Zephyr Scientific Library (zscilib)

The Zephyr Scientific Library (zscilib) is an attempt to provide a set of
functions useful for scientific computing, data analysis and data manipulation
in the context of resource constrained embedded hardware devices.

It is written entirely in C, and while the main development target for the
library is the Zephyr Project,
it tries to be as portable as possible, and a standalone reference project
is included to use this library in non-Zephyr-based projects.

This version of zscilib has been developed and tested against Zephyr 3.3.0.

Motivation

As the processing power of small, embedded MCUs increases and costs fall, more
computation can be done on the endnode itself. This allows for more of the
‘complex’ data analysis that used to take place at the PC or server level
(data aggregation, statistical analysis, etc.) to be done in less time,
using less data storage, and at a lower overall processing cost on small,
embedded devices.

A key goal of zscilib is to allow more data processing to happen on the
endnode.

By generating scientifically-relevant data points (standard SI units,
pre-filtered data, etc.) directly on the endnode, zscilib aims to be a bridge
between raw data and more numerically complex toolkits like gsl, numpy
or R.

What makes zscilib distinct?

Numerous high quality, mature, open source scientific libraries already exist:

• GNU scientific library (gsl)
• Lis (Library of Iterative Solvers for linear systems)
• CMSIS-DSP

Despite the wealth of mature functions in these existing libraries, though,
they tend to have the following two problems in an embedded context:

• They are overly broad and resource intensive (GSL, etc.), and thus aren’t
  appropriate for small, resource constrained devices like the ARM Cortex M
  family.
• They are missing many of the domain-specific features required to convert
  raw sensor data into actionable information (CMSIS-DSP, Lis).

The second item is of particular importance, since the goal of embedded systems
is often ‘sensing’ via raw data, correlating that data, and acting on the final
data points or passing them on for further analysis.

CMSIS-DSP contains a number of highly efficient algorithms for filtering
raw sensor data, but it doesn’t offer any domain-specific assistance converting
filtered accelerometer vectors into orientation data, for example, or reading
a set of photodiodes and converting that data into a useful photometric value
like lux. It is excellent at ‘conditioning’ data, but not at ‘understanding’ it.

zscilib aims to find a middle ground between these two, allowing for richer
processing of raw data, but within the confines and limitations of the class
of microcontrollers commonly used on low-cost sensor endnodes.

Quick Start: Standalone

A few makefile-based projects are included in samples/standalone showing
how zscilib can be used independent of Zephyr.

If you already have an appropriate GNU toolchain and build tools (make, etc.)
installed, you can simply execute the following commands:

$ cd samples/standalone/svd_pinv
$ make
$ bin/zscilib
  Hello, zscilib!
  ...

Quick Start: Zephyr RTOS

Running a sample application

To run one of the sample applications using qemu, run the following commands:

Be sure to run source zephyr/zephyr-env.sh (OS X or Linux) or
.\zephyr\zephyr-env.cmd (Windows) before the commands below! This also
assumes qemu-system-arm is available on your local system.

$ west build -p -b mps2/an521/cpu0 \
  modules/lib/zscilib/samples/matrix/mult -t run
...
*** Booting Zephyr OS build zephyr-v2.6.0-536-g89212a7fbf5f  ***
zscilib matrix mult demo

mtx multiply output (4x3 * 3x4 = 4x4):

14.000000 17.000000 20.000000 23.000000 
35.000000 44.000000 53.000000 62.000000 
56.000000 71.000000 86.000000 101.000000 
7.000000 9.000000 11.000000 13.000000 

Press CTRL+A then x to quit qemu.

Running Unit Tests

To run the unit tests for this library, run the following command:

$ twister --inline-logs -p mps2/an521/cpu0 -T modules/lib/zscilib/tests

See the tests folder for further details.

