File: tri_demo.out

package info (click to toggle)
suitesparse 1%3A5.8.1%2Bdfsg-2
links: PTS, VCS
area: main
in suites: bullseye
size: 152,716 kB
sloc: ansic: 774,385; cpp: 24,213; makefile: 6,310; fortran: 1,927; java: 1,826; csh: 1,686; ruby: 725; sh: 535; perl: 225; python: 209; sed: 164; awk: 60
file content (2040 lines) | stat: -rw-r--r-- 97,735 bytes
--------------------------------------------------------------
Wathen: nx 4 ny 4 n 65 nz 752 method 0, time: 0.000 sec

total time to read A matrix:       0.000279 sec

n 65 # edges 376
U=triu(A) time:        0.000032 sec
L=tril(A) time:        0.000008 sec

------------------------------------- dot product method:
# triangles 872
L*U' time (dot):         0.000055 sec
tricount time:         0.000071 sec (dot product method)
tri+prep time:         0.000111 sec (incl time to compute L and U)
compute C time:        0.000055 sec
reduce (C) time:       0.000016 sec
rate     3.39 million edges/sec (incl time for U=triu(A))
rate     5.27 million edges/sec (just tricount itself)
L*U' time (dot):         0.000015 sec (nthreads: 2 speedup 3.70945)
tricount time:         0.000020 sec (dot product method)
tri+prep time:         0.000059 sec (incl time to compute L and U)
compute C time:        0.000015 sec
reduce (C) time:       0.000005 sec
rate     6.34 million edges/sec (incl time for U=triu(A))
rate    19.13 million edges/sec (just tricount itself)
L*U' time (dot):         0.000013 sec (nthreads: 4 speedup 4.16316)
tricount time:         0.000017 sec (dot product method)
tri+prep time:         0.000057 sec (incl time to compute L and U)
compute C time:        0.000013 sec
reduce (C) time:       0.000004 sec
rate     6.58 million edges/sec (incl time for U=triu(A))
rate    21.52 million edges/sec (just tricount itself)
L*U' time (dot):         0.000012 sec (nthreads: 8 speedup 4.43079)
tricount time:         0.000016 sec (dot product method)
tri+prep time:         0.000056 sec (incl time to compute L and U)
compute C time:        0.000012 sec
reduce (C) time:       0.000004 sec
rate     6.72 million edges/sec (incl time for U=triu(A))
rate    23.04 million edges/sec (just tricount itself)
L*U' time (dot):         0.000016 sec
tricount time:         0.000021 sec (dot product method)
tri+prep time:         0.000060 sec (incl time to compute L and U)
compute C time:        0.000016 sec
reduce (C) time:       0.000004 sec
rate     6.25 million edges/sec (incl time for U=triu(A))
rate    18.32 million edges/sec (just tricount itself)
L*U' time (dot):         0.000013 sec (nthreads: 2 speedup 1.23168)
tricount time:         0.000017 sec (dot product method)
tri+prep time:         0.000057 sec (incl time to compute L and U)
compute C time:        0.000013 sec
reduce (C) time:       0.000004 sec
rate     6.65 million edges/sec (incl time for U=triu(A))
rate    22.27 million edges/sec (just tricount itself)
L*U' time (dot):         0.000013 sec (nthreads: 4 speedup 1.27601)
tricount time:         0.000017 sec (dot product method)
tri+prep time:         0.000056 sec (incl time to compute L and U)
compute C time:        0.000013 sec
reduce (C) time:       0.000004 sec
rate     6.67 million edges/sec (incl time for U=triu(A))
rate    22.52 million edges/sec (just tricount itself)
L*U' time (dot):         0.000012 sec (nthreads: 8 speedup 1.31332)
tricount time:         0.000016 sec (dot product method)
tri+prep time:         0.000056 sec (incl time to compute L and U)
compute C time:        0.000012 sec
reduce (C) time:       0.000004 sec
rate     6.77 million edges/sec (incl time for U=triu(A))
rate    23.59 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 872
C<L>=L*L time (saxpy):         0.000045 sec
tricount time:         0.000047 sec (saxpy method)
tri+prep time:         0.000055 sec (incl time to compute L)
compute C time:        0.000045 sec
reduce (C) time:       0.000001 sec
rate     6.88 million edges/sec (incl time for L=tril(A))
rate     8.06 million edges/sec (just tricount itself)
triangles, method 3: 872
C<L>=L*L time (saxpy):         0.000021 sec (nthreads: 2 speedup 2.10986)
tricount time:         0.000023 sec (saxpy method)
tri+prep time:         0.000031 sec (incl time to compute L)
compute C time:        0.000021 sec
reduce (C) time:       0.000001 sec
rate    12.24 million edges/sec (incl time for L=tril(A))
rate    16.56 million edges/sec (just tricount itself)
triangles, method 3: 872
C<L>=L*L time (saxpy):         0.000022 sec (nthreads: 4 speedup 2.06334)
tricount time:         0.000023 sec (saxpy method)
tri+prep time:         0.000031 sec (incl time to compute L)
compute C time:        0.000022 sec
reduce (C) time:       0.000001 sec
rate    12.00 million edges/sec (incl time for L=tril(A))
rate    16.12 million edges/sec (just tricount itself)
triangles, method 3: 872
C<L>=L*L time (saxpy):         0.000019 sec (nthreads: 8 speedup 2.35071)
tricount time:         0.000021 sec (saxpy method)
tri+prep time:         0.000029 sec (incl time to compute L)
compute C time:        0.000019 sec
reduce (C) time:       0.000001 sec
rate    13.13 million edges/sec (incl time for L=tril(A))
rate    18.22 million edges/sec (just tricount itself)

--------------------------------------------------------------
random 5 by 5, nz: 18, method 1 time 0.000 sec

total time to read A matrix:       0.000128 sec

n 5 # edges 9
U=triu(A) time:        0.000041 sec
L=tril(A) time:        0.000006 sec

------------------------------------- dot product method:
# triangles 7
L*U' time (dot):         0.000039 sec
tricount time:         0.000053 sec (dot product method)
tri+prep time:         0.000100 sec (incl time to compute L and U)
compute C time:        0.000039 sec
reduce (C) time:       0.000014 sec
rate     0.09 million edges/sec (incl time for U=triu(A))
rate     0.17 million edges/sec (just tricount itself)
L*U' time (dot):         0.000005 sec (nthreads: 2 speedup 7.69034)
tricount time:         0.000008 sec (dot product method)
tri+prep time:         0.000054 sec (incl time to compute L and U)
compute C time:        0.000005 sec
reduce (C) time:       0.000002 sec
rate     0.17 million edges/sec (incl time for U=triu(A))
rate     1.18 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 4 speedup 11.3518)
tricount time:         0.000006 sec (dot product method)
tri+prep time:         0.000053 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000003 sec
rate     0.17 million edges/sec (incl time for U=triu(A))
rate     1.50 million edges/sec (just tricount itself)
L*U' time (dot):         0.000006 sec (nthreads: 8 speedup 6.84178)
tricount time:         0.000009 sec (dot product method)
tri+prep time:         0.000056 sec (incl time to compute L and U)
compute C time:        0.000006 sec
reduce (C) time:       0.000003 sec
rate     0.16 million edges/sec (incl time for U=triu(A))
rate     0.98 million edges/sec (just tricount itself)
L*U' time (dot):         0.000008 sec
tricount time:         0.000010 sec (dot product method)
tri+prep time:         0.000057 sec (incl time to compute L and U)
compute C time:        0.000008 sec
reduce (C) time:       0.000003 sec
rate     0.16 million edges/sec (incl time for U=triu(A))
rate     0.87 million edges/sec (just tricount itself)
L*U' time (dot):         0.000005 sec (nthreads: 2 speedup 1.63061)
tricount time:         0.000007 sec (dot product method)
tri+prep time:         0.000054 sec (incl time to compute L and U)
compute C time:        0.000005 sec
reduce (C) time:       0.000002 sec
rate     0.17 million edges/sec (incl time for U=triu(A))
rate     1.25 million edges/sec (just tricount itself)
L*U' time (dot):         0.000006 sec (nthreads: 4 speedup 1.29289)
tricount time:         0.000009 sec (dot product method)
tri+prep time:         0.000055 sec (incl time to compute L and U)
compute C time:        0.000006 sec
reduce (C) time:       0.000002 sec
rate     0.16 million edges/sec (incl time for U=triu(A))
rate     1.06 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 8 speedup 2.37394)
tricount time:         0.000005 sec (dot product method)
tri+prep time:         0.000052 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000002 sec
rate     0.17 million edges/sec (incl time for U=triu(A))
rate     1.73 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 7
C<L>=L*L time (saxpy):         0.000029 sec
tricount time:         0.000030 sec (saxpy method)
tri+prep time:         0.000036 sec (incl time to compute L)
compute C time:        0.000029 sec
reduce (C) time:       0.000001 sec
rate     0.25 million edges/sec (incl time for L=tril(A))
rate     0.30 million edges/sec (just tricount itself)
triangles, method 3: 7
C<L>=L*L time (saxpy):         0.000007 sec (nthreads: 2 speedup 4.44424)
tricount time:         0.000007 sec (saxpy method)
tri+prep time:         0.000013 sec (incl time to compute L)
compute C time:        0.000007 sec
reduce (C) time:       0.000000 sec
rate     0.69 million edges/sec (incl time for L=tril(A))
rate     1.29 million edges/sec (just tricount itself)
triangles, method 3: 7
C<L>=L*L time (saxpy):         0.000005 sec (nthreads: 4 speedup 5.59661)
tricount time:         0.000006 sec (saxpy method)
tri+prep time:         0.000012 sec (incl time to compute L)
compute C time:        0.000005 sec
reduce (C) time:       0.000000 sec
rate     0.78 million edges/sec (incl time for L=tril(A))
rate     1.61 million edges/sec (just tricount itself)
triangles, method 3: 7
C<L>=L*L time (saxpy):         0.000010 sec (nthreads: 8 speedup 3.02562)
tricount time:         0.000011 sec (saxpy method)
tri+prep time:         0.000017 sec (incl time to compute L)
compute C time:        0.000010 sec
reduce (C) time:       0.000001 sec
rate     0.54 million edges/sec (incl time for L=tril(A))
rate     0.85 million edges/sec (just tricount itself)

--------------------------------------------------------------
matrix 3 by 3, 0 entries, from stdin

total time to read A matrix:       0.000168 sec

n 3 # edges 0
U=triu(A) time:        0.000052 sec
L=tril(A) time:        0.000007 sec

