tf.keras.ops.lstsq

Return the least-squares solution to a linear matrix equation.

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Main aliases

tf.keras.ops.linalg.lstsq

tf.keras.ops.lstsq(
    a, b, rcond=None
)

Computes the vector x that approximately solves the equation a @ x = b. The equation may be under-, well-, or over-determined (i.e., the number of linearly independent rows of a can be less than, equal to, or greater than its number of linearly independent columns). If a is square and of full rank, then x (but for round-off error) is the exact solution of the equation. Else, x minimizes the L2 norm of b - a * x.

If there are multiple minimizing solutions, the one with the smallest L2 norm is returned.

Args
a	"Coefficient" matrix of shape (M, N).
b	Ordinate or "dependent variable" values, of shape (M,) or (M, K). If b is two-dimensional, the least-squares solution is calculated for each of the K columns of b.
rcond	Cut-off ratio for small singular values of a. For the purposes of rank determination, singular values are treated as zero if they are smaller than rcond times the largest singular value of a.

Returns
Tensor with shape (N,) or (N, K) containing the least-squares solutions.

Note: The output differs from numpy.linalg.lstsq. NumPy returns a tuple with four elements, the first of which being the least-squares solutions and the others being essentially never used. Keras only returns the first value. This is done both to ensure consistency across backends (which cannot be achieved for the other values) and to simplify the API.