将锯齿状数组转换为2D数组C＃

Question

I'm trying to convert this function from Jagged Array to 2D array, and I'm not able to convert everything Original Function:

public static double[][] InvertMatrix(double[][] A)
{
    int n = A.Length;
    //e will represent each column in the identity matrix
    double[] e;
    //x will hold the inverse matrix to be returned
    double[][] x = new double[n][];
    for (int i = 0; i < n; i++)
    {
        x[i] = new double[A[i].Length];
    }
    /*
    * solve will contain the vector solution for the LUP decomposition as we solve
    * for each vector of x.  We will combine the solutions into the double[][] array x.
    * */
    double[] solve;

    //Get the LU matrix and P matrix (as an array)
    Tuple<double[][], int[]> results = LUPDecomposition(A);

    double[][] LU = results.Item1;
    int[] P = results.Item2;

    /*
    * Solve AX = e for each column ei of the identity matrix using LUP decomposition
    * */
    for (int i = 0; i < n; i++)
    {
        e = new double[A[i].Length];
        e[i] = 1;
        solve = LUPSolve(LU, P, e);
        for (int j = 0; j < solve.Length; j++)
        {
            x[j][i] = solve[j];
        }
    }
    return x;
}

What I have converted until now:

public static double[,] InvertMatrix(double[,] A)
{
    int n = A.Length;
    //e will represent each column in the identity matrix
    double[] e;
    //x will hold the inverse matrix to be returned
    double[,] x = new double[n][];
    for (int i = 0; i < n; i++)
    {
        //how to convert this line?
        x[i] = new double[A[i].Length];
    }
    /*
    * solve will contain the vector solution for the LUP decomposition as we solve
    * for each vector of x.  We will combine the solutions into the double[][] array x.
    * */
    double[] solve;

    //Get the LU matrix and P matrix (as an array)
    Tuple<double[,], int[]> results = LUPDecomposition(A);

    double[,] LU = results.Item1;
    int[] P = results.Item2;

    /*
    * Solve AX = e for each column ei of the identity matrix using LUP decomposition
    * */
    for (int i = 0; i < n; i++)
    {
        //This one too?!
        e = new double[A[i].Length];
        e[i] = 1;
        solve = LUPSolve(LU, P, e);
        for (int j = 0; j < solve.Length; j++)
        {
            x[j,i] = solve[i,j];
        }
    }
    return x;
}

How to convert x[i] = new double[A[i].Length] to 2D array?

Answer 1

This snippet can be helpful

static T[,] To2D<T>(T[][] source)
{
    try
    {
        int FirstDim = source.Length;
        int SecondDim = source.GroupBy(row => row.Length).Single().Key; // throws InvalidOperationException if source is not rectangular

        var result = new T[FirstDim, SecondDim];
        for (int i = 0; i < FirstDim; ++i)
            for (int j = 0; j < SecondDim; ++j)
                result[i, j] = source[i][j];

        return result;
    }
    catch (InvalidOperationException)
    {
        throw new InvalidOperationException("The given jagged array is not rectangular.");
    } 
}

Usage:

double[][] array = { new double[] { 52, 76, 65 }, new double[] { 98, 87, 93 }, new double[] { 43, 77, 62 }, new double[] { 72, 73, 74 } };
double[,] D2 = To2D(array);

UPD: For those scenarios where unsafe context is acceptable there is a faster solution, thanks Styp: https://stackoverflow.com/a/51450057/3909293

Answer 2

NOTE: your jagged array should be orthogonal, hence sub arrays lengths should all be equal, otherwise you cannot convert it to a 2D array.

the part:

double[,] x = new double[n][];
for (int i = 0; i < n; i++)
{
    //how to convert this line?
    x[i] = new double[A[i].Length];
}

is just for initializing a new jagged array which can easily replaced with

double[,] x = new double[A.GetLength(0),A.GetLength(1)];

and in

   //This one too?!
    e = new double[A[i].Length];

you are essentially creating an array with same length of sub array i in A so we can replace it with

    e = new double[A.GetLength(1)]; //NOTE: second dimension

as mentioned before, All sub arrays length are equal so we can use second dimension length instead.

and the whole method would be:

    public static double[,] InvertMatrix2D(double[,] A)
    {
        int n = A.Length;
        //e will represent each column in the identity matrix
        double[] e;
        //x will hold the inverse matrix to be returned
        double[,] x = new double[A.GetLength(0),A.GetLength(1)];

        /*
        * solve will contain the vector solution for the LUP decomposition as we solve
        * for each vector of x.  We will combine the solutions into the double[][] array x.
        * */
        double[] solve;

