\underline{OM}.\ez)^2 = \cos(\theta)^2 \|\underline{OM}\|^2 +$$ + +Given that: +$$ +\begin{array}{lll} + \underline{OM} & = \underline{OF} + \underline{FM}\\ + & = Z_F\ez + x_1\ei + x_2\et\\ + & = Z_F\ez + x_1\lt(\cos(\phi)\ex + \sin(\phi)\ey\rt) + x_2\lt(\lt(-\sin(\phi)\ex + \cos(\phi)\ey\rt)\cos(\psi) + \sin(\psi)\ez\rt)\\ + & = Z_F\ez + x_1\cos(\phi)\ex + x_1\sin(\phi)\ey - x_2\sin(\phi)\cos(\psi)\ex + x_2\cos(\phi)\cos(\psi)\ey + x_2\sin(\psi)\ez\\ + & = \lt(x_1\cos(\phi) - x_2\sin(\phi)\cos(\psi)\rt)\ex + \lt(x_1\sin(\phi) + x_2\cos(\phi)\cos(\psi)\rt)\ey + \lt(Z_F + x_2\sin(\psi)\rt)\ez\\ +\end{array} +$$ + +We have: +$$ +\begin{array}{lll} + (\underline{OM}.\ez)^2 & = \lt(Z_F + x_2\sin(\psi)\rt)^2\\ + & = Z_F^2 + 2Z_Fx_2\sin(\psi) + x_2^2\sin(\psi)^2 +\end{array} +$$ + +And: +$$ +\begin{array}{lll} + \|\underline{OM}\|^2 & = & \| \lt(x_1\cos(\phi) - x_2\sin(\phi)\cos(\psi)\rt)\ex + \lt(x_1\sin(\phi) + x_2\cos(\phi)\cos(\psi)\rt)\ey + \lt(Z_F + x_2\sin(\psi)\rt)\ez\|^2\\ + & = & \lt( x_1\cos(\phi) - x_2\sin(\phi)\cos(\psi) \rt)^2\\ + & & + \lt(x_1\sin(\phi) + x_2\cos(\phi)\cos(\psi)\rt)^2\\ + & & + \lt(Z_F + x_2\sin(\psi)\rt)^2\\ + & = & x_1^2\cos(\phi)^2 - 2x_1x_2\cos(\phi)\sin(\phi)\cos(\psi) + x_2^2\sin(\phi)^2\cos(\psi)^2\\ + & & + x_1^2\sin(\phi)^2 + 2x_1x_2\sin(\phi)\cos(\phi)\cos(\psi) + x_2^2\cos(\phi)^2\cos(\psi)^2\\ + & & + Z_F^2 + 2Z_Fx_2\sin(\psi) + x_2^2\sin(\psi)^2\\ + & = & x_1^2 + x_2^2\cos(\psi)^2\\ + & & + Z_F^2 + 2Z_Fx_2\sin(\psi) + x_2^2\sin(\psi)^2\\ + & = & x_1^2 + x_2^2 + 2Z_Fx_2\sin(\psi) + Z_F^2\\ +\end{array} +$$ + +Thus: +$$ +\begin{array}{lll} + & (\underline{OM}.\ez)^2 = \cos(\theta)^2 \|\underline{OM}\|^2\\ + \Leftrightarrow & Z_F^2 + 2Z_Fx_2\sin(\psi) + x_2^2\sin(\psi)^2 = \cos(\theta)^2 \lt(x_1^2 + x_2^2 + 2Z_Fx_2\sin(\psi) + Z_F^2\rt)\\ + \Leftrightarrow & Z_F^2\lt(1-\cos(\theta)^2\rt) + 2Z_Fx_2\sin(\psi)\lt(1-\cos(\theta)^2\rt) = x_1^2\cos(\theta)^2 + x_2^2\lt(\cos(\theta)^2 - \sin(\psi)^2\rt)\\ + \Leftrightarrow & Z_F^2\sin(\theta)^2 + 2Z_Fx_2\sin(\psi)\sin(\theta)^2 = x_1^2\cos(\theta)^2 + x_2^2\lt(\cos(\theta)^2 - \sin(\psi)^2\rt)\\ +\end{array} +$$ + +Considering that by hypothesis $\theta>0$: +$$ +\begin{array}{lll} + & (\underline{OM}.\ez)^2 = \cos(\theta)^2 \|\underline{OM}\|^2\\ + \Leftrightarrow & x_1^2\cos(\theta)^2 + x_2^2\lt(\DD\rt) - 2Z_Fx_2\sin(\psi)\sin(\theta)^2 - Z_F^2\sin(\theta)^2 = 0\\ +\end{array} +$$ + +This looks like an almost reduced conic equation, except that $x_2$ needs to be rescaled, because $F$, the intersection between the axis $(O, \ez)$ and plane $P_1$ is in fact not the center of the conic but one of its focal points.\\ +Computing the $x_2$ coordinate of the center is easy by testing the particular case $x_1=0$, finding 2 solutions (the two extrema of the conic), and taking the middle. + +$$ +\begin{array}{lll} + & x_1 = 0\\ + \Rightarrow & x_2^2\lt(\DD\rt) - 2Z_Fx_2\sin(\psi)\sin(\theta)^2 - Z_F^2\sin(\theta)^2 = 0\\ +\end{array} +$$ + +Introducing +$$ +\begin{array}{lll} + \Delta & = 4Z_F^2\sin(\psi)^2\sin(\theta)^4 + 4Z_F^2\sin(\theta)^2\lt(\DD\rt)\\ + & = 4Z_F^2\sin(\theta)^2 \lt( \sin(\psi)^2\sin(\theta)^2 + \DD \rt)\\ + & = 4Z_F^2\sin(\theta)^2 \lt( -\sin(\psi)^2\cos(\theta)^2 + \cos(\theta)^2 \rt)\\ + & = 4Z_F^2\sin(\theta)^2 \cos(\theta)^2\cos(\psi)^2 +\end{array} +$$ + +Hence, solutions always exist. +The solutions are: +$$ +\begin{array}{lll} + x_2^{1,2} & = \frac{2Z_F\sin(\psi)\sin(\theta)^2 \pm 2Z_F\sin(\theta) \cos(\theta) \cos(\psi)}{2\lt(\DD\rt)}\\ + & = Z_F\sin(\theta) \frac{\sin(\psi)\sin(\theta) \pm \cos(\theta)\cos(\psi)}{\DD} +\end{array} +$$ + +Thus, the average is: +$$ +\begin{array}{lll} + x_2(C) = & = \frac{1}{2} 2 Z_F\sin(\theta) \frac{\sin(\psi)\sin(\theta)}{\DD} + & = Z_F\sin(\theta)^2 \frac{\sin(\psi)}{\DD} +\end{array} +$$ + +Hence, let's introduce the new coordinate: +$$ +X_2 = x_2 - x_2(C) = x_2 - Z_F\sin(\theta)^2 \frac{\sin(\psi)}{\DD} +$$ + +Then: +$$ +\begin{array}{lll} + & X_2^2 & = x_2^2 - 2Z_Fx_2\sin(\theta)^2 \frac{\sin(\psi)}{\DD} + \sin(\theta)^4 \lt[\frac{\sin(\psi)}{\DD}\rt]^2\\ + \Leftrightarrow & X_2^2\lt(\DD\rt) & = x_2^2\lt(\DD\rt) - 2Z_Fx_2\sin(\theta)^2\sin(\psi) + \sin(\theta)^4 \frac{\sin(\psi)^2}{\DD}\\ +\end{array} +$$ + +Hence: + +$$ +\begin{array}{lll} + & (\underline{OM}.\ez)^2 = \cos(\theta)^2 \|\underline{OM}\|^2\\ + \Leftrightarrow & x_1^2\cos(\theta)^2 + X_2^2\lt(\DD\rt) - \frac{\sin(\psi)^2\sin(\theta)^4}{\DD} - Z_F^2\sin(\theta)^2 = 0\\ + \Leftrightarrow & x_1^2\cos(\theta)^2 + X_2^2\lt(\DD\rt) = \lt[\frac{\sin(\psi)^2\sin(\theta)^2}{\DD} + Z_F^2\rt]\sin(\theta)^2\\ +\end{array} +$$ + +Of the form $\frac{x_1^2}{a^2} + \frac{X_2^2}{b^2} = 1$: +$$ +\begin{array}{lll} + & \frac{x_1^2}{\lt[\frac{\sin(\psi)^2\sin(\theta)^2}{\DD} + Z_F^2\rt]\tan(\theta)^2} + \frac{X_2^2}{\lt[\frac{\sin(\psi)^2\sin(\theta)^2}{\DD} + Z_F^2\rt]\frac{\sin(\theta)^2}{\DD}} = 1\\ +\end{array} +$$ + +With $b^2 = \lt(1-\frac{\sin(\psi)^2}{\cos(\theta)^2}\rt)a^2$ + +\section{Focal-centered polar coordinates} + +In our case, only the axes $(O, \ez)$, fixed by the crystal's summit and normal, is independent from the cone's angular opening $\theta$. +It makes sense to design an ad-hoc coordinate system centered not on the ellipse's center $C$, but on the focal point $F$. +The ellipse will be parameterized by an angle $\epsilon$ around $F$, which is in fact the angle around the crystal's summit $O$ at which the ray beam is coming / leaving. +The other coordinate will thus be the radius $r$, in the plane, from $F$. + +We have seen that the ellipse can be defined by: +$$ +\begin{array}{lll} + & \frac{x_1^2}{\lt[\frac{\sin(\psi)^2\sin(\theta)^2}{\DD} + Z_F^2\rt]\tan(\theta)^2} + \frac{X_2^2}{\lt[\frac{\sin(\psi)^2\sin(\theta)^2}{\DD} + Z_F^2\rt]\frac{\sin(\theta)^2}{\DD}} = 1\\ +\end{array} +$$ + +By definition, in the local frame defined from the plane's orientation: +$$ +\ud{FM} = r\cos(\epsilon)\ei + r\sin(\epsilon)\et +$$ + +Hence: +$$ +\lt\{ + \begin{array}{ll} + r\cos(\epsilon) = x_1\\ + r\sin(\epsilon) = x_2 = X_2 + Z_F\sin(\theta)^2 \frac{\sin(\psi)}{\DD} + \end{array}{ll} +\rt. +$$ + +Necesarrily: +$$ +r^2 = x_1^2 + \lt(X_2 + Z_F\sin(\theta)^2 \frac{\sin(\psi)}{\DD}\rt)^2 +$$ + + + + +%\section{Coordinate Transforms} + +%Let's consider the same cone and plane as before. +%But this time we are looking at a small fraction of the ellipse, the fraction intersecting a bounded box on the plane, with a local frame $(R, \ud{e}_i, \ud{e}_j)$, rotated by an angle $\ksi$ from the natural plane frame such that: +%$$ +%\lt\{ + %\begin{array}{lll} + %\ud{e}_i = \cos(\ksi)\ei + \sin(\ksi)\et\\ + %\ud{e}_j = -\sin(\ksi)\ei + \cos(\ksi)\et\\ + %\end{array} +%\rt. +%$$ + +%And reciprocately: +%$$ +%\lt\{ + %\begin{array}{lll} + %\ei = \cos(\ksi)\ud{e}_i - \sin(\ksi)\ud{e}_j\\ + %\et = \sin(\ksi)\ud{e}_i + \cos(\ksi)\ud{e}_j\\ + %\end{array} +%\rt. +%$$ + +%Such that: +%$$ +%\begin{array}{lll} + %\ud{CM} & = \ud{CR} + \ud{RM}\\ + %& = x_1(R)\ei + X_2(R)\et + i\ud{e}_i + j\ud{e}_j\\ + %& = \lt(x_1(R) + i\cos(\ksi) - j\sin(\ksi)\rt)\ei + \lt(X_2(R) + i\sin(\ksi) + j\cos(\ksi)\rt)\et\\ +%\end{array} +%$$ + +%Keeping in mind that: +%$$ +%X_2 = x_2 - Z_F\sin(\theta)^2 \frac{\sin(\psi)}{\DD} +%$$ + +%We can write: +%$$ +%x_1 = x_1(R) + i\cos(\ksi) - j\sin(\ksi) +%X_2 = x_2(R) - Z_F\sin(\theta)^2 \frac{\sin(\psi)}{\DD} + i\sin(\ksi) + j\cos(\ksi) +%$$ + +%We want to easily transform between $(i,j)$ and $(\theta, \espilon)$, where $\epsilon$ is the angle of a point along the ellipse of cone width $\theta$, with respect to its center $C$. + + +%\subsection{From cone to local cartesian} + +%Knowing all geometrical parameters, we can infer: +%$$ +%\begin{array}{lll} + %\underline{RM} & = i\ud{e}_i + j\ud{e}_j\\ + %& = \underline{RC} + \underline{CM}\\ + %& = -x_1(R)\ei - X_2(R)\et + x_1\ei + X_2\et\\ +%\end{array} +%$$ + + + + +%\subsection{From local cartesian to cone} + +%$$ +%x1 = +%$$ + + + +\appendix +\chapter{Acceleration radiation from a unique point-like charge} + +\section{Retarded time and potential} +\subsection{Retarded time} + + +Hence $\frac{dR(t_r)}{c} + dt_r = dt$ + + +\end{document} diff --git a/Notes_Upgrades/SpectroX2D_ConePlaneEllipse.toc b/Notes_Upgrades/SpectroX2D_ConePlaneEllipse.toc new file mode 100644 index 000000000..1d7b23b4e --- /dev/null +++ b/Notes_Upgrades/SpectroX2D_ConePlaneEllipse.toc @@ -0,0 +1,8 @@ +\select@language {english} +\contentsline {chapter}{\numberline {1}Geometry}{5}{chapter.1} +\contentsline {section}{\numberline {1.1}Generic cone and plane}{5}{section.1.1} +\contentsline {section}{\numberline {1.2}Intersection}{5}{section.1.2} +\contentsline {section}{\numberline {1.3}Focal-centered polar coordinates}{7}{section.1.3} +\contentsline {chapter}{\numberline {A}Acceleration radiation from a unique point-like charge}{9}{appendix.A} +\contentsline {section}{\numberline {A.1}Retarded time and potential}{9}{section.A.1} +\contentsline {subsection}{\numberline {A.1.1}Retarded time}{9}{subsection.A.1.1} diff --git a/tofu/version.py b/tofu/version.py index ab0cc2b65..72b8624c4 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-147-gfaac425' +__version__ = '1.4.1-148-gee04449' From 54d77e7e6fbb78a4e2ebb74cfa9bee9e1d7ffd81 Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Wed, 16 Oct 2019 08:35:05 +0200 Subject: [PATCH 08/51] [Issue203] Moved notes to Notes_Upgrades/SpectroX2D --- .../SpectroX2D_ConePlaneEllipse.out | 0 .../SpectroX2D_ConePlaneEllipse.pdf | Bin .../SpectroX2D_ConePlaneEllipse.tex | 0 .../SpectroX2D_ConePlaneEllipse.toc | 0 tofu/version.py | 2 +- 5 files changed, 1 insertion(+), 1 deletion(-) rename Notes_Upgrades/{ => SpectroX2D}/SpectroX2D_ConePlaneEllipse.out (100%) rename Notes_Upgrades/{ => SpectroX2D}/SpectroX2D_ConePlaneEllipse.pdf (100%) rename Notes_Upgrades/{ => SpectroX2D}/SpectroX2D_ConePlaneEllipse.tex (100%) rename Notes_Upgrades/{ => SpectroX2D}/SpectroX2D_ConePlaneEllipse.toc (100%) diff --git a/Notes_Upgrades/SpectroX2D_ConePlaneEllipse.out b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out similarity index 100% rename from Notes_Upgrades/SpectroX2D_ConePlaneEllipse.out rename to Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out diff --git a/Notes_Upgrades/SpectroX2D_ConePlaneEllipse.pdf b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.pdf similarity index 100% rename from Notes_Upgrades/SpectroX2D_ConePlaneEllipse.pdf rename to Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.pdf diff --git a/Notes_Upgrades/SpectroX2D_ConePlaneEllipse.tex b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.tex similarity index 100% rename from Notes_Upgrades/SpectroX2D_ConePlaneEllipse.tex rename to Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.tex diff --git a/Notes_Upgrades/SpectroX2D_ConePlaneEllipse.toc b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.toc similarity index 100% rename from Notes_Upgrades/SpectroX2D_ConePlaneEllipse.toc rename to Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.toc diff --git a/tofu/version.py b/tofu/version.py index 72b8624c4..1ef9913d5 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-148-gee04449' +__version__ = '1.4.1-149-gc4146ac' From a6825f52cb2c709041f3a5d211e1c52851ce4850 Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Wed, 16 Oct 2019 12:33:10 +0200 Subject: [PATCH 09/51] [Issue203] Ellipses coordinates transform ok until direct problem (Notes) => try with crystal method --- .../SpectroX2D_ConePlaneEllipse.out | 2 +- .../SpectroX2D_ConePlaneEllipse.pdf | Bin 97581 -> 96316 bytes .../SpectroX2D_ConePlaneEllipse.tex | 171 +++++++++--------- .../SpectroX2D_ConePlaneEllipse.toc | 2 +- tofu/version.py | 2 +- 5 files changed, 89 insertions(+), 88 deletions(-) diff --git a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out index 895e632ad..46f992615 100644 --- a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out +++ b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out @@ -1,7 +1,7 @@ \BOOKMARK [0][-]{chapter.1}{Geometry}{} \BOOKMARK [1][-]{section.1.1}{Generic cone and plane}{chapter.1} \BOOKMARK [1][-]{section.1.2}{Intersection}{chapter.1} -\BOOKMARK [1][-]{section.1.3}{Focal-centered polar coordinates}{chapter.1} +\BOOKMARK [1][-]{section.1.3}{Parametric equation}{chapter.1} \BOOKMARK [0][-]{appendix.A}{Acceleration radiation from a unique point-like charge}{} \BOOKMARK 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It's angular opening is $\theta$. -Let's consider plane $P_1$, of normal $\n$, intersection axis $(O,\ez)$ at point $F$ of coordinates $(0,0,Z_F)$. -Vector $\n$ is oriented by angles $\phi$ and $\psi$ such that one can define the local frame $(F, \ei, \et, \n)$: +Let's consider plane $P_1$, of normal $\n$, intersection axis $(O,\ez)$ at point $P$ of coordinates $(0,0,Z_P)$. +Vector $\n$ is oriented by angles $\phi$ and $\psi$ such that one can define the local frame $(P, \ei, \et, \n)$: $$ \lt\{ \begin{array}{ll} @@ -62,11 +62,11 @@ \section{Generic cone and plane} We want to find all points $M$ of coordinates $(x, y, z)$ and $(x_1, x_2)$ belonging both to the cone $C_1$ and the plane $P_1$. $$ -M \in F_1 \Leftrightarrow \underline{OM}.\ez = \cos(\theta) \|\underline{OM}\| +M \in C_1 \Leftrightarrow \underline{OM}.\ez = \cos(\theta) \|\underline{OM}\| $$ $$ -M \in P_1 \Leftrightarrow \underline{FM}.\n = 0 +M \in P_1 \Leftrightarrow \underline{PM}.\n = 0 $$ @@ -80,35 +80,35 @@ \section{Intersection} Given that: $$ \begin{array}{lll} - \underline{OM} & = \underline{OF} + \underline{FM}\\ - & = Z_F\ez + x_1\ei + x_2\et\\ - & = Z_F\ez + x_1\lt(\cos(\phi)\ex + \sin(\phi)\ey\rt) + x_2\lt(\lt(-\sin(\phi)\ex + \cos(\phi)\ey\rt)\cos(\psi) + \sin(\psi)\ez\rt)\\ - & = Z_F\ez + x_1\cos(\phi)\ex + x_1\sin(\phi)\ey - x_2\sin(\phi)\cos(\psi)\ex + x_2\cos(\phi)\cos(\psi)\ey + x_2\sin(\psi)\ez\\ - & = \lt(x_1\cos(\phi) - x_2\sin(\phi)\cos(\psi)\rt)\ex + \lt(x_1\sin(\phi) + x_2\cos(\phi)\cos(\psi)\rt)\ey + \lt(Z_F + x_2\sin(\psi)\rt)\ez\\ + \underline{OM} & = \underline{OP} + \underline{PM}\\ + & = Z_P\ez + x_1\ei + x_2\et\\ + & = Z_P\ez + x_1\lt(\cos(\phi)\ex + \sin(\phi)\ey\rt) + x_2\lt(\lt(-\sin(\phi)\ex + \cos(\phi)\ey\rt)\cos(\psi) + \sin(\psi)\ez\rt)\\ + & = Z_P\ez + x_1\cos(\phi)\ex + x_1\sin(\phi)\ey - x_2\sin(\phi)\cos(\psi)\ex + x_2\cos(\phi)\cos(\psi)\ey + x_2\sin(\psi)\ez\\ + & = \lt(x_1\cos(\phi) - x_2\sin(\phi)\cos(\psi)\rt)\ex + \lt(x_1\sin(\phi) + x_2\cos(\phi)\cos(\psi)\rt)\ey + \lt(Z_P + x_2\sin(\psi)\rt)\ez\\ \end{array} $$ We have: $$ \begin{array}{lll} - (\underline{OM}.\ez)^2 & = \lt(Z_F + x_2\sin(\psi)\rt)^2\\ - & = Z_F^2 + 2Z_Fx_2\sin(\psi) + x_2^2\sin(\psi)^2 + (\underline{OM}.\ez)^2 & = \lt(Z_P + x_2\sin(\psi)\rt)^2\\ + & = Z_P^2 + 2Z_Px_2\sin(\psi) + x_2^2\sin(\psi)^2 \end{array} $$ And: $$ \begin{array}{lll} - \|\underline{OM}\|^2 & = & \| \lt(x_1\cos(\phi) - x_2\sin(\phi)\cos(\psi)\rt)\ex + \lt(x_1\sin(\phi) + x_2\cos(\phi)\cos(\psi)\rt)\ey + \lt(Z_F + x_2\sin(\psi)\rt)\ez\|^2\\ + \|\underline{OM}\|^2 & = & \| \lt(x_1\cos(\phi) - x_2\sin(\phi)\cos(\psi)\rt)\ex + \lt(x_1\sin(\phi) + x_2\cos(\phi)\cos(\psi)\rt)\ey + \lt(Z_P + x_2\sin(\psi)\rt)\ez\|^2\\ & = & \lt( x_1\cos(\phi) - x_2\sin(\phi)\cos(\psi) \rt)^2\\ & & + \lt(x_1\sin(\phi) + x_2\cos(\phi)\cos(\psi)\rt)^2\\ - & & + \lt(Z_F + x_2\sin(\psi)\rt)^2\\ + & & + \lt(Z_P + x_2\sin(\psi)\rt)^2\\ & = & x_1^2\cos(\phi)^2 - 2x_1x_2\cos(\phi)\sin(\phi)\cos(\psi) + x_2^2\sin(\phi)^2\cos(\psi)^2\\ & & + x_1^2\sin(\phi)^2 + 2x_1x_2\sin(\phi)\cos(\phi)\cos(\psi) + x_2^2\cos(\phi)^2\cos(\psi)^2\\ - & & + Z_F^2 + 2Z_Fx_2\sin(\psi) + x_2^2\sin(\psi)^2\\ + & & + Z_P^2 + 2Z_Px_2\sin(\psi) + x_2^2\sin(\psi)^2\\ & = & x_1^2 + x_2^2\cos(\psi)^2\\ - & & + Z_F^2 + 2Z_Fx_2\sin(\psi) + x_2^2\sin(\psi)^2\\ - & = & x_1^2 + x_2^2 + 2Z_Fx_2\sin(\psi) + Z_F^2\\ + & & + Z_P^2 + 2Z_Px_2\sin(\psi) + x_2^2\sin(\psi)^2\\ + & = & x_1^2 + x_2^2 + 2Z_Px_2\sin(\psi) + Z_P^2\\ \end{array} $$ @@ -116,9 +116,9 @@ \section{Intersection} $$ \begin{array}{lll} & (\underline{OM}.\ez)^2 = \cos(\theta)^2 \|\underline{OM}\|^2\\ - \Leftrightarrow & Z_F^2 + 2Z_Fx_2\sin(\psi) + x_2^2\sin(\psi)^2 = \cos(\theta)^2 \lt(x_1^2 + x_2^2 + 2Z_Fx_2\sin(\psi) + Z_F^2\rt)\\ - \Leftrightarrow & Z_F^2\lt(1-\cos(\theta)^2\rt) + 2Z_Fx_2\sin(\psi)\lt(1-\cos(\theta)^2\rt) = x_1^2\cos(\theta)^2 + x_2^2\lt(\cos(\theta)^2 - \sin(\psi)^2\rt)\\ - \Leftrightarrow & Z_F^2\sin(\theta)^2 + 2Z_Fx_2\sin(\psi)\sin(\theta)^2 = x_1^2\cos(\theta)^2 + x_2^2\lt(\cos(\theta)^2 - \sin(\psi)^2\rt)\\ + \Leftrightarrow & Z_P^2 + 2Z_Px_2\sin(\psi) + x_2^2\sin(\psi)^2 = \cos(\theta)^2 \lt(x_1^2 + x_2^2 + 2Z_Px_2\sin(\psi) + Z_P^2\rt)\\ + \Leftrightarrow & Z_P^2\lt(1-\cos(\theta)^2\rt) + 2Z_Px_2\sin(\psi)\lt(1-\cos(\theta)^2\rt) = x_1^2\cos(\theta)^2 + x_2^2\lt(\cos(\theta)^2 - \sin(\psi)^2\rt)\\ + \Leftrightarrow & Z_P^2\sin(\theta)^2 + 2Z_Px_2\sin(\psi)\sin(\theta)^2 = x_1^2\cos(\theta)^2 + x_2^2\lt(\cos(\theta)^2 - \sin(\psi)^2\rt)\\ \end{array} $$ @@ -126,112 +126,113 @@ \section{Intersection} $$ \begin{array}{lll} & (\underline{OM}.\ez)^2 = \cos(\theta)^2 \|\underline{OM}\|^2\\ - \Leftrightarrow & x_1^2\cos(\theta)^2 + x_2^2\lt(\DD\rt) - 2Z_Fx_2\sin(\psi)\sin(\theta)^2 - Z_F^2\sin(\theta)^2 = 0\\ + \Leftrightarrow & x_1^2\cos(\theta)^2 + x_2^2\lt(\DD\rt) - 2Z_Px_2\sin(\psi)\sin(\theta)^2 - Z_P^2\sin(\theta)^2 = 0\\ + \Leftrightarrow & x_1^2\frac{\cos(\theta)^2}{\DD} + x_2^2 - 2x_2Z_P\frac{\sin(\psi)\sin(\theta)^2}{\DD} - Z_P^2\frac{\sin(\theta)^2}{\DD} = 0\\ + \Leftrightarrow & x_1^2\frac{\cos(\theta)^2}{\DD} + \lt(x_2 - Z_P\frac{\sin(\psi)\sin(\theta)^2}{\DD}\rt)^2 - Z_P^2\frac{\sin(\psi)^2\sin(\theta)^4}{\lt(\DD\rt)^2} - Z_P^2\frac{\sin(\theta)^2}{\DD} = 0\\ + \Leftrightarrow & x_1^2\frac{\cos(\theta)^2}{\DD} + \lt(x_2 - Z_P\frac{\sin(\psi)\sin(\theta)^2}{\DD}\rt)^2 = Z_P^2 \frac{\sin(\theta)^2}{\lt(\DD\rt)^2} \lt(\sin(\psi)^2\sin(\theta)^2 + \DD \rt)\\ + \Leftrightarrow & x_1^2\frac{\cos(\theta)^2}{\DD} + \lt(x_2 - Z_P\frac{\sin(\psi)\sin(\theta)^2}{\DD}\rt)^2 = Z_P^2 \frac{\sin(\theta)^2}{\lt(\DD\rt)^2} \lt(-\sin(\psi)^2\cos(\theta)^2 + \cos(\theta)^2 \rt)\\ + \Leftrightarrow & x_1^2\frac{\cos(\theta)^2}{\DD} + \lt(x_2 - Z_P\frac{\sin(\psi)\sin(\theta)^2}{\DD}\rt)^2 = Z_P^2 \frac{\sin(\theta)^2\cos(\psi)^2\cos(\theta)^2}{\lt(\DD\rt)^2} \\ + \Leftrightarrow & \frac{x_1^2}{ Z_P^2\frac{\sin(\theta)^2\cos(\psi)^2}{\DD} } + \frac{\lt(x_2-Z_P\frac{\sin(\psi)\sin(\theta)^2}{\DD}\rt)^2}{ Z_P^2\frac{\sin(\theta)^2\cos(\psi)^2\cos(\theta)^2}{\lt(\DD\rt)^2} } = 1 \end{array} $$ -This looks like an almost reduced conic equation, except that $x_2$ needs to be rescaled, because $F$, the intersection between the axis $(O, \ez)$ and plane $P_1$ is in fact not the center of the conic but one of its focal points.\\ -Computing the $x_2$ coordinate of the center is easy by testing the particular case $x_1=0$, finding 2 solutions (the two extrema of the conic), and taking the middle. +Or, in a reduced conic form: $$ -\begin{array}{lll} - & x_1 = 0\\ - \Rightarrow & x_2^2\lt(\DD\rt) - 2Z_Fx_2\sin(\psi)\sin(\theta)^2 - Z_F^2\sin(\theta)^2 = 0\\ -\end{array} +\frac{x_1^2}{ a^2 } + \frac{\lt(x_2-x_2(C)\rt)^2}{b^2} = 1 $$ -Introducing + +With: $$ -\begin{array}{lll} - \Delta & = 4Z_F^2\sin(\psi)^2\sin(\theta)^4 + 4Z_F^2\sin(\theta)^2\lt(\DD\rt)\\ - & = 4Z_F^2\sin(\theta)^2 \lt( \sin(\psi)^2\sin(\theta)^2 + \DD \rt)\\ - & = 4Z_F^2\sin(\theta)^2 \lt( -\sin(\psi)^2\cos(\theta)^2 + \cos(\theta)^2 \rt)\\ - & = 4Z_F^2\sin(\theta)^2 \cos(\theta)^2\cos(\psi)^2 -\end{array} +\lt\{ + \begin{array}{lll} + x_2(C) & = Z_P\frac{\sin(\psi)\sin(\theta)^2}{\DD} & \text{ $x_2$ coordinate of the center} \\ + a^2 & = Z_P^2\frac{\sin(\theta)^2\cos(\psi)^2}{\DD} & \text{ squared minor radius} \\ + b^2 & = Z_P^2\frac{\sin(\theta)^2\cos(\psi)^2\cos(\theta)^2}{\lt(\DD\rt)^2} & \text{ squared major radius} \\ + b^2 & = a^2\frac{\cos(\theta)^2}{\DD} \Leftrightarrow a^2 = b^2\lt(1-\frac{\sin(\psi)^2}{\cos(\theta)^2}\rt) + \end{array} +\rt. $$ -Hence, solutions always exist. -The solutions are: +The distance $d_{CF}$ between the center $C$ and the focal point $F$ can be deduced from: $$ \begin{array}{lll} - x_2^{1,2} & = \frac{2Z_F\sin(\psi)\sin(\theta)^2 \pm 2Z_F\sin(\theta) \cos(\theta) \cos(\psi)}{2\lt(\DD\rt)}\\ - & = Z_F\sin(\theta) \frac{\sin(\psi)\sin(\theta) \pm \cos(\theta)\cos(\psi)}{\DD} + d_{CF}^2 & = b^2-a^2\\ + & = b^2\frac{\sin(\psi)^2}{\cos(\theta)^2}\\ + & = Z_P^2\frac{\sin(\theta)^2\cos(\psi)^2\sin(\psi)^2}{\lt(\DD\rt)^2} \end{array} $$ -Thus, the average is: +Hence, the $x_2$ coordinate of $F$ is: $$ \begin{array}{lll} - x_2(C) = & = \frac{1}{2} 2 Z_F\sin(\theta) \frac{\sin(\psi)\sin(\theta)}{\DD} - & = Z_F\sin(\theta)^2 \frac{\sin(\psi)}{\DD} + x_2(F) & = x_2(C) \pm d_{CF}\\ + & = Z_P\frac{\sin(\psi)\sin(\theta)^2}{\DD} \pm Z_P\frac{\sin(\theta)\cos(\psi)\sin(\psi)}{\DD}\\ + & = Z_P\frac{\sin(\psi)\sin(\theta)^2 \pm \sin(\theta)\cos(\psi)\sin(\psi)}{\DD}\\ + & = Z_P\frac{\sin(\psi)\sin(\theta)}{\DD}\lt(\sin(\theta) \pm \cos(\psi)\rt)\\ \end{array} $$ -Hence, let's introduce the new coordinate: -$$ -X_2 = x_2 - x_2(C) = x_2 - Z_F\sin(\theta)^2 \frac{\sin(\psi)}{\DD} -$$ +It is worth noticing that the neither the focal point nor the center correspond to the intersection between the axes and the plane $P$. -Then: -$$ -\begin{array}{lll} - & X_2^2 & = x_2^2 - 2Z_Fx_2\sin(\theta)^2 \frac{\sin(\psi)}{\DD} + \sin(\theta)^4 \lt[\frac{\sin(\psi)}{\DD}\rt]^2\\ - \Leftrightarrow & X_2^2\lt(\DD\rt) & = x_2^2\lt(\DD\rt) - 2Z_Fx_2\sin(\theta)^2\sin(\psi) + \sin(\theta)^4 \frac{\sin(\psi)^2}{\DD}\\ -\end{array} -$$ -Hence: +\section{Parametric equation} -$$ -\begin{array}{lll} - & (\underline{OM}.