YouTip

# PyTorch torch.orgqr Function * * PyTorch torch Reference Manual](#) `torch.orgqr` is a PyTorch function for reconstructing the orthogonal matrix Q from QR decomposition. It uses Householder reflectors obtained from QR decomposition to compute the Q matrix. ### Function Definition torch.orgqr(input) **Parameters**: * `input` (Tensor): Input tensor containing Householder reflectors. **Returns**: * `torch.Tensor`: Returns the orthogonal matrix Q. * * * ## Usage Example ## Example import torch # Create matrix A = torch.tensor([[12.0, -51.0,4.0], [6.0,167.0, -68.0], [-4.0,24.0, -41.0]], dtype=torch.float64) # QR decomposition Q, R = torch.linalg.qr(A) print("Matrix A:") print(A) print("nOrthogonal Matrix Q:") print(Q) print("nVerify Q.T @ Q = I:") print(Q.T@ Q) Output: Matrix A: tensor([[ 12., -51., 4.], [ 6., 167., -68.], [ -4., 24., -41.]], dtype=torch.float64)Orthogonal Matrix Q: tensor([[-0.8571, 0.3943, 0.3314], [-0.4286, -0.9029, -0.0343], [ 0.2857, -0.1714, 0.9428]], dtype=torch.float64)Verify Q.T @ Q = I: tensor([[ 1.0000e+00, -1.4895e-16, 2.2204e-16], [-1.4895e-16, 1.0000e+00, 9.8601e-32], [ 2.2204e-16, 9.8601e-32, 1.0000e+00]], dtype=torch.float64) * * PyTorch torch Reference Manual](#)