        //Get the LU matrix and P matrix (as an array)
        Tuple<double[,], int[]> results = LUPDecomposition(A);

        double[,] LU = results.Item1;
        int[] P = results.Item2;

        /*
        * Solve AX = e for each column ei of the identity matrix using LUP decomposition
        * */
        for (int i = 0; i < n; i++)
        {
            e = new double[A.GetLength(1)]; //NOTE: second dimension
            e[i] = 1;
            solve = LUPSolve(LU, P, e);
            for (int j = 0; j < solve.Length; j++)
            {
                x[j,i] = solve[j];
            }
        }
        return x;
    }

Answer 3

Diligent Key Pressers' answer is the right one if runtime is unimportant. I work a lot with 3D Arrays and I learned that copy value-by-value operations are incredibly expensive! Keep that in mind! Another thing is Linq is slow and preconditions are eating up times as well!

In my opinion, if time is of importance, this solution might be useful:

using System;
using System.Linq;
using BenchmarkDotNet.Attributes;
using BenchmarkDotNet.Running;

namespace ArrayConverter {
   public class Benchmark {
        [Params(10, 100, 1000, 10000)] 
        public int size;

        public double[][] data;

        [GlobalSetup]
        public void Setup() {
            var rnd = new Random();

            data = new double[size][];
            for (var i = 0; i < size; i++) {
                data[i] = new double[size];
                for (var j = 0; j < size; j++) {
                    data[i][j] = rnd.NextDouble();
                }
            }
        }

        [Benchmark]
        public void ComputeTo2D() {
            var output = To2D(data);
        }

       [Benchmark]
       public void ComputeTo2DFast() {
           var output = To2DFast(data);
       }

       public static T[,] To2DFast<T>(T[][] source) where T : unmanaged{
           var dataOut = new T[source.Length, source.Length];
           var assertLength = source[0].Length;

           unsafe {
               for (var i=0; i<source.Length; i++){
                   if (source[i].Length != assertLength) {
                       throw new InvalidOperationException("The given jagged array is not rectangular.");
                   }

                   fixed (T* pDataIn = source[i]) {
                       fixed (T* pDataOut = &dataOut[i,0]) {
                           CopyBlockHelper.SmartCopy<T>(pDataOut, pDataIn, assertLength);
                       }
                   }
               }
           }

           return dataOut;
       }

        public static T[,] To2D<T>(T[][] source) {
            try {
                var FirstDim = source.Length;
                var SecondDim =
                    source.GroupBy(row => row.Length).Single()
                        .Key; // throws InvalidOperationException if source is not rectangular

                var result = new T[FirstDim, SecondDim];
                for (var i = 0; i < FirstDim; ++i)
                for (var j = 0; j < SecondDim; ++j)
                    result[i, j] = source[i][j];

                return result;
            }
            catch (InvalidOperationException) {
                throw new InvalidOperationException("The given jagged array is not rectangular.");
            }
        }
    }

    public class Programm {
        public static void Main(string[] args) {
            BenchmarkRunner.Run<Benchmark>();
//            var rnd = new Random();
//            
//            var size = 100;
//            var data = new double[size][];
//            for (var i = 0; i < size; i++) {
//                data[i] = new double[size];
//                for (var j = 0; j < size; j++) {
//                    data[i][j] = rnd.NextDouble();
//                }
//            }
//
//            var outSafe = Benchmark.To2D(data);
//            var outFast = Benchmark.To2DFast(data);
//
//            for (var i = 0; i < outSafe.GetLength(0); i++) {
//                for (var j = 0; j < outSafe.GetLength(1); j++) {
//                    if (outSafe[i, j] != outFast[i, j]) {
//                        Console.WriteLine("Error at: {0}, {1}", i, j);
//                    }
//                }
//            }
//
//            Console.WriteLine("All Good!");

        }
    }
}

The CopyBlock Helper was obtained from here: https://gist.github.com/theraot/1bfd0deb4a1aab0a27d8

I just made a Wrapper for the IL-functions:

using System;
using System.Reflection.Emit;

namespace ArrayConverter {

    // Inspired by:
    // http://xoofx.com/blog/2010/10/23/high-performance-memcpy-gotchas-in-c/
    public class CopyBlockHelper {

        private const int BlockSize = 16384;

        private static readonly CopyBlockDelegate CpBlock = GenerateCopyBlock();

        private unsafe delegate void CopyBlockDelegate(void* des, void* src, uint bytes);

        private static unsafe void CopyBlock(void* dest, void* src, uint count) {
            var local = CpBlock;
            local(dest, src, count);
        }

        static CopyBlockDelegate GenerateCopyBlock() {
            // Don't ask...
            var method = new DynamicMethod("CopyBlockIL", typeof(void),
                new[] {typeof(void*), typeof(void*), typeof(uint)}, typeof(CopyBlockHelper));
            var emitter = method.GetILGenerator();
            // emit IL
            emitter.Emit(OpCodes.Ldarg_0);
            emitter.Emit(OpCodes.Ldarg_1);
            emitter.Emit(OpCodes.Ldarg_2);
            emitter.Emit(OpCodes.Cpblk);
            emitter.Emit(OpCodes.Ret);