------------------------------------- dot product method:
# triangles 0
L*U' time (dot):         0.000039 sec
tricount time:         0.000043 sec (dot product method)
tri+prep time:         0.000102 sec (incl time to compute L and U)
compute C time:        0.000039 sec
reduce (C) time:       0.000004 sec
rate     0.00 million edges/sec (incl time for U=triu(A))
rate     0.00 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec (nthreads: 2 speedup 9.51825)
tricount time:         0.000005 sec (dot product method)
tri+prep time:         0.000064 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000000 sec
rate     0.00 million edges/sec (incl time for U=triu(A))
rate     0.00 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 4 speedup 13.9081)
tricount time:         0.000003 sec (dot product method)
tri+prep time:         0.000062 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000000 sec
rate     0.00 million edges/sec (incl time for U=triu(A))
rate     0.00 million edges/sec (just tricount itself)
L*U' time (dot):         0.000002 sec (nthreads: 8 speedup 15.989)
tricount time:         0.000003 sec (dot product method)
tri+prep time:         0.000062 sec (incl time to compute L and U)
compute C time:        0.000002 sec
reduce (C) time:       0.000000 sec
rate     0.00 million edges/sec (incl time for U=triu(A))
rate     0.00 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec
tricount time:         0.000003 sec (dot product method)
tri+prep time:         0.000062 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000000 sec
rate     0.00 million edges/sec (incl time for U=triu(A))
rate     0.00 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 2 speedup 0.949015)
tricount time:         0.000003 sec (dot product method)
tri+prep time:         0.000062 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000000 sec
rate     0.00 million edges/sec (incl time for U=triu(A))
rate     0.00 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 4 speedup 0.985999)
tricount time:         0.000003 sec (dot product method)
tri+prep time:         0.000062 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000000 sec
rate     0.00 million edges/sec (incl time for U=triu(A))
rate     0.00 million edges/sec (just tricount itself)
L*U' time (dot):         0.000002 sec (nthreads: 8 speedup 1.04575)
tricount time:         0.000003 sec (dot product method)
tri+prep time:         0.000062 sec (incl time to compute L and U)
compute C time:        0.000002 sec
reduce (C) time:       0.000000 sec
rate     0.00 million edges/sec (incl time for U=triu(A))
rate     0.00 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000022 sec
tricount time:         0.000023 sec (saxpy method)
tri+prep time:         0.000029 sec (incl time to compute L)
compute C time:        0.000022 sec
reduce (C) time:       0.000000 sec
rate     0.00 million edges/sec (incl time for L=tril(A))
rate     0.00 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000005 sec (nthreads: 2 speedup 4.57078)
tricount time:         0.000005 sec (saxpy method)
tri+prep time:         0.000012 sec (incl time to compute L)
compute C time:        0.000005 sec
reduce (C) time:       0.000000 sec
rate     0.00 million edges/sec (incl time for L=tril(A))
rate     0.00 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000004 sec (nthreads: 4 speedup 5.3183)
tricount time:         0.000005 sec (saxpy method)
tri+prep time:         0.000011 sec (incl time to compute L)
compute C time:        0.000004 sec
reduce (C) time:       0.000000 sec
rate     0.00 million edges/sec (incl time for L=tril(A))
rate     0.00 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000006 sec (nthreads: 8 speedup 3.45239)
tricount time:         0.000007 sec (saxpy method)
tri+prep time:         0.000014 sec (incl time to compute L)
compute C time:        0.000006 sec
reduce (C) time:       0.000000 sec
rate     0.00 million edges/sec (incl time for L=tril(A))
rate     0.00 million edges/sec (just tricount itself)

--------------------------------------------------------------
matrix 4 by 4, 4 entries, from stdin

total time to read A matrix:       0.000174 sec

n 4 # edges 2
U=triu(A) time:        0.000044 sec
L=tril(A) time:        0.000007 sec

------------------------------------- dot product method:
# triangles 0
L*U' time (dot):         0.000029 sec
tricount time:         0.000039 sec (dot product method)
tri+prep time:         0.000090 sec (incl time to compute L and U)
compute C time:        0.000029 sec
reduce (C) time:       0.000009 sec
rate     0.02 million edges/sec (incl time for U=triu(A))
rate     0.05 million edges/sec (just tricount itself)
L*U' time (dot):         0.000007 sec (nthreads: 2 speedup 4.16357)
tricount time:         0.000012 sec (dot product method)
tri+prep time:         0.000064 sec (incl time to compute L and U)
compute C time:        0.000007 sec
reduce (C) time:       0.000005 sec
rate     0.03 million edges/sec (incl time for U=triu(A))
rate     0.16 million edges/sec (just tricount itself)
L*U' time (dot):         0.000005 sec (nthreads: 4 speedup 5.49784)
tricount time:         0.000009 sec (dot product method)
tri+prep time:         0.000060 sec (incl time to compute L and U)
compute C time:        0.000005 sec
reduce (C) time:       0.000003 sec
rate     0.03 million edges/sec (incl time for U=triu(A))
rate     0.23 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 8 speedup 9.85422)
tricount time:         0.000005 sec (dot product method)
tri+prep time:         0.000057 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000002 sec
rate     0.04 million edges/sec (incl time for U=triu(A))
rate     0.36 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec
tricount time:         0.000006 sec (dot product method)
tri+prep time:         0.000058 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000003 sec
rate     0.03 million edges/sec (incl time for U=triu(A))
rate     0.32 million edges/sec (just tricount itself)
L*U' time (dot):         0.000005 sec (nthreads: 2 speedup 0.592958)
tricount time:         0.000008 sec (dot product method)
tri+prep time:         0.000060 sec (incl time to compute L and U)
compute C time:        0.000005 sec
reduce (C) time:       0.000003 sec
rate     0.03 million edges/sec (incl time for U=triu(A))
rate     0.24 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 4 speedup 1.04212)
tricount time:         0.000005 sec (dot product method)
tri+prep time:         0.000057 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000002 sec
rate     0.04 million edges/sec (incl time for U=triu(A))
rate     0.38 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 8 speedup 1.20878)
tricount time:         0.000006 sec (dot product method)
tri+prep time:         0.000057 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000003 sec
rate     0.03 million edges/sec (incl time for U=triu(A))
rate     0.36 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000042 sec
tricount time:         0.000043 sec (saxpy method)
tri+prep time:         0.000050 sec (incl time to compute L)
compute C time:        0.000042 sec
reduce (C) time:       0.000001 sec
rate     0.04 million edges/sec (incl time for L=tril(A))
rate     0.05 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000014 sec (nthreads: 2 speedup 2.90987)
tricount time:         0.000015 sec (saxpy method)
tri+prep time:         0.000022 sec (incl time to compute L)
compute C time:        0.000014 sec
reduce (C) time:       0.000000 sec
rate     0.09 million edges/sec (incl time for L=tril(A))
rate     0.13 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000014 sec (nthreads: 4 speedup 3.02766)
tricount time:         0.000014 sec (saxpy method)
tri+prep time:         0.000022 sec (incl time to compute L)
compute C time:        0.000014 sec
reduce (C) time:       0.000001 sec
rate     0.09 million edges/sec (incl time for L=tril(A))
rate     0.14 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000017 sec (nthreads: 8 speedup 2.42674)
tricount time:         0.000018 sec (saxpy method)
tri+prep time:         0.000025 sec (incl time to compute L)
compute C time:        0.000017 sec
reduce (C) time:       0.000000 sec
rate     0.08 million edges/sec (incl time for L=tril(A))
rate     0.11 million edges/sec (just tricount itself)

--------------------------------------------------------------
matrix 4 by 4, 10 entries, from stdin

total time to read A matrix:       0.000112 sec

n 4 # edges 5
U=triu(A) time:        0.000024 sec
L=tril(A) time:        0.000005 sec

------------------------------------- dot product method:
# triangles 2
L*U' time (dot):         0.000021 sec
tricount time:         0.000027 sec (dot product method)
tri+prep time:         0.000056 sec (incl time to compute L and U)
compute C time:        0.000021 sec
reduce (C) time:       0.000006 sec
rate     0.09 million edges/sec (incl time for U=triu(A))
rate     0.18 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec (nthreads: 2 speedup 4.75515)
tricount time:         0.000007 sec (dot product method)
tri+prep time:         0.000035 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000002 sec
rate     0.14 million edges/sec (incl time for U=triu(A))
rate     0.74 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 4 speedup 6.41806)
tricount time:         0.000005 sec (dot product method)
tri+prep time:         0.000034 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000002 sec
rate     0.15 million edges/sec (incl time for U=triu(A))
rate     0.98 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 8 speedup 7.51145)
tricount time:         0.000004 sec (dot product method)
tri+prep time:         0.000033 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000002 sec
rate     0.15 million edges/sec (incl time for U=triu(A))
rate     1.12 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec
tricount time:         0.000005 sec (dot product method)
tri+prep time:         0.000033 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000002 sec
rate     0.15 million edges/sec (incl time for U=triu(A))
rate     1.00 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 2 speedup 1.02638)
tricount time:         0.000005 sec (dot product method)
tri+prep time:         0.000033 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000002 sec
rate     0.15 million edges/sec (incl time for U=triu(A))
rate     1.07 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 4 speedup 1.11222)
tricount time:         0.000004 sec (dot product method)
tri+prep time:         0.000033 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000002 sec
rate     0.15 million edges/sec (incl time for U=triu(A))
rate     1.14 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 8 speedup 1.11541)
tricount time:         0.000004 sec (dot product method)
tri+prep time:         0.000033 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000002 sec
rate     0.15 million edges/sec (incl time for U=triu(A))
rate     1.16 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 2
C<L>=L*L time (saxpy):         0.000018 sec
tricount time:         0.000019 sec (saxpy method)
tri+prep time:         0.000024 sec (incl time to compute L)
compute C time:        0.000018 sec
reduce (C) time:       0.000000 sec
rate     0.21 million edges/sec (incl time for L=tril(A))
rate     0.27 million edges/sec (just tricount itself)
triangles, method 3: 2
C<L>=L*L time (saxpy):         0.000006 sec (nthreads: 2 speedup 3.25856)
tricount time:         0.000006 sec (saxpy method)
tri+prep time:         0.000011 sec (incl time to compute L)
compute C time:        0.000006 sec
reduce (C) time:       0.000000 sec
rate     0.46 million edges/sec (incl time for L=tril(A))
rate     0.84 million edges/sec (just tricount itself)
triangles, method 3: 2
C<L>=L*L time (saxpy):         0.000005 sec (nthreads: 4 speedup 3.87265)
tricount time:         0.000005 sec (saxpy method)
tri+prep time:         0.000010 sec (incl time to compute L)
compute C time:        0.000005 sec
reduce (C) time:       0.000000 sec
rate     0.50 million edges/sec (incl time for L=tril(A))
rate     0.99 million edges/sec (just tricount itself)
triangles, method 3: 2
C<L>=L*L time (saxpy):         0.000005 sec (nthreads: 8 speedup 3.318)
tricount time:         0.000006 sec (saxpy method)
tri+prep time:         0.000011 sec (incl time to compute L)
compute C time:        0.000005 sec
reduce (C) time:       0.000000 sec
rate     0.46 million edges/sec (incl time for L=tril(A))
rate     0.84 million edges/sec (just tricount itself)

--------------------------------------------------------------
matrix 7 by 7, 16 entries, from stdin

total time to read A matrix:       0.000151 sec

n 7 # edges 8
U=triu(A) time:        0.000020 sec
L=tril(A) time:        0.000005 sec

