³ò u\Kc @sSdZddkZddkZddkZddkZddkZeiZdefd„ƒYZ de fd„ƒYZ de fd„ƒYZ e d dd „Zd e fd„ƒYZdefd„ƒYZde fd„ƒYZde fd„ƒYZde fd„ƒYZde fd„ƒYZde fd„ƒYZdefd„ƒYZdS(s  nmrfit.py Fit NMR spectra SpectrumModel - base class for all fit models FilteredStep - models a spectrum of a step function passed through a high-pass filter FitError - exception, raised when a fit diverges 12 September 2008, Lev, based on Michael's stunning code iÿÿÿÿNtFitErrorcBs#eZdZdd„Zd„ZRS(sm This exception is raised when a fit diverged 'self.fit', if not None, points to the fit results cCs ||_dS(N(tfit(tselfR((sc:\py\lib\nmrfit.pyt__init__)scCsdS(Ns Fit Error((R((sc:\py\lib\nmrfit.pyt__repr__,sN(t__name__t __module__t__doc__tNoneRR(((sc:\py\lib\nmrfit.pyR$s t SpectrumModelcBs)eZdZd„Zd„Zd„ZRS(s8 A base class for models used to fit spetra cCs9t|tiƒo |i}nti||i|ƒƒS(s¾ Construct an nmr.Spectrum representation of the fit at at given frequencies. 'f' is expected to be either an array of frequencies or an nmr.Spectrum object. (t isinstancetnmrtSpectrumtft calculate(RR ((sc:\py\lib\nmrfit.pytmodel3s cCs||i|ƒS(sj Return a difference between an NMR.Spectrum object 'spectrum' and the fit model. (R(Rtspectrum((sc:\py\lib\nmrfit.pytsubtract=scCstit|ƒƒS(s§ This function is to be overriden in child classes. It returns an array of frequency domain complex amplitudes for given array of frequencies. (tnumpytzerostlen(RR ((sc:\py\lib\nmrfit.pyRDs(RRRRRR(((sc:\py\lib\nmrfit.pyR .s t FilteredStepcBsMeZdZd„Zd„Zedd„ƒZeed„ƒZ d„Z RS(s This model describes a step function going through a high-pass filter. The model is: w(f) = B/(f1 + i*f) where B is the step amplitude, f1 is the filter -3dB frequency and i is the imaginary unit. The fit assumes B to be real. cCs||_||_||_dS(N(tBtf1tfit_f1(RRRR((sc:\py\lib\nmrfit.pyRVs  cCs|i|id|S(Nyð?(RR(RR ((sc:\py\lib\nmrfit.pyR[scCs~|djo1ti|i|iƒ|iƒƒ }t}nt}ti||iƒ|i|iƒƒ}t|||ƒS(sŠ Fit a spectrum to a FilteredStep. If filter cutoff frequency 'f1' is not specified, it is inferred from the fit. N( RRtmeanR tretimtTruetFalseR(RRRR((sc:\py\lib\nmrfit.pyR]s  ' *cCs3ti|iddddƒd|odndƒS(sk Take care of transient in the ULT Run 20 Lowfield NMR due to a filtered FLL reset tfminiôtfmaxgjø@RiÐi¤(RRtfrange(RtusePXI((sc:\py\lib\nmrfit.pyt fitRun20LFmscCsd|i|ifS(NsFilteredStep(f1=%g, B=%g)(RR(R((sc:\py\lib\nmrfit.pyRusN( RRRRRt