            // compile to delegate
            return (CopyBlockDelegate) method.CreateDelegate(typeof(CopyBlockDelegate));
        }

        public static unsafe void SmartCopy<T>(T* pointerDataOutCurrent, T* pointerDataIn, int length) where T : unmanaged {
            var sizeOfType = sizeof(T);

            var numberOfBytesInBlock = Convert.ToUInt32(sizeOfType * length);

            var numOfIterations = numberOfBytesInBlock / BlockSize;
            var overheadOfLastIteration = numberOfBytesInBlock % BlockSize;

            uint offset;
            for (var idx = 0u; idx < numOfIterations; idx++) {
                offset = idx * BlockSize;
                CopyBlock(pointerDataOutCurrent + offset / sizeOfType, pointerDataIn + offset / sizeOfType, BlockSize);
            }

            offset = numOfIterations * BlockSize;
            CopyBlock(pointerDataOutCurrent + offset / sizeOfType, pointerDataIn + offset / sizeOfType, overheadOfLastIteration);
        }
    }
}

This results in the following results:

          Method |  size |             Mean |            Error |           StdDev |
---------------- |------ |-----------------:|-----------------:|-----------------:|
     ComputeTo2D |    10 |         972.2 ns |        18.981 ns |        17.755 ns |
 ComputeTo2DFast |    10 |         233.1 ns |         6.672 ns |         6.852 ns |
     ComputeTo2D |   100 |      21,082.5 ns |       278.679 ns |       247.042 ns |
 ComputeTo2DFast |   100 |       6,100.2 ns |        66.566 ns |        62.266 ns |
     ComputeTo2D |  1000 |   2,481,061.0 ns |    13,724.850 ns |    12,166.721 ns |
 ComputeTo2DFast |  1000 |   1,939,575.1 ns |    18,519.845 ns |    16,417.358 ns |
     ComputeTo2D | 10000 | 340,687,083.2 ns | 1,671,837.229 ns | 1,563,837.429 ns |
 ComputeTo2DFast | 10000 | 279,996,210.4 ns |   955,032.923 ns |   745,626.822 ns |

If possible, try to use ArrayCopy, BlockCopy or IL-CopyBlock to increase conversion performance. The value-by-value copy operation is slow and therefore not the best option to use! Further speedup can be found by optimizing a few things and removing the if-clause. A factor of at least 2x should be achievable!

Answer 4

Just to make sure we are at the same understanding, a jagged array is an array of arrays. So when you do

for (int i = 0; i < n; i++)
{
    //how to convert this line?
    x[i] = new double[A[i].Length];
}

you are adding a array for each position of the first dimension's array.

In your case (in the jagged array) A.Length represented the length of the first dimension of the array while A[i].Length represented the length of the array of the second dimension that is contained in this index (i) of the first dimension. If you are using a 2D array, A.Length represents the length of both dimensions multiplied. While with a jagged can have different length for each second dimension arrays, a 2D array must have the same length on both dimension.

So, in your case you would have to get n = A.GetLength(0) (means get the length of the first dimension) and m = A.GetLength(1) (means get the length of the second dimension). You would then initialize 'x' double[,] x = new double[n, m]; and you would no longer need the for loop.

Your code should then look like this :

public static double[,] InvertMatrix(double[,] A)
{
    int n = A.Length;
    //e will represent each column in the identity matrix
    double[] e;
    //x will hold the inverse matrix to be returned
    double[,] x = new double[n, m];

    /*
    * solve will contain the vector solution for the LUP decomposition as we solve
    * for each vector of x.  We will combine the solutions into the double[][] array x.
    * */
    double[] solve;

    //Get the LU matrix and P matrix (as an array)
    Tuple<double[,], int[]> results = LUPDecomposition(A);

    double[,] LU = results.Item1;
    int[] P = results.Item2;

    /*
    * Solve AX = e for each column ei of the identity matrix using LUP decomposition
    * */
    for (int i = 0; i < n; i++)
    {
        //This one too?! /// this one would become 
        e = new double[m];
        e[i] = 1;
        solve = LUPSolve(LU, P, e);
        for (int j = 0; j < solve.Length; j++)
        {
            x[j,i] = solve[i,j];
        }
    }
    return x;
}

So, if what I did is ok, this should fix your problem and answer your question.