------------------------------------- dot product method:
# triangles 0
L*U' time (dot):         0.000027 sec
tricount time:         0.000034 sec (dot product method)
tri+prep time:         0.000059 sec (incl time to compute L and U)
compute C time:        0.000027 sec
reduce (C) time:       0.000007 sec
rate     0.14 million edges/sec (incl time for U=triu(A))
rate     0.24 million edges/sec (just tricount itself)
L*U' time (dot):         0.000005 sec (nthreads: 2 speedup 5.12151)
tricount time:         0.000009 sec (dot product method)
tri+prep time:         0.000034 sec (incl time to compute L and U)
compute C time:        0.000005 sec
reduce (C) time:       0.000003 sec
rate     0.24 million edges/sec (incl time for U=triu(A))
rate     0.93 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 4 speedup 9.05404)
tricount time:         0.000005 sec (dot product method)
tri+prep time:         0.000030 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000002 sec
rate     0.26 million edges/sec (incl time for U=triu(A))
rate     1.46 million edges/sec (just tricount itself)
L*U' time (dot):         0.000006 sec (nthreads: 8 speedup 4.59057)
tricount time:         0.000010 sec (dot product method)
tri+prep time:         0.000035 sec (incl time to compute L and U)
compute C time:        0.000006 sec
reduce (C) time:       0.000004 sec
rate     0.23 million edges/sec (incl time for U=triu(A))
rate     0.79 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec
tricount time:         0.000007 sec (dot product method)
tri+prep time:         0.000032 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000003 sec
rate     0.25 million edges/sec (incl time for U=triu(A))
rate     1.16 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 2 speedup 1.18959)
tricount time:         0.000006 sec (dot product method)
tri+prep time:         0.000031 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000003 sec
rate     0.26 million edges/sec (incl time for U=triu(A))
rate     1.28 million edges/sec (just tricount itself)
L*U' time (dot):         0.000006 sec (nthreads: 4 speedup 0.659947)
tricount time:         0.000009 sec (dot product method)
tri+prep time:         0.000034 sec (incl time to compute L and U)
compute C time:        0.000006 sec
reduce (C) time:       0.000004 sec
rate     0.23 million edges/sec (incl time for U=triu(A))
rate     0.86 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 8 speedup 1.16779)
tricount time:         0.000006 sec (dot product method)
tri+prep time:         0.000031 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000003 sec
rate     0.26 million edges/sec (incl time for U=triu(A))
rate     1.31 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000029 sec
tricount time:         0.000029 sec (saxpy method)
tri+prep time:         0.000035 sec (incl time to compute L)
compute C time:        0.000029 sec
reduce (C) time:       0.000001 sec
rate     0.23 million edges/sec (incl time for L=tril(A))
rate     0.27 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000014 sec (nthreads: 2 speedup 2.0437)
tricount time:         0.000014 sec (saxpy method)
tri+prep time:         0.000020 sec (incl time to compute L)
compute C time:        0.000014 sec
reduce (C) time:       0.000000 sec
rate     0.41 million edges/sec (incl time for L=tril(A))
rate     0.55 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000013 sec (nthreads: 4 speedup 2.19743)
tricount time:         0.000014 sec (saxpy method)
tri+prep time:         0.000019 sec (incl time to compute L)
compute C time:        0.000013 sec
reduce (C) time:       0.000001 sec
rate     0.43 million edges/sec (incl time for L=tril(A))
rate     0.59 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000035 sec (nthreads: 8 speedup 0.811284)
tricount time:         0.000036 sec (saxpy method)
tri+prep time:         0.000041 sec (incl time to compute L)
compute C time:        0.000035 sec
reduce (C) time:       0.000001 sec
rate     0.20 million edges/sec (incl time for L=tril(A))
rate     0.22 million edges/sec (just tricount itself)

--------------------------------------------------------------
matrix 304 by 304, 876 entries, from stdin

total time to read A matrix:       0.000324 sec

n 304 # edges 438
U=triu(A) time:        0.000021 sec
L=tril(A) time:        0.000007 sec

------------------------------------- dot product method:
# triangles 0
L*U' time (dot):         0.000029 sec
tricount time:         0.000039 sec (dot product method)
tri+prep time:         0.000066 sec (incl time to compute L and U)
compute C time:        0.000029 sec
reduce (C) time:       0.000010 sec
rate     6.59 million edges/sec (incl time for U=triu(A))
rate    11.34 million edges/sec (just tricount itself)
L*U' time (dot):         0.000011 sec (nthreads: 2 speedup 2.6523)
tricount time:         0.000017 sec (dot product method)
tri+prep time:         0.000045 sec (incl time to compute L and U)
compute C time:        0.000011 sec
reduce (C) time:       0.000007 sec
rate     9.66 million edges/sec (incl time for U=triu(A))
rate    25.07 million edges/sec (just tricount itself)
L*U' time (dot):         0.000010 sec (nthreads: 4 speedup 3.01903)
tricount time:         0.000015 sec (dot product method)
tri+prep time:         0.000043 sec (incl time to compute L and U)
compute C time:        0.000010 sec
reduce (C) time:       0.000006 sec
rate    10.12 million edges/sec (incl time for U=triu(A))
rate    28.41 million edges/sec (just tricount itself)
L*U' time (dot):         0.000009 sec (nthreads: 8 speedup 3.12291)
tricount time:         0.000015 sec (dot product method)
tri+prep time:         0.000043 sec (incl time to compute L and U)
compute C time:        0.000009 sec
reduce (C) time:       0.000005 sec
rate    10.29 million edges/sec (incl time for U=triu(A))
rate    29.82 million edges/sec (just tricount itself)
L*U' time (dot):         0.000009 sec
tricount time:         0.000014 sec (dot product method)
tri+prep time:         0.000042 sec (incl time to compute L and U)
compute C time:        0.000009 sec
reduce (C) time:       0.000005 sec
rate    10.50 million edges/sec (incl time for U=triu(A))
rate    31.63 million edges/sec (just tricount itself)
L*U' time (dot):         0.000008 sec (nthreads: 2 speedup 1.04126)
tricount time:         0.000013 sec (dot product method)
tri+prep time:         0.000041 sec (incl time to compute L and U)
compute C time:        0.000008 sec
reduce (C) time:       0.000005 sec
rate    10.69 million edges/sec (incl time for U=triu(A))
rate    33.47 million edges/sec (just tricount itself)
L*U' time (dot):         0.000008 sec (nthreads: 4 speedup 1.02962)
tricount time:         0.000013 sec (dot product method)
tri+prep time:         0.000041 sec (incl time to compute L and U)
compute C time:        0.000008 sec
reduce (C) time:       0.000005 sec
rate    10.66 million edges/sec (incl time for U=triu(A))
rate    33.15 million edges/sec (just tricount itself)
L*U' time (dot):         0.000008 sec (nthreads: 8 speedup 1.06811)
tricount time:         0.000013 sec (dot product method)
tri+prep time:         0.000041 sec (incl time to compute L and U)
compute C time:        0.000008 sec
reduce (C) time:       0.000005 sec
rate    10.79 million edges/sec (incl time for U=triu(A))
rate    34.38 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000028 sec
tricount time:         0.000028 sec (saxpy method)
tri+prep time:         0.000036 sec (incl time to compute L)
compute C time:        0.000028 sec
reduce (C) time:       0.000000 sec
rate    12.34 million edges/sec (incl time for L=tril(A))
rate    15.52 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000020 sec (nthreads: 2 speedup 1.37094)
tricount time:         0.000021 sec (saxpy method)
tri+prep time:         0.000028 sec (incl time to compute L)
compute C time:        0.000020 sec
reduce (C) time:       0.000000 sec
rate    15.64 million edges/sec (incl time for L=tril(A))
rate    21.15 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000019 sec (nthreads: 4 speedup 1.46644)
tricount time:         0.000019 sec (saxpy method)
tri+prep time:         0.000027 sec (incl time to compute L)
compute C time:        0.000019 sec
reduce (C) time:       0.000000 sec
rate    16.49 million edges/sec (incl time for L=tril(A))
rate    22.72 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000025 sec (nthreads: 8 speedup 1.09045)
tricount time:         0.000026 sec (saxpy method)
tri+prep time:         0.000033 sec (incl time to compute L)
compute C time:        0.000025 sec
reduce (C) time:       0.000000 sec
rate    13.17 million edges/sec (incl time for L=tril(A))
rate    16.87 million edges/sec (just tricount itself)

--------------------------------------------------------------
matrix 48 by 48, 352 entries, from stdin

total time to read A matrix:       0.000230 sec

n 48 # edges 176
U=triu(A) time:        0.000027 sec
L=tril(A) time:        0.000006 sec

------------------------------------- dot product method:
# triangles 160
L*U' time (dot):         0.000027 sec
tricount time:         0.000034 sec (dot product method)
tri+prep time:         0.000068 sec (incl time to compute L and U)
compute C time:        0.000027 sec
reduce (C) time:       0.000007 sec
rate     2.60 million edges/sec (incl time for U=triu(A))
rate     5.16 million edges/sec (just tricount itself)
L*U' time (dot):         0.000010 sec (nthreads: 2 speedup 2.57265)
tricount time:         0.000014 sec (dot product method)
tri+prep time:         0.000048 sec (incl time to compute L and U)
compute C time:        0.000010 sec
reduce (C) time:       0.000004 sec
rate     3.70 million edges/sec (incl time for U=triu(A))
rate    12.62 million edges/sec (just tricount itself)
L*U' time (dot):         0.000008 sec (nthreads: 4 speedup 3.32946)
tricount time:         0.000012 sec (dot product method)
tri+prep time:         0.000045 sec (incl time to compute L and U)
compute C time:        0.000008 sec
reduce (C) time:       0.000004 sec
rate     3.90 million edges/sec (incl time for U=triu(A))
rate    15.24 million edges/sec (just tricount itself)
L*U' time (dot):         0.000010 sec (nthreads: 8 speedup 2.6774)
tricount time:         0.000013 sec (dot product method)
tri+prep time:         0.000047 sec (incl time to compute L and U)
compute C time:        0.000010 sec
reduce (C) time:       0.000003 sec
rate     3.78 million edges/sec (incl time for U=triu(A))
rate    13.55 million edges/sec (just tricount itself)
L*U' time (dot):         0.000011 sec
tricount time:         0.000015 sec (dot product method)
tri+prep time:         0.000048 sec (incl time to compute L and U)
compute C time:        0.000011 sec
reduce (C) time:       0.000004 sec
rate     3.64 million edges/sec (incl time for U=triu(A))
rate    11.91 million edges/sec (just tricount itself)
L*U' time (dot):         0.000010 sec (nthreads: 2 speedup 1.10836)
tricount time:         0.000014 sec (dot product method)
tri+prep time:         0.000048 sec (incl time to compute L and U)
compute C time:        0.000010 sec
reduce (C) time:       0.000004 sec
rate     3.67 million edges/sec (incl time for U=triu(A))
rate    12.25 million edges/sec (just tricount itself)
L*U' time (dot):         0.000010 sec (nthreads: 4 speedup 1.10109)
tricount time:         0.000013 sec (dot product method)
tri+prep time:         0.000047 sec (incl time to compute L and U)
compute C time:        0.000010 sec
reduce (C) time:       0.000003 sec
rate     3.77 million edges/sec (incl time for U=triu(A))
rate    13.40 million edges/sec (just tricount itself)
L*U' time (dot):         0.000007 sec (nthreads: 8 speedup 1.50666)
tricount time:         0.000010 sec (dot product method)
tri+prep time:         0.000043 sec (incl time to compute L and U)
compute C time:        0.000007 sec
reduce (C) time:       0.000002 sec
rate     4.06 million edges/sec (incl time for U=triu(A))
rate    17.96 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 160
C<L>=L*L time (saxpy):         0.000031 sec
tricount time:         0.000032 sec (saxpy method)
tri+prep time:         0.000038 sec (incl time to compute L)
compute C time:        0.000031 sec
reduce (C) time:       0.000001 sec
rate     4.59 million edges/sec (incl time for L=tril(A))
rate     5.51 million edges/sec (just tricount itself)
triangles, method 3: 160
C<L>=L*L time (saxpy):         0.000015 sec (nthreads: 2 speedup 2.0114)
tricount time:         0.000016 sec (saxpy method)
tri+prep time:         0.000022 sec (incl time to compute L)
compute C time:        0.000015 sec
reduce (C) time:       0.000001 sec
rate     7.84 million edges/sec (incl time for L=tril(A))
rate    10.98 million edges/sec (just tricount itself)
triangles, method 3: 160
C<L>=L*L time (saxpy):         0.000012 sec (nthreads: 4 speedup 2.52172)
tricount time:         0.000013 sec (saxpy method)
tri+prep time:         0.000020 sec (incl time to compute L)
compute C time:        0.000012 sec
reduce (C) time:       0.000001 sec
rate     8.98 million edges/sec (incl time for L=tril(A))
rate    13.34 million edges/sec (just tricount itself)
triangles, method 3: 160
C<L>=L*L time (saxpy):         0.000015 sec (nthreads: 8 speedup 2.03312)
tricount time:         0.000016 sec (saxpy method)
tri+prep time:         0.000023 sec (incl time to compute L)
compute C time:        0.000015 sec
reduce (C) time:       0.000001 sec
rate     7.78 million edges/sec (incl time for L=tril(A))
rate    10.86 million edges/sec (just tricount itself)

