turns-00030.parquet:8166
265cca374a5fe373b76008ee
turn 1/1o1-preview-2024-09-12EnglishEgypt5679 words
degenerate_repetitionAbsentFinal dense release
USER
using System.Buffers; using System.Collections; using System.Collections.Immutable; using System.Numerics; using System.Text; using System.Text.Json; namespace HyperMath.Core { public partial class Tensor : IDisposable, ICloneable, IEquatable<Tensor>, IEnumerable where T : unmanaged, INumber, IExponentialFunctions, ITrigonometricFunctions { #region Fields and Properties private readonly T[] data; private readonly int[] shape; private readonly int[] strides; private readonly int totalSize; private bool disposed = false; private readonly bool isRowMajor; public int[] Shape => (int[])shape.Clone(); public int TotalSize => totalSize; public static int ParallelizationThreshold { get; set; } = 1000; public int Rank => shape.Length; #endregion #region Constructors public Tensor(bool isRowMajor, params int[] dimensions) { if (dimensions == null || dimensions.Length == 0) throw new ArgumentException("Tensor must have at least one dimension.", nameof(dimensions)); foreach (var dim in dimensions) { if (dim <= 0) throw new ArgumentException("Each dimension size must be positive.", nameof(dimensions)); } shape = dimensions.ToArray(); this.isRowMajor = isRowMajor; strides = CalculateStrides(shape, isRowMajor); totalSize = strides[0] * shape[0]; data = ArrayPool.Shared.Rent(totalSize); Array.Clear(data, 0, totalSize); } public Tensor(params int[] dimensions) : this(true, dimensions) { } private Tensor(T[] data, int[] shape, int[] strides) { this.data = data; this.shape = shape; this.strides = strides; this.totalSize = strides[0] * shape[0]; } #endregion #region Indexer and Element Access public T this[params int[] indices] { get { EnsureNotDisposed(); int flatIndex = CalculateFlatIndex(indices); return data[flatIndex]; } set { EnsureNotDisposed(); int flatIndex = CalculateFlatIndex(indices); data[flatIndex] = value; } } #endregion #region Cloning and Equality public object Clone() { EnsureNotDisposed(); T[] newData = ArrayPool.Shared.Rent(totalSize); Array.Copy(data, 0, newData, 0, totalSize); int[] newShape = (int[])shape.Clone(); int[] newStrides = (int[])strides.Clone(); return new Tensor(newData, newShape, newStrides); } public bool Equals(Tensor? other) { EnsureNotDisposed(); if (other == null) return false; if (ReferenceEquals(this, other)) return true; if (!shape.SequenceEqual(other.shape)) return false; for (int i = 0; i < totalSize; i++) { if (!data[i].Equals(other.data[i])) return false; } return true; } #endregion #region IEnumerable Implementation public IEnumerator GetEnumerator() { EnsureNotDisposed(); for (int i = 0; i < totalSize; i++) { yield return data[i]; } } IEnumerator IEnumerable.GetEnumerator() { return GetEnumerator(); } #endregion #region Arithmetic Operations public static Tensor operator +(Tensor a, Tensor b) { return a.Add(b); } public static Tensor operator -(Tensor a, Tensor b) { return a.Subtract(b); } public static Tensor operator *(Tensor a, Tensor b) { return a.Multiply(b); } public static Tensor operator /(Tensor a, Tensor b) { return a.Divide(b); } public static Tensor operator +(Tensor a, T scalar) { return a.AddScalar(scalar); } public static Tensor operator +(T scalar, Tensor a) { return a.AddScalar(scalar); } public static Tensor operator -(Tensor a, T scalar) { return a.SubtractScalar(scalar); } public static Tensor operator -(T scalar, Tensor a) { return a.Negate().AddScalar(scalar); } public static Tensor operator *(Tensor a, T scalar) { return a.MultiplyScalar(scalar); } public static Tensor operator *(T scalar, Tensor a) { return a.MultiplyScalar(scalar); } public static Tensor operator /(Tensor a, T scalar) { return a.DivideScalar(scalar); } public static Tensor operator /(T scalar, Tensor a) { return a.Reciprocal().MultiplyScalar(scalar); } public Tensor