staticmethodRRRR"R(((sc:\py\lib\nmrfit.pyRKs   giUMuÿ>iicCsO|i|ƒid|ƒidƒid|ƒ}ti||ƒ}|i|ƒS(sµ Take care of mismatch between the start and the end of the data and subtract eddy current transient in the ULT Run 20 Lowfield NMR Return a modified spectrum iitNpad(tperiodtrangetsubtract_linearbgtfftRR"R(ttraceR!ttruncateR$Rt transient((sc:\py\lib\nmrfit.pyt distilRun20LFws0t LorentziancBs‰eZdZd„Zd„Zed„ƒZed„ƒZed„ƒZed„ƒZ d„Z d„Z d „Z d „Z d „ZRS( sµ This model describes a phase-rich Lorentzian: w(f) = 1/2 * A * T2 * exp(i*phi) / (1 + 2*pi*i*(f-f0)*T2) f0 - resonance frequency A - amplitude T2 - relaxation time phi - phase w(f) is a Fourier Transform of: u(t) = A * cos(2*pi*f0 * t + phase) * exp(-t / T2) for t >= 0, 0 for t < 0 Parameters derived from f0, A, T2 and phi are available as phase_deg(), linewidth() and Q() cCsR|djo| }|t7}n||_||_||_|dt|_dS(Nii(tpitf0tAtT2tphi(RR/R0R1R2((sc:\py\lib\nmrfit.pyR•s    cCs%ti|i|i|i|i|ƒS(N(R-tlR/R0R1R2(RR ((sc:\py\lib\nmrfit.pyRŸscCs5d||tid|ƒddt|||S(sä For a frequency or an array of frequencies 'f' return a lorentzian defined by: f0 - resonance frequency A - amplitude T2 - relaxation time phi - phase gà?yð?iy@(RtexpR.(R/R0R1R2R ((sc:\py\lib\nmrfit.pyR3¡s c Cs³|iƒ\}}ti|ƒdt}|iƒt|ƒdd}|i|t|ƒjd}ddtt||ƒ}dt|ƒ|}td|d|d|d|ƒS(sF Make an initial guess for Lorentzian fit parameters. iiiR/R0R1R2(tfindpeaktflibtphaseR.tabsR tminR-(RR/tpeakR2tKtf_halfR1R0((sc:\py\lib\nmrfit.pytguess­scCs5|\}}}}t|ti|||||ƒƒS(s1 Calculate residuals for the fit (R8R-R3(tparamR twR/R0R1R2((sc:\py\lib\nmrfit.pyt residualsÂsc CsÍti|ƒ}tiiti|i|i|i|i gd|i |i fdddt dƒƒ}td|ddd|dd d |dd d |dd ƒ}|d d jo|Sn t |ƒ‚dS(Ntargstxtolgê-™—q=tmaxfevgjø@R/iR0iR1iR2i(R-R=tscipytoptimizetleastsqR@R/R0R1R2R R?tintR(RtgtresR ((sc:\py\lib\nmrfit.pyRÊs TAcCs|idtS(sphase in degreesi´(R2R.(R((sc:\py\lib\nmrfit.pyt phase_degÔscCst|i|iS(squality factor of resonance(R.R/R1(R((sc:\py\lib\nmrfit.pytQÕscCsdt|iS(t linewidthi(R.R1(R((sc:\py\lib\nmrfit.pyRLÖscCs#d|i|i|i|iƒfS(Ns:Lorentzian(f0 = %.2f, A = %g, T2 = %g, phase = %g degrees)(R/R0R1RJ(R((sc:\py\lib\nmrfit.pyR×scCs t|id|i|idƒS(s³ Return a normalised Lorentzian with a peak height of 1 and zero phase. This is to adjust phases of signals aquired with tuned sensors/amplifiers. ii(R-R/R1(R((sc:\py\lib\nmrfit.pyt normaliseÙs(RRRRRR#R3R=R@RRJRKRLRRM(((sc:\py\lib\nmrfit.pyR-ƒs      