mojolearn.lstsq#

mojolearn.lstsq(a, b, rcond=None, *, numeric_mode=None)[source]#

Least-squares solution of a @ x = b.

Follows numpy.linalg.lstsq, solved through the SVD of a. Singular values at or below rcond * s.max() are treated as zero.

Parameters:

  • a (array-like of shape (M, N))

  • b (array-like of shape (M,) or (M, K))

  • rcond (float or None, default None) – Relative cutoff for small singular values. None uses float32 machine epsilon times max(M, N).

  • numeric_mode ({“identical”, “fast”} or None, default None) – Numeric mode for this call. None uses the package default ("identical" unless changed). "identical" gives the same bits on NVIDIA and AMD GPUs; "fast" applies on Apple GPUs.

Returns:

  • x (ndarray of shape (N,) or (N, K), float32)

  • residuals (ndarray of shape (K,) or (0,), float32) – Squared column norms of b - a @ x when rank == N < M; otherwise empty.

  • rank (int) – Effective rank of a.

  • s (ndarray of shape (min(M, N),), float32) – Singular values of a, descending.

Raises:

ValueError – If a and b have different numbers of rows.

Examples

>>> import numpy as np, mojolearn
>>> rng = np.random.default_rng(0)
>>> A = rng.random((100, 4), dtype=np.float32)
>>> x, res, rank, s = mojolearn.lstsq(A, rng.random(100, dtype=np.float32))
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