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Annotation of OpenXM_contrib/gnuplot/demo/fit.dem, Revision 1.1.1.3

1.1       maekawa     1: #
1.1.1.3 ! ohara       2: # $Id: fit.dem,v 1.1.1.1.2.3 2001/12/04 14:12:53 lhecking Exp $
1.1       maekawa     3: #
                      4:
                      5: print "Some examples how data fitting using nonlinear least squares fit"
                      6: print "can be done."
                      7: print ""
                      8: pause -1 "first plotting the pure data set  (-> return)"
                      9:
                     10: set title 'data for first fit demo'
                     11: plot 'lcdemo.dat'
                     12: set xlabel "Temperature T  [deg Cels.]"
                     13: set ylabel "Density [g/cm3]"
1.1.1.2   maekawa    14: set key below
1.1       maekawa    15:
                     16: print "now fitting a straight line to the data :-)"
                     17: print "only as a demo without physical meaning"
                     18: load 'line.fnc'
                     19: y0 = 0.0
                     20: m = 0.0
                     21: show variables
                     22: pause -1 "first a plot with all parameters set to zero  (-> return)"
                     23: set title 'all fit params set to 0'
                     24: plot 'lcdemo.dat', l(x)
                     25: pause -1 "now start fitting...  (-> return)"
                     26: fit l(x) 'lcdemo.dat' via y0, m
                     27: pause -1 "now look at the result (-> return)"
                     28: set title 'unweighted fit'
                     29: plot 'lcdemo.dat', l(x)
                     30:
                     31: pause -1 "see the influence of weights for single data points   (-> return)"
                     32: fit l(x) 'lcdemo.dat' using 1:2:3 via y0, m
                     33: pause -1 "now look at the result (-> return)"
                     34: set title 'fit weighted towards low temperatures'
                     35: plot 'lcdemo.dat', l(x)
                     36:
                     37: pause -1 "now prefer the high temperature data   (-> return)"
                     38: fit l(x) 'lcdemo.dat' using 1:2:4 via y0, m
                     39: pause -1 "now look at the result (-> return)"
                     40: set title 'bias to high-temperates'
                     41: plot 'lcdemo.dat', l(x)
                     42:
                     43: pause  0 "now use real single-measurement errors to reach such a result (-> return)"
                     44: pause  0 "(look at the file lcdemo.dat and compare the columns to see the difference)"
                     45: pause -1 "(-> return)"
                     46: set title 'data with experimental errors'
                     47: plot 'lcdemo.dat' using 1:2:5 with errorbars
                     48: fit l(x) 'lcdemo.dat' using 1:2:5 via y0, m
                     49: pause -1 "now look at the result (-> return)"
                     50: set title 'fit weighted by experimental errors'
                     51: plot 'lcdemo.dat' using 1:2:5 with errorbars, l(x)
                     52:
                     53: print "It's time now to try a more realistic model function"
                     54: load 'density.fnc'
                     55: show functions
                     56: print "density(x) is a function which shall fit the whole temperature"
1.1.1.3 ! ohara      57: print "range using a ?: expression. It contains 6 model parameters which"
1.1       maekawa    58: print "will all be varied. Now take the start parameters out of the"
                     59: pause -1 "file 'start.par' and plot the function    (-> return)"
                     60: load 'start.par'
                     61: set title 'initial parameters for realistic model function'
                     62: plot 'lcdemo.dat', density(x)
                     63: fit density(x) 'lcdemo.dat' via 'start.par'
                     64: pause -1 "now look at the result (-> return)"
                     65: set title 'fitted to realistic model function'
                     66: plot 'lcdemo.dat', density(x)
                     67:
                     68: print  "looks already rather nice? We will do now the following: set"
                     69: print  "the epsilon limit higher so that we need more iteration steps"
                     70: print  "to convergence. During fitting please hit ctrl-C. You will be asked"
                     71: print  "Stop, Continue, Execute: Try everything. You may define a script"
                     72: print  "using the FIT_SCRIPT environment variable. An example would be"
                     73: print  "'FIT_SCRIPT=plot nonsense.dat'. Normally you don't need to set"
                     74: print  "FIT_SCRIPT since it defaults to 'replot'. Please note that FIT_SCRIPT"
                     75: print  "cannot be set from inside gnuplot."
