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Add LU and PLU decompositions. (#26)
* Add LU and PLU decompositions. * Refactor & add description for LUP decomposition. * Add docs for algorithms & fix some minor issues. * Codestyle & format. * Nullables added
1 parent 8df6dda commit ebbdd1b

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-64
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‎.gitignore

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*.vs*
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*/bin/*
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*/obj/*
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*/packages/*
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*/packages/*
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GenericTensor.sln.DotSettings.user

‎GenericTensor.sln.DotSettings.user

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This file was deleted.

‎GenericTensor/Core/Exceptions.cs

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@@ -55,4 +55,13 @@ public class InvalidDeterminantException : DataException
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internal InvalidDeterminantException(string msg) : base(msg) {}
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internal InvalidDeterminantException() : base() {}
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}
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/// <summary>
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/// Thrown when there is no decomposition for provided matrix
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/// </summary>
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public class ImpossibleDecomposition : DataException
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{
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internal ImpossibleDecomposition(string msg) : base(msg) {}
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internal ImpossibleDecomposition() : base() {}
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}
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}

‎GenericTensor/Declaration.cs

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@@ -1,4 +1,5 @@
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#region copyright
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/*
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* MIT License
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*
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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* SOFTWARE.
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*/
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#endregion
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@@ -40,6 +42,7 @@ public sealed partial class GenTensor<T, TWrapper>
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: ICloneable where TWrapper : struct, IOperations<T>
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{
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#region Composition
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/// <summary>
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/// Creates a new axis that is put backward
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/// and then sets all elements as children
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#endregion
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#region Constructors
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/// <summary>
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/// Creates a tensor whose all matrices are identity matrices
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/// <para>1 is achieved with <see cref="IOperations{T}.CreateOne"/></para>
@@ -145,36 +149,31 @@ public static GenTensor<T, TWrapper> CreateMatrix(int width, int height)
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/// (its only argument is an array of integers which are indices of the tensor)
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> CreateTensor(TensorShape shape, Func<int[], T> operation, Threading threading = Threading.Single)
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=> Constructors<T, TWrapper>.CreateTensor(shape, operation, threading);
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public static GenTensor<T, TWrapper> CreateTensor(TensorShape shape, Func<int[], T> operation, Threading threading = Threading.Single) => Constructors<T, TWrapper>.CreateTensor(shape, operation, threading);
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/// <summary>
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/// Creates a tensor from an array
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> CreateTensor(T[] data)
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=> Constructors<T, TWrapper>.CreateTensor(data);
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public static GenTensor<T, TWrapper> CreateTensor(T[] data) => Constructors<T, TWrapper>.CreateTensor(data);
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/// <summary>
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/// Creates a tensor from a two-dimensional array
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> CreateTensor(T[,] data)
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=> Constructors<T, TWrapper>.CreateTensor(data);
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public static GenTensor<T, TWrapper> CreateTensor(T[,] data) => Constructors<T, TWrapper>.CreateTensor(data);
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/// <summary>
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/// Creates a tensor from a three-dimensional array
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> CreateTensor(T[,,] data)
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=> Constructors<T, TWrapper>.CreateTensor(data);
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public static GenTensor<T, TWrapper> CreateTensor(T[,,] data) => Constructors<T, TWrapper>.CreateTensor(data);
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/// <summary>
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/// Creates a tensor from an n-dimensional array
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> CreateTensor(Array data)
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=> Constructors<T, TWrapper>.CreateTensor(data);
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public static GenTensor<T, TWrapper> CreateTensor(Array data) => Constructors<T, TWrapper>.CreateTensor(data);
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#endregion
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@@ -186,6 +185,42 @@ public static GenTensor<T, TWrapper> CreateTensor(Array data)
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/// </summary>
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public GenTensor<T, TWrapper> RowEchelonFormSimple()
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=> EchelonForm<T, TWrapper>.RowEchelonFormSimple(this);
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/// <summary>
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/// Decomposes a matrix into a triangular one.
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/// Is of the Row Echelon Form (leading elements might be differ from ones).
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///
