ó
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 Z
 m Z m Z m Z d d l m Z m Z d d	 l m Z d d
 l m Z d d l m Z d d l m Z m Z d d l m Z d d l Z d d l m Z d d d d d d d d d d d d g Z d d d d d d d g Z  e! e ƒ Z" e! e  ƒ Z# d  Z$ d! g d" d  d# g d$ g d% d& g d' d( d) g d* g d+ g g Z% d! d  d% d& g Z& d" d# d$ g Z' e( d" g ƒ Z) e( d" d d! g d! d" d g d" d! d g d" d! d! g g ƒ Z* e( d" g ƒ Z+ e( d" d g d d" g d" d! g g ƒ Z, e( d" d d! g d! d" d g d" d! d g d! d" d! g g ƒ Z- e( d" g ƒ Z. e( d" g ƒ Z/ e e) e* e+ e, e- e. e/ f ƒ Z0 e0 j1 ƒ  Z0 d" d  d# d% d& d' d( d) g Z2 d" d  d# d& d' d) d* d+ g Z3 e4 d, d- d. ƒZ5 e6 e5 e3 <e0 d d … e2 f e3 d d … f Z7 e8 e9 j e0 ƒ ƒ Z: d/ „  Z; d0 „  Z< d1 „  Z= d d2 l> m? Z? e@ e: jA ƒ Z: d3 „  ZB d4 „  ZC d5 „  ZD d6 „  ZE d S(7   sŽ  
 Estimate electron temperature and ion concentration based on their the spectral lines intensity. 
 
 Ions intensity is descrimed by a very simple model with minimal number of parameters:
 Expectations:
  1) that line intesity is proportional to impurity density and fnction of the temperature
  2) ratio of lines of the different ionization states of the impuritie as 
    function of the temperature is polynome of order k (k = 1 now)
  3) shape of f(T_e) of the first ionozation stage is gaussian with width a and center T0
    (for k = 1  => all other are also gaussians)
  4) this model can not exactly estimate the temperature, only something which is 
    monotonous function of the T_E => caibration from the spitzer resistivity was necassary. 
  5) it is expected that during the shot is impurity density as constant as possible. 
  
  Advantages:
  simple model => robust
  most of the spectra are explained very well even by this simple model 

  
  
  Disadvantages:
  
   OI and NI can be observed in low temperatures a  deviation from model, f(T) if this
  ions don't have a gaussian shape, it radiates strongyl alte low temperatures and the the radiation
  is alomost constant over large range of temperatures. 

 In helium shots is probably a different physic or a week he lines mess estimate of the NI density. 
 NI radiation is significantly underestimated. 
 
