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Unformatted text preview: 14:440:127 Introduction to Computers for Engineers Lecture 6 LEASE TAKE LECTURE 6 NOTES PLEASE TAKE LECTURE 6 NOTES AS YOU ENTER THE ROOM! Lecturer: Blase E. Ur Recitation Instructor: Bo Jin Recitation Instructor: Cyrus Gerami Recitation Instructor: Vishnu Vijayakumar Recitation Instructor: Wen Yueh 14:440:127 Lecture 6 polyfit polyfit(x,y,degree) x = [1 2 3 4 5]; y = [9 22 41 66 97]; Coeffs = polyfit(x,y,2) Rutgers University BuffaLOL %%% We find that >>coeffs = 3.0000 4.000 2.000 %%% The curve it found was y=3x 2 + 4x + 2 14:440:127 Lecture 6 What if theres data and dont know what to do? Plot it a bunch of ways (plot, semilogx, semilogy, loglog) and look for something recognizable. Rutgers University BuffaLOL 14:440:127 Lecture 6 Semilogx y = K*x 2 + C Display the x axis as powers of 10equivalent to taking the log of the x points Use semilogx(x,y) instead of plot(x,y) Logarithmic Data: y = K * log(x) + C Rutgers University BuffaLOL y = K * log(x) + C 14:440:127 Lecture 6 Semilogy y 2 = K*x + C 2 Display the y axis as powers of 10equivalent to taking the log of the y points Use semilogy(x,y) instead of plot(x,y) Exponential Data: = C*e kx Rutgers University BuffaLOL y = C*e 14:440:127 Lecture 6 Loglog y 2 = K*x 2 + C 2 Display the x and y axis as powers of 10equivalent to taking the log of the x and y points Use loglog (x,y) instead of plot(x,y) Power Function Data: = C*x k Rutgers University BuffaLOL y = C*x 14:440:127 Lecture 6 Semilogx is Straight Logarithmic Data: y = K * log(x) + C semilogx(x,y) % straightish coeffs = polyfit(log(x),y,1) % y = K*x 2 + C K = coeffs(1) Rutgers University BuffaLOL K = coeffs(1) C = coeffs(2) 14:440:127 Lecture 6 Semilogy is straight Exponential Data: y = C*e kx semilogy(x,y) % straightish coeffs = polyfit(x,log(y),1) % y 2 = K*x + C 2 = coeffs(1) Rutgers University BuffaLOL K = coeffs(1) C = exp(coeffs(2)) 14:440:127 Lecture 6 Loglog Power Function Data: y = C*x k loglog(x,y) % straightish coeffs = polyfit(log(x),log(y),1) % y 2 = K*x 2 + C 2 = coeffs(1) Rutgers University BuffaLOL K = coeffs(1) C = exp(coeffs(2)) 14:440:127 Lecture 6 Pseudorandom numbers rand(m,n) rand(s) Rutgers University BuffaLOL All values are in the unit interval [0,1] 14:440:127 Lecture 6 Pseudorandom numbers Interval [0,b] Rutgers University BuffaLOL 14:440:127 Lecture 6 Pseudorandom numbers Interval [a,b] Rutgers University BuffaLOL 14:440:127 Lecture 6 Pseudorandom numbers Integers [1,x] Rutgers University BuffaLOL 14:440:127 Lecture 6 randperm randperm(15) Rutgers University BuffaLOL 14:440:127 Lecture 6 Why PSEUDOrandom? Rutgers University BuffaLOL rand(seed,x) rand(state,x) Linear Congruential Generator= x n+1 = a*x n + c (mod n) BAD! 14:440:127 Lecture 6 Announcements Problem Set 1 due (for Tuesday lecture) or was due (Wednesday lecture) Project 2 (Sudoku) imminent ill feature the greatest ever contest....
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