Shrewd.m - Revision history

Kuprov: Update function See also links and function index membership

2026-06-06T18:41:26Z

Update function See also links and function index membership

Kuprov: Rename Arguments section heading to Parameters

2026-06-05T17:52:17Z

Rename Arguments section heading to Parameters

Kuprov: Normalise sequential blank lines

2026-04-25T11:30:19Z

Normalise sequential blank lines

Kuprov: Restore pre-bulk-edit wiki content

2026-04-05T14:50:08Z

Restore pre-bulk-edit wiki content

Kuprov: Sync syntax/arguments/outputs with current Spinach source

2026-04-05T14:06:34Z

Sync syntax/arguments/outputs with current Spinach source

Kuprov at 19:16, 29 June 2021

2021-06-29T19:16:24Z

Kuprov at 19:15, 29 June 2021

2021-06-29T19:15:38Z

Kuprov at 19:15, 29 June 2021

2021-06-29T19:15:15Z

Admin: 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..."

2017-07-13T13:49:13Z

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..."

New page

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 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==

alphas - alpha Euler angles of the grid, in radians

betas - beta Euler angles of the grid, in radians

gammas - gamma Euler angles 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

==Returns==
The output is a vector of grid weights for each [alpha beta gamma] point supplied.

==Examples==
See kernel/grids directory for a long list of one-, two- and three angle grids.

==Notes==
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.

==See also==
[[get_hull.m]], [[grid_kron.m]], [[grid_test.m]], [[repulsion.m]]

''Version 1.10, authors: [[Ilya Kuprov]]''

@@ Line 30: / Line 30: @@
 ==See also==
-[[Kernel_utilities#Integration_grids|Integration grids]], [[Appendix I: powder grids]]
+[[arclength.m]], [[gaussleg.m]], [[get_hull.m]], [[grid_fibon.m]], [[grid_igloo.m]], [[grid_kron.m]], [[grid_plot.m]], [[grid_polar.m]], [[grid_test.m]], [[grid_trian.m]], [[one_vcell_solidangle.m]], [[repulsion.m]], [[sphtarea.m]], [[sphtrsubd.m]], [[vcell_solidangle.m]], [[voitlander.m]], [[voronoisphere.m]], [[zfs_sampling.m]], [[Kernel_utilities]], [[Appendix I: powder grids]]
 ''Version 2.6, authors: [[Ilya Kuprov]]''

@@ Line 6: / Line 6: @@
       weights=shrewd(alphas,betas,gammas,max_rank,max_error)
-==Arguments==
+==Parameters==
        alphas - alpha Euler angles (ZYZ active) of the

@@ Line 31: / Line 31: @@
 ==See also==
 [[Kernel_utilities#Integration_grids|Integration grids]], [[Appendix I: powder grids]]
 ''Version 2.6, authors: [[Ilya Kuprov]]''

@@ Line 9: / Line 9: @@
        alphas - alpha Euler angles (ZYZ active) of the
-                grid, in radians
+                grid, in radians, set to all-zeros for
         betas - beta Euler angles (ZYZ active) of the
@@ Line 15: / Line 16: @@
        gammas - gamma Euler angles (ZYZ active) of the
-                grid,in radians, set to all-zeros for
+                grid, in radians
      max_rank - maximum spherical rank to take into consi-

← Older revision		Revision as of 19:15, 29 June 2021
Line 1:		Line 1:
−	{{DISPLAYTITLE:~~function~~.m}} __NOTOC__	+	{{DISPLAYTITLE:shrewd.m}} __NOTOC__
	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		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

@@ Line 1: / Line 1: @@
-Computes SHREWD weights for a given two- or three-angle spherical grid.
+{{DISPLAYTITLE:function.m}} __NOTOC__
 ==Syntax==
       weights=shrewd(alphas,betas,gammas,max_rank,max_error)
 ==Arguments==
-       alphas - alpha Euler angles of the grid, in radians
+       alphas - alpha Euler angles (ZYZ active) of the
-        betas - beta Euler angles of the grid, in radians
+        betas - beta Euler angles (ZYZ active) of the
-       gammas - gamma Euler angles of the grid,in radians,
+       gammas - gamma Euler angles (ZYZ active) of the
-               set to all-zeros for two-angle grids
+               grid,in radians, set to all-zeros for
      max_rank - maximum spherical rank to take into consi-
@@ Line 23: / Line 24: @@
                 cal function
-==Returns==
+==Outputs==
-==Notes==
+     weights - a vector of grid weights for each
-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.
+               [alpha beta gamma] point supplied.
 ==See also==
-[[get_hull.m]], [[grid_kron.m]], [[grid_test.m]], [[repulsion.m]]
+[[Kernel_utilities#Integration_grids|Integration grids]], [[Appendix I: powder grids]]
-''Version 1.10, authors: [[Ilya Kuprov]]''
+''Version 2.6, authors: [[Ilya Kuprov]]''