                     76: print  ""
                     77: pause -1  "(-> return)"
                     78: FIT_LIMIT = 1e-10
                     79: fit density(x) 'lcdemo.dat' via 'start.par'
                     80: pause -1 "now look at the result (-> return)"
                     81: set title 'fit with more iterations'
                     82: plot 'lcdemo.dat', density(x)
                     83:
                     84: FIT_LIMIT = 1e-5
                     85: print "\nNow a brief demonstration of 3d fitting."
                     86: print "hemisphr.dat contains random points on a hemisphere of"
                     87: print "radius 1, but we let fit figure this out for us."
                     88: print "It takes many iterations, so we limit FIT_MAXITER to 50."
                     89: #HBB: made this a lot harder: also fit the center of the sphere
                     90: #h(x,y) = sqrt(r*r - (x-x0)**2 - (y-y0)**2) + z0
                     91: #HBB 970522: distort the function, so it won't fit exactly:
                     92: h(x,y) = sqrt(r*r - (abs(x-x0))**2.2 - (abs(y-y0))**1.8) + z0
                     93: x0 = 0.1
                     94: y0 = 0.2
                     95: z0 = 0.3
                     96: r=0.5
                     97: FIT_MAXITER=50
                     98: set title 'the scattered points, and the initial parameter'
                     99: splot 'hemisphr.dat' using 1:2:3, h(x,y)
                    100: pause -1 "(-> return)"
                    101:
                    102: # we *must* provide 4 columns for a 3d fit. We fake errors=1
                    103: fit h(x,y) 'hemisphr.dat' using 1:2:3:(1) via r, x0, y0, z0
                    104: set title 'the scattered points, fitted curve'
                    105: splot 'hemisphr.dat' using 1:2:3, h(x,y)
                    106: print "\n\nNotice, however, that this would converge much faster when"
                    107: print "fitted in a more appropriate co-ordinate system:"
                    108: print "fit r 'hemisphr.dat' using 0:($1*$1+$2*$2+$3*$3) via r"
                    109: print "where we are fitting f(x)=r to the radii calculated as the data"
1.1.1.3 ! ohara     110: print "is read from the file. No x value is required in this case."
1.1       maekawa   111: pause -1 "(This is left as an excercise for the user). (-> return)"
                    112: FIT_MAXITER=0   # no limit : we cannot delete the variable once set
                    113:
                    114: print "\n\nNow an example how to fit multi-branch functions\n"
                    115: print  "The model consists of two branches, the first describing longitudinal"
                    116: print  "sound velocity as function of propagation direction (upper data),"
                    117: print  "the second describing transverse sound velocity (lower data).\n"
                    118: print  "The model uses these data in order to fit elastic stiffnesses"
                    119: print  "which occur differently in both branches.\n"
                    120: pause -1 "(-> return)"
                    121: load 'hexa.fnc'
                    122: load 'sound.par'
                    123: set title 'sound data, and model with initial parameters'
                    124: plot 'soundvel.dat', vlong(x), vtrans(x)
                    125: # Must provide an error estimate for a 3d fit. Use constant 1
                    126: fit f(x,y) 'soundvel.dat' using 1:-2:2:(1) via 'sound.par'
                    127: #create soundfit.par, reading from sound.par and updating values
                    128: update 'sound.par' 'soundfit.par'
                    129: print  ""
                    130: pause -1 "(-> return)"
                    131: set title 'pseudo-3d multi-branch fit to velocity data'
                    132: plot 'soundvel.dat', vlong(x), vtrans(x)
                    133: print  "Look at the file 'hexa.fnc' to see how the branches are realized"
                    134: print  "using the data index as a pseudo-3d fit"
                    135: print  ""
                    136: print  "Next we only use every fifth data point for fitting by using the"
                    137: print  "'every' keyword. Look at the fitting-speed increase and at"
                    138: print  "fitting result."