--------------------------------------------------------------
matrix 4884 by 4884, 285494 entries, from stdin

total time to read A matrix:       0.070533 sec

n 4884 # edges 142747
U=triu(A) time:        0.000237 sec
L=tril(A) time:        0.000177 sec

------------------------------------- dot product method:
# triangles 1512964
L*U' time (dot):         0.015604 sec
tricount time:         0.016610 sec (dot product method)
tri+prep time:         0.017023 sec (incl time to compute L and U)
compute C time:        0.015604 sec
reduce (C) time:       0.001006 sec
rate     8.39 million edges/sec (incl time for U=triu(A))
rate     8.59 million edges/sec (just tricount itself)
L*U' time (dot):         0.007760 sec (nthreads: 2 speedup 2.01076)
tricount time:         0.008425 sec (dot product method)
tri+prep time:         0.008838 sec (incl time to compute L and U)
compute C time:        0.007760 sec
reduce (C) time:       0.000664 sec
rate    16.15 million edges/sec (incl time for U=triu(A))
rate    16.94 million edges/sec (just tricount itself)
L*U' time (dot):         0.004202 sec (nthreads: 4 speedup 3.71338)
tricount time:         0.004798 sec (dot product method)
tri+prep time:         0.005212 sec (incl time to compute L and U)
compute C time:        0.004202 sec
reduce (C) time:       0.000596 sec
rate    27.39 million edges/sec (incl time for U=triu(A))
rate    29.75 million edges/sec (just tricount itself)
L*U' time (dot):         0.002794 sec (nthreads: 8 speedup 5.58414)
tricount time:         0.003421 sec (dot product method)
tri+prep time:         0.003834 sec (incl time to compute L and U)
compute C time:        0.002794 sec
reduce (C) time:       0.000626 sec
rate    37.23 million edges/sec (incl time for U=triu(A))
rate    41.73 million edges/sec (just tricount itself)
L*U' time (dot):         0.014963 sec
tricount time:         0.015630 sec (dot product method)
tri+prep time:         0.016043 sec (incl time to compute L and U)
compute C time:        0.014963 sec
reduce (C) time:       0.000667 sec
rate     8.90 million edges/sec (incl time for U=triu(A))
rate     9.13 million edges/sec (just tricount itself)
L*U' time (dot):         0.007483 sec (nthreads: 2 speedup 1.99945)
tricount time:         0.007839 sec (dot product method)
tri+prep time:         0.008253 sec (incl time to compute L and U)
compute C time:        0.007483 sec
reduce (C) time:       0.000356 sec
rate    17.30 million edges/sec (incl time for U=triu(A))
rate    18.21 million edges/sec (just tricount itself)
L*U' time (dot):         0.004180 sec (nthreads: 4 speedup 3.57986)
tricount time:         0.004810 sec (dot product method)
tri+prep time:         0.005223 sec (incl time to compute L and U)
compute C time:        0.004180 sec
reduce (C) time:       0.000630 sec
rate    27.33 million edges/sec (incl time for U=triu(A))
rate    29.68 million edges/sec (just tricount itself)
L*U' time (dot):         0.002833 sec (nthreads: 8 speedup 5.28111)
tricount time:         0.003473 sec (dot product method)
tri+prep time:         0.003887 sec (incl time to compute L and U)
compute C time:        0.002833 sec
reduce (C) time:       0.000640 sec
rate    36.73 million edges/sec (incl time for U=triu(A))
rate    41.10 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 1512964
C<L>=L*L time (saxpy):         0.013017 sec
tricount time:         0.013408 sec (saxpy method)
tri+prep time:         0.013585 sec (incl time to compute L)
compute C time:        0.013017 sec
reduce (C) time:       0.000392 sec
rate    10.51 million edges/sec (incl time for L=tril(A))
rate    10.65 million edges/sec (just tricount itself)
triangles, method 3: 1512964
C<L>=L*L time (saxpy):         0.006626 sec (nthreads: 2 speedup 1.96461)
tricount time:         0.006824 sec (saxpy method)
tri+prep time:         0.007000 sec (incl time to compute L)
compute C time:        0.006626 sec
reduce (C) time:       0.000198 sec
rate    20.39 million edges/sec (incl time for L=tril(A))
rate    20.92 million edges/sec (just tricount itself)
triangles, method 3: 1512964
C<L>=L*L time (saxpy):         0.004039 sec (nthreads: 4 speedup 3.22239)
tricount time:         0.004249 sec (saxpy method)
tri+prep time:         0.004426 sec (incl time to compute L)
compute C time:        0.004039 sec
reduce (C) time:       0.000210 sec
rate    32.25 million edges/sec (incl time for L=tril(A))
rate    33.59 million edges/sec (just tricount itself)
triangles, method 3: 1512964
C<L>=L*L time (saxpy):         0.002870 sec (nthreads: 8 speedup 4.53567)
tricount time:         0.003111 sec (saxpy method)
tri+prep time:         0.003288 sec (incl time to compute L)
compute C time:        0.002870 sec
reduce (C) time:       0.000241 sec
rate    43.42 million edges/sec (incl time for L=tril(A))
rate    45.88 million edges/sec (just tricount itself)

--------------------------------------------------------------
matrix 183 by 183, 1402 entries, from stdin

total time to read A matrix:       0.000648 sec

n 183 # edges 701
U=triu(A) time:        0.000034 sec
L=tril(A) time:        0.000010 sec

------------------------------------- dot product method:
# triangles 863
L*U' time (dot):         0.000067 sec
tricount time:         0.000081 sec (dot product method)
tri+prep time:         0.000125 sec (incl time to compute L and U)
compute C time:        0.000067 sec
reduce (C) time:       0.000014 sec
rate     5.62 million edges/sec (incl time for U=triu(A))
rate     8.68 million edges/sec (just tricount itself)
L*U' time (dot):         0.000041 sec (nthreads: 2 speedup 1.64645)
tricount time:         0.000048 sec (dot product method)
tri+prep time:         0.000092 sec (incl time to compute L and U)
compute C time:        0.000041 sec
reduce (C) time:       0.000007 sec
rate     7.60 million edges/sec (incl time for U=triu(A))
rate    14.54 million edges/sec (just tricount itself)
L*U' time (dot):         0.000037 sec (nthreads: 4 speedup 1.80399)
tricount time:         0.000044 sec (dot product method)
tri+prep time:         0.000088 sec (incl time to compute L and U)
compute C time:        0.000037 sec
reduce (C) time:       0.000007 sec
rate     7.96 million edges/sec (incl time for U=triu(A))
rate    15.91 million edges/sec (just tricount itself)
L*U' time (dot):         0.000036 sec (nthreads: 8 speedup 1.86393)
tricount time:         0.000042 sec (dot product method)
tri+prep time:         0.000086 sec (incl time to compute L and U)
compute C time:        0.000036 sec
reduce (C) time:       0.000006 sec
rate     8.12 million edges/sec (incl time for U=triu(A))
rate    16.58 million edges/sec (just tricount itself)
L*U' time (dot):         0.000041 sec
tricount time:         0.000048 sec (dot product method)
tri+prep time:         0.000092 sec (incl time to compute L and U)
compute C time:        0.000041 sec
reduce (C) time:       0.000007 sec
rate     7.62 million edges/sec (incl time for U=triu(A))
rate    14.61 million edges/sec (just tricount itself)
L*U' time (dot):         0.000038 sec (nthreads: 2 speedup 1.07256)
tricount time:         0.000045 sec (dot product method)
tri+prep time:         0.000089 sec (incl time to compute L and U)
compute C time:        0.000038 sec
reduce (C) time:       0.000007 sec
rate     7.91 million edges/sec (incl time for U=triu(A))
rate    15.69 million edges/sec (just tricount itself)
L*U' time (dot):         0.000036 sec (nthreads: 4 speedup 1.12909)
tricount time:         0.000042 sec (dot product method)
tri+prep time:         0.000086 sec (incl time to compute L and U)
compute C time:        0.000036 sec
reduce (C) time:       0.000006 sec
rate     8.11 million edges/sec (incl time for U=triu(A))
rate    16.51 million edges/sec (just tricount itself)
L*U' time (dot):         0.000035 sec (nthreads: 8 speedup 1.15865)
tricount time:         0.000041 sec (dot product method)
tri+prep time:         0.000085 sec (incl time to compute L and U)
compute C time:        0.000035 sec
reduce (C) time:       0.000006 sec
rate     8.22 million edges/sec (incl time for U=triu(A))
rate    16.99 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 863
C<L>=L*L time (saxpy):         0.000055 sec
tricount time:         0.000056 sec (saxpy method)
tri+prep time:         0.000066 sec (incl time to compute L)
compute C time:        0.000055 sec
reduce (C) time:       0.000001 sec
rate    10.62 million edges/sec (incl time for L=tril(A))
rate    12.41 million edges/sec (just tricount itself)
triangles, method 3: 863
C<L>=L*L time (saxpy):         0.000035 sec (nthreads: 2 speedup 1.57783)
tricount time:         0.000036 sec (saxpy method)
tri+prep time:         0.000046 sec (incl time to compute L)
compute C time:        0.000035 sec
reduce (C) time:       0.000001 sec
rate    15.33 million edges/sec (incl time for L=tril(A))
rate    19.36 million edges/sec (just tricount itself)
triangles, method 3: 863
C<L>=L*L time (saxpy):         0.000032 sec (nthreads: 4 speedup 1.74196)
tricount time:         0.000033 sec (saxpy method)
tri+prep time:         0.000042 sec (incl time to compute L)
compute C time:        0.000032 sec
reduce (C) time:       0.000001 sec
rate    16.51 million edges/sec (incl time for L=tril(A))
rate    21.29 million edges/sec (just tricount itself)
triangles, method 3: 863
C<L>=L*L time (saxpy):         0.000031 sec (nthreads: 8 speedup 1.78544)
tricount time:         0.000032 sec (saxpy method)
tri+prep time:         0.000042 sec (incl time to compute L)
compute C time:        0.000031 sec
reduce (C) time:       0.000001 sec
rate    16.75 million edges/sec (incl time for L=tril(A))
rate    21.69 million edges/sec (just tricount itself)

--------------------------------------------------------------
matrix 63 by 63, 246 entries, from stdin

total time to read A matrix:       0.000285 sec

n 63 # edges 123
U=triu(A) time:        0.000035 sec
L=tril(A) time:        0.000008 sec

