human
Solve the following python programming problem given the following code:
def _exp_pade(ctx, a) : 
    "
        Exponential of a matrix using Pade approximants.

        See G. H. Golub, C. F. van Loan 'Matrix Computations',
        third Ed., page 572

        TODO:
         - find a good estimate for q
         - reduce the number of matrix multiplications to improve
           performance
        " 
    def eps_pade(p) : 
        return (((ctx.mpf (2) ** (3 - (2 * p))) * (ctx.factorial (p) ** 2)) / ((ctx.factorial ((2 * p)) ** 2) * ((2 * p) + 1))) 
q = 4 
    extraq = 8 
    while 1 : 
        if (eps_pade (q) < ctx.eps) : 
            break 
q += 1 
q += extraq 
    j = int (max (1, ctx.mag (ctx.mnorm (a, 'inf')))) 
    extra = q 
    prec = ctx.prec 
    ctx.dps += (extra + 3) 
    try : 
        a = (a / (2 ** j)) 
        na = a.rows 
        den = ctx.eye (na) 
        num = ctx.eye (na) 
        x = ctx.eye (na) 
        c = ctx.mpf (1) 
        for k in range (1, (q + 1)) : 
            c *= (ctx.mpf (((prec - k) + 1)) / ((((2 * q) - k) + 1) * k)) 
            x = (a * x) 
            cx = (c * x) 
            num += cx 
            den += (((- 1) ** k) * cx) 
f = ctx.lu_solve_mat (den, num) 
        for k in range (j) : 
            f = (f * f) 
finally : 
        ctx.prec = prec 
return (f * 1) 

    
    

    Fix the buggy line: c *= (ctx.mpf (((prec - k) + 1)) / ((((2 * q) - k) + 1) * k))
assistant
#Here is Python program to find a good estimate for q
.

c *= (ctx.mpf (((q - k) + 1)) / ((((2 * q) - k) + 1) * k))