Page - 50 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

50 2 AFewMoreSteps In [5]: x Out[5]: array([ 0., 1., 2.]) Note the use of “dots” to get floating point numbers and that we call arraywith bracketed12 numbers, i.e.,[0, 1, 2]and[0., 1., 2.]. 2.3.2 IndexinganArrayfromtheEnd Byuseofaminussign, theelementsofanarraymaybeindexedfromtheend,rather fromthebeginning.That is,withourarrayxhere,wecouldgetholdof theverylast element by writing x[-1], the second last element by writing x[-2], and so on. Continuingtheprevious interactivesession,we maywrite In [6]: x[-1] Out[6]: 2.0 In [7]: x[-2] Out[7]: 1.0 In [8]: x[-3] Out[8]: 0.0 2.3.3 IndexOutofBounds A typical error to make when working with arrays, is to accidentally use an illegal index.With thearrayx inourongoingdialogue,wemay illustrate thisby In [9]: x[3] Traceback (most recent call last): File "<ipython-input-18-ed224ad0520d>", line 1, in <module> x[3] IndexError: index 3 is out of bounds for axis 0 with size 3 Ourindex3is illegalandweget theerrormessageshown.Fromtheabove,it should beclear that legalindicesare0,1and2.Alternatively,if indexingfromtheend, legal indicesare−1,−2and−3.Note thatcounting is a bit “different” then, causing−3 tobea legal index(aswesaw above),while3 isnot. 2.3.4 CopyinganArray Copyingarraysrequiressomecare,ascanbeseennext,whenwetry tomakeacopy of thexarrayfromabove: In [10]: y = x In [11]: y Out[11]: array([ 0., 1., 2.]) # ...as expected 12 The arguments toarrayare two examples of lists,which will be addressed in Sect.5.1.