physlab 1.0.7

Library for physical quantities with automatic uncertainty propagation

PhysLab

Modern Python library for physical quantities with automatic uncertainty propagation

Quick Start

Installation

pip install physlab

Basic Usage

import numpy as np
from physlab import phys, LabProcessor, graph, sin, cos, tg, ctg, exp, ln, log10, sqrt, arcsin, arccos, arctg

# Create physical quantities
length = phys(10.5, 0.1)    # 10.5 ± 0.1 m
time = phys(2.3, 0.05)      # 2.3 ± 0.05 s

# Automatic uncertainty calculation
velocity = length / time
print(f"Velocity: {velocity}")

# Working with arrays
temperatures = phys([20.1, 22.3, 25.7], 0.5)
print(f"Temperatures: {temperatures}")

Core Features

Physical Quantities with Uncertainties

Creating Objects:

# Scalars
scalar = phys(15.7, 0.2)

# Arrays with uniform uncertainty
array_uniform = phys([1, 2, 3, 4], 0.1)

# Arrays with variable uncertainty  
array_variable = phys([1.0, 2.0, 3.0], [0.1, 0.2, 0.3])

# From NumPy arrays
np_array = phys(np.array([0.1, 0.2, 0.3]), 0.01)

Properties and Access:

x = phys(25.0, 0.5)

# Basic properties
print(f"Value: {x.value}")
print(f"Absolute uncertainty: {x.sigma}")
print(f"Relative uncertainty: {x.eps:.4f}")

# Setting uncertainties
x.sigma = 0.8      # Set absolute uncertainty
x.eps = 0.05       # Set relative uncertainty (5%)

# For arrays
arr = phys([10, 20, 30])
arr.eps = 0.1      # Automatically creates uncertainty array

Mathematical Operations

Automatic Uncertainty Propagation:

• Addition/Subtraction: σ = √(σ₁² + σ₂²)
• Multiplication/Division: ε = √(ε₁² + ε₂²)
• Power: Full calculation for base and exponent

a = phys(10.0, 0.1)
b = phys(2.0, 0.05)

print(f"a + b = {a + b}")
print(f"a - b = {a - b}") 
print(f"a * b = {a * b}")
print(f"a / b = {a / b}")
print(f"a ** 2 = {a ** 2}")
print(f"2 ** a = {2 ** a}")

# Operations with numbers
print(f"a + 5 = {a + 5}")
print(f"3 * a = {3 * a}")

# Complex expressions
complex_expr = (a + b) * phys(3, 0.1) / 2

Mathematical Functions

Supported functions with automatic uncertainty calculation:

from physlab import cos, sin, tg, ctg, exp, ln, sqrt

angle = phys(0.5, 0.01)  # 0.5 ± 0.01 radians

print(f"cos({angle}) = {cos(angle)}")
print(f"sin({angle}) = {sin(angle)}")
print(f"tg({angle}) = {tg(angle)}")
print(f"ctg({angle}) = {ctg(angle)}")

# Exponential and logarithms
x = phys(2.0, 0.1)
print(f"exp({x}) = {exp(x)}")
print(f"ln({x}) = {ln(x)}")
print(f"sqrt({x}) = {sqrt(x)}")

# Working with arrays
angles_array = phys([0, np.pi/6, np.pi/4, np.pi/3], 0.01)
sines = sin(angles_array)

Array Operations

# Creation and basic operations
data = phys([1.0, 2.0, 3.0, 4.0], 0.1)

# Indexing
print(f"First element: {data[0]}")
print(f"Slice [1:3]: {data[1:3]}")

# Element-wise operations
multiplied = data * phys([2, 2, 2, 2], 0.05)

# Operations with scalars
shifted = data + 10

Scalar-Array Transformations

# Unpacking array into individual quantities
voltages = phys([3.3, 5.0, 12.0], [0.1, 0.1, 0.2])
v1, v2, v3 = voltages

# Combining into array
combined = phys.concatenate([v1, v2, v3])

# Adding elements
measurements = phys(1.5, 0.1)
measurements.append(phys(1.6, 0.1))
measurements.append(phys(1.4, 0.1))

Sorting and Reordering

unsorted = phys([3, 1, 4, 2], [0.3, 0.1, 0.4, 0.2])

# Sorting
sorted_data = unsorted.sort()
print(f"Sort order: {unsorted.sort_order}")

# Using sorted property
print(f"Via sorted property: {unsorted.sorted}")

# Reordering
reordered = unsorted.in_order([2, 0, 3, 1])

Data Analysis with LabProcessor

Statistical Methods

lab = LabProcessor()

# Weighted mean
measurements = [phys(10.0, 0.1), phys(10.5, 0.2), phys(9.8, 0.15)]
weighted_avg = lab.weighted_mean(measurements)

# Least squares method
x_data = phys([1, 2, 3, 4], 0.1)
y_data = phys([2.1, 3.9, 6.2, 8.1], [0.2, 0.3, 0.25, 0.4])

k, b = lab.weighted_least_squares(x_data, y_data)

# Multiple datasets
x_sets = [phys([1, 2, 3], 0.1), phys([4, 5, 6], 0.1)]
y_sets = [phys([2, 4, 6], 0.2), phys([8, 10, 12], 0.2)]

k_multi, b_multi = lab.weighted_least_squares(x_sets, y_sets)

LaTeX Generation

# Tables
experiment_data = [
    phys(1.234e-6, 0.001e-6),
    phys(2.345e-6, 0.002e-6), 
    phys(3.456e-6, 0.003e-6)
]

table_latex = lab.latex_table(
    experiment_data, 
    header=["Measurement", "Value"], 
    exp=True
)

