Sum of products of two arrays (dotproduct)
First off, I know my title can be formulated better, but my math classes are so far gone I can\'t remember the correct words anymore..
I need to do something like this (
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Solutions with LINQ
int[] digits1 = new int[10]{0,1,2,3,4,5,6,7,8,9}; int[] digits2 = new int[10]{0,1,2,3,4,5,6,7,8,9}; int result1 = digits1.Zip(digits2, (x, y) => x * y).Sum(); int result2 = digits1.Select((x, y) => x * digits2.ElementAt(y)).Sum(); int result3 = digits1.Select((n, i) => n * digits2[i]).Sum(); // Ani answer int result4 = Enumerable.Range(0, digits1.Length) .Sum(i => digits1[i] * digits2[i]);Performance test
100000iterations:Queries Fn: Result 1 Ticks 135306 Fn: Result 2 Ticks 2470614 Fn: Result 3 Ticks 130034 Fn: Result 4 Ticks 123374 ------------- Fastest Fn: Result 4 Ticks 123374 Fn: Result 3 Ticks 130034 Fn: Result 1 Ticks 135306 Fn: Result 2 Ticks 2470614讨论(0) -
Even faster is to unroll the loop
Test("Regular Loop", () => { int result = 0; for (int i = 0; i < digits1.Length; i++) { result += digits1[i] * digits2[i]; } return result; }); // This will fail if vectors are not a multiple of 4 in length. Test("Unroll 4x", () => { int result = 0; for (int i = 0; i < digits1.Length; i+=4) { result += digits1[i] * digits2[i]; result += digits1[i+1] * digits2[i+1]; result += digits1[i+2] * digits2[i+2]; result += digits1[i+3] * digits2[i+3]; } return result; }); Test("Dynamic unroll", () => { int result = 0; int limit = (digits1.Length/8)*8; int reminderLimit = digits1.Length; if (digits1.Length >= 8) { for (int i = 0; i < limit; i+=8) { result += digits1[i] * digits2[i]; result += digits1[i+1] * digits2[i+1]; result += digits1[i+2] * digits2[i+2]; result += digits1[i+3] * digits2[i+3]; result += digits1[i+4] * digits2[i+4]; result += digits1[i+5] * digits2[i+5]; result += digits1[i+6] * digits2[i+6]; result += digits1[i+7] * digits2[i+7]; } reminderLimit = digits1.Length % 8; } switch(reminderLimit) { case 7: { result += digits1[limit] * digits2[limit]; result += digits1[limit+1] * digits2[limit+1]; result += digits1[limit+2] * digits2[limit+2]; result += digits1[limit+3] * digits2[limit+3]; result += digits1[limit+4] * digits2[limit+4]; result += digits1[limit+5] * digits2[limit+5]; result += digits1[limit+6] * digits2[limit+6]; break; } case 6: { result += digits1[limit] * digits2[limit]; result += digits1[limit+1] * digits2[limit+1]; result += digits1[limit+2] * digits2[limit+2]; result += digits1[limit+3] * digits2[limit+3]; result += digits1[limit+4] * digits2[limit+4]; result += digits1[limit+5] * digits2[limit+5]; break; } case 5: { result += digits1[limit] * digits2[limit]; result += digits1[limit+1] * digits2[limit+1]; result += digits1[limit+2] * digits2[limit+2]; result += digits1[limit+3] * digits2[limit+3]; result += digits1[limit+4] * digits2[limit+4]; break; } case 4: { result += digits1[limit] * digits2[limit]; result += digits1[limit+1] * digits2[limit+1]; result += digits1[limit+2] * digits2[limit+2]; result += digits1[limit+3] * digits2[limit+3]; break; } case 3: { result += digits1[limit] * digits2[limit]; result += digits1[limit+1] * digits2[limit+1]; result += digits1[limit+2] * digits2[limit+2]; break; } case 2: { result += digits1[limit] * digits2[limit]; result += digits1[limit+1] * digits2[limit+1]; break; } case 1: { result += digits1[limit] * digits2[limit]; break; } default : { break; } } return result; });There is a huge difference is running time between debug and release mode of C# code, this is run with release mode:
Regular Loop Iterations: 1000000 Time(ms): 0/ 0/ 0 ( 596) Ticks: 1/ 2,071213/ 455 ( 2154248) Unroll 4x Iterations: 1000000 Time(ms): 0/ 2E-06/ 1 ( 575) Ticks: 1/ 1,984301/ 3876 ( 2076105) Dynamic unroll Iterations: 1000000 Time(ms): 0/ 0/ 0 ( 430) Ticks: 1/ 1,4635/ 3228 ( 1554830)Debug mode:
Regular Loop Iterations: 1000000 Time(ms): 0/ 1E-06/ 1 ( 1296) Ticks: 4/ 4,529916/ 3907 ( 4678354) Unroll 4x Iterations: 1000000 Time(ms): 0/ 0/ 0 ( 871) Ticks: 2/ 3,048466/ 701 ( 3145277) Dynamic unroll Iterations: 1000000 Time(ms): 0/ 0/ 0 ( 819) Ticks: 2/ 2,858588/ 1398 ( 2957179)讨论(0) -
I wrote a test bench to compare the these methods' times on my machine.
