Page - 52 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

52 2 AFewMoreSteps When copying a slice, the same logic applies as when copying the whole array. To demonstrate theproblem,wecontinue thedialogueas In [6]: y[0] = -1.0 In [7]: y Out[7]: array([-1., 13., 14., 15.]) # ...changed In [8]: x Out[8]: array([ 11., -1., 13., 14., 15., 16.]) # ...changed As for the whole array, the function copy may be used (after importing: from numpy import copy)asy = copy(x[1:5]) togivea“real”copy. 2.3.6 Two-DimensionalArraysandMatrixComputations For readers who are into linear algebra, it might be useful to see how matrices and vectors may be handled with NumPy arrays.13 Above, we saw arrays where the individual elements could be addressed with a single index only. Such arrays are oftencalledvectors. To calculate with matrices, we need arrays with more than one “dimension”. Such arrays may be generated in different ways, for example by use of the same zerosfunctionthatwehaveseenbefore, it justhas tobecalledabitdifferently.Let usillustratebydoingasimplematrix-vectormultiplicationwith thenumpyfunction dot: In [1]: import numpy as np In [2]: I = np.zeros((3, 3)) # create matrix (note parentheses!) In [3]: I Out[3]: array([[ 0., 0., 0.], [ 0., 0., 0.], [ 0., 0., 0.]]) In [4]: type(I) # confirm that type is ndarray Out[4]: numpy.ndarray In [5]: I[0, 0] = 1.0; I[1, 1] = 1.0; I[2, 2] = 1.0 # identity matrix In [6]: x = np.array([1.0, 2.0, 3.0]) # create vector In [7]: y = np.dot(I, x) # computes matrix-vector product In [8]: y Out[8]: array([ 1., 2., 3.]) 13 If you are not familiar with matrices and vectors, and such calculations are not on your agenda, you should consider skipping (or at least wait with) this section, as it is not required for understanding the remaining parts of the book.