Looking for feature requests related to small matrices

[FantasyVR]

In many engineering fields, we need to use functions related to small matrices (2x2 or 3x3) such as single value decomposition (SVD), eigendecomposition, and more. Some are already implemented in Taichi shown in the following table.

Vector	Matrix
V.normalized()	ti.polar_decompose(M)
V.norm()	ti.svd(M)
V.norm_inv()	ti.sym_eig(M)
V.norm_sqr()	ti.eig(M)
V.sum()	ti.solve(M, b)
V1.dot(V2)	M.norm()
V1.cross(V2)	M.norm_inv()
	M.norm_sqr()
	M.sum()
	M.transpose()
	M.determinant()
	M.trace()

Note : V for vector, M for matrix

But we feel that there may be functions that are needed in areas we are unaware of. In that spirit, we'd like to hear more from the community.

If you ever tried to implement a feature by yourself, chances are high that many people in the community also need it. We encourage you to bring up relevant features to this discussion. Together, we will implement these wanted small linear algebra functions to make our Taichi kernels easier to write.

[eatcosmos]

Any recommendations for books for teaching how to write code of matrix from scratch without calling exsited libary

[FantasyVR]

Hi @eatcosmos , I think this doc is good to learn.

[EnochZhu]

nice doc

[EnochZhu]

V.prod() or M.prod() for the product of array elements over.

[EnochZhu]

Hi,please consider extending 'taichi.math.reflect()' to Matrix . This would be helpful to treat eigenvectors matrix.

[tengzhang48]

It will be nice to be able to calculate Logarithm of a matrix.

[kurt-rhee]

I would like to be able to use quaternions. I would like to go back and froth between quaternions and matrix rotations

[kurt-rhee]

I would also like a projection matrix

[kurt-rhee]

specifically an orthographic projection matrix

[bobcao3]

Currently, there's a hacky way to get a perspective projection matrix

camera = ti.ui.Camera()
camera.position(1, 1, 1)  # set camera position
camera.lookat(0, 0, 0)  # set camera lookat
camera.up(0, 1, 0)  # set camera up vector

proj_mtx = camera.get_projection_matrix(aspect_ratio)

[kurt-rhee]

Also projections of a vector onto another vector