Waterfilling algorithm (from [Palomar and Fonollosa, Trans-SP2004]) to compute:
pi = (mu*ai - bi)^+
sum(pi) = Pt
By Daniel Perez Palomar (last revision: May 10, 2004).
1) Write a function reverse(A) which takes a matrix A of arbitrary dimensions as input and returns a matrix B consisting of the columns of A in reverse order. Thus for example, if
A = 1 2 3 then B = 3 2 1
4 5 6 6 5 4
7 8 9 9 8 7
Write a main program to call reverse(A) for the matrix A = magic(5). Print to the screen both A and reverse(A).
2) Write a program which accepts an input k from the keyboard, and which prints out the smallest fibonacci number that is at least as large as k. The program should also print out its position in the fibonacci sequence. Here is a sample of input and output:
Enter k>0: 100
144 is the smallest fibonacci number greater than or equal to 100.
It is the 12th fibonacci number.
