Difference between revisions of "Shrewd.m"

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(Created page with "Computes SHREWD weights for a given two- or three-angle spherical grid. ==Syntax== weights=shrewd(alphas,betas,gammas,max_rank,max_error) ==Description== See the paper...")
 
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Computes SHREWD weights for a given two- or three-angle spherical grid.
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{{DISPLAYTITLE:function.m}} __NOTOC__
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Computes SHREWD weights for a given two- or three-angle spherical grid. See the paper by Eden and Levitt for details on now the algorithm works: http://dx.doi.org/10.1006/jmre.1998.1427
  
 
==Syntax==
 
==Syntax==
  
 
     weights=shrewd(alphas,betas,gammas,max_rank,max_error)
 
     weights=shrewd(alphas,betas,gammas,max_rank,max_error)
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==Description==
 
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See the paper by Eden and Levitt for details on now the algorithm works: http://dx.doi.org/10.1006/jmre.1998.1427 - it is not entirely clear, in the magnetic resonance context, whether this procedure is even necessary.
 
  
 
==Arguments==
 
==Arguments==
  
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       alphas - alpha Euler angles of the grid, in radians
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       alphas - alpha Euler angles (ZYZ active) of the  
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              grid, in radians
 
   
 
   
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       betas - beta Euler angles of the grid, in radians
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       betas - beta Euler angles (ZYZ active) of the  
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              grid, in radians
 
   
 
   
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       gammas - gamma Euler angles of the grid,in radians,
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       gammas - gamma Euler angles (ZYZ active) of the
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              set to all-zeros for two-angle grids
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              grid,in radians, set to all-zeros for
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              two-angle grids
 
   
 
   
 
     max_rank - maximum spherical rank to take into consi-
 
     max_rank - maximum spherical rank to take into consi-
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               cal function
 
               cal function
  
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==Returns==
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==Outputs==
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The output is a vector of grid weights for each [alpha beta gamma] point supplied.
 
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==Examples==
 
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See kernel/grids directory for a long list of one-, two- and three angle grids.
 
  
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==Notes==
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    weights - a vector of grid weights for each
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for a given arrangement of angles, this is the most consistent weight selection procedure in the literature. Lebedev grids satisfy SHREWD condition by definition, all other grids may be rebalanced towards better description of low spherical ranks by the use of this procedure.
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              [alpha beta gamma] point supplied.
  
 
==See also==
 
==See also==
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[[get_hull.m]], [[grid_kron.m]], [[grid_test.m]], [[repulsion.m]]
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[[Kernel_utilities#Integration_grids|Integration grids]], [[Appendix I: powder grids]]
  
  
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''Version 1.10, authors: [[Ilya Kuprov]]''
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''Version 2.6, authors: [[Ilya Kuprov]]''

Revision as of 20:15, 29 June 2021

Computes SHREWD weights for a given two- or three-angle spherical grid. See the paper by Eden and Levitt for details on now the algorithm works: http://dx.doi.org/10.1006/jmre.1998.1427

Syntax

    weights=shrewd(alphas,betas,gammas,max_rank,max_error)

Arguments

     alphas - alpha Euler angles (ZYZ active) of the 
              grid, in radians

      betas - beta Euler angles (ZYZ active) of the 
              grid, in radians

     gammas - gamma Euler angles (ZYZ active) of the
              grid,in radians, set to all-zeros for
              two-angle grids

   max_rank - maximum spherical rank to take into consi-
              deration when minimizing residuals

  max_error - maximum residual absolute error per spheri-
              cal function

Outputs

    weights - a vector of grid weights for each 
              [alpha beta gamma] point supplied.

See also

Integration grids, Appendix I: powder grids


Version 2.6, authors: Ilya Kuprov

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