Specs:
Windows 7 Professional 64-bit
Intel Core 2 Quad Q9550 @ 2.83GHz
4x1GiB Corsair Dominator DDR2 1066 (PC2-8500)using System; using System.Linq; namespace Testbench { class Program { static void Main(string[] args) { var digits1 = Enumerable.Range(0, 500).ToArray(); var digits2 = digits1.ToArray(); // create a copy Test("Regular Loop", () => { int result = 0; for (int i = 0; i < digits1.Length; i++) { result += digits1[i] * digits2[i]; } return result; }); // using LINQ Test("Enumerable \"Loop\"", () => Enumerable.Range(0, digits1.Length).Sum(i => digits1[i] * digits2[i])); Test("Using Zip", () => digits1.Zip(digits2, (x, y) => x * y).Sum()); Test("Using Indexed Select", () => digits1.Select((n, i) => n * digits2[i]).Sum()); Test("Using Indexed Select with ElementAt", () => digits1.Select((n, i) => n * digits2.ElementAt(i)).Sum()); // using PLINQ Test("Parallel Enumerable \"Loop\"", () => ParallelEnumerable.Range(0, digits1.Length).Sum(i => digits1[i] * digits2[i])); Test("Using Parallel Zip", () => digits1.AsParallel().Zip(digits2.AsParallel(), (x, y) => x * y).Sum()); Test("Using Parallel Indexed Select", () => digits1.AsParallel().Select((n, i) => n * digits2[i]).Sum()); Test("Using Parallel Indexed Select with ElementAt", () => digits1.AsParallel().Select((n, i) => n * digits2.ElementAt(i)).Sum()); Console.Write("Press any key to continue . . . "); Console.ReadKey(true); Console.WriteLine(); } static void Test<T>(string testName, Func<T> test, int iterations = 1000000) { Console.WriteLine(testName); Console.WriteLine("Iterations: {0}", iterations); var results = Enumerable.Repeat(0, iterations).Select(i => new System.Diagnostics.Stopwatch()).ToList(); var timer = System.Diagnostics.Stopwatch.StartNew(); for (int i = 0; i < results.Count; i++) { results[i].Start(); test(); results[i].Stop(); } timer.Stop(); Console.WriteLine("Time(ms): {0,3}/{1,10}/{2,8} ({3,10})", results.Min(t => t.ElapsedMilliseconds), results.Average(t => t.ElapsedMilliseconds), results.Max(t => t.ElapsedMilliseconds), timer.ElapsedMilliseconds); Console.WriteLine("Ticks: {0,3}/{1,10}/{2,8} ({3,10})", results.Min(t => t.ElapsedTicks), results.Average(t => t.ElapsedTicks), results.Max(t => t.ElapsedTicks), timer.ElapsedTicks); Console.WriteLine(); } } }32-bit target:
Regular Loop Iterations: 1000000 Time(ms): 0/ 0/ 0 ( 1172) Ticks: 3/ 3.101365/ 526 ( 3244251) Enumerable "Loop" Iterations: 1000000 Time(ms): 0/ 4.3E-05/ 25 ( 9054) Ticks: 24/ 24.93989/ 69441 ( 25052172) Using Zip Iterations: 1000000 Time(ms): 0/ 2.4E-05/ 16 ( 16282) Ticks: 41/ 44.941406/ 45395 ( 45052491) Using Indexed Select Iterations: 1000000 Time(ms): 0/ 5.3E-05/ 32 ( 13473) Ticks: 34/ 37.165088/ 89602 ( 37280177) Using Indexed Select with ElementAt Iterations: 1000000 Time(ms): 0/ 1.5E-05/ 6 ( 160215) Ticks: 405/443.154147/ 