# Linear least squares with singular value deconposition - single experiment

Determine the coefficients of a linear combination of noises and comapre with lscov

## Make data

```
fs    = 10;
nsecs = 10;

% Elements of the fit basis
B1 = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', nsecs, 'yunits', 'T'));
B1.setName;
B2 = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', nsecs, 'yunits', 'T'));
B2.setName;
B3 = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', nsecs, 'yunits', 'T'));
B3.setName;

n  = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', nsecs, 'yunits', 'm'));

% coefficients of the linear combination
c1 = ao(1,plist('yunits','m/T'));
c1.setName;

c2 = ao(2,plist('yunits','m/T'));
c2.setName;

c3 = ao(3,plist('yunits','m T^-1'));
c3.setName;

% build output of linear system
y = c1*B1 + c2*B2 + c3*B3 + n;
y.simplifyYunits;

```

## Do fit and check results

```
% Get a fit with linlsqsvd
pobj1 = linlsqsvd(B1, B2, B3, y)

```
```
---- pest 1 ----
name: a1*B1+a2*B2+a3*B3
param names: {'a1', 'a2', 'a3'}
y: [0.81162366736073077;1.8907151217948008;3.0098623857384701]
dy: [0.091943725803872112;0.089863977231447567;0.097910574305897308]
yunits: [m T^(-1)][m T^(-1)][m T^(-1)]
pdf: []
cov: [3x3], ([0.00845364871469762 0.000268768332741779 0.000180072770333592;0.000268768332741779 0.00807553440385413 0.00125972375325089;0.000180072770333592 0.00125972375325089 0.00958648056091064])
corr: [3x3], ([1 0.0325289738130578 0.020003055941376;0.0325289738130578 1 0.143172656986983;0.020003055941376 0.143172656986983 1])
chain: []
chi2: 0.87276552675043451
dof: 97
models: B1/tsdata Ndata=[100x1], fs=10, nsecs=10, t0=1970-01-01 00:00:00.000 UTC, B2/tsdata Ndata=[100x1], fs=10, nsecs=10, t0=1970-01-01 00:00:00.000 UTC, B3/tsdata Ndata=[100x1], fs=10, nsecs=10, t0=1970-01-01 00:00:00.000 UTC
description:
----------------

```
```
% do linear combination: using eval
yfit = pobj1.eval(B1, B2, B3);

% Plot - compare data with fit result
iplot(y, yfit)

```