functions in drat.i -

             adjust_ireg(ireg)  
 
     returns the input IREG with the regions specified in drat_ireg_adj  
     zeroed.  Beware-- the ireg array is actually modified.  

             apply_funcs(streak_result)  
          or apply_funcs(transp, selfem)  
          or apply_funcs(transp, selfem, time)  
          or apply_funcs(transp, selfem, times)  
 
     applies the drat_backlight and drat_channel options (if any)  
     to the input streak_result.  This destroys the separate  
     transparency and self-emission information returned by streak.  
     transp= streak_result(,1,..) and selfem= streak_result(,2,..).  
     If time is not given, time=0.0 is passed to the functions.  
     If times is a vector, it must match the final dimension of  
     transp and selfem.  

             B_nu(hnu, kt)  
 
     returns the specific intensity emitted by a black surface at  
     photon energy HNU and temperature KT.  The units of HNU and KT  
     must be the same.  The units of the result are determined by  
     the variable B_nu_scale, which must be consistent with the units  
     of HNU and KT.  B_nu_scale is the Stefan-Boltzmann constant  
     (sigma in sigma*T^4) times 15/pi^5.  By default, B_nu_scale is  
     set to 0.05040366 ((jrk/sh)/(cm^2 ster))/keV^4.  (1 jrk/sh =  
     10^17 W)  
     HNU and KT may be arrays, provided they are conformable.  

             B_nu_bar(hnub, kt)  
 
     returns the specific intensity emitted by a black surface at  
     temperature KT in the energy bins whose boundary energies are  
     HNUB.  HNUB must be a 1-D array of bin boundary energies; the  
     units of KT must match the units of KT.  Both are in keV, by  
     default; see B_nu for a discussion of units.  
     The result will have dimensions (numberof(HNUB)-1)-by-dimsof(KT).  
     The algorithm has an accuracy of 0.2 percent.  The idea is to  
     difference an analytic approximation to the integral of B_nu.  

             default_gate(times)  
 
     initial value of drat_gate.  Refer to the source code  
     to learn how to write your own gate function, making proper use  
     of drat_start and drat_stop options in addition to the input times.  

             atten_emit= default_integrate(f, mesh, time, irays, slimits)  
 
     is the default drat_integrate routine.  
     On entry, file F is positioned at TIME, from which MESH has already  
     been read.  IRAYS and SLIMITS are the rays coordinates (in internal  
     format) and integration limits.  
     The result should be ngroup-by-2-by-raydims, where the second index  
     is 1 for the attenuation factor, 2 for the self-emission (specific  
     intensity due to emission along the ray).  
   OPTIONS: drat_linear, drat_ocompute, drat_oadjust,  
            drat_emult, drat_amult, drat_omult, drat_nomilne,  
            drat_ekap, drat_akap, drat_glist  

             default_ocompute(f, time)  
 
     initial value of drat_ocompute.  Extracts drat_akap and drat_ekap  
     from file F, possibly using the subset drat_glist.  TIME is unused.  

 drat_akap  
 

             drat_amult, drat_emult, drat_omult  
 
     are optional opacity multipliers used by the streak, snap, and  
     streak_save functions.  The multipliers are applied to the  
     opacity and source functions before the transport equation is  
     integrated.  Setting them to [] is the same as setting them  
     to 1.0.  
     DRAT_EMULT     - multiply the emissivity by this factor,  
                         without affecting the absorption  
            opac   <- opac  
            source <- source*DRAT_EMULT  
     DRAT_AMULT   - multiply the absorption opacity by this  
                         factor, without affecting the emissivity  
            opac   <- opac*(DRAT_AMULT+1.e-20)  
            source <- source/(DRAT_AMULT+1.e-20)  
     DRAT_OMULT      - multiply BOTH the absorption opacity and the  
                         emissivity by this factor  
            opac   <- opac*DRAT_OMULT  
            source <- source  
     DRAT_IREG_ADJ   - list of region numbers to be zeroed.  This  
                       has the same effect as a zero DRAT_OMULT in  
                       the corresponding zones, but is more efficient.  
     Since opac and source are mesh-by-ngroup (where mesh is usually  
     kmax-by-lmax), DRAT_EMULT, DRAT_AMULT, DRAT_OMULT can  
     be scalars, mesh arrays, 1-by-1-by-ngroup arrays, or  
     kmax-by-lmax-by-ngroup arrays.  If DRAT_GLIST is non-nil, ngroup  
     should be numberof(DRAT_GLIST), not the total number of groups.  

