[Lang] Add ti.eig for 2x2 matrices #2303
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| else: | ||
| lambda1 = ti.Vector([tr, ti.sqrt(-gap)]) * 0.5 | ||
| lambda2 = ti.Vector([tr, -ti.sqrt(-gap)]) * 0.5 | ||
| A1r = A - lambda1[0] * ti.Matrix.identity(dt, 2) | ||
| A1i = -lambda1[1] * ti.Matrix.identity(dt, 2) | ||
| A2r = A - lambda2[0] * ti.Matrix.identity(dt, 2) | ||
| A2i = -lambda2[1] * ti.Matrix.identity(dt, 2) | ||
| v1 = ti.Vector([A2r[0, 0], A2i[0, 0], A2r[1, 0], | ||
| A2i[1, 0]]).cast(dt).normalized() | ||
| v2 = ti.Vector([A1r[0, 0], A1i[0, 0], A1r[1, 0], | ||
| A1i[1, 0]]).cast(dt).normalized() | ||
| eigenvalues = ti.Matrix.rows([lambda1, lambda2]) | ||
| eigenvectors = ti.Matrix.cols([v1, v2]) |
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I think there is one thing that needs to be discussed. From my knowledge, taichi doesn't have such a datatype to represent complex numbers, which could be generated by eigensolvers.
Currently, I use 2 numbers to store the real part and imaginary part of a complex number. That is to say, for a 2x2 matrix, function ti.eig() returns a 2x2 matrix v and a 4x2 matrix w. Each row of matrix v stores one eigenvalue represented by a 2d vector for its real and imaginary part. Each column of w stores one eigenvector with 2 entries each represented by two numbers for its real and imaginary part. I'm not sure whether this is the best way to handle this problem. Is there any advice on this? @k-ye
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I see. Yeah this sounds good, thanks! Could you write this as the docstring?
python/taichi/lang/__init__.py
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| if dt is None: | ||
| dt = impl.get_runtime().default_fp | ||
| from .linalg import eig | ||
| return eig(A, dt) |
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While this style is probably following how svd() is implemented, it could be a bit confusing to have multiple eig() symbols. I'd suggest to change to this:
def eig(A, dt=None):
if dt is None:
dt = impl.get_runtime().default_fp
from taichi.lang import linalg
if A.n == 2:
return linalg.eig2x2(A, dt)
raise Exception("Eigen solver only supports 2D matrices.")There was a problem hiding this comment.
I see. I will change to this and commit my implementation of sym_eig3x3() together.
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Actually, I think it's better to split into two PRs. This makes the review process easier ;-)
| else: | ||
| lambda1 = ti.Vector([tr, ti.sqrt(-gap)]) * 0.5 | ||
| lambda2 = ti.Vector([tr, -ti.sqrt(-gap)]) * 0.5 | ||
| A1r = A - lambda1[0] * ti.Matrix.identity(dt, 2) | ||
| A1i = -lambda1[1] * ti.Matrix.identity(dt, 2) | ||
| A2r = A - lambda2[0] * ti.Matrix.identity(dt, 2) | ||
| A2i = -lambda2[1] * ti.Matrix.identity(dt, 2) | ||
| v1 = ti.Vector([A2r[0, 0], A2i[0, 0], A2r[1, 0], | ||
| A2i[1, 0]]).cast(dt).normalized() | ||
| v2 = ti.Vector([A1r[0, 0], A1i[0, 0], A1r[1, 0], | ||
| A1i[1, 0]]).cast(dt).normalized() | ||
| eigenvalues = ti.Matrix.rows([lambda1, lambda2]) | ||
| eigenvectors = ti.Matrix.cols([v1, v2]) |
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I see. Yeah this sounds good, thanks! Could you write this as the docstring?
Robslhc
changed the title
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The CI of GPU failed but I have no idea about the error. It seems the error is not related to my changes, is it? |
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No, it's an issue on the CI bot itself #2307 .. |
Related issue = #2208, #2293
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This PR aims to implement utility functions
ti.eig()for 2x2 matrices as described in #2293.