mt.glm.linear

Additional functions for PyGLM

Reimplementation of MT’s GLSL implementation of some linear algebra functions in 3D.

Source: CRL_oven/assets/glsl/linear.glsl

Functions

  • mat3diag(): Constructs a 3x3 diagonal matrix.

  • diag3(): Extracts the diagonal vector of a 3x3 matrix.

  • sort3(): Sorts 3 elements in descending order in-place.

  • cbrt(): Cubic root.

  • solveCubic(): Solves cubic polynomial in-place.

  • ldu3(): Computes the LDUP decomposition (LU with partial pivoting) in-place

  • lduBSolve3(): Does the backward-solve step, or U*x = y

  • evd3(): Eigenvalue decomposes a symmetric positive semidefinite 3x3 matrix

  • svd3(): Singularvalue decomposes a 3x3 matrix.

  • sop3(): Finds the nearest rotation.

  • mat2diag(): Constructs a 2x2 diagonal matrix.

  • diag2(): Extracts the diagonal vector of a 2x2 matrix.

  • rot2(): Gets a 2D rotation matrix given the rotation angle in radian.

  • svd2(): Singularvalue decomposes a 2x2 matrix.

  • evd2(): Eigenvalue decomposes a symmetric positive semidefinite 2x2 matrix

mt.glm.linear.mat3diag(x: vec3) → mat3x3

Constructs a 3x3 diagonal matrix.

mt.glm.linear.diag3(x: mat3x3) → vec3

Extracts the diagonal vector of a 3x3 matrix.

mt.glm.linear.sort3(x: vec3) → vec3

Sorts 3 elements in descending order in-place.

mt.glm.linear.cbrt(x: float) → float

Cubic root.

mt.glm.linear.solveCubic(c: vec3) → vec3

Solves cubic polynomial in-place.

Given polynomial: c[0] + c[1]*x + c[2]*x^2 + x^3 = 0, assuming it has 3 real roots, find the roots and store them in c[0], c[1], c[2].

mt.glm.linear.ldu3(A: mat3x3) → Tuple[mat3x3, ivec3]

Computes the LDUP decomposition (LU with partial pivoting) in-place

Parameters:

A (glm.mat3) – the input and output matrix

Returns:

  • A (glm.mat3) – the input and output matrix

  • P (glm.ivec3) – the output pivoting integer vector

mt.glm.linear.lduBSolve3(y: vec3, LDU: mat3x3, P: ivec3) → vec3

Does the backward-solve step, or U*x = y

mt.glm.linear.evd3(A: mat3x3) → Tuple[mat3x3, vec3]

Eigenvalue decomposes a symmetric positive semidefinite 3x3 matrix

Compute: A = V mat3diag(S) V.T. Eigenvalues are sorted in the descending order.

Parameters:

A (glm.mat3) – input 3x3 matrix

Returns:

  • V (glm.mat3) – output rotation matrix

  • S (glm.vec3) – output diagonal vector

mt.glm.linear.svd3(A: mat3x3, thr: float = 1e-06) → Tuple[mat3x3, vec3, mat3x3]

Singularvalue decomposes a 3x3 matrix.

Compute A = U mat3diag(S) V^T. Singularvalues are sorted in descending order.

Parameters:

  • A (glm.mat3) – input 3x3 matrix

  • thr (float) – small threshold for computing the rank

Returns:

  • U (glm.mat3) – output rotation matrix

  • S (glm.vec3) – output diagonal vector

  • V (glm.mat3) – output rotation matrix

mt.glm.linear.sop3(A: mat3x3) → mat3x3

Finds the nearest rotation.

mt.glm.linear.mat2diag(x: vec2) → mat2x2

Constructs a 2x2 diagonal matrix.

mt.glm.linear.diag2(x: mat2x2) → vec2

Extracts the diagonal vector of a 2x2 matrix.

mt.glm.linear.rot2(angle: float) → mat2x2

Gets a 2D rotation matrix given the rotation angle in radian.

mt.glm.linear.svd2(A: mat2x2) → vec4

Singularvalue decomposes a 2x2 matrix.

Compute A = U mat2diag(S) V^T. Singularvalues are sorted in descending order.

Source from here

Parameters:

A (glm.mat2) – input 2x2 matrix

Returns:

Parameter (s1, s2, u, v) where A = rot2(u) * mat2diag(s1, s2) * rot2(-v).

Return type:

glm.vec4

mt.glm.linear.evd2(A: mat2x2) → vec3

Eigenvalue decomposes a symmetric positive semidefinite 2x2 matrix

Compute: A = V mat2diag(S) V.T. Eigenvalues are sorted in the descending order.

Parameters:

A (glm.mat2) – input 2x2 matrix

Returns:

Parameter (s1, s2, u) where A = rot2(u) * mat2diag(s1, s2) * rot2(-u).

Return type:

glm.vec3