 Autor :Tomas Odstrcil
 Date 12.12.2012


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   block_diag(   t   repmat(   t   time(   t   save_advt   load_adv(   t	   saveconst(   t	   fmin_bfgst   HIt   OIt   OIIt   OIIIt   HeIt   CIIt   CIIIt   NIt   NIIt   NIIIt   M1t   MIVt   Ht   Ot   Het   Ct   Ni   i    i   i   i   i   i   i   i   i	   i
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
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 |	 | d f ƒ j }	 t | |	 d d d |	 | d ƒ}
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 ƒ } d G| GH|
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   chi2 temp:(   t   sizet   onest   arrayt   Mt   bound_inter_jt   dott   logR(   t   sqrtt   outert   tilet   averaget   sumt   newaxisR   (   t   pt   pEt   coefft   nt   mt   It   cutMt   Rt   Ret   BR(   t   chi2(    (    sW   /golem/database/velin//includes/analysis/Radiation/1212Impurities_TO.ON/CalcDensTemp.pyt	   EstimateTw   s"    (#$6,	c
         C   s“  t  d t f ƒ }
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 t | d  d  … t |	 f ƒ t | ƒ ƒ \ } } t | ƒ d t | ƒ } t t t | ƒ ƒ ƒ } | | :} | d C} | t | t d | d | ƒ ƒ t | ƒ } d d d d	 g } x*t t t |	 ƒ ƒ D]} | } t | d  d  … t |	 | f t | d  d  … |	 f ƒ ƒ } t | d  d  … t |	 | f t | d  d  … |	 f ƒ ƒ } | | d k } t | | | | | | d
 | | d d d d d d d ƒt j | | d  d  … | f | | d t t |	 | ƒq¬Wt j d ƒ t j d ƒ t j d d d t ƒ } | j ƒ  j d ƒ t j  t! |	 ƒ | j" d d d | | | f d d d d ƒt j# d d ƒ t j$ d  d ƒ t j% d! t! |	 d" t& d# ƒ t' j( ƒ  d  S($   Nid   iýÿÿÿi   i   i   R,   t   rt   kt   yt   fmtt   .t   capsizei    t	   linewidthgš™™™™™¹?t
   markersizeg      à?t   labels   f(T) [-]s   intensity [a.u.]t   locs
   upper leftt   fancyboxgffffffæ?gffffffþ¿s7   $\chi^2$ = %2.1f 
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   ions_indext   et   pltt   subplotR   t   ravelR   R8   t   doublet   amaxt   absRC   R?   t   ranget   lent   squeezeR&   t   errorbart   plott	   ion_namest   xlabelt   ylabelt   legendt   Truet	   get_framet	   set_alphat   titlet   element_namest   textt   ylimt   xlimt   savefigt   namet   figt   clf(   t   T0R+   t   densityR!   R(   RN   RG   RE   RF   t   it   density_modelt   T_modelt   N_modelt   c2RJ   t   Residt   axt   r_tott   _RO   t	   max_Residt   chi2_robustt   colourRR   t   xRS   t   y_errt   noisyt   leg(    (    sW   /golem/database/velin//includes/analysis/Radiation/1212Impurities_TO.ON/CalcDensTemp.pyt   plotTprofiles“   s@    )%65

0>>?>!(   t   cdistc         C   sä   d | | d k <t  | d ƒ } t | d f d d ƒ}	 t | | j ƒ |	 d  d  … t f <t |  t d ƒ j }  |  | 8}  |  |  9}  |  | 9}  |  | 8}  |  | 7}  |  |	 d  d  … t f <t t |	 t d  d  … | f ƒ d ƒ }
 |
 S(   Nid   i    i   R"   Rj   i   (	   R8   t   emptyR=   R(   t   bound_interR   Ra   R&   t   iM(   R(   Rƒ   R!   R‚   R+   RN   RG   t   indexRH   t   FRJ   (    (    sW   /golem/database/velin//includes/analysis/Radiation/1212Impurities_TO.ON/CalcDensTemp.pyRd   Ã   s    "

