Page - 53 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

2.3 NumericalPythonArrays 53 Note how zerosmust be called with double parentheses now. The accessing of individualmatrix elements should be according to intuition. With some experience from matrix-vector algebra, it is clear thaty is correctly computed here. Note that mostprogrammerswoulduse theNumPyfunctioneyehere, togeneratethe identity matrix directly. One would then callI = eye(3) and getI as a two dimensional arraywithoneson thediagonal. Ifyouareexperiencedwithmatricesandvectors in Matlab, there is anotherway to handle matrices and vectors with NumPy, which will appear more like you are usedto.Forexample,amatrix-vectorproductis thencodedasA*xandnotbyuseof thedot function.Toachieve this,we mustuseobjectsofanother type, i.e.,matrix objects (note that amatrixobject will have different properties than anndarray object!). If we do the same matrix-vector calculation as above, we can show how ndarrayobjects may be converted into matrixobjects and how the calculations thencanbe fulfilled: In [1]: import numpy as np In [2]: I = np.eye(3) # create identity matrix In [3]: I Out[3]: array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) In [4]: type(I) # confirm that type is ndarray Out[4]: numpy.ndarray In [5]: I = np.matrix(I) # convert to matrix object In [6]: type(I) # confirm that type is matrix Out[6]: numpy.matrixlib.defmatrix.matrix In [7]: x = np.array([1.0, 2.0, 3.0]) # create ndarray vector In [8]: x = np.matrix(x) # convert to matrix object (row vector) In [9]: x = x.transpose() # convert to column vector In [10]: y = I*x # computes matrix-vector product In [11]: y Out[11]: matrix([[ 1.], [ 2.], [ 3.]]) Note thatnp.matrix(x) turnsx, with typendarray, into a row vector by default (type matrix), so x must be transposed with x.transpose() before it can be multipliedwith thematrixI.