Do gradient descent entirely in BigFloat

The previos version accidentally returned steps in Float64.

engine-proto/gram-test/descent-test.jl

@@ -11,7 +11,7 @@ using PolynomialRoots
 # subspace of matrices whose entries vanish at each empty index of `target`
 function proj_diff(target, attempt)
   J, K, values = findnz(target)
-  result = zeros(size(target)...)
+  result = zeros(BigFloat, size(target)...)
   for (j, k, val) in zip(J, K, values)
     result[j, k] = val - attempt[j, k]
   end
@@ -65,7 +65,7 @@ guess = sqrt(0.5) * BigFloat[
 steps = 600
 line_search_max_steps = 100
 init_stepsize = BigFloat(1)
-step_shrink_factor = BigFloat(0.5)
+step_shrink_factor = BigFloat(0.9)
 target_improvement_factor = BigFloat(0.5)
 
 # complete the gram matrix using gradient descent