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)c         C   su  t  |  d ƒ } t g  t t ƒ D] } | | ^ q ƒ j }	 t | t f ƒ }
 t | |
 |	 | | | | t d d ƒ ƒ } d | | d k  <t	 |  | d ƒ } | |  d } xf t
 t ƒ D]X \ } } t | d  d  … | f d d d d | d  d  … | f ƒ|
 d  d  … | f <q¶ Wt | |
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 ƒ } d G| GH|
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   chi2 dens:(   R8   Rc   Rm   RR   R(   t   zerosRa   Rd   t   sliceR>   t	   enumerateRe   RB   R   (   RE   RF   R(   R‚   R+   RN   RG   RH   t   jR!   Rƒ   RJ   RQ   t   reR„   R)   RO   (    (    sW   /golem/database/velin//includes/analysis/Radiation/1212Impurities_TO.ON/CalcDensTemp.pyt   EstimateDensityÛ   s    ,*P*,	c    3         sp
  t  d ƒ ‰ t  d ƒ ‰  t  d ƒ ‰ t  d ƒ ‰ t d ƒ \ }  } | ‰ | j ‰	 t ˆ d  d  … t f d d ƒd k } t d	 d t ˆ d	 ƒ d
 t ƒ} ˆ | d  d  … f ‰ ˆ	 | d  d  … f ‰	 |  | }  | | } t ˆ d	 ƒ ‰ ˆ d	 k rù d  St ˆ d t	 f ƒ } t
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 t ˆ ˆ	 |
 ˆ ˆ  ˆ ˆ ƒ } t |
 t | ƒ f ƒ } d ‰ d GHt |	 | d d d d d t ƒ} | ˆ  } t g  t t ƒ D] } | | ^ q—ƒ j ‰ t | ˆ t ˆ t f ƒ } t | | ˆ ˆ ˆ  ˆ ˆ t d ƒ ƒ } ‡  ‡ ‡ ‡ ‡ ‡ f d †  } ‡ f d †  } | | | ƒ } t d d d d d d d d d d d d g ƒ } t ˆ	 ƒ } | t | ƒ 9} t | ƒ } | | :} t | | j ƒ } | j  d  d  t | d	 ƒ d … c d 7<t! | d t d t" ƒ} t# | j$ d	 ƒ } t% | | d d	 d t" d t" ƒ} t& | d | ƒ} | d  C} t t | d	 ƒ ƒ } t' d! ƒ } ˆ | } t | d ƒ } | ˆ  } t | ˆ ˆ t f ƒ } t( | | ƒ \ }  }! }" t) | ƒ d" }# t* | |# d  d  … f d d	 d# | |# d  d  … f ƒ}$ t+ |$ ƒ }$ x= t, |$ t- ƒ D], \ }% }& d$ |& |% f GHt. d% |& |% ƒ qWt* |  |# d# d |" |# d  ƒ}' d& |' GHt. d' |' ƒ t t ƒ } x× t t ƒ D]É } t | | ˆ ˆ ˆ  ˆ ˆ t/ | ƒ } ˆ d  d  … t/ | f | ˆ	 d  d  … t/ | f }( t0 t1 t
 |( ƒ ƒ ƒ }) |( |) :}( |( d  C}( |) t |( t d |) d  |( ƒ ƒ t |( ƒ ˆ d | | <q“Wt2 d( |  | d) | d* d ƒt2 d+ |  |  d) |" |! g d* d ƒt2 d, t t ƒ | ƒ y6 t' d- ƒ }* t3 t