To run compliance tests to make sure submitted code matches Zephyr PR
requirements, run this (updating HEAD~2 for the number of commits to check,
or setting it to origin/master.. to check everything):

$ ../../../zephyr/scripts/ci/check_compliance.py \
  -m Gitlint -m Identity -m Nits -m pylint -m checkpatch \
  -c HEAD~2..

Debugging with QEMU

If you wish to debug using QEMU (and with minor variation actual hardware),
you can run the following commands to start a new GDB debug session.

For an overview of debugging in GDB, you may find the following presentation
useful: LVC21-308: Essential ARM Cortex-M Debugging with GDB

In one terminal window, run:

$ west build -p auto -b mps2/an521/cpu0 modules/lib/zscilib/samples/matrix/pinv

Once the ELF file has been built, we can start a GDB server on the default
1234 socket, and wait for a new connection via:

$ cd build
$ ninja debugserver

In a new terminal window, connect to the GDB server via:

$ cd <zephyr_path>
$ arm-none-eabi-gdb-py \
  --eval-command="target remote localhost:1234" \
  --se=build/zephyr/zephyr.elf

The -py extension is optional, and makes use of a version of GDB from the
ARM GNU toolchain releases that enables Python scripts to be used with your
debug sessions. See the LVC21-308 presentation at the top of this
section for details.

From here, you can start debugging with the (gdb) prompt.

For example:

(gdb) b main
(gdb) c
Continuing.

Breakpoint 1, main () at modules/lib/zscilib/samples/matrix/pinv/src/main.c:70
70              printf("\n\nzscilib pseudo-inverse demo\n\n");
(gdb) n
72              pinv_demo();
(gdb) step
pinv_demo () at modules/lib/zscilib/samples/matrix/pinv/src/main.c:25
25              zsl_real_t vi[18 * 3] = {
(gdb) n
... 
(gdb) quit

Floating-Point Usage

zscilib can be configured to make use of single-precision (32-bit) or
double-precision (64-bit) floating point values via the
CONFIG_ZSL_SINGLE_PRECISION flag, which will determine the size of
zsl_real_t used throughout the library. The default setting for this
flag is n, meaning 64-bit values are used by default.

There is a tradeoff between the added range and precision that 64-bit
(double-precision) floating point values offer, and the memory and performance
gains of the smaller, less-precise but faster 32-bit (single-precision)
operations.

Due to the reduced precision of single-precision values, certain complex
functions in zscilib are only available when double-precision is enabled
(PINV, SVD, etc.).

Comparison

Single-Precision (32-bit) Floats

• Require 4 bytes of memory to store
• Have about 7 significant digits of precision
• Have a range of about 1.E-36 to 1.E+36
• HW acceleration available on Cortex-M4F, Cortex-M7 and most Cortex-M33 MCUs.
• Generates smaller, more efficient code than double

Double-Precision (64-bit) Floats

• Requires 8 bytes of memory to store
• Have about 13 significant digits of precision
• Have a range of about 1.E-303 to 1.E+303
• HW acceleration generally only available on large, Cortex-M7 MCUs
• Generates larger code, with more processing overhead per operation

Float Stack Usage in Zephyr

The sample code in this library typically has the CONFIG_FPU option set,
meaning that floating-point support is configured for
Unshared FP registers mode. This mode is used when the application
has a single thread that uses floating point registers.

If your application makes use of multiple threads, and more than one of
these threads uses floating-point operations, you should also enable the
CONFIG_FPU_SHARING config flag, which configures the kernel for
Shared FP registers mode. In this mode, the floating point registers are
saved and restored during each context switch, even when the associated threads
are not using them. This feature comes at the expense of an extra 72 bytes of
stack memory per stack frame (s0..s15 + FPCSR, plus an alignment word
to ensure that the stack pointer is double-word aligned).

Current Features

Features marked with the
v0.2.0 flag are in progress
or planned as part of the current release cycle, and may be partially
implemented or stubbed at present.
v0.3.0 indicates features planned for that later release.