\ez)^2 = \cos(\theta)^2 \|\underline{OM}\|^2\\ - \Leftrightarrow & x_1^2\cos(\theta)^2 + X_2^2\lt(\DD\rt) - \frac{\sin(\psi)^2\sin(\theta)^4}{\DD} - Z_F^2\sin(\theta)^2 = 0\\ - \Leftrightarrow & x_1^2\cos(\theta)^2 + X_2^2\lt(\DD\rt) = \lt[\frac{\sin(\psi)^2\sin(\theta)^2}{\DD} + Z_F^2\rt]\sin(\theta)^2\\ -\end{array} -$$ +In our case, only the axes $(O, \ez)$, fixed by the crystal's summit and normal, is independent from the cone's angular opening $\theta$. +It makes sense to design an ad-hoc coordinate system centered on the ellipse's center $C$ to use its parameterized equation. -Of the form $\frac{x_1^2}{a^2} + \frac{X_2^2}{b^2} = 1$: +Knowing all geometrical parameters, it is possible to compute all points on the ellipse parameterizing them with angle $\epsilon$: $$ -\begin{array}{lll} - & \frac{x_1^2}{\lt[\frac{\sin(\psi)^2\sin(\theta)^2}{\DD} + Z_F^2\rt]\tan(\theta)^2} + \frac{X_2^2}{\lt[\frac{\sin(\psi)^2\sin(\theta)^2}{\DD} + Z_F^2\rt]\frac{\sin(\theta)^2}{\DD}} = 1\\ -\end{array} +\lt\{ + \begin{array}{lll} + x_1 = a\cos(\epsilon)\\ + x_2 = x_2(C) + b\sin(\epsilon) + \end{array} +\rt. $$ -With $b^2 = \lt(1-\frac{\sin(\psi)^2}{\cos(\theta)^2}\rt)a^2$ - -\section{Focal-centered polar coordinates} - -In our case, only the axes $(O, \ez)$, fixed by the crystal's summit and normal, is independent from the cone's angular opening $\theta$. -It makes sense to design an ad-hoc coordinate system centered not on the ellipse's center $C$, but on the focal point $F$. -The ellipse will be parameterized by an angle $\epsilon$ around $F$, which is in fact the angle around the crystal's summit $O$ at which the ray beam is coming / leaving. -The other coordinate will thus be the radius $r$, in the plane, from $F$. +Keep in mind that the frame $(P, \ei, \et)$ is, by definition ligned on the minor and major axes of the ellipse. +Hence, for an arbitrary frame $(R, \ud{e}_i, \ud{e}_j)$ on plane $P_1$, translated and rotated by $\alpha$ with respect to $(P, \ei, \et)$: -We have seen that the ellipse can be defined by: $$ -\begin{array}{lll} - & \frac{x_1^2}{\lt[\frac{\sin(\psi)^2\sin(\theta)^2}{\DD} + Z_F^2\rt]\tan(\theta)^2} + \frac{X_2^2}{\lt[\frac{\sin(\psi)^2\sin(\theta)^2}{\DD} + Z_F^2\rt]\frac{\sin(\theta)^2}{\DD}} = 1\\ -\end{array} +\lt\{ + \begin{array}{lll} + \ud{e}_i = \cos(\alpha)\ei + \sin(\alpha)\et\\ + \ud{e}_j = -\sin(\alpha)\ei + \cos(\alpha)\et\\ + \ei = \cos(\alpha)\ud{e_i} - \sin(\alpha)\ud{e}_j + \et = \sin(\alpha)\ud{e_i} + \cos(\alpha)\ud{e}_j + \end{array} +\rt. $$ -By definition, in the local frame defined from the plane's orientation: +Or, in coordinate tranforms: $$ -\ud{FM} = r\cos(\epsilon)\ei + r\sin(\epsilon)\et +\lt\{ + \begin{array}{lll} + x_1 = x_1(R) + x_i\cos(\alpha) - x_j\sin(\alpha)\\ + x_2 = x_2(R) + x_i\sin(\alpha) + x_j\cos(\alpha)\\ + x_i = (x_1-x_1(R))\cos(\alpha) + (x_2-x_2(R))\sin(\alpha)\\ + x_j = -(x_1-x_1(R))\sin(\alpha) + (x_2-x_2(R))\cos(\alpha) + \end{array} +\rt. $$ Hence: $$ \lt\{ - \begin{array}{ll} - r\cos(\epsilon) = x_1\\ - r\sin(\epsilon) = x_2 = X_2 + Z_F\sin(\theta)^2 \frac{\sin(\psi)}{\DD} - \end{array}{ll} + \begin{array}{lll} + x_i = \lt(a\cos(\epsilon)-x_1(R)\rt)\cos(\alpha) + \lt(x_2(C)-x_2(R) + b\sin(\epsilon)\rt)\sin(\alpha)\\ + x_j = -\lt(a\cos(\epsilon)-x_1(R)\rt)\sin(\alpha) + \lt(x_2(C)-x_2(R) + b\sin(\epsilon)\rt)\cos(\alpha) + \end{array} \rt. $$ -Necesarrily: -$$ -r^2 = x_1^2 + \lt(X_2 + Z_F\sin(\theta)^2 \frac{\sin(\psi)}{\DD}\rt)^2 -$$ + + + + + diff --git a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.toc b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.toc index 1d7b23b4e..82a95eb3b 100644 --- a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.toc +++ b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.toc @@ -2,7 +2,7 @@ \contentsline {chapter}{\numberline {1}Geometry}{5}{chapter.1} \contentsline {section}{\numberline {1.1}Generic cone and plane}{5}{section.1.1} \contentsline {section}{\numberline {1.2}Intersection}{5}{section.1.2} -\contentsline {section}{\numberline {1.3}Focal-centered polar coordinates}{7}{section.1.3} +\contentsline {section}{\numberline {1.3}Parametric equation}{7}{section.1.3} \contentsline {chapter}{\numberline {A}Acceleration radiation from a unique point-like charge}{9}{appendix.A} \contentsline {section}{\numberline {A.1}Retarded time and potential}{9}{section.A.1} \contentsline {subsection}{\numberline {A.1.1}Retarded time}{9}{subsection.A.1.1} diff --git a/tofu/version.py b/tofu/version.py index 1ef9913d5..58e3b1fb8 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-149-gc4146ac' +__version__ = '1.4.1-150-g54d77e7' From 7177f0c6601240f067f02f275a6b34cc80db1c58 Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Wed, 16 Oct 2019 16:15:38 +0200 Subject: [PATCH 10/51] [Issue202] Advanced CrystalBragg class up to public class methods, including local plot from geom to ellipses, to be continued --- tofu/geom/__init__.py | 1 + tofu/geom/_core_Optics.py | 478 +++++++++++++++++++++++++++++++++++--- tofu/version.py | 2 +- 3 files changed, 450 insertions(+), 31 deletions(-) diff --git a/tofu/geom/__init__.py b/tofu/geom/__init__.py index 40ed5f2e4..5156990bb 100644 --- a/tofu/geom/__init__.py +++ b/tofu/geom/__init__.py @@ -11,6 +11,7 @@ from tofu.geom._core import PlasmaDomain, Ves, PFC, CoilPF, CoilCS, Config from tofu.geom._core import Rays, CamLOS1D, CamLOS2D +from tofu.geom._core_Optics import * from . import utils __all__ = ['_GG', '_comp', '_plot', '_def', 'utils'] diff --git a/tofu/geom/_core_Optics.py b/tofu/geom/_core_Optics.py index a05bbfe49..dff5c39d8 100644 --- a/tofu/geom/_core_Optics.py +++ b/tofu/geom/_core_Optics.py @@ -5,6 +5,7 @@ """ # Built-in +import sys import os import warnings #import copy @@ -13,6 +14,7 @@ # Common import numpy as np import datetime as dtm +import matplotlib.pyplot as plt # ToFu-specific from tofu import __version__ as __version__ @@ -29,7 +31,7 @@ from . import _comp as _comp from . import _plot as _plot -__all__ = ['Crystal'] +__all__ = ['CrystalBragg'] @@ -48,7 +50,7 @@ class CrystalBragg(utils.ToFuObject): """ A class defining crystals for Bragg diffraction - A crystal can be of Type flat, cylindrical, spherical or elliptical + A crystal can be of Type flat, cylindrical or spherical It is characterized by its: - geometry (Type, dimensions, curvature radii and position/orientation) - Material and lattice @@ -76,10 +78,9 @@ class CrystalBragg(utils.ToFuObject): _ddef = {'Id':{'shot':0, 'include':['Mod','Cls','Exp','Diag', 'Name','shot','version']}, - 'dgeom':{'Type':'Tor', 'Lim':[], 'arrayorder':'C'}, - 'dsino':{}, - 'dphys':{}, - 'dreflect':{'Type':'specular'}, + 'dgeom':{'Type':'sph', 'outline_Type':'rect'}, + 'dmat':{}, + 'dbragg':{}, 'dmisc':{'color':'k'}} _dplot = {'cross':{'Elt':'P', 'dP':{'color':'k','lw':2}, @@ -92,34 +93,26 @@ class CrystalBragg(utils.ToFuObject): 'dI':{'color':'k','ls':'--'}, 'dBs':{'color':'b','ls':'--'}, 'dBv':{'color':'g','ls':'--'}, - 'Nstep':50}, - '3d':{'Elt':'P', - 'dP':{'color':(0.8,0.8,0.8,1.), - 'rstride':1,'cstride':1, - 'linewidth':0., 'antialiased':False}, - 'Lim':None, - 'Nstep':50}} + 'Nstep':50}} _DREFLECT_DTYPES = {'specular':0, 'diffusive':1, 'ccube':2} # Does not exist beofre Python 3.6 !!! def __init_subclass__(cls, color='k', **kwdargs): # Python 2 - super(Struct,cls).__init_subclass__(**kwdargs) + super(CrystalBragg,cls).__init_subclass__(**kwdargs) # Python 3 #super().__init_subclass__(**kwdargs) - cls._ddef = copy.deepcopy(Struct._ddef) - cls._dplot = copy.deepcopy(Struct._dplot) + cls._ddef = copy.deepcopy(CrystalBragg._ddef) + cls._dplot = copy.deepcopy(CrystalBragg._dplot) cls._set_color_ddef(cls._color) @classmethod def _set_color_ddef(cls, color): cls._ddef['dmisc']['color'] = mpl.colors.to_rgba(color) - def __init__(self, Poly=None, Type=None, - Lim=None, pos=None, extent=None, mobile=False, - Id=None, Name=None, Exp=None, shot=None, - sino_RefPt=None, sino_nP=_def.TorNP, - Clock=False, arrayorder='C', fromdict=None, + def __init__(self, dgeom=None, dmat=None, dbragg=None, + Id=None, Name=None, Exp=None, + fromdict=None, SavePath=os.path.abspath('./'), SavePath_Include=tfpf.defInclude, color=None): @@ -134,26 +127,25 @@ def __init__(self, Poly=None, Type=None, kwdargs = locals() del kwdargs['self'] # super() - super(Struct,self).__init__(**kwdargs) + super(CrystalBragg,self).__init__(**kwdargs) def _reset(self): # super() - super(Struct,self)._reset() + super(CrystalBragg,self)._reset() self._dgeom = dict.fromkeys(self._get_keys_dgeom()) - self._dsino = dict.fromkeys(self._get_keys_dsino()) - self._dphys = dict.fromkeys(self._get_keys_dphys()) - self._dreflect = dict.fromkeys(self._get_keys_dreflect()) + self._dmat = dict.fromkeys(self._get_keys_dmat()) + self._dbragg = dict.fromkeys(self._get_keys_dbragg()) self._dmisc = dict.fromkeys(self._get_keys_dmisc()) #self._dplot = copy.deepcopy(self.__class__._ddef['dplot']) @classmethod def _checkformat_inputs_Id(cls, Id=None, Name=None, - Exp=None, shot=None, Type=None, + Exp=None, Type=None, include=None, **kwdargs): if Id is not None: assert isinstance(Id,utils.ID) - Name, Exp, shot, Type = Id.Name, Id.Exp, Id.shot, Id.Type + Name, Exp, Type = Id.Name, Id.Exp, Id.Type if shot is None: shot = cls._ddef['Id']['shot'] if Type is None: @@ -163,17 +155,443 @@ def _checkformat_inputs_Id(cls, Id=None, Name=None, dins = {'Name':{'var':Name, 'cls':str}, 'Exp': {'var':Exp, 'cls':str}, - 'shot': {'var':shot, 'cls':int}, 'Type': {'var':Type, 'in':['Tor','Lin']}, 'include':{'var':include, 'listof':str}} dins, err, msg = cls._check_InputsGeneric(dins) if err: raise Exception(msg) - kwdargs.update({'Name':Name, 'Exp':Exp, 'shot':shot, 'Type':Type, + kwdargs.update({'Name':Name, 'Exp':Exp, 'Type':Type, 'include':include}) return kwdargs ########### # Get largs ########### + + @staticmethod + def _get_largs_dgeom(sino=True): + largs = ['dgeom'] + return largs + + @staticmethod + def _get_largs_dmat(): + largs = ['dmat'] + return largs + + @staticmethod + def _get_largs_dbragg(): + largs = ['dbragg'] + return largs + + @staticmethod + def _get_largs_dmisc(): + largs = ['color'] + return largs + + ########### + # Get check and format inputs + ########### + + @classmethod + def _checkformat_dgeom(cls, dgeom=None): + if dgeom is None: + return + assert isinstance(dgeom, dict) + lkok = ['Type', 'Type_outline', 'summit', 'extent', + 'nIn', 'e1', 'e2', 'curve_radius'] + assert all([isinstance(ss, str) for ss in dgeom.keys()]) + assert all([ss in lkok for ss in dgeom.keys()]) + + for kk in cls._ddef['dgeom'].keys(): + dgeom[kk] = dgeom.get(kk, cls._ddef['dgeom'][kk]) + return dgeom + + @classmethod + def _checkformat_dmat(cls, dmat=None): + if dmat is None: + return + assert isinstance(dmat, dict) + lkok = ['formula'] + assert all([isinstance(ss, str) for ss in dmat.keys()]) + assert all([ss in lkok for ss in dmat.keys()]) + + for kk in cls._ddef['dmat'].keys(): + dmat[kk] = dmat.get(kk, cls._ddef['dmat'][kk]) + return dmat + + @classmethod + def _checkformat_dbragg(cls, dbragg=None): + if dbragg is None: + return + assert isinstance(dbragg, dict) + lkok = ['angle'] + assert all([isinstance(ss, str) for ss in dbragg.keys()]) + assert all([ss in lkok for ss in dbragg.keys()]) + + for kk in cls._ddef['dbragg'].keys(): + dbragg[kk] = dbragg.get(kk, cls._ddef['dbragg'][kk]) + return dbragg + + ########### + # Get keys of dictionnaries + ########### + + @staticmethod + def _get_keys_dgeom(): + lk = ['Type', 'Type_outline', + 'summit', 'extent', + 'nIn', 'e1', 'e2', + 'curve_rad'] + return lk + + @staticmethod + def _get_keys_dmat(): + lk = ['lattice', 'formula', 'slice'] + return lk + + @staticmethod + def _get_keys_dbragg(): + largs = ['bragg_ang'] + return lk + + @staticmethod + def _get_keys_dmisc(): + lk = ['color'] + return lk + + ########### + # _init + ########### + + def _init(self, dgeom=None, dmat=None, dbragg=None, + color=None, **kwdargs): + allkwds = dict(locals(), **kwdargs) + largs = self._get_largs_dgeom() + kwd = self._extract_kwdargs(allkwds, largs) + self._set_dgeom(**kwds) + largs = self._get_largs_dmat() + kwd = self._extract_kwdargs(allkwds, largs) + self.set_dmat(**kwds) + largs = self._get_largs_dbragg() + kwd = self._extract_kwdargs(allkwds, largs) + self.set_dbragg(**kwds) + largs = self._get_largs_dmisc() + kwd = self._extract_kwdargs(allkwds, largs) + self._set_dmisc(**kwdmisc) + self._dstrip['strip'] = 0 + + ########### + # set dictionaries + ########### + + def _set_dgeom(self, dgeom=None): + dgeom = self._checkformat_inputs_dgeom(dgeom) + self._dgeom = dgeom + + def _set_dmat(self, dmat=None): + dmat = self._checkformat_inputs_dgeom(dmat) + self._dmat = dmat + + def _set_dbragg(self, dbragg=None): + dbragg = self._checkformat_inputs_dgeom(dbragg) + self._dbragg = dbragg + + def _set_color(self, color=None): + color = self._checkformat_inputs_dmisc(color=color) + self._dmisc['color'] = color + self._dplot['cross']['dP']['color'] = color + self._dplot['hor']['dP']['color'] = color + self._dplot['3d']['dP']['color'] = color + + def _set_dmisc(self, color=None): + self._set_color(color) + + ########### + # strip dictionaries + ########### + + def _strip_dgeom(self, lkeep=None): + lkeep = self._get_keys_dgeom() + utils.ToFuObject._strip_dict(self._dgeom, lkeep=lkeep) + + def _strip_dmat(self, lkeep=None): + lkeep = self._get_keys_dmat() + utils.ToFuObject._strip_dict(self._dmat, lkeep=lkeep) + + def _strip_dbragg(self, lkeep=None): + lkeep = self._get_keys_dbragg() + utils.ToFuObject._strip_dict(self._dbragg, lkeep=lkeep) + + def _strip_dmisc(self, lkeep=['color']): + utils.ToFuObject._strip_dict(self._dmisc, lkeep=lkeep) + + ########### + # rebuild dictionaries + ########### + + def _rebuild_dgeom(self, lkeep=None): + lkeep = self._get_keys_dgeom() + reset = utils.ToFuObject._test_Rebuild(self._dgeom, lkeep=lkeep) + if reset: + utils.ToFuObject._check_Fields4Rebuild(self._dgeom, + lkeep=lkeep, dname='dgeom') + self._set_dgeom(dgeom=self._dgeom) + + def _rebuild_dmat(self, lkeep=None): + lkeep = self._get_keys_dmat() + reset = utils.ToFuObject._test_Rebuild(self._dmat, lkeep=lkeep) + if reset: + utils.ToFuObject._check_Fields4Rebuild(self._dmat, + lkeep=lkeep, dname='dmat') + self.set_dmat(self._dmat) + + def _rebuild_dbragg(self, lkeep=None): + lkeep = self._get_keys_dbragg() + reset = utils.ToFuObject._test_Rebuild(self._dbragg, lkeep=lkeep) + if reset: + utils.ToFuObject._check_Fields4Rebuild(self._dbragg, + lkeep=lkeep, dname='dbragg') + self.set_dbragg(self._dbragg) + + def _rebuild_dmisc(self, lkeep=['color']): + reset = utils.ToFuObject._test_Rebuild(self._dmisc, lkeep=lkeep) + if reset: + utils.ToFuObject._check_Fields4Rebuild(self._dmisc, + lkeep=lkeep, dname='dmisc') + self._set_dmisc(color=self.dmisc['color']) + + ########### + # _strip and get/from dict + ########### + + @classmethod + def _strip_init(cls): + cls._dstrip['allowed'] = [0,1] + nMax = max(cls._dstrip['allowed']) + doc = """ + 1: Remove nothing""" + doc = utils.ToFuObjectBase.strip.__doc__.format(doc,nMax) + if sys.version[0]=='2': + cls.strip.__func__.__doc__ = doc + else: + cls.strip.__doc__ = doc + + def strip(self, strip=0): + # super() + super(CrystalBragg, self).strip(strip=strip) + + def _strip(self, strip=0): + if strip==0: + self._rebuild_dgeom() + self._rebuild_dmat() + self._rebuild_dbragg() + self._rebuild_dmisc() + else: + self._strip_dgeom() + self._strip_dmat() + self._strip_dbragg() + self._strip_dmisc() + + def _to_dict(self): + dout = {'dgeom':{'dict':self._dgeom, 'lexcept':None}, + 'dmat':{'dict':self._dmat, 'lexcept':None}, + 'dbragg':{'dict':self._dbragg, 'lexcept':None}, + 'dmisc':{'dict':self._dmisc, 'lexcept':None}, + 'dplot':{'dict':self._dplot, 'lexcept':None}} + return dout + + def _from_dict(self, fd): + self._dgeom.update(**fd['dgeom']) + self._dmat.update(**fd['dmat']) + self._dbragg.update(**fd['dbragg']) + self._dmisc.update(**fd['dmisc']) + if 'dplot' in fd.keys(): + self._dplot.update(**fd['dplot']) + + # ----------- + # Properties + # ----------- + + @property + def Type(self): + """Return the type of structure """ + return self._Id.Type + + @property + def dgeom(self): + return self._dgeom + + @property + def dmat(self): + """Return the polygon defining the structure cross-section""" + return self._dmat + + @property + def dbragg(self): + """Return the polygon defining the structure cross-section""" + return self._dbragg + + @property + def dmisc(self): + return self._dmisc + + + # ----------------- + # methods for color + # ----------------- + + def set_color(self, col): + self._set_color(col) + + def get_color(self): + return self._dmisc['color'] + + # ----------------- + # methods for generic first-approx + # ----------------- + + @classmethod + def _get_bragg_from_lamb(cls, lamb, d, n=1): + lamb = np.atleast_1d(lamb).ravel() + nord = np.atleast_1d(n).ravel() + + theta = np.full((lamb.size, nord.size), np.nan) + sin = nord[None, :]*lamb[:, None]/(2.*d) + indok = np.abs(sin) <= 1. + theta[indok] = np.arcsin(sin[indok]) + return theta + + def get_bragg_from_lamb(self, lamb, n=1, d=None): + """ Braggs' law: n*lamb = 2dsin(theta) """ + + if d is None: + if self._dmat['d'] is None: + msg = "Instance mesh size not set !\n" + msg += " => please provide d !" + raise Exception(msg) + else: + d = float(d) + return self._get_bragg_from_lamb(lamb, d, n=n) + + @classmethod + def calc_ellipses_on_plane_2d(cls, + Z, nn, frame_cent, frame_ang, + ang_bragg, ang_param, + return_C=False, Test=True): + """ Assuming crystal's summit as frame origin + + According to [1], this assumes a local frame centered on the crystal + + These calculations are independent from the tokamak's frame: + The origin of the local frame is the crystal's summit + The (O, ez) axis is the crystal's normal + The crystal is tangent to (O, ex, ey) + + [1] tofu/Notes_Upgrades/SpectroX2D/SpectroX2D_EllipsesOnPlane.pdf + + Parameters: + ----------- + Z: float + Detector's plane intersection with (O, ez) axis + n: np.ndarray + (3,) array containing local (x,y,z) coordinates of the plane's + normal vector + """ + + if Test: + # Check / format inputs + nn = np.atleast_1d(nn).ravel() + assert nn.size == 3 + nn = nn / np.linalg.norm(nn) + Z = float(Z) + + frame_cent = np.atleast_1d(frame_cent).ravel() + assert frame_cent.size == 2 + frame_ang = float(frame_ang) + + ang_bragg = np.atleast_1d(ang_bragg).ravel() + ang_param = np.atleast_1d(ang_param).ravel() + + # By definition, here, nIn = ez + nIn = np.array([0., 0., 1.]) + + # Deduce natural plane frame (P, e1, e2) + P = np.array([0., 0., Z]) + e1 = np.cross(nIn, nn) + e1n = np.linalg.norm(e1) + if e1n < 1.e-10: + e1 = np.array([1., 0., 0.]) + else: + e1 = e1 / e1n + e2 = np.cross(nn, e1) + e2 = e2 / np.linalg.norm(e2) + + # Deduce key angles + costheta = np.cos(ang_bragg) + sintheta = np.sin(ang_bragg) + cospsi = np.sum(nIn*nn) + sinpsi = np.sum(np.cross(nIn, nn)*e1) + + # Deduce ellipse parameters + cos2sin2 = costheta**2 - sinpsi**2 + x2C = Z * sinpsi * sintheta**2 / cos2sin2 + a = Z * sintheta * cospsi / np.sqrt(cos2sin2) + b = Z * sintheta * cospsi * costheta / cos2sin2 + + # Deduce xi, xj + rot = np.array([np.cos(frame_ang), np.sin(frame_ang)]) + rot2 = np.array([-np.sin(frame_ang), np.cos(frame_ang)]) + ellipse_trans = np.array([a[None, :]*np.cos(ang_param[:, None]) + - frame_cent[0], + b[None, :]*np.sin(ang_param[:, None]) + - frame_cent[1] + x2C[None, :]]) + xi = np.sum(ellipse_trans*rot[:, None,None], axis=0) + xj = np.sum(ellipse_trans*rot2[:, None,None], axis=0) + + if return_C: + Ci = None + Cj = None + return xi, xj, Ci, Cj + else: + return xi, xj + + @classmethod + def plot_ellipses_on_plane_2d(cls, Z, nn, frame_cent, frame_ang, + ang_bragg, ang_param, ax=None): + + # Check / format inputs + nn = np.atleast_1d(nn).ravel() + assert nn.size == 3 + nn = nn / np.linalg.norm(nn) + Z = float(Z) + + frame_cent = np.atleast_1d(frame_cent).ravel() + assert frame_cent.size == 2 + frame_ang = float(frame_ang) + + ang_bragg = np.atleast_1d(ang_bragg).ravel() + ang_param = np.atleast_1d(ang_param).ravel() + + # Compute + xi, xj, Ci, Cj = cls.calc_ellipses_on_plane_2d(Z, nn, + frame_cent, frame_ang, + ang_bragg, ang_param, + return_C=True, + Test=False) + nbragg = ang_bragg.size + + # Separate by bragg angle + if ax is None: + fig = plt.figure() + ax = fig.add_axes([0.1,0.1,0.8,0.8], aspect='equal') + + for ii in range(nbragg): + deg ='{0:07.3f}'.format(ang_bragg[ii]*180/np.pi) + ax.plot(xi[:,ii], xj[:,ii], '.', label='bragg %s'%deg) + #ax.plot(Ci[:,ii], Cj[:,ii], 'x', label='bragg %s - center'%deg) + ax.set_xlabel(r'xi') + ax.set_ylabel(r'yi') + ax.legend(loc='upper left', bbox_to_anchor=(1.05, 1.), frameon=False) + + return ax diff --git a/tofu/version.py b/tofu/version.py index 58e3b1fb8..bb8f6d966 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-150-g54d77e7' +__version__ = '1.4.1-151-ga6825f5' From 59bec07ebc781fe26253c9367d1b37cebdd5499f Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Wed, 16 Oct 2019 19:32:27 +0200 Subject: [PATCH 11/51] [Issue202] Tested, about to merge with Issue203 --- tofu/geom/_core_Optics.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tofu/geom/_core_Optics.py b/tofu/geom/_core_Optics.py index dff5c39d8..444dd34c4 100644 --- a/tofu/geom/_core_Optics.py +++ b/tofu/geom/_core_Optics.py @@ -567,7 +567,7 @@ def plot_ellipses_on_plane_2d(cls, Z, nn, frame_cent, frame_ang, Z = float(Z) frame_cent = np.atleast_1d(frame_cent).ravel() - assert frame_cent.size == 2 + ssue202_SpectroX2DCrystalassert frame_cent.size == 2 frame_ang = float(frame_ang) ang_bragg = np.atleast_1d(ang_bragg).ravel() From 27e5416736b80a46d04a4635a3b11814ca5d3094 Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Wed, 16 Oct 2019 22:18:13 +0200 Subject: [PATCH 12/51] [Issue202] Advanced reverse coordinates transform in Notes --- .../SpectroX2D_ConePlaneEllipse.tex | 143 +++++++++--------- 1 file changed, 71 insertions(+), 72 deletions(-) diff --git a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.tex b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.tex index b677baec2..c10b3a43a 100644 --- a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.tex +++ b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.tex @@ -192,7 +192,9 @@ \section{Parametric equation} \rt. $$ -Keep in mind that the frame $(P, \ei, \et)$ is, by definition ligned on the minor and major axes of the ellipse. +\subsection{From bragg angle and to local cartesian coordinates} + +Keep in mind that the frame $(P, \ei, \et)$ is, by definition aligned on the minor and major axes of the ellipse. Hence, for an arbitrary frame $(R, \ud{e}_i, \ud{e}_j)$ on plane $P_1$, translated and rotated by $\alpha$ with respect to $(P, \ei, \et)$: $$ @@ -229,90 +231,87 @@ \section{Parametric equation} $$ +\subsection{From local cartesian coordinates to bragg angle} +Knowing $(x_i, x_j)$ and all geometric parameters, we now want to derive $(\theta, \epsilon)$. +From the previous equation, we can write: +$$ +\lt\{ + \begin{array}{lll} + x_i\cos(\alpha) - x_j\sin(\alpha) = a\cos(\epsilon)-x_1(R) & (1)\\ + x_i\sin(\alpha) + x_j\cos(\alpha) = x_2(C)-x_2(R) + b\sin(\epsilon) & + (2) + \end{array} +\rt. +$$ +The dependency in $\theta$ is hidden in the expressions of $a$, $b$ and +$x_2(C)$. +By squaring and summing, it is possible to get rid of the $\epsilon$ +dependency: +$$ +\lt\{ + \begin{array}{lll} + a^2\cos(\epsilon)^2 = \lt(x_i\cos(\alpha) - x_j\sin(\alpha) + + x_1(R)\rt)^2\\ + b^2\sin(\epsilon)^2 = \lt(x_i\sin(\alpha) + x_j\cos(\alpha) - x_2(C) + + x_2(R)\rt)^2 + \end{array} +\rt. +$$ +Hence, keeping in mind that $a^2 = b^2\frac{\DD}{\cos(\theta)^2}$: +$$ +\begin{array}{lll} + & b^2 = \frac{\cos(\theta)^2}{\DD}\lt(x_i\cos(\alpha) - x_j\sin(\alpha) + + x_1(R)\rt)^2 + \lt(x_i\sin(\alpha) + x_j\cos(\alpha) - x_2(C) + + x_2(R)\rt)^2\\ + \Leftrightarrow & + b^2\DD = \cos(\theta)^2\lt(x_i\cos(\alpha) - x_j\sin(\alpha) + + x_1(R)\rt)^2 + \lt(\DD\rt)\lt(x_i\sin(\alpha) + x_j\cos(\alpha) - x_2(C) + + x_2(R)\rt)^2\\ + \Leftrightarrow & + Z_P^2\frac{\sin(\theta)^2\cos(\psi)^2\cos(\theta)^2}{\DD} = \cos(\theta)^2\lt(x_i\cos(\alpha) - x_j\sin(\alpha) + + x_1(R)\rt)^2 + \lt(\DD\rt)\lt(x_i\sin(\alpha) + x_j\cos(\alpha) - x_2(C) + + x_2(R)\rt)^2\\ + \Leftrightarrow & + Z_P^2\sin(\theta)^2\cos(\psi)^2\cos(\theta)^2 = \cos(\theta)^2\lt\DD\rt)\lt(x_i\cos(\alpha) - x_j\sin(\alpha) + + x_1(R)\rt)^2 + \lt(\DD\rt)^2\lt(x_i\sin(\alpha) + x_j\cos(\alpha) - Z_P\frac{\sin(\psi)\sin(\theta)^2}{\DD} + + x_2(R)\rt)^2\\ +\end{array} +$$ -%\section{Coordinate Transforms} - -%Let's consider the same cone and plane as before. -%But this time we are looking at a small fraction of the ellipse, the fraction intersecting a bounded box on the plane, with a local frame $(R, \ud{e}_i, \ud{e}_j)$, rotated by an angle $\ksi$ from the natural plane frame such that: -%$$ -%\lt\{ - %\begin{array}{lll} - %\ud{e}_i = \cos(\ksi)\ei + \sin(\ksi)\et\\ - %\ud{e}_j = -\sin(\ksi)\ei + \cos(\ksi)\et\\ - %\end{array} -%\rt. -%$$ - -%And reciprocately: -%$$ -%\lt\{ - %\begin{array}{lll} - %\ei = \cos(\ksi)\ud{e}_i - \sin(\ksi)\ud{e}_j\\ - %\et = \sin(\ksi)\ud{e}_i + \cos(\ksi)\ud{e}_j\\ - %\end{array} -%\rt. -%$$ - -%Such that: -%$$ -%\begin{array}{lll} - %\ud{CM} & = \ud{CR} + \ud{RM}\\ - %& = x_1(R)\ei + X_2(R)\et + i\ud{e}_i + j\ud{e}_j\\ - %& = \lt(x_1(R) + i\cos(\ksi) - j\sin(\ksi)\rt)\ei + \lt(X_2(R) + i\sin(\ksi) + j\cos(\ksi)\rt)\et\\ -%\end{array} -%$$ - -%Keeping in mind that: -%$$ -%X_2 = x_2 - Z_F\sin(\theta)^2 \frac{\sin(\psi)}{\DD} -%$$ - -%We can write: -%$$ -%x_1 = x_1(R) + i\cos(\ksi) - j\sin(\ksi) -%X_2 = x_2(R) - Z_F\sin(\theta)^2 \frac{\sin(\psi)}{\DD} + i\sin(\ksi) + j\cos(\ksi) -%$$ - -%We want to easily transform between $(i,j)$ and $(\theta, \espilon)$, where $\epsilon$ is the angle of a point along the ellipse of cone width $\theta$, with respect to its center $C$. - - -%\subsection{From cone to local cartesian} - -%Knowing all geometrical parameters, we can infer: -%$$ -%\begin{array}{lll} - %\underline{RM} & = i\ud{e}_i + j\ud{e}_j\\ - %& = \underline{RC} + \underline{CM}\\ - %& = -x_1(R)\ei - X_2(R)\et + x_1\ei + X_2\et\\ -%\end{array} -%$$ - - - - -%\subsection{From local cartesian to cone} +$$ +\lt\{ + \begin{array}{lll} + x_2(c) & = z_p\frac{\sin(\psi)\sin(\theta)^2}{\dd}\\ + a & = z_p\frac{\sin(\theta)\cos(\psi)}{\sqrt{\dd}}\\ + b & = z_p\frac{\sin(\theta)\cos(\psi)\cos(\theta)}{\dd} + \end{array} +\rt. +$$ -%$$ -%x1 = -%$$ +Hence: +$$ +\lt\{ + \begin{array}{lll} + \lt(x_i\cos(\alpha) - x_j\sin(\alpha) + x_1(R)\rt)\sqrt{\dd} = z_p\sin(\theta)\cos(\psi)\cos(\epsilon)\\ + \lt(x_i\sin(\alpha) + x_j\cos(\alpha) + x_2(R)\rt)\dd = + z_p\sin(\theta)\lt(\sin(\psi)\sin(\theta) + \cos(\psi)\cos(\theta)\sin(\epsilon)\rt) + \end{array} +\rt. +$$ \appendix -\chapter{Acceleration radiation from a unique point-like charge} - -\section{Retarded time and potential} -\subsection{Retarded time} - - -Hence $\frac{dR(t_r)}{c} + dt_r = dt$ +\chapter{Appendices} +\section{Section} +\subsection{Subsection} \end{document} From 78e1ec3fe410b5f53c811121e8b8f69367bed1b6 Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Thu, 17 Oct 2019 13:30:08 +0200 Subject: [PATCH 13/51] [Issue202] Completed Notes on SpectroX2D up to reverse coordinates transform => to be tested and validated in code --- .../SpectroX2D_ConePlaneEllipse.out | 8 +- .../SpectroX2D_ConePlaneEllipse.pdf | Bin 96316 -> 103977 bytes .../SpectroX2D_ConePlaneEllipse.tex | 115 +++++++++++++----- .../SpectroX2D_ConePlaneEllipse.toc | 8 +- tofu/version.py | 2 +- 5 files changed, 98 insertions(+), 35 deletions(-) diff --git a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out index 46f992615..12cd3d597 100644 --- a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out +++ b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out @@ -2,6 +2,8 @@ \BOOKMARK [1][-]{section.1.1}{Generic cone and plane}{chapter.1} \BOOKMARK [1][-]{section.1.2}{Intersection}{chapter.1} \BOOKMARK [1][-]{section.1.3}{Parametric equation}{chapter.1} -\BOOKMARK [0][-]{appendix.A}{Acceleration radiation from a unique point-like charge}{} -\BOOKMARK [1][-]{section.A.1}{Retarded time and potential}{appendix.A} -\BOOKMARK [2][-]{subsection.A.1.1}{Retarded time}{section.A.1} +\BOOKMARK [2][-]{subsection.1.3.1}{From bragg angle and to local cartesian coordinates}{section.1.3} +\BOOKMARK [2][-]{subsection.1.3.2}{From local cartesian coordinates to bragg angle}{section.1.3} +\BOOKMARK 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a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.tex +++ b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.tex @@ -262,50 +262,109 @@ \subsection{From local cartesian coordinates to bragg angle} \rt. $$ -Hence, keeping in mind that $a^2 = b^2\frac{\DD}{\cos(\theta)^2}$: +Hence, keeping in mind that $a^2 = b^2\frac{\DD}{\cos(\theta)^2}$ and re-using the definitions of $x_1$ and $x_2$ which do not depend on the unknowns $(\theta, \epsilon)$: +$$ +\begin{array}{lllll} + & b^2 & = & \frac{\cos(\theta)^2}{\DD}x_1^2 + \lt(x_2 - x_2(C)\rt)^2\\ + \Leftrightarrow + & b^2\lt(\DD\rt) & = & \cos(\theta)^2x_1^2 + \lt(\DD\rt)\lt(x_2^2 - 2x_2x_2(C) + x_2(C)^2\rt)\\ + \Leftrightarrow + & Z_P^2\frac{\sin(\theta)^2\cos(\psi)^2\cos(\theta)^2}{\DD} & = & \cos(\theta)^2x_1^2 + \lt(\DD\rt)\lt(x_2^2 - 2x_2x_2(C) + x_2(C)^2\rt)\\ + \Leftrightarrow + & Z_P^2\frac{\sin(\theta)^2\cos(\psi)^2\cos(\theta)^2}{\DD} & = & \cos(\theta)^2\lt(x_1^2+x_2^2\rt) - \sin(\psi)^2x_2^2 - \lt(\DD\rt)\lt(2x_2x_2(C) - x_2(C)^2\rt)\\ + \Leftrightarrow + & Z_P^2\sin(\theta)^2\cos(\psi)^2\cos(\theta)^2 & = & \cos(\theta)^2\lt(\DD\rt)\lt(x_1^2+x_2^2\rt) - \sin(\psi)^2\lt(\DD\rt)x_2^2\\ + \Leftrightarrow + & & & - \lt(\DD\rt)^2\lt(2x_2x_2(C) - x_2(C)^2\rt)\\ + \Leftrightarrow + & Z_P^2\sin(\theta)^2\cos(\psi)^2\cos(\theta)^2 & = &\cos(\theta)^4\lt(x_1^2+x_2^2\rt) - \cos(\theta)^2\sin(\psi)^2\lt(x_1^2+2x_2^2\rt) + \sin(\psi)^4x_2^2\\ + & & & - \lt(\DD\rt)^2\lt(2x_2x_2(C) - x_2(C)^2\rt)\\ + \Leftrightarrow + & Z_P^2\sin(\theta)^2\cos(\psi)^2\cos(\theta)^2 & = & \cos(\theta)^4\lt(x_1^2+x_2^2\rt) - \cos(\theta)^2\sin(\psi)^2\lt(x_1^2+2x_2^2\rt) + \sin(\psi)^4x_2^2\\ + & & & - \lt[2x_2Z_P\sin(\psi)\sin(\theta)^2\lt(\DD\rt) - Z_P^2\sin(\psi)^2\sin(\theta)^4\rt]\\ + \Leftrightarrow + & Z_P^2\cos(\psi)^2\lt(\cos(\theta)^2-\cos(\theta)^4\rt) & = &\cos(\theta)^4\lt(x_1^2+x_2^2\rt) - \cos(\theta)^2\sin(\psi)^2\lt(x_1^2+2x_2^2\rt) + \sin(\psi)^4x_2^2\\ + & & & - 2x_2Z_P\sin(\psi)\sin(\theta)^2\lt(\DD\rt)\\ + & & & + Z_P^2\sin(\psi)^2\lt(1-2\cos(\theta)^2+\cos(\theta)^4\rt)\\ + \Leftrightarrow + & Z_P^2\cos(\psi)^2\lt(\cos(\theta)^2-\cos(\theta)^4\rt) & = &\cos(\theta)^4\lt(x_1^2+x_2^2\rt) - \cos(\theta)^2\sin(\psi)^2\lt(x_1^2+2x_2^2\rt) + \sin(\psi)^4x_2^2\\ + & & & - 2x_2Z_P\sin(\psi)\lt(\cos(\theta)^2 - \cos(\theta)^4 - \sin(\psi)^2\lt(1-\cos(\theta)^2\rt)\rt)\\ + & & & + Z_P^2\sin(\psi)^2\lt(1-2\cos(\theta)^2+\cos(\theta)^4\rt) +\end{array} $$ -\begin{array}{lll} - & b^2 = \frac{\cos(\theta)^2}{\DD}\lt(x_i\cos(\alpha) - x_j\sin(\alpha) + - x_1(R)\rt)^2 + \lt(x_i\sin(\alpha) + x_j\cos(\alpha) - x_2(C) + - x_2(R)\rt)^2\\ - \Leftrightarrow & - b^2\DD = \cos(\theta)^2\lt(x_i\cos(\alpha) - x_j\sin(\alpha) + - x_1(R)\rt)^2 + \lt(\DD\rt)\lt(x_i\sin(\alpha) + x_j\cos(\alpha) - x_2(C) + - x_2(R)\rt)^2\\ - \Leftrightarrow & - Z_P^2\frac{\sin(\theta)^2\cos(\psi)^2\cos(\theta)^2}{\DD} = \cos(\theta)^2\lt(x_i\cos(\alpha) - x_j\sin(\alpha) + - x_1(R)\rt)^2 + \lt(\DD\rt)\lt(x_i\sin(\alpha) + x_j\cos(\alpha) - x_2(C) + - x_2(R)\rt)^2\\ - \Leftrightarrow & - Z_P^2\sin(\theta)^2\cos(\psi)^2\cos(\theta)^2 = \cos(\theta)^2\lt\DD\rt)\lt(x_i\cos(\alpha) - x_j\sin(\alpha) + - x_1(R)\rt)^2 + \lt(\DD\rt)^2\lt(x_i\sin(\alpha) + x_j\cos(\alpha) - Z_P\frac{\sin(\psi)\sin(\theta)^2}{\DD} + - x_2(R)\rt)^2\\ + +Then introducing $X = \cos(\theta)^2$: +$$ +\begin{array}{lllll} + & b^2 & = & \frac{\cos(\theta)^2}{\DD}x_1^2 + \lt(x_2 - x_2(C)\rt)^2\\ + \Leftrightarrow + & Z_P^2\cos(\psi)^2\lt(X-X^2\rt) & = & X^2\lt(x_1^2+x_2^2\rt) - X\sin(\psi)^2\lt(x_1^2+2x_2^2\rt) + \sin(\psi)^4x_2^2\\ + & & & - 2x_2Z_P\sin(\psi)\lt(X - X^2 - \sin(\psi)^2 + X\sin(\psi)^2\rt)\\ + & & & + Z_P^2\sin(\psi)^2\lt(1 - 2X + X^2\rt) \end{array} $$ +Which boils down to: +$$ +\begin{array}{lllll} + & 0 & = & X^2\lt[ x_1^2+x_2^2 + 2x_2Z_P\sin(\psi) + Z_P^2\sin(\psi)^2 + Z_P^2\cos(\psi)^2 \rt]\\ + & & & + X\lt[ -\sin(\psi)^2\lt(x_1^2+2x_2^2\rt) - \lt(1+\sin(\psi)^2\rt)2x_2Z_P\sin(\psi) - 2Z_P^2\sin(\psi)^2 - Z_P^2\cos(\psi)^2\rt]\\ + & & & + \sin(\psi)^4x_2^2 + 2x_2Z_P\sin(\psi)^3 + Z_P^2\sin(\psi)^2\\ + \Leftrightarrow + & 0 & = & X^2\lt[ x_1^2 + \lt(x_2 + Z_P\sin(\psi)\rt)^2 + Z_P^2\cos(\psi)^2 \rt]\\ + & & & + X\lt[ -\sin(\psi)^2\lt(x_1^2+2x_2^2\rt) - \lt(1+\sin(\psi)^2\rt)2x_2Z_P\sin(\psi) - 2Z_P^2\sin(\psi)^2 - Z_P^2\cos(\psi)^2\rt]\\ + & & & + \sin(\psi)^2\lt(\sin(\psi)^2x_2^2 + 2x_2Z_P\sin(\psi) + Z_P^2\rt)\\ + \Leftrightarrow + & 0 & = & X^2\lt[ x_1^2 + \lt(x_2 + Z_P\sin(\psi)\rt)^2 + Z_P^2\cos(\psi)^2 \rt]\\ + & & & - X\lt[ \sin(\psi)^2\lt(x_1^2+2x_2^2\rt) + \lt(1+\sin(\psi)^2\rt)2x_2Z_P\sin(\psi) + 2Z_P^2\sin(\psi)^2 + Z_P^2\cos(\psi)^2\rt]\\ + & & & + \sin(\psi)^2\lt(x_2\sin(\psi) + Z_P\rt)\\ + \Leftrightarrow + & 0 & = & X^2\lt[ x_1^2 + \lt(x_2 + Z_P\sin(\psi)\rt)^2 + Z_P^2\cos(\psi)^2 \rt]\\ + & & & - X\lt[ \sin(\psi)^2\lt(x_1^2+x_2^2\rt) + x_2^2\sin(\psi)^2 + 2x_2Z_P\sin(\psi) + 2x_2Z_P\sin(\psi)^3 + Z_P^2 + Z_P^2\sin(\psi)^2\rt]\\ + & & & + \sin(\psi)^2\lt(x_2\sin(\psi) + Z_P\rt)\\ + \Leftrightarrow + & 0 & = & X^2\lt[ x_1^2 + \lt(x_2 + Z_P\sin(\psi)\rt)^2 + Z_P^2 - Z_P^2\sin(\psi)^2 \rt]\\ + & & & - X\lt[ \sin(\psi)^2\lt(x_1^2+x_2^2\rt) + \lt(x_2\sin(\psi) + Z_P\rt)^2 + Z_P\sin(\psi)^2\lt(2x_2\sin(\psi) + Z_P\rt)\rt]\\ + & & & + \sin(\psi)^2\lt(x_2\sin(\psi) + Z_P\rt)\\ + \Leftrightarrow + & 0 & = & X^2\lt[ x_1^2 + x_2^2 + \lt(x_2\sin(\psi) + Z_P\rt)^2 - x_2^2\sin(\psi)^2 \rt]\\ + & & & - X\lt[ \sin(\psi)^2\lt(x_1^2+x_2^2\rt) + \lt(x_2\sin(\psi) + Z_P\rt)^2 + Z_P\sin(\psi)^2\lt(2x_2\sin(\psi) + Z_P\rt)\rt]\\ + & & & + \sin(\psi)^2\lt(x_2\sin(\psi) + Z_P\rt)\\ + \Leftrightarrow + & 0 & = & AX^2 - BX + C +\end{array} +$$ +With: $$ \lt\{ \begin{array}{lll} - x_2(c) & = z_p\frac{\sin(\psi)\sin(\theta)^2}{\dd}\\ - a & = z_p\frac{\sin(\theta)\cos(\psi)}{\sqrt{\dd}}\\ - b & = z_p\frac{\sin(\theta)\cos(\psi)\cos(\theta)}{\dd} + A = x_1^2 + x_2^2 + \lt(x_2\sin(\psi) + Z_P\rt)^2 - x_2^2\sin(\psi)^2\\ + B = \sin(\psi)^2\lt(x_1^2+x_2^2\rt) + \lt(x_2\sin(\psi) + Z_P\rt)^2 + Z_P\sin(\psi)^2\lt(2x_2\sin(\psi) + Z_P\rt)\\ + C = \sin(\psi)^2\lt(x_2\sin(\psi) + Z_P\rt) \end{array} \rt. $$ -Hence: +Solutions exist if: $$ -\lt\{ - \begin{array}{lll} - \lt(x_i\cos(\alpha) - x_j\sin(\alpha) + x_1(R)\rt)\sqrt{\dd} = z_p\sin(\theta)\cos(\psi)\cos(\epsilon)\\ - \lt(x_i\sin(\alpha) + x_j\cos(\alpha) + x_2(R)\rt)\dd = - z_p\sin(\theta)\lt(\sin(\psi)\sin(\theta) + \cos(\psi)\cos(\theta)\sin(\epsilon)\rt) - \end{array} -\rt. +\begin{array}{lllll} + & \Delta & \geq & 0\\ + \Leftrightarrow + & B^2 - 4AC & \geq & 0\\ +\end{array} +$$ + +In which case, only solutions in $\lt[0,1\rt]$ are acceptable: +$$ +\cos(\theta)^2 = \frac{B \pm \sqrt(\Delta)}{2A} \in \lt[0,1\rt] $$ +And by definition, $\theta \in \lt[0,\frac{\pi}{2}\rt]$, hence $\cos(\theta)\geq0$ and: +$$ +\theta = \arccos\lt(\sqrt{\frac{B \pm \sqrt(\Delta)}{2A}}\rt) +$$ \appendix diff --git a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.toc b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.toc index 82a95eb3b..a73843554 100644 --- a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.toc +++ b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.toc @@ -3,6 +3,8 @@ \contentsline {section}{\numberline {1.1}Generic cone and plane}{5}{section.1.1} \contentsline {section}{\numberline {1.2}Intersection}{5}{section.1.2} \contentsline {section}{\numberline {1.3}Parametric equation}{7}{section.1.3} -\contentsline {chapter}{\numberline {A}Acceleration radiation from a unique point-like charge}{9}{appendix.A} -\contentsline {section}{\numberline {A.1}Retarded time and potential}{9}{section.A.1} -\contentsline {subsection}{\numberline {A.1.1}Retarded time}{9}{subsection.A.1.1} +\contentsline {subsection}{\numberline {1.3.1}From bragg angle and to local cartesian coordinates}{7}{subsection.1.3.1} +\contentsline {subsection}{\numberline {1.3.2}From local cartesian coordinates to bragg angle}{7}{subsection.1.3.2} +\contentsline {chapter}{\numberline {A}Appendices}{11}{appendix.A} +\contentsline {section}{\numberline {A.1}Section}{11}{section.A.1} +\contentsline {subsection}{\numberline {A.1.1}Subsection}{11}{subsection.A.1.1} diff --git a/tofu/version.py b/tofu/version.py index bb8f6d966..57abe3dfb 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-151-ga6825f5' +__version__ = '1.4.1-154-g27e5416' From 65155bb1e5a2d9c120cf57c38b46ec85b8816862 Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Thu, 17 Oct 2019 16:13:02 +0200 Subject: [PATCH 14/51] [Issue202] First version of CrystalBragg.get_braggangle_from_xixj() => reveals probable errors in analytical calculations in Notes/SpectroX2D... to be recalculated with an alternative method --- tofu/geom/_comp_optics.py | 98 ++++++++++++++++++++++ tofu/geom/_core_Optics.py | 168 +++++++++++++------------------------- tofu/version.py | 2 +- 3 files changed, 154 insertions(+), 114 deletions(-) create mode 100644 tofu/geom/_comp_optics.py diff --git a/tofu/geom/_comp_optics.py b/tofu/geom/_comp_optics.py new file mode 100644 index 000000000..4353dfccd --- /dev/null +++ b/tofu/geom/_comp_optics.py @@ -0,0 +1,98 @@ + + +import numpy as np + + + + +def checkformat_vectang(Z, nn, frame_cent, frame_ang): + # Check / format inputs + nn = np.atleast_1d(nn).ravel() + assert nn.size == 3 + nn = nn / np.linalg.norm(nn) + + Z = float(Z) + + frame_cent = np.atleast_1d(frame_cent).ravel() + assert frame_cent.size == 2 + frame_ang = float(frame_ang) + + return Z, nn, frame_cent, frame_ang + + +def get_e1e2_detectorplane(nn, nIn): + e1 = np.cross(nIn, nn) + e1n = np.linalg.norm(e1) + if e1n < 1.e-10: + e1 = np.array([nIn[2], -nIn[1], 0.]) + else: + e1 = e1 / e1n + e2 = np.cross(nn, e1) + e2 = e2 / np.linalg.norm(e2) + return e1, e2 + +def get_bragg_from_lamb(lamb, d, n=1): + lamb = np.atleast_1d(lamb).ravel() + nord = np.atleast_1d(n).ravel() + + theta = np.full((lamb.size, nord.size), np.nan) + sin = nord[None, :]*lamb[:, None]/(2.*d) + indok = np.abs(sin) <= 1. + theta[indok] = np.arcsin(sin[indok]) + return theta + +def calc_xixj_from_braggangle(Z, nIn, + frame_cent, frame_ang, + nn, e1, e2, + ang_bragg, ang_param): + # Deduce key angles + costheta = np.cos(ang_bragg) + sintheta = np.sin(ang_bragg) + cospsi = np.sum(nIn*nn) + sinpsi = np.sum(np.cross(nIn, nn)*e1) + + # Deduce ellipse parameters + cos2sin2 = costheta**2 - sinpsi**2 + x2C = Z * sinpsi * sintheta**2 / cos2sin2 + a = Z * sintheta * cospsi / np.sqrt(cos2sin2) + b = Z * sintheta * cospsi * costheta / cos2sin2 + + # Deduce xi, xj + rot = np.array([np.cos(frame_ang), np.sin(frame_ang)]) + rot2 = np.array([-np.sin(frame_ang), np.cos(frame_ang)]) + ellipse_trans = np.array([a[None, :]*np.cos(ang_param[:, None]) + - frame_cent[0], + b[None, :]*np.sin(ang_param[:, None]) + - frame_cent[1] + x2C[None, :]]) + xi = np.sum(ellipse_trans*rot[:, None,None], axis=0) + xj = np.sum(ellipse_trans*rot2[:, None,None], axis=0) + + return xi, xj + +def calc_braggangle_from_xixj(xi, xj, Z, nn, frame_cent, frame_ang, + nIn, e1, e2): + sinpsi = np.sum(np.cross(nIn, nn)*e1) + sinpsi2 = sinpsi**2 + xij2 = xi[:,None]**2 + xj[None,:]**2 + xjsz = xj[None,:]*sinpsi + Z + + A = xij2 + xjsz**2 - ((xj*sinpsi)**2)[None,:] + B = xij2*sinpsi2 + xjsz**2 + Z*sinpsi2*(2.*xj[None,:]*sinpsi + Z) + C = xjsz*sinpsi2 + + Delta = B**2 - 4*A*C + indok = Delta >= 0 + costheta = np.full(A.shape, np.nan) + + s1 = (B[indok] + np.sqrt(Delta[indok])) / (2*A[indok]) + s2 = (B[indok] - np.sqrt(Delta[indok])) / (2*A[indok]) + + ind = (s1 >= 0) & (s1 <= 1) + iok0, iok1 = indok.nonzero() + import ipdb # DB + ipdb.set_trace() # DB + + costheta[iok0[ind], iok1[ind]] = np.sqrt(s1[ind]) + ind[:] = (s2 >= 0) & (s2 <= 1) + costheta[iok0[ind], iok1[ind]] = np.sqrt(s2[ind]) + return np.arccos(costheta) diff --git a/tofu/geom/_core_Optics.py b/tofu/geom/_core_Optics.py index 444dd34c4..12db26e6b 100644 --- a/tofu/geom/_core_Optics.py +++ b/tofu/geom/_core_Optics.py @@ -23,12 +23,12 @@ try: import tofu.geom._def as _def import tofu.geom._GG as _GG - import tofu.geom._comp as _comp + import tofu.geom._comp_optics as _comp_optics import tofu.geom._plot as _plot except Exception: from . import _def as _def from . import _GG as _GG - from . import _comp as _comp + from . import _comp_optics as _comp_optics from . import _plot as _plot __all__ = ['CrystalBragg'] @@ -451,34 +451,19 @@ def get_color(self): # methods for generic first-approx # ----------------- - @classmethod - def _get_bragg_from_lamb(cls, lamb, d, n=1): - lamb = np.atleast_1d(lamb).ravel() - nord = np.atleast_1d(n).ravel() - - theta = np.full((lamb.size, nord.size), np.nan) - sin = nord[None, :]*lamb[:, None]/(2.*d) - indok = np.abs(sin) <= 1. - theta[indok] = np.arcsin(sin[indok]) - return theta - - def get_bragg_from_lamb(self, lamb, n=1, d=None): + def get_bragg_from_lamb(self, lamb, n=1): """ Braggs' law: n*lamb = 2dsin(theta) """ - - if d is None: - if self._dmat['d'] is None: - msg = "Instance mesh size not set !\n" - msg += " => please provide d !" - raise Exception(msg) - else: - d = float(d) - return self._get_bragg_from_lamb(lamb, d, n=n) + if self._dmat['d'] is None: + msg = "Instance mesh size not set !\n" + msg += " => please provide d !" + raise Exception(msg) + return _comp_optics.get_bragg_from_lamb(lamb, d, n=n) @classmethod - def calc_ellipses_on_plane_2d(cls, + def calc_xixj_from_braggangle(cls, Z, nn, frame_cent, frame_ang, ang_bragg, ang_param, - return_C=False, Test=True): + plot=True, ax=None): """ Assuming crystal's summit as frame origin According to [1], this assumes a local frame centered on the crystal @@ -499,99 +484,56 @@ def calc_ellipses_on_plane_2d(cls, normal vector """ - if Test: - # Check / format inputs - nn = np.atleast_1d(nn).ravel() - assert nn.size == 3 - nn = nn / np.linalg.norm(nn) - Z = float(Z) - - frame_cent = np.atleast_1d(frame_cent).ravel() - assert frame_cent.size == 2 - frame_ang = float(frame_ang) - - ang_bragg = np.atleast_1d(ang_bragg).ravel() - ang_param = np.atleast_1d(ang_param).ravel() - - # By definition, here, nIn = ez nIn = np.array([0., 0., 1.]) - - # Deduce natural plane frame (P, e1, e2) - P = np.array([0., 0., Z]) - e1 = np.cross(nIn, nn) - e1n = np.linalg.norm(e1) - if e1n < 1.e-10: - e1 = np.array([1., 0., 0.]) - else: - e1 = e1 / e1n - e2 = np.cross(nn, e1) - e2 = e2 / np.linalg.norm(e2) - - # Deduce key angles - costheta = np.cos(ang_bragg) - sintheta = np.sin(ang_bragg) - cospsi = np.sum(nIn*nn) - sinpsi = np.sum(np.cross(nIn, nn)*e1) - - # Deduce ellipse parameters - cos2sin2 = costheta**2 - sinpsi**2 - x2C = Z * sinpsi * sintheta**2 / cos2sin2 - a = Z * sintheta * cospsi / np.sqrt(cos2sin2) - b = Z * sintheta * cospsi * costheta / cos2sin2 - - # Deduce xi, xj - rot = np.array([np.cos(frame_ang), np.sin(frame_ang)]) - rot2 = np.array([-np.sin(frame_ang), np.cos(frame_ang)]) - ellipse_trans = np.array([a[None, :]*np.cos(ang_param[:, None]) - - frame_cent[0], - b[None, :]*np.sin(ang_param[:, None]) - - frame_cent[1] + x2C[None, :]]) - xi = np.sum(ellipse_trans*rot[:, None,None], axis=0) - xj = np.sum(ellipse_trans*rot2[:, None,None], axis=0) - - if return_C: - Ci = None - Cj = None - return xi, xj, Ci, Cj + out = _comp_optics.checkformat_vectang(Z, nn, frame_cent, frame_ang) + Z, nn, frame_cent, frame_ang = out + e1, e2 = _comp_optics.get_e1e2_detectorplane(nn, nIn) + ang_bragg = np.atleast_1d(ang_bragg).ravel() + ang_param = np.atleast_1d(ang_param).ravel() + xi, xj = _comp_optics.calc_xixj_from_braggangle(Z, nIn, + frame_cent, frame_ang, + nn, e1, e2, + ang_bragg, ang_param) + if plot: + if ax is None: + fig = plt.figure() + ax = fig.add_axes([0.1,0.1,0.8,0.8], aspect='equal') + + for ii in range(len(ang_bragg)): + deg ='{0:07.3f}'.format(ang_bragg[ii]*180/np.pi) + ax.plot(xi[:,ii], xj[:,ii], '.', label='bragg %s'%deg) + #ax.plot(Ci[:,ii], Cj[:,ii], 'x', label='bragg %s - center'%deg) + ax.set_xlabel(r'xi') + ax.set_ylabel(r'yi') + ax.legend(loc='upper left', bbox_to_anchor=(1.05, 1.), frameon=False) + return xi, xj, ax else: return xi, xj @classmethod - def plot_ellipses_on_plane_2d(cls, Z, nn, frame_cent, frame_ang, - ang_bragg, ang_param, ax=None): - - # Check / format inputs - nn = np.atleast_1d(nn).ravel() - assert nn.size == 3 - nn = nn / np.linalg.norm(nn) - Z = float(Z) - - frame_cent = np.atleast_1d(frame_cent).ravel() - ssue202_SpectroX2DCrystalassert frame_cent.size == 2 - frame_ang = float(frame_ang) - - ang_bragg = np.atleast_1d(ang_bragg).ravel() - ang_param = np.atleast_1d(ang_param).ravel() + def calc_braggangle_from_xixj(cls, + Z, nn, frame_cent, frame_ang, + xi, xj, plot=True, ax=None): - # Compute - xi, xj, Ci, Cj = cls.calc_ellipses_on_plane_2d(Z, nn, + nIn = np.array([0., 0., 1.]) + out = _comp_optics.checkformat_vectang(Z, nn, frame_cent, frame_ang) + Z, nn, frame_cent, frame_ang = out + e1, e2 = _comp_optics.get_e1e2_detectorplane(nn, nIn) + xi = np.atleast_1d(xi).ravel() + xj = np.atleast_1d(xj).ravel() + theta = _comp_optics.calc_braggangle_from_xixj(xi, xj, Z, nn, frame_cent, frame_ang, - ang_bragg, ang_param, - return_C=True, - Test=False) - nbragg = ang_bragg.size - - # Separate by bragg angle - if ax is