tProperLorentziancBs€eZdZd„Zed„ƒZed„ƒZed„ƒZed„ƒZd„Z d„Z d„Z d „Z d „Z RS( s This model describes a phase-rich Lorentzian with a peak at negative frequencies: w(f) = 1/2 * A * T2 * exp(i*phi) / (1 + 2*pi*i*(f-f0)*T2) + 1/2 * A * T2 * exp(-i*phi) / (1 + 2*pi*i*(f+f0)*T2) f0 - resonance frequency A - amplitude T2 - relaxation time phi - phase w(f) is a Fourier Transform of: u(t) = A * cos(2*pi*f0 * t + phase) * exp(-t / T2) for t >= 0, 0 for t < 0 Parameters derived from f0, A, T2 and phi are available as phase_deg(), linewidth() and Q() cCs%ti|i|i|i|i|ƒS(N(RNR3R/R0R1R2(RR ((sc:\py\lib\nmrfit.pyRóscCsjd||tid|ƒddt|||d||tid|ƒddt|||S(sä For a frequency or an array of frequencies 'f' return a lorentzian defined by: f0 - resonance frequency A - amplitude T2 - relaxation time phi - phase gà?yð?iy@yð¿(RR4R.(R/R0R1R2R ((sc:\py\lib\nmrfit.pyR3õs 4c Cs³|iƒ\}}ti|ƒdt}|iƒt|ƒdd}|i|t|ƒjd}ddtt||ƒ}dt|ƒ|}td|d|d|d|ƒS(sF Make an initial guess for Lorentzian fit parameters. iiiR/R0R1R2(R5R6R7R.R8R R9RN(RR/R:R2R;R<R1R0((sc:\py\lib\nmrfit.pyR=scCs5|\}}}}t|ti|||||ƒƒS(s1 Calculate residuals for the fit (R8RNR3(R>R R?R/R0R1R2((sc:\py\lib\nmrfit.pyR@sc CsÍti|ƒ}tiiti|i|i|i|i gd|i |i fdddt dƒƒ}td|ddd|dd d |dd d |dd ƒ}|d d jo|Sn t |ƒ‚dS(NRARBgê-™—q=RCgjø@R/iR0iR1iR2i(RNR=RDRERFR@R/R0R1R2R R?RGR(RRHRIR ((sc:\py\lib\nmrfit.pyRs TAcCs|idtS(sphase in degreesi´(R2R.(R((sc:\py\lib\nmrfit.pyRJ)scCst|i|iS(squality factor of resonance(R.R/R1(R((sc:\py\lib\nmrfit.pyRK*scCsdt|iS(RLi(R.R1(R((sc:\py\lib\nmrfit.pyRL+scCs#d|i|i|i|iƒfS(Ns:Lorentzian(f0 = %.2f, A = %g, T2 = %g, phase = %g degrees)(R/R0R1RJ(R((sc:\py\lib\nmrfit.pyR,scCs t|id|i|idƒS(s³ Return a normalised Lorentzian with a peak height of 1 and zero phase. This is to adjust phases of signals aquired with tuned sensors/amplifiers. ii(RNR/R1(R((sc:\py\lib\nmrfit.pyRM.s(RRRRR#R3R=R@RRJRKRLRRM(((sc:\py\lib\nmrfit.pyRNás      tPhaselessLorentziancBsweZdZd„Zd„Zed„ƒZed„ƒZed„ƒZed„ƒZ d„Z d„Z d „Z RS( s  This model describes a phase-poor Lorentzian: |w(f)| = 1/2 * A * T2 / (1 + 2*pi*i*(f-f0)*T2) f0 - resonance frequency A - amplitude T2 - relaxation time Parameters derived from f0, A, T2 are available as linewidth() and Q() cCs7|djo | }n||_||_||_dS(Ni(R/R0R1(RR/R0R1((sc:\py\lib\nmrfit.pyRDs     cCsti|i|i|i|ƒS(N(ROR3R/R0R1(RR ((sc:\py\lib\nmrfit.pyRLscCs-d||tiddt|||ƒS(sÌ For a frequency or an array of frequencies 'f' return a lorentzian defined by: f0 - resonance frequency A - amplitude T2 - relaxation time gà?iy@(RR8R.