Linear Algebra

Vector Operations

• f32: Single-precision floating-point operations
• f64: Double-precision floating-point operations
• ARM: Optimised Arm Thumb-2 ASM implementation

Feature	Func	f32	f64	Arm	Notes
Array to vector	zsl_vec_from_arr	x	x
Copy	zsl_vec_copy	x	x
Get subset	zsl_vec_get_subset	x	x
Add	zsl_vec_add	x	x
Subtract	zsl_vec_sub	x	x
Negate	zsl_vec_neg	x	x
Sum	zsl_vec_sum	x	x		2 or more vects
Scalar add	zsl_vec_scalar_add	x	x
Scalar multiply	zsl_vec_scalar_mult	x	x
Scalar divide	zsl_vec_scalar_div	x	x
Distance	zsl_vec_dist	x	x		Between 2 vects
Dot product	zsl_vec_dot	x	x
Norm/abs value	zsl_vec_norm	x	x
Project	zsl_vec_project	x	x
To unit vector	zsl_vec_to_unit	x	x
Cross product	zsl_vec_cross	x	x
Sum of squares	zsl_vec_sum_of_sqrs	x	x
Comp-wise mean	zsl_vec_mean	x	x
Arithmetic mean	zsl_vec_ar_mean	x	x
Reverse	zsl_vec_rev	x	x
Zero to end	zsl_vec_zte	x	x		0 vals to end
Equality check	zsl_vec_is_equal	x	x
Non-neg check	zsl_vec_is_nonneg	x	x		All values >= 0
Contains	zsl_vec_contains	x	x
Quicksort	zsl_vec_sort	x	x
Print	zsl_vec_print	x	x

Matrix Operations

• f32: Single-precision floating-point operations
• f64: Double-precision floating-point operations
• ARM: Optimised Arm Thumb-2 ASM implementation

Feature	Func	f32	f64	Arm	Notes
Array to matrix	zsl_mtx_from_arr	x	x
Copy	zsl_mtx_copy	x	x
Get value	zsl_mtx_get	x	x
Set value	zsl_mtx_set	x	x
Get row	zsl_mtx_get_row	x	x
Set row	zsl_mtx_set_row	x	x
Get col	zsl_mtx_get_col	x	x
Set col	zsl_mtx_set_col	x	x
Add	zsl_mtx_add	x	x
Add (d)	zsl_mtx_add_d	x	x		Destructive
Sum rows	zsl_mtx_sum_rows_d	x	x		Destructive
Sum rows scaled	zsl_mtx_sum_rows_scaled_d	x	x		Destructive
Subtract	zsl_mtx_sub	x	x
Subtract (d)	zsl_mtx_sub_d	x	x		Destructive
Multiply	zsl_mtx_mult	x	x
Multiply (d)	zsl_mtx_mult_d	x	x		Destructive
Multiply sc (d)	zsl_mtx_scalar_mult_d	x	x		Destructive
Multiple row sc (d)	zsl_mtx_scalar_mult_row_d	x	x		Destructive
Transpose	zsl_mtx_trans	x	x
Adjoint 3x3	zsl_mtx_adjoint_3x3	x	x
Adjoint	zsl_mtx_adjoint	x	x
Wedge product	zsl_mtx_vec_wedge		x
Reduce	zsl_mtx_reduce	x	x		Row+col removal
Reduce (iter)	zsl_mtx_reduce_iter	x	x		Iterative ver.
Augment	zsl_mtx_augm_diag	x	x		Adds row+col(s)
Determinant 3x3	zsl_mtx_deter_3x3	x	x
Determinant	zsl_mtx_deter	x	x
Gaussian El.	zsl_mtx_gauss_elim	x	x
Gaussian El. (d)	zsl_mtx_gauss_elim_d	x	x		Destructive
Gaussian Rd.	zsl_mtx_gauss_reduc	x	x
Column norm.	zsl_mtx_cols_norm	x	x		Unitary col vals
Gram-Schimdt	zsl_mtx_gram_schmidt	x	x
Elem. norm.	zsl_mtx_norm_elem	x	x		Norm vals to i,j
Elem. norm. (d)	zsl_mtx_norm_elem_d	x	x		Destructive
Invert 3x3	zsl_mtx_inv_3x3	x	x
Invert	zsl_mtx_inv	x	x
Balance	zsl_mtx_balance	x	x
Householder Ref.	zsl_mtx_householder	x	x
QR decomposition	zsl_mtx_qrd	x	x
QR decomp. iter.	zsl_mtx_qrd_iter		x
Eigenvalues	zsl_mtx_eigenvalues		x
Eigenvectors	zsl_mtx_eigenvectors		x
SVD	zsl_mtx_svd		x
Pseudoinverse	zsl_mtx_pinv		x
Min value	zsl_mtx_min	x	x
Max value	zsl_mtx_max	x	x
Min index	zsl_mtx_min_idx	x	x
Max index	zsl_mtx_max_idx	x	x
Equality check	zsl_mtx_is_equal	x	x
Non-neg check	zsl_mtx_is_notneg	x	x		All values >= 0
Symmetr. check	zsl_mtx_is_sym	x	x
Print	zsl_mtx_print	x	x