None: - fig = plt.figure() - ax = fig.add_axes([0.1,0.1,0.8,0.8], aspect='equal') - - for ii in range(nbragg): - deg ='{0:07.3f}'.format(ang_bragg[ii]*180/np.pi) - ax.plot(xi[:,ii], xj[:,ii], '.', label='bragg %s'%deg) - #ax.plot(Ci[:,ii], Cj[:,ii], 'x', label='bragg %s - center'%deg) - ax.set_xlabel(r'xi') - ax.set_ylabel(r'yi') - ax.legend(loc='upper left', bbox_to_anchor=(1.05, 1.), frameon=False) + nIn, e1, e2) - return ax + if plot: + if ax is None: + fig = plt.figure() + ax = fig.add_axes([0.1,0.1,0.8,0.8], aspect='equal') + ax.pcolor(xi, xj, theta) + #ax.plot(Ci[:,ii], Cj[:,ii], 'x', label='bragg %s - center'%deg) + ax.set_xlabel(r'xi') + ax.set_ylabel(r'yi') + ax.legend(loc='upper left', bbox_to_anchor=(1.05, 1.), frameon=False) + return theta, ax + else: + return theta diff --git a/tofu/version.py b/tofu/version.py index 57abe3dfb..980075663 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-154-g27e5416' +__version__ = '1.4.1-155-g78e1ec3' From 6c3b6898ade67d8af5c0b31104aa16c8647539a0 Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Thu, 17 Oct 2019 18:22:26 +0200 Subject: [PATCH 15/51] [Issue202] CrystalBragg now performing coordinates tranforms in both directions, successfull but need to check bragg vs theta and ang_param vs epsilon (axis vs center), to test and validate --- .../SpectroX2D_ConePlaneEllipse.tex | 18 +++++ tofu/geom/_comp_optics.py | 81 +++++++++++-------- tofu/geom/_core_Optics.py | 65 +++++++++++---- tofu/version.py | 2 +- 4 files changed, 119 insertions(+), 47 deletions(-) diff --git a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.tex b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.tex index c2af17a53..8e5b0f187 100644 --- a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.tex +++ b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.tex @@ -366,6 +366,24 @@ \subsection{From local cartesian coordinates to bragg angle} \theta = \arccos\lt(\sqrt{\frac{B \pm \sqrt(\Delta)}{2A}}\rt) $$ +\subsubsection{Alternative method for $\theta$} + +By definition: +$$ +\underline{OM}.\ez = \cos(\theta)\|OM\| +$$ + +And: +$$ +\begin{array}{lllll} + \underline{OM} & = & \underline{OP} + \underline{PR} + \underline{RM}\\ + & = & \\ +\end{array} +$$ + + + + \appendix \chapter{Appendices} diff --git a/tofu/geom/_comp_optics.py b/tofu/geom/_comp_optics.py index 4353dfccd..bce6705c2 100644 --- a/tofu/geom/_comp_optics.py +++ b/tofu/geom/_comp_optics.py @@ -32,22 +32,31 @@ def get_e1e2_detectorplane(nn, nIn): return e1, e2 def get_bragg_from_lamb(lamb, d, n=1): + """ n*lamb = 2d*sin(bragg) """ lamb = np.atleast_1d(lamb).ravel() nord = np.atleast_1d(n).ravel() - theta = np.full((lamb.size, nord.size), np.nan) + bragg= np.full((lamb.size, nord.size), np.nan) sin = nord[None, :]*lamb[:, None]/(2.*d) indok = np.abs(sin) <= 1. - theta[indok] = np.arcsin(sin[indok]) - return theta + bragg[indok] = np.arcsin(sin[indok]) + return bragg + +def get_lamb_from_bragg(bragg, d, n=1): + """ n*lamb = 2d*sin(bragg) """ + bragg = np.atleast_1d(bragg).ravel() + nord = np.atleast_1d(n).ravel() + + lamb = 2*d*np.sin(bragg[:, None]) / nord[None, :] + return lamb def calc_xixj_from_braggangle(Z, nIn, frame_cent, frame_ang, nn, e1, e2, ang_bragg, ang_param): # Deduce key angles - costheta = np.cos(ang_bragg) - sintheta = np.sin(ang_bragg) + costheta = np.cos(np.pi/2 - ang_bragg) + sintheta = np.sin(np.pi/2 - ang_bragg) cospsi = np.sum(nIn*nn) sinpsi = np.sum(np.cross(nIn, nn)*e1) @@ -57,12 +66,16 @@ def calc_xixj_from_braggangle(Z, nIn, a = Z * sintheta * cospsi / np.sqrt(cos2sin2) b = Z * sintheta * cospsi * costheta / cos2sin2 + # ang_param with respect to axis => epsilon with respect to center + epsilon = None + + # Deduce xi, xj rot = np.array([np.cos(frame_ang), np.sin(frame_ang)]) rot2 = np.array([-np.sin(frame_ang), np.cos(frame_ang)]) - ellipse_trans = np.array([a[None, :]*np.cos(ang_param[:, None]) + ellipse_trans = np.array([a[None, :]*np.cos(epsilon[:, None]) - frame_cent[0], - b[None, :]*np.sin(ang_param[:, None]) + b[None, :]*np.sin(epsilon[:, None]) - frame_cent[1] + x2C[None, :]]) xi = np.sum(ellipse_trans*rot[:, None,None], axis=0) xj = np.sum(ellipse_trans*rot2[:, None,None], axis=0) @@ -71,28 +84,32 @@ def calc_xixj_from_braggangle(Z, nIn, def calc_braggangle_from_xixj(xi, xj, Z, nn, frame_cent, frame_ang, nIn, e1, e2): - sinpsi = np.sum(np.cross(nIn, nn)*e1) - sinpsi2 = sinpsi**2 - xij2 = xi[:,None]**2 + xj[None,:]**2 - xjsz = xj[None,:]*sinpsi + Z - - A = xij2 + xjsz**2 - ((xj*sinpsi)**2)[None,:] - B = xij2*sinpsi2 + xjsz**2 + Z*sinpsi2*(2.*xj[None,:]*sinpsi + Z) - C = xjsz*sinpsi2 - - Delta = B**2 - 4*A*C - indok = Delta >= 0 - costheta = np.full(A.shape, np.nan) - - s1 = (B[indok] + np.sqrt(Delta[indok])) / (2*A[indok]) - s2 = (B[indok] - np.sqrt(Delta[indok])) / (2*A[indok]) - - ind = (s1 >= 0) & (s1 <= 1) - iok0, iok1 = indok.nonzero() - import ipdb # DB - ipdb.set_trace() # DB - - costheta[iok0[ind], iok1[ind]] = np.sqrt(s1[ind]) - ind[:] = (s2 >= 0) & (s2 <= 1) - costheta[iok0[ind], iok1[ind]] = np.sqrt(s2[ind]) - return np.arccos(costheta) + + # We have e1, e2 => compute x1, x2 + x1 = (frame_cent[0] + + xi[:,None]*np.cos(frame_ang) + - xj[None,:]*np.sin(frame_ang)) + x2 = (frame_cent[1] + + xi[:,None]*np.sin(frame_ang) + + xj[None,:]*np.cos(frame_ang)) + + # Deduce OM + sca = Z + x1*np.sum(e1*nIn) + x2*np.sum(e2*nIn) + norm = np.sqrt((x1*e1[0] + x2*e2[0])**2 + + (x1*e1[1] + x2*e2[1])**2 + + (Z + x1*e1[2] + x2*e2[2])**2) + costheta = sca/norm + bragg = np.pi/2 - np.arccos(costheta) + + # Get angle with respect to axis ! (not center) + ang = np.arctan2(x2, x1) + + # costheta = np.cos(bragg) + # sintheta = np.sin(bragg) + # cospsi = np.sum(nIn*nn) + # sinpsi = np.sum(np.cross(nIn, nn)*e1) + # cos2sin2 = costheta**2 - sinpsi**2 + # x2C = Z * sinpsi * sintheta**2 / cos2sin2 + # ang = np.arctan2(x2-x2C, x1) + + return bragg, ang diff --git a/tofu/geom/_core_Optics.py b/tofu/geom/_core_Optics.py index 12db26e6b..02c58d83d 100644 --- a/tofu/geom/_core_Optics.py +++ b/tofu/geom/_core_Optics.py @@ -452,13 +452,21 @@ def get_color(self): # ----------------- def get_bragg_from_lamb(self, lamb, n=1): - """ Braggs' law: n*lamb = 2dsin(theta) """ + """ Braggs' law: n*lamb = 2dsin(bragg) """ if self._dmat['d'] is None: msg = "Instance mesh size not set !\n" msg += " => please provide d !" raise Exception(msg) return _comp_optics.get_bragg_from_lamb(lamb, d, n=n) + def get_lamb_from_bragg(self, bragg, n=1): + """ Braggs' law: n*lamb = 2dsin(bragg) """ + if self._dmat['d'] is None: + msg = "Instance mesh size not set !\n" + msg += " => please provide d !" + raise Exception(msg) + return _comp_optics.get_lamb_from_bragg(lamb, d, n=n) + @classmethod def calc_xixj_from_braggangle(cls, Z, nn, frame_cent, frame_ang, @@ -513,7 +521,8 @@ def calc_xixj_from_braggangle(cls, @classmethod def calc_braggangle_from_xixj(cls, Z, nn, frame_cent, frame_ang, - xi, xj, plot=True, ax=None): + xi, xj, + plot=True, ax=None, **kwdargs): nIn = np.array([0., 0., 1.]) out = _comp_optics.checkformat_vectang(Z, nn, frame_cent, frame_ang) @@ -521,19 +530,47 @@ def calc_braggangle_from_xixj(cls, e1, e2 = _comp_optics.get_e1e2_detectorplane(nn, nIn) xi = np.atleast_1d(xi).ravel() xj = np.atleast_1d(xj).ravel() - theta = _comp_optics.calc_braggangle_from_xixj(xi, xj, Z, nn, - frame_cent, frame_ang, - nIn, e1, e2) + bragg, ang = _comp_optics.calc_braggangle_from_xixj(xi, xj, Z, nn, + frame_cent, frame_ang, + nIn, e1, e2) + + if plot != False: + braggplot = bragg.T * 180./np.pi + angplot = ang.T * 180./np.pi + if isinstance(plot, bool): + plot = 'contour' - if plot: if ax is None: fig = plt.figure() - ax = fig.add_axes([0.1,0.1,0.8,0.8], aspect='equal') - ax.pcolor(xi, xj, theta) - #ax.plot(Ci[:,ii], Cj[:,ii], 'x', label='bragg %s - center'%deg) - ax.set_xlabel(r'xi') - ax.set_ylabel(r'yi') - ax.legend(loc='upper left', bbox_to_anchor=(1.05, 1.), frameon=False) - return theta, ax + ax0 = fig.add_axes([0.1, 0.1, 0.35, 0.8], aspect='equal') + ax1 = fig.add_axes([0.55, 0.1, 0.35, 0.8], aspect='equal') + ax = [ax0, ax1] + if plot == 'contour': + if 'levels' in kwdargs.keys(): + lvls = kwdargs['levels'] + del kwdargs['levels'] + obj = ax[0].contour(xi, xj, braggplot, lvls, **kwdargs) + obj = ax[1].contour(xi, xj, angplot, lvls, **kwdargs) + else: + obj = ax[0].contour(xi, xj, braggplot, **kwdargs) + obj = ax[1].contour(xi, xj, angplot, **kwdargs) + elif plot == 'imshow': + extent=(xi.min(), xi.max(), xj.min(), xj.max()) + obj = ax[0].imshow(braggplot, extent=extent, aspect='equal', + adjustable='datalim', **kwdargs) + obj = ax[1].imshow(angplot, extent=extent, aspect='equal', + adjustable='datalim', **kwdargs) + elif plot == 'pcolor': + obj = ax[0].pcolor(xi, xj, braggplot, **kwdargs) + obj = ax[1].pcolor(xi, xj, angplot, **kwdargs) + ax[0].set_xlabel(r'xi') + ax[1].set_xlabel(r'xi') + ax[0].set_ylabel(r'yi') + ax[1].set_ylabel(r'yi') + cax0 = plt.colorbar(obj, ax=ax[0]) + cax1 = plt.colorbar(obj, ax=ax[1]) + cax0.ax.set_ylabel(r'$\theta_{bragg}$ (deg)') + cax1.ax.set_ylabel(r'$ang$ (deg)') + return bragg, ang, ax else: - return theta + return bragg, ang diff --git a/tofu/version.py b/tofu/version.py index 980075663..555401689 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-155-g78e1ec3' +__version__ = '1.4.1-156-g65155bb' From 6dedc3a8717eab45d29ef7bd57d7568e0ac0c7bc Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Fri, 18 Oct 2019 08:34:50 +0200 Subject: [PATCH 16/51] [Issue202] Renamed tofu/geom/_core_Optics.py to tofu/geom/_core_optics.py --- tofu/geom/{_core_Optics.py => _core_optics.py} | 0 tofu/version.py | 2 +- 2 files changed, 1 insertion(+), 1 deletion(-) rename tofu/geom/{_core_Optics.py => _core_optics.py} (100%) diff --git a/tofu/geom/_core_Optics.py b/tofu/geom/_core_optics.py similarity index 100% rename from tofu/geom/_core_Optics.py rename to tofu/geom/_core_optics.py diff --git a/tofu/version.py b/tofu/version.py index 555401689..2ecf134fc 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-156-g65155bb' +__version__ = '1.4.1-157-g6c3b689' From d60d8353204b1b622f0d14900cde6588f9dc4515 Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Fri, 18 Oct 2019 14:55:24 +0200 Subject: [PATCH 17/51] [Issue202] Added l = f(\beta) in Notes_Upgrades/SpectroX2D --- .../SpectroX2D_ConePlaneEllipse.out | 2 +- .../SpectroX2D_ConePlaneEllipse.pdf | Bin 103977 -> 116558 bytes .../SpectroX2D_ConePlaneEllipse.tex | 104 +++++++++++++++++- .../SpectroX2D_ConePlaneEllipse.toc | 5 +- tofu/geom/__init__.py | 2 +- tofu/geom/_comp_optics.py | 19 ++-- tofu/geom/_core_optics.py | 12 +- tofu/version.py | 2 +- 8 files changed, 122 insertions(+), 24 deletions(-) diff --git a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out index 12cd3d597..48db5cdbe 100644 --- a/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out +++ b/Notes_Upgrades/SpectroX2D/SpectroX2D_ConePlaneEllipse.out @@ -2,7 +2,7 @@ \BOOKMARK [1][-]{section.1.1}{Generic cone and plane}{chapter.1} \BOOKMARK [1][-]{section.1.2}{Intersection}{chapter.1} \BOOKMARK [1][-]{section.1.3}{Parametric equation}{chapter.1} -\BOOKMARK [2][-]{subsection.1.3.1}{From bragg angle and to local cartesian coordinates}{section.1.3} +\BOOKMARK [2][-]{subsection.1.3.1}{From bragg angle and parameter to local cartesian coordinates}{section.1.3} \BOOKMARK 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z7#=@>ws;6)P>6qB7W?