------------------------------------- dot product method:
# triangles 0
L*U' time (dot):         0.000037 sec
tricount time:         0.000047 sec (dot product method)
tri+prep time:         0.000091 sec (incl time to compute L and U)
compute C time:        0.000037 sec
reduce (C) time:       0.000010 sec
rate     1.35 million edges/sec (incl time for U=triu(A))
rate     2.61 million edges/sec (just tricount itself)
L*U' time (dot):         0.000005 sec (nthreads: 2 speedup 7.05837)
tricount time:         0.000009 sec (dot product method)
tri+prep time:         0.000053 sec (incl time to compute L and U)
compute C time:        0.000005 sec
reduce (C) time:       0.000004 sec
rate     2.31 million edges/sec (incl time for U=triu(A))
rate    12.98 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec (nthreads: 4 speedup 9.18526)
tricount time:         0.000008 sec (dot product method)
tri+prep time:         0.000051 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000004 sec
rate     2.39 million edges/sec (incl time for U=triu(A))
rate    16.02 million edges/sec (just tricount itself)
L*U' time (dot):         0.000006 sec (nthreads: 8 speedup 6.37217)
tricount time:         0.000010 sec (dot product method)
tri+prep time:         0.000054 sec (incl time to compute L and U)
compute C time:        0.000006 sec
reduce (C) time:       0.000004 sec
rate     2.28 million edges/sec (incl time for U=triu(A))
rate    12.12 million edges/sec (just tricount itself)
L*U' time (dot):         0.000006 sec
tricount time:         0.000010 sec (dot product method)
tri+prep time:         0.000054 sec (incl time to compute L and U)
compute C time:        0.000006 sec
reduce (C) time:       0.000004 sec
rate     2.29 million edges/sec (incl time for U=triu(A))
rate    12.29 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec (nthreads: 2 speedup 1.65)
tricount time:         0.000007 sec (dot product method)
tri+prep time:         0.000051 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000003 sec
rate     2.43 million edges/sec (incl time for U=triu(A))
rate    18.14 million edges/sec (just tricount itself)
L*U' time (dot):         0.000006 sec (nthreads: 4 speedup 1.08933)
tricount time:         0.000010 sec (dot product method)
tri+prep time:         0.000054 sec (incl time to compute L and U)
compute C time:        0.000006 sec
reduce (C) time:       0.000005 sec
rate     2.27 million edges/sec (incl time for U=triu(A))
rate    11.81 million edges/sec (just tricount itself)
L*U' time (dot):         0.000007 sec (nthreads: 8 speedup 0.944525)
tricount time:         0.000012 sec (dot product method)
tri+prep time:         0.000055 sec (incl time to compute L and U)
compute C time:        0.000007 sec
reduce (C) time:       0.000005 sec
rate     2.22 million edges/sec (incl time for U=triu(A))
rate    10.53 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000038 sec
tricount time:         0.000039 sec (saxpy method)
tri+prep time:         0.000048 sec (incl time to compute L)
compute C time:        0.000038 sec
reduce (C) time:       0.000001 sec
rate     2.59 million edges/sec (incl time for L=tril(A))
rate     3.15 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000018 sec (nthreads: 2 speedup 2.11677)
tricount time:         0.000019 sec (saxpy method)
tri+prep time:         0.000027 sec (incl time to compute L)
compute C time:        0.000018 sec
reduce (C) time:       0.000001 sec
rate     4.52 million edges/sec (incl time for L=tril(A))
rate     6.55 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000018 sec (nthreads: 4 speedup 2.10611)
tricount time:         0.000019 sec (saxpy method)
tri+prep time:         0.000027 sec (incl time to compute L)
compute C time:        0.000018 sec
reduce (C) time:       0.000001 sec
rate     4.52 million edges/sec (incl time for L=tril(A))
rate     6.55 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000030 sec (nthreads: 8 speedup 1.2624)
tricount time:         0.000031 sec (saxpy method)
tri+prep time:         0.000039 sec (incl time to compute L)
compute C time:        0.000030 sec
reduce (C) time:       0.000001 sec
rate     3.12 million edges/sec (incl time for L=tril(A))
rate     3.97 million edges/sec (just tricount itself)

--------------------------------------------------------------
matrix 63 by 63, 246 entries, from stdin

total time to read A matrix:       0.000222 sec

n 63 # edges 123
U=triu(A) time:        0.000024 sec
L=tril(A) time:        0.000005 sec

------------------------------------- dot product method:
# triangles 0
L*U' time (dot):         0.000030 sec
tricount time:         0.000037 sec (dot product method)
tri+prep time:         0.000067 sec (incl time to compute L and U)
compute C time:        0.000030 sec
reduce (C) time:       0.000008 sec
rate     1.84 million edges/sec (incl time for U=triu(A))
rate     3.28 million edges/sec (just tricount itself)
L*U' time (dot):         0.000005 sec (nthreads: 2 speedup 6.03715)
tricount time:         0.000008 sec (dot product method)
tri+prep time:         0.000038 sec (incl time to compute L and U)
compute C time:        0.000005 sec
reduce (C) time:       0.000003 sec
rate     3.26 million edges/sec (incl time for U=triu(A))
rate    14.95 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec (nthreads: 4 speedup 7.86954)
tricount time:         0.000007 sec (dot product method)
tri+prep time:         0.000037 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000003 sec
rate     3.36 million edges/sec (incl time for U=triu(A))
rate    17.25 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec (nthreads: 8 speedup 8.28384)
tricount time:         0.000006 sec (dot product method)
tri+prep time:         0.000036 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000003 sec
rate     3.45 million edges/sec (incl time for U=triu(A))
rate    19.84 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec
tricount time:         0.000007 sec (dot product method)
tri+prep time:         0.000037 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000003 sec
rate     3.35 million edges/sec (incl time for U=triu(A))
rate    17.09 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec (nthreads: 2 speedup 1.06995)
tricount time:         0.000007 sec (dot product method)
tri+prep time:         0.000036 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000003 sec
rate     3.37 million edges/sec (incl time for U=triu(A))
rate    17.57 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec (nthreads: 4 speedup 1.17271)
tricount time:         0.000006 sec (dot product method)
tri+prep time:         0.000036 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000003 sec
rate     3.46 million edges/sec (incl time for U=triu(A))
rate    20.24 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec (nthreads: 8 speedup 1.19076)
tricount time:         0.000006 sec (dot product method)
tri+prep time:         0.000035 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000002 sec
rate     3.47 million edges/sec (incl time for U=triu(A))
rate    20.68 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000021 sec
tricount time:         0.000022 sec (saxpy method)
tri+prep time:         0.000027 sec (incl time to compute L)
compute C time:        0.000021 sec
reduce (C) time:       0.000000 sec
rate     4.63 million edges/sec (incl time for L=tril(A))
rate     5.69 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000012 sec (nthreads: 2 speedup 1.768)
tricount time:         0.000012 sec (saxpy method)
tri+prep time:         0.000017 sec (incl time to compute L)
compute C time:        0.000012 sec
reduce (C) time:       0.000000 sec
rate     7.09 million edges/sec (incl time for L=tril(A))
rate     9.95 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000011 sec (nthreads: 4 speedup 1.90467)
tricount time:         0.000012 sec (saxpy method)
tri+prep time:         0.000016 sec (incl time to compute L)
compute C time:        0.000011 sec
reduce (C) time:       0.000000 sec
rate     7.46 million edges/sec (incl time for L=tril(A))
rate    10.69 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000013 sec (nthreads: 8 speedup 1.69722)
tricount time:         0.000013 sec (saxpy method)
tri+prep time:         0.000018 sec (incl time to compute L)
compute C time:        0.000013 sec
reduce (C) time:       0.000000 sec
rate     6.88 million edges/sec (incl time for L=tril(A))
rate     9.53 million edges/sec (just tricount itself)

--------------------------------------------------------------
matrix 78 by 78, 204 entries, from stdin

total time to read A matrix:       0.000178 sec

n 78 # edges 102
U=triu(A) time:        0.000021 sec
L=tril(A) time:        0.000006 sec

------------------------------------- dot product method:
# triangles 0
L*U' time (dot):         0.000031 sec
tricount time:         0.000038 sec (dot product method)
tri+prep time:         0.000066 sec (incl time to compute L and U)
compute C time:        0.000031 sec
reduce (C) time:       0.000008 sec
rate     1.55 million edges/sec (incl time for U=triu(A))
rate     2.66 million edges/sec (just tricount itself)
L*U' time (dot):         0.000005 sec (nthreads: 2 speedup 5.82485)
tricount time:         0.000009 sec (dot product method)
tri+prep time:         0.000036 sec (incl time to compute L and U)
compute C time:        0.000005 sec
reduce (C) time:       0.000004 sec
rate     2.81 million edges/sec (incl time for U=triu(A))
rate    11.53 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec (nthreads: 4 speedup 7.9056)
tricount time:         0.000007 sec (dot product method)
tri+prep time:         0.000034 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000003 sec
rate     2.99 million edges/sec (incl time for U=triu(A))
rate    15.34 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 8 speedup 9.02629)
tricount time:         0.000008 sec (dot product method)
tri+prep time:         0.000035 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000005 sec
rate     2.88 million edges/sec (incl time for U=triu(A))
rate    12.84 million edges/sec (just tricount itself)
L*U' time (dot):         0.000006 sec
tricount time:         0.000010 sec (dot product method)
tri+prep time:         0.000037 sec (incl time to compute L and U)
compute C time:        0.000006 sec
reduce (C) time:       0.000004 sec
rate     2.76 million edges/sec (incl time for U=triu(A))
rate    10.69 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec (nthreads: 2 speedup 1.45911)
tricount time:         0.000007 sec (dot product method)
tri+prep time:         0.000034 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000003 sec
rate     2.98 million edges/sec (incl time for U=triu(A))
rate    15.00 million edges/sec (just tricount itself)
L*U' time (dot):         0.000004 sec (nthreads: 4 speedup 1.47275)
tricount time:         0.000006 sec (dot product method)
tri+prep time:         0.000034 sec (incl time to compute L and U)
compute C time:        0.000004 sec
reduce (C) time:       0.000003 sec
rate     3.01 million edges/sec (incl time for U=triu(A))
rate    15.96 million edges/sec (just tricount itself)
L*U' time (dot):         0.000003 sec (nthreads: 8 speedup 1.66235)
tricount time:         0.000006 sec (dot product method)
tri+prep time:         0.000033 sec (incl time to compute L and U)
compute C time:        0.000003 sec
reduce (C) time:       0.000002 sec
rate     3.07 million edges/sec (incl time for U=triu(A))
rate    17.70 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000030 sec
tricount time:         0.000030 sec (saxpy method)
tri+prep time:         0.000037 sec (incl time to compute L)
compute C time:        0.000030 sec
reduce (C) time:       0.000001 sec
rate     2.77 million edges/sec (incl time for L=tril(A))
rate     3.36 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000013 sec (nthreads: 2 speedup 2.37011)
tricount time:         0.000013 sec (saxpy method)
tri+prep time:         0.000019 sec (incl time to compute L)
compute C time:        0.000013 sec
reduce (C) time:       0.000000 sec
rate     5.29 million edges/sec (incl time for L=tril(A))
rate     7.92 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000013 sec (nthreads: 4 speedup 2.26979)
tricount time:         0.000014 sec (saxpy method)
tri+prep time:         0.000020 sec (incl time to compute L)
compute C time:        0.000013 sec
reduce (C) time:       0.000001 sec
rate     5.06 million edges/sec (incl time for L=tril(A))
rate     7.41 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000026 sec (nthreads: 8 speedup 1.16697)
tricount time:         0.000026 sec (saxpy method)
tri+prep time:         0.000033 sec (incl time to compute L)
compute C time:        0.000026 sec
reduce (C) time:       0.000001 sec
rate     3.13 million edges/sec (incl time for L=tril(A))
rate     3.89 million edges/sec (just tricount itself)

--------------------------------------------------------------
matrix 982 by 982, 99840 entries, from stdin

total time to read A matrix:       0.027242 sec

n 982 # edges 49920
U=triu(A) time:        0.000163 sec
L=tril(A) time:        0.000136 sec

