pythonnumpymatrixscipyorthogonal

Generating a tall-and-thin random orthonormal matrix in SciPy

I need to generate a tall-and-thin random column-orthonormal matrix in SciPy; that is, the number of rows n is far greater than the number of columns of p by many orders of magnitude (say n = 1e5 and p = 100. I know that scipy.stats.ortho_group generates a square orthogonal matrix. However, in my case it's simply infeasible to generate an n-by-n random orthogonal matrix and then keep the first p columns... Is there a more time- and space- efficient approach?

Solution

  • You can first generate a tall and thin random matrix, and then perform a qr decomposition.

    a = np.random.random(size=(100000, 100))
q, _ = np.linalg.qr(a)

    Here q is the matrix you want.