Page - 21 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

1.5 MoreBasicConcepts 21 plt.savefig(’some_plot.png’) # PNG format plt.savefig(’some_plot.pdf’) # PDF format plt.savefig(’some_plot.jpg’) # JPG format plt.savefig(’some_plot.eps’) # Encanspulated PostScript format For the readerwho is into linear algebra, itmaybeuseful toknowthat standard matrix/vector operationsare straightforwardwith arrays, e.g.,matrix-vectormulti- plication.What is needed though, is to create the right variable types (after having importedanappropriatemodule). Forexample, assumeyouwould like tocalculate thevectory (note thatboldface isused forvectorsandmatrices) asyDAx,where A is a2 2matrix andx is a vector.Wemaydo this as illustratedby theprogram matrix_vector_product.pyreading from numpy import zeros, mat, transpose x = zeros(2) x = mat(x) x = transpose(x) x[0] = 3; x[1] = 2 # Pick some values A = zeros((2,2)) A = mat(A) A[0,0] = 1; A[0,1] = 0 A[1,0] = 0; A[1,1] = 1 # The following gives y = x since A = I, the identity matrix y = A*x print y Here, x is first created as an array, just as we did above. Then the variable type of x is changed to mat, i.e., matrix, by the line x = mat(x). This is followed by a transpose of x from dimension 1 2 (the default dimension) to 2 1with the statement x = transpose(x), before some test values are plugged in. The matrixA isfirstcreatedasa twodimensionalarraywithA = zeros((2,2))before conversionandfilling invalues takeplace. Finally, themultiplication is performed as y = A*x. Note the number of parentheseswhen creating the two dimensional arrayA.Running theprogramgives the followingoutputon thescreen: [[3.] [2.]] 1.5.8 ErrorMessagesandWarnings Allprogrammersexperienceerrormessages,andusually toalargeextentduringthe early learning process. Sometimes errormessages are understandable, sometimes theyarenot. Anyway, it is important toget used to them. One idea is to startwith aprogramthat initially isworking, and thendeliberately introduceerrors in it, one byone. (Butrememberto takeacopyof theoriginalworkingcode!) Foreacherror,