------------------------------------- dot product method:
# triangles 0
L*U' time (dot):         0.000341 sec
tricount time:         0.000413 sec (dot product method)
tri+prep time:         0.000711 sec (incl time to compute L and U)
compute C time:        0.000341 sec
reduce (C) time:       0.000072 sec
rate    70.16 million edges/sec (incl time for U=triu(A))
rate   120.85 million edges/sec (just tricount itself)
L*U' time (dot):         0.000306 sec (nthreads: 2 speedup 1.11459)
tricount time:         0.000369 sec (dot product method)
tri+prep time:         0.000668 sec (incl time to compute L and U)
compute C time:        0.000306 sec
reduce (C) time:       0.000064 sec
rate    74.75 million edges/sec (incl time for U=triu(A))
rate   135.12 million edges/sec (just tricount itself)
L*U' time (dot):         0.000250 sec (nthreads: 4 speedup 1.36541)
tricount time:         0.000314 sec (dot product method)
tri+prep time:         0.000613 sec (incl time to compute L and U)
compute C time:        0.000250 sec
reduce (C) time:       0.000065 sec
rate    81.48 million edges/sec (incl time for U=triu(A))
rate   158.86 million edges/sec (just tricount itself)
L*U' time (dot):         0.001259 sec (nthreads: 8 speedup 0.270668)
tricount time:         0.001334 sec (dot product method)
tri+prep time:         0.001632 sec (incl time to compute L and U)
compute C time:        0.001259 sec
reduce (C) time:       0.000075 sec
rate    30.58 million edges/sec (incl time for U=triu(A))
rate    37.42 million edges/sec (just tricount itself)
L*U' time (dot):         0.000366 sec
tricount time:         0.000436 sec (dot product method)
tri+prep time:         0.000734 sec (incl time to compute L and U)
compute C time:        0.000366 sec
reduce (C) time:       0.000070 sec
rate    67.98 million edges/sec (incl time for U=triu(A))
rate   114.50 million edges/sec (just tricount itself)
L*U' time (dot):         0.000291 sec (nthreads: 2 speedup 1.2581)
tricount time:         0.000355 sec (dot product method)
tri+prep time:         0.000654 sec (incl time to compute L and U)
compute C time:        0.000291 sec
reduce (C) time:       0.000064 sec
rate    76.36 million edges/sec (incl time for U=triu(A))
rate   140.49 million edges/sec (just tricount itself)
L*U' time (dot):         0.000247 sec (nthreads: 4 speedup 1.4854)
tricount time:         0.000319 sec (dot product method)
tri+prep time:         0.000617 sec (incl time to compute L and U)
compute C time:        0.000247 sec
reduce (C) time:       0.000072 sec
rate    80.90 million edges/sec (incl time for U=triu(A))
rate   156.64 million edges/sec (just tricount itself)
L*U' time (dot):         0.002759 sec (nthreads: 8 speedup 0.132738)
tricount time:         0.002832 sec (dot product method)
tri+prep time:         0.003130 sec (incl time to compute L and U)
compute C time:        0.002759 sec
reduce (C) time:       0.000073 sec
rate    15.95 million edges/sec (incl time for U=triu(A))
rate    17.63 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000248 sec
tricount time:         0.000248 sec (saxpy method)
tri+prep time:         0.000384 sec (incl time to compute L)
compute C time:        0.000248 sec
reduce (C) time:       0.000001 sec
rate   130.04 million edges/sec (incl time for L=tril(A))
rate   200.99 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000232 sec (nthreads: 2 speedup 1.06781)
tricount time:         0.000233 sec (saxpy method)
tri+prep time:         0.000368 sec (incl time to compute L)
compute C time:        0.000232 sec
reduce (C) time:       0.000001 sec
rate   135.59 million edges/sec (incl time for L=tril(A))
rate   214.58 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000231 sec (nthreads: 4 speedup 1.07507)
tricount time:         0.000231 sec (saxpy method)
tri+prep time:         0.000367 sec (incl time to compute L)
compute C time:        0.000231 sec
reduce (C) time:       0.000001 sec
rate   136.18 million edges/sec (incl time for L=tril(A))
rate   216.05 million edges/sec (just tricount itself)
triangles, method 3: 0
C<L>=L*L time (saxpy):         0.000232 sec (nthreads: 8 speedup 1.06746)
tricount time:         0.000233 sec (saxpy method)
tri+prep time:         0.000368 sec (incl time to compute L)
compute C time:        0.000232 sec
reduce (C) time:       0.000001 sec
rate   135.55 million edges/sec (incl time for L=tril(A))
rate   214.48 million edges/sec (just tricount itself)

--------------------------------------------------------------
matrix 67 by 67, 574 entries, from stdin

total time to read A matrix:       0.000244 sec

n 67 # edges 287
U=triu(A) time:        0.000023 sec
L=tril(A) time:        0.000007 sec

------------------------------------- dot product method:
# triangles 120
L*U' time (dot):         0.000029 sec
tricount time:         0.000036 sec (dot product method)
tri+prep time:         0.000066 sec (incl time to compute L and U)
compute C time:        0.000029 sec
reduce (C) time:       0.000007 sec
rate     4.35 million edges/sec (incl time for U=triu(A))
rate     7.90 million edges/sec (just tricount itself)
L*U' time (dot):         0.000012 sec (nthreads: 2 speedup 2.40315)
tricount time:         0.000016 sec (dot product method)
tri+prep time:         0.000046 sec (incl time to compute L and U)
compute C time:        0.000012 sec
reduce (C) time:       0.000004 sec
rate     6.29 million edges/sec (incl time for U=triu(A))
rate    18.03 million edges/sec (just tricount itself)
L*U' time (dot):         0.000010 sec (nthreads: 4 speedup 2.98421)
tricount time:         0.000013 sec (dot product method)
tri+prep time:         0.000043 sec (incl time to compute L and U)
compute C time:        0.000010 sec
reduce (C) time:       0.000003 sec
rate     6.69 million edges/sec (incl time for U=triu(A))
rate    21.80 million edges/sec (just tricount itself)
L*U' time (dot):         0.000009 sec (nthreads: 8 speedup 3.27907)
tricount time:         0.000012 sec (dot product method)
tri+prep time:         0.000042 sec (incl time to compute L and U)
compute C time:        0.000009 sec
reduce (C) time:       0.000003 sec
rate     6.89 million edges/sec (incl time for U=triu(A))
rate    24.07 million edges/sec (just tricount itself)
L*U' time (dot):         0.000012 sec
tricount time:         0.000016 sec (dot product method)
tri+prep time:         0.000045 sec (incl time to compute L and U)
compute C time:        0.000012 sec
reduce (C) time:       0.000004 sec
rate     6.31 million edges/sec (incl time for U=triu(A))
rate    18.20 million edges/sec (just tricount itself)
L*U' time (dot):         0.000011 sec (nthreads: 2 speedup 1.12003)
tricount time:         0.000014 sec (dot product method)
tri+prep time:         0.000044 sec (incl time to compute L and U)
compute C time:        0.000011 sec
reduce (C) time:       0.000003 sec
rate     6.59 million edges/sec (incl time for U=triu(A))
rate    20.81 million edges/sec (just tricount itself)
L*U' time (dot):         0.000010 sec (nthreads: 4 speedup 1.22214)
tricount time:         0.000012 sec (dot product method)
tri+prep time:         0.000042 sec (incl time to compute L and U)
compute C time:        0.000010 sec
reduce (C) time:       0.000003 sec
rate     6.81 million edges/sec (incl time for U=triu(A))
rate    23.09 million edges/sec (just tricount itself)
L*U' time (dot):         0.000009 sec (nthreads: 8 speedup 1.3117)
tricount time:         0.000011 sec (dot product method)
tri+prep time:         0.000041 sec (incl time to compute L and U)
compute C time:        0.000009 sec
reduce (C) time:       0.000002 sec
rate     6.97 million edges/sec (incl time for U=triu(A))
rate    25.02 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 120
C<L>=L*L time (saxpy):         0.000028 sec
tricount time:         0.000029 sec (saxpy method)
tri+prep time:         0.000035 sec (incl time to compute L)
compute C time:        0.000028 sec
reduce (C) time:       0.000001 sec
rate     8.17 million edges/sec (incl time for L=tril(A))
rate    10.03 million edges/sec (just tricount itself)
triangles, method 3: 120
C<L>=L*L time (saxpy):         0.000016 sec (nthreads: 2 speedup 1.73448)
tricount time:         0.000017 sec (saxpy method)
tri+prep time:         0.000023 sec (incl time to compute L)
compute C time:        0.000016 sec
reduce (C) time:       0.000001 sec
rate    12.39 million edges/sec (incl time for L=tril(A))
rate    17.24 million edges/sec (just tricount itself)
triangles, method 3: 120
C<L>=L*L time (saxpy):         0.000013 sec (nthreads: 4 speedup 2.10791)
tricount time:         0.000014 sec (saxpy method)
tri+prep time:         0.000020 sec (incl time to compute L)
compute C time:        0.000013 sec
reduce (C) time:       0.000001 sec
rate    14.15 million edges/sec (incl time for L=tril(A))
rate    20.84 million edges/sec (just tricount itself)
triangles, method 3: 120
C<L>=L*L time (saxpy):         0.000012 sec (nthreads: 8 speedup 2.27045)
tricount time:         0.000013 sec (saxpy method)
tri+prep time:         0.000019 sec (incl time to compute L)
compute C time:        0.000012 sec
reduce (C) time:       0.000001 sec
rate    14.77 million edges/sec (incl time for L=tril(A))
rate    22.23 million edges/sec (just tricount itself)

--------------------------------------------------------------
Wathen: nx 200 ny 200 n 120801 nz 1762400 method 0, time: 0.126 sec

total time to read A matrix:       0.127766 sec

n 120801 # edges 881200
U=triu(A) time:        0.002563 sec
L=tril(A) time:        0.002483 sec

