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}@/H??s?@|?q@z?1?D@? ?c???S?@?`??@Ӏui@?͔?ۃ?R?S2@?A?&??ڪ`?=?1?@NǞ?,ʀ?>;h@ͩ??@?ʄ#?Ž`?ƀ<`a?y??Ӹ@?@Ϛ? ܕ??@.`??6H?9:?N?1?RƯB???e?ݳ?Հ?$@?Ț?門u@?؏#% b`?>\Gw@?᥀?݀?~g?3?(?A?*? ӆ?@@??ɐ?P?)@B@pyy mmaaUUUUUVI$I$yy矿aaI$I$aaaa?aa ?aa?I$I$?aa?yy@I$I$@UUUUUV@aa@ mm@yy?3*8?7O@-@pb@,~Rm>@<)L@I=ء@T%Uv<@[Yqm @`U.@bK<"uq@`ZB'@\ HL@Tj@J's5P@=||6iH@-@'@b^|@f?ꅄLҠ?ύZLyy mmaaUUUUUVI$I$yy矿aaI$I$aaaa?aa ?aa?I$I$?aa?yy@I$I$@UUUUUV@aa@ mm@yy?@@&@7@P@Q@^@`@`@a@@^@@S@I@>@(@?Plot 0<1"'/4<*32<<}#??;:8 8 -  4 |  8  ; 4199:-~?9<;@*0 4=~1=  +!!'""#(#$0$0%%&/&'='(()4)%**)++.,,---.#./6/$00>11522833:44{525+667478989.9:-:6;z;7<~<==>>??/@@A ABB+C{CD5DE'E(FF7GG#HH-II2JJK.KL5L*MM3NNO.O/PPQ/Q4RR@SST/T>UU9VV)WWX>XY3YZ7Z[3[1\\)]]^^}_1_1`z`a+ab?bc$c+dde:e,ff6gg1hhi0ij'j9kkxl+l6mm.nno<opp4qq&rr1s{sttu:u-vvw>w.xxy*y;zz{/{;||5}}~8~2/247<@3}(0.3. 1;{./2(1/48=~@7~+2956&0+3(;{14*8;/38+2-$;3"*-<5'07z5%|012y1.2|5375|98084;E5=>2!07C,2 B Sample Number Intensity@??? @È@@@o@?a*exp(-(1/2)*((x-b)/c)^2)abcx@i??@ba\*g?z3I? %!/Plot 0UTi qr!),s7[BMX^dKo#z$>\dIUU B Bin Value AmplitudeI@DI@$@?@??ə?6hDjPX V dpx  mD PX   r h@,h0l(d@@@B&|l@8@`@ @ngVIDS gauss_fit.viVIDSLevenberg Marquardt.vidPTH0VIDSGeneral Histogram.vi`PTH0VIDSGaussian White Noise.vi\PTH0i386`codedE{E`ETPUEd$=t1= Ð9 Ӏ}#t} uE(E!E"ɍ HHH HHHHƅ thhUEP QRhhP$hiQPd$ZY=! fx$ ƅ ƅ SQRVWPEEXPE EXQRhhuhPED$XhPPd$ZY=tMEEQRhhuhPED$XhPPd$ZY=t_^ZY[ÐuP$P|$>d$ =Ffxi ƅ dts<ts$ DT\tsDdtsTtts\| EX E`ETd.UR@␐}zt}zƅ QRhhP$lh[OPd$ZY=GQRhhP$lh$OPd$ZY=*}(u ƅ hhUEP8d$ =}(u ƅdhhUEP8d$ fx ƅ =tNǃ Dž =t#ƃ; } Dž  Dž !ꃽ t[=t9 tB QRP $P$hh7DQd$ZY=ƅ fxƅ QRhhP$h_MPd$ZY=QRhhPG$h+MPd$ZY=ƅ }(u ƅ hhUEP8d$ =}fxƅ ƅ fx"ƅ Dž  EQRP $WhPx$>Qd$ZY=?7?SQRVWPEEXPE EXQRhhuhPED$XhKPd$ZY=tMEEQRhhuhPED$XhKPd$ZY=t_^ZY[ÐuP$P$Fd$ =6*SQRVWPEEXPE EXQRhhuhPED$XhKPd$ZY=tEEE=tEMEE=t9Et0EEQRPE$uhhAQd$ZY=tPE=tEPEEX%}uEEm}޸_^ZY[ÐuP$P$d$ =ƅ }(u ƅ hhUEP8d$ =fx&}#t}"uH}!v}/uvQRPED$ʇhd$ZY=#=t p h搐ÐE{ E`ETPUEd$=t=t=t=tE{ E{‰ppVLFX@'PUEd$=uÐT lT T 4 T iT OT <%5T X T @T 3T )MT ;gT xT 6T 4eT 4KT 1T T T 7T lQp~p @'PUEd$=uÐT9 @ T ^Ty  $Tn   GT  T2 vT .@P @total @below @above # outside@ minB2P@@ Axis@@ Best Fit4(@@ Initial Guess Coefficient ^N@P@0model@@0 Parameters @0xModel Description @0x0.