R Under development (unstable) (2025-06-09 r88292 ucrt) -- "Unsuffered Consequences"
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> 
> library( polarzonoid )
> 
> #library( logger )
> #log_threshold( TRACE, "polarzonoid" )
> 
> 
> options( width=160 )
> 
> #   count   # of random rotation 3x3 matrices  
> #   tol     round-trip tolerance
> #
> #   maps from rotation to arcs, and back again
> #   return TRUE or FALSE
> 
> testinversionrotation  <- function( count=1000, tol=5.e-11 )
+     {
+     set.seed(0)
+ 
+     delta   = numeric(count)
+ 
+     #   make count random points on the sphere
+     for( i in 1:count )
+         {
+         quat    = polarzonoid:::unitize( rnorm( 4 ) )
+         
+         M   = polarzonoid:::rotationfromquat( quat )
+ 
+         arcmat  = arcsfromrotation( M )
+ 
+         if( is.null(arcmat) )
+             {
+             return(FALSE)
+             }
+ 
+         Mp  = rotationfromarcs( arcmat )
+ 
+         delta[i]    = max( abs(M-Mp) )
+         }
+ 
+     maxdelta = max(delta)
+ 
+     cat( "testinversionsphere().    maxdelta = ", maxdelta , '\n', file=stderr() )
+ 
+ 
+     if( tol < maxdelta )
+         {
+         mask    = tol < delta
+ 
+         mess    = sprintf( "ERR.  testinversionrotation().   %g of %d rotation inversions are invalid.  tol=%g. maxdelta=%g\n",
+                         sum(mask), length(mask), tol, maxdelta )
+         cat( mess, file=stderr() )
+ 
+         return(FALSE)
+         }
+ 
+     return(TRUE)
+     }
> 
> 
> 
> 
> 
> #   return TRUE or FALSE
> testinversion_singlearc  <- function( count=1000, tol=5.e-11 )
+     {
+     set.seed(0)
+ 
+     delta  = numeric(count)
+ 
+     for( i in 1:count )
+         {
+         arcmat1 = polarzonoid:::randomarcs( 1, L=pi )
+ 
+ 
+         M = rotationfromarcs( arcmat1  )
+         if( is.null(M) )
+             return(FALSE)
+ 
+         # p   = res$point
+ 
+         #   in the next call, tol is tricky
+         #   tol is passed to arcsfromboundary()
+         #   tol=5.e-9 sometimes yields 2 arcs, not the right substratum
+         #   tol=5.e-8 leads to "boundary gradient cannot be computed"
+         #   tol=1.e-7 and 1.e-6  are OK
+         arcmat1p = arcsfromrotation( M , tol=1.e-7 )    
+         if( is.null(arcmat1p) )
+             {
+             print( arcmat1 )
+             return(FALSE)
+             }
+             
+         if( nrow(arcmat1p) != 1 )
+             {
+             cat( "For test arcs i=", i, "   row(arcmat1p) = ",nrow(arcmat1p), " but expected 1.\n" )
+             print( arcmat1 )
+             print( arcmat1p )
+             return(FALSE)
+             }            
+  
+         delta[i]    = arcsdistance( arcmat1, arcmat1p )        
+ 
+         if( 6 < delta[i] )
+             {
+             #   probably got the complementary arc, so take complement
+             arcmat1p    = complementaryarcs( arcmat1p )
+             delta[i]    = arcsdistance( arcmat1, arcmat1p ) 
+             }
+             
+         # cat( sprintf( "delta[%d] = %g\n", i, delta[i] ) )                
+         }
+ 
+     maxdelta = max(delta)
+ 
+     cat( "testinversion_singlearc().  ", "   maxdelta = ", maxdelta , '\n', file=stderr() )
+ 
+     if( tol < maxdelta )
+         {
+         mask    = tol < delta
+ 
+         mess    = sprintf( "ERR.  testinversion_singlearc().   %g of %d single arc inversions are invalid.  tol=%g\n",
+                          sum(mask), length(mask), tol )
+         cat( mess, file=stderr() )
+ 
+         return(FALSE)
+         }
+ 
+     return( TRUE )
+     }
> 
> 
> 
> if( ! testinversion_singlearc(count=1000) )  stop( "testinversion_singlearc() failed !" )
testinversion_singlearc().      maxdelta =  4.618528e-14 
> 
> 
> 
> if( ! testinversionrotation(count=1000) )  stop( "testinversionrotation() failed !" )
testinversionsphere().    maxdelta =  5.143108e-13 
> 
> 
> 
> 
> 
> cat( "Passed all rotation inversion tests !\n", file=stderr() )
Passed all rotation inversion tests !
> 
> proc.time()
   user  system elapsed 
   6.60    0.18    6.78