Base Functions on arbitrary Reference Element

dimension, order = 3, 2
from numpy.linalg import inv

degreesOfFreedom = []
monomials = []

if dimension == 2:
    for i in range(order+1):
        for j in range(order+1):
            if i + j > order:
                break
            t = map(lambda x: x/float(order), [i,j] )
            degreesOfFreedom.append( tuple(t) )
            monomials.append( (i,j) )

elif dimension == 3:
    for i in range(order+1):
        for j in range(order+1):
            for k in range(order+1):
                if i + j + k > order:
                    break
                t = map(lambda x: x/float(order), [i,j,k] )
                degreesOfFreedom.append( tuple(t) )
                monomials.append( (i,j,k) )


referenceBaseFunctions = []

if dimension == 2:
    for i in range( len(degreesOfFreedom) ):
        matrix = []
        for (x,y) in degreesOfFreedom:
            row = []
            for (ex,ey) in monomials:
                row.append( pow(x,ex) * pow(y,ey) )
            matrix.append(row)
        inverse = inv(matrix)
        column = list( inverse[:,i] )       # inverse * vector
        def baseFunc(x,y):
            s = 0
            for i in range( len(monomials) ):
                C = column[i]
                (ex,ey) = monomials[i]
                s += C * (pow(x,ex) * pow(y,ey))
            return s
        referenceBaseFunctions.append(baseFunc)

elif dimension == 3:
    for i in range( len(degreesOfFreedom) ):
        matrix = []
        for (x,y,z) in degreesOfFreedom:
            row = []
            for (ex,ey,ez) in monomials:
                row.append( pow(x,ex) * pow(y,ey) * pow(z,ez) )
            matrix.append(row)
        inverse = inv(matrix)
        column = list( inverse[:,i] )       # inverse * vector
        def baseFunc(x,y,z):
            s = 0
            for i in range( len(monomials) ):
                C = column[i]
                (ex,ey,ez) = monomials[i]
                s += C * (pow(x,ex) * pow(y,ey) * pow(z,ez))
            return s
        referenceBaseFunctions.append(baseFunc)