Example lmfit

# <examples/doc_parameters_basic.py>
import numpy as np

from lmfit import Minimizer, Parameters, create_params, report_fit

# create data to be fitted
x = np.linspace(0, 15, 301)
np.random.seed(2021)
data = (5.0 * np.sin(2.0*x - 0.1) * np.exp(-x*x*0.025) +
        np.random.normal(size=x.size, scale=0.2))


# define objective function: returns the array to be minimized
def fcn2min(params, x, data):
    """Model a decaying sine wave and subtract data."""
    amp = params['amp']
    shift = params['shift']
    omega = params['omega']
    decay = params['decay']
    model = amp * np.sin(x*omega + shift) * np.exp(-x*x*decay)
    return model - data


# create a set of Parameters
params = Parameters()
params.add('amp', value=10, min=0)
params.add('decay', value=0.1)
params.add('shift', value=0.0, min=-np.pi/2., max=np.pi/2.)
params.add('omega', value=3.0)

# ... or use
# params = create_params(amp=dict(value=10, min=0),
#                      decay=0.1,
#                      omega=3,
#                      shift=dict(value=0, min=-np.pi/2, max=np.pi/2))

# do fit, here with the default leastsq algorithm
minner = Minimizer(fcn2min, params, fcn_args=(x, data))
result = minner.minimize()

# calculate final result
final = data + result.residual

# write error report
report_fit(result)

# try to plot results
try:
    import matplotlib.pyplot as plt
    plt.plot(x, data, '+')
    plt.plot(x, final)
    plt.show()
except ImportError:
    pass
# <end of examples/doc_parameters_basic.py>

A module that was compiled using NumPy 1.x cannot be run in
NumPy 2.2.6 as it may crash. To support both 1.x and 2.x
versions of NumPy, modules must be compiled with NumPy 2.0.
Some module may need to rebuild instead e.g. with 'pybind11>=2.12'.

If you are a user of the module, the easiest solution will be to
downgrade to 'numpy<2' or try to upgrade the affected module.
We expect that some modules will need time to support NumPy 2.