             func drat_backlight(time) { extern gb, gav;  ... }  
          or drat_backlight=   
          or drat_backlight=   
 
     supplies a backlighter for the snap function.  
     Given ngroup-by-nrays transparency fraction transp and self-emission  
     selfem (in specific intensity units), snap applies the backlighter  
     using:  
        result= backlighter*transp + selfem;  
     where backlighter is drat_backlight(time), if drat_backlight is  
     a function, or drat_backlight itself, if drat_backlight is an  
     array.  
     Note that the result (or value) of backlighter_func must be  
     conformable with transp and selfem.  Most commonly, drat_backlight  
     will be a vector of length ngroup -- a Planckian backlighter at  
     temperature Tr would be  
        drat_backlight= B_nu(gav, Tr);  
     -- but that a scalar, 1-by-nrays, or ngroup-by-nrays are all  
     possible.  
     Note also that if drat_backlight is a function, the gb and gav  
     arrays read from the history file are available as external  
     variables.  

             func drat_channel(time) { extern gb, gav;  ... }  
          or drat_channel=   
          or drat_channel=   
 
     supplies a channel response for the snap function.  
     Use the drat_glist option to select a subset of the groups;  
     drat_channel can be used in addition to drat_glist.  
     Given ngroup-by-nrays specific intensity, snap applies the  
     channel response using:  
        result= drat_channel(..,+)*specific_intensity(+,..);  
     if drat_channel is an array, or  
        result= drat_channel(specific_intensity, time);  
     if drat_channel is a function.  
     Note that if drat_channel is an array, its final dimension must  
     be of length ngroup.  A multidimensional drat_channel represents  
     more than one channel response function.  Most drat_channel  
     arrays will be proportional to the bin widths gb(dif).  The  
     correct way to interpolate a filter function transmission  
     fraction known at photon enrgies efa is:  
        drat_channel= integ(ffa, efa, f.gb)(dif)  
     If you have more than one channel, the first dimension of  
     drat_channel should be the channel number.  
     The best way to generate a filter response function is to  
     use Yorick's cold opacity library.  To do this:  
        #include "coldopac/xray.i"  
     This will define the functions cold_opacity and cold_reflect,  
     which you can use to build up channel response functions from  
     filter materials and thicknesses and mirror compositions.  
     Note also that if drat_channel is a function, the gb and gav  
     arrays read from the history file are available as external  
     variables.  

             func drat_compress(transp, selfem, time)  
          or drat_compress=   
 
     supplies a compression algorithm to the streak function.  
     The drat_compress can return anything, as long as it returns the  
     same shape array (or nil) at each time.  The snap_worker and  
     streak_saver routines are examples of compression algorithms.  

 drat_ekap  
 

 drat_emult  
 

             func drat_gate(times) { extern gb, gav;  ... }  
          or drat_gate=   
 
     supplies a gate (to make gated images) for the snap function.  
     For a simple gate, the drat_start and drat_stop options will  
     be more efficient than drat_gate.  
     The input to drat_gate is the list of dump times; the output  
     should be the "effective dt" for each of these dumps.  This is  
     the product of the actual time interval and the gate transparency;  
     the sum of the return vector is the gate time.  See the default_gate  
     and gaussian_gate functions for examples.  
     Note that the gb and gav arrays read from the history file are  
     available as external variables, in case the gate transparency is  
     frequency dependent.  