Unary matrix operations

The following component-wise unary operations can be executed on a matrix
using the zsl_mtx_unary_op function:

• [x] Increment (++)
• [x] Decrement (--)
• [x] Negative (-)
• [x] Logical negation (!)
• [x] Round
• [x] Abs
• [x] Floor
• [x] Ceiling
• [x] Exponent
• [x] Natural log
• [x] Log10
• [x] Square root
• [x] Sin, cos, tan
• [x] Asin, acos, atan
• [x] Sinh, cosh, tanh

Binary matrix operations

The following component-wise binary operations can be executed on a pair
of symmetric matrices using the zsl_mtx_binary_op function:

• [x] Add (a + b)
• [x] Subtract (a - b)
• [x] Multiply (a * b)
• [x] Divide (a / b)
• [x] Mean (mean(a, b)
• [x] Exponent (a^b)
• [x] Min (min(a, b))
• [x] Max (max(a, b))
• [x] Equal (a == b)
• [x] Not equal (a != b)
• [x] Less than (a < b)
• [x] Greater than (a > b)
• [x] Less than or equal to (a <= b)
• [x] Greater than or equal to (a >= b)

NOTE: Component-wise unary and binary matrix operations can also
make use of user-defined functions at the application level if the existing
operand list is not sufficient. See zsl_mtx_unary_func and
zsl_mtx_binary_func for details.

Numerical Analysis

Statistics

• [x] Mean
• [x] Trimmed mean
• [x] Weighted mean
• [x] Time-weighted mean
• [x] De-mean
• [x] Percentile (AKA quantile)
• [x] Median
• [x] Weighted median
• [x] Quartile
• [x] Interquartile range
• [x] Mode
• [x] Data range
• [x] Mean absolute deviation
• [x] Median absolute deviation from median
• [x] Variance
• [x] Standard deviation
• [x] Covariance
• [x] Covariance matrix
• [x] Linear regression
• [x] Multiple linear regression [1]
• [x] Weighted multiple minear regression [1]
• [x] Quadrid fitting (Least-squars fitting of a quadric surface) [1]
• [x] Absolute error
• [x] Relative error
• [x] Standard error

[1] Only available in double-precision

Probability Operations

• [X] Uniform probability density function (PDF)
• [X] Uniform distribution mean
• [X] Uniform distribution variance
• [X] Uniform cumulative distribution function (CDF)
• [X] Normal probability density function (PDF)
• [X] Normal cumulative distribution function (CDF)
• [X] Inverse Error function
• [X] Inverse normal cumulative distribution function (CDF)
• [x] Factorial
• [X] Binomial coefficient
• [X] Binomial probability density function (PDF)
• [X] Binomial distribution mean
• [X] Binomial distribution variance
• [X] Binomial cumulative distribution function (CDF)
• [X] Information entropy
• [x] Bayes’ Theorem