                    139: print  ""
                    140: pause -1 "(-> return)"
                    141: load 'sound.par'
                    142: fit f(x,y) 'soundvel.dat' every 5 using 1:-2:2:(1) via 'sound.par'
                    143: set title 'fitted only every 5th data point'
                    144: plot 'soundvel.dat', vlong(x), vtrans(x)
                    145: print  "When you compare the results (see 'fit.log') you remark that"
                    146: print  "the uncertainties in the fitted constants have become larger,"
                    147: print  "the quality of the plot is only slightly affected."
                    148: print  ""
                    149: print  "By marking some parameters as '# FIXED' in the parameter file"
                    150: print  "you fit only the others (c44 and c13 fixed here)."
                    151: print  ""
                    152: pause -1 "(-> return)"
                    153: load 'sound2.par'
                    154: set title 'initial parameters'
                    155: plot 'soundvel.dat', vlong(x), vtrans(x)
                    156: fit f(x,y) 'soundvel.dat' using 1:-2:2:(1) via 'sound2.par'
                    157: set title 'fit with c44 and c13 fixed'
                    158: plot 'soundvel.dat', vlong(x), vtrans(x)
                    159: print  "This has the same effect as specifying only the real free"
                    160: print  "parameters by the 'via' syntax."
                    161: print  ""
                    162: print  "fit f(x) 'soundvel.dat' via c33, c11, phi0"
                    163: print  ""
                    164: pause -1 "(-> return)"
                    165: load 'sound.par'
                    166: set title 'initial parameters'
                    167: plot 'soundvel.dat', vlong(x), vtrans(x)
                    168: fit f(x,y) 'soundvel.dat' using 1:-2:2:(1) via c33, c11, phi0
                    169: set title 'fit via c33,c11,phi0'
                    170: plot 'soundvel.dat', vlong(x), vtrans(x)
                    171:
                    172: print  "Here comes an example of a very complex function..."
                    173: print  ""
                    174: pause -1 "first plotting the pure data set  (-> return)"
                    175:
                    176: set xlabel "Delta [degrees]"
                    177: set ylabel "Reflectivity"
                    178: set title 'raw data'
                    179: #HBB 970522: here and below, use the error column present in moli3.dat:
                    180: plot 'moli3.dat' w e
                    181:
                    182: print "now fitting the model function to the data"
                    183: load 'reflect.fnc'
                    184:
                    185: #HBB 970522: Changed initial values to something sensible, i.e.
                    186: #  something an experienced user of fit would actually use.
                    187: #  FIT_LIMIT is also raised, to ensure a better fit.
                    188: eta = 1.2e-4
                    189: tc = 1.8e-3
                    190: FIT_LIMIT=1e-10
                    191:
                    192: show variables
                    193: show functions
                    194: pause -1 "first a plot with all parameters set to initial values  (-> return)"
                    195: set title 'initial parameters'
                    196: plot 'moli3.dat' w e, R(x)
                    197: pause -1 "now start fitting...  (-> return)"
                    198: fit R(x) 'moli3.dat' u 1:2:3 via eta, tc
1.1.1.3 ! ohara     199: pause -1 "Hit return to continue"
1.1       maekawa   200: set title 'fitted parameters'
                    201: replot
                    202:
                    203: #HBB 970522: added comment on result of last fit.
                    204: print "Looking at the plot of the resulting fit curve, you can see"
                    205: print "that this function doesn't really fit this set of data points."
                    206: print "This would normally be a reason to check for measurement problems"
                    207: print "not yet accounted for, and maybe even re-think the theoretic"
                    208: print "prediction in use."
                    209: print ""
                    210:
                    211: print  "You can have a look at all previous fit results by looking into"
                    212: print  "the file 'fit.log' or whatever you defined the env-variable 'FIT_LOGFILE'."
                    213: print  "Remember that this file will always be appended, so remove it"
                    214: print  "from time to time!"
                    215: print  ""
                    216: pause -1 "Done with fitting demo  (-> return)"
1.1.1.2   maekawa   217: reset

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