(R/R0R1R ((sc:\py\lib\nmrfit.pyR3Ns cCs–|iƒ\}}|iƒt|ƒdd}|i|t|ƒjd}ddtt||ƒ}dt|ƒ|}td|d|d|ƒS(sF Make an initial guess for Lorentzian fit parameters. iiiR/R0R1(R5R8R R9R.RO(RR/R:R;R<R1R0((sc:\py\lib\nmrfit.pyR=Ys cCs/|\}}}t|ti||||ƒƒS(s1 Calculate residuals for the fit (R8ROR3(R>R R?R/R0R1((sc:\py\lib\nmrfit.pyR@ksc Cs¿ti|ƒ}tiiti|i|i|igd|i t |i ƒfdddt dƒƒ}td|ddd|dd d |dd ƒ}|d d jo|Sn t |ƒ‚dS( NRARBgê-™—q=RCgjø@R/iR0iR1i(ROR=RDRERFR@R/R0R1R R8R?RGR(RRHRIR ((sc:\py\lib\nmrfit.pyRss T3cCst|i|iS(squality factor of resonance(R.R/R1(R((sc:\py\lib\nmrfit.pyRK}scCsdt|iS(RLi(R.R1(R((sc:\py\lib\nmrfit.pyRL~scCsd|i|i|ifS(Ns/PhaselessLorentzian(f0 = %.2f, A = %g, T2 = %g)(R/R0R1(R((sc:\py\lib\nmrfit.pyRs( RRRRRR#R3R=R@RRKRLR(((sc:\py\lib\nmrfit.pyRO7s      tBurstcBsneZdZd„Zd„Zed„ƒZed„ƒZed„ƒZed„ƒZ d„Z d„Z RS( sp This model describes a burst of sinewave: w(f) = A * exp(i*phi) / 2 * (1 - exp(-2i*pi*(f-f0)*T)) / (2i*pi*(f-f0)) w(f0) = A * exp(i*phi) * T / 2 f0 - resonance frequency A - amplitude T - burst length phi - phase w(f) is a Fourier Transform of: u(t) = A * cos(2*pi*f0 * t + phase) for 0 <= t <= T, 0 otherwise. cCs0||_||_||_|dt|_dS(Ni(R/R0tTR.R2(RR/R0RQR2((sc:\py\lib\nmrfit.pyR’s   cCs%ti|i|i|i|i|ƒS(N(RPtbR/R0RQR2(RR ((sc:\py\lib\nmrfit.pyR˜scCsyd|tid|ƒdtidt|||ƒdt||}d|tid|ƒ||||j<|S(sÛ For a frequency or an array of frequencies 'f' return a lorentzian defined by: f0 - resonance frequency A - amplitude T - length phi - phase gà?yð?iyÀy@(RR4R.(R/R0RQR2R ts((sc:\py\lib\nmrfit.pyRRšs L)c Cs\|iƒ\}}ti|ƒdt}dt|ƒ|}td|d|d|d|ƒS(sF Make an initial guess for Lorentzian fit parameters. iR/R0RQR2(R5R6R7R.R8RP(RRQR/R:R2R0((sc:\py\lib\nmrfit.pyR=¨scCs2|\}}}t|ti|||||ƒƒS(s1 Calculate residuals for the fit (R8RPRR(R>R R?RQR/R0R2((sc:\py\lib\nmrfit.pyR@·sc CsÅti||ƒ}tiiti|i|i|igd|i |i |fdddt dƒƒ}td|ddd|dd d |d |dd ƒ}|d d jo|Sn t |ƒ‚dS( NRARBgê-™—q=RCgjø@R/iR0iRQR2i( RPR=RDRERFR@R/R0R2R R?RGR(RRQRHRIR ((sc:\py\lib\nmrfit.pyR¿s Q9cCs|idtS(sphase in degreesi´(R2R.