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m2_svd

m2_svd(U, S, V, sig, m)​

Performs Singular Value Decomposition (SVD) on a 2x2 matrix, optimized for MLS-MPM.

This function computes the SVD of a 2x2 matrix m such that m = U * Σ * V^T, where:

  • U is a 2x2 orthogonal matrix (rotation).
  • Σ (sig) is a 2x2 diagonal matrix containing the singular values.
  • V is a 2x2 orthogonal matrix (rotation).

The function modifies U, sig, and V in-place. The input matrix m and the intermediate matrix S are overwritten during the computation. The algorithm uses a closed-form solution and optimizations specific to 2x2 matrices, making it very fast. It also handles the case where the off-diagonal elements of the intermediate matrix S are close to zero, simplifying calculations. The results are transposed, consistent with the Taichi programming language.

Kind: global function

ParamTypeDescription
UArray.<number>Output: 2x2 orthogonal matrix (rotation), stored as a flattened array [c, s, -s, c]. Modified in-place.
SArray.<number>Output: Intermediate 2x2 matrix, overwritten during calculation. Modified in-place.
VArray.<number>Output: 2x2 orthogonal matrix (rotation), stored as a flattened array. Modified in-place.
sigArray.<number>Output: 2x2 diagonal matrix containing singular values, stored as a flattened array [σ1, 0, 0, σ2]. Modified in-place.
mArray.<number>Input: 2x2 matrix, stored as a flattened array [a, b, c, d], representing [[a, c], [b, d]]. Will be overwritten.