-Ej6~x>h(RJCCn3b3FnH{TAYpJk0TCEHe}_PkC)f|nf53_Z zKFMGV8erE68$&Q~yx9?gf#N|8K_b8>c?7}0kSEKa&|gIVh5tWLLxGxjnqUy9lTZVW z_;WY;hv|St=6?(V!{FBgZ1PWA?CXgl>|{L{ z42IVh3j>@MuOb}JBcL!e9=QNLFejM~g=6psMj)Xlc?3m5kw4pB0aW=Hek2NwrwIy< zx9&rMbqH@@G!z5e`Dg&qWARR5V0biv0fZx|ef=PWQd2K}$Kej5u8EJr7Sgac0S zS3R6x4d@IOjzHmUW#GUHb5b}26oW@4#Q(570s+UfG6I3bqb9Ji`02EN@*0@UkSBQ! z=!)mHC@ALVZubv*p->RKSpbECp-)m14gIgv{>5uFun{~79~yzcqXQZN%&sQ}1~zwi zn<+FP-${mGppc&r>;4cLqYK;zJ1HSBbKz-+frJ0t5CPp_5NJH10T%qsZq^LY3vYbP z|JZc^{hrhZSRC<;fWZLtJ}En}89pI81d!@)FW~vxU49mx+#CXB5HuW@-vZ*mB7y58 zZD(iT>geaN+}dQ~s!rC epsilon with respect to center - epsilon = None - + x1 = None + x2 = None + PMnorm = np.sqrt(x1**2 + (x2-x2C)**2) + acose = PMnorm[None, :]*np.cos(angle[:, None]) + bsinePx2C = PMnorm[None, :]*np.sin(angle[:, None]) # Deduce xi, xj rot = np.array([np.cos(frame_ang), np.sin(frame_ang)]) rot2 = np.array([-np.sin(frame_ang), np.cos(frame_ang)]) - ellipse_trans = np.array([a[None, :]*np.cos(epsilon[:, None]) - - frame_cent[0], - b[None, :]*np.sin(epsilon[:, None]) - - frame_cent[1] + x2C[None, :]]) + ellipse_trans = np.array([acose - frame_cent[0], + bsinePx2C - frame_cent[1]]) xi = np.sum(ellipse_trans*rot[:, None,None], axis=0) xj = np.sum(ellipse_trans*rot2[:, None,None], axis=0) diff --git a/tofu/geom/_core_optics.py b/tofu/geom/_core_optics.py index 02c58d83d..6d62e0c65 100644 --- a/tofu/geom/_core_optics.py +++ b/tofu/geom/_core_optics.py @@ -470,7 +470,7 @@ def get_lamb_from_bragg(self, bragg, n=1): @classmethod def calc_xixj_from_braggangle(cls, Z, nn, frame_cent, frame_ang, - ang_bragg, ang_param, + bragg, angle, plot=True, ax=None): """ Assuming crystal's summit as frame origin @@ -496,19 +496,19 @@ def calc_xixj_from_braggangle(cls, out = _comp_optics.checkformat_vectang(Z, nn, frame_cent, frame_ang) Z, nn, frame_cent, frame_ang = out e1, e2 = _comp_optics.get_e1e2_detectorplane(nn, nIn) - ang_bragg = np.atleast_1d(ang_bragg).ravel() - ang_param = np.atleast_1d(ang_param).ravel() + bragg = np.atleast_1d(bragg).ravel() + angle = np.atleast_1d(angle).ravel() xi, xj = _comp_optics.calc_xixj_from_braggangle(Z, nIn, frame_cent, frame_ang, nn, e1, e2, - ang_bragg, ang_param) + bragg, angle) if plot: if ax is None: fig = plt.figure() ax = fig.add_axes([0.1,0.1,0.8,0.8], aspect='equal') - for ii in range(len(ang_bragg)): - deg ='{0:07.3f}'.format(ang_bragg[ii]*180/np.pi) + for ii in range(len(bragg)): + deg ='{0:07.3f}'.format(bragg[ii]*180/np.pi) ax.plot(xi[:,ii], xj[:,ii], '.', label='bragg %s'%deg) #ax.plot(Ci[:,ii], Cj[:,ii], 'x', label='bragg %s - center'%deg) ax.set_xlabel(r'xi') diff --git a/tofu/version.py b/tofu/version.py index 2ecf134fc..43d3541ee 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-157-g6c3b689' +__version__ = '1.4.1-158-g6dedc3a' From 38727e88393b692b3db947e4c72548ec51441f58 Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Fri, 18 Oct 2019 15:32:49 +0200 Subject: [PATCH 18/51] [Issue202] CrystalBragg now performs coordinates transforms in both directions with proper parameters (bragg,angle) vs (xi, xj), tested and validated => optimize numerically or start testing on real data --- tofu/geom/_comp_optics.py | 31 ++++++++++++++----------------- tofu/geom/_core_optics.py | 20 ++++++++++---------- tofu/version.py | 2 +- 3 files changed, 25 insertions(+), 28 deletions(-) diff --git a/tofu/geom/_comp_optics.py b/tofu/geom/_comp_optics.py index c8aef8dd7..1e6b3f3b5 100644 --- a/tofu/geom/_comp_optics.py +++ b/tofu/geom/_comp_optics.py @@ -66,21 +66,19 @@ def calc_xixj_from_braggangle(Z, nIn, a = Z * sintheta * cospsi / np.sqrt(cos2sin2) b = Z * sintheta * cospsi * costheta / cos2sin2 - # ang_param with respect to axis => epsilon with respect to center - x1 = None - x2 = None - PMnorm = np.sqrt(x1**2 + (x2-x2C)**2) - acose = PMnorm[None, :]*np.cos(angle[:, None]) - bsinePx2C = PMnorm[None, :]*np.sin(angle[:, None]) - - # Deduce xi, xj - rot = np.array([np.cos(frame_ang), np.sin(frame_ang)]) - rot2 = np.array([-np.sin(frame_ang), np.cos(frame_ang)]) - ellipse_trans = np.array([acose - frame_cent[0], - bsinePx2C - frame_cent[1]]) - xi = np.sum(ellipse_trans*rot[:, None,None], axis=0) - xj = np.sum(ellipse_trans*rot2[:, None,None], axis=0) - + # Get radius from axis => x1, x2 => xi, xj + asin2bcos2 = (b[None,:]**2*np.cos(angle[:,None])**2 + + a[None,:]**2*np.sin(angle[:,None])**2) + l = ((a[None,:]**2*x2C[None,:]*np.sin(angle[:,None]) + + a[None,:]*b[None,:]*np.sqrt(asin2bcos2 - + x2C[None,:]**2*np.cos(angle[:,None])**2)) + / asin2bcos2) + + x1_frame = l*np.cos(angle[:,None]) - frame_cent[0] + x2_frame = l*np.sin(angle[:,None]) - frame_cent[1] + + xi = x1_frame*np.cos(frame_ang) + x2_frame*np.sin(frame_ang) + xj = -x1_frame*np.sin(frame_ang) + x2_frame*np.cos(frame_ang) return xi, xj def calc_braggangle_from_xixj(xi, xj, Z, nn, frame_cent, frame_ang, @@ -99,8 +97,7 @@ def calc_braggangle_from_xixj(xi, xj, Z, nn, frame_cent, frame_ang, norm = np.sqrt((x1*e1[0] + x2*e2[0])**2 + (x1*e1[1] + x2*e2[1])**2 + (Z + x1*e1[2] + x2*e2[2])**2) - costheta = sca/norm - bragg = np.pi/2 - np.arccos(costheta) + bragg = np.pi/2 - np.arccos(sca/norm) # Get angle with respect to axis ! (not center) ang = np.arctan2(x2, x1) diff --git a/tofu/geom/_core_optics.py b/tofu/geom/_core_optics.py index 6d62e0c65..af57f04a7 100644 --- a/tofu/geom/_core_optics.py +++ b/tofu/geom/_core_optics.py @@ -549,26 +549,26 @@ def calc_braggangle_from_xixj(cls, if 'levels' in kwdargs.keys(): lvls = kwdargs['levels'] del kwdargs['levels'] - obj = ax[0].contour(xi, xj, braggplot, lvls, **kwdargs) - obj = ax[1].contour(xi, xj, angplot, lvls, **kwdargs) + obj0 = ax[0].contour(xi, xj, braggplot, lvls, **kwdargs) + obj1 = ax[1].contour(xi, xj, angplot, lvls, **kwdargs) else: - obj = ax[0].contour(xi, xj, braggplot, **kwdargs) - obj = ax[1].contour(xi, xj, angplot, **kwdargs) + obj0 = ax[0].contour(xi, xj, braggplot, **kwdargs) + obj1 = ax[1].contour(xi, xj, angplot, **kwdargs) elif plot == 'imshow': extent=(xi.min(), xi.max(), xj.min(), xj.max()) - obj = ax[0].imshow(braggplot, extent=extent, aspect='equal', + obj0 = ax[0].imshow(braggplot, extent=extent, aspect='equal', adjustable='datalim', **kwdargs) - obj = ax[1].imshow(angplot, extent=extent, aspect='equal', + obj1 = ax[1].imshow(angplot, extent=extent, aspect='equal', adjustable='datalim', **kwdargs) elif plot == 'pcolor': - obj = ax[0].pcolor(xi, xj, braggplot, **kwdargs) - obj = ax[1].pcolor(xi, xj, angplot, **kwdargs) + obj0 = ax[0].pcolor(xi, xj, braggplot, **kwdargs) + obj1 = ax[1].pcolor(xi, xj, angplot, **kwdargs) ax[0].set_xlabel(r'xi') ax[1].set_xlabel(r'xi') ax[0].set_ylabel(r'yi') ax[1].set_ylabel(r'yi') - cax0 = plt.colorbar(obj, ax=ax[0]) - cax1 = plt.colorbar(obj, ax=ax[1]) + cax0 = plt.colorbar(obj0, ax=ax[0]) + cax1 = plt.colorbar(obj1, ax=ax[1]) cax0.ax.set_ylabel(r'$\theta_{bragg}$ (deg)') cax1.ax.set_ylabel(r'$ang$ (deg)') return bragg, ang, ax diff --git a/tofu/version.py b/tofu/version.py index 43d3541ee..5bb8f21e4 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-158-g6dedc3a' +__version__ = '1.4.1-159-gd60d835' From 346b58a304ee76d47d9427e816707d1e3ed4cc55 Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Fri, 18 Oct 2019 16:27:00 +0200 Subject: [PATCH 19/51] [Issue202] Preparing CrystalBragg for tests with experimental data --- tofu/geom/_core_optics.py | 52 ++++++++++----------------------------- tofu/version.py | 2 +- 2 files changed, 14 insertions(+), 40 deletions(-) diff --git a/tofu/geom/_core_optics.py b/tofu/geom/_core_optics.py index af57f04a7..9f37065e3 100644 --- a/tofu/geom/_core_optics.py +++ b/tofu/geom/_core_optics.py @@ -507,10 +507,14 @@ def calc_xixj_from_braggangle(cls, fig = plt.figure() ax = fig.add_axes([0.1,0.1,0.8,0.8], aspect='equal') - for ii in range(len(bragg)): - deg ='{0:07.3f}'.format(bragg[ii]*180/np.pi) - ax.plot(xi[:,ii], xj[:,ii], '.', label='bragg %s'%deg) - #ax.plot(Ci[:,ii], Cj[:,ii], 'x', label='bragg %s - center'%deg) + if data is None: + for ii in range(len(bragg)): + deg ='{0:07.3f}'.format(bragg[ii]*180/np.pi) + ax.plot(xi[:,ii], xj[:,ii], '.', label='bragg %s'%deg) + else: + ax.scatter(xi.ravel(), xj.ravel(), c=data.ravel(), + s=10, marker='s', edgecolors='None') + ax.set_xlabel(r'xi') ax.set_ylabel(r'yi') ax.legend(loc='upper left', bbox_to_anchor=(1.05, 1.), frameon=False) @@ -537,40 +541,10 @@ def calc_braggangle_from_xixj(cls, if plot != False: braggplot = bragg.T * 180./np.pi angplot = ang.T * 180./np.pi - if isinstance(plot, bool): - plot = 'contour' - - if ax is None: - fig = plt.figure() - ax0 = fig.add_axes([0.1, 0.1, 0.35, 0.8], aspect='equal') - ax1 = fig.add_axes([0.55, 0.1, 0.35, 0.8], aspect='equal') - ax = [ax0, ax1] - if plot == 'contour': - if 'levels' in kwdargs.keys(): - lvls = kwdargs['levels'] - del kwdargs['levels'] - obj0 = ax[0].contour(xi, xj, braggplot, lvls, **kwdargs) - obj1 = ax[1].contour(xi, xj, angplot, lvls, **kwdargs) - else: - obj0 = ax[0].contour(xi, xj, braggplot, **kwdargs) - obj1 = ax[1].contour(xi, xj, angplot, **kwdargs) - elif plot == 'imshow': - extent=(xi.min(), xi.max(), xj.min(), xj.max()) - obj0 = ax[0].imshow(braggplot, extent=extent, aspect='equal', - adjustable='datalim', **kwdargs) - obj1 = ax[1].imshow(angplot, extent=extent, aspect='equal', - adjustable='datalim', **kwdargs) - elif plot == 'pcolor': - obj0 = ax[0].pcolor(xi, xj, braggplot, **kwdargs) - obj1 = ax[1].pcolor(xi, xj, angplot, **kwdargs) - ax[0].set_xlabel(r'xi') - ax[1].set_xlabel(r'xi') - ax[0].set_ylabel(r'yi') - ax[1].set_ylabel(r'yi') - cax0 = plt.colorbar(obj0, ax=ax[0]) - cax1 = plt.colorbar(obj1, ax=ax[1]) - cax0.ax.set_ylabel(r'$\theta_{bragg}$ (deg)') - cax1.ax.set_ylabel(r'$ang$ (deg)') - return bragg, ang, ax + func = _plot_optics.CrystalBragg_plot_braggangle_from_xixj + lax = func(xi=xi, xj=xj, ax=ax, plot=plot, + bragg=bragg.T * 180./np.pi, angle=ang.T * 180./np.pi, + braggunits='deg', angunits='deg', **kwdargs) + return bragg, ang, lax else: return bragg, ang diff --git a/tofu/version.py b/tofu/version.py index 5bb8f21e4..fa252eaec 100644 --- a/tofu/version.py +++ b/tofu/version.py @@ -1,2 +1,2 @@ # Do not edit, pipeline versioning governed by git tags! -__version__ = '1.4.1-159-gd60d835' +__version__ = '1.4.1-160-g38727e8' From c4ff052efede59b741e8314bc537ff0610ddab6b Mon Sep 17 00:00:00 2001 From: VEZINET Didier Date: Fri, 18 Oct 2019 16:27:48 +0200 Subject: [PATCH 20/51] [Issue202] Creating tofu/geom/inputs/test_data/ for SpectroX2D (to be moved later to units tests --- .../SpectroX2D_WEST_55562_t39.145s.npz | Bin 0 -> 5716124 bytes tofu/version.py | 2 +- 2 files changed, 1 insertion(+), 1 deletion(-) create mode 100644 tofu/geom/inputs/test_data/SpectroX2D_WEST_55562_t39.145s.npz diff --git a/tofu/geom/inputs/test_data/SpectroX2D_WEST_55562_t39.145s.npz b/tofu/geom/inputs/test_data/SpectroX2D_WEST_55562_t39.145s.npz new file mode 100644 index 0000000000000000000000000000000000000000..c2b8d33bddafd8c81ffefc1fcc35fc76decc972c GIT binary patch literal 5716124 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