Interpolation

• [x] Nearest neighbour (AKA ‘piecewise constant’)
• [x] Linear (AKA ‘piecewise linear’)
• [x] Natural cubic spline

Physics

Atomic

• [x] Nuclear radius
• [x] Atomic Radioactive decay
• [x] Bohr orbital radius
• [x] Bohr orbital velocity
• [x] Bohr orbital energy
• [x] Bragg’s law

Dynamics

• [x] Newton’s second law
• [x] Mass-acceleration relationship
• [x] Friction (Fn, uK/s)
• [x] Normal force on an incline (in newtons based on mass, gravity, angle)
• [x] Tension
• [x] Dynamic lever
• [x] Pendulums
  • [x] Period
  • [x] Max Speed

Electrical Components

• [x] Capacitance
  • [x] Charge, voltage
  • [x] Area, distance
• [x] Energy stored in capacitor
• [x] Energy stored in inductor
• [x] Transformer turns to voltage
• [x] Resistor/inductor/capacitor voltage relationship
• [x] Resistor/capacitor charge/discharge
  • [x] Current during charge
  • [x] Current during discharge
  • [x] Charge (in coulombs) during charge
  • [x] Charge (in coulombs) during discharge
• [x] Current of RL circuit in time

Electric

• [x] Coulomb’s law
• [x] Charge density
• [x] Potential energy
• [x] Electric field
• [x] Coulombs potential
• [x] Electric flux
• [x] Force from a charge

Electricity

• [x] Current (charge per second)
• [x] Resistors in series/parallel
• [x] Capacitors in series/parallel
• [x] Resistivity of wire
• [x] Ohm’s law
• [x] Power
  • [x] Current, voltage
  • [x] Voltage, resistance
  • [x] Current, resistance

Energy

• [x] Kinetic energy
• [x] Elastic potential energy
• [x] Gravitational potential energy
• [x] Power (work/energy over time)
• [x] Energy lost to friction
• [x] Energy of a photon
• [x] Mechanical energy of a system
• [x] Total energy of a system

Fluids

• [x] Density (of substance in Kg/m^2)
• [x] Simple pressure (force, area)
• [x] Pressure in a fluid (at a certain height/depth, gravity, density, surf. pres.)
• [x] Bouyant Force
• [x] Fluid flow rate proportion
• [x] Fluid force rate proportion
• [x] Bernoulli’s equation
• [x] Volume flow rate

Gases

• [x] Average velocity of a gas molecule (mass, temp, moles)
• [x] Ideal gas law (pressure based on moles, temp, volume)
• [x] Boyle’s law (relationship of pressure, volume)
• [x] Charles/Gay-Lussac law (relationship of pressure, volume)

Gravitation

• [x] Orbital period
• [x] Escape velocity
• [x] Gravitational acceleration
• [x] Orbital velocity
• [x] Gravitational force
• [x] Gravitational potential energy

Kinematics

• [x] Change in distance (initial velocity, time, acceleration)
• [x] Initial position (final pos, init velocity, accel, time)
• [x] Initial position (final pos, init velocity, final velocity, accel)
• [x] Change in time (initial and final velocity, acceleration)
• [x] Instantaneous velocity (initial velocity, time, acceleration)
• [x] Velocity (initial velocity, distance, acceleration)
• [x] Average velocity (distance, time)
• [x] Acceleration (initial and final velocity, time)
• [x] Centripetal acceleration (radius, period, via radius/speed or radius/period)

Magnetics

• [x] Magnetic force
• [x] Force on current carrying wire
• [x] Torque on current loop
• [x] Potential energy from a dipole
• [x] Orbital radius in magnetic field
• [x] Magnetic flux
• [x] Magnetic moment

Mass

• [x] Calculate the CoM of a group of objects based on their mass and
  distance from an arbitrary point

