Follow a question through the data.

1. Compare spectra along the energy axis

Four sampling sites × three energy channels. Find each spectrum’s maximum minus minimum, select site 2, then plot it. Inputs use floating-point values in both languages. The calculation has no file I/O.

The useful difference: NumPy already expresses this reduction concisely with np.ptp(..., axis=1). VKF makes the selected dimension part of function application: span_u(spectra_pu) keeps energy intact and lifts over sites. The function does not need to know which positional axis it occupies.

This is a clarity comparison, not a claim that VKF is always shorter. Setup and the complete core task are shown for both; no helper implementation or plotting work is hidden.

import numpy as np
import matplotlib.pyplot as plt

energy = np.array([-1., 0., 1.], dtype=np.float64)
spectra = np.array([[1., 5., 2.], [2., 3., 4.],
                    [3., 8., 4.], [4., 5., 6.]], dtype=np.float64)

contrast = np.ptp(spectra, axis=1)
selected = spectra[2, :]
print(contrast)
print(selected)
fig, ax = plt.subplots(dpi=96)
ax.plot(energy, selected, color=(.25, .72, 1., 1.), linewidth=.75)
ax.set(xlim=(-1, 1), ylim=(0, 10))
plt.show()

stat:.stat
energy:[-1.0,0.0,1.0]_u
spectra:[[1.0,5.0,2.0],[2.0,3.0,4.0],
         [3.0,8.0,4.0],[4.0,5.0,6.0]]_pu

span(x):stat.max(x)-stat.min(x)
contrast:span_u(spectra)
::contrast
selected:spectra.(2,:)
::selected
view:.ui.viewport
view.add(x:energy_u,y:selected_u,color:[0.25,0.72,1,1])
view.push(x_lim:[-1,1],y_lim:[0,10])
view.show()

Run this exact VKF program →

Expected numerical results: contrast [4, 2, 5, 2]; selected spectrum [3, 8, 4]. Both plots request the same blue RGBA color and x/y bounds. The VKF packet contains three float32 render vertices; Python computes with float64 arrays. The fixture values are exactly representable; this is not a general precision or pixel-equivalence claim. Native plot defaults, fonts and controls differ.

Reference APIs: NumPy ptp and Matplotlib plot. NumPy supports reductions over one or several axes; this working VKF workflow verifies one selected energy axis only.

Bind a model parameter without a wrapper

Keep a cubic response function while leaving its input free. Both languages support this naturally: Python provides functools.partial; VKF makes named argument binding part of the call grammar. This removes a separate import and keeps the binding alongside the language’s ordinary function syntax.

from functools import partial

def power(x, n):
    return x ** n

cube = partial(power, n=3)
print(cube(2))

power(x,n):x^n
cube:power[n:3]
::cube(2)

Both print 8. The shorter function definition and built-in binding syntax are visible here; no speed advantage is inferred. Run the canonical partial-application examples →

2. Inspect a small part of an HDF5 dataset

Python can already read selected elements and slices directly. Apply the transformation after selecting the data. This is the appropriate baseline, rather than loading an entire dataset just to inspect one element.

Python · optional fixture-file setup

import h5py

with h5py.File("spectra.h5", "w") as file:
    file.create_dataset("intensity", data=spectra)

Python · complete selected-read task

with h5py.File("spectra.h5", "r") as file:
    dataset = file["intensity"]
    one = np.sin(dataset[2, 1])
    region = np.sin(dataset[1:3, 0:2])

The logical selection is one scalar and a 2 × 2 region. Physical disk reads depend on storage layout, compression, chunks and caches; bytes read and cold/warm performance are unmeasured here. h5py documents direct hyperslab selection and chunked I/O.

VKF · design goal, no runnable equivalent yet

The goal is for consumer demand to flow through transformations so that asking for one transformed value avoids unrelated work. This 0.7.2 site has no verified public HDF5 reader or out-of-core pipeline. There is intentionally no invented VKF import, API or Run button for that workflow. The finite-demand range example establishes a smaller capability only.

3. Browse related maps without rebuilding the viewer

The founder once built a viewer simply to step through 100 images. VKF’s visual design aims to reuse one layer/property model and append states for stacked views. That would reduce the glue between a calculation and the views used to inspect it.

Matplotlib already has image display, widgets and animation tools; a fixed imshow image can be updated with set_data. A custom stack browser still needs an input/control connection. No executed, equivalent 100-image comparison is claimed here.

Current boundary: the preview’s coordinate layers, push with explicit bounds, and displayed plots are tested. General append-driven image stacks and a published HDF5-to-viewer path remain unqualified. See the UI module inventory. Automatic CPU/GPU placement and speed are also not established by this example.

4. Solve constraints, derive a path, inspect its motion

A cubic trajectory is useful when designing an experimental scan or controlled motion. This unchanged program solves four endpoint constraints, differentiates the resulting parameterized function and draws time curves and a position–velocity portrait. It demonstrates .linalg.solve and an exact function transform, not a complete first-class symbolic library.

Run it, then change exit_slope:0 to exit_slope:-2. A requested negative arrival velocity makes the path overshoot and reverse before reaching its endpoint.

la:.linalg
exit_slope:0
c:la.solve([[1,0,0,0],[1,1,1,1],
            [0,1,0,0],[0,1,2,3]], [0,1,0,exit_slope])
path(t,a,b,d,e):a+b*t+d*t^2+e*t^3
slope:deriv_t(path)
::c
::path(0.5,c.0,c.1,c.2,c.3)
::slope(0.5,c.0,c.1,c.2,c.3)
t:0.005*[0..200]
curves:.ui.viewport
curves.add(x:t_u,y:path(t_u,c.0,c.1,c.2,c.3),color:[0.25,0.72,1,1])
curves.add(x:t_u,y:slope(t_u,c.0,c.1,c.2,c.3),color:[1,0.45,0.18,1])
curves.show()
phase:.ui.viewport
phase.add(x:path(t_u,c.0,c.1,c.2,c.3),y:slope(t_u,c.0,c.1,c.2,c.3),color:[0.3,0.9,0.55,1])
phase.show()

What is verified, and what is not

Machine-readable comparison coverage records the fixture, code hashes, version pins, actual checks and remaining claims. The site verification report records each promoted source program. Fewer lines do not establish less I/O, lower memory use or greater speed.