For all problems, include one or two examples to demonstrate that your function works as intended. For all functions, include code that checks whether the arguments satisfy the specifications in the problem. If not, the code should throw an error with a meaningful error code. Code up the algorithm yourself whenever possible. For example, you should implement the forward solving algorithm instead of calling forwardsolve 1. Write a function that takes in a 'n' by `n` lower triangular matrix `L`, and an `n by 1 vector `b`, and returns the solution to 'L x = b`. 2. Write a function that takes in a `n by `n` upper triangular matrix U`, and an `n` by 1 vector b`, and returns the solution to 'U x = b`. 3. Write a function that takes in an `n by `n matrix A and returns the lower triangular matrix `L` such that `A = L LAT`. If the calculation fails because you cannot take the square root of a negative number, your function should return the current upper-left corner of Land print a warning message.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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In R, 

For all problems, include one or two examples to demonstrate that your
function works as intended. For all functions, include code that
checks whether the arguments satisfy the specifications in the
problem. If not, the code should throw an error with a meaningful
error code.
Code up the algorithm yourself whenever possible. For example, you should
implement the forward solving algorithm instead of calling forwardsolve
1. Write a function that takes in a `n` by `n lower triangular matrix
L, and an `n` by 1 vector b`, and returns the solution to `L x =
b`.
2. Write a function that takes in a `n` by `n` upper triangular matrix
`u`, and an `n by 1 vector b`, and returns the solution to 'U x =
b`.
3. Write a function that takes in an `n` by `n matrix `A` and returns
the lower triangular matrix L such that A = L LAT. If the
calculation fails because you cannot take the square root of a
negative number, your function should return the current upper-left
corner of L and print a warning message.
Transcribed Image Text:For all problems, include one or two examples to demonstrate that your function works as intended. For all functions, include code that checks whether the arguments satisfy the specifications in the problem. If not, the code should throw an error with a meaningful error code. Code up the algorithm yourself whenever possible. For example, you should implement the forward solving algorithm instead of calling forwardsolve 1. Write a function that takes in a `n` by `n lower triangular matrix L, and an `n` by 1 vector b`, and returns the solution to `L x = b`. 2. Write a function that takes in a `n` by `n` upper triangular matrix `u`, and an `n by 1 vector b`, and returns the solution to 'U x = b`. 3. Write a function that takes in an `n` by `n matrix `A` and returns the lower triangular matrix L such that A = L LAT. If the calculation fails because you cannot take the square root of a negative number, your function should return the current upper-left corner of L and print a warning message.
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