From measurements to a question you can test

01 / SPECTRAL ANALYSIS

Find a feature, then inspect its source.

Generate four Lorentzian spectra on 257 energy samples each. Calculate the peak-to-peak contrast at each site, then inspect site 2 on a denser 513-sample curve. These are synthetic model data, not measurements.

import numpy as np
import matplotlib.pyplot as plt

site = np.arange(4, dtype=np.float64)
energy = np.linspace(-1., 1., 257)
profile = 1 / (1 + 100 * energy ** 2)
spectra = 1 + (1 + site[:, None]) * profile[None, :]
contrast = np.ptp(spectra, axis=1)
curve_energy = np.linspace(-1., 1., 513)
selected_site = 2
selected = 1 + (1 + selected_site) / (1 + 100 * curve_energy ** 2)
print(contrast)
print(selected[256])
fig, ax = plt.subplots()
ax.plot(curve_energy, selected, color=(.25, .72, 1., 1.))
ax.set(xlim=(-1, 1), ylim=(0, 5),
       xlabel="Energy coordinate", ylabel="Generated intensity")
plt.show()

NumPy's ptp already states the reduction concisely. VKF makes the selected dimension part of calling an ordinary span function. These are two readable ways to express the same numerical task; the plots are not claimed to be pixel-identical.

stat:.stat
site:[0..3]_p
energy:(-1.0+0.0078125*[0..256])_u
profile:1.0/(1.0+100.0*energy^2)
spectra:1.0+(1.0+site_p)*profile_u
span(x):stat.max(x)-stat.min(x)
::span_u(spectra)
curve_energy:-1.0+0.00390625*[0..512]
selected_site:2
selected:1.0+(1.0+selected_site)/(1.0+100.0*curve_energy^2)
::selected.(256)
view:.ui.viewport
view.add(x:curve_energy_u,y:selected_u,color:[0.25,0.72,1,1])
view.push(x_lim:[-1,1],y_lim:[0,5])
view.show()

Change selected_site from 2 to 1 to inspect another generated spectrum. Both analysis grids include the peak and endpoints, so the sampled peak-to-peak contrasts are exact for this model.

02 / PARAMETER BINDING

Carry a decision into the next calculation.

When a model parameter is fixed, keep the resulting function as a value. Python provides this through functools.partial; VKF places parameter binding in the language syntax. Both examples below produce 8.

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)

Run the parameter-binding examples →

03 / LARGE-DATA BOUNDARY

Request a region without inventing an API.

For a dataset already stored in HDF5, idiomatic h5py can select a scalar or a region directly. It does not require reading the complete dataset. Physical reads still depend on chunking, compression and caches.

The scalar selection reads intensity 8; the selected 2 × 2 input region is [[2,3],[3,8]]. NumPy applies sine after each selection. Inspect one and region in Python to see the transformed values. File setup stays separate from the selected-read task.

import h5py
import numpy as np

site = np.arange(4, dtype=np.float64)
energy = np.linspace(-1., 1., 257)
profile = 1 / (1 + 100 * energy ** 2)
spectra = 1 + (1 + site[:, None]) * profile[None, :]
with h5py.File("spectra.h5", "w") as file:
    file.create_dataset("intensity", data=spectra)
with h5py.File("spectra.h5", "r") as file:
    dataset = file["intensity"]
    one = np.sin(dataset[2, 128])
    region = np.sin(dataset[1:3, 100:157])
print(one)
print(region.shape)

04 / A CONSTRAINED MODEL

Solve the path. Inspect its rate of change.

Choose a cubic path that begins at 0, ends at 1 and has selected endpoint slopes. Solve its four coefficients as a linear system, derive its slope, then inspect both time curves and a phase view.

The default endpoint slope is zero. At the midpoint the program prints position 0.5 and slope 1.5. Change exit_slope to explore how the solution changes.

The parameter t spans 0 to 1 in 257 samples. These are static position, derivative and phase plots; t is the model coordinate, not a live playback clock.

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:0.00390625*[0..256]
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()

This is a sampled model with two retained views. It is not a benchmark or a qualification of large animated scenes. Inspect the linear-algebra source →