Traceback (most recent call last):  File "/usr/lib/python3.10/runpy.py", line 196, in _run_module_as_main
    return _run_code(code, main_globals, None,
  File "/usr/lib/python3.10/runpy.py", line 86, in _run_code
    exec(code, run_globals)
  File "/usr/lib/python3/dist-packages/sage/repl/ipython_kernel/__main__.py", line 3, in <module>
    IPKernelApp.launch_instance(kernel_class=SageKernel)
  File "/usr/lib/python3/dist-packages/traitlets/config/application.py", line 846, in launch_instance
    app.start()
  File "/usr/lib/python3/dist-packages/ipykernel/kernelapp.py", line 677, in start
    self.io_loop.start()
  File "/usr/lib/python3/dist-packages/tornado/platform/asyncio.py", line 199, in start
    self.asyncio_loop.run_forever()
  File "/usr/lib/python3.10/asyncio/base_events.py", line 603, in run_forever
    self._run_once()
  File "/usr/lib/python3.10/asyncio/base_events.py", line 1909, in _run_once
    handle._run()
  File "/usr/lib/python3.10/asyncio/events.py", line 80, in _run
    self._context.run(self._callback, *self._args)
  File "/usr/lib/python3/dist-packages/ipykernel/kernelbase.py", line 461, in dispatch_queue
    await self.process_one()
  File "/usr/lib/python3/dist-packages/ipykernel/kernelbase.py", line 450, in process_one
    await dispatch(*args)
  File "/usr/lib/python3/dist-packages/ipykernel/kernelbase.py", line 357, in dispatch_shell
    await result
  File "/usr/lib/python3/dist-packages/ipykernel/kernelbase.py", line 652, in execute_request
    reply_content = await reply_content
  File "/usr/lib/python3/dist-packages/ipykernel/ipkernel.py", line 353, in do_execute
    res = shell.run_cell(code, store_history=store_history, silent=silent)
  File "/usr/lib/python3/dist-packages/ipykernel/zmqshell.py", line 532, in run_cell
    return super().run_cell(*args, **kwargs)
  File "/usr/lib/python3/dist-packages/IPython/core/interactiveshell.py", line 2914, in run_cell
    result = self._run_cell(
  File "/usr/lib/python3/dist-packages/IPython/core/interactiveshell.py", line 2960, in _run_cell
    return runner(coro)
  File "/usr/lib/python3/dist-packages/IPython/core/async_helpers.py", line 78, in _pseudo_sync_runner
    coro.send(None)
  File "/usr/lib/python3/dist-packages/IPython/core/interactiveshell.py", line 3185, in run_cell_async
    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,
  File "/usr/lib/python3/dist-packages/IPython/core/interactiveshell.py", line 3377, in run_ast_nodes
    if (await self.run_code(code, result,  async_=asy)):
  File "/usr/lib/python3/dist-packages/IPython/core/interactiveshell.py", line 3457, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "/tmp/ipykernel_11379/813903233.py", line 4, in <module>
    from lmfit import Minimizer, Parameters, create_params, report_fit
  File "/home/runner/.sage/local/lib/python3.10/site-packages/lmfit/__init__.py", line 42, in <module>
    from .model import Model, CompositeModel
  File "/home/runner/.sage/local/lib/python3.10/site-packages/lmfit/model.py", line 44, in <module>
    import matplotlib  # noqa: F401
  File "/usr/lib/python3/dist-packages/matplotlib/__init__.py", line 109, in <module>
    from . import _api, _version, cbook, docstring, rcsetup
  File "/usr/lib/python3/dist-packages/matplotlib/rcsetup.py", line 27, in <module>
    from matplotlib.colors import Colormap, is_color_like
  File "/usr/lib/python3/dist-packages/matplotlib/colors.py", line 56, in <module>
    from matplotlib import _api, cbook, scale
  File "/usr/lib/python3/dist-packages/matplotlib/scale.py", line 23, in <module>
    from matplotlib.ticker import (
  File "/usr/lib/python3/dist-packages/matplotlib/ticker.py", line 136, in <module>
    from matplotlib import transforms as mtransforms
  File "/usr/lib/python3/dist-packages/matplotlib/transforms.py", line 46, in <module>
    from matplotlib._path import (

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
AttributeError: _ARRAY_API not found

[[Fit Statistics]]
    # fitting method   = leastsq
    # function evals   = 64
    # data points      = 301
    # variables        = 4
    chi-square         = 12.1867036
    reduced chi-square = 0.04103267
    Akaike info crit   = -957.236198
    Bayesian info crit = -942.407756
[[Variables]]
    amp:    5.03088059 +/- 0.04005824 (0.80%) (init = 10)
    decay:  0.02495457 +/- 4.5396e-04 (1.82%) (init = 0.1)
    shift: -0.10264952 +/- 0.01022294 (9.96%) (init = 0)
    omega:  2.00026310 +/- 0.00326183 (0.16%) (init = 3)
[[Correlations]] (unreported correlations are < 0.100)
    C(shift, omega) = -0.7852
    C(amp, decay)   = +0.5840
    C(amp, shift)   = -0.1179

A module that was compiled using NumPy 1.x cannot be run in
NumPy 2.2.6 as it may crash. To support both 1.x and 2.x
versions of NumPy, modules must be compiled with NumPy 2.0.
Some module may need to rebuild instead e.g. with 'pybind11>=2.12'.

If you are a user of the module, the easiest solution will be to
downgrade to 'numpy<2' or try to upgrade the affected module.
We expect that some modules will need time to support NumPy 2.

