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NYC 9/11 Public Portal Document •«S»C3CJCSS»***

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Table 5.2 is intended to compare MINPACK with the CATLAS technique. Two problems are solved, one with a high vacancy rate and the other with a low vacancy rate. It is seen that the analytic evaluation of the Jacobian diagonals is 387 times faster than the numerical evaluation of the full Jacobian. The number of iterations needed by MINPACK is higher than the number n*}eded by the CATLAS technique. This means that ignoring the off-diagonals but accurately computing the diagonals is much more accurate than numerically evaluating the whole matrix. Given the bad starting point of the last column, the CATLAS technique converges within about 2.5 seconds, whereas MINPACK takes in excess of 900 seconds.

Table 5.3 Solution of a Problem Using CATLAS with Alternative Starting Points and Vacancy Rates (Dimensions: i=300, j=2200, k=l, m=2, 1=60, n=2)

Vacancy Equilibrium 0.9 X (Equil. 0.7 X (Equil. Rate Rents Rents) Rents) n 1 6 7 20% CPU 12.59 68.65 79.841 n 1 9 11 5% CPU 12.59 106.94 130.312 0.5% n 1 11 14 CPU 12.59 125.42 159.490 n : the number of iterations needed to converge. CPU : the computational time does not include input-output time, (19.641 additional seconds were used to input the data).

Table 5.3 shows the computational experience obtained from applyirig the CATLAS technique to a much larger problem in which there are 2200 residential zones (equations), 300 work zones and 60 shopping zones. The hardest of these problems is solved within 160 seconds and takes only 14 iterations. To summarize, NYREG appears computationally feasible for fairly large problems using the Newton-Raphson type technique developed and applied in CATLAS. iConvergence is rapid and obtainable at reasonable clock times on the CRAY-2 machine of NCSA at the University of Illinois at Urbana-Champaign. As a result of these computational experiments, the CATLAS technique was selected for use with the model and a streamlined and vectorized algorithm was developed.

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