 drat_gav  
 

 drat_gb  
 

             drat_glist  
 
     if non-nil, an index list into the final dimension of akap and ekap.  
     Only these groups will be read from disk and used in the transport  
     calculation.  All other options which depend on "ngroup" or "gav"  
     should use numberof(DRAT_GLIST) or gav(DRAT_GLIST) instead.  The  
     "gb" group boundary array is not well-defined in this case, since  
     the group boundaries need not be contiguous.  The best strategy is  
     to save drat_glist and the original gb array.  
     DRAT_GLIST must be a 1-D, 1-origin index list.  (1-origin even if  
     gav and gb are not 1-origin, since use_origins(0) will be in effect  
     when DRAT_GLIST is used.)  The streak function will be most efficient  
     if DRAT_GLIST is strictly increasing.  

             func drat_integrate(file, mesh, time, irays, slimits) { ... }  
          or drat_integrate=   
 
     integrate the transport equation.  FILE is positioned to TIME, and  
     MESH has already been read.  IRAYS are the rays in internal format  
     and SLIMITS is the integration limits.  The return value should be  
     ngroup-by-2-by-raydims (where irays is 6-by-raydims).  The default  
     integrator is default_integrate, which handles the drat_ocompute,  
     drat_oadjust, drat_amult, drat_emult, drat_omult, drat_akap,  
     drat_ekap, drat_glist, drat_linear, and drat_nomilne options.  
     Reasons to replace the default routine include: (1) Some or all of  
     the opacities come from a source other than the FILE, e.g.- a second  
     post processing file.  (2) The total number of zones times number of  
     groups is debilitatingly large, even though the number of rays times  
     the number of groups is not.  

 drat_ireg  
 

 drat_ireg_adj  
 

 drat_isymz  
 

 drat_khold  
 

 drat_lhold  
 

             drat_linear, drat_nomilne  
 
     Set DRAT_LINEAR to 1 in order to use integ_linear to perform the  
     transport integration instead of the default integ_flat.  
     The DRAT_NOMILNE option, if non-nil, is a list of "norad"  
     edges in the (rt,zt) mesh (other than the khold and lhold lines),  
     which is required for the source function point centering operation.  
     DRAT_NOMILNE is a 2 or 3-D array with the format:  
        [[k1,l1], [k2,l2]]  
     or an array of elements of that form, where either k1==k2 or  
     l1==l2.  (Where k is the first index of rt or zt and l is the second.)  
     DRAT_NOMILNE must always be a 1-origin index list into the (rt,zt)  
     mesh, independent of the index origins of rt and/or zt.  

 drat_nomilne  
 

 drat_oadjust  
 

             func drat_ocompute(file, time) { extern opac, source; ...}  
          or drat_ocompute=   
 
        and func drat_oadjust(file, time) { extern opac, source; ...}  
         or drat_oadjust=   
     supply opacities from a source other than the file.drat_akap and  
     file.drat_ekap, or adjust these values.  You need to be cognizant of  
     the drat_glist option (see get_kaps source code).  
     DRAT_OCOMPUTE must set opac and source entirely on its own;  
     DRAT_OADJUST will be called afterwards.  
     The default DRAT_OCOMPUTE (default_ocompute) reads drat_akap and  
     drat_ekap from FILE, optionally extracting drat_glist, and places  
     them in opac and source.  
     DRAT_OADJUST is free to modify opac and source them at will; the  
     default DRAT_OADJUST is nil, which means no adjustment.  
     Any opacity or emissivity multipliers will be applied after  
     DRAT_OADJUST, as will the point centering operation if necessary  
     (DRAT_OADJUST should return zone centered opacities).  

 drat_omult  
 

             drat_quiet  
 
     By default, Drat prints the total number of records it will process,  
     and the number of the record it is currently processing.  If drat_quiet  
     is non-nil and non-zero, the printout is supressed.  