Traceback (most recent call last):  File "/usr/lib/python3.10/runpy.py", line 196, in _run_module_as_main
    return _run_code(code, main_globals, None,
  File "/usr/lib/python3.10/runpy.py", line 86, in _run_code
    exec(code, run_globals)
  File "/usr/lib/python3/dist-packages/sage/repl/ipython_kernel/__main__.py", line 3, in <module>
    IPKernelApp.launch_instance(kernel_class=SageKernel)
  File "/usr/lib/python3/dist-packages/traitlets/config/application.py", line 846, in launch_instance
    app.start()
  File "/usr/lib/python3/dist-packages/ipykernel/kernelapp.py", line 677, in start
    self.io_loop.start()
  File "/usr/lib/python3/dist-packages/tornado/platform/asyncio.py", line 199, in start
    self.asyncio_loop.run_forever()
  File "/usr/lib/python3.10/asyncio/base_events.py", line 603, in run_forever
    self._run_once()
  File "/usr/lib/python3.10/asyncio/base_events.py", line 1909, in _run_once
    handle._run()
  File "/usr/lib/python3.10/asyncio/events.py", line 80, in _run
    self._context.run(self._callback, *self._args)
  File "/usr/lib/python3/dist-packages/ipykernel/kernelbase.py", line 461, in dispatch_queue
    await self.process_one()
  File "/usr/lib/python3/dist-packages/ipykernel/kernelbase.py", line 450, in process_one
    await dispatch(*args)
  File "/usr/lib/python3/dist-packages/ipykernel/kernelbase.py", line 357, in dispatch_shell
    await result
  File "/usr/lib/python3/dist-packages/ipykernel/kernelbase.py", line 652, in execute_request
    reply_content = await reply_content
  File "/usr/lib/python3/dist-packages/ipykernel/ipkernel.py", line 353, in do_execute
    res = shell.run_cell(code, store_history=store_history, silent=silent)
  File "/usr/lib/python3/dist-packages/ipykernel/zmqshell.py", line 532, in run_cell
    return super().run_cell(*args, **kwargs)
  File "/usr/lib/python3/dist-packages/IPython/core/interactiveshell.py", line 2914, in run_cell
    result = self._run_cell(
  File "/usr/lib/python3/dist-packages/IPython/core/interactiveshell.py", line 2960, in _run_cell
    return runner(coro)
  File "/usr/lib/python3/dist-packages/IPython/core/async_helpers.py", line 78, in _pseudo_sync_runner
    coro.send(None)
  File "/usr/lib/python3/dist-packages/IPython/core/interactiveshell.py", line 3185, in run_cell_async
    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,
  File "/usr/lib/python3/dist-packages/IPython/core/interactiveshell.py", line 3377, in run_ast_nodes
    if (await self.run_code(code, result,  async_=asy)):
  File "/usr/lib/python3/dist-packages/IPython/core/interactiveshell.py", line 3457, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "/tmp/ipykernel_11379/813903233.py", line 49, in <module>
    import matplotlib.pyplot as plt
  File "/usr/lib/python3/dist-packages/matplotlib/__init__.py", line 109, in <module>
    from . import _api, _version, cbook, docstring, rcsetup
  File "/usr/lib/python3/dist-packages/matplotlib/rcsetup.py", line 27, in <module>
    from matplotlib.colors import Colormap, is_color_like
  File "/usr/lib/python3/dist-packages/matplotlib/colors.py", line 56, in <module>
    from matplotlib import _api, cbook, scale
  File "/usr/lib/python3/dist-packages/matplotlib/scale.py", line 23, in <module>
    from matplotlib.ticker import (
  File "/usr/lib/python3/dist-packages/matplotlib/ticker.py", line 136, in <module>
    from matplotlib import transforms as mtransforms
  File "/usr/lib/python3/dist-packages/matplotlib/transforms.py", line 46, in <module>
    from matplotlib._path import (

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
AttributeError: _ARRAY_API not found

x = np.linspace(0, 15, 301)
print(x.size)

301