 t4 |* ƒ t5 ƒ d k  ƒ d	 }+ Wn n Xt6 j7 d. d  d/ dR d2 d3 d4 d5 d6 d7 ƒ }, |, j9 d8 ƒ }- t | | ˆ ˆ ˆ  ˆ ˆ t d ƒ ƒ } t6 j: t t ˆ ƒ ƒ t ˆ j ƒ d9 t ˆ	 j ƒ ƒt6 j; t | j ƒ ƒ t< ˆ | ˆ	 ƒ d  t ˆ t | ƒ ƒ }. |- j= d: ƒ t ˆ ˆ	 ˆ ƒ }/ t ˆ ˆ	 |/ ˆ ˆ  ˆ ˆ ƒ }0 t |/ |0 ˆ ˆ ˆ  ˆ ˆ t d ƒ ƒ } t6 j; t | j ƒ d; ƒ |- j> d< ƒ |- j? d= ƒ |- j@ d	 t1 ˆ ƒ d> ƒ |- jA d  d  t1 ˆ ƒ d d? |. d@ dA dB dC ƒxK tB tC ƒ D]= \ } }& |- jA | ˆ d t1 ˆ ƒ dD |& d@ dA dB dC ƒq¹W|, j9 dE ƒ }- t6 j: |  dF | | dG d ƒt6 j; |  dF |/ ˆ  dH ƒ y0 t' dI ƒ }1 t6 j; |* |+ t5 |1 |+ dJ ƒ Wn n X|- j@ dK d ƒ |- j? dL ƒ |, j9 dM ƒ }- t6 jD |  dF t+ | ƒ ƒ y^ t' dN ƒ }2 |2 ˆ d  d  … tE f 7}2 t6 jD |* |+ t5 t+ |2 d  d  … |+ f j ƒ dJ ƒ Wn n X|- j@ d d ƒ |- j? dO ƒ |- jF dP ƒ |, jG dQ ƒ |, jH ƒ  d  S(S   Ns   model_constants/C.txts   model_constants/A.txts   model_constants/T0.txts   model_constants/B.txts   ./data/projectionR6   i   g{®Gáz„?i    t   endpointiÿÿÿÿg      à?gš™™™™™¹?gü©ñÒMbP?c            s¾  |  ˆ  } t  |  ˆ t ˆ t f ƒ } t g  t t ƒ D] } | | ^ q8 ƒ j } t | | | ˆ ˆ  ˆ ˆ t d d ƒ ƒ } t ˆ ƒ t ˆ ƒ t |  ƒ ˆ } t	 j
 d ƒ } t	 j
 d ƒ | } t | | d k ƒ }	 |	 t | | d k  ƒ 7}	 t | d d d ƒ}
 |
 d d  d  … f c d	 :<|
 d
 d  d  … f c d	 :<t |
 ƒ t |
 ƒ }
 t | d	 ƒ } d | | d k <t | ƒ } t t t | ƒ ƒ ƒ } | | d ˆ |
 d | d |	 S(   Ni    i   s   ((p-I)/(pE+1e-5))**2s   sum(Resid/sqrt(1 + Resid))i   iýÿÿÿi   R6   i   iÿÿÿÿgš™™™™™¹?g333333ã?i
   (   t   reshapeRa   Rc   Rm   RR   R(   Rd   Rœ   R8   t   net   evaluateR   t   diffRn   Ri   R&   (   R   R(   Rƒ   Rž   R!   RJ   t   doFR‰   RO   R,   R.   t   Tdt   spars(	   t   ARN   R    R‚   t   lamRH   t   n_inftyRE   RF   (    sW   /golem/database/velin//includes/analysis/Radiation/1212Impurities_TO.ON/CalcDensTemp.pyt   f_optim2  s&    
,*
i
   R   t   gtolt   maxiterg    €„.At   dispi   c      
      sT   |  ˆ  } t  |  ˆ ˆ t f ƒ } t | | ˆ ˆ ˆ  ˆ ˆ t d ƒ ƒ } t | ƒ S(   Ni   (   R¢   Ra   Rd   Rm   Ri   (   R   t   Tempt   DensRJ   (   R©   RN   R    R!   R‚   RH   (    sW   /golem/database/velin//includes/analysis/Radiation/1212Impurities_TO.ON/CalcDensTemp.pyt   RetrofitFunctiont  s    
