spectral-norm benchmark N=550

Each chart bar shows how many times slower, one ↓ spectral-norm program was, compared to the fastest program.

These are not the only programs that could be written. These are not the only compilers and interpreters. These are not the only programming languages.

Column × shows how many times more each program used compared to the benchmark program that used least.

    sort sortsort
  ×   Program Source Code CPU secs Elapsed secs Memory KB Code B ≈ CPU Load
1.0Python 2 #2 0.080.08?394  0% 13% 0% 89%
1.0Python 2 #2 0.080.08?394  0% 0% 11% 100%
1.5Python 3 #2 0.120.12?394  8% 100% 8% 0%
1.5Python 3 #2 0.120.12?394  14% 100% 15% 0%
1.6Nuitka #2 0.130.13?394  0% 8% 100% 0%
1.6Nuitka #2 0.130.13?394  0% 0% 100% 0%
1.6Nuitka #2 0.130.13?394  0% 100% 0% 0%
1.7Python 3 #2 0.130.14?394  100% 0% 0% 8%
1.7Python 2 #2 0.090.14?394  7% 29% 67% 7%
2.4PyPy 2 #8 0.190.20?594  0% 5% 100% 0%
2.4PyPy 2 #8 0.200.20?594  0% 5% 0% 100%
2.5PyPy 3 #8 0.200.20?594  0% 5% 100% 5%
2.5PyPy 3 #8 0.200.20?594  100% 0% 5% 10%
2.6PyPy 3 #8 0.200.211,036594  62% 48% 29% 10%
2.9PyPy 2 #6 0.230.231,420498  100% 14% 4% 4%
2.9PyPy 2 #6 0.230.231,408498  0% 9% 4% 100%
3.0PyPy 2 #8 0.240.241,412594  100% 12% 0% 4%
3.1PyPy 2 #6 0.230.251,412498  4% 92% 4% 0%
3.7PyPy 3 #6 0.300.301,116498  0% 3% 0% 97%
3.8PyPy 3 #6 0.300.311,136498  100% 6% 3% 3%
4.5PyPy 3 #6 0.340.361,116498  3% 97% 5% 0%
4.8Python 3 #3 0.390.391,812642  10% 100% 5% 0%
4.8Python 3 #3 0.380.391,900642  8% 3% 5% 95%
5.0Nuitka #3 0.400.411,788642  3% 7% 100% 0%
5.0Nuitka #3 0.410.4138,512642  0% 7% 0% 100%
5.1Python 3 #3 0.390.4131,192642  100% 5% 5% 2%
5.2Pyston #2 0.420.4255,652394  2% 0% 0% 100%
5.2Pyston #2 0.420.4256,036394  0% 0% 0% 100%
5.2Pyston #2 0.420.4257,532394  0% 10% 83% 12%
5.2Nuitka #3 0.420.4335,692642  2% 27% 77% 0%
10PyPy 2 #5 1.430.82305,776595  46% 41% 63% 34%
10PyPy 2 #5 1.450.83300,748595  43% 41% 36% 66%
11PyPy 2 #5 1.440.8787,344595  40% 58% 36% 41%
11Numba 0.910.9184,284663  0% 0% 0% 100%
11Numba 0.920.9284,664663  0% 3% 49% 48%
11Numba 0.930.9383,916663  1% 0% 0% 99%
12Graal #8 1.250.98326,668594  18% 1% 15% 98%
12Graal #8 1.260.98324,632594  16% 3% 24% 94%
12Graal #8 1.270.99324,848594  98% 19% 3% 16%
17PyPy 3 #5 2.391.3787,412575  38% 41% 39% 68%
17PyPy 3 #5 2.391.4086,904575  40% 38% 36% 65%
17PyPy 3 #5 2.391.4187,660575  35% 67% 36% 40%
18Pyston #5 4.751.43158,316595  86% 81% 85% 82%
18Pyston #5 4.791.49158,188595  88% 79% 76% 79%
19Pyston #5 4.821.50158,392595  88% 79% 76% 77%
21Pyston #8 1.691.6927,440594  100% 1% 0% 0%
21Pyston #8 1.691.6927,568594  0% 100% 0% 0%
21Pyston #8 1.731.7327,432594  1% 0% 2% 98%
23Python 2 #5 6.381.8441,668595  90% 93% 91% 92%
23Nuitka #5 6.661.8758,160575  90% 92% 91% 92%
23Nuitka #5 6.671.8757,496575  93% 90% 91% 89%
23Python 2 #5 6.451.8941,868595  95% 91% 92% 93%
23Nuitka #5 6.861.8958,720575  92% 95% 93% 90%
24Python 2 #5 6.341.9541,648595  92% 92% 91% 93%
25Python 3 #5 7.592.0652,984575  95% 95% 94% 97%
25Python 3 #5 7.632.0653,464575  94% 98% 93% 96%
27Python 3 #5 7.582.1753,204575  90% 92% 91% 90%
27Pyston #6 2.202.2127,500498  0% 0% 100% 0%
27Pyston #6 2.212.2127,340498  2% 98% 0% 0%
