vanish87 / svd3

Fast singular value decomposition, diagonalization, QR decomposition of 3x3 matrices.

Fast 3x3 SVD

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". I implemented this as part of a group project for a computer graphics course.

Execution time per svd call on the CPU is about 2.0 microseconds. Tested on a AMD Phenom(tm) II X4 965 Processor.

Execution time on the GPU is about 174 microseconds. Tested on a NVIDIA GeForce GTX 460 (profiled using nvvp).

Also included are routines for diagonalization / QR decomposition of 3x3 matrices, which may be useful in their own right.

##Usage

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

#include "svd3.h"
float a11, a12, a13, a21, a22, a23, a31, a32, a33;

a11= -0.558253; a12 = -0.0461681; a13 = -0.505735;
a21 = -0.411397; a22 = 0.0365854; a23 = 0.199707;
a31 = 0.285389; a32 =-0.313789; a33 = 0.200189;

float 	u11, u12, u13, 
		u21, u22, u23, 
		u31, u32, u33;

float 	s11, s12, s13, 
		s21, s22, s23, 
		s31, s32, s33;

float 	v11, v12, v13, 
		v21, v22, v23, 
		v31, v32, v33;

svd(a11, a12, a13, a21, a22, a23, a31, a32, a33,
    u11, u12, u13, u21, u22, u23, u31, u32, u33,
    s11, s12, s13, s21, s22, s23, s31, s32, s33,
    v11, v12, v13, v21, v22, v23, v31, v32, v33);

See the included Mathematica notebook for derivations of numerical shortcuts.

License

MIT License, Eric V. Jang 2014