Preconditioners in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the preconditioner module from scipy.

SciPy

from scipy.sparse.linalg import [1]

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Aaslinearoperator

Bcg

CLinearOperator

Dspilu

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing 'cg' which is a solver, not a preconditioner.

Choosing 'LinearOperator' which is a class, not a preconditioner function.

The spilu function is used to create an incomplete LU preconditioner.

2fill in blank

medium

Complete the code to create an incomplete LU preconditioner for matrix A.

SciPy

M_x = spilu([1])

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AA

Bx

Cb

DM

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the right-hand side vector b instead of the matrix.

Passing the preconditioner variable M before it is defined.

The spilu function requires the matrix A to compute the preconditioner.

3fill in blank

hard

Fix the error in creating a LinearOperator for the preconditioner.

SciPy

M = LinearOperator(A.shape, matvec=[1].solve)

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Ab

BA

CM_x

Dspilu

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the matrix A instead of the preconditioner object.

Passing the function spilu itself instead of its result.

The matvec parameter needs a function that applies the preconditioner, which is M_x.solve.

4fill in blank

hard

Fill both blanks to solve the linear system using the preconditioner.

SciPy

x, info = cg([1], [2], M=M)

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AA

Bb

Cx0

DM_x

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping the matrix and vector arguments.

Passing the preconditioner as a positional argument.

The conjugate gradient solver cg takes the matrix A and the right-hand side vector b as first arguments.

5fill in blank

hard

Fill all three blanks to create and apply a preconditioner in a solver.

SciPy

M_x = spilu([1])
M = LinearOperator([2], matvec=M_x.solve)
x, info = cg([3], b, M=M)

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AA

BA.shape

Db

Attempts:

3 left

💡 Hint

Common Mistakes

Using the vector b instead of the matrix A for preconditioner.

Passing the wrong shape to LinearOperator.

Passing b instead of A to the solver.

First, create the preconditioner from matrix A. Then create a LinearOperator with shape A.shape. Finally, solve the system with matrix A and vector b.