@@0 Parameters@0model:*@@ Gaussian Distributed Noise0$@P0!!!$@@ Best FitB2@(P@@ Axis@ B2P@@ Axis@@ Histogram0$@@ Best Fit Coefficientsxl@@(P@@ Axis@ 9Histogram of Noise Values Together with Best Fit Gaussian!*P0!!!L@  @@ X@@ HistogramT@@DP @ lower @ upper*@lowerupperbothneithers inclusionBins@@ Axis@ max.@P @total @below @above # outside@ min @error @# bins@lowerupper inclusion$@@ Histogram@@ Xl` x  @ticks@ mse@@ Best Fit$@@ Best Fit Coefficients @error@@ CovarianceN@P@0model@@0 Parameters @0xmodel description"@@ Standard Deviation@ max iteration(@@ Initial Guess Coefficient@@ Y@@ X@@ Y"@ max iteration2"@@ Standard Deviation^N@P@0model@@0 Parameters @0xmodel description.@@ Covariance@ mse @# bins(@lowerupper inclusion @ticksB2@P@@ Axis@ Residuals@ 4(P@@ Axis@ `||||@t@Hd0pt(dpP0||| X@ t |p L ` x  (  | $  ] Number of SamplesHIffJJ999Histogram of Noise Values Together with Best Fit GaussianHD$TUD$XY Bin ValueV D$Kz\i No. in BinHD**X Gaussian FitQDRySyerrorHSTD):*:1IFitting a Gaussian Function to a Histogram of Gaussian Distributed Noise]DffModel DescriptionH0fGaussian Distributed NoiseHD$YD$CD Sample NumberU D$Mu[h IntensityHD&((N;;0.H HDHD  QDmodelHI2q(qVD<I'<I' ParametersHOMZ MZ eD22Initial Guess CoefficientH@=O=O N=J=J HOPd/Pd/MDxHI  N( :( :  HH@Tv@TvHNN@[SNA[SaD.B.BBest Fit CoefficientsN>ZKa>[Ka H4 Q\eQ]eUD ResidualsHD$GUD$M{N{  Bin ValueU D$EtVc AmplitudeHDIN~R~S0.HDIN[pN[pcDdaqdbqGaussian White Noise.viRDBundleHD<IR<IRRD#E$EBundleHDxITaTaHD Q8^NQ9^NWDwx Build Array`D##General Histogram.viHD\I(5(5HDTI:G:GHDN'C'CbD;H6;H6Levenberg Marquardt.viHD8 HD|XeXeHDHHD`K$$  %% PP ##  (( MM !!   BB FPHP gauss_fit.viN@FPHP 8U$:N?(DL xXLFE~/m7,  @PDl| 4 B 0  i4  2 g@ 2 @p_p_lc0l06@ 2 o`o`kd|&Tp^q x58p&wP_|<S`-Dy`6 d$H$x 04 B K00 o! N>0 C 8x>4 6d$@O@4L" @ :J!,@fifi]r@ :L!o`vYo`@ :K!+nanagh@O`40| 0 2d(j0 2d-%&k4 3d^W 0 2d-PQl4 3d^J{4 6d+ 8h0 2d(#$m0  >4 $ 80  H R5- 9#3  1T2,2l1$ 113 22H R0 ..L @ P P 9:@4N(  d  X 4 |0 l ,Dj0  P4 F  QzD4  2 R@L :  RX0v0v/w.x-y@ :  @IPp_p_lc@ :  IPo`o`kd0l9 d4 l(;<$)l)*D**$%d,||,%d$|0l UVYou enter your initial-guesses for the parameters a, b and c here. Try to make good guesses so your program will converge