Is there an easier command to compute vector projection? I am instead using the following:
x = np.array([ 3, -4, 0])
y = np.array([10, 5, -6])
z=float(np.dot(x, y))
z1=float(np.dot(x, x))
z2=np.sqrt(z1)
z3=(z/z2**2)
x*z3
2 Answers
Maybe this is what you really want:
np.dot(x, y) / np.linalg.norm(y)
This should give the projection of vector x onto vector y - see . Alternatively, if you want to compute the projection of y onto x, then replace y with x in the denominator (norm) of the above equation.
EDIT: As @VaidAbhishek commented, the above formula is for the scalar projection. To obtain vector projection multiply scalar projection by a unit vector in the direction of the vector onto which the first vector is projected. The formula then can be modified as:
y * np.dot(x, y) / np.dot(y, y)
for the vector projection of x onto y.
The projection of a onto b is defined as
So either
(np.dot(a, b) / np.dot(b, b)) * b
or
(np.dot(a, b) / np.linalg.norm(b)**2 ) * b
