and similarly for lsqcurvefit

diff -r 0a88bfac372f inst/lsqcurvefit.m
--- a/inst/lsqcurvefit.m        Thu Mar 28 09:00:55 2024 +0100
+++ b/inst/lsqcurvefit.m        Fri Mar 29 21:20:02 2024 +0100
@@ -293,6 +293,7 @@
     outp.iterations = outp.niter;
     outp = rmfield (outp, "niter");
     varargout{5} = outp;
+    outp = curvefit_out{4};
   endif

There are inconsistencies between matlab and optim in the lsqnonlin and lsqcurvefit functions.

The 1st issue is that for multi-column ydata a non-scalar resnorm is returned.

The 2nd issue is that the Lagrange multiplier output lambda is empty.

octave 10, optim-1.6.2 output:

lsqnonlin
resnorm =   0.020000   0.048223
lambda = [](0x0)

lsqcurvefit
resnorm =    0.020000   0.048223
lambda = [](0x0)

matlab R2019b output

resnorm = 0.1759
lambda = struct with fields:
    lower: 0
    upper: 5.2781e-05

lsqcurvefit
resnorm = 0.1759
lambda = struct with fields:
    lower: 0
    upper: 5.2781e-05

test script:

if exist('OCTAVE_VERSION', 'builtin') > 0
  pkg load optim;
end
rng('default'); % for reproducibility
xdata = reshape(linspace(0,3,40), [], 2);
ydata = exp(-1.3*xdata) + 0.05*randn(size(xdata));
x0 = 2; lb = 1; ub = 3;
opts.Display='off';

fprintf('lsqnonlin\n');
fun_lsqnonlin = @(r)exp(-xdata*r) -ydata;
[x,resnorm,residual,exitflag,output,lambda] = ...
     lsqnonlin(fun_lsqnonlin,x0, lb, ub, opts);
resnorm
lambda

fprintf('lsqcurvefit\n');
fun_lsqcurvefit = @(r, x) exp(-x*r);
[x,resnorm,residual,exitflag,output,lambda] = ...
     lsqcurvefit(fun_lsqcurvefit, x0, xdata, ydata, lb, ub, opts);
resnorm
lambda

The lambda field is correctly calculated, but unintentionally cleared because I think the user_interaction detection in this snippet around line 283 is incorrect, since there is no use_interaction in this example to my understanding.

  if (out_args >= 5)
    outp = residmin_out{4};
    if (isfield (outp, "user_interaction")) # not set if stopped by user_interaction
      outp = rmfield (outp, "lambda");
    endif
    if (isfield (outp, "user_interaction"))
      outp = rmfield (outp, "user_interaction");
    endif
    varargout{5} = outp;
  endif