to the optimal answer in as short a time as possible. L : 0v0v/w.x-y~ld)N@U6Nu<t]The user enters the number of samples of gaussian distributed random values to be generated. The random numbers are displayed in the order in which they are generated. This allows the user to verify (qualitatively) that there is no correlation among the values in the sequence. )),*t*4 F$ g` H(HRO olS X4 v (@P~$B4TA<Sp$$cPR#$#X  Hp^q |< $ | 8h4 B  0 o! O>0 K >4 6@O@4d @ :J!-Afifi]r@ :L!o`vYo`@ :K!,nanagh@O`40[0 2(n0 2-()o4 3^B0 2-MNp4 3^Lv4 6) 00 2(!"q0  >4 $<0  p 2 4bmbmbmp 2 8@clclcl0 w dk0 _$ 0 w$ c0 W$ o>0 7 a0  cHR O pF  4 v @P~HB4Ap 2 4bmbmbm< 0H8xd<Sp$Hd+p 2 8@clclcl0 w dk0 _H 0 wH d0 WH p>4Q p*4 6< 400 7 b0  d4O 6)@ 6`V;R\SXR\4O6L(0 <  dkp 2V8=lcdd8=KKlc8=ddlc4OLb',<`,`< ` 6* 6. 6* 6. 6*8| Lb.Lb.Lb*Lb.Lb* 6L*6L.6L*6L.6L*4 6 ,0  dk4O 5 P! 4QhQ  x 5* 5. 5* 5. 5*4O5 K"O@ 6 xV:R\SXR\""p 2!V7Parameters is an array of strings of the unknown parameters. @" 2& S[o`o`kd0" _& L[ 0" W%d J]  ",<,p-t,4" r& L[ T@# 2& @LSp_p_lc0# s%d M20# U%d J 5#L.@# 2) @<Fp_p_lc4# F @ 3X@$P 2 @B4<PA4$  r) <Ph0% _) <P0% W @ :R@% 2) FPo`o`kd0% s @ =y0% U @ :|(%-.0000p.4% J+ <Kd4& 2+ Oe0\0' + Mg24'Q%dMg2'74'Q$ (8(4' F, 04( 2,  0) ,  p) 5++ OeOeOe0)l <$p) 5,+ 4) J.L ' ;\4* 2.L ? UwP@+P @=Wy+ , 0+ .L = Wyt+^Initial Guess Coefficient denotes your initial-guessed solution. Using this function successfully depends on how close your initial guess coefficients are to the solution. Therefore, it is always worth taking the time and effort to obtain good initial guess coefficients to the solution from any available resources before using the function. @+ 2.L JW o`o`kdL+ :.L D P0v0v/w.x-y@+ 2.L @=J p_p_lc0+l P @D (+3<3p5445X4+  r1 M?\TP4, F -C@-P rB4M8\T$A0- _1 M?\T@- 21 @M8T?p_p_lc@- 21 T8\?o`o`kd0- s NY0- U KV0- W K6^V4- J3 =YLb4. 23 P[f@/PNYh1,3%d /Best Fit Coefficients is the array of coefficients that minimize the chi-square error between the solution vector and the observed Y values. @/ :3 [RhYo`o`kdL/ :3 U[aa0v0v/w.x-y@/ :3 @NR[Yp_p_lc0/ 3 NYh0/l- L/ $$dd  / This is a cluster containing the fitting equation. It includes the algegraic formulation of the model, the definition of the parameters