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--- del_parameter [2015/08/14 09:14] – johnsoevans
+++ del_parameter [2022/11/03 15:08] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
+====== del parameter ======
+The del parameter is important when searching for a minimum of the penalties as a function of an independent parameter. For example, for each independent parameter ‘x’ the minimum of the penalties P is determined using ‘del’. ‘del’ is set automatically for parameters that Topas knows about (fractional coordinates, temperature factors, etc).
+For user defined parameters del defaults to 1e-5 which may be too small for some parameters. An optimum value of del is one that traverses the minimum in around 5 steps, with each step increasing by 1.6. Thus a search is performed as follows:
+  Let s = x
+  First point evaluated at P(x)
+  s = s + 1.6 del
+  Next point evaluated at P(x+s)
+  Do
+   s = s + 1.6 del
+   If P is decreasing then
+    evaluate at P(x+s)
+   else
+    evaluate at P(x-s)
+   endif
+   Loop
+Some built in values are:
+<code topas>
+cell parameter       %min = Max(1.5, 0.995 Val - .05);  %max = 1.005 Val + .05;         del = 0.0001 Val;
+cell angle           %min = Max(1.5, Val - .2);         %max = Val + .2;                del 0.01
+scale                 min 1e-15                                                         del = Abs(Val) 0.003 + 1e-10;
+fractional_coordinate min = Val-Constant(1/Get(a));      max = Val+Constant(1/Get(a));  del = Constant(.1 / Get(a));
+sh_Cij_prm            min = -Abs(Val) 2 - .1;            max =  Abs(Val) 2 + .1;        del = If(Val < 0, -0.01, .01) + .01 Val;
+</code>