In addition to being mathematical entities studied in linear algebra, Vectors are widely used in physics and engineering as a convenient way to represent physical quantities as displacement, velocity, acceleration, force, and so on. Accordingly, basic operations between vectors can be performed via Numpy/SciPy operations as follows:
Addition/subtraction of vectors does not require any explicit loop to perform them. Let's take a look at addition of two vectors:
>>> vectorC = vectorA + vectorB >>> vectorC
The output is shown as follows:
array([8, 8, 8, 8, 8, 8, 8])
Further, we perform subtraction on two vectors:
>>> vectorD = vectorB - vectorA >>> vectorD
The output is shown as follows:
array([ 6, 4, 2, 0, -2, -4, -6])
Numpy has the built-in function dot to compute the scalar (dot) product between two vectors. We show you its use computing the dot product of vectorA and vectorB from the previous code snippet:
>>> dotProduct1 = numpy.dot(vectorA,vectorB) >>> dotProduct1
The output is shown as follows:
84
Alternatively, to compute this product we could perform the element-wise product between the components of the vectors and then add the respective results. This is implemented in the following lines of code:
>>> dotProduct2 = (vectorA*vectorB).sum() >>> dotProduct2
The output is shown as follows:
84
First, two vectors in 3 dimensions are created before applying the built-in function from NumPy to compute the cross product between the vectors:
>>> vectorA = numpy.array([5, 6, 7]) >>> vectorB = numpy.array([7, 6, 5]) >>> crossProduct = numpy.cross(vectorA,vectorB) >>> crossProduct
The output is shown as follows:
array([-12, 24, -12])
Further, we perform a cross operation of vectorB over vectorA:
>>> crossProduct = numpy.cross(vectorB,vectorA) >>> crossProduct
The output is shown as follows:
array([ 12, -24, 12])
Notice that the last expression shows the expected result that vectorA cross vectorB is the negative of vectorB cross vectorA.