diff options
Diffstat (limited to 'numpy/lib/financial.py')
| -rw-r--r-- | numpy/lib/financial.py | 68 |
1 files changed, 35 insertions, 33 deletions
diff --git a/numpy/lib/financial.py b/numpy/lib/financial.py index c085a5d53..5b96e5b8e 100644 --- a/numpy/lib/financial.py +++ b/numpy/lib/financial.py @@ -119,7 +119,8 @@ def fv(rate, nper, pmt, pv, when='end'): temp = (1+rate)**nper miter = np.broadcast(rate, nper, pmt, pv, when) zer = np.zeros(miter.shape) - fact = np.where(rate==zer, nper+zer, (1+rate*when)*(temp-1)/rate+zer) + fact = np.where(rate == zer, nper + zer, + (1 + rate*when)*(temp - 1)/rate + zer) return -(pv*temp + pmt*fact) def pmt(rate, nper, pv, fv=0, when='end'): @@ -210,7 +211,8 @@ def pmt(rate, nper, pv, fv=0, when='end'): temp = (1+rate)**nper miter = np.broadcast(rate, nper, pv, fv, when) zer = np.zeros(miter.shape) - fact = np.where(rate==zer, nper+zer, (1+rate*when)*(temp-1)/rate+zer) + fact = np.where(rate == zer, nper + zer, + (1 + rate*when)*(temp - 1)/rate + zer) return -(fv + pv*temp) / fact def nper(rate, pmt, pv, fv=0, when='end'): @@ -279,7 +281,7 @@ def nper(rate, pmt, pv, fv=0, when='end'): B = np.log((-fv+z) / (pv+z))/np.log(1.0+rate) miter = np.broadcast(rate, pmt, pv, fv, when) zer = np.zeros(miter.shape) - return np.where(rate==zer, A+zer, B+zer) + 0.0 + return np.where(rate == zer, A + zer, B + zer) + 0.0 def ipmt(rate, per, nper, pv, fv=0.0, when='end'): """ @@ -365,7 +367,8 @@ def ipmt(rate, per, nper, pv, fv=0.0, when='end'): """ when = _convert_when(when) - rate, per, nper, pv, fv, when = np.broadcast_arrays(rate, per, nper, pv, fv, when) + rate, per, nper, pv, fv, when = np.broadcast_arrays(rate, per, nper, + pv, fv, when) total_pmt = pmt(rate, nper, pv, fv, when) ipmt = _rbl(rate, per, total_pmt, pv, when)*rate try: @@ -507,12 +510,16 @@ def pv(rate, nper, pmt, fv=0.0, when='end'): return -(fv + pmt*fact)/temp # Computed with Sage -# (y + (r + 1)^n*x + p*((r + 1)^n - 1)*(r*w + 1)/r)/(n*(r + 1)^(n - 1)*x - p*((r + 1)^n - 1)*(r*w + 1)/r^2 + n*p*(r + 1)^(n - 1)*(r*w + 1)/r + p*((r + 1)^n - 1)*w/r) +# (y + (r + 1)^n*x + p*((r + 1)^n - 1)*(r*w + 1)/r)/(n*(r + 1)^(n - 1)*x - +# p*((r + 1)^n - 1)*(r*w + 1)/r^2 + n*p*(r + 1)^(n - 1)*(r*w + 1)/r + +# p*((r + 1)^n - 1)*w/r) def _g_div_gp(r, n, p, x, y, w): t1 = (r+1)**n t2 = (r+1)**(n-1) - return (y + t1*x + p*(t1 - 1)*(r*w + 1)/r)/(n*t2*x - p*(t1 - 1)*(r*w + 1)/(r**2) + n*p*t2*(r*w + 1)/r + p*(t1 - 1)*w/r) + return ((y + t1*x + p*(t1 - 1)*(r*w + 1)/r) / + (n*t2*x - p*(t1 - 1)*(r*w + 1)/(r**2) + n*p*t2*(r*w + 1)/r + + p*(t1 - 1)*w/r)) # Use Newton's iteration until the change is less than 1e-6 # for all values or a maximum of 100 iterations is reached. @@ -572,7 +579,7 @@ def rate(nper, pmt, pv, fv, when='end', guess=0.10, tol=1e-6, maxiter=100): while (iter < maxiter) and not close: rnp1 = rn - _g_div_gp(rn, nper, pmt, pv, fv, when) diff = abs(rnp1-rn) - close = np.all(diff<tol) + close = np.all(diff < tol) iter += 1 rn = rnp1 if not close: @@ -593,9 +600,9 @@ def irr(values): ---------- values : array_like, shape(N,) Input cash flows per time period. By convention, net "deposits" - are negative and net "withdrawals" are positive. Thus, for example, - at least the first element of `values`, which represents the initial - investment, will typically be negative. + are negative and net "withdrawals" are positive. Thus, for + example, at least the