Run NestWhile in parallel mode.

Questions
1

Are there methods to run NestWhile in parallel mode?

Regards,
Zhao

2

I do not think this is possible - how could parallelize a function where each iteration uses the result from the previous iteration?

3

So how do we take advantage of parallel computing in this scenario?

4

How would you propose that might be done?

(What I’m asking, in slightly more detail, is that questions lacking algorithmic answers be avoided. Absent a clear suggestion in the initial post as to how parallelism might be attained in principle, this is simply not a suitable question for the forum.)

5

How would you propose that might be done?

I don’t know. I ask, only because I have a time-consuming calculation based on NestWhile, so I want to take advantage of parallelism to improve the efficiency.

6

Can the computation performed by the function passed to NestWhile be parallelized?

7

See the following example code snippet, which is based on the method here:

In[19]:= gMatrix = 
  SparseArray[{{1, 3} -> 1, {2, 1} -> 1, {3, 2} -> 
     1, {4, 4} -> -(1/2), {4, 5} -> -(1/2), {4, 6} -> -(1/2), {4, 
      7} -> -(1/2), {5, 4} -> 1/2, {5, 5} -> -(1/2), {5, 6} -> 
     1/2, {5, 7} -> -(1/2), {6, 4} -> 
     1/2, {6, 5} -> -(1/2), {6, 6} -> -(1/2), {6, 7} -> 1/2, {7, 4} ->
      1/2, {7, 5} -> 
     1/2, {7, 6} -> -(1/2), {7, 7} -> -(1/2), {_, _} -> 0}, 7];

hMatrix = 
  SparseArray[{{1, 5} -> 
     1, {2, 2} -> -(1/2), {2, 3} -> -(1/2), {2, 6} -> 1/2, {2, 7} -> 
     1/2, {3, 2} -> 1/2, {3, 3} -> -(1/2), {3, 6} -> -(1/2), {3, 7} ->
      1/2, {4, 1} -> 1, {5, 4} -> 1, {6, 2} -> -(1/2), {6, 3} -> 
     1/2, {6, 6} -> -(1/2), {6, 7} -> 
     1/2, {7, 2} -> -(1/2), {7, 3} -> -(1/2), {7, 6} -> -(1/2), {7, 
      7} -> -(1/2), {_, _} -> 0}, 7];

kMatrix = 
  SparseArray[{{1, 4} -> -1, {2, 2} -> -(1/2), {2, 3} -> -(1/2), {2, 
      6} -> -(1/2), {2, 7} -> 1/2, {3, 2} -> 
     1/2, {3, 3} -> -(1/2), {3, 6} -> -(1/2), {3, 7} -> -(1/2), {4, 
      5} -> -1, {5, 1} -> 1, {6, 2} -> 1/2, {6, 3} -> 
     1/2, {6, 6} -> -(1/2), {6, 7} -> 1/2, {7, 2} -> -(1/2), {7, 3} ->
      1/2, {7, 6} -> -(1/2), {7, 7} -> -(1/2), {_, _} -> 0}, 7];
      
gen=  {gMatrix, hMatrix, kMatrix};    
count = 0; (matrices = NestWhile[(Print[count++]; 
             Union[#~Join~Flatten[Outer[Dot, gen, #, 1], 1]]) &, 
               {IdentityMatrix[7]}, Length[#2] != Length[#1] &, 2, 99]) // Length // Timing

During evaluation of In[19]:= 0

During evaluation of In[19]:= 1

During evaluation of In[19]:= 2

During evaluation of In[19]:= 3

During evaluation of In[19]:= 4

During evaluation of In[19]:= 5

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During evaluation of In[19]:= 7

During evaluation of In[19]:= 8

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During evaluation of In[19]:= 12

During evaluation of In[19]:= 13

Out[23]= {2.27465, 6048}