             drat_rt, drat_zt, drat_ireg,  
             drat_akap, drat_ekap,  
             drat_isymz,  
             drat_khold, drat_lhold,  
             drat_gb, drat_gav  
 
     can be set to strings other than "rt", "zt", etc. (their default  
     values) to force the streak, snap, and streak_save routines to use  
     alternative names to look up these quantites in the history file.  
     The following 4 variables are NOT optional:  
     (rt, zt) must be a 2-D mesh in cylindrical coordinates  
     akap is a mesh-by-ngroup array of absorption opacities, in units  
          of reciprocal length (1/rt or 1/zt)  
     ekap is a mesh-by-ngroup array of source functions, in (arbitrary)  
          specific intensity units  
     The akap and ekap arrays must be zone centered; the first row and  
     column of akap and ekap will be ignored.  
     The remaining variables are all optional -- set the drat_.. variable  
     to [] to ignore them completely.  Otherwise, they will be ignored if  
     they are not present in the history file, and used as follows  
     otherwise:  
     ireg is a mesh-size region number array (zone centered as akap and  
          ekap).  Zones where ireg==0 do not exist.  
     isymz is non-zero if the problem has reflection symmetry about z=0,  
          zero otherwise.  The drat_symmetry option overrides this value.  
     khold and lhold are mesh indices specifying "hold lines" --  
          khold is an index into the first dimension of (rt,zt), and  
          lhold is an index into the second dimension of (rt,zt).  
          These are used only if the drat_linear option is specified.  
     gb and gav are, respectively, the group boundary energies and group  
          center energies.  These are used by the snap and streak_save  
          functions.  

             drat_start, drat_stop  
 
     if non-nil, specify the minimum and maximum dump times which will  
     be considered by the streak, snap, or streak_save functions.  

             drat_static  
 
     if non-nil, a list of strings representing variable names in the  
     input file which the streak_save function should copy to the  
     output file.  

 drat_stop  
 

             drat_symmetry  
 
     set to 2 to force spherical symmetry, 1 to force reflection symmetry  
     about the z=0 plane, 0 to force no symmetry, [] (the default) to  
     use the guess_symmetry function to compute problem symmetry.  
     Special value drat_symmetry=2+khold where k=khold is a hold-line  
     causes ray to reflect at the hold line.  This doesn't mean anything  
     physically (in fact, it is wrong), but may give qualitatively useful  
     pictures in problems that are polar wedges.  

 drat_zt  
 

             boundary= find_boundary(mesh)  
          or boundary= find_boundary(mesh, region, sense)  
 
     returns an array of 4 pointers representing the boundary of the  
     MESH, or of a particular REGION of the MESH, with a particular  
     SENSE -- 0 for counterclockwise in the (r,z)-plane, 1 for  
     clockwise.  The returned arrays are:  
        *boundary(1)   zone index list -- always 1-origin values  
        *boundary(2)   side list 0, 1, 2, or 3  
                       side 0 is from point zone to zone-1, side 1 is  
                       from zone-1 to zone-imax-1  
        *boundary(3)   z values of boundary points  
        *boundary(4)   r values of boundary points  

             form_mesh(zsym, khold, lhold)  
 
     returns an opaque "mesh" object, which will hold rt, zt, ireg,  
     and a boundary edge list.  This opaque mesh object is required  
     as an input to the integ_flat and integ_linear routines.  
     ZSYM is 2 for spherical symmetry, 1 for z=0 reflection symmetry,  
          or 0 for no symmetry  
     KHOLD and LHOLD are the 1-origin indices of "hold" lines in the  
          mesh, or 0 if none.  This information is used only during the  
          pcen_source operation before integ_linear is called.  

             gauss_gate(times)  
 
     gate function used by gaussian_gate.  Refer to the source code  
     to learn how to write your own gate function, making proper use  
     of drat_start and drat_stop options in addition to the input times.  

             gauss_int(t)  
 
     returns time integral of Gaussian specified in call to gaussian_gate.  

             gaussian_gate(t0, tsigma, max_trans)  
 
     sets the drat_gate for the snap function to be a Gaussian  
     centered at time T0, with sigma TSIGMA, and maximum transmission  
     fraction MAX_TRANS.  

