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i/test2 Home Manual Packages Global Index Keywords Quick Reference ``` /* TEST2.I Highly vectorizing physics problem for timing Yorick. \$Id: test2.i,v 1.1 1993/08/27 18:50:06 munro Exp \$ */ /* Copyright (c) 1994. The Regents of the University of California. All rights reserved. */ func test2 (npass) /* DOCUMENT test2 or test2, npass Given a slab divided into zones by parallel planes, and given a set of photon group boundary energies, compute the contribution of each zone to the radiation flux emerging from one surface of the slab. If NPASS is given, the calculation is repeated that many times. The zoning, photon group structure, opacities, and source functions are all computed arbitrarily, but the number of zones and groups are taken to be representative of a typical 1-D radiation transport calculation. */ { if (is_void(npass) || npass<=0) npass= 1; now= split= exponential= array(0.0, 3); timer, now; n= npass; while (n--) esc= escout(zt, akap, srcfun); timer, now, split; timer_print, "Time per pass", split/npass, "Total time", split,\ "Computing exponentials", exponential; if (esc(0,mxx)!=29 || !approx_eq(esc(0,max),0.001875213417) || !approx_eq(esc(0,1),0.001694423767) || !approx_eq(esc(0,0),5.434635527e-05) || esc(1,mxx)!=39 || !approx_eq(esc(1,max),0.000440460566)) write, "***WARNING*** values returned by escout are not correct"; if (flxout(0,mxx)!=34 || !approx_eq(flxout(0,max),0.06615472064) || !approx_eq(flxout(0,1),0.003187516911) || !approx_eq(flxout(0,0),0.005280842058) || flxout(1,mxx)!=29 || !approx_eq(flxout(1,max),0.001805157164)) write, "***WARNING*** values of flxout are not correct"; if (!approx_eq(min(tau(:-1,)),6.982090961e-05) || !approx_eq(max(tau),45.80160946)) write, "***WARNING*** values of tau are not correct"; } func approx_eq(x, y) { return (abs(x-y)/(abs(x+y)+1.e-35))<1.e-6; } #if 0 CPU seconds per pass: IDL Yorick Basis DAP FORTRAN(-O) HP730 - 0.60 2.04 1.84 0.27 (0.60 -g) Solbourne 2.81 1.90 6.02 5.90 1.00 (varies by ~10%) Using forum (Solbourne) on 8/Dec/92: forum time /usr/local/lib/idl/bin.sunos.4.1.sun4/idl IDL. Version 2.3.0 (sunos sparc). Copyright 1989-1992, Research Systems, Inc. All rights reserved. Unauthorized reproduction prohibited. Site: 1491. Licensed for use by: LLNL - X Division IDL> .rnew /home/miggle/munro/Yorick/include/test2 % Compiled module: ESCOUT. % Compiled module: APPROX_EQ. % Compiled module: TEST2. % Compiled module: BNU. % Compiled module: OPACSET. % Compiled module: SPAN. % Compiled module: SPANL. % Compiled module: \$MAIN\$. IDL> test2,1 IDL> exit 3.2u 0.4s 0:12 29% 0+2496k 1+2io 1pf+0w forum time time /usr/local/lib/idl/bin.sunos.4.1.sun4/idl IDL. Version 2.3.0 (sunos sparc). Copyright 1989-1992, Research Systems, Inc. All rights reserved. Unauthorized reproduction prohibited. Site: 1491. Licensed for use by: LLNL - X Division IDL> .rnew /home/miggle/munro/Yorick/include/test2 % Compiled module: ESCOUT. % Compiled module: APPROX_EQ. % Compiled module: TEST2. % Compiled module: BNU. % Compiled module: OPACSET. % Compiled module: SPAN. % Compiled module: SPANL. % Compiled module: \$MAIN\$. IDL> test2,11 IDL> exit 31.3u 0.9s 0:58 54% 0+3544k 0+0io 0pf+0w forum time yorick Yorick ready. For help type 'help' > #include "/home/miggle/munro/Yorick/include/test2.i" > test2,1 Timing Category CPU sec System sec Wall sec Time per pass 1.840 0.300 2.270 Total time 1.840 0.300 2.270 Computing exponentials 0.600 0.120 0.760 -----Total Elapsed Times----- 2.510 0.490 27.500 > test2,10 Timing Category CPU sec System sec Wall sec Time per pass 1.932 0.050 1.986 Total time 19.320 0.500 19.860 Computing exponentials 6.360 0.080 6.440 -----Total Elapsed Times----- 21.860 1.020 53.080 > quit 21.9u 1.0s 0:59 38% 0+3560k 31+0io 85pf+0w forum basis Basis (basis, Version 921125) Run at 13:02:49 on 12/08/92 on the forum machine, suffix 10797x Initializing Basis System Basis 7.0 Initializing EZCURVE/NCAR Graphics Ezcurve/NCAR 2.0 Basis> echo=0 Basis> read /home/miggle/munro/Yorick/include/test2.bas End of input file /home/miggle/munro/Yorick/include/test2.bas Resuming input from TERMINAL Basis> test2(1) CPU (sec) SYS (sec) 6.017 0.300 Basis> test2(10) CPU (sec) SYS (sec) 60.233 0.017 Basis> end CPU (sec) SYS (sec) 68.617 0.917 68.6u 0.9s 2:07 54% 0+6144k 19+1io 213pf+0w forum dap DAP> read /home/miggle/munro/Yorick/include/test2.bas DAP> test2(1) CPU (sec) SYS (sec) 5.883 0.400 DAP> test2(10) CPU (sec) SYS (sec) 59.533 0.000 DAP> end 69.1u 1.5s 1:47 65% 0+6488k 20+1io 218pf+0w Yorick results (test2.bas) on tonto (HP730) 21:53 4/Dec/92 top showed SIZE/RES 764K/244K at prompt 3636K/3052K after test2,1 4628K/4012K after test2,20 tonto yorick Yorick ready. For help type 'help' > #include "/home/miggle/munro/Yorick/include/test2.i" > test2,1 Timing Category CPU sec System sec Wall sec Time per pass 0.550 0.100 0.670 Total time 0.550 0.100 0.670 Computing exponentials 0.240 0.030 0.270 -----Total Elapsed Times----- 0.930 0.220 34.950 > test2,20 Timing Category CPU sec System sec Wall sec Time per pass 0.599 0.001 0.906 Total time 11.980 0.020 18.110 Computing exponentials 5.030 0.000 7.270 -----Total Elapsed Times----- 12.920 0.240 83.120 Basis results (test2.bas) on tonto (HP730) 21:53 4/Dec/92 top showed SIZE/RES 5356K/540K at prompt 8960K/4108K after test2(1) 8960K/4112K after test2(20) tonto basis Basis (basis, Version 921125) Run at 21:45:42 on 12/04/92 on the tonto machine, suffix 27713x Initializing Basis System Basis 7.0 Initializing EZCURVE/NCAR Graphics Ezcurve/NCAR 2.0 Basis> echo=0 Basis> read /home/miggle/munro/Yorick/include/test2.bas End of input file /home/miggle/munro/Yorick/include/test2.bas Resuming input from TERMINAL Basis> test2(1) CPU (sec) SYS (sec) 1.990 .120 Basis> test2(20) CPU (sec) SYS (sec) 40.800 .000 DAP results (test2.bas) on tonto (HP730) 21:53 4/Dec/92 top showed SIZE/RES 6796K/844K at prompt 10360K/4352K after test2(1) 10360K/4352K after test2(20) tonto dap DAP> echo=0 DAP> read /home/miggle/munro/Yorick/include/test2.bas DAP> test2(1) CPU (sec) SYS (sec) 1.840 .080 DAP> test2(20) CPU (sec) SYS (sec) 36.830 .000 #endif /* This routine computes the optical depth through each zone at every frequency and then uses that to compute the radiation emitted in each zone that escapes from the problem, assuming plane parallel geometry. The returned result is an nzones-by-ngroups array of power per unit photon energy per unit area. */ func escout (zt, /* npoints zone boundary positions (cm) */ akap, /* nzones-by-ngroups opacities (1/cm) */ srcfun) /* nzones-by-ngroups source (specific intensity units) */ { extern flxout; /* (output) nzones-by-ngroups outgoing fluxes */ extern dtau; /* (output) nzones-by-ngroups optical depths (ODs) */ extern tau; /* (output) npoints-by-ngroups cumulative ODs */ extern mu, wmu; /* Gauss-Legendre cos(theta) and weight arrays for integration over escape angles */ /* compute tau, the optical depth to each zone along the zt-direction */ dtau= akap*zt(dif); tau= array(0.0, dimsof(zt), dimsof(akap)(3)); tau(2:,)= dtau(psum,); /* consider the outward going radiation, and thus use tau measured from the right boundary */ tau= tau(0,)(-,) - tau; /* compute exf, the fraction of the srcfun which escapes from each zone in each bin at each angle mu relative to the zt direction */ enow= array(0.0, 3); timer, enow; /* most of the actual work is computing these exponentials */ exf= exp(-tau(,,-)/mu(-,-,)); timer, enow, exponential; /* compute the escaping flux per unit surface area in each bin contributed by each zone -- units are 10^17 W/kev/cm^2 */ /* Note: dI/dtau = -I + S (S is srcfun, which is Bnu) implies I = integral of ( S * exp(tau) ) dtau from tau -infinity to tau 0 Hence, the contribution of a single zone to this integral is S12 * (exp(tau1) - exp(tau2)), which explains the exf(dif,,) below. The wmu are Gauss-Legendre integration weights, and the mu is the cos(theta) to project the specific intensity onto the direction normal to the surface (zt). */ esfun= 2*pi*exf(dif,,)*srcfun(,,-)*(mu*wmu)(-,-,); /* Also compute what the total flux WOULD have been if each successive zone were at the surface. This is the same as the "one-sided" flux directed outward across each zone boundary. */ fuzz= 1.0e-10; flxout= (esfun(psum,,)/(exf(2:,,)+fuzz))(,,sum); return esfun(,,sum); } /* This function is used to set a dummy opacity to be used by the transport calculation */ func opacset (tmp, rho, gav, gb) { extern srcfun; /* (output) nzones-by-ngroups Bnu, LTE source function */ extern akap; /* (output) nzones-by-ngroups opacities (1/cm) */ /* the opacity is proportional to the density to the rhopow power and the temperature to the tempow power */ rhopow= 2; tempow= 3; factr= (tmp/1.0)^tempow*(rho/1.0)^rhopow; /* set the constants in front of the terms for the two edges */ con0= 1.0e+4; cona= 2.5e+2; conb= 5.0e+0; /* set the energies of the two edges */ edg0= 0.1; edga= 0.5; edgb= 2.0; /* set up arrays that are zero below the edges and one above them */ vala= double(gav>edga); valb= double(gav>edgb); /* frequency dependence is the same for all zones, so calculate it once */ frval= con0*(edg0/gav)^3+cona*vala*(edga/gav)^3+conb*valb*(edgb/gav)^3; /* set the opacity */ akap= factr(,-)*frval(-,); /* the source function is always a blackbody */ srcfun= bnu(tmp, gb); } /* Make a blackbody using the analytic formula -- the units are 10^17 W/kev/g/ster */ func bnu (tmp, freqb) { /* Note that tmp and freqb are one dimensional and the output array should be 2D */ /* compute the derivative using the exact black body, not the average over the bin */ exf= exp(-(freqb(zcen)(-,)/tmp)); return 0.0504*(freqb(zcen)^3)(-,)*exf/(1.0-exf); } /* set up default params. etc. */ /* set the number of spatial zones and photon groups */ npoints= 100; ngroups= 64; nzones= npoints-1; /* set the zone boundary positions */ zt= span(0.0, 0.0050, npoints); /* set the frequency bins */ gb= spanl(0.1, 4.0, ngroups+1); gav= gb(zcen); /* set the density and temperature */ rho= spanl(1.0, 1.0, nzones); tmp= spanl(1.0, 1.0, nzones); /* set the opacity akap and source function srcfun */ opacset, tmp, rho, gav, gb; /* set up for a Gauss-Legendre angular quadrature */ xmu= [0.1488743389, 0.4333953941, 0.6794095682, 0.8650633666, 0.9739065285]; mu= -xmu(::-1); grow, mu, xmu; xmu= [0.2955242247, 0.2692667193, 0.2190863625, 0.1494513491, 0.0666713443]; wmu= xmu(::-1); grow, wmu, xmu; /* correct the Gauss-Legendre abcissas-- interval is only 0 to 1 */ mu= 0.5 + 0.5*mu; ```