Momentum

• [x] Calculate momentum (mass, velocity)
• [x] Impulse (force, time)
• [x] Change in momentum/force (mass, initial and final velocity)
• [x] Elastic collision (when two objects collide and bounce)
• [x] Inelastic collision (when two objects collide and stick)

Optics

• [x] Refraction index
• [x] Snell’s law
• [x] Focus distance
• [x] Critical angle of incision
• [x] Power (based on focal length)
• [x] Magnification (real and apparent length)
• [x] Diffraction

Photons

• [x] Energy
• [x] Linear momentum
• [x] Wavelength
• [x] Frequency
• [x] Kinetic energy of photoelectric effect

Projectiles

• [x] Horizontal and vertical velocity components (initial velocity, theta)
• [x] Total time of flight
  • Formula 1: gravity, y2, y1, Vy
  • Formula 2: initial and final vertical velocity and gravity
• [x] Vertical motion: position at time (Vy, gravity, time, initial height)
• [x] Horizontal motion: horizontal change of distance at time
• [x] Velocity (overall velocity from vertical and horizontal components)
• [x] Trajectory
• [x] Theta (angle between vertical and horizontal velocity)
• [x] Range (distance travelled from ground using initial velocity, gravity, angle)

Relativity (v0.3.0)

• [ ] Time dilatation
• [ ] Lorentz contraction
• [ ] Relativistic momentum
• [ ] Kinetic energy
• [ ] Mass to energy
• [ ] Lorenz velocity transformation
• [ ] Relativistic doppler affect

Rotation

• [x] Change in theta (analog to distance in kinematics)
• [x] Distance travelled in circular motion
• [x] Number of rotations around circle
• [x] Change in time (analog to time in kinematics)
• [x] Instantaneous angular velocity
• [x] Angular velocity
• [x] Average angular velocity
• [x] Angular acceleration
• [x] Rotational kinetic energy
• [x] Rotational period
• [x] Rotational frequency
• [x] Centripetal acceleration
• [x] Total acceleration
• [x] Mechanical power (torque multiplied by angular velocity)

Sound

• [x] Pressure amplitude
• [x] Decibels (sound level between two intensities of the same frequency)
• [x] Intensity (pressure amplitude, bulk modulus, density)
• [x] Shock wave angle (speed of sound and velocity through medium)
• [x] Doppler effect
• [x] Beats (frequency resulting from overlap of two similar frequencies)

Thermodynamics

• [x] Temperature conversion (fahrenheit, celsius, kelvin)
• [x] Latent heat of fusion/vaporisation
• [x] Heat (in joules of a material based on mass, specific heat and delta temp)
• [x] Linear expansion of metal (length, alpha constant, change in temperature)
• [x] Mean free path
• [x] Efficiency of a heat engine (based on energy of hot and cold chambers)
• [x] Carnot engine proportion

Waves

• TBD

Work

• [x] Work done over an interval of distance and constant applied force
• [x] Work done cosine (as above but with x-component or on an incline)
• [x] Work done sine (as above but with y-component or on an incline)
• [x] Work-KE theorem

Motion and Orientation

AHRS/Attitude (Degrees)

• [x] Basic struct definitions
• [x] Conversion
  • [x] To vector (access vector API)
  • [x] To Euler (degrees to radian)
  • [x] From Euler (radians to degrees)
  • [x] From Accel + Mag (roll, pitch, yaw)
  • [x] From Accel (roll, pitch)
• [x] Angle between two accelerometers

Compass

• [x] Degrees, Minutes, Seconds to Decimal Degrees (dms to dd)
• [x] Magnetic north
• [x] Geographic (AKA true) north

Euler Angles (Radians)

• [x] Basic struct definitions
• [x] Conversion
  • [x] To vector (access vector API)