             ray_info= get_ray_path(path, rt, zt)  
 
     where PATH is one element of an array returned by track_rays,  
     returns the points where the ray cut the edges of the mesh (ZT, RT).  
     The returned RAY_INFO has two components: RAY_INFO(,1) is the z  
     coordinates and RAY_INFO(,2) is the r coordinates.  

             get_std_limits(rays, slimits)  
 
     returns slimits suitable for internal routines: 2-by-nrays,  
     with s=0 at point of closest approach to origin  

             guess_symmetry, f  
          or guess_symmetry(f)  
 
     guesses the symmetry of the problem in the dump file F based on  
     the variables f.isymz, f.rt, and f.zt.  
     If called as a subroutine, prints one of:  
     "no symmetry", "z=0 reflection symmetry", or "spherical symmetry"  
     If called as a function, returns 0, 1, or 2, respectively.  

             integ_flat(opac, source, rays, mesh, slimits)  
          or integ_flat(opac, source, ray_paths)  
 
     returns ngroup-by-2-by-nrays result, where result(,1,..) is  
     the transparency factors, and result(,2,..) is the self-emission  
     for each group on each ray.  The input OPAC and SOURCE are the  
     opacity (an inverse length) and the source function (a specific  
     intensity).  They are mesh-by-ngroups zone centered arrays.  The  
     result has the same units as SOURCE.  
     In the second form, RAY_PATHS was returned by the track_rays  
     function.  

             integ_linear(opac, source, rays, mesh, slimits)  
          or integ_linear(opac, source, ray_paths)  
 
     returns ngroup-by-2-by-nrays result, where result(,1,..) is  
     the transparency factors, and result(,2,..) is the self-emission  
     for each group on each ray.  The input OPAC and SOURCE are the  
     opacity (an inverse length) and the source function (a specific  
     intensity).  They are mesh-by-ngroups arrays; OPAC is zone centered,  
     while SOURCE is point centered (using pcen_source).  The result  
     has the same units as SOURCE.  
     In the second form, RAY_PATHS was returned by the track_rays  
     function.  
     The integ_linear routine assumes that the SOURCE function varies  
     linearly between the entry and exit points from each zone.  This  
     assumption is poor near the turning point, and causes the result  
     to be a discontinuous function of the ray coordinates, unlike the  
     integ_flat result.  

             is_present(get_vars(f), name)  
 
     returns 1 if variable NAME is present in file F, 0 if not.  

             pcen_source, opac, source, mesh, drat_nomilne  
 
     point centers the SOURCE array (in place) using a complicated  
     algorithm involving the OPAC and MESH (from form_mesh and update_mesh).  
     If non-nil, DRAT_NOMILNE must have the same format as the  
     drat_nomilne option.  

 Ray_Path  
 
struct Ray_Path {  
  pointer zone;   /* list of zones (1-origin) cut by the ray */  
  pointer ds;     /* list of path lengths in above zones */  
  double fi, ff;  /* fraction of 1st and last ds, respectively, outside  
                     the specified slimits */  
  pointer pt1, pt2;  /* lists of endpoints of edges cut by ray -- ray cuts  
                        directed edge pt1->pt2 from right to left  
                        Like zone, always 1-origin values.  */  
  pointer f;         /* list of fractions -- (f+0.5) is the fraction of  
                        distance from pt1 to pt2 where ray cuts edge */  
}  

             reset_options  
          or reset_options, 1  
 
     resets all options for the streak, snap, and streak_save functions  
     to their default values.  With a non-zero, non-nil argument, only  
     resets options which are currently nil, but have non-nil defaults.  

             set_tolerances()  
          or old_tols= set_tolerances([tol1, tol2, lost_tol])  
 
     returns the current tolerances for the ray tracking.  Initially,  
     these are [1.e-3, 1.e-6, 0.0].  In the second form, sets new  
     tolerances.  If any of TOL1, TOL2, or LOST_TOL is zero, that  
     tolerance is restored to its default value.  If TOL1 is less  
     than zero, the root polishing operation which requires TOL1  
     and TOL2 is not done at all.  

