Page - 86 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

86 4 FunctionsandtheWritingofCode Alternatively, with default values for all the parameters, and again aiming for the sameprintout,ourprogram(ball_position_xy.py)appearsas def xy(v0x=2.0, v0y=5.0, t=0.6): """Computes horizontal and vertical positions at time t""" g = 9.81 # acceleration of gravity return v0x*t, v0y*t - 0.5*g*t**2 x, y = xy() print(’Horizontal position: {:g} , Vertical position: {:g}’.format(x, y)) Running thecode,we get theprintout Horizontal position: 1.2 , Vertical position: 1.2342 Some,orall, of thedefaultvaluesmayalsobeoverridden,e.g., like x, y = xy(v0y=6.0) # override default value for v0y only whichmeansthatxywill runwithdefaultvaluesforv0xandt,whilev0ywillhave thevalue6.0, as specified in the functioncall. Theoutput then,becomes Horizontal position: 1.2 , Vertical position: 1.8342 which is reasonable, since the initial velocity for the vertical direction was higher than in thepreviouscase. 4.1.8 AFunctionwithAnotherFunctionasInputArgument Functions are straightforwardly passed as arguments to other functions. This is illustrated by the following scriptfunction_as_argument.py,where a function sumsupfunctionvaluesofanother function: def f(x): return x def g(x): return x**2 def sum_function_values(f, start, stop): """Sum up function values for integer arguments as f(start) + f(start+1) + f(start+2) + ... + f(stop)""" S = 0 for i in range(start, stop+1, 1): S = S + f(i) return S print(’Sum with f becomes {:g}’.format(sum_function_values(f, 1, 3))) print(’Sum with g becomes {:g}’.format(sum_function_values(g, 1, 3))) We note that the function sum_function_values takes a function as its first argument and repeatedly calls that function without (of course) knowing what that functiondoes, it justgets the functionvaluesbackandsums themup! Remember that the argument f in the function header sum_funcion_values (f, start, stop) and the function defined by the namef, is not the same. The