first element of `values`, which represents + the initial investment, will typically be negative. Returns ------- @@ -605,13 +612,13 @@ def irr(values): Notes ----- The IRR is perhaps best understood through an example (illustrated - using np.irr in the Examples section below). Suppose one invests - 100 units and then makes the following withdrawals at regular - (fixed) intervals: 39, 59, 55, 20. Assuming the ending value is 0, - one's 100 unit investment yields 173 units; however, due to the - combination of compounding and the periodic withdrawals, the - "average" rate of return is neither simply 0.73/4 nor (1.73)^0.25-1. - Rather, it is the solution (for :math:`r`) of the equation: + using np.irr in the Examples section below). Suppose one invests 100 + units and then makes the following withdrawals at regular (fixed) + intervals: 39, 59, 55, 20. Assuming the ending value is 0, one's 100 + unit investment yields 173 units; however, due to the combination of + compounding and the periodic withdrawals, the "average" rate of return + is neither simply 0.73/4 nor (1.73)^0.25-1. Rather, it is the solution + (for :math:`r`) of the equation: .. math:: -100 + \\frac{39}{1+r} + \\frac{59}{(1+r)^2} + \\frac{55}{(1+r)^3} + \\frac{20}{(1+r)^4} = 0 @@ -663,18 +670,18 @@ def npv(rate, values): The discount rate. values : array_like, shape(M, ) The values of the time series of cash flows. The (fixed) time - interval between cash flow "events" must be the same as that - for which `rate` is given (i.e., if `rate` is per year, then - precisely a year is understood to elapse between each cash flow - event). By convention, investments or "deposits" are negative, - income or "withdrawals" are positive; `values` must begin with - the initial investment, thus `values[0]` will typically be - negative. + interval between cash flow "events" must be the same as that for + which `rate` is given (i.e., if `rate` is per year, then precisely + a year is understood to elapse between each cash flow event). By + convention, investments or "deposits" are negative, income or + "withdrawals" are positive; `values` must begin with the initial + investment, thus `values[0]` will typically be negative. Returns ------- out : float - The NPV of the input cash flow series `values` at the discount `rate`. + The NPV of the input cash flow series `values` at the discount + `rate`. Notes ----- @@ -705,8 +712,9 @@ def mirr(values, finance_rate, reinvest_rate): Parameters ---------- values : array_like - Cash flows (must contain at least one positive and one negative value) - or nan is returned. The first value is considered a sunk cost at time zero. + Cash flows (must contain at least one positive and one negative + value) or nan is returned. The first value is considered a sunk + cost at time zero. finance_rate : scalar Interest rate paid on the cash flows reinvest_rate : scalar @@ -718,7 +726,6 @@ def mirr(values, finance_rate, reinvest_rate): Modified internal rate of return """ - values = np.asarray(values, dtype=np.double) n = values.size pos = values > 0 @@ -728,8 +735,3 @@ def mirr(values, finance_rate, reinvest_rate): numer = np.abs(npv(reinvest_rate, values*pos)) denom = np.abs(npv(finance_rate, values*neg)) return (numer/denom)**(1.0/(n - 1))*(1 + reinvest_rate) - 1 - -if __name__ == '__main__': - import doctest - import numpy as np - doctest.testmod(verbose=True) |