- We Have Seen That It Is Possible To Do Linear Algebra In Numpy With Matrices Described By 2 Dimensional Arrays In This 1 (97.75 KiB) Viewed 26 times
# YOUR CODE HERE
raise NotImplementedError()
# Tests that the algorithm finds the correct value
# Marks: 5
from nose.tools import assert_equal
import numpy as np
A = np.array([[ 9, 6, 7, 8, 1, 7,
2], [ 8, 2, 6, 5, 1, 5,
3], [ 7, 3, 1, 4, 5, 10,
1],
[10, 5,
7, 5, 4, 6, 2], [ 5, 5,
2, 6, 4, 2, 7]])
assert_equal(find_max_column_value(A,0,0),(10,3))
# Tests that the algorithm finds the correct value
# Marks: 5
from nose.tools import assert_equal
import numpy as np
A = np.array([[ 9, 6, 7, 8, 1, 7,
2], [ 8, 2, 6, 5, 1, 5,
3], [ 7, 3, 1, 4, 5, 10,
1],
[10, 5,
7, 5, 4, 6, 2], [ 5, 5,
2, 6, 4, 2, 7]])
assert_equal(find_max_column_value(A,2,4),(5,2))
# Tests that the algorithm raises IndexError
# Marks: 5
from nose.tools import assert_raises
import numpy as np
A = np.array([[ 9, 6, 7, 8, 1, 7,
2], [ 8, 2, 6, 5, 1, 5,
3], [ 7, 3, 1, 4, 5, 10,
1],
[10, 5,
7, 5, 4, 6, 2], [ 5, 5,
2, 6, 4, 2, 7]])
assert_raises(IndexError,find_max_column_value,A,-1,0)
# Tests that the algorithm raises IndexError
# Marks: 5
from nose.tools import assert_raises
import numpy as np
A = np.array([[ 9, 6, 7, 8, 1, 7,
2], [ 8, 2, 6, 5, 1, 5,
3], [ 7, 3, 1, 4, 5, 10,
1],
[10, 5,
7, 5, 4, 6, 2], [ 5, 5,
2, 6, 4, 2, 7]])
assert_raises(IndexError,find_max_column_value,A,10,0)
# Tests that algorithm finds the correct value for another
matrix
# Marks: 5
from nose.tools import assert_equal
import numpy as np\
# Tests that the algorithm finds the correct value for another
matrix
# Marks: 5
from nose.tools import assert_equal
import numpy as np
We have seen that it is possible to do linear algebra in NumPy with matrices described by 2-dimensional arrays. In this question we will write a function to perform Gaussian Elimination in Python using NumPy. (a) [30 Marks] Write a function that takes as input a Matrix A (given as a 2-dimensional NumPy-array) and two integers i and j and returns the entry in column j with maximum absolute value amongst rows i, i + 1,.. together with its row index (counted in the entire matrix). In other words, if A is an rx k matrix, A = (amn) where 0 <m <r-1 and 0 <n<k – 1, then the function should return max{\amil : i sm<r}, together with the value of m for which this maximum occurs. Note that indexing for rows and columns are counted from 0 as usual. The function should raise a ValueError if the input i is not the index of a column of A or if j is not the index of a row of A. def find_max_column_value (A, i, j):