subroutine aptscav (np, pm, au, av, aw, bu, bv, bw, nerr) ccbeg. cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c SUBROUTINE APTSCAV c c call aptscav (np, pm, au, av, aw, bu, bv, bw, nerr) c c Version: aptscav Updated 1991 August 26 15:20. c aptscav Originated 1991 August 26 15:20. c c Author: Arthur L. Edwards, LLNL, L-298, Telephone (925) 422-4123. c c c Purpose: To randomly sample np unit direction vectors b = (bu, bv, bw) c from a cosine**pm distribution in 3-D space, centered on an c axis in the direction of unit vector a = (au, av, aw). c Flag nerr indicates any input error. c c If "ba" is the expected value of the component of unit vector c "b" in the direction of unit vector "a", then: c c ba = (pm + 1.0) / (pm + 2.0). (ba .ge. 0.5). c pm = (2.0 * ba - 1.0) / (1.0 - ba). (pm .ge. 0.0). c pm = 0.0: isotropic in half-space. c pm = 1.0: cosine distribution in half-space. c c Input: np, pm, au, av, aw. c c Output: bu, bv, bw, nerr. c c Glossary: c c au,av,aw Input The u, v and w components of a unit vector in the c direction of the center of a cosine**pm distribution. c Size np. c c bu,bv,bw Output The u, v, w components of a unit vector representing a c direction chosen randomly from a cosine**pm c distribution in 3-D space, centered in the direction c of unit vector "a". Coordinates u, v and w may c be any 3 orthogonal coordinates. Size np. c c nerr Output Indicates an input error, if not 0. c 1 if np is not positive. c 2 if pm is -1.0 or less. c c np Input Size of arrays. c c pm Input Power used for the cosine**pm spatial distribution c from which unit vector "b" is to be chosen. c Must be greater than -1.0. c cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc ccend. c.... Dimensioned arguments. c---- Component u of reference vector. dimension au (1) c---- Component v of reference vector. dimension av (1) c---- Component w of reference vector. dimension aw (1) c---- Component u of random unit vector. dimension bu (1) c---- Component v of random unit vector. dimension bv (1) c---- Component w of random unit vector. dimension bw (1) c.... Local variables. c---- Cosine of angle phi. common /laptscav/ cosph c---- Cosine of angle theta. common /laptscav/ costh c---- Component u of unit vector "c". common /laptscav/ cu (64) c---- Component v of unit vector "c". common /laptscav/ cv (64) c---- Component w of unit vector "c". common /laptscav/ cw (64) c---- Function 1.0 / (1.0 + aw + fuz). common /laptscav/ faw c---- A very small number. common /laptscav/ fuz c---- Index in unit vector array. common /laptscav/ n c---- First index of subset of data. common /laptscav/ n1 c---- Last index of subset of data. common /laptscav/ n2 c---- Index in external array. common /laptscav/ nn c---- Size of current subset of data. common /laptscav/ ns c---- Numerical constant pi. common /laptscav/ pi c---- Random number (0.0 to 1.0). common /laptscav/ ranfp1 (64) c---- Random number (0.0 to 1.0). common /laptscav/ ranfp2 (64) c---- Rotation matrix. common /laptscav/ rotm (3,3) c---- Sine of angle phi. common /laptscav/ sinph c---- Sine of angle of "a" from w axis. common /laptscav/ sinr c---- Function sinr + fuz. common /laptscav/ sinr1 c---- Sine of angle theta. common /laptscav/ sinth c---- Angle from v axis in vw plane. common /laptscav/ theta cbugc***DEBUG begins. cbug common /laptscav/ avgu, avgv, avgw, devu, devv, devw cbug common /laptscav/ avgu2, avgv2, avgw2, sumsqs cbug common /laptscav/ vdot, vdota, vdot2a cbug 9901 format (/ 'aptscav finding cos**pm random directions.' / cbug & ' np=',i3,' pm=',1pe22.14 / cbug & (i3,' au,av,aw=',1p3e22.14)) cbug write (3, 9901) np, pm, (n, au(n), av(n), aw(n), n = 1, np) cbugc***DEBUG ends. c.... initialize. c---- A very small number. fuz = 1.e-99 c++++ Dimensionless. 