I have a problem with a task using scipy. optimize. minimize execution through the following methods: CG, BFG, Newton-CG, L-BFGS-B Consider the following area: D = [-5.10]x[0.15]. This task, given below, must be performed in this domain. And executed in Jupyter notebook

Draw N = 100 random points uniformly distributed over D. For each point, run a local minimization of f using scipy. optimize. minimize with the following methods: CG, BFGS, Newton-CG, L-BFGS-B. For this task, you will have to write two other functions, one that returns the Jacobian matrix of f and one that returns the Hessian matrix of f . Store the answers in an array with shape N x 6, each row of which has the following data:

(x1, y1,x2, y2,v, c),

where (x1, y1) and (x2, y2) are respectively the starting and the final point of the optimization, while v is the final value of f . The final element of the row c is code of the used method, according to this correspondence: CG:1, BFGS:2, Newton-CG:3, L-BFGS-B:4

Show that there is a language a ⚆ {0, 1} â— with the following properties: 1. for all x â a, |x| ≤ 5. 2. no dfa with fewer than 9 states recognizes a. hint: you don’t have to define a explicitly; just show that it has to exist. count the number of languages satisfying (1) and the number of dfas satisfying (2), and argue that there aren’t enough dfas to recognize all those languages. to count the number of languages satisfying (1), think about writing down all the strings of length at most 5, and then to define such a language, you have to make a binary decision for each string about whether to include it in the language or not. how many ways are there to make these choices? to count the number of dfas satisfying (2), consider that a dfa behaves identically even if you rename all the states, so you can assume without loss of generality that any dfa with k states has the state set {q1, q2, . . , qk}. now think about how to count how many ways there are to choose the other four parts of the dfa.

Which cultural aspect does this type of song best portray? a german polka dance

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