2016-11-06 18:00 GMT-02:00 Stephen J. Turnbull < turnbull.stephen...@u.tsukuba.ac.jp>:
> Danilo J. S. Bellini writes: > > > About the effort, do you really find the examples below with the new > > proposed syntax difficult to understand? > > No. I just don't see how they would become tools I would use. My main > interest here was in your claim to have economic applications, but the > examples you give don't seem to offer big wins for the kind of > calculations I, my students, or my colleagues do. Perhaps you will > have better luck interesting/persuading others. > If you want something simple, the itertools.accumulate examples from docs.python.org include a simple "loan amortization" example: >>> # Amortize a 5% loan of 1000 with 4 annual payments of 90 >>> cashflows = [1000, -90, -90, -90, -90] >>> list(accumulate(cashflows, lambda bal, pmt: bal*1.05 + pmt)) [1000, 960.0, 918.0, 873.9000000000001, 827.5950000000001] >>> # With the proposed syntax >>> payments = [90, 90, 90, 90] >>> [bal * 1.05 - pmt for pmt in payments from bal = 1000] [1000, 960.0, 918.0, 873.9000000000001, 827.5950000000001] >From the Wilson J. Rugh "Linear Systems Theory" book, chapter 20 "Discrete Time State Equations", p. 384-385 (the very first example on the topic): """ A simple, classical model in economics for national income y(k) in year k describes y(k) in terms of consumer expenditure c(k), private investment i(k), and government expenditure g(k) according to: y(k) = c(k) + i(k) + g(k) These quantities are interrelated by the following assumptions. First, consumer expenditure in year k+1 is proportional to the national income in year k, c(k+1) = α·y(k) where the constant α is called, impressively enough, the marginal propensity to consume. Second, the private investment in year k+1 is proportional to the increase in consumer expenditure from year k to year k+1, i(k+1) = β·[c(k+1) - c(k)] where the constant β is a growth coefficient. Typically 0 < α < 1 and β > 0. >From these assumptions we can write the two scalar difference equations c(k+1) = α·c(k) + α·i(k) + α·g(k) i(k+1) = (β·α-β)·c(k) + β·α·i(k) + β·α·g(k) Defining state variables as x₁(k) = c(k) and x₂(k) = i(k), the output as y(k), and the input as g(k), we obtain the linear state equation # ⎡ α α ⎤ ⎡ α ⎤ # x(k+1) = ⎢ ⎥·x(k) + ⎢ ⎥·g(k) # ⎣β·(α-1) β·α⎦ ⎣β·α⎦ # # y(k) = [1 1]·x(k) + g(k) Numbering the years by k = 0, 1, ..., the initial state is provided by c(0) and i(0). """ You can use my "ltiss" or "ltvss" (if alpha/beta are time varying) functions from the PyScanPrev state-space example to simulate that, or some dedicated function. The linear time varying version with the proposed syntax would be (assuming alpha, beta and g are sequences like lists/tuples): >>> from numpy import mat >>> def first_digital_linear_system_example_in_book(alpha, beta, c0, i0, g): ... A = (mat([[a, a ], ... [b*(a-1), b*a]]) for a, b in zip(alpha, beta)) ... B = (mat([[a ], ... [b*a]]) for a, b in zip(alpha, beta)) ... x0 = mat([[c0], ... [i0]]) ... x = (Ak*xk + Bk*gk for Ak, Bk, gk in zip(A, B, g) from xk = x0) ... return [xk.sum() + gk for xk, gk in zip(x, g)] If A and B were constants, it's simpler, as the scan line would be: x = (A*xk + B*gk for gk in g from xk = x0) -- Danilo J. S. Bellini --------------- "*It is not our business to set up prohibitions, but to arrive at conventions.*" (R. Carnap)
_______________________________________________ Python-ideas mailing list Python-ideas@python.org https://mail.python.org/mailman/listinfo/python-ideas Code of Conduct: http://python.org/psf/codeofconduct/
