This is an implementation of the method described in Computing the Singular Value Decomposition of 3x3 matrices with minimal branching and elementary floating point operations, based on an implementation by Eric Jang. I've updated the syntax of the library to reflect a more modern c++ style, and included Python bindings & unit tests.

Just include the header file and you are good to go!

#include "svd3.h"
double a[3][3] = {
  {-0.558253, -0.0461681, -0.505735},
  {-0.411397, 0.0365854, 0.199707},
  {0.285389, -0.313789, 0.200189}
};

double u[3][3], s[3][3], v[3][3];

svd(a, u, s, v);

Import the svd method from the library.

from svd3x3 import svd

a = [
    [-0.558253, -0.0461681, -0.505735],
    [-0.411397, 0.0365854, 0.199707],
    [0.285389, -0.313789, 0.200189],
]
svd(a)

Benchmarks for the C and Python APIs can be run as follows:

# Python
python -c "import svd3x3; svd3x3._bench()"

# C++
clang++ -O3 bench.cpp -o bench # To benchmark the original library, set -DBENCH_ORIGINAL
ulimit -s 65500 # Required to prevent stack overflow, otherwise decrease N_SAMPLES
./bench

All execution time tests were evaluated on an M1 Pro, with CPU temperature maintained below 55°C for the entire duration.

Our implementation is both faster and more accurate than the original C source despite using double precision, and is significantly faster than Numpy. Note that the original source code was reported to run a factor of 4 faster than this (although they may be counting throughput via SIMD intrinsics rather than raw time per computation).

MIT License, Eric V. Jang 2014, Jenna Bradley 2025