![]() ![]() LU Decomposition for Solving Linear Equations Many of the on-line articles on the procedures for decomposition (including Wikipedia) are very hard to follow, but I found a clear and comprehensive tutorial at: It is then a simple process to find the vector x such that LUx = b, for any values of b, without having to repeat the decomposition process. A is decomposed into a lower triangular matrix, L, and an Upper triangular matrix, U, such that LU = A. LU decomposition is an efficient method for solving systems of linear equations of the form Ax = b, where A is a square matrix and b is a vector. This post looks at the question in more detail, including examples of the basic procedures, and how and why the variations are used. The short answer was that there is more than one way to do LU decomposition. Which asked why Mathcad was generating LU matrices different to those calculated from the basic theory. I hope you find the tutorial useful.This post was prompted by a question at the Eng-Tips forum: The idea is about merging iterables, which comes handy in many cases. Working with zip function in Python is pretty neat and easy. We can convert the zip object to a tuple then to a string and write the string to the file: f.write(str(tuple(zip(list_1,list_2)))) The following will be the contents of the file:Īlso, there is a shorter code instead of using the for loop. Now close the file and check the saved data. List_2 = įinally, use the for loop to iterate through lists in zip function and write the result in the file (after converting a tuple to string): for i in zip(list_1, list_2): Now let’s create two lists to zip together. If the file doesn’t exist, it will be created. Use the following line: f = open("zipOutput.txt", "a+") The first step is to open a file (we will use the append mode so nothing of existing content will be deleted). To save the output from the zip function into a file. If you pass one iterable to the arguments of zip() function, there would be one item in each tuple. > float_zip = zip(float_list1, float_list2) In this section, we will create an example where zip function iterates through a list of floats: > float_list1 = The floating-point numbers contain decimal points like 10.3, 14.44, etc. The zip function also works on floating-point numbers. The for loop uses two iterative variables to iterate through the lists that are zipped together to work in parallel. ![]() In the above example, we have two different lists. The tuple() function converts the zip object to a tuple. That’s why we said before the length of the output equals the length of the smallest iterator, which is 2 in this case. Similarly, the second elements of all of them are joined together.īut there is no third element in the iterator y therefore, the third elements of remaining iterators are not included in the output object. The first elements of all of them are joined together. In the above example, we defined three iterators of different lengths. ![]() are the iterator objects that we need to join using the zip function.Ĭonsider the following snippet, where we have three iterables and the zip function joins them together. In the syntax above, the iterable0, iterable1, etc. Iterables can be Python lists, dictionary, strings, or any iterable object. Syntax: zip(iterable0, iterable1, interable2, …) If the iterables in the zip function are not the same length, then the smallest length iterable decides the length of the generated output. The zip function pairs the first elements of each iterator together, then pairs the second elements together and so on. 10 Output to a file How zip function works? ![]()
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