Error solving Matrix equation with numpy

Question

I'm writing my own Newton-Raphson algorithm in Python using sympy and numpy.

The code is below but you can ignore this and skip on to the error:

CODE

def newtonRhapson(fncList, varz, x0):

    jacob = []

    for fnc in fncList:
        vec = []
        for var in varz:
            res = fnc.diff(var)
            for i in range(len(varz)):
                res = res.subs(varz[i], x0[i])
            vec.append(res)
        jacob.append(numpy.array(vec, dtype='float64'))

    fx0=[]

    for fnc in fncList:
        res2 = fnc
        for i in range(len(varz)):
            res2 = res2.subs(varz[i], x0[i])
        fx0.append(res2)

    j = jacob
    f = fx0

    print j
    print ''
    print f

    print numpy.linalg.solve(j,f).tolist()

The arguments to the function are:

fncList - a python list of functions using Sympy symbols

varz - a list containing those symbols (variables)

x0 - initial guess

ERROR

Up until the point where we print j and f it works fine and prints the following:

[array([-9.13378682, -5.91269838]), array([ 4.84401379,  1.01980286])]

[-5.15598620617611, 5.13378681611922]

when I run:

newtonRhapson([5*cos(a)+6*cos(a+b)-10, 5*sin(a)+6*sin(a+b)-4], [a,b], [0.7,0.7])

But on running the line:

print numpy.linalg.solve(j,f).tolist()

I get the error:

File "/Users/me/anaconda/lib/python2.7/site-  packages/numpy/linalg/linalg.py", line 384, in solve
r = gufunc(a, b, signature=signature, extobj=extobj)
TypeError: No loop matching the specified signature and casting was found for ufunc solve1

Answer 1

Your issue is in your second for loop.

for fnc in fncList:
    res2 = fnc
    for i in range(len(varz)):
        res2 = res2.subs(varz[i], x0[i])
    fx0.append(res2)

When you append to fx0, you need to ensure that you are appending the same type (float64) such that NumPy can compute the determinant of your system with LAPACK (see this answer for more info). You are currently appending <class 'sympy.core.numbers.Float'> - your errror message is telling you that you have an incorrect type signature for usage.

To correct this issue, you can simply append numpy.array with a dtype specification for float64 as you did above

for fnc in fncList:
    res2 = fnc
    for i in range(len(varz)):
        res2 = res2.subs(varz[i], x0[i])
    fx0.append(numpy.array(res2, dtype='float'))