(R((sc:\py\lib\nmrfit.pyRJÉscCs#d|i|i|i|iƒfS(Ns4Burst(f0 = %.2f, A = %g, T = %g, phase = %g degrees)(R/R0RQRJ(R((sc:\py\lib\nmrfit.pyRÊs( RRRRRR#RRR=R@RRJR(((sc:\py\lib\nmrfit.pyRPs   tDoubleLorentziancBsVeZdZd„Zd„Zed„ƒZed„ƒZed„ƒZd„Z RS(sÅ This model describes a pair of phase-rich Lorentzians a.f0, b.f0 - resonance frequency a.A, b.A - amplitude a.T2, b.T2 - relaxation time a.phi, b.phi - phase cCs||_||_dS(N(taRR(RRURR((sc:\py\lib\nmrfit.pyR×s cCs |ii|ƒ|ii|ƒS(N(RURRR(RR ((sc:\py\lib\nmrfit.pyRÛsc CsZ|\}}}}}}} } t|ti|||||ƒti||| | |ƒƒS(s1 Calculate residuals for the fit (R8R-R3( R>R R?tf0atAatT2atphiatf0btAbtT2btphib((sc:\py\lib\nmrfit.pyR@Ýsc Cs„t|tƒpti|i|Œƒ}nt|tƒpti|i|Œƒ}n|i|i|i|i|i|i|i|ig}ti i t i |d|i |ifdddtdƒƒ}td|ddd|dd d |dd d |dd ƒ}td|ddd|ddd |ddd |ddƒ}t ||ƒ}|d d jo|Sn t|ƒ‚dS(s6 fit a double lorentzian to the 'spectrum'. 'guess_a' and 'guess_b' are either initial guesses for the lorentzians (objects of 'LorentzianFit' type) or tuples containing the frequency ranges to run the single Lorentzian fits on in order to obtain these guesses. RARBgê-™—q=RCgjø@R/iR0iR1iR2iiiiiN(R R-RR R/R0R1R2RDRERFRTR@R R?RGR(Rtguess_atguess_bR=RIRURRR ((sc:\py\lib\nmrfit.pyRås 6<AAcCs+ti||iƒ|g||iƒgƒS(s× fit a double lorentzian to the 'spectrum'. Initial guesses are obtained by fitting single Lorentzians on parts of the spectrum below (a) and above (b) the frequency 'f_cut'. (RTRRR(Rtf_cut((sc:\py\lib\nmrfit.pyt cut_and_fitþscCsd|i|ifS(Ns%s, %s(RURR(R((sc:\py\lib\nmrfit.pyRs( RRRRRR#R@RRaR(((sc:\py\lib\nmrfit.pyRTÌs    tNoisePowerLorentziancBskeZdZd„Zd„Zed„ƒZeed„ƒZed„ƒZ eed„ƒZ d„Z RS(sú This model describes a Lorentzian peak in the noise power: S(f) = Sp / (1 + {2*Q*(1 - f/f0)}^2) + S0 Sp - peak noise level f0 - resonance frequency Q - quality factor of the resonance S0 - offresonance noise level cCsLti|ƒiƒ|_ti|ƒiƒ|_t|ƒ|_||_dS(N(RtrealRtSpR/R8RKtS0(RRdR/RKRe((sc:\py\lib\nmrfit.pyRscCs%ti|i|i|i|i|ƒS(N(RbtplRdR/RKRe(RR ((sc:\py\lib\nmrfit.pyRscCs$|dd|d||d|S(s For a frequency or an array of frequencies 'f' return a power lorentzian defined by: Sp - peak noise level f0 - resonance frequency Q - quality factor of the resonance S0 - offresonance noise level ii((RdR/RKReR ((sc:\py\lib\nmrfit.pyRfs c Cs»|o1ti|id|idfƒ}||}nd}|iƒ\}}t|i|dƒ}|i|t|ƒjd}d|t||ƒ}td|d|d|d|ƒS( sR Make an initial guess for noise power Lorentzian fit parameters. iiÿÿÿÿgiR/RKRdRe(RRR?R5R8R R9Rb(Rt allowOffLevelReR/RdR;R<RK((sc:\py\lib\nmrfit.pyR=+s#cCsat|ƒdjo|\}}}d}n|\}}}}t|ti|||||ƒƒS(s1 Calculate residuals for the fit ig(RR8RbRf(R>R R?RdR/RKRe((sc:\py\lib\nmrfit.pyR@>s  c Cs:ti||ƒ}|o|i|i|i|ign|i|i|ig}tiiti |d|i |i fdddt dƒƒ}|oEtd|ddd|dd d |dd d |dd ƒ}n:td|ddd|dd d |dd d dƒ}|d d jo|Sn t |ƒ‚dS(sš Fit a (noise) power Lorentzian to the data. allowOffLevel (True/False) determines if off-resonance spectrum is non-zero RARBgê-™—q=RCgjø@RdiR/iRKiReigN(RbR=RdR/RKReRDRERFR@R R?RGR(RRgRHRIR3((sc:\py\lib\nmrfit.pyRJs><E9cCs d|i|i|i|ifS(Ns9NoisePowerLorentzian(Sp = %g, f0 = %.2f, Q = %g, S0 = %g)(RdR/RKRe(R((sc:\py\lib\nmrfit.pyR]s( RRRRRR#RfRR=R@RR(((sc:\py\lib\nmrfit.pyRb s     t TraceModelcBs)eZdZd„Zd„Zd„ZRS(sA A base class for models used to fit time domain signals cCs<t|tiƒo|iƒ}nti||i|ƒƒS(s» Construct an nmr.Trace representation of the fit at at given frequencies. 't' is expected to be either an array of sampling times or an nmr.Trace object. (R R tTracettR(RRj((sc:\py\lib\nmrfit.pyRdscCs||i|ƒS(sƒ Return a difference between an NMR.Trace object 'trace' and the fit model. Subtrace the fit FROM the data (R(RR)((sc:\py\lib\nmrfit.pyRnscCstittƒƒS(s† This function is to be overriden in child classes. It returns an array of signal samples at given times 't'. (RRRR (RRj((sc:\py\lib\nmrfit.pyRus(RRRRRR(((sc:\py\lib\nmrfit.pyRh_s t CosineWavecBszeZdZd„Zed„ƒZd„Zed d d„ƒZed d d„ƒZ ed„ƒZ d„Z d„Z RS( s” A cosine wave fit in time domain A - amplitude, f0 - frequency, phi - initial phase S(t) = A * cos(2*pi*f0*t + phi) cCs'||_||_|dt|_dS(Ni(R/R0R.R2(RR/R0R2((sc:\py\lib\nmrfit.pyRˆs  cCs!|tidt|||ƒS(Ni(RtcosR.(R/R0R2Rj((sc:\py\lib\nmrfit.pyR?scCsti|i|i|i|ƒS(N(RkR?R/R0R2(RRj((sc:\py\lib\nmrfit.pyRscCsS|iƒi||ƒ}t|iƒt|iƒƒ|iƒti|iƒƒƒS(sw Make a guess. Optional arguments fmin and fmax restrict the frequency range for the sinewave. ( R(R RktpeakfR8R:ttimespanR6R7(R)RRR?((sc:\py\lib\nmrfit.pyR=’sc CsÂti|||ƒ}tiiti|i|i|igd|i ƒ|i fdddt dƒƒ}td|ddd|dd d |dd ƒ}|d d jo|Sn t |ƒ‚d S( s4 Fit a cosine wave through a trace. RARBgê-™—q=RCgjø@R/iR0iR2iN( RkR=RDRERFR@R/R0R2RjRSRGR(R)RRRHRIR ((sc:\py\lib\nmrfit.pyR›s Q3cCs/|\}}}t|ti||||ƒƒS(s1 Calculate residuals for the fit (R8RkR?(R>R R?R/R0R2((sc:\py\lib\nmrfit.pyR@¨scCs|idtS(sphase in degreesi´(R2R.(R((sc:\py\lib\nmrfit.pyRJ°scCsd|i|i|iƒfS(Ns1CosineWave(f0 = %.2f, A = %g, phase = %g degrees)(R/R0RJ(R((sc:\py\lib\nmrfit.pyR±sN( RRRRR#R?RRR=RR@RJR(((sc:\py\lib\nmrfit.pyRk}s     i(RR6R Rtmathtscipy.optimizeRDR.t ExceptionRtobjectR RRR,R-RNRORPRTRbRhRk(((sc:\py\lib\nmrfit.pys s$       , ^VJK?T