Add(Tensor other) { return ElementWiseOperation(other, (x, y) => x + y); } public Tensor Subtract(Tensor other) { return ElementWiseOperation(other, (x, y) => x - y); } public Tensor Multiply(Tensor other) { return ElementWiseOperation(other, (x, y) => x * y); } public Tensor Divide(Tensor other) { return ElementWiseOperation(other, (x, y) => x / y); } public Tensor AddScalar(T scalar) { return ScalarOperation((x) => x + scalar); } public Tensor SubtractScalar(T scalar) { return ScalarOperation((x) => x - scalar); } public Tensor MultiplyScalar(T scalar) { return ScalarOperation((x) => x * scalar); } public Tensor DivideScalar(T scalar) { return ScalarOperation((x) => x / scalar); } public Tensor Negate() { return ScalarOperation((x) => -x); } public Tensor Reciprocal() { return ScalarOperation((x) => T.One / x); } public async Task<Tensor> AddAsync(Tensor other) { return await Task.Run(() => Add(other)); } public async Task<Tensor> SubtractAsync(Tensor other) { return await Task.Run(() => Subtract(other)); } public async Task<Tensor> MultiplyAsync(Tensor other) { return await Task.Run(() => Multiply(other)); } public async Task<Tensor> DivideAsync(Tensor other) { return await Task.Run(() => Divide(other)); } #endregion #region Reduction Operations public T Sum() { EnsureNotDisposed(); if (totalSize >= ParallelizationThreshold) { T sum = T.Zero; object lockObj = new object(); Parallel.For(0, totalSize, () => T.Zero, (i, state, localSum) => { localSum += data[i]; return localSum; }, (localSum) => { lock (lockObj) { sum += localSum; } }); return sum; } else { T sum = T.Zero; for (int i = 0; i < totalSize; i++) { sum += data[i]; } return sum; } } public T Mean() { EnsureNotDisposed(); T sum = Sum(); return sum / T.CreateChecked(totalSize); } public T Max() { EnsureNotDisposed(); if (totalSize == 0) throw new InvalidOperationException("Cannot compute Max of an empty tensor."); if (totalSize >= ParallelizationThreshold) { T max = data[0]; object lockObj = new object(); Parallel.For(0, totalSize, () => data[0], (i, state, localMax) => { if (data[i] > localMax) localMax = data[i]; return localMax; }, (localMax) => { lock (lockObj) { if (localMax > max) max = localMax; } }); return max; } else { T max = data[0]; for (int i = 1; i < totalSize; i++) { if (data[i] > max) max = data[i]; } return max; } } public T Min() { EnsureNotDisposed(); if (totalSize == 0) throw new InvalidOperationException("Cannot compute Min of an empty tensor."); if (totalSize >= ParallelizationThreshold) { T min = data[0]; object lockObj = new object(); Parallel.For(0, totalSize, () => data[0], (i, state, localMin) => { if (data[i] < localMin) localMin = data[i]; return localMin; }, (localMin) => { lock (lockObj) { if (localMin < min) min = localMin; } }); return min; } else { T min = data[0]; for (int i = 1; i < totalSize; i++) { if (data[i] < min) min = data[i]; } return min; } } public Tensor Sum(int axis) { return Reduce(axis, (a, b) => a + b, T.Zero); } public Tensor Mean(int axis) { var sumTensor = Sum(axis); int reduceDim = shape[axis]; T divisor = T.CreateChecked(reduceDim); return sumTensor.DivideScalar(divisor); } public Tensor Max(int axis) { return Reduce(axis, (a, b) => a > b ? a : b); } public Tensor Min(int axis) { return Reduce(axis, (a, b) => a < b ? a : b); } #endregion #region Advanced Operations public Tensor MatMul(Tensor other) { EnsureNotDisposed(); other.EnsureNotDisposed(); var aShape = this.shape; var bShape = other.shape; if (this.Rank == 1 && other.Rank == 1) { if (this.shape[0] != other.shape[0]) throw new ArgumentException("Shapes are not aligned for dot product."); T sum = T.Zero; for (int i = 0; i < this.shape[0]; i++) { sum += this[i] * other[i]; } var resultTensor = new Tensor(); resultTensor.data[0] = sum; return resultTensor; } if (this.Rank == 1) { var aReshaped = this.Reshape(1, this.shape[0]); var partialResult = aReshaped.MatMul(other); return