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# Lab7 - Engineering 7 Introduction to Programming for...

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Engineering 7: Prof. Alexandre Bayen Introduction to Programming for Engineers Spring 2011 Lab 7: Least Squares Regression Date Assigned: 5:00pm, Friday – Mar 25. Date Due: 5:00pm, Friday – April 1. Problem 1: Do Problem 12.8 in the Reader. Clarifications : You may assume that b is a column vector and that the number of elements in b is the same as the number of rows in A . The output x should be a column vector. You may assume that in the case of an infinite number of solutions, the A matrix has more columns than rows, i.e. A is fat. In the case that there are an infinite number of solutions, you should solve the system using x = pinv(A)*b . >> A = reshape(1:15, 3, 5); >> b = [-5; -4; -3]; >> [N, x] = myNumSols(A,b) N = Inf x = 1.0000 0.6000 0.2000 -0.2000 -0.6000 >> b = [-1.5; 2; 7]; >> [N, x] = myNumSols(A,b) N = 0 x = [] >> A = 3*eye(5); >>b = [1; 2; 3; 4; 5]; >> [N, x] = myNumSols(A,b) N = 1 x = 0.3333 0.6667 1.0000 1.3333 1.6667

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Engineering 7: Prof. Alexandre Bayen Introduction to Programming for Engineers Spring 2011 Problem 2: Consider the following network consisting of two power supply stations denoted by S1 and S2 and five power recipient nodes denoted by N1 to N5. The nodes are connected by power lines which are denoted by arrows, and power can flow between nodes along these lines in both directions. Let d i be a positive scalar denoting the power demands for node i, and assume that this demand must be met exactly. The capacity of the power supply stations is denoted by S. Power supply stations must run at their capacity. For each arrow, let f j be the power flow along that arrow. Negative flow implies that power is running in the opposite direction of the arrow. Write a function with header [f] = myFlowCalculator(S, d) where S is 1x2 vector representing the capacity of each power supply station, and d is a 1x5 row vector representing the demands at each node, i.e.
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