`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(___)

All supported lsqcurvefit forms

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

Name	Type	Required	Default	Description
`fun`	`Any`	Yes	—	Model callback evaluated as fun(x,xdata).
`x0`	`NumericArray`	Yes	—	Initial parameter guess.
`xdata`	`Any`	Yes	—	Independent data passed to the model callback.
`ydata`	`NumericArray`	Yes	—	Observed response data.
`lb`	`NumericArray`	No	`[]`	Lower parameter bounds. Empty means unbounded.
`ub`	`NumericArray`	No	`[]`	Upper parameter bounds. Empty means unbounded.
`options`	`Any`	No	—	Options struct from optimset or optimoptions.

Returns

Name	Type	Description
`x`	`NumericArray`	Estimated fit parameters with the same shape as x0.
`resnorm`	`NumericScalar`	Squared 2-norm of the final residual.
`residual`	`NumericArray`	Final model residual fun(x,xdata)-ydata.
`exitflag`	`NumericScalar`	Solver exit condition.
`output`	`Any`	Iteration and convergence metadata struct.
`lambda`	`Any`	Approximate bound multiplier struct with lower and upper fields.
`jacobian`	`NumericArray`	Finite-difference Jacobian of fun at the solution.

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

Errors

Identifier	When	Message
`RunMat:lsqcurvefit:InvalidArgument`	Argument grammar, bounds, options, or output arity are invalid.	`lsqcurvefit: invalid argument`
`RunMat:lsqcurvefit:InvalidInput`	Initial guess, model callback, data shape, or solver semantics are invalid.	`lsqcurvefit: invalid input`
`RunMat:lsqcurvefit:TooManyOutputs`	`lsqcurvefit` is called with more than seven requested outputs.	`lsqcurvefit: too many output arguments`

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.
The documented numeric solver domain is floating point. Native integer x0, xdata, ydata, bounds, numeric options, and callback results are independently gated RunMat extensions.
Integer x0, ydata, bounds, floating options, and callback results must be exactly representable at the double solver boundary. Integer xdata remains an exact callback payload and is not eagerly converted.
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.

Run a small lsqcurvefit example, explain the result, then change one input and compare the output.

FAQ

Does lsqcurvefit run on the GPU?⌄

The solver itself is host-side because it repeatedly invokes user callbacks and adapts finite-difference steps. The callback can still use GPU-aware builtins, but the residual vector is gathered before each solver step.

What is returned in lambda?⌄

lambda.lower and lambda.upper are approximate bound multipliers computed from the final finite-difference Jacobian and residual.

Are nonlinear constraints supported?⌄

RunMat currently supports the core curve-fitting forms with optional lower and upper parameter bounds. Linear-constraint, nonlinear-constraint, and problem-structure forms are not yet implemented.

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

RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.

RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing

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

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(___)

All supported lsqcurvefit forms

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

Name	Type	Required	Default	Description
`fun`	`Any`	Yes	—	Model callback evaluated as fun(x,xdata).
`x0`	`NumericArray`	Yes	—	Initial parameter guess.
`xdata`	`Any`	Yes	—	Independent data passed to the model callback.
`ydata`	`NumericArray`	Yes	—	Observed response data.
`lb`	`NumericArray`	No	`[]`	Lower parameter bounds. Empty means unbounded.
`ub`	`NumericArray`	No	`[]`	Upper parameter bounds. Empty means unbounded.
`options`	`Any`	No	—	Options struct from optimset or optimoptions.

Returns

Name	Type	Description
`x`	`NumericArray`	Estimated fit parameters with the same shape as x0.
`resnorm`	`NumericScalar`	Squared 2-norm of the final residual.
`residual`	`NumericArray`	Final model residual fun(x,xdata)-ydata.
`exitflag`	`NumericScalar`	Solver exit condition.
`output`	`Any`	Iteration and convergence metadata struct.
`lambda`	`Any`	Approximate bound multiplier struct with lower and upper fields.
`jacobian`	`NumericArray`	Finite-difference Jacobian of fun at the solution.