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/// In addition, returns a permutation that algorithm performs with rows.
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/// Permutation array is size of rows there are in matrix.
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///
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/// Initial state of that array is:
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/// 1 2 3 ... numberOfRows
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///
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/// For example, algorithm swaps first and third rows then:
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/// 3 2 1 ... numberOfRows
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///
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/// It can be useful performing decompositions
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/// </summary>
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public (GenTensor<T, TWrapper>, int[]) RowEchelonFormPermuteSimple()
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=> EchelonForm<T, TWrapper>.RowEchelonFormPermuteSimple(this);
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/// <summary>
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/// Decomposes a matrix into a triangular one.
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/// Is of the Row Echelon Form (leading elements might be differ from ones).
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///
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/// In addition, returns a permutation that algorithm performs with rows.
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/// Permutation array is size of rows there are in matrix.
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///
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/// Initial state of that array is:
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/// 1 2 3 ... numberOfRows
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///
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/// For example, algorithm swaps first and third rows then:
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/// 3 2 1 ... numberOfRows
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///
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/// It can be useful performing decompositions
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/// </summary>
222+
public (GenTensor<T, TWrapper>, int[]) RowEchelonFormPermuteSafeDivision()
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=> EchelonForm<T, TWrapper>.RowEchelonFormPermuteSafeDivision(this);
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/// <summary>
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/// Decomposes a matrix into a triangular one.
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=> EchelonForm<T, TWrapper>.RowEchelonFormSafeDivision(this);
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/// <summary>
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/// Decomposes a matrix into a triangular one.
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/// Is of the Row Echelon Form (leading elements are ones).
@@ -215,7 +249,6 @@ public GenTensor<T, TWrapper> RowEchelonFormLeadingOnesSafeDivision()
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=> EchelonForm<T, TWrapper>.RowEchelonFormLeadingOnesSafeDivision(this);
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/// <summary>
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/// Finds the reduced echelon form of a matrix.
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/// </summary>
@@ -228,6 +261,16 @@ public GenTensor<T, TWrapper> ReducedRowEchelonFormSimple()
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/// </summary>
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public GenTensor<T, TWrapper> ReducedRowEchelonFormSafeDivision()
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=> EchelonForm<T, TWrapper>.ReducedRowEchelonFormSafeDivision(this);
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/// <summary>
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/// Finds the reduced echelon form of a matrix.
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/// Uses safe division, i. e. perform division only when computing the final result.
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///
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/// Additionally returns row permutation
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/// </summary>
271+
public (GenTensor<T, TWrapper>, int[]) ReducedRowEchelonFormPermuteSafeDivision()
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=> EchelonForm<T, TWrapper>.ReducedRowEchelonFormPermuteSafeDivision(this);
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#endregion
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#region Determinant
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/// </summary>
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public void TensorMatrixInvert()
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=> Inversion<T, TWrapper>.TensorMatrixInvert(this);
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#endregion
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#region Elementary matrix operations
@@ -398,70 +442,80 @@ public static GenTensor<T, TWrapper> TensorMatrixMultiply(GenTensor<T, TWrapper>
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/// T1 + T2
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> PiecewiseAdd(GenTensor<T, TWrapper> a, GenTensor<T, TWrapper> b, Threading threading = Threading.Single)
445+
public static GenTensor<T, TWrapper> PiecewiseAdd(GenTensor<T, TWrapper> a, GenTensor<T, TWrapper> b,
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Threading threading = Threading.Single)
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=> PiecewiseArithmetics<T, TWrapper>.PiecewiseAdd(a, b, threading);
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/// <summary>
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/// T1 - T2
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> PiecewiseSubtract(GenTensor<T, TWrapper> a, GenTensor<T, TWrapper> b, Threading threading = Threading.Single)
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public static GenTensor<T, TWrapper> PiecewiseSubtract(GenTensor<T, TWrapper> a, GenTensor<T, TWrapper> b,
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Threading threading = Threading.Single)
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=> PiecewiseArithmetics<T, TWrapper>.PiecewiseSubtract(a, b, threading);
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/// <summary>
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/// T1 * T2
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> PiecewiseMultiply(GenTensor<T, TWrapper> a, GenTensor<T, TWrapper> b, Threading threading = Threading.Single)
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public static GenTensor<T, TWrapper> PiecewiseMultiply(GenTensor<T, TWrapper> a, GenTensor<T, TWrapper> b,
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Threading threading = Threading.Single)
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=> PiecewiseArithmetics<T, TWrapper>.PiecewiseMultiply(a, b, threading);
