lsqcurvefit — Fit nonlinear parametric curves in the least-squares sense.

x = lsqcurvefit(fun, x0, xdata, ydata) estimates parameters x so that fun(x, xdata) matches ydata in the least-squares sense. RunMat preserves the shape of x0, supports scalar and vector parameters, accepts lower and upper parameter bounds, and can return solver diagnostics through MATLAB-compatible multi-output forms.

Syntax

x = lsqcurvefit(fun, x0, xdata, ydata)
x = lsqcurvefit(fun, x0, xdata, ydata, lb, ub)
x = lsqcurvefit(fun, x0, xdata, ydata, lb, ub, options)
[x, resnorm] = lsqcurvefit(___)
[x, resnorm, residual] = lsqcurvefit(___)
[x, resnorm, residual, exitflag] = lsqcurvefit(___)

x = lsqcurvefit(fun, x0, xdata, ydata)
x = lsqcurvefit(fun, x0, xdata, ydata, lb, ub)
x = lsqcurvefit(fun, x0, xdata, ydata, lb, ub, options)
[x, resnorm] = lsqcurvefit(___)
[x, resnorm, residual] = lsqcurvefit(___)
[x, resnorm, residual, exitflag] = lsqcurvefit(___)
[x, resnorm, residual, exitflag, output] = lsqcurvefit(___)
[x, resnorm, residual, exitflag, output, lambda] = lsqcurvefit(___)
[x, resnorm, residual, exitflag, output, lambda, jacobian] = lsqcurvefit(___)

Inputs

Returns

Returned values from lsqcurvefit depend on how many outputs the caller requests.

Errors

How lsqcurvefit works

• The model callback is evaluated as fun(x, xdata) and must return a finite real scalar or array with the same shape as ydata.
• Unbounded problems use finite-difference Levenberg-Marquardt iterations.
• Bounded problems project trial points into [lb, ub] and estimate finite-difference Jacobians without stepping outside finite bounds.
• lb and ub may be empty, scalar, or arrays with the same number of elements as x0; scalar bounds are broadcast to every parameter.
• optimset and optimoptions option structs are accepted. TolX, TolFun, MaxIter, MaxFunEvals, Display, and Algorithm are recognized.
• Algorithm accepts levenberg-marquardt and trust-region-reflective; both currently use RunMat's projected Levenberg-Marquardt implementation.
• With requested outputs, RunMat supports [x, resnorm, residual, exitflag, output, lambda, jacobian].

Examples

Fit a line

xdata = [0 1 2 3];
ydata = 2.*xdata + 1;
p = lsqcurvefit(@(p,x) p(1).*x + p(2), [0; 0], xdata, ydata)

Expected output:

p =
    2.0000
    1.0000

Fit an exponential decay

xdata = 0:0.2:2;
ydata = 2.5.*exp(-0.7.*xdata);
p = lsqcurvefit(@(p,x) p(1).*exp(-p(2).*x), [1; 0.1], xdata, ydata)

Expected output:

p =
    2.5000
    0.7000

Fit with bounds and diagnostics

opts = optimoptions("lsqcurvefit", "TolX", 1e-8, "Display", "off");
[p, resnorm, residual, exitflag, output] = lsqcurvefit(@(p,x) p(1).*x, 0.5, [1 2 3], [2 4 6], 0, 1, opts)

Expected output:

p =
    1.0000

Using lsqcurvefit with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how lsqcurvefit changes the result.

FAQ

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how lsqcurvefit is executed, line by line, in Rust.

• View the source for lsqcurvefit in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

About RunMat

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