17821 ( 443306156) Parallel Enumerable "Loop" Iterations: 1000000 Time(ms): 0/ 0.000103/ 29 ( 17194) Ticks: 38/ 47.412312/ 81906 ( 47576133) Using Parallel Zip Iterations: 1000000 Time(ms): 0/ 9.4E-05/ 19 ( 21703) Ticks: 49/ 59.859005/ 53200 ( 60051081) Using Parallel Indexed Select Iterations: 1000000 Time(ms): 0/ 0.000114/ 27 ( 20579) Ticks: 45/ 56.758491/ 75455 ( 56943627) Using Parallel Indexed Select with ElementAt Iterations: 1000000 Time(ms): 0/ 8.1E-05/ 19 ( 61137) Ticks: 144/ 168.97909/ 53320 ( 169165086)
64-bit target:
Regular Loop Iterations: 1000000 Time(ms): 0/ 0/ 0 ( 506) Ticks: 1/ 1.254137/ 1491 ( 1401969) Enumerable "Loop" Iterations: 1000000 Time(ms): 0/ 2.9E-05/ 15 ( 10118) Ticks: 27/ 27.850086/ 41954 ( 27995994) Using Zip Iterations: 1000000 Time(ms): 0/ 2.2E-05/ 13 ( 17089) Ticks: 45/ 47.132834/ 38506 ( 47284608) Using Indexed Select Iterations: 1000000 Time(ms): 0/ 3.1E-05/ 12 ( 14057) Ticks: 37/ 38.740923/ 33846 ( 38897274) Using Indexed Select with ElementAt Iterations: 1000000 Time(ms): 0/ 3.8E-05/ 29 ( 117412) Ticks: 304/324.711279/ 82726 ( 324872753) Parallel Enumerable "Loop" Iterations: 1000000 Time(ms): 0/ 9.9E-05/ 28 ( 24234) Ticks: 38/ 66.79389/ 77578 ( 67054956) Using Parallel Zip Iterations: 1000000 Time(ms): 0/ 0.000111/ 24 ( 30193) Ticks: 46/ 83.264037/ 69029 ( 83542711) Using Parallel Indexed Select Iterations: 1000000 Time(ms): 0/ 6.5E-05/ 20 ( 28417) Ticks: 45/ 78.337831/ 56354 ( 78628396) Using Parallel Indexed Select with ElementAt Iterations: 1000000 Time(ms): 0/ 9.2E-05/ 16 ( 65233) Ticks: 112/180.154663/ 44799 ( 180496754)
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int result = 0; for(int i = 0; i < digits1.length; i++) { result += digits1[i] * digits2[i]; }讨论(0) -
Very simply, do a loop.
int sum = 0; for(int i = 0; i < digits1.length && i < digits2.length; i++) { sum += digits1[i] * digits2[i]; }Boom.
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With LINQ:
int dotProduct = digits1.Zip(digits2, (d1, d2) => d1 * d2) .Sum();Zipwill produce a streaming sequence containing the products of corresponding elements from both arrays, which is then summed into an integer withSum.Note that this will not fail like it should when the arrays of unequal length, so you probably need to validate the input:
//null checks here if(digits1.Length != digits2.Length) throw new ArgumentException("...");EDIT: As Jeff M points out,
Enumerable.Zipwas only added to the framework in .NET 4.0. In .NET 3.5, you can do this (the idea is only efficient for collections that expose fast indexers):int dotProduct = Enumerable.Range(0, digits1.Length) .Sum(i => digits1[i] * digits2[i]); //from Jeff M's comment: int dotProduct = digits1.Select((n, i) => n * digits2[i]) .Sum();讨论(0)
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