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/// <summary>
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/// T1 / T2
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> PiecewiseDivide(GenTensor<T, TWrapper> a, GenTensor<T, TWrapper> b, Threading threading = Threading.Single)
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public static GenTensor<T, TWrapper> PiecewiseDivide(GenTensor<T, TWrapper> a, GenTensor<T, TWrapper> b,
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Threading threading = Threading.Single)
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=> PiecewiseArithmetics<T, TWrapper>.PiecewiseDivide(a, b, threading);
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/// <summary>
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/// T1 + const
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> PiecewiseAdd(GenTensor<T, TWrapper> a, T b, Threading threading = Threading.Single)
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public static GenTensor<T, TWrapper> PiecewiseAdd(GenTensor<T, TWrapper> a, T b,
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Threading threading = Threading.Single)
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=> PiecewiseArithmetics<T, TWrapper>.PiecewiseAdd(a, b, threading);
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/// <summary>
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/// T1 - const
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> PiecewiseSubtract(GenTensor<T, TWrapper> a, T b, Threading threading = Threading.Single)
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public static GenTensor<T, TWrapper> PiecewiseSubtract(GenTensor<T, TWrapper> a, T b,
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Threading threading = Threading.Single)
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=> PiecewiseArithmetics<T, TWrapper>.PiecewiseSubtract(a, b, threading);
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/// <summary>
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/// const - T1
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> PiecewiseSubtract(T a, GenTensor<T, TWrapper> b, Threading threading = Threading.Single)
493+
public static GenTensor<T, TWrapper> PiecewiseSubtract(T a, GenTensor<T, TWrapper> b,
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Threading threading = Threading.Single)
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=> PiecewiseArithmetics<T, TWrapper>.PiecewiseSubtract(a, b, threading);
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/// <summary>
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/// T1 * const
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> PiecewiseMultiply(GenTensor<T, TWrapper> a, T b, Threading threading = Threading.Single)
501+
public static GenTensor<T, TWrapper> PiecewiseMultiply(GenTensor<T, TWrapper> a, T b,
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Threading threading = Threading.Single)
451503
=> PiecewiseArithmetics<T, TWrapper>.PiecewiseMultiply(a, b, threading);
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/// <summary>
454506
/// T1 / const
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
457-
public static GenTensor<T, TWrapper> PiecewiseDivide(GenTensor<T, TWrapper> a, T b, Threading threading = Threading.Single)
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public static GenTensor<T, TWrapper> PiecewiseDivide(GenTensor<T, TWrapper> a, T b,
510+
Threading threading = Threading.Single)
458511
=> PiecewiseArithmetics<T, TWrapper>.PiecewiseDivide(a, b, threading);
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460513
/// <summary>
461514
/// const / T1
462515
/// </summary>
463516
[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GenTensor<T, TWrapper> PiecewiseDivide(T a, GenTensor<T, TWrapper> b, Threading threading = Threading.Single)
517+
public static GenTensor<T, TWrapper> PiecewiseDivide(T a, GenTensor<T, TWrapper> b,
518+
Threading threading = Threading.Single)
465519
=> PiecewiseArithmetics<T, TWrapper>.PiecewiseDivide(a, b, threading);
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#endregion
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494548
#endregion
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550+
#region Decompositions
551+
552+
/// <summary>
553+
/// https://www.geeksforgeeks.org/l-u-decomposition-system-linear-equations/
554+
/// </summary>
555+
/// <returns>
556+
/// LU decomposition
557+
/// </returns>
558+
public (GenTensor<T, TWrapper> l, GenTensor<T, TWrapper> u) LuDecomposition()
559+
=> LuDecomposition<T, TWrapper>.Decompose(this);
560+
561+
/// <summary>
562+
/// Find PLU decomposition: matrices P, L, U such that for original matrix A: PA = LU.
563+
///
564+
/// P stands for permutation matrix, permutations are made during the Gauss elimination process
565+
/// L stands for LIBERTY lower triangle matrix
566+
/// U stands for upper triangle matrix
567+
///
568+
/// Algorithm, given matrix A:
569+
/// 1. Form an adjacent matrix (A|E)
570+
/// 2. Find row echelon form of that matrix (U|L_0) and permutation of the rows
571+
/// 3. Form permutation matrix P such that P_ij = \delta_{}
572+
/// 4. Compute L = P * L_0^{-1}
573+
///
574+
/// Results are: P, L, U
575+
/// </summary>
576+
/// <returns>
577+
/// LUP decomposition of given matrix
578+
/// </returns>
579+
public (GenTensor<T, TWrapper> p, GenTensor<T, TWrapper> l, GenTensor<T, TWrapper> u) PluDecomposition()
580+
=> PluDecomposition<T, TWrapper>.Decompose(this);
581+
582+
#endregion
583+
496584
#region ToString & GetHashCode
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498586
/// <inheritdoc/>
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517605
/// <summary>
518606
/// Calls VectorCrossProduct for every vector in the tensor
519607
/// </summary>
520-
public static GenTensor<T, TWrapper> TensorVectorCrossProduct(GenTensor<T, TWrapper> a, GenTensor<T, TWrapper> b)
608+
public static GenTensor<T, TWrapper> TensorVectorCrossProduct(GenTensor<T, TWrapper> a,
609+
GenTensor<T, TWrapper> b)
521610
=> VectorProduct<T, TWrapper>.TensorVectorCrossProduct(a, b);
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523612
/// <summary>
@@ -562,6 +651,7 @@ public GenTensor<T, TWrapper> Forward()
562651
#endregion
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564653
#region Serialization
654+
565655
/*
566656
* Serialization protocol:
567657
*
@@ -595,6 +685,7 @@ public byte[] Serialize()
595685
/// </returns>
596686
public static GenTensor<T, TWrapper> Deserialize(byte[] data)
597687
=> Serializer<T, TWrapper>.Deserialize(data);
688+
598689
#endregion
599690
}
600-
}
691+
}

‎GenericTensor/Functions/Determinant.cs

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@@ -87,7 +87,7 @@ internal static T DeterminantGaussianSafeDivision(GenTensor<T, TWrapper> t, int
8787
return t.GetValueNoCheck(0, 0);
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8989
var n = diagLength;
90-
var elemMatrix = EchelonForm<T, TWrapper>.InnerGaussianEliminationSafeDivision(t, n, n, out var swapCount);
90+
var elemMatrix = EchelonForm<T, TWrapper>.InnerGaussianEliminationSafeDivision(t, n, n, null, out var swapCount);
9191

9292
var det = default(EchelonForm<T, TWrapper>.WrapperSafeDivisionWrapper<T, TWrapper>).CreateOne();
9393
for (int i = 0; i < n; i++)

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