29Pyston #6 2.332.3327,464498  0% 100% 0% 0%
35Python 2 #6 2.802.806,664498  2% 2% 100% 2%
35Python 2 #6 2.802.806,720498  1% 3% 1% 100%
35Python 2 #6 2.812.826,724498  2% 1% 100% 1%
36Nuitka #8 2.912.919,772594  1% 4% 1% 100%
37Nuitka #8 2.873.009,800594  0% 100% 0% 1%
37Nuitka #6 3.003.019,812498  100% 5% 2% 1%
37Nuitka #6 3.013.0210,020498  100% 5% 2% 1%
38Nuitka #8 2.993.049,808594  1% 41% 0% 62%
38Nuitka #6 3.053.059,804498  0% 5% 0% 100%
39Python 2 #8 3.123.126,864594  1% 2% 100% 1%
39Python 2 #8 3.153.156,932594  2% 3% 1% 100%
39Python 2 #8 3.163.166,796594  2% 1% 100% 1%
40Python 3 #6 3.273.278,848498  7% 2% 4% 99%
41Python 3 #6 3.343.348,696498  5% 2% 100% 1%
41Python 3 #6 3.293.368,664498  44% 1% 59% 1%
46Python development version #6 3.753.758,172498  1% 5% 100% 1%
46Python development version #6 3.763.768,368498  1% 6% 100% 1%
47Python development version #6 3.803.808,248498  1% 5% 100% 0%
51Python 3 #8 4.114.118,876594  7% 100% 2% 3%
51Python 3 #8 4.134.148,824594  7% 3% 100% 3%
51IronPython #8 3.984.1657,520594  0% 63% 8% 24%
52IronPython #8 3.994.1861,472594  92% 0% 1% 1%
52IronPython #8 4.004.1957,200594  0% 92% 1% 1%
52Python 3 #8 4.114.208,804594  47% 1% 58% 2%
56Graal #6 9.124.52519,528498  31% 46% 73% 62%
57IronPython #6 4.344.5974,580498  1% 2% 13% 79%
57IronPython #6 4.354.6170,740498  7% 57% 1% 29%
57IronPython #6 4.454.6271,112498  46% 1% 48% 1%
59Jython #8 8.084.77294,356594  43% 34% 60% 31%
60Jython #8 8.374.87297,264594  51% 45% 38% 38%
61Jython #8 8.414.96294,976594  31% 64% 46% 29%
63Python development version #8 5.075.077,928594  1% 6% 100% 1%
63Python development version #8 5.125.128,132594  1% 5% 1% 100%
64Python development version #8 5.175.188,000594  0% 5% 1% 100%
64Graal #6 10.785.21587,280498  55% 78% 63% 27%
64Graal #6 10.705.22558,084498  61% 66% 70% 19%
84Jython #6 9.576.83284,740498  43% 37% 27% 33%
85Jython #6 9.826.89290,672498  30% 38% 31% 44%
85Jython #6 9.966.90294,640498  31% 36% 56% 21%
87MicroPython #6 7.007.014,216498  100% 0% 0% 0%
87MicroPython #6 7.007.014,396498  0% 100% 1% 0%
87MicroPython #6 7.027.034,364498  0% 1% 0% 100%
missing benchmark programs
Cython No program
Shedskin No program
Grumpy No program

 spectral-norm benchmark : Eigenvalue using the power method

diff program output N = 100 with this output file to check your program is correct before contributing.

We are trying to show the performance of various programming language implementations - so we ask that contributed programs not only give the correct result, but also use the same algorithm to calculate that result.

Each program should calculate the spectral norm of an infinite matrix A, with entries a11=1, a12=1/2, a21=1/3, a13=1/4, a22=1/5, a31=1/6, etc

For more information see challenge #3 in Eric W. Weisstein, "Hundred-Dollar, Hundred-Digit Challenge Problems" and "Spectral Norm".

From MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/Hundred-DollarHundred-DigitChallengeProblems.html
http://mathworld.wolfram.com/SpectralNorm.html

Thanks to Sebastien Loisel for this benchmark.

Revised BSD license

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