'c            s¸   t  ˆ  ƒ } d } t t |  ƒ | f d d ƒ} x t t |  ƒ ƒ D]m } t |  ƒ t |  ƒ } } | | c | 8<| | c | 7<| | ƒ | | ƒ d | | | d  d  … f <qC W| S(   Ngíµ ÷Æ°>R"   t   float32i   (   R8   R›   Rn   Rm   R$   (   t   x0t   funt   n2t   dxt   JR„   t   xlt   xr(   RE   (    sW   /golem/database/velin//includes/analysis/Radiation/1212Impurities_TO.ON/CalcDensTemp.pyt
   CalcJacobiz  s    2i   i   t   lowert   overwrite_at   transt   overwrite_bt   outi   s   ./data/energy_constants.npyiþÿÿÿR7   s   ion %2s concentration = %1.2fs   ./HistoricalAnalysis/s   flattop temperatute %1.1fs    ./HistoricalAnalysis/temperatures   ./data/densityt   data_errt   tvec_errs   ./data/temperatures   ./data/TempDensChi2s	   shots.npyt   numt   figsizei   i   t   dpiiP   t	   facecolort   wt	   edgecolorRR   i7  t   yerrs   Spectral data retrofits   r:t   tightt	   intensityg333333ó?s   $\chi^2$/doF = %.2fR\   R]   R^   R_   gÍÌÌÌÌÌð?i8  g     @@RX   t   :s   temperature.npys   --iüÿÿÿs   pseudo temperaturei9  s   density.npyt   Densitys   t [ms]s   ./graphs/proj_retrofit.png(   i   i   (I   R0   R   RÁ   RC   t   bound_inter_iRb   R8   t   FalseR›   t   n_ionsRl   R¥   t
   zeros_likeRm   t   aranget   interpt   inftyRP   R    t   hstackRi   R   Rc   RR   R(   R¢   Ra   Rd   R:   R$   R?   R=   t   flatR   Rv   t   identityt   shapeR   t   absolutet   loadR5   t   argsortRB   R&   t   zipRz   R   Re   Rj   Rk   R   R%   t   floort   shot_numberRg   t   figuret   Nonet   add_subplotRp   Rq   R   t	   set_titleR6   t
   set_ylabelt   set_ylimR{   R   Rr   t   semilogyRD   t
   set_xlabelR~   R   (3   t   tvect	   proj_dictt   st
   shots_partt   dpt   dp_R„   R   t   xpR¬   t   temp0t   dens0R´   RS   R(   Rž   Rƒ   RJ   R²   R»   R¸   RO   t   correctedPEt   errt   JJt   Lt   iLt   energy_constantst   p_calibt   P_totalt   temp_errt   dens_errt   T_calibt   T_calib_err_ut   T_calib_err_dR)   t   max_densR.   R   t   flt_tempR‰   R   t   shotst
   shot_indexR€   RŠ   t   chi2doFt   T_estt   d_estt   temperature_fullt   density_full(    (
   R©   RN   R    R!   R‚   Rª   RH   R«   RE   RF   sW   /golem/database/velin//includes/analysis/Radiation/1212Impurities_TO.ON/CalcDensTemp.pyt   CalcDensTempû   sú    	(!

