Please only answer part d) using python.

Here is the psuedo-code for part b :

Let an n n Hessenberg matrix A be given. b) pseudo-code for the LUP decomposition of an upper Hessenberg matrix: Step 1) Let H be an n-by-n upper Hessenberg matrix. algorithm computes the unique LU factorization of H. Step 2) a)Let H be an nn upper Hessenberg matrix with an LU factorization. b)Let H = LU be the unique LU factorization of H. If L, U are the factors obtained by applying Step 1 to the matrix H with floating entries . Step 3) a) Let H be any n n upper Hessenberg matrix with an LU factorization. b) L, U are the factors obtained by applying Step 2 to H Step 4) In this step , O(^2) terms are ignored for simplicity. Step 5) Let H be an n-by-n upper Hessenberg matrix with an LU factorization. Let H = LU be the unique LU factorization of H where L is a unit lower triangular matrix. If L and U are the factors computed by step 2 when applied to H Step 6) Let H = LU be the exact LU factorization of the n-by-n upper Hessenberg matrix H. Let L and U be the factors computed by step 2. Step 7) Let L and U be the matrices obtained from the exact LU factorization of H, where H is an nn upper Hessenberg matrix. Let L+L and U+U be the factors obtained from the LU factorization of H +H. Step 8) Let H = LU be the exact LU factorization of the upper Hessenberg matrix H. Let L and U be the factors computed by Step 2.

An n n upper Hessenberg matrix A has the property that Aij 0 if i +1. (a) Compute is PLU decomposition by hand for the following example matrix: 1 4-2.3 0 -3 5-5 0 0 31 You will find that a lot of the multipliers are zero. (b) Write a pseudo-code for the LUP decomposition of an upper Hessenberg matrix that avoids unnecessary FLOPs (i.e. adding and multiplying by zero) (c) Compute the number of FLOPs necessary to complete the pseudo-code. (d) Write a function in Python that implements the pseudo-code of part (b). Also write a test script that 1. generates a n x n random upper Hessenberg matrix., 2. computes its PLU decomposition, 3. measures the time it takes to compute the decomposition for n-2P, p-4,...,11 and 4. plots the wall time on an appropriate scale to see the behaviour predicted by the FLOP count of part (c). An n n upper Hessenberg matrix A has the property that Aij 0 if i +1. (a) Compute is PLU decomposition by hand for the following example matrix: 1 4-2.3 0 -3 5-5 0 0 31 You will find that a lot of the multipliers are zero. (b) Write a pseudo-code for the LUP decomposition of an upper Hessenberg matrix that avoids unnecessary FLOPs (i.e. adding and multiplying by zero) (c) Compute the number of FLOPs necessary to complete the pseudo-code. (d) Write a function in Python that implements the pseudo-code of part (b). Also write a test script that 1. generates a n x n random upper Hessenberg matrix., 2. computes its PLU decomposition, 3. measures the time it takes to compute the decomposition for n-2P, p-4,...,11 and 4. plots the wall time on an appropriate scale to see the behaviour predicted by the FLOP count of part (c)