Gravity

• [x] Gravitational field from latitude and altitude

Quaternions

• [x] Basic struct definitions
• [x] Magnitude
• [x] Unit check
• [x] Scaling
• [x] Multiplication
• [x] Exp
• [x] Log
• [x] Exponentiation
• [x] Conjugate
• [x] Inverse
• [x] Difference
• [x] Rotate
• [x] Interpolation
  • [x] Lerp
  • [x] Slerp
• [x] Integration
  • [x] Angular velocity (rad/s + time + current value)
  • [x] Angular momentum (Same as above, plus rotational mass)
• [x] Conversion
  • [x] To unit (Normalise)
  • [x] To Euler (radians)
  • [x] From Euler (radians)
  • [x] To rotation matrix
  • [x] From rotation matrix
  • [x] To axis-angle
  • [x] From axis-angle
• [x] Special Forms
  • [x] Identity

Sensor Fusion

• [x] Define generic fusion interface/struct (accel+mag+gyro -> quaternion)
• [x] Matrix rotation (adjust device orientation)
• [x] Axis-angle rotation (adjust device orientation)
• [x] Calibration
  • [x] Magnetometer (hard-iron and soft-iron errors)
  • [x] Correct magnetometer (apply correction coefficients)
  • [x] Madgwick calibration
  • [x] Mahoney calibration
• [x] Implementations
  • [x] AQUA
  • [x] Complementary
  • [x] Extended Kalman
  • [x] Madgwick
  • [x] Mahoney
  • [x] SAAM

Colorimetry

Types/Structs

• [x] Spectral power distribution (SPD)
• [x] CIE 1931 XYZ tristimulus
• [x] CIE 1931 xyY chromaticity
• [x] CIE 1960 UCS chromaticity
• [x] CIE 1976 UCS chromaticity
• [x] RGBA color using floating-space notation (0.0 … 1.0)
• [x] RGBA color using 8-bit values
• [x] RGBA color using 16-bit values
• [x] CIE 1960 CCT, Duv value pair
• [x] CIE 1931 XYZ tristimulus values for a standard illuminant
• [x] CIE 1931 XYZ tristimulus values for a standard observer model

Functions

• [x] SPD normalisation
• [x] SPD to XYZ tristimulus
• [x] CIE 1931 xyY chromaticity to XYZ tristimulus
• [x] CIE 1931 XYZ tristimulus values to xyY chromaticity
• [x] CIE 1931 xyY chromaticity to CIE 1960 uv
• [x] CIE 1931 XYZ tristimulus to CIE 1960 uv
• [x] CIE 1960 uv to CIE 1931 XYZ tristimulus
• [x] CIE 1960 uv to CIE 1931 xyY chromaticity
• [x] CIE 1960 uv to CIE 1976 u’v’
• [x] CIE 1976 u’v’ value to CIE 1960 uv
• [x] Color temperature to (u,v) chromaticity
• [x] CIE 1960 CCT (Duv = 0.0) to CIE 1931 XYZ tristimulus
• [x] CIE 1960 CCT (Duv = 0.0) to 8-bit RGBA (supplied XYZ to RGB color space correlation matrix)
• [x] CIE 1960 CCT (Duv = 0.0) to float RGBA (supplied XYZ to RGB color space correlation matrix)
• [x] CIE 1960 CCT and Duv pair to CIE 1931 xyY chromaticity
• [x] CIE 1960 CCT and Duv pair to CIE 1931 XYZ tristimulus
• [x] CIE 1960 (u, v) pair to CIE 1960 CCT and Duv pair using:
  • [x] McCamy
  • [x] Ohno 2014
• [x] CIE 1931 XYZ tristimulus to 8-bit RGBA (supplied XYZ to RGB color space correlation matrix)
• [x] CIE 1931 XYZ tristimulus to float RGBA (supplied XYZ to RGB color space correlation matrix)
• [ ] Gamma encode
• [ ] Gamma decode

Color Data

Illuminants

• [x] A
• [x] B
• [x] C
• [x] D50
• [x] D55
• [x] D65
• [x] E
• [x] ICC

CIE Standard Observer Models

• [x] CIE 1931 2 degree standard observer color matching functions
• [x] CIE 1964 10 degree standard observer color matching functions