# Value formatting
resistance = phys(1.234e3, 0.015e3)
value_latex = lab.latex_value(resistance, name="R", exp=True)

# Scientific notation conversion
text_with_exp = "Resistance value 1.23e3 Ω at current 2.5e-2 A"
converted_text = lab.e_to_tex(text_with_exp)

Professional Visualization with Graph

Basic Usage

# Simple plot with approximation
x = phys([1, 2, 3, 4, 5], 0.1)
y = phys([2.1, 3.9, 6.0, 8.2, 9.8], [0.2, 0.3, 0.25, 0.4, 0.35])

g = graph(x, y, approx=True)
g.xlabel('Time, s')
g.ylabel('Velocity, m/s')
g.title('Velocity vs Time')
g.add_params_text()
g.show()

Multiple Data Series

# Multiple experiments with common X
x_common = phys([1, 2, 3, 4, 5], 0.1)

y_experiments = [
    phys([2.1, 3.9, 6.0, 8.2, 9.8], [0.2, 0.3, 0.25, 0.4, 0.35]),
    phys([1.8, 3.7, 5.8, 7.9, 9.5], [0.15, 0.25, 0.3, 0.35, 0.4]),
    phys([2.3, 4.1, 6.3, 8.5, 10.1], [0.25, 0.35, 0.2, 0.45, 0.3])
]

g = graph(x_common, y_experiments, approx=True)
g.xlabel('Voltage, V')
g.ylabel('Current, A') 
g.title('Current-Voltage Characteristics')
g.add_params_text(series_names=['Experiment 1', 'Experiment 2', 'Experiment 3'])
g.show()

Paired Datasets

# Independent X and Y sets
x_sets = [
    phys([1, 2, 3], 0.1),
    phys([4, 5, 6], 0.1)
]

y_sets = [
    phys([2, 4, 6], 0.2),
    phys([8, 10, 12], 0.2)
]

g = graph(x_sets, y_sets, approx=True)
g.xlabel('Distance, m')
g.ylabel('Force, N')
g.title('Dependencies for Different Conditions')
g.show()

Advanced Features

# Scientific style with method chaining
graph(x, y, approx=True)\
    .style_scientific()\
    .title('Experimental Dependency', fontsize=16)\
    .auto_legend(loc='upper left')\
    .add_stats(x=0.65, y=0.15)\
    .xlabel('$t$, s', fontsize=14)\
    .ylabel('$v$, m/s', fontsize=14)\
    .quick_save('experiment.png', dpi=300)

Practical Examples

Example 1: Experimental Data Processing

# Free fall acceleration experiment data
times = phys([0.1, 0.2, 0.3, 0.4, 0.5], 0.01)  # time, s
distances = phys([0.049, 0.196, 0.441, 0.784, 1.225], 
                [0.001, 0.002, 0.003, 0.004, 0.005])  # distance, m

# Acceleration calculation via LSM (s = gt²/2 => s ~ t²)
times_squared = times ** 2
k, b = lab.weighted_least_squares(times_squared, distances)

# Free fall acceleration g = 2k
g_experimental = 2 * k
print(f"Measured free fall acceleration: {g_experimental}")

# Visualization
graph(times_squared, distances, approx=True)\
    .xlabel('$t^2$, s²')\
    .ylabel('$s$, m')\
    .title('Free Fall Acceleration Determination')\
    .add_params_text()\
    .show()

Example 2: Statistical Processing

# Resistance measurement series
resistance_measurements = [
    phys(998, 5), phys(1002, 5), phys(995, 5),
    phys(1005, 10), phys(997, 5), phys(1001, 5)
]

# Statistical processing
mean_resistance = lab.weighted_mean(resistance_measurements)

# LaTeX report generation
report_table = lab.latex_table(
    resistance_measurements,
    header=['No.', 'Resistance, Ω'],
    first_column=list(range(1, 7)),
    caption='Resistance Measurement Results'
)

Example 3: Complex Physics Calculations

# Mathematical pendulum period calculation
length = phys(1.0, 0.01)  # length, m
g = phys(9.81, 0.01)     # gravitational acceleration, m/s²

# T = 2π√(L/g)
period = 2 * np.pi * sqrt(length / g)

# Length vs period dependency
lengths = phys(np.linspace(0.5, 2.0, 10), 0.02)
periods = 2 * np.pi * sqrt(lengths / g)

graph(lengths, periods)\
    .xlabel('Pendulum Length, m')\
    .ylabel('Oscillation Period, s')\
    .title('Period vs Length Dependency')\
    .show()

API Reference

Class phys

Constructor:

phys(value, abs_err=0.0)  # value: number, list, np.array

Properties:

• value - main value
• sigma - absolute uncertainty (read/write)
• eps - relative uncertainty (read/write)

Mathematical Operations:

• +, -, *, /, ** - with automatic uncertainty propagation
• Support for operations with numbers and other phys objects

Array Methods:

• sort(), sorted - sorting
• in_order(order) - reordering
• concatenate() - combining
• append() - adding elements

Class LabProcessor

Statistical Methods:

• weighted_mean(arr) - weighted average
• weighted_least_squares(x, y) - least squares method

LaTeX Generators:

• latex_table() - tables
• latex_value() - value formatting
• e_to_tex() - scientific notation conversion

Class graph

Main Methods:

• init(x, y, approx=True) - graph creation
• title(), xlabel(), ylabel() - styling
• add_params_text() - approximation parameters
• quick_save() - saving

Styles:

• style_scientific() - scientific style
• Full matplotlib compatibility

Conclusion

PhysLab provides complete toolkit for:

• Working with physical quantities and uncertainties
• Statistical processing of experimental data
• Professional results visualization
• Automatic scientific report generation

Perfect for educational projects, laboratory works, and scientific research.