Annotation of OpenXM_contrib/gnuplot/demo/fit.dem, Revision 1.1
1.1 ! maekawa 1: #
! 2: # $Id: fit.dem,v 1.9 1997/05/27 01:29:34 drd Exp $
! 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]"
! 14:
! 15: print "now fitting a straight line to the data :-)"
! 16: print "only as a demo without physical meaning"
! 17: load 'line.fnc'
! 18: y0 = 0.0
! 19: m = 0.0
! 20: show variables
! 21: pause -1 "first a plot with all parameters set to zero (-> return)"
! 22: set title 'all fit params set to 0'
! 23: plot 'lcdemo.dat', l(x)
! 24: pause -1 "now start fitting... (-> return)"
! 25: fit l(x) 'lcdemo.dat' via y0, m
! 26: pause -1 "now look at the result (-> return)"
! 27: set title 'unweighted fit'
! 28: plot 'lcdemo.dat', l(x)
! 29:
! 30: pause -1 "see the influence of weights for single data points (-> return)"
! 31: fit l(x) 'lcdemo.dat' using 1:2:3 via y0, m
! 32: pause -1 "now look at the result (-> return)"
! 33: set title 'fit weighted towards low temperatures'
! 34: plot 'lcdemo.dat', l(x)
! 35:
! 36: pause -1 "now prefer the high temperature data (-> return)"
! 37: fit l(x) 'lcdemo.dat' using 1:2:4 via y0, m
! 38: pause -1 "now look at the result (-> return)"
! 39: set title 'bias to high-temperates'
! 40: plot 'lcdemo.dat', l(x)
! 41:
! 42: pause 0 "now use real single-measurement errors to reach such a result (-> return)"
! 43: pause 0 "(look at the file lcdemo.dat and compare the columns to see the difference)"
! 44: pause -1 "(-> return)"
! 45: set title 'data with experimental errors'
! 46: plot 'lcdemo.dat' using 1:2:5 with errorbars
! 47: fit l(x) 'lcdemo.dat' using 1:2:5 via y0, m
! 48: pause -1 "now look at the result (-> return)"
! 49: set title 'fit weighted by experimental errors'
! 50: plot 'lcdemo.dat' using 1:2:5 with errorbars, l(x)
! 51:
! 52: print "It's time now to try a more realistic model function"
! 53: load 'density.fnc'
! 54: show functions
! 55: print "density(x) is a function which shall fit the whole temperature"
! 56: print "range using a ?: expression. It contains 6 model parameters which
! 57: print "will all be varied. Now take the start parameters out of the"
! 58: pause -1 "file 'start.par' and plot the function (-> return)"
! 59: load 'start.par'
! 60: set title 'initial parameters for realistic model function'
! 61: plot 'lcdemo.dat', density(x)
! 62: fit density(x) 'lcdemo.dat' via 'start.par'
! 63: pause -1 "now look at the result (-> return)"
! 64: set title 'fitted to realistic model function'
! 65: plot 'lcdemo.dat', density(x)
! 66:
! 67: print "looks already rather nice? We will do now the following: set"
! 68: print "the epsilon limit higher so that we need more iteration steps"
! 69: print "to convergence. During fitting please hit ctrl-C. You will be asked"
! 70: print "Stop, Continue, Execute: Try everything. You may define a script"
! 71: print "using the FIT_SCRIPT environment variable. An example would be"
! 72: print "'FIT_SCRIPT=plot nonsense.dat'. Normally you don't need to set"
! 73: print "FIT_SCRIPT since it defaults to 'replot'. Please note that FIT_SCRIPT"
! 74: print "cannot be set from inside gnuplot."
! 75: print ""
! 76: pause -1 "(-> return)"
! 77: FIT_LIMIT = 1e-10
! 78: fit density(x) 'lcdemo.dat' via 'start.par'
! 79: pause -1 "now look at the result (-> return)"
! 80: set title 'fit with more iterations'
! 81: plot 'lcdemo.dat', density(x)
! 82:
! 83: FIT_LIMIT = 1e-5
! 84: print "\nNow a brief demonstration of 3d fitting."
! 85: print "hemisphr.dat contains random points on a hemisphere of"
! 86: print "radius 1, but we let fit figure this out for us."
! 87: print "It takes many iterations, so we limit FIT_MAXITER to 50."
! 88: #HBB: made this a lot harder: also fit the center of the sphere
! 89: #h(x,y) = sqrt(r*r - (x-x0)**2 - (y-y0)**2) + z0
! 90: #HBB 970522: distort the function, so it won't fit exactly:
! 91: h(x,y) = sqrt(r*r - (abs(x-x0))**2.2 - (abs(y-y0))**1.8) + z0
! 92: x0 = 0.1
! 93: y0 = 0.2
! 94: z0 = 0.3
! 95: r=0.5
! 96: FIT_MAXITER=50
! 97: set title 'the scattered points, and the initial parameter'
! 98: splot 'hemisphr.dat' using 1:2:3, h(x,y)
! 99: pause -1 "(-> return)"
! 100:
! 101: # we *must* provide 4 columns for a 3d fit. We fake errors=1
! 102: fit h(x,y) 'hemisphr.dat' using 1:2:3:(1) via r, x0, y0, z0
! 103: set title 'the scattered points, fitted curve'
! 104: splot 'hemisphr.dat' using 1:2:3, h(x,y)
! 105: print "\n\nNotice, however, that this would converge much faster when"
! 106: print "fitted in a more appropriate co-ordinate system:"
! 107: print "fit r 'hemisphr.dat' using 0:($1*$1+$2*$2+$3*$3) via r"
! 108: print "where we are fitting f(x)=r to the radii calculated as the data"
! 109: print "is read from the file. No x value is required in this case.