to be varied and defines the independent variable. Note that the parameters and independent varible must ALL be LOWER CASE letters. l/XThis is a string describing the model equation. Use the same format as the formula box. /parameters is an array of strings of the parameters whose starting values are to be refined by non-linear least squares fitting. H/2xis a string defining the independent variable. /The histogram of noise values is plotted. Superimposed is a Gaussian distribution with the optimized values of the parameters. /Best Fit Coefficients is the array of parameter values that minimize the chi-square error between the solution vector and the observed Y values (data). X/Cthis indicator returns any error or warning condition from the VI. :_) <P; LME2 ) @<F_p_pcl/|4 /CCC=0/ C; >;ld (>00 k;! K>@0 :;J!)=fifi]r40 6CL@1O@4;@  @F@  3PA2 @ B4<PA5r ) <PT1_) <P?)>,)X:t*- DNM;NA2 ) FP`o`odk1s @  =y]L@ EPAlAF1W @  :RA@ =Wy+ , ]DAt*L?*>D*?*?*1U @ :| 1DD DPDE:L. D Pv0v0w/x.y-1L. = Wy}Elt*3$YFF~/4)B5JL. ' ;XA2L. @=J _p_pclA2L. JW `o`odkEdL @1 :;L!vYvYo`@1 :;K!(nanagh@1O`4;0: 01 2CL(02 2CL-43 3CL^L|H04 2=-BC45 3=^Du46 6=@07 2=(08 ; >48 $;}Q09l:Z;r09 ; <9 EL50-D Fld$D@U6Nu<&F<9  -D05EL1K PALE50D-  = EPAlAEFK252  gx1  idHLA2  @_p_pclA2  `o`odk52  g`Y`JG HxM: v0v0w/x.y-] lADEFLGGLG HxGldI@6Nu<ADl5B 1  iMKLA2  @_p_pcl52L. ? Uw,<9 <:=tBC =DCL=E|DN82  `o`odkM0 .L. 18N: v0v0w/x.y-] 0I`,  >@$| T>&T> 4> 2$ S~b0? 3$ R}c4?` <$?d0?562B:? X ?@| ?@+ X ?@p 0?5 72B:4? BP7_O4@@1` T +K#`.(E@ @ d @ @4@ Bv4A C d$PB @X$xHdh4B3 d 8+2.B B dd h4B3 d I+;3 B d @4B3 d K+;3BX4B3 d J+;34B3 dL+2.B$ B dp $Bx B d `X B dx4B3 d 285B B d+BH4B3 dD 285 B dH4B3 d 8>;B B dh4B3 d >DA Bd4B3 d 8>;4B3 d>DA B B dL4B3 dGDKG B B d',4B3 dPH;KC B B d dB B d4B3 dW;KCB B d4B3 dTVDKGBh B d h B d4B3 dX;KC B@BH8B4` *$)L B@)LP B@)Lp B@+)4B` hP,B2t0l4B 2t '60C 3t &7@CP&71@CDC C@ 4C 20 9H@DP8I/@0D 30 8I0D@5(804D` '`PD84D B(DhERBundles the bin values(x array) and the counts in each bin (y array) for plotting.&<24E`( E',[[GGZ8E:` |EEEEP E@PpE0E;!