Numerical Methods¶
- pbeis.bicgstab(A, b, start_point=None, callback=None, tol=0.001)¶
Solves the linear equation Ax = b using the BiCGSTAB method.
Parameters¶
- Ascipy.sparse.csr_matrix
A square matrix represented as a SciPy sparse CSR matrix.
- bnumpy.ndarray
Right-hand side vector in the equation Ax = b, expected to be an n x 1 dimensional array.
- start_pointnumpy.ndarray, optional
The starting guess for the iteration. Defaults to a zero vector if not provided.
- callbackcallable, optional
A function callback(xk) that is called after each iteration, where xk is the current solution vector. If no function is provided, no action is taken at each iteration.
- tolfloat, optional
The tolerance level for convergence. The iteration will stop when the residual is below this tolerance. Default is 1e-3.
Returns¶
- xknumpy.ndarray
The solution vector to the equation Ax = b, as an n x 1 dimensional array.
- pbeis.prebicgstab(A, b, LU, start_point=None, callback=None, tol=0.001)¶
Solves the linear equation Ax = b using the preconditioned BiCGSTAB method. The preconditioner is specified as LU, which could be the form of an LU decomposition.
Parameters¶
- Ascipy.sparse.csr_matrix
A square matrix.
- bnumpy.ndarray
Right-hand side vector in the equation Ax = b, expected to be an n x 1 dimensional array.
- LUscipy.sparse.csr_matrix
The LU decomposition of A, typically a scipy.sparse.linalg.SuperLU object.
- start_pointnumpy.ndarray, optional
The starting guess for the iteration. Defaults to a zero vector if not provided.
- callbackcallable, optional
A function callback(xk) that is called after each iteration, where xk is the current solution vector. The default behavior is to perform no action on callback.
- tolfloat, optional
The tolerance level for convergence. The iteration will stop when the residual is below this tolerance. Default is 1e-3.
Returns¶
- xknumpy.ndarray
The solution vector to the equation Ax = b, as an n x 1 dimensional array.