.6'$!
,'0
)!


8"	%6

@"**'4,'15$8
c          C   s_  t  d ƒ \ }  } | j } t  d ƒ \ }  } | j } | d  d  … d f | d  d  … d f g } t  d ƒ \ } } d t j f d „  ƒ  Y} t j d d  d	 dA d d d d d d ƒ } t j d d d d ƒ xàt d t ƒ D]Ï}	 | j	 t d |	 d ƒ }
 |	 d k r|
 j
 d ƒ n  |
 j j t j ƒ  ƒ |
 j j | ƒ  ƒ t | d  d  … |	 f ƒ } t | d  d  … |	 f ƒ | } t | d  d  … |	 f ƒ | } t | d t | ƒ ƒ} t t | | ƒ d ƒ t t | ƒ ƒ d } t j |  d | d | | g d d d t |	 ƒ|
 j j t ƒ |
 j d d d | |	 | | f d d  d! d" d# |
 j ƒ|
 j d t d$ t | ƒ ƒ d% ƒ t j d& d' d( t ƒ } | j ƒ  j d ƒ qÝ W|
 j j t j ƒ  ƒ |
 j  d) ƒ | j! d* d+ d, ƒ| j" ƒ  t j d d  d	 dB d d d d d d ƒ } | j	 d. ƒ }
 |
 j
 d/ ƒ t j |  d | d | d d ƒ|
 j# d0 ƒ |
 j  d) ƒ |
 j d d ƒ |
 j j t ƒ | j! d1 d+ d, ƒt j$ ƒ  yŸt j d d  d	 dC d d d d d d ƒ } | j	 d. ƒ }
 t% d2 t& t' ƒ d3 ƒ } | d4 | d5 } t( | d6 | d7 t) | ƒ ƒ } y8 t* d2 t& t' ƒ d8 ƒ } t* d2 t& t' ƒ d9 ƒ } Wn n Xt' d: k r| d 9} n( | d :} | d 8} | d; :} | d; :} |
 j
 d< ƒ t j+ | d | ƒ |
 j# d0 ƒ |
 j  d) ƒ |
 j d d ƒ |
 j, | d; | d; ƒ | j! d= t& t' ƒ d> d+ d, ƒt j$ ƒ  d? GHWn d@ GHn Xd  S(D   Ns   ./data/densitys   ./data/temperaturei    i   s   ./data/TempDensChi2t   MyFormatterc           B   s   e  Z d d  „ Z RS(   c         S   s*   | d k r d St  j j |  | | ƒ Sd  S(   Ni    t    (   Rg   t   ScalarFormattert   __call__(   t   selfR   t   pos(    (    sW   /golem/database/velin//includes/analysis/Radiation/1212Impurities_TO.ON/CalcDensTemp.pyR
    s    N(   t   __name__t
   __module__Rà   R
  (    (    (    sW   /golem/database/velin//includes/analysis/Radiation/1212Impurities_TO.ON/CalcDensTemp.pyR    s   RÃ   RÄ   i
   RÅ   iP   RÆ   RÇ   RÈ   RR   t   hspacet   wspaces   Relative ions concentrationR7   gü©ñÒMbP?i   g     @@RÉ   RX   g      à?RY   gš™™™™™©?gš™™™™™É?s*   $\chi^2/doF = %2.1f$ 
 $n = %1.2f\pm%1.1g$R\   R]   R^   R_   t	   transformgš™™™™™¹?g      ø?RZ   s
   upper leftR[   s   t [ms]s   ./graphs/density.pngt   bbox_inchesRÊ   i   io   s   Estimated temperatures
   $T_e$ [eV]s   ./graphs/temperature.pngs   ./electronTemperatures/s   /electron_temperature.npzt   datat   scalet   t_startt   t_ends   /PlasmaStarts
   /PlasmaEndiT$  iè  s   Spitzer temperatures   ./graphs/temperatures
   _spitz.pngs
   Te plotteds   no electron temperature(   i
   i
   (   i
   i   (   i
   i   (-   R   RÁ   Rg   R	  Rß   Rà   t   subplots_adjustRm   Ra   Rá   Râ   t   xaxist   set_major_formattert   NullFormattert   yaxisR&   t   expm1RB   Rl   R	   Rp   Rz   t   gridRv   R{   t	   transAxesRä   t   maxRk   Ru   Rw   Rx   Ræ   R~   R   Rã   t   closeRÚ   t   strRÞ   Rb   Rn   R0   Rq   t   set_xlim(   Rç   Rƒ   Rù   R(   Rø   RŒ   R  R  R€   R„   RŠ   RS   t   y_err_upt
   y_err_downt   y_medt	   y_err_medR“   R  t   tempt
   tvec_spitzt   plasma_startt
   plasma_end(    (    sW   /golem/database/velin//includes/analysis/Radiation/1212Impurities_TO.ON/CalcDensTemp.pyt   plotDensTemp  sŠ    		,	* ".09#
* 
* 



!
	(F   t   __doc__t
   matplotlibt   rcParamst   numpyt   matplotlib.pyplott   pyplotRg   t   numpy.linalgR   t   scipy.linalgR   R   R   R   t   scipy.stats.statsR   R	   t   scipy.sparseR
   t   numpy.matlibR   R   t   pygolem_lite.modulesR   R   t   pygolem_liteR   t   numexprR£   t   scipy.optimizeR   Rr   Rz   Rn   RÐ   Ra   RR   Re   t
   single_iont	   multi_iont   matrixR   t   M2t   M3t   M4t   M5t   M6t   M7R;   t   todenseRÎ   R<   R›   R—   Rv   t	   M_limitedR:   t   linalgR˜   R5   RP   R”   t   scipy.spatial.distanceR•   R$   R(   Rd   R    R  R+  (    (    (    sW   /golem/database/velin//includes/analysis/Radiation/1212Impurities_TO.ON/CalcDensTemp.pyt   <module>%   s^   
"*?<'<!
&			.		 	ÿ 