Compression and compressed inversion of interaction data

Abstract

A compression technique compresses interaction data. A fast method processes the compressed data without the need to first decompress the data. In one embodiment, the compression technique is used to compress data in an interaction matrix. The interaction matrix (such as a moment method impedance matrix) contains interaction data between sources (e.g., basis functions or expansion functions) and testers (e.g., testing functions). The sources are collected into groups of sources according to specified criteria. One useful criteria is based on grouping sources relatively close to one another. For each group of sources, a composite source is calculated. The testers are also collected into groups and composite testers are calculated. The use of composite sources and composite testers to compute couplings when the source and tester are not close to each other allows the interaction matrix to be computed as a sparse matrix with a block format.

1 . A method, comprising: 
 calculating at least one composite source, said composite source representing a combination of N energy sources;    using a computer system, calculating at least one composite tester as a combination of M testers, where at least one of N or M is greater than one, said at least one composite tester testing an effect produced by said at least one composite source, said at least one composite source interacting relatively weakly with said at least one composite tester; and    transforming at least a portion of a first system of linear equations into a second system of linear equations based at least on said at least one composite source and said at least one composite tester.    
   
   
       2 . The method of  claim 1 , wherein said at least one composite source represents a linear combination of one or more energy sources such that said at least one composite source radiates relatively little energy into a portion of angular region disposed about said at least one source.  
   
   
       3 . The method of  claim 1 , wherein said at least one composite tester is affected relatively weakly by energy propagating from a portion of space around said at least one composite tester.  
   
   
       4 . The method of  claim 1 , wherein said second system of linear equations is represented by a block sparse matrix.  
   
   
       5 . The method of  claim 2 , wherein said at least one composite tester is affected relatively weakly by energy propagating from a portion of space proximate to said at least one composite tester.  
   
   
       6 . The method of  claim 5 , wherein said second system of linear equations is substantially represented by a block sparse matrix.  
   
   
       7 . The method of  claim 5 , wherein said second system of linear equations is relatively more sparse than said first system of equations.  
   
   
       8 . The method of  claim 7 , wherein said at least one composite source is spatially relatively close to said at least one composite tester.  
   
   
       9 . The method of  claim 5 , wherein said at least one composite source is spatially relatively close to said at least one composite tester.  
   
   
       10 . The method of  claim 1 , wherein said second system of linear equations is relatively more sparse than said portion of a first system of equations.  
   
   
       11 . An apparatus comprising: 
 means for calculating at least one composite source by combining N sources;    means for calculating at least one composite tester by combining M testers, where at least N or M is greater than one; and    means for transforming at least a portion of a first system of equations into a second system of equations based at least on said at least one composite source and said at least one composite tester said at least one composite tester testing an effect produced by said at least one composite source, said at least one composite source interacting relatively weakly with said at least one composite tester.    
   
   
       12 . A method of data compression, comprising: 
 calculating a group of N composite sources as a combination of one or more basis functions, wherein at least one of said composite sources produces a relatively weak product in a portion of space;    using a computer system, calculating one or more composite testers as a combination of a group of M weighting functions, wherein at least one of said composite testers interacts relatively weakly with said at least one composite tester and wherein either N or M is greater than one; and    transforming at least a portion of a first array of interaction data based on said basis functions and said weighting functions into a second array of interaction data based on said composite sources and said composite testers.    
   
   
       13 . The method of  claim 12 , wherein said disturbance is at least one of, an electromagnetic field, a heat flux, an electric field, a magnetic field, vector potential, a pressure, a sound wave, a particle flux, a weak nuclear force, strong nuclear force, a gravity force, and an image element.  
   
   
       14 . The method of  claim 12 , wherein each of said composite sources corresponds to a region.  
   
   
       15 . The method of  claim 12 , wherein said second array of interaction data is described by a sparse block diagonal matrix.  
   
   
       16 . The method of  claim 12 , further comprising the step of using said second array of interaction data to compute a first solution vector, said first solution vector expressed in terms of said composite testers.  
   
   
       17 . The method of  claim 16 , further comprising the step of transforming said first solution vector into a second solution vector, said second solution vector expressed in terms of said weighting functions.  
   
   
       18 . The method of  claim 12 , wherein said at least one composite tester is affected relatively weakly by energy propagating from a portion of space relatively near said at least one composite tester.  
   
   
       19 . The method of  claim 18 , wherein said second system of linear equations is relatively more sparse than said portion of a first array.  
   
   
       20 . The method of  claim 18 , wherein said at least one composite source is spatially relatively close to said at least one composite tester.  
   
   
       21 . The method of  claim 12 , wherein said second system of linear equations is represented by a block-sparse matrix.  
   
   
       22 . The method of  claim 21 , wherein said at least one composite source is spatially relatively close to said at least one composite tester.  
   
   
       23 . The method of  claim 12 , wherein said second system of linear equations is more sparse than said portion of a first array.