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

Errors

Identifier	When	Message
`RunMat:lsqcurvefit:InvalidArgument`	Argument grammar, bounds, options, or output arity are invalid.	`lsqcurvefit: invalid argument`
`RunMat:lsqcurvefit:InvalidInput`	Initial guess, model callback, data shape, or solver semantics are invalid.	`lsqcurvefit: invalid input`
`RunMat:lsqcurvefit:TooManyOutputs`	`lsqcurvefit` is called with more than seven requested outputs.	`lsqcurvefit: too many output arguments`

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.
The documented numeric solver domain is floating point. Native integer x0, xdata, ydata, bounds, numeric options, and callback results are independently gated RunMat extensions.
Integer x0, ydata, bounds, floating options, and callback results must be exactly representable at the double solver boundary. Integer xdata remains an exact callback payload and is not eagerly converted.
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.

Run a small lsqcurvefit example, explain the result, then change one input and compare the output.

FAQ

Does lsqcurvefit run on the GPU?⌄

What is returned in lambda?⌄

lambda.lower and lambda.upper are approximate bound multipliers computed from the final finite-difference Jacobian and residual.

Are nonlinear constraints supported?⌄

RunMat currently supports the core curve-fitting forms with optional lower and upper parameter bounds. Linear-constraint, nonlinear-constraint, and problem-structure forms are not yet implemented.

Optim

coneprog · fminbnd · fminunc · fsolve · fzero · integral · linprog · lsqnonlin · optimoptions · optimset · quad · secondordercone

Elementwise

Trigonometry

acos · acosh · asin · asinh · atan · atan2 · atanh · cos · cosd · cosh · cospi · deg2rad · pol2cart · rad2deg · sin · sind · sinh · sinpi · tan · tand · tanh

Reduction

Structure

bandwidth · isdiag · ishermitian · issymmetric · istril · istriu · symrcm

Signal

Rounding

ceil · fix · floor · mod · rem · round

Factor

chol · decomposition · eig · eigs · lu · qr · svd

Solve

cond · det · inv · linsolve · norm · null · pinv · rank · rcond · rref · vecnorm

Ops

cross · ctranspose · dot · mldivide · mpower · mrdivide · mtimes · pagemtimes · pagetranspose · trace · transpose

Symbolic

digits · int · limit · piecewise · sym · syms · vpa

Fft

fft · fft2 · fftn · fftshift · ifft · ifft2 · ifftn · ifftshift

Interpolation

griddedInterpolant · interp1 · interp1q · interp2 · pchip · ppval · spline

Discrete

lcm · primes

Ode

ode15s · ode23 · ode45

Poly

polyder · polyfit · polyint · polyval · roots

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

RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.

RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing

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

Syntax

Inputs

Returns

Errors

How lsqcurvefit works

Examples

Fit a line

Fit an exponential decay

Fit with bounds and diagnostics

Using lsqcurvefit with coding agents

FAQ

Related Math functions

Optim

Elementwise

Trigonometry

Reduction

Structure

Signal

Rounding

Factor

Solve

Ops

Symbolic

Fft

Interpolation

Discrete

Ode

Poly

Open-source implementation

About RunMat

Download RunMat

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

Syntax

Inputs

Returns

Errors

How lsqcurvefit works

Examples

Fit a line

Fit an exponential decay

Fit with bounds and diagnostics

Using lsqcurvefit with coding agents

FAQ

Related Math functions

Optim

Elementwise

Trigonometry

Reduction

Structure

Signal

Rounding

Factor

Solve

Ops

Symbolic

Fft

Interpolation

Discrete

Ode

Poly

Open-source implementation

About RunMat

Download RunMat

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

How `lsqcurvefit` works

Using `lsqcurvefit` with coding agents

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

How `lsqcurvefit` works

Using `lsqcurvefit` with coding agents