solve¶

SPQRFactor.solve(b, *, transpose=False, rhs_batch_size=100)[source]¶

Solve a linear system using the SPQR factorization.

Solve a linear system for \(x\) given the right-hand side \(b\) as either a vector or a matrix with multiple right-hand sides.

If transpose=False, solve

\[A x = b\]

or, if transpose=True, solve

\[A^{\top} x = b.\]

Parameters:

b ((M,) or (M, K) numpy.ndarray) – The right-hand side vector or matrix. M should be the number of rows in A if transpose=False, otherwise the number of columns.
transpose (bool, optional) – Whether to solve the transposed system. Default is False.
rhs_batch_size (int, optional) – If b is a 2D sparse array, this parameter controls the number of columns to be solved simultaneously. A larger number will increase memory consumption by converting more columns at a time to dense arrays, but may improve runtime.

Returns:

x ((N,) or (N, K) numpy.ndarray or sparse array) – The solution vector or matrix. If b is a 1D array, then x is returned as a 1D array. If b is a 2D array with K columns, then x is returned as a 2D array with K columns. If b is a sparse array, then x is also returned as a sparse array. N is the number of columns in A if transpose=False, otherwise the number of rows.