CIE Luminous Efficiency Functions

• [x] CIE 1988 Photopic
• [x] CIE 1951 Scotopic
• [x] CIE LERP interpolation helper function

XYZ to RGB Color Space Correlation Matrices

• [x] XYZ to linear sRGB (D65)
• [x] XYZ to linear sRGB (D50)
• [x] XYZ to Adobe RGB 98
• [x] XYZ to Sony S-Gamut3.cine D65
• [x] XYZ to NTSC
• [x] XYZ to PAL/SECAM
• [x] XYZ to ITU-R BT.709
• [x] XYZ to ITU-R BT.2020
• [x] XYZ to ACES Primaries #0 (AP0)
• [x] XYZ to ACES Primaries #1 (AP1)
• [x] XYZ to DCI-P3
• [x] XYZ to DCI-P3+
• [x] XYZ to CIE RGB

Chemistry

• [ ] Periodic table data including:
  • [ ] Full name
  • [ ] Abbreviation
  • [x] Atomic number
  • [x] Standard atomic weight

Measurement API (v0.2.0)

The zsl_measurement struct is a proof of concept attempt at representing
measurements in a concise but unambiguous manner.

It consists of:

• A measurement type (Base Type + Extended Type)
• The SI unit it uses (SI Unit Type)
• The specific C type used to represent it in memory (C Type)
• Additional meta-data to help interpret the measurement payload

There is an option to adjust the measurement’s scale in +/- 10^n steps
(Scale Factor) from the default SI unit and scale indicated by the SI Unit
Type. For example, if ‘Ampere’ is indicated as the SI unit, the measurement
could indicate that the value is in uA by setting the scale factor to -6.

• [x] Measurement struct(s) (see: zsl_measurement)
• [x] Base Measurement Types
• [ ] Extended Measurement Types
  • [x] Color
  • [x] Light
  • [x] Temperature
  • [ ] Other groups TBD
• [x] SI Units
• [x] SI Scales
• [x] C Types

Longer Term Planned Features

Help is welcome on the following planned or desirable features.

Scalar Operations

• Fast trigonometry approximations

Digital Signal Processing (v0.3.0)

• Simple moving average filter
• Windowed moving average filter
• Weighted moving average filter
• Other basic IIR and FIR-type filters and helper functions.

Spectrometry

• Conversion between radiometric and photometric units
• Radiometric data to lux
• Radiometric data to CCT/Duv
• Spectral analysis

Calibration

• Offset management
• Correlation matrix generation
• Non-linear compensation

Architecture-Specific Optimisations

Basic tooling has been added to allow for optimised architecture-specific
implementations of key functions in assembly.

At present, this feature isn’t being actively used or developed, but an aim
of zscilib is to add optimised versions of key functions to try to get the
best possible performance out of limited resources.

Initial optimisation will target the Arm Cortex-M family of devices and the
Thumb and Thumb-2 instruction sets, though other architectures can be
accommodated if necessary or useful.

Code Style

Since the primary target of this codebase is running as a module in
Zephyr OS, it follows the same coding style, which is itself
based on the Linux kernel coding style.

You can format the source code to match this style automatically using the
uncrustify command line tool, which has plugins available for many
common text editors (Atom Beautify, for example).

• Crustify rules file

Contributing

If you wish to contribute to this library, you can raise a PR as follows:

1. Fork the repository: https://github.com/zephyrproject-rtos/zscilib/fork
2. git clone your forked repository.
3. Update your local repo and commit any changes.
4. Push the changes out to your fork on Github.
5. Navigate to https://github.com/zephyrproject-rtos/zscilib and to the
   right of the Branch menu click New pull request.
6. Fill out the form that is presented.
7. Click the Create Pull Request button to submit the PR.

Also have a look at the Issues page to see if there is any outstanding
work or issues that you might be able to help with!

License

Apache 2.0.