partialResult.Reshape(partialResult.shape.Skip(1).ToArray()); } if (other.Rank == 1) { var bReshaped = other.Reshape(other.shape[0], 1); var partialResult = this.MatMul(bReshaped); return partialResult.Reshape(partialResult.shape.Take(this.Rank - 1).ToArray()); } int n = this.shape[this.Rank - 1]; int k = other.shape[other.Rank - 2]; if (n != k) throw new ArgumentException("Inner dimensions do not match for MatMul."); int[] aBatchShape = this.shape.Take(this.Rank - 2).ToArray(); int[] bBatchShape = other.shape.Take(other.Rank - 2).ToArray(); int[] resultBatchShape = BroadcastShapes(aBatchShape, bBatchShape); int m = this.shape[this.Rank - 2]; int p = other.shape[other.Rank - 1]; int[] resultShape = resultBatchShape.Concat(new int[] { m, p }).ToArray(); Tensor result = new Tensor(resultShape); var aStrides = this.strides; var bStrides = other.strides; var resultStrides = result.strides; int batchSize = resultBatchShape.Aggregate(1, (a, b) => a * b); if (batchSize >= ParallelizationThreshold) { Parallel.For(0, batchSize, batchIndex => { var batchIndices = UnflattenIndex(batchIndex, resultBatchShape); int aBatchOffset = GetBatchOffset(batchIndices, aBatchShape, aStrides); int bBatchOffset = GetBatchOffset(batchIndices, bBatchShape, bStrides); int resultBatchOffset = GetBatchOffset(batchIndices, resultBatchShape, resultStrides); for (int i = 0; i < m; i++) { for (int j = 0; j < p; j++) { T sum = T.Zero; for (int l = 0; l < n; l++) { int aIndex = aBatchOffset + i * aStrides[this.Rank - 2] + l * aStrides[this.Rank - 1]; int bIndex = bBatchOffset + l * bStrides[other.Rank - 2] + j * bStrides[other.Rank - 1]; sum += this.data[aIndex] * other.data[bIndex]; } int resultIndex = resultBatchOffset + i * resultStrides[result.Rank - 2] + j * resultStrides[result.Rank - 1]; result.data[resultIndex] = sum; } } }); } else { for (int batchIndex = 0; batchIndex < batchSize; batchIndex++) { var batchIndices = UnflattenIndex(batchIndex, resultBatchShape); int aBatchOffset = GetBatchOffset(batchIndices, aBatchShape, aStrides); int bBatchOffset = GetBatchOffset(batchIndices, bBatchShape, bStrides); int resultBatchOffset = GetBatchOffset(batchIndices, resultBatchShape, resultStrides); for (int i = 0; i < m; i++) { for (int j = 0; j < p; j++) { T sum = T.Zero; for (int l = 0; l < n; l++) { int aIndex = aBatchOffset + i * aStrides[this.Rank - 2] + l * aStrides[this.Rank - 1]; int bIndex = bBatchOffset + l * bStrides[other.Rank - 2] + j * bStrides[other.Rank - 1]; sum += this.data[aIndex] * other.data[bIndex]; } int resultIndex = resultBatchOffset + i * resultStrides[result.Rank - 2] + j * resultStrides[result.Rank - 1]; result.data[resultIndex] = sum; } } } } return result; } public Tensor Reshape(params int[] newShape) { EnsureNotDisposed(); int newTotalSize = 1; int unknownDimensionIndex = -1; for (int i = 0; i < newShape.Length; i++) { if (newShape[i] == -1) { if (unknownDimensionIndex != -1) throw new ArgumentException("Only one dimension can be set to -1.", nameof(newShape)); unknownDimensionIndex = i; } else if (newShape[i] <= 0) { throw new ArgumentException("Each dimension size must be positive, except for -1.", nameof(newShape)); } else { newTotalSize *= newShape[i]; } } if (unknownDimensionIndex != -1) { if (totalSize % newTotalSize != 0) throw new ArgumentException("The total size of new dimensions must be divisible by the total size of the tensor."); newShape[unknownDimensionIndex] = totalSize / newTotalSize; newTotalSize *= newShape[unknownDimensionIndex]; } else { if (newTotalSize != totalSize) throw new ArgumentException("The total size of new dimensions must be the same as the total size of the tensor."); } var newStrides = CalculateStrides(newShape, isRowMajor); return new Tensor(this.data, newShape, newStrides); } private static int GetBatchOffset(int[] batchIndices, int[] batchShape, int[] strides) { int offset = 0; int rankOffset = strides.Length