[Solved] Which of the following is the correct way to create a simple Jacobi preconditioner using scipy.sparse.linalg.LinearOperator?import numpy as np from scipy.sparse.linalg import LinearOperator A = np.... | SciPy

SciPy - Sparse Linear Algebra

Which of the following is the correct way to create a simple Jacobi preconditioner using scipy.sparse.linalg.LinearOperator?

import numpy as np
from scipy.sparse.linalg import LinearOperator

A = np.array([[4, 1], [1, 3]])
M = LinearOperator(shape=A.shape, matvec=lambda x: ...)

Amatvec=lambda x: x / np.diag(A)

Bmatvec=lambda x: np.dot(A, x)

Cmatvec=lambda x: x * np.diag(A)

Dmatvec=lambda x: np.linalg.solve(A, x)

Step-by-Step Solution

Solution:

Step 1: Recall Jacobi preconditioner definition
Jacobi preconditioner uses the inverse of the diagonal elements of matrix A.
Step 2: Implement matvec for Jacobi
Applying the preconditioner means dividing each element of x by the corresponding diagonal element of A.
Final Answer:
matvec=lambda x: x / np.diag(A) -> Option A
Quick Check:
Jacobi preconditioner = divide by diagonal [OK]

Quick Trick: Jacobi preconditioner divides vector by matrix diagonal [OK]

Common Mistakes:

Using matrix multiplication instead of division
Trying to solve full system instead of diagonal scaling
Multiplying by diagonal instead of dividing

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More SciPy Quizzes

Which of the following is the correct way to create a simple Jacobi preconditioner using scipy.sparse.linalg.LinearOperator?

Step 1: Recall Jacobi preconditioner definition

Step 2: Implement matvec for Jacobi

Final Answer:

Quick Check:

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