18 digits. pi = 3.14159265358979323 nerr = 0 c.... Test for input errors. if (np .le. 0) then nerr = 1 go to 210 endif if (pm .le. -1.0) then nerr = 2 go to 210 endif c.... Set up the indices of the first subset of data. n1 = 1 n2 = min (np, 64) c.... Loop over the data subsets. 110 ns = n2 - n1 + 1 c.... Generate the needed random numbers. c---- Loop over subset of data. do 120 n = 1, ns ranfp1(n) = ranf( ) c---- End of loop over subset of data. 120 continue c---- Loop over subset of data. do 130 n = 1, ns ranfp2(n) = ranf( ) c---- End of loop over subset of data. 130 continue c.... Find unit vectors "c" with the w component sampled from a cos**pm c.... distribution. c---- Loop over vectors. do 140 n = 1, ns cosph = ranfp1(n)**(1.0 / (1.0 + pm)) sinph = sqrt (1.0 - cosph**2) theta = 2.0 * pi * ranfp2(n) costh = cos (theta) sinth = sin (theta) cu(n) = costh * sinph cv(n) = sinth * sinph cw(n) = cosph c---- End of loop over vectors. 140 continue c.... Rotate all the unit vectors "c" by the angle required to align the c.... vector (0., 0., 1.) with the unit vector a = (au, av, aw). c---- Loop over vectors. do 150 n = 1, ns nn = n + n1 - 1 sinr = sqrt (au(nn)**2 + av(nn)**2) sinr1 = sinr + fuz faw = (1.0 - aw(nn)) / sinr1**2 rotm(1,1) = av(nn)**2 * faw + aw(nn) rotm(1,2) = -au(nn) * av(nn) * faw rotm(1,3) = au(nn) * sinr / sinr1 rotm(2,1) = -au(nn) * av(nn) * faw rotm(2,2) = au(nn)**2 * faw + aw(nn) rotm(2,3) = av(nn) * sinr / sinr1 rotm(3,1) = -au(nn) * sinr / sinr1 rotm(3,2) = -av(nn) * sinr / sinr1 rotm(3,3) = aw(nn) bu(nn) = cu(n) * rotm(1,1) + cv(n) * rotm(1,2) + & cw(n) * rotm(1,3) bv(nn) = cu(n) * rotm(2,1) + cv(n) * rotm(2,2) + & cw(n) * rotm(2,3) bw(nn) = cu(n) * rotm(3,1) + cv(n) * rotm(3,2) + & cw(n) * rotm(3,3) c---- End of loop over vectors. 150 continue c.... See if all data subsets are done. c---- Do another subset of data. if (n2 .lt. np) then n1 = n2 + 1 n2 = min (np, n1 + 63) go to 110 endif cbugc***DEBUG begins. cbug cbug 9902 format (/ 'aptscav results:') cbug 9903 format (i3,' bu,bv,bw=',1p3e22.14 / cbug & ' sumsq= ',1pe22.14,' vdot=',1pe22.14) cbug 9904 format (/ 'aptscav mean and deviation:' / cbug & ' avg(u,v,w)=',1p3e22.14 / cbug & ' dev(u,v,w)=',1p3e22.14 / cbug & ' vdota,dev= ',1p2e22.14) cbug cbug write ( 3, 9902) cbug cbug avgu = 0.0 cbug avgv = 0.0 cbug avgw = 0.0 cbug avgu2 = 0.0 cbug avgv2 = 0.0 cbug avgw2 = 0.0 cbug vdota = 0.0 cbug vdot2a = 0.0 cbug cbug do 160 n = 1, np cbug avgu = avgu + bu(n) cbug avgv = avgv + bv(n) cbug avgw = avgw + bw(n) cbug avgu2 = avgu2 + bu(n)**2 cbug avgv2 = avgv2 + bv(n)**2 cbug avgw2 = avgw2 + bw(n)**2 cbug sumsqs = bu(n)**2 + bv(n)**2 + bw(n)**2 cbug vdot = au(n) * bu(n) + av(n) * bv(n) + aw(n) * bw(n) cbug vdota = vdota + vdot cbug vdot2a = vdot2a + vdot**2 cbug write ( 3, 9903) n, bu(n), bv(n), bw(n), sumsqs, vdot cbug 160 continue cbug cbug avgu = avgu / np cbug avgv = avgv / np cbug avgw = avgw / np cbug avgu2 = avgu2 / np cbug avgv2 = avgv2 / np cbug avgw2 = avgw2 / np cbug devu = sqrt (avgu2 - avgu**2) cbug devv = sqrt (avgv2 - avgv**2) cbug devw = sqrt (avgw2 - avgw**2) cbug vdota = vdota / np cbug vdot2a = vdot2a / np cbug devdot = sqrt (vdot2a - vdota**2) cbug cbug write ( 3, 9904) avgu, avgv, avgw, devu, devv, devw, cbug & vdota, devdot cbugc***DEBUG ends. 210 return c.... End of subroutine aptscav. (+1 line.) end UCRL-WEB-209832