             snap(f, rays)  
          or snap(f, rays, slimits)  
 
     returns the time-integrated specific intensity for the rad-hydro  
     problem dumped in file F, on the specified RAYS, with the  
     specified limits SLIMITS on the transport integrals.  
     The first dimension of RAYS may be length 3, 5, or 6 to represent  
     the ray(s) in TDG/DIRT coordinates (x,y,theta), "best" coordinates  
     (x,y,z,theta,phi), or internal coordinates (cos,sin,y,z,x,r),  
     respectively.  The remaining dimensions of RAYS, if any, will be  
     called "nrays" below.  
     The SLIMITS parameter, if present, is the value of the s-coordinate  
     -- position along the ray -- at which to start and stop the  
     integration of the transport equation.  SLIMITS may be nil, a 1-D  
     array of length 2, or a 2-by-nrays array.  Each component of SLIMITS  
     is [s_start, s_stop]; if s_stop

             snap_worker(transp, selfem, time)  
 
     The snap function actually works by replacing the drat_compress  
     with snap_worker.  See the source for snap in drat.i for details.  

             streak(f, rays)  
          or streak(f, rays, slimits)  
 
     returns the transparency and self-emission as functions of time for  
     the rad-hydro problem dumped in file F, on the specified RAYS, with  
     the specified limits SLIMITS on the transport integrals.  
     The first dimension of RAYS may be length 3, 5, or 6 to represent  
     the ray(s) in TDG/DIRT coordinates (x,y,theta), "best" coordinates  
     (x,y,z,theta,phi), or internal coordinates (cos,sin,y,z,x,r),  
     respectively.  The remaining dimensions of RAYS, if any, will be  
     called "nrays" below.  
     The SLIMITS parameter, if present, is the value of the s-coordinate  
     -- position along the ray -- at which to start and stop the  
     integration of the transport equation.  SLIMITS may be nil, a 1-D  
     array of length 2, or a 2-by-nrays array.  Each component of SLIMITS  
     is [s_start, s_stop]; if s_stop

             streak_save, outname, f, rays  
          or streak_save, outname, f, rays, slimits  
          or streak_save, outfile, f, rays, slimits  
 
     is the same as the streak function, except that the results of  
     the transport calculation are placed into a PDB file called  
     OUTNAME, instead of being accumulated in memory.  All of the  
     options for the streak function are available, except for  
     drat_compress (which is set to streak_saver).  
     If the first argument is OUTFILE, a file variable instead of a  
     file name, then that file is used for output.  You can create  
     OUTFILE and add static variables to it with save (but do NOT call  
     add_record) which streak_save otherwise wouldn't know about.  
     The output file has history records at the same times as the  
     input file.  Each record contains "time" (a double scalar),  
     and the two arrays "transp", the transparency (between 0 and 1),  
     and "selfem", the self emission (which has the same units as  
     ekap in the file F).  The dimensions of transp and selfem  
     are ngroup-by-2-by-nrays (where nrays represents zero or more  
     dimensions, copied from the RAYS input array).  The RAYS and  
     SLIMITS inputs are placed into the output file as non-record  
     variables, and any variables in the drat_static option are  
     copied form F to the output file.  The gb and gav variables  
     are copied from F into the output file as well.  If the drat_glist  
     option is present, that is stored in the output file also.  
   OPTIONS: all options available for streak except drat_compress,  
            drat_gb, drat_gav, drat_static  

             streak_saver(transp, selfem, time)  
 
     The streak_save function actually works by replacing the drat_compress  
     with streak_saver.  See the source for streak_saver in drat.i for  
     details.  

             streak_times(f)  
 
     returns the times from file F whic lie between the optional  
     drat_start and drat_stop.  

             ray_paths= track_rays(rays, mesh, slimits)  
 
     returns array of Ray_Path structs representing the progress of  
     RAYS through the MESH between the given SLIMITS.  

             update_mesh, mesh, rt, zt  
          or update_mesh, mesh, rt, zt, ireg  
 
     updates the opaque MESH object to reflect a new RT, ZT, and  
     (optionally) IREG.  The boundary edges are recomputed and stored  
     in MESH, as well.