Evaluating a multivariable function on an array with python/numpy

Question

I know that python allows a fast evalutation of a real-valued, one variable function f(x) on a numpy array xarr = np.array([x0,x1,...xN]):

f(xarr) = np.array([f(x0), f(x1), ..., f(xN)])

However, this doesn't seem to work syntax-wise for a multivariable function. Say I have a real-valued function f(x,y), where x and y are two real numbers. Is there a correct syntax to evaluate the function on, say, [(0,0), (0,1), (1,0), (1,1)], avoiding a loop (which is always slow on python...)?

Edit: below are the functions involved:

The 5-variable function I refer to is:

def chisqr(BigOmega, inc, taustar, Q0, U0):
      QU = QandU(nusdata, BigOmega, inc, taustar, Q0, U0)
      Q = QU[:,0]
      U = QU[:,1]
      return 1./(2.*N) * (np.sum(((Q - Qs)/errQs)**2.) + np.sum(((U - Us)/errUs)**2.))

where nusdata, Qs, and Us are arrays defined before calling the function. The function calls the following function:

def QandU(nu, BigOmega, inc, taustar, Q0, U0):
      lambdalong = nu+omega-np.pi/2.
      tau3 = taustar * ((1+ecc*np.cos(nu))/(1-ecc**2.))**gamma
      delQ = -tau3 * (1+np.cos(inc)*np.cos(inc))*(np.cos(2.*lambdalong) np.sin(inc)*np.sin(inc))
      delU = -2*tau3*np.cos(inc)*np.sin(2*lambdalong)
      Q = Q0 + delQ*np.cos(BigOmega) - delU * np.sin(BigOmega)
      U = U0 + delQ*np.sin(BigOmega) + delU * np.cos(BigOmega)
      bounds = (inc < 0) or (inc > np.pi/2.) or (BigOmega < -2*np.pi) or (BigOmega > 2*np.pi) or (taustar < 0.) or (taustar > 1.)
      if bounds:
            Q = 10E10
            U = 10E10
      #return U
      return np.column_stack((Q,U))

All variables which aren't the function's arguments are defined outside the function.

You just need to define your function to take one argument (the tuple or pair) but operate on the elements of the tuple. Something as simple as f = lambda x: x[0]*x[1] can work. — wflynny
– wflynny, Commented May 24, 2016 at 15:49
There are often ways to do this, but there's no generalized answer. Some functions are easy and some are impossible. You need to show the actual function. — tom10
– tom10, Commented May 24, 2016 at 15:59
Tnx for the comments. syntonym: The function I want to evaluate is a complicated function involving trigonometric functions etc, and it's a function of 5 parameters (it's actually a chi2). It's not defined using lambdas but with a simple def .... return ... syntax. I could write it down, but I can't imagine why this should help... — user3310059
– user3310059, Commented May 24, 2016 at 16:00
Can you explain the connection between the functions you're rtrying to call and your question? Which function do you want to call over what array? — Eric
– Eric, Commented May 24, 2016 at 18:01

Eric · Accepted Answer · 2016-05-24 18:05:45Z

Using a simple example:

def add_squares(x, y):
    return x*x + y*y

xs = np.array([0, 0, 1, 1])
ys = np.array([0, 1, 1, 0])

res = add_squares(x, y)

np.array([0, 1, 2, 1])

Your statement that f(xarr) = np.array([f(x0), f(x1), ..., f(xN)]) is not in general true. This entirely depends on the definition of f. If f consists only of arithmetic operations, then it is true, but in general, it is not.

Your QandU function should almost work as intended:

def QandU(nu, BigOmega, inc, taustar, Q0, U0):
    # left unchanged
    lambdalong = nu+omega-np.pi/2.
    tau3 = taustar * ((1+ecc*np.cos(nu))/(1-ecc**2.))**gamma
    delQ = -tau3 * (1+np.cos(inc)*np.cos(inc))*(np.cos(2.*lambdalong) np.sin(inc)*np.sin(inc))
    delU = -2*tau3*np.cos(inc)*np.sin(2*lambdalong)
    Q = Q0 + delQ*np.cos(BigOmega) - delU * np.sin(BigOmega)
    U = U0 + delQ*np.sin(BigOmega) + delU * np.cos(BigOmega)

    # or doesn't vectorize, use bitwise or
    bounds = (inc < 0) | (inc > np.pi/2.) | (BigOmega < -2*np.pi) | (BigOmega > 2*np.pi) | (taustar < 0.) | (taustar > 1.)

    # if statements also don't vectorize
    Q[bounds] = 10E10
    U[bounds] = 10E10

    # stacking is more trouble that it's worth
    return Q, U

Your chisqr function will probably need an axis= argument passed to sum, depending exactly which dimensions you want to sum over.

Collectives™ on Stack Overflow

Evaluating a multivariable function on an array with python/numpy

1 Answer 1

Comments

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

1 Answer 1

Comments

Your Answer

Sign up or log in

Post as a guest

Related