| E@$ E@0E;"|0E;< E4E`p@ E@E1`d<d; CE0E@& -Dh ElD4E C:I7@F D8dH""\%%F0F@ 0~&F"\ F8F4F3M4<8 F<4F`D04  F~`d'2TB*Hdg<  FdFMCombines the data arrays and the model arrays for plotting on one x,y graph. F*<04F3XC,<4 F dFd4F3F,40 F& 4F"|pF"DF A@A@F # FFH4F3E$,( F!H4F BHG `G"4G3D$ 4G3B,$4G3A,<4GrrG;1.1.4G3@,$G"\ G"("4G3?4<8 G %LG :0 :F0v0v/w.x-yLG :t (40v0v/w.x-yGA histogram of the gaussian distributed numbers is generated. The numbers are sorted into 21 bins ranging in values between -4 and +4. LG :$ Ty`0v0v/w.x-y G A series of gaussian distributed random values characterized by a mean of zero and a standard deviation of one are genserated. A random seed is used to select a different starting value for each set of numbers from among the sequence of (pseudo) random numbers. Gp%<%4G3%p=$,( G% G+%4G3%<$  G%4G3!>,40 4G`-|P0G@*< fvn&4G B&TWfH-*dl:&84H B~dI44I`(LI imiOiOiII~g"g\\0I5D  I@<))|0I5)II)|0I5)I))4I` t. =+/&8+,Ih Id UU.4I`EH   Y.0=.-0<(.I$hNhI 00I& 4/|B M\q5B M\q(5 0I6I;I*<nmm40`d2H*Hdg<0@ 0I 00 3\`d2,J*Hdg<0@ +3`d2IXG*Hdg<@ -x1<\.`d2 JXG*Hdg<@ IThe difference between the histogram values and the computed 'best fit' Gaussian are calculated. These are called the residuals.4`d2`OXG*Hdg<@  50I@9EL=4TI6;64I B4%8J4`8Hy6D=?J98=5h326l9`d2KXG*Hdg<0@ <J  &T456|P7D646 |64J/`48?2hDJ/The bin values and residuals are combined here.U7D`H8y=?D7 D7 J6B;; J6p7$4J06:X]%/*h8`d2NXG*Hdg<0@ -8<&8J?!8h6;,J98=?>9``9 95B~X5B~!`9 J@49?98J>]9`84?h)9 4J`JhKP]:`BBG1@LE84T4J6)<`d2N*Hdg<0@ <@LE848XHT4-24;T4`;5KB48i4J06.\/:4h J6<;;4J06.[%/*h]<64T&d  J)|;)=`d2NXG*Hdg<@ =.;;.67X:`<<p*<l95`&0 J@4?=!>67J@>]>p$<*+< ,' &d ,J$ %65?`/  J@4B>;0J549X`y@<<p$<*+ ,' &d M<@P7`7 ?>;(8<>x<4C/0J544_ J@4+@?0J548^ymBP4`t5>(.6=p=p>&@0!@4>LJp : :..( (  *     * \J464&T d MD$6;-$D<< ?<J  d644J`CF J6>J<  ((  *  [  ! ![F"84H889?4=?@8>>X9=`|BB<B<FF`d2@JXG*HdN< ]EBCF`t8(F ?>@6\B,J %?G B<p$<*+ ,' &d -BB(F!@4@\JB4I``d2KXG*HdN< ]+B<p$<* ,' &d LJ+! ! 5:   5   : 5     J`+1  M,GG(F`F H1+lI?FE+!@4?]l:9hJK`9JG4(:89IT4JJ984\J9+B<p$*< ',& d 5KB4%J9 (  @UUAo*>>n>>@#       YfPJ!Microsoft Sans SerifMicrosoft Sans SerifMicrosoft Sans Serif010000RSRC LVINLBVW: 1 :x"` 4 $RSIDHLVSR\BDPWpLIviCPTMDSTMDFDSLIdsVICDversDLDRFPTD$CPMp8STRGLICON`icl4ticl8DTHPTRec<PICC tLIfpdFPHPxLIbdBDHPHISTPRT FTAB`JNPNtNS?S@TSASBSC`SDSESFD`SGdSHXSID\SJPStJN H T?,<L D2\S3lS5|S8SSSTSpS8tS8@S9PDS gauss_fit.vi