3j%%SrSSKJr SSKrSSKJr SSKJrJrJ r SSK J r SSK J r SrS \S 'S S jrSSS jjrg)z2Module with the functionalities for triangulation.) annotationsN)KORNIA_CHECK_SHAPE) _normalize_to_float32_or_float64_torch_svd_castis_mps_tensor_safe)convert_points_from_homogeneous)null_vector_3x4i`mint_CUSOLVER_EIGH_BATCH_LIMITc NURSnU[::a&[RR U5up#US$[ SU[5Vs/sH1n[RR XU[-5SSPM3 nn[R "USS9$s snf)aReturn the eigenvector for the smallest eigenvalue of each symmetric matrix. Handles cuSOLVER's batch-size limit by chunking when necessary. Args: M: batch of symmetric PSD matrices, shape ``(N, k, k)``. Returns: Eigenvectors of shape ``(N, k)``. r).rdim)shaper torchlinalgeighrangecat)MN_Vipartss `/home/wildlama/miniconda3/lib/python3.13/site-packages/kornia/geometry/epipolar/triangulation.py_eigh_smallest_vecr$s  A &&||  #yq!78 8A  !$> >?@CFK8   99U ""  s8B"c[U/SQ5 [U/SQ5 [U/SQ5 [U/SQ5 USSS24USSS2SS24-USSS2SS24- nUSSS24USSS2SS24-USSS2SS24- nUSSS24USSS2SS24-USSS2SS24- nUSSS24USSS2SS24-USSS2SS24- n[R"XVXx5upVpxUS :Xa,[R"XVXx/S S 9n [ U 5u pU S n GO]US :Xa[R"XVXx/S S 9n [ U 5(a[R n ODU R[R :Xa[Rn O[U R5n U RSS nU RU 5nURU-nURSS5n[U5RU R5nUR"/UQSP76n GO`US:XGaJ[UR5n URU 5nURU 5nURU 5nURU 5n[R"UUU/S S 9n[R"UUU/S S 9n[!U5RUR5n[!U5RUR5nUR#SSS9R%SS9nUR#SSS9R%SS9nUU- nUU- nUU-R'SSS9n[R("US:U*U5nUU-n O[+SUS35e[-U 5n U $)u Reconstructs a bunch of points by triangulation. Triangulates the 3d position of 2d correspondences between several images. Reference: Internally it uses DLT formulation from Hartley/Zisserman 12.2 pag.312 The input points are assumed to be in homogeneous coordinate system and being inliers correspondences. The method does not perform any robust estimation. Args: P1: The projection matrix for the first camera with shape :math:`(*, 3, 4)`. P2: The projection matrix for the second camera with shape :math:`(*, 3, 4)`. points1: The set of points seen from the first camera frame in the camera plane coordinates with shape :math:`(*, N, 2)`. points2: The set of points seen from the second camera frame in the camera plane coordinates with shape :math:`(*, N, 2)`. solver: Back-end used to find the null vector of the :math:`4 \times 4` DLT constraint matrix. One of: * ``"svd"`` — most numerically stable. Promotes to fp64 and uses a full SVD (via :func:`~kornia.core.utils._torch_svd_cast`). Suitable when maximum accuracy is required regardless of speed. * ``"eigh"`` *(default)* — forms :math:`X^\top X` and finds the eigenvector for its smallest eigenvalue via :func:`torch.linalg.eigh`. Algebraically equivalent to the SVD solution; slightly less numerically stable because forming :math:`X^\top X` squares the singular values. Typically **10-26x faster** than ``"svd"`` on GPU for large batches. * ``"cofactor"`` — solves two :math:`3 \times 4` sub-systems analytically using :func:`~kornia.geometry.solvers.null_vector_3x4` (closed-form cofactor expansion, no LAPACK call). The two solutions are averaged after normalisation. This matches the full DLT solution when the constraint system is exactly consistent, but is only an approximation in the noisy inconsistent case. Fastest option for all batch sizes. Returns: The reconstructed 3d points in the world frame with shape :math:`(*, N, 3)`. Example: >>> P1 = torch.eye(3, 4)[None] # 1x3x4 >>> P2 = torch.eye(3, 4)[None] >>> pts1 = torch.rand(1, 5, 2) >>> pts2 = torch.rand(1, 5, 2) >>> pts3d = triangulate_points(P1, P2, pts1, pts2) >>> pts3d.shape torch.Size([1, 5, 3]) )*34)rr2.rr Nsvdr).rcofactorr'T)rkeepdimg:0yE>)minzUnknown solver 'z*'. Choose from: 'svd', 'eigh', 'cofactor'.)rrbroadcast_tensorsstackrrfloat32dtypefloat64rrtomTflattenrreshaper normclampsumwhereNotImplementedErrorr)!P1P2points1points2solverrow0row1row2row3Xrr points3d_h compute_dtype batch_shapeX_castXTXflatv_flatr0r1r2r3A_012A_123h_012h_123n012n123v012v123dotpoints3ds! rtriangulate_pointsrZ;sjr?+r?+w0w0 3!8 r#qsA+ .C1aK @D 3!8 r#qsA+ .C1aK @D 3!8 r#qsA+ .C1aK @D 3!8 r#qsA+ .C1aK @D"44TLD  KKT0b 9 "!$1wZ 6  KKT0b 9 a !MMM WW %!MMMr\r?strr]r\)__doc__ __future__rrkornia.core.checkrkornia.core.utilsrrrkornia.geometry.conversionsrkornia.geometry.solversr r __annotations__rrZr[rrgsz$9" 0ccG3 #)C(#8 KKKK K  K  Kr[