! 110: pause -1 "(This is left as an excercise for the user). (-> return)"
! 111: FIT_MAXITER=0 # no limit : we cannot delete the variable once set
! 112:
! 113: print "\n\nNow an example how to fit multi-branch functions\n"
! 114: print "The model consists of two branches, the first describing longitudinal"
! 115: print "sound velocity as function of propagation direction (upper data),"
! 116: print "the second describing transverse sound velocity (lower data).\n"
! 117: print "The model uses these data in order to fit elastic stiffnesses"
! 118: print "which occur differently in both branches.\n"
! 119: pause -1 "(-> return)"
! 120: load 'hexa.fnc'
! 121: load 'sound.par'
! 122: set title 'sound data, and model with initial parameters'
! 123: plot 'soundvel.dat', vlong(x), vtrans(x)
! 124: # Must provide an error estimate for a 3d fit. Use constant 1
! 125: fit f(x,y) 'soundvel.dat' using 1:-2:2:(1) via 'sound.par'
! 126: #create soundfit.par, reading from sound.par and updating values
! 127: update 'sound.par' 'soundfit.par'
! 128: print ""
! 129: pause -1 "(-> return)"
! 130: set title 'pseudo-3d multi-branch fit to velocity data'
! 131: plot 'soundvel.dat', vlong(x), vtrans(x)
! 132: print "Look at the file 'hexa.fnc' to see how the branches are realized"
! 133: print "using the data index as a pseudo-3d fit"
! 134: print ""
! 135: print "Next we only use every fifth data point for fitting by using the"
! 136: print "'every' keyword. Look at the fitting-speed increase and at"
! 137: print "fitting result."
! 138: print ""
! 139: pause -1 "(-> return)"
! 140: load 'sound.par'
! 141: fit f(x,y) 'soundvel.dat' every 5 using 1:-2:2:(1) via 'sound.par'
! 142: set title 'fitted only every 5th data point'
! 143: plot 'soundvel.dat', vlong(x), vtrans(x)
! 144: print "When you compare the results (see 'fit.log') you remark that"
! 145: print "the uncertainties in the fitted constants have become larger,"
! 146: print "the quality of the plot is only slightly affected."
! 147: print ""
! 148: print "By marking some parameters as '# FIXED' in the parameter file"
! 149: print "you fit only the others (c44 and c13 fixed here)."
! 150: print ""
! 151: pause -1 "(-> return)"
! 152: load 'sound2.par'
! 153: set title 'initial parameters'
! 154: plot 'soundvel.dat', vlong(x), vtrans(x)
! 155: fit f(x,y) 'soundvel.dat' using 1:-2:2:(1) via 'sound2.par'
! 156: set title 'fit with c44 and c13 fixed'
! 157: plot 'soundvel.dat', vlong(x), vtrans(x)
! 158: print "This has the same effect as specifying only the real free"
! 159: print "parameters by the 'via' syntax."
! 160: print ""
! 161: print "fit f(x) 'soundvel.dat' via c33, c11, phi0"
! 162: print ""
! 163: pause -1 "(-> return)"
! 164: load 'sound.par'
! 165: set title 'initial parameters'
! 166: plot 'soundvel.dat', vlong(x), vtrans(x)
! 167: fit f(x,y) 'soundvel.dat' using 1:-2:2:(1) via c33, c11, phi0
! 168: set title 'fit via c33,c11,phi0'
! 169: plot 'soundvel.dat', vlong(x), vtrans(x)
! 170:
! 171: print "Here comes an example of a very complex function..."
! 172: print ""
! 173: pause -1 "first plotting the pure data set (-> return)"
! 174:
! 175: set xlabel "Delta [degrees]"
! 176: set ylabel "Reflectivity"
! 177: set title 'raw data'
! 178: #HBB 970522: here and below, use the error column present in moli3.dat:
! 179: plot 'moli3.dat' w e
! 180:
! 181: print "now fitting the model function to the data"
! 182: load 'reflect.fnc'
! 183:
! 184: #HBB 970522: Changed initial values to something sensible, i.e.
! 185: # something an experienced user of fit would actually use.
! 186: # FIT_LIMIT is also raised, to ensure a better fit.
! 187: eta = 1.2e-4
! 188: tc = 1.8e-3
! 189: FIT_LIMIT=1e-10
! 190:
! 191: show variables
! 192: show functions
! 193: pause -1 "first a plot with all parameters set to initial values (-> return)"
! 194: set title 'initial parameters'
! 195: plot 'moli3.dat' w e, R(x)
! 196: pause -1 "now start fitting... (-> return)"
! 197: fit R(x) 'moli3.dat' u 1:2:3 via eta, tc
! 198: pause -1 "now look at the result (-> return)"
! 199: set title 'fitted parameters'
! 200: replot
! 201:
! 202: #HBB 970522: added comment on result of last fit.
! 203: print "Looking at the plot of the resulting fit curve, you can see"
! 204: print "that this function doesn't really fit this set of data points."
! 205: print "This would normally be a reason to check for measurement problems"
! 206: print "not yet accounted for, and maybe even re-think the theoretic"
! 207: print "prediction in use."
! 208: print ""
! 209:
! 210: print "You can have a look at all previous fit results by looking into"
! 211: print "the file 'fit.log' or whatever you defined the env-variable 'FIT_LOGFILE'."
! 212: print "Remember that this file will always be appended, so remove it"
! 213: print "from time to time!"
! 214: print ""
! 215: pause -1 "Done with fitting demo (-> return)"
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