Non linear regression on Scilab - regression

Question

I'm new to scilab (I'm using 5.5.2), and I need to make a non linear regression.
I have a dataset of points which behaves like a sinewave, so I want to find the parameters of this sinewave.
Here is my dataset :
t1=[11800, 11805, 11810, 11817, 11824, 11829, 11834, 11839, 11844, 11849, 11854, 11859, 11866, 11871, 11878, 11883, 11888, 11893, 11898, 11903, 11908, 11915, 11920, 11928, 11933, 11938, 11943, 11948, 11953, 11958, 11965, 11970, 11975, 11980, 11987, 11992, 11997, 12002, 12007, 12014, 12019, 12024, 12029, 12037, 12042, 12047, 12052, 12057, 12063, 12069, 12074, 12079, 12084, 12091, 12096, 12101, 12106, 12111, 12119, 12123, 12128, 12133, 12138, 12146, 12151, 12156, 12161, 12169, 12174, 12179, 12184, 12188, 12193, 12201, 12206, 12211, 12218, 12223, 12228, 12233, 12238, 12243, 12251, 12256, 12260, 12268, 12273, 12278, 12283, 12288, 12292, 12297, 12302, 12310, 12317, 12322, 12327, 12332, 12337]
v1=[
0.36
0.59
0.81
0.92
0.90
0.76
0.54
0.31
0.17
0.19
0.36
0.59
0.81
0.92
0.90
0.76
0.54
0.31
0.17
0.19
0.36
0.59
0.81
0.92
0.90
0.77
0.54
0.31
0.17
0.19
0.35
0.59
0.81
0.92
0.90
0.77
0.55
0.32
0.18
0.19
0.35
0.59
0.80
0.92
0.90
0.77
0.55
0.32
0.17
0.19
0.35
0.59
0.80
0.92
0.90
0.79
0.55
0.32
0.18
0.18
0.35
0.59
0.80
0.92
0.92
0.79
0.57
0.32
0.18
0.18
0.35
0.58
0.80
0.92
0.92
0.79
0.57
0.32
0.18
0.18
0.35
0.58
0.80
0.92
0.92
0.79
0.57
0.34
0.18
0.18
0.34
0.58
0.80
0.92
0.92
0.80
0.57
0.34
0.18
]
In order to make the non linear regression I added the toolbox which contains the nlinregr function and called it like this :
fun='A*sin(W*t1+P)'
dfun='[sin(W*t1+P), A*t1*cos(W*t1+P), A*cos(W*t1+P)]'
[p, yhat,stat]=nlinregr([t1 v1], 't1 v1', fun, dfun,'A W P', 'v1')
With 'fun' the sinewave function I'm trying to fit, 'dfun' the matrix made of the analytical derivative depending on my parameters A, W and P.
While executing this function I'm getting the error "Incoherent Multiplication" but after 2 hours I'm still not able to point out where the problem is ....
Can someone help me please ?

Answer 1

datafit is dedicated to such non-linear fitting. It's a native Scilab function.
Code to perform the fitting and to show results:
t1 = [11800, 11805, 11810, 11817, 11824, 11829, 11834, 11839, 11844, 11849, 11854, 11859, 11866, 11871, 11878, 11883, 11888, 11893, 11898, 11903, 11908, 11915, 11920, 11928, 11933, 11938, 11943, 11948, 11953, 11958, 11965, 11970, 11975, 11980, 11987, 11992, 11997, 12002, 12007, 12014, 12019, 12024, 12029, 12037, 12042, 12047, 12052, 12057, 12063, 12069, 12074, 12079, 12084, 12091, 12096, 12101, 12106, 12111, 12119, 12123, 12128, 12133, 12138, 12146, 12151, 12156, 12161, 12169, 12174, 12179, 12184, 12188, 12193, 12201, 12206, 12211, 12218, 12223, 12228, 12233, 12238, 12243, 12251, 12256, 12260, 12268, 12273, 12278, 12283, 12288, 12292, 12297, 12302, 12310, 12317, 12322, 12327, 12332, 12337];
v1 = [0.36 0.59 0.81 0.92 0.9 0.76 0.54 0.31 0.17 0.19 0.36 0.59 0.81 0.92 0.9 0.76 0.54 0.31 0.17 0.19 0.36 0.59 0.81 0.92 0.9 0.77 0.54 0.31 0.17 0.19 0.35 0.59 0.81 0.92 0.9 0.77 0.55 0.32 0.18 0.19 0.35 0.59 0.8 0.92 0.9 0.77 0.55 0.32 0.17 0.19 0.35 0.59 0.8 0.92 0.9 0.79 0.55 0.32 0.18 0.18 0.35 0.59 0.8 0.92 0.92 0.79 0.57 0.32 0.18 0.18 0.35 0.58 0.8 0.92 0.92 0.79 0.57 0.32 0.18 0.18 0.35 0.58 0.8 0.92 0.92 0.79 0.57 0.34 0.18 0.18 0.34 0.58 0.8 0.92 0.92 0.8 0.57 0.34 0.18];
function g = gap(p, Data)
// v = p(1) + p(2)*sin(p(3)*t+p(4))
// p = [v_offset, amplitude, angular_frequency, phase]
t = Data(1,:)
v = Data(2,:)
g = v - (p(1) + p(2)*sin(p(3)*t+p(4)))
endfunction
p0 = [0.50 0.35 2*%pi/50 0.5]; // initial guess of fitting parameters
[p, dmin, status] = datafit(gap, [t1 ; v1], p0, "ar",200)
vfit = p(1) + p(2)*sin(p(3)*t1+p(4));
clf
subplot(2,1,1), plot(t1,v1), title "Given data" fontsize 3
subplot(2,1,2), plot(t1, vfit-v1), title "Fit - data" fontsize 3
Results:
--> [p, dmin, status] = datafit(gap, [t1 ; v1], p0, "ar",200)
p =
0.572807 0.3879044 0.114452 131.77806
offset amplitude angular phase
frequency
dmin =
0.0331676 average v distance between data and fit
status =
9. means "OK"