------------------------------------- dot product method:
# triangles 2160400
L*U' time (dot):         0.031311 sec
tricount time:         0.037246 sec (dot product method)
tri+prep time:         0.042292 sec (incl time to compute L and U)
compute C time:        0.031311 sec
reduce (C) time:       0.005935 sec
rate    20.84 million edges/sec (incl time for U=triu(A))
rate    23.66 million edges/sec (just tricount itself)
L*U' time (dot):         0.011505 sec (nthreads: 2 speedup 2.72157)
tricount time:         0.014218 sec (dot product method)
tri+prep time:         0.019264 sec (incl time to compute L and U)
compute C time:        0.011505 sec
reduce (C) time:       0.002713 sec
rate    45.74 million edges/sec (incl time for U=triu(A))
rate    61.98 million edges/sec (just tricount itself)
L*U' time (dot):         0.007691 sec (nthreads: 4 speedup 4.07101)
tricount time:         0.010764 sec (dot product method)
tri+prep time:         0.015810 sec (incl time to compute L and U)
compute C time:        0.007691 sec
reduce (C) time:       0.003073 sec
rate    55.74 million edges/sec (incl time for U=triu(A))
rate    81.87 million edges/sec (just tricount itself)
L*U' time (dot):         0.009845 sec (nthreads: 8 speedup 3.18048)
tricount time:         0.011741 sec (dot product method)
tri+prep time:         0.016787 sec (incl time to compute L and U)
compute C time:        0.009845 sec
reduce (C) time:       0.001896 sec
rate    52.49 million edges/sec (incl time for U=triu(A))
rate    75.05 million edges/sec (just tricount itself)
L*U' time (dot):         0.023385 sec
tricount time:         0.027309 sec (dot product method)
tri+prep time:         0.032355 sec (incl time to compute L and U)
compute C time:        0.023385 sec
reduce (C) time:       0.003925 sec
rate    27.24 million edges/sec (incl time for U=triu(A))
rate    32.27 million edges/sec (just tricount itself)
L*U' time (dot):         0.010843 sec (nthreads: 2 speedup 2.1567)
tricount time:         0.013844 sec (dot product method)
tri+prep time:         0.018890 sec (incl time to compute L and U)
compute C time:        0.010843 sec
reduce (C) time:       0.003001 sec
rate    46.65 million edges/sec (incl time for U=triu(A))
rate    63.65 million edges/sec (just tricount itself)
L*U' time (dot):         0.007708 sec (nthreads: 4 speedup 3.03387)
tricount time:         0.011627 sec (dot product method)
tri+prep time:         0.016673 sec (incl time to compute L and U)
compute C time:        0.007708 sec
reduce (C) time:       0.003919 sec
rate    52.85 million edges/sec (incl time for U=triu(A))
rate    75.79 million edges/sec (just tricount itself)
L*U' time (dot):         0.006164 sec (nthreads: 8 speedup 3.79354)
tricount time:         0.008035 sec (dot product method)
tri+prep time:         0.013081 sec (incl time to compute L and U)
compute C time:        0.006164 sec
reduce (C) time:       0.001871 sec
rate    67.36 million edges/sec (incl time for U=triu(A))
rate   109.67 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 2160400
C<L>=L*L time (saxpy):         0.028242 sec
tricount time:         0.030344 sec (saxpy method)
tri+prep time:         0.032826 sec (incl time to compute L)
compute C time:        0.028242 sec
reduce (C) time:       0.002101 sec
rate    26.84 million edges/sec (incl time for L=tril(A))
rate    29.04 million edges/sec (just tricount itself)
triangles, method 3: 2160400
C<L>=L*L time (saxpy):         0.024173 sec (nthreads: 2 speedup 1.16837)
tricount time:         0.025586 sec (saxpy method)
tri+prep time:         0.028068 sec (incl time to compute L)
compute C time:        0.024173 sec
reduce (C) time:       0.001413 sec
rate    31.39 million edges/sec (incl time for L=tril(A))
rate    34.44 million edges/sec (just tricount itself)
triangles, method 3: 2160400
C<L>=L*L time (saxpy):         0.012087 sec (nthreads: 4 speedup 2.33654)
tricount time:         0.012740 sec (saxpy method)
tri+prep time:         0.015223 sec (incl time to compute L)
compute C time:        0.012087 sec
reduce (C) time:       0.000653 sec
rate    57.89 million edges/sec (incl time for L=tril(A))
rate    69.17 million edges/sec (just tricount itself)
triangles, method 3: 2160400
C<L>=L*L time (saxpy):         0.008452 sec (nthreads: 8 speedup 3.34138)
tricount time:         0.008817 sec (saxpy method)
tri+prep time:         0.011300 sec (incl time to compute L)
compute C time:        0.008452 sec
reduce (C) time:       0.000365 sec
rate    77.99 million edges/sec (incl time for L=tril(A))
rate    99.94 million edges/sec (just tricount itself)

--------------------------------------------------------------
random 10000 by 10000, nz: 199768, method 0 time 0.023 sec

total time to read A matrix:       0.023617 sec

n 10000 # edges 99884
U=triu(A) time:        0.000328 sec
L=tril(A) time:        0.000219 sec

------------------------------------- dot product method:
# triangles 1357
L*U' time (dot):         0.008270 sec
tricount time:         0.008607 sec (dot product method)
tri+prep time:         0.009154 sec (incl time to compute L and U)
compute C time:        0.008270 sec
reduce (C) time:       0.000337 sec
rate    10.91 million edges/sec (incl time for U=triu(A))
rate    11.60 million edges/sec (just tricount itself)
L*U' time (dot):         0.004090 sec (nthreads: 2 speedup 2.02205)
tricount time:         0.004246 sec (dot product method)
tri+prep time:         0.004793 sec (incl time to compute L and U)
compute C time:        0.004090 sec
reduce (C) time:       0.000156 sec
rate    20.84 million edges/sec (incl time for U=triu(A))
rate    23.53 million edges/sec (just tricount itself)
L*U' time (dot):         0.002451 sec (nthreads: 4 speedup 3.37446)
tricount time:         0.002603 sec (dot product method)
tri+prep time:         0.003150 sec (incl time to compute L and U)
compute C time:        0.002451 sec
reduce (C) time:       0.000153 sec
rate    31.71 million edges/sec (incl time for U=triu(A))
rate    38.37 million edges/sec (just tricount itself)
L*U' time (dot):         0.002521 sec (nthreads: 8 speedup 3.28008)
tricount time:         0.002687 sec (dot product method)
tri+prep time:         0.003234 sec (incl time to compute L and U)
compute C time:        0.002521 sec
reduce (C) time:       0.000165 sec
rate    30.89 million edges/sec (incl time for U=triu(A))
rate    37.18 million edges/sec (just tricount itself)
L*U' time (dot):         0.007348 sec
tricount time:         0.007734 sec (dot product method)
tri+prep time:         0.008280 sec (incl time to compute L and U)
compute C time:        0.007348 sec
reduce (C) time:       0.000386 sec
rate    12.06 million edges/sec (incl time for U=triu(A))
rate    12.92 million edges/sec (just tricount itself)
L*U' time (dot):         0.004463 sec (nthreads: 2 speedup 1.64641)
tricount time:         0.004677 sec (dot product method)
tri+prep time:         0.005224 sec (incl time to compute L and U)
compute C time:        0.004463 sec
reduce (C) time:       0.000214 sec
rate    19.12 million edges/sec (incl time for U=triu(A))
rate    21.36 million edges/sec (just tricount itself)
L*U' time (dot):         0.002655 sec (nthreads: 4 speedup 2.76719)
tricount time:         0.002886 sec (dot product method)
tri+prep time:         0.003433 sec (incl time to compute L and U)
compute C time:        0.002655 sec
reduce (C) time:       0.000231 sec
rate    29.09 million edges/sec (incl time for U=triu(A))
rate    34.60 million edges/sec (just tricount itself)
L*U' time (dot):         0.004552 sec (nthreads: 8 speedup 1.61416)
tricount time:         0.004864 sec (dot product method)
tri+prep time:         0.005411 sec (incl time to compute L and U)
compute C time:        0.004552 sec
reduce (C) time:       0.000311 sec
rate    18.46 million edges/sec (incl time for U=triu(A))
rate    20.54 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 1357
C<L>=L*L time (saxpy):         0.003086 sec
tricount time:         0.003091 sec (saxpy method)
tri+prep time:         0.003310 sec (incl time to compute L)
compute C time:        0.003086 sec
reduce (C) time:       0.000005 sec
rate    30.17 million edges/sec (incl time for L=tril(A))
rate    32.31 million edges/sec (just tricount itself)
triangles, method 3: 1357
C<L>=L*L time (saxpy):         0.001912 sec (nthreads: 2 speedup 1.61403)
tricount time:         0.001916 sec (saxpy method)
tri+prep time:         0.002136 sec (incl time to compute L)
compute C time:        0.001912 sec
reduce (C) time:       0.000004 sec
rate    46.77 million edges/sec (incl time for L=tril(A))
rate    52.12 million edges/sec (just tricount itself)
triangles, method 3: 1357
C<L>=L*L time (saxpy):         0.001379 sec (nthreads: 4 speedup 2.23754)
tricount time:         0.001383 sec (saxpy method)
tri+prep time:         0.001603 sec (incl time to compute L)
compute C time:        0.001379 sec
reduce (C) time:       0.000004 sec
rate    62.32 million edges/sec (incl time for L=tril(A))
rate    72.20 million edges/sec (just tricount itself)
triangles, method 3: 1357
C<L>=L*L time (saxpy):         0.001191 sec (nthreads: 8 speedup 2.59029)
tricount time:         0.001196 sec (saxpy method)
tri+prep time:         0.001416 sec (incl time to compute L)
compute C time:        0.001191 sec
reduce (C) time:       0.000005 sec
rate    70.56 million edges/sec (incl time for L=tril(A))
rate    83.49 million edges/sec (just tricount itself)

--------------------------------------------------------------
random 10000 by 10000, nz: 199768, method 1 time 0.018 sec

total time to read A matrix:       0.019086 sec

n 10000 # edges 99884
U=triu(A) time:        0.000581 sec
L=tril(A) time:        0.000302 sec

------------------------------------- dot product method:
# triangles 1357
L*U' time (dot):         0.008025 sec
tricount time:         0.008343 sec (dot product method)
tri+prep time:         0.009226 sec (incl time to compute L and U)
compute C time:        0.008025 sec
reduce (C) time:       0.000319 sec
rate    10.83 million edges/sec (incl time for U=triu(A))
rate    11.97 million edges/sec (just tricount itself)
L*U' time (dot):         0.004084 sec (nthreads: 2 speedup 1.96498)
tricount time:         0.004253 sec (dot product method)
tri+prep time:         0.005136 sec (incl time to compute L and U)
compute C time:        0.004084 sec
reduce (C) time:       0.000169 sec
rate    19.45 million edges/sec (incl time for U=triu(A))
rate    23.48 million edges/sec (just tricount itself)
L*U' time (dot):         0.002465 sec (nthreads: 4 speedup 3.25503)
tricount time:         0.002619 sec (dot product method)
tri+prep time:         0.003501 sec (incl time to compute L and U)
compute C time:        0.002465 sec
reduce (C) time:       0.000154 sec
rate    28.53 million edges/sec (incl time for U=triu(A))
rate    38.14 million edges/sec (just tricount itself)
L*U' time (dot):         0.002651 sec (nthreads: 8 speedup 3.02704)
tricount time:         0.003370 sec (dot product method)
tri+prep time:         0.004252 sec (incl time to compute L and U)
compute C time:        0.002651 sec
reduce (C) time:       0.000719 sec
rate    23.49 million edges/sec (incl time for U=triu(A))
rate    29.64 million edges/sec (just tricount itself)
L*U' time (dot):         0.007855 sec
tricount time:         0.008275 sec (dot product method)
tri+prep time:         0.009157 sec (incl time to compute L and U)
compute C time:        0.007855 sec
reduce (C) time:       0.000420 sec
rate    10.91 million edges/sec (incl time for U=triu(A))
rate    12.07 million edges/sec (just tricount itself)
L*U' time (dot):         0.004511 sec (nthreads: 2 speedup 1.7412)
tricount time:         0.004818 sec (dot product method)
tri+prep time:         0.005701 sec (incl time to compute L and U)
compute C time:        0.004511 sec
reduce (C) time:       0.000307 sec
rate    17.52 million edges/sec (incl time for U=triu(A))
rate    20.73 million edges/sec (just tricount itself)
L*U' time (dot):         0.002717 sec (nthreads: 4 speedup 2.89116)
tricount time:         0.002905 sec (dot product method)
tri+prep time:         0.003787 sec (incl time to compute L and U)
compute C time:        0.002717 sec
reduce (C) time:       0.000188 sec
rate    26.37 million edges/sec (incl time for U=triu(A))
rate    34.39 million edges/sec (just tricount itself)
L*U' time (dot):         0.002350 sec (nthreads: 8 speedup 3.34247)
tricount time:         0.002517 sec (dot product method)
tri+prep time:         0.003400 sec (incl time to compute L and U)
compute C time:        0.002350 sec
reduce (C) time:       0.000167 sec
rate    29.38 million edges/sec (incl time for U=triu(A))
rate    39.68 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 1357
C<L>=L*L time (saxpy):         0.002995 sec
tricount time:         0.002999 sec (saxpy method)
tri+prep time:         0.003301 sec (incl time to compute L)
compute C time:        0.002995 sec
reduce (C) time:       0.000004 sec
rate    30.26 million edges/sec (incl time for L=tril(A))
rate    33.31 million edges/sec (just tricount itself)
triangles, method 3: 1357
C<L>=L*L time (saxpy):         0.001938 sec (nthreads: 2 speedup 1.54549)
tricount time:         0.001942 sec (saxpy method)
tri+prep time:         0.002244 sec (incl time to compute L)
compute C time:        0.001938 sec
reduce (C) time:       0.000005 sec
rate    44.51 million edges/sec (incl time for L=tril(A))
rate    51.43 million edges/sec (just tricount itself)
triangles, method 3: 1357
C<L>=L*L time (saxpy):         0.001348 sec (nthreads: 4 speedup 2.22153)
tricount time:         0.001352 sec (saxpy method)
tri+prep time:         0.001654 sec (incl time to compute L)
compute C time:        0.001348 sec
reduce (C) time:       0.000004 sec
rate    60.40 million edges/sec (incl time for L=tril(A))
rate    73.86 million edges/sec (just tricount itself)
triangles, method 3: 1357
C<L>=L*L time (saxpy):         0.001254 sec (nthreads: 8 speedup 2.38776)
tricount time:         0.001259 sec (saxpy method)
tri+prep time:         0.001561 sec (incl time to compute L)
compute C time:        0.001254 sec
reduce (C) time:       0.000005 sec
rate    63.99 million edges/sec (incl time for L=tril(A))
rate    79.32 million edges/sec (just tricount itself)

--------------------------------------------------------------
random 100000 by 100000, nz: 19980330, method 0 time 2.296 sec

total time to read A matrix:       2.325069 sec

n 100000 # edges 9990165
U=triu(A) time:        0.017604 sec
L=tril(A) time:        0.019649 sec

------------------------------------- dot product method:
# triangles 1330131
L*U' time (dot):         7.128369 sec
tricount time:         7.163533 sec (dot product method)
tri+prep time:         7.200786 sec (incl time to compute L and U)
compute C time:        7.128369 sec
reduce (C) time:       0.035164 sec
rate     1.39 million edges/sec (incl time for U=triu(A))
rate     1.39 million edges/sec (just tricount itself)
L*U' time (dot):         3.510440 sec (nthreads: 2 speedup 2.03062)
tricount time:         3.532405 sec (dot product method)
tri+prep time:         3.569658 sec (incl time to compute L and U)
compute C time:        3.510440 sec
reduce (C) time:       0.021965 sec
rate     2.80 million edges/sec (incl time for U=triu(A))
rate     2.83 million edges/sec (just tricount itself)
L*U' time (dot):         1.912733 sec (nthreads: 4 speedup 3.7268)
tricount time:         1.929098 sec (dot product method)
tri+prep time:         1.966351 sec (incl time to compute L and U)
compute C time:        1.912733 sec
reduce (C) time:       0.016365 sec
rate     5.08 million edges/sec (incl time for U=triu(A))
rate     5.18 million edges/sec (just tricount itself)
L*U' time (dot):         1.096600 sec (nthreads: 8 speedup 6.50043)
tricount time:         1.113480 sec (dot product method)
tri+prep time:         1.150733 sec (incl time to compute L and U)
compute C time:        1.096600 sec
reduce (C) time:       0.016880 sec
rate     8.68 million edges/sec (incl time for U=triu(A))
rate     8.97 million edges/sec (just tricount itself)
L*U' time (dot):         8.085635 sec
tricount time:         8.117637 sec (dot product method)
tri+prep time:         8.154890 sec (incl time to compute L and U)
compute C time:        8.085635 sec
reduce (C) time:       0.032002 sec
rate     1.23 million edges/sec (incl time for U=triu(A))
rate     1.23 million edges/sec (just tricount itself)
L*U' time (dot):         3.666974 sec (nthreads: 2 speedup 2.20499)
tricount time:         3.686753 sec (dot product method)
tri+prep time:         3.724006 sec (incl time to compute L and U)
compute C time:        3.666974 sec
reduce (C) time:       0.019779 sec
rate     2.68 million edges/sec (incl time for U=triu(A))
rate     2.71 million edges/sec (just tricount itself)
L*U' time (dot):         2.156598 sec (nthreads: 4 speedup 3.74925)
tricount time:         2.181005 sec (dot product method)
tri+prep time:         2.218258 sec (incl time to compute L and U)
compute C time:        2.156598 sec
reduce (C) time:       0.024407 sec
rate     4.50 million edges/sec (incl time for U=triu(A))
rate     4.58 million edges/sec (just tricount itself)
L*U' time (dot):         1.662084 sec (nthreads: 8 speedup 4.86476)
tricount time:         1.681525 sec (dot product method)
tri+prep time:         1.718778 sec (incl time to compute L and U)
compute C time:        1.662084 sec
reduce (C) time:       0.019441 sec
rate     5.81 million edges/sec (incl time for U=triu(A))
rate     5.94 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 1330131
C<L>=L*L time (saxpy):         5.713133 sec
tricount time:         5.717672 sec (saxpy method)
tri+prep time:         5.737321 sec (incl time to compute L)
compute C time:        5.713133 sec
reduce (C) time:       0.004539 sec
rate     1.74 million edges/sec (incl time for L=tril(A))
rate     1.75 million edges/sec (just tricount itself)
triangles, method 3: 1330131
C<L>=L*L time (saxpy):         3.236083 sec (nthreads: 2 speedup 1.76545)
tricount time:         3.240762 sec (saxpy method)
tri+prep time:         3.260411 sec (incl time to compute L)
compute C time:        3.236083 sec
reduce (C) time:       0.004679 sec
rate     3.06 million edges/sec (incl time for L=tril(A))
rate     3.08 million edges/sec (just tricount itself)
triangles, method 3: 1330131
C<L>=L*L time (saxpy):         2.169659 sec (nthreads: 4 speedup 2.63319)
tricount time:         2.172323 sec (saxpy method)
tri+prep time:         2.191972 sec (incl time to compute L)
compute C time:        2.169659 sec
reduce (C) time:       0.002664 sec
rate     4.56 million edges/sec (incl time for L=tril(A))
rate     4.60 million edges/sec (just tricount itself)
triangles, method 3: 1330131
C<L>=L*L time (saxpy):         2.109164 sec (nthreads: 8 speedup 2.70872)
tricount time:         2.110115 sec (saxpy method)
tri+prep time:         2.129765 sec (incl time to compute L)
compute C time:        2.109164 sec
reduce (C) time:       0.000952 sec
rate     4.69 million edges/sec (incl time for L=tril(A))
rate     4.73 million edges/sec (just tricount itself)

--------------------------------------------------------------
random 100000 by 100000, nz: 19980330, method 1 time 2.239 sec

total time to read A matrix:       2.273442 sec

n 100000 # edges 9990165
U=triu(A) time:        0.021285 sec
L=tril(A) time:        0.019572 sec

------------------------------------- dot product method:
# triangles 1330131
L*U' time (dot):         7.395066 sec
tricount time:         7.429692 sec (dot product method)
tri+prep time:         7.470549 sec (incl time to compute L and U)
compute C time:        7.395066 sec
reduce (C) time:       0.034626 sec
rate     1.34 million edges/sec (incl time for U=triu(A))
rate     1.34 million edges/sec (just tricount itself)
L*U' time (dot):         3.486968 sec (nthreads: 2 speedup 2.12077)
tricount time:         3.508906 sec (dot product method)
tri+prep time:         3.549763 sec (incl time to compute L and U)
compute C time:        3.486968 sec
reduce (C) time:       0.021938 sec
rate     2.81 million edges/sec (incl time for U=triu(A))
rate     2.85 million edges/sec (just tricount itself)
L*U' time (dot):         2.862556 sec (nthreads: 4 speedup 2.58338)
tricount time:         2.902115 sec (dot product method)
tri+prep time:         2.942972 sec (incl time to compute L and U)
compute C time:        2.862556 sec
reduce (C) time:       0.039559 sec
rate     3.39 million edges/sec (incl time for U=triu(A))
rate     3.44 million edges/sec (just tricount itself)
L*U' time (dot):         1.379506 sec (nthreads: 8 speedup 5.36066)
tricount time:         1.406556 sec (dot product method)
tri+prep time:         1.447413 sec (incl time to compute L and U)
compute C time:        1.379506 sec
reduce (C) time:       0.027050 sec
rate     6.90 million edges/sec (incl time for U=triu(A))
rate     7.10 million edges/sec (just tricount itself)
L*U' time (dot):        13.986013 sec
tricount time:        14.047180 sec (dot product method)
tri+prep time:        14.088037 sec (incl time to compute L and U)
compute C time:       13.986013 sec
reduce (C) time:       0.061167 sec
rate     0.71 million edges/sec (incl time for U=triu(A))
rate     0.71 million edges/sec (just tricount itself)
L*U' time (dot):         5.212362 sec (nthreads: 2 speedup 2.68324)
tricount time:         5.232665 sec (dot product method)
tri+prep time:         5.273522 sec (incl time to compute L and U)
compute C time:        5.212362 sec
reduce (C) time:       0.020303 sec
rate     1.89 million edges/sec (incl time for U=triu(A))
rate     1.91 million edges/sec (just tricount itself)
L*U' time (dot):         2.603460 sec (nthreads: 4 speedup 5.37209)
tricount time:         2.621100 sec (dot product method)
tri+prep time:         2.661957 sec (incl time to compute L and U)
compute C time:        2.603460 sec
reduce (C) time:       0.017640 sec
rate     3.75 million edges/sec (incl time for U=triu(A))
rate     3.81 million edges/sec (just tricount itself)
L*U' time (dot):         1.643353 sec (nthreads: 8 speedup 8.51066)
tricount time:         1.678784 sec (dot product method)
tri+prep time:         1.719641 sec (incl time to compute L and U)
compute C time:        1.643353 sec
reduce (C) time:       0.035431 sec
rate     5.81 million edges/sec (incl time for U=triu(A))
rate     5.95 million edges/sec (just tricount itself)

----------------------------------- saxpy method:
triangles, method 3: 1330131
C<L>=L*L time (saxpy):         8.392654 sec
tricount time:         8.397451 sec (saxpy method)
tri+prep time:         8.417023 sec (incl time to compute L)
compute C time:        8.392654 sec
reduce (C) time:       0.004796 sec
rate     1.19 million edges/sec (incl time for L=tril(A))
rate     1.19 million edges/sec (just tricount itself)
triangles, method 3: 1330131
C<L>=L*L time (saxpy):         3.096104 sec (nthreads: 2 speedup 2.71071)
tricount time:         3.099485 sec (saxpy method)
tri+prep time:         3.119057 sec (incl time to compute L)
compute C time:        3.096104 sec
reduce (C) time:       0.003381 sec
rate     3.20 million edges/sec (incl time for L=tril(A))
rate     3.22 million edges/sec (just tricount itself)
triangles, method 3: 1330131
C<L>=L*L time (saxpy):         1.860165 sec (nthreads: 4 speedup 4.51178)
tricount time:         1.862493 sec (saxpy method)
tri+prep time:         1.882065 sec (incl time to compute L)
compute C time:        1.860165 sec
reduce (C) time:       0.002328 sec
rate     5.31 million edges/sec (incl time for L=tril(A))
rate     5.36 million edges/sec (just tricount itself)
triangles, method 3: 1330131
C<L>=L*L time (saxpy):         2.169445 sec (nthreads: 8 speedup 3.86857)
tricount time:         2.170250 sec (saxpy method)
tri+prep time:         2.189823 sec (incl time to compute L)
compute C time:        2.169445 sec
reduce (C) time:       0.000806 sec
rate     4.56 million edges/sec (incl time for L=tril(A))
rate     4.60 million edges/sec (just tricount itself)