rotate(): multi-thread random starts

src/rotate.jl

@@ -75,6 +75,7 @@ Perform a rotation of the factor loading matrix `Λ` using a rotation `method`.
                   starting matrices.
 - `reflect`: Switch signs of the columns of the rotated loading matrix such that the sum of
              loadings is non-negative for all columns (default: true)
+- `use_threads`: Parallelize random starts using threads (default: false)
 - `verbose`: Print logging statements (default: true)
 - `logperiod`: How frequently to report the optimization state (default: 100).
 
@@ -109,6 +110,7 @@ function rotate(
     reflect = true,
     f_atol = 1e-6,
     g_atol = 1e-6,
+    use_threads::Bool = false,
     kwargs...,
 )
     loglevel = verbose ? Logging.Info : Logging.Debug
@@ -130,44 +132,51 @@ function rotate(
             @warn "Requested random starts but keyword argument `init` was provided. Ignoring initial starting values in `init`."
         end
 
+        Q_lock = ReentrantLock()
         Q_min = Inf
         rotation = initialize(rotation_type(method), nothing, L; loglevel = Logging.Debug)
-        n_diverged = 0
+        n_diverged = Threads.Atomic{Int}(0)
         n_at_Q_min = 0
 
-        for _ in 1:starts
+        start_chan = Channel{Int}(1) do ch
+            foreach(Base.Fix1(put!, ch), 1:starts)
+        end
+        (use_threads ? Threads.foreach : foreach)(start_chan) do _
             init = random_orthogonal_matrix(size(L, 2))
             random_rotation = try
                 _rotate(L, method; g_atol, loglevel, kwargs..., init)
             catch err
                 if err isa ConvergenceError
                     @logmsg loglevel err.msg
-                    n_diverged += 1
-                    continue
+                    Threads.atomic_add!(n_diverged, 1)
+                    return nothing
                 else
                     rethrow()
                 end
             end
 
             Q_current = minimumQ(random_rotation)
 
-            if isapprox(Q_current, Q_min, atol = f_atol)
-                n_at_Q_min += 1
-            elseif Q_current < Q_min
-                @logmsg loglevel "Found new minimum at Q = $(Q_current)"
-                n_at_Q_min = 1
-                Q_min = Q_current
-                rotation = random_rotation
+            lock(Q_lock) do
+                if isapprox(Q_current, Q_min, atol = f_atol)
+                    n_at_Q_min += 1
+                elseif Q_current < Q_min
+                    @logmsg loglevel "Found new minimum at Q = $(Q_current)"
+                    n_at_Q_min = 1
+                    Q_min = Q_current
+                    rotation = random_rotation
+                end
             end
+            return nothing
         end
 
         @logmsg loglevel "Finished $(starts) rotations with random starts."
 
-        if n_diverged == starts
+        if n_diverged[] == starts
             msg = "All $(starts) rotations did not converge. Please check the provided rotation method and/or loading matrix."
             throw(ConvergenceError(msg))
-        elseif n_diverged > 0
-            @warn "There were $(n_diverged) rotations that did not converge. Please check the provided rotation method and/or loading matrix."
+        elseif n_diverged[] > 0
+            @warn "There were $(n_diverged[]) rotations that did not converge. Please check the provided rotation method and/or loading matrix."
         else
             @logmsg loglevel "There were 0 rotations that did not converge."
         end