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/*
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[18] 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[19] 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[20] 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[21] 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[22] 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[9] 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[8] 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[11] 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;
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