fimx

fimx provides functions for dense Fisher information matrices stored as ordinary xarray.DataArray objects. NumPy handles the computation; xarray handles labels, metadata containers, and persistence.

uv add fimx
# Optional NetCDF backend:
uv add 'fimx[io]'
# Optional Gaussian plotting backend:
uv add 'fimx[plotting]'

Quickstart

from fimx import combine, errors, fix, gaussian_prior, inv, marginalize, matrix

F = matrix([[4, 1], [1, 2]], ["a", "b"])
fixed = fix(F, "b")  # [[4.0]]: b is held fixed
reduced = marginalize(F, "b")  # [[3.5]]: uncertainty in b is integrated out
C = inv(F)  # covariance, with the same row/col labels
sigma = errors(F)  # sqrt(diag(C)), dimension "parameter"

prior = gaussian_prior({"a": 0.5})  # standard deviation 0.5 -> information 4
posterior = combine(F, prior)

Array contract

• Matrices have dimensions exactly ("row", "col"), a nonempty square shape, and explicit, identical, ordered coordinates of unique string names. Batches, inferred dimensions, and coordinate repair are unsupported.
• Values must be real, finite, and symmetric. They are converted to float64.
• Positive semidefiniteness is not checked, so singular matrices can be built, fixed, transformed, or combined. inv and errors require positive definite input; marginalize only requires the removed block to be.
• Functions return fresh DataArrays and never mutate their inputs. Attributes, names, and auxiliary coordinates are not preserved.
• Arrays built directly with xarray work if they meet the contract.

Behavior worth knowing:

• fix and marginalize accept one name or a sequence and keep the remaining order. Unknown names raise KeyError; duplicates or removing every parameter raise ValueError.
• expand embeds a matrix in a larger or reordered set of names, filling new entries with zeros. The target must contain every existing name. Matrices expanded to the same names add with plain +, whereas + on mismatched names silently keeps only the overlap.
• combine keeps the first matrix's order and appends new parameters as they appear. Missing entries contribute zero.
• gaussian_prior takes standard deviations, not information values.
• Failures are explicit: ValueError for malformed or non-finite data, TypeError for non-DataArray inputs, and numpy.linalg.LinAlgError for singular or indefinite matrices. By default inv and errors use Cholesky and require positive definiteness. method="inv" only fails on exactly singular matrices, and method="pinv" uses the pseudoinverse, which assigns zero variance to unconstrained directions. There is no regularization.

Changes of variables

The Jacobian has dimensions ("old", "new") and orientation J[i, j] = d theta_i / d phi_j, where theta are the old parameters and phi the new ones. Every old parameter must appear exactly once (rows are reordered to match F), and the order of the new parameters sets the output order. Rectangular Jacobians are supported.

import xarray as xr
from fimx import transform

# theta_a = 2 * phi_x, theta_b = phi_x
# Rows deliberately appear in reverse order to F.
J = xr.DataArray(
    [[1.0], [2.0]],
    dims=("old", "new"),
    coords={"old": ["b", "a"], "new": ["x"]},
)
G = transform(F, J)  # [[22.0]]

Plotting

Plotting needs the plotting extra (GetDist and Matplotlib, loaded lazily).

Forecast Datasets

Keep fiducials separate from the Fisher matrix and bundle them with dataset(). In the mapping of extra variables, 1D arrays use row and 2D arrays use (row, col); plain arrays follow matrix order and indexed axes are aligned by label. Strings, units, and nonfinite metadata are allowed. The names fisher, row, and col are reserved.

Corner plots

from fimx import dataset, plot

fiducials = xr.DataArray([1.0, 2.0], dims="row", coords={"row": ["a", "b"]})
survey_a = dataset(F, {"fiducials": fiducials, "units": ["km", "s"]})
survey_b = dataset(2 * F, {"fiducials": fiducials})

fig = plot({"Survey A": survey_a, "Survey B": survey_b})
fig.savefig("constraints.pdf")

# Explicit order and GetDist customization:
fig = plot(
    {"Survey A": survey_a, "Survey B": survey_b},
    parameters=["b", "a"],
    backend="getdist",
    filled=False,
    backend_kwargs={"contour_colors": ["C0", "C1"]},
)

• plot() takes a nonempty mapping of labels to Datasets with fisher and finite, real fiducials. Each forecast is centered on its own fiducials; mapping order sets the overlay order and keys become legend labels.
• By default, the plot uses the parameters shared by all forecasts, in the first forecast's order. An explicit parameters list must be unique and present in every forecast.
• Each full Fisher matrix is inverted before selecting parameters, so omitted parameters are marginalized and every complete matrix (nuisance blocks included) must be positive definite.
• The GetDist backend draws analytic Gaussians, with no sampling, and returns a Matplotlib Figure without showing or saving it. Filled contours are the default. backend_kwargs is forwarded to triangle_plot, except roots, params, legend_labels, and filled, which plot() controls.
• Additional backends implement fimx.plotting.base.PlotBackend.

Command line

With both extras installed, fimx-plot draws a corner plot from NetCDF Datasets that contain fisher and fiducials:

uv add 'fimx[io,plotting]'
fimx-plot --file survey-a.nc --file survey-b.nc \
    --figure-file constraints.png --figure-dpi 200 \
    --parameters a b --no-filled --backend getdist \
    --backend-kwargs '{"contour_colors": ["C0", "C1"]}'

Each file stem becomes a legend label, so stems must be unique. The output defaults to plot.png at 150 dpi. --parameters selects and orders parameters, --no-filled draws line contours, --inversion-method picks cholesky, inv, or pinv, --backend picks a backend, and --backend-kwargs takes a JSON object. fimx.io.load_dataset(path) loads the same files from Python.

Storage

There is no fimx file format; use xarray. The io extra supplies h5netcdf.

F.to_netcdf("fisher.nc", engine="h5netcdf")
restored = xr.load_dataarray("fisher.nc", engine="h5netcdf")
C_restored = inv(restored)

More

See CHANGELOG.md for release notes. fimx is released under the MIT license; see LICENSE.