Julia & IJulia Cheat-Sheet

Julia & IJulia Cheat-sheet (for 18.xxx at MIT, Julia 1.x) Basics: — run Julia online github.com/mitmath/julia-mit installation & tutorial using IJulia; IJulia.notebook() start IJulia browser shift-return execute input cell in IJulia using LinearAlgebra load functions for blue-highlighted code below julialang.org — documentation; juliabox.com Defining/changing variables: Arithmetic and functions of numbers: mult., add, sub., divide numbers compute 3 or 3 power −5 as a complex number 3*4, 7+4, 2-6, 8/3 3^7, 3^(8+2im) 7 8+2i sqrt(-5+0im) exp(12) e12 log(3), log10(100) natural log (ln), base-10 log (log ) absolute value |–5| or |2+3i| compute sin(5π/3) 10 abs(-5), abs(2+3im) define variable x to be 3 array/“column”-vector (1,2,3) [1 2 3] 1×3 matrix (1,2,3) x = 3 sin(5pi/3) x = [1,2,3] y = A = [1 2 3 4; 5 6 7 8; 9 10 11 12] x[2] = 7 change x from (1,2,3) to set A to 3×4 matrix (1,7,3) change A from 5 to 0 u, v = (15.03, 1.2e-27) set u=15.03, v=1.2×10 f(x) = 3x define a function f(x) x -> 3x an “anonymous” function \alphaTAB tab-complete \alpha to α A[2,1] = 0 2,1 –27 Constructing a few simple matrices: random length-12 vector or 12×4 matrix with uniform random numbers in [0,1) randn(12) Gaussian random numbers (mean 0, std. dev. 1) Matrix(I,3,3) 5×5 identity matrix I range(1.2,4.7,length=100) 100 equally spaced points from 1.2 to 4.7 Diagonal(x) matrix whose diagonal is the entries of x rand(12), rand(12,4) Portions of matrices and vectors: x[2:12] x[2:end] A[5,1:3] A[5,:] diag(A) the 2 to 12 elements of x the 2 to the last elements of x row vector of 1 3 elements in 5 row of A row vector of 5 row of A vector of diagonals of A nd th nd st th th Arithmetic and functions of vectors and matrices: x * 3, x .+ 3 multiply/add 3 x + y element-wise addition to every element of x of two vectors x and y A*y, A*B product of matrix A and vector y or matrix B x * y not defined for two vectors! x .* y element-wise product of vectors x and y x .^ 3 every element of x is cubed cos.(x), cos.(A) cosine of every element of x or A exp.(A), exp(A) exponential of each element, matrix exponential x', A' conjugate-transpose of vector or matrix x'y, dot(x,y), sum(conj(x).*y) three ways to compute x · y A \ b, inv(A) return solution to Ax=b, or the matrix A eigvals(A), eigvecs(A) eigenvalues and eigenvectors (columns) –1 Plotting (type using PyPlot first) plot(y), plot(x,y) plot y vs. 0,1,2,3,… or versus x loglog(x,y), semilogx(x,y), semilogy(x,y) log-scale plots title("A title"), xlabel("x-axis"), ylabel("foo") set labels legend at upper-left grid(), axis("equal") add grid lines, use equal x and y scaling title(L"the curve $e^\sqrt{x}$") title with LaTeX equation savefig("fig.png"), savefig("fig.pdf") save PNG or PDF image legend(["curve 1", "curve 2"], "northwest")