Update README.md

README.md

@@ -136,4 +136,89 @@ done.
   All pass: True
   Compiled: 0.72× vs cuSOLVER
 ========================================================================
+```
+
+
+
+Testing the barrage setup is reveals much information about parallel processing capacity.
+
+```
+==============================================================================
+  Diagnostic: Parallel Root-Finding
+==============================================================================
+  B=512 N=6
+  True eigenvalue range: [-2.106, 2.099]
+  Diagonal init range:   [-1.561, 1.722]
+
+  --- Test 1: Pure Laguerre (no Aberth) ---
+   PurL it= 0  max_err=1.75e+00  min_gap=1.73e-06  |p(z)|=3.93e+00
+   PurL it= 1  max_err=1.84e+00  min_gap=1.67e-16  |p(z)|=5.39e-01
+   PurL it= 2  max_err=1.89e+00  min_gap=0.00e+00  |p(z)|=2.01e-02
+   PurL it= 3  max_err=1.90e+00  min_gap=0.00e+00  |p(z)|=1.73e-04
+   PurL it= 4  max_err=1.90e+00  min_gap=0.00e+00  |p(z)|=7.12e-07
+   PurL it= 9  max_err=1.90e+00  min_gap=0.00e+00  |p(z)|=2.88e-15
+   PurL it=14  max_err=1.90e+00  min_gap=0.00e+00  |p(z)|=2.88e-15
+   PurL it=19  max_err=1.90e+00  min_gap=0.00e+00  |p(z)|=2.88e-15
+
+  --- Test 2: Laguerre + Aberth (full) ---
+   LA-F it= 0  max_err=1.03e+02  min_gap=5.69e-07  |p(z)|=1.33e+12
+   LA-F it= 1  max_err=3.70e+02  min_gap=1.71e-06  |p(z)|=2.62e+15
+   LA-F it= 2  max_err=4.63e+02  min_gap=5.12e-06  |p(z)|=1.00e+16
+   LA-F it= 3  max_err=1.58e+03  min_gap=1.54e-05  |p(z)|=1.59e+19
+   LA-F it= 4  max_err=1.98e+03  min_gap=4.61e-05  |p(z)|=6.05e+19
+   LA-F it= 9  max_err=6.05e+03  min_gap=5.26e-04  |p(z)|=4.89e+22
+   LA-F it=14  max_err=1.85e+04  min_gap=8.50e-04  |p(z)|=3.95e+25
+   LA-F it=19  max_err=5.63e+04  min_gap=1.92e-02  |p(z)|=3.19e+28
+
+  --- Test 3: Laguerre + weak Aberth (0.1x) ---
+   LA.1 it= 0  max_err=2.89e+01  min_gap=5.69e-05  |p(z)|=7.50e+08
+   LA.1 it= 1  max_err=2.09e+01  min_gap=2.84e-06  |p(z)|=1.23e+08
+   LA.1 it= 2  max_err=1.35e+01  min_gap=6.74e-07  |p(z)|=1.06e+07
+   LA.1 it= 3  max_err=6.44e+00  min_gap=4.80e-08  |p(z)|=2.25e+05
+   LA.1 it= 4  max_err=1.89e+00  min_gap=4.16e-09  |p(z)|=1.99e+01
+   LA.1 it= 9  max_err=1.90e+00  min_gap=1.45e-14  |p(z)|=4.90e-03
+   LA.1 it=14  max_err=1.90e+00  min_gap=0.00e+00  |p(z)|=6.48e-04
+   LA.1 it=19  max_err=1.90e+00  min_gap=0.00e+00  |p(z)|=8.53e-05
+
+  --- Test 4: Pure Laguerre + re-sort ---
+   PL+S it= 0  max_err=1.75e+00  min_gap=1.73e-06  |p(z)|=3.93e+00
+   PL+S it= 1  max_err=1.84e+00  min_gap=1.67e-16  |p(z)|=5.39e-01
+   PL+S it= 2  max_err=1.89e+00  min_gap=0.00e+00  |p(z)|=2.01e-02
+   PL+S it= 3  max_err=1.90e+00  min_gap=0.00e+00  |p(z)|=1.73e-04
+   PL+S it= 4  max_err=1.90e+00  min_gap=0.00e+00  |p(z)|=7.12e-07
+   PL+S it= 9  max_err=1.90e+00  min_gap=0.00e+00  |p(z)|=2.88e-15
+   PL+S it=14  max_err=1.90e+00  min_gap=0.00e+00  |p(z)|=2.88e-15
+   PL+S it=19  max_err=1.90e+00  min_gap=0.00e+00  |p(z)|=2.88e-15
+
+  --- Test 5: Laguerre + Aberth damped (0.1 → 1.0) ---
+   LADa it= 0  max_err=2.89e+01  min_gap=5.69e-05  |p(z)|=7.50e+08
+   LADa it= 1  max_err=3.72e+02  min_gap=3.82e-06  |p(z)|=2.69e+15
+   LADa it= 2  max_err=1.13e+03  min_gap=4.82e-06  |p(z)|=2.08e+18
+   LADa it= 3  max_err=2.26e+03  min_gap=1.90e-06  |p(z)|=1.34e+20
+   LADa it= 4  max_err=3.77e+03  min_gap=9.02e-07  |p(z)|=2.88e+21
+   LADa it= 9  max_err=1.70e+04  min_gap=2.34e-05  |p(z)|=2.38e+25
+   LADa it=14  max_err=5.17e+04  min_gap=2.25e-03  |p(z)|=1.91e+28
+   LADa it=19  max_err=1.58e+05  min_gap=8.72e-03  |p(z)|=1.54e+31
+
+  --- Test 6: Newton + Aberth ---
+   NwAb it= 0  max_err=4.35e+02  min_gap=3.29e-05  |p(z)|=6.91e+15
+   NwAb it= 1  max_err=1.57e+01  min_gap=9.86e-05  |p(z)|=2.43e+07
+   NwAb it= 2  max_err=5.28e+01  min_gap=1.70e-05  |p(z)|=2.54e+10
+   NwAb it= 3  max_err=5.37e+01  min_gap=5.22e-05  |p(z)|=2.75e+10
+   NwAb it= 4  max_err=3.34e+02  min_gap=1.91e-04  |p(z)|=1.41e+15
+   NwAb it= 9  max_err=2.02e+00  min_gap=1.92e-02  |p(z)|=6.78e+02
+   NwAb it=14  max_err=1.05e-06  min_gap=1.92e-02  |p(z)|=1.24e-14
+   NwAb it=19  max_err=1.05e-06  min_gap=1.92e-02  |p(z)|=1.24e-14
+
+  --- Test 7: Pure Newton ---
+   PurN it= 0  max_err=3.51e+02  min_gap=6.24e-06  |p(z)|=1.93e+15
+   PurN it= 1  max_err=2.93e+02  min_gap=1.69e-09  |p(z)|=6.46e+14
+   PurN it= 2  max_err=2.44e+02  min_gap=0.00e+00  |p(z)|=2.16e+14
+   PurN it= 3  max_err=2.03e+02  min_gap=0.00e+00  |p(z)|=7.25e+13
+   PurN it= 4  max_err=1.69e+02  min_gap=0.00e+00  |p(z)|=2.43e+13
+   PurN it= 9  max_err=6.69e+01  min_gap=0.00e+00  |p(z)|=1.02e+11
+   PurN it=14  max_err=2.60e+01  min_gap=0.00e+00  |p(z)|=4.31e+08
+   PurN it=19  max_err=9.63e+00  min_gap=0.00e+00  |p(z)|=1.81e+06
+==============================================================================
+
 ```