# fitmulti.dem
#
# Use up to 5D fitting to determine coefficients in linear combinations
# of arbitrarily chosen, but linearly independent basis functions.
# The fit should reproduce these coefficients with high precision.
# Hanno Hoffstadt	August 2007
#
# Increase to 6 dimensions to test revised fit code.
# Replace a recursive call statement with a while <expr> { ... } loop.
# Use "set dummy x, y, x2, x3" to specify dummy parameter names used
# by the fit functions.
# Ethan A Merritt	June 2013
#


# the basis functions
f1(x) = sin(x)
f2(x) = exp(-x)
f3(x) = sqrt(x)
f4(x) = cos(x)
f5(x) = x*x
f6(x) = sin(x+3.)/(x+3.)

# the coefficients for linear combinations
k1=   2.5
k2=  -1.8
k3=  70.0
k4=  -3.2
k5=   0.4
k6=  -0.25

# generate data table containing functions f1(x) to f6(x),
# and linear combinations k1*f1(x) to k1*f1(x)+...+k6*f6(x)
# in increments of dx, up to a value xmax
#
set print "fitmulti.dat"
#
x=0
dx=0.5
xmax=10
while (x <= xmax) {

    lc1 = k1 * f1(x)
    lc2 = lc1 + k2 * f2(x)
    lc3 = lc2 + k3 * f3(x)
    lc4 = lc3 + k4 * f4(x)
    lc5 = lc4 + k5 * f5(x)
    lc6 = lc5 + k6 * f6(x)

    # columns 1-5,11 contain the "tabulated basis functions"
    # columns 6-10,12 contain linear combinations with given coefficients
    # and increasing number of components

    print f1(x), f2(x), f3(x), f4(x), f5(x), lc1, lc2, lc3, lc4, lc5, f6(x), lc6

    x = x + dx

}  # End of while loop

unset print

# fitting models
m1(f1) = c1*f1
m2(f1,f2) = c1*f1 + c2*f2
m3(f1,f2,f3) = c1*f1 + c2*f2 + c3*f3
m4(f1,f2,f3,f4) = c1*f1 + c2*f2 + c3*f3 + c4*f4
m5(f1,f2,f3,f4,f5) = c1*f1 + c2*f2 + c3*f3 + c4*f4 + c5*f5
m6(f1,f2,f3,f4,f5,f6) = c1*f1 + c2*f2 + c3*f3 + c4*f4 + c5*f5 + c6*f6

# 1D fit:
# basis function in column 1,
# combination with one component in column 6
#
# since column 6 contains k1 * f1(x), i.e. k1 times column 1,
# the fit is expected to find c1 == k1.
#
# for all fits, the assumed error is 1, and is given last in the using spec.

c1=1
fit m1(x) "fitmulti.dat" u 1:6:(1) via c1
print "---------------------------------------------------------"
print "1D fit: expected ", k1, " c1 = ", c1
print "---------------------------------------------------------"
pause -1 "Hit return to try for a 2D fit"

# 2D fit:
# basis functions in columns 1 and 2,
# combination with two components in column 7
#
# do not forget to reset the c values so that the fit needs to search anew.
# Check the functioning of preset axis range limit on y

c1=1
c2=1
set yrange [0:.99]
fit m2(x,y) "fitmulti.dat" u 1:2:7:(1) via c1,c2
print "---------------------------------------------------------"
print "2D fit: expected ", k1, " c1 = ", c1
print "2D fit: expected ", k2, " c2 = ", c2
print "---------------------------------------------------------"
set yrange [*:*]
pause -1 "Hit return to try for a 3D fit"

# 3D fit:
# basis functions in columns 1, 2, 3,
# combination with three components in column 8

print "3D fit will fail without patch..."
c1=1
c2=1
c3=1

fit [] [] [x2=*:*] m3(x,y,x2) "fitmulti.dat" u 1:2:3:8:(1) via c1,c2,c3
print "---------------------------------------------------------"
print "3D fit: expected ", k1, " c1 = ", c1
print "3D fit: expected ", k2, " c2 = ", c2
print "3D fit: expected ", k3, " c3 = ", c3
print "---------------------------------------------------------"
pause -1 "Hit return to try for a 4D fit"

# 4D fit:
# basis functions in columns 1, 2, 3, 4,
# combination with four components in column 9

c1=1
c2=1
c3=1
c4=1
fit [][][x2=*:*][x3=*:*] m4(x,y,x2,x3) "fitmulti.dat" u 1:2:3:4:9:(1) via c1,c2,c3,c4
print "---------------------------------------------------------"
print "4D fit: expected ", k1, " c1 = ", c1
print "4D fit: expected ", k2, " c2 = ", c2
print "4D fit: expected ", k3, " c3 = ", c3
print "4D fit: expected ", k4, " c4 = ", c4
print "---------------------------------------------------------"
pause -1 "Hit return to try for a 5D fit"

# 5D fit:
# basis functions in columns 1, 2, 3, 4, 5,
# combination with five components in column 10

c1=1
c2=1
c3=1
c4=1
c5=1
fit [][][x2=*:*][x3=*:*][x4=*:*] \
    m5(x,y,x2,x3,x4) "fitmulti.dat" u 1:2:3:4:5:10:(1) via c1,c2,c3,c4,c5
print "---------------------------------------------------------"
print "5D fit: expected ", k1, " c1 = ", c1
print "5D fit: expected ", k2, " c2 = ", c2
print "5D fit: expected ", k3, " c3 = ", c3
print "5D fit: expected ", k4, " c4 = ", c4
print "5D fit: expected ", k5, " c5 = ", c5
print "---------------------------------------------------------"
pause -1 "Hit return to try for a 6D fit"

# 6D fit:
# basis functions in columns 1, 2, 3, 4, 5, 11
# combination with five components in column 12
# test inline range spec
print "6D not possible in version 4.6"

c1=1
c2=1
c3=1
c4=1
c5=1
c6=1
fit [][][][][][-0.2:*] m6(x,y,x2,x3,x4,x5) "fitmulti.dat" u 1:2:3:4:5:11:12:(1) via c1,c2,c3,c4,c5,c6
print "---------------------------------------------------------"
print "6D fit: expected ", k1, " c1 = ", c1
print "6D fit: expected ", k2, " c2 = ", c2
print "6D fit: expected ", k3, " c3 = ", c3
print "6D fit: expected ", k4, " c4 = ", c4
print "6D fit: expected ", k5, " c5 = ", c5
print "6D fit: expected ", k6, " c6 = ", c6
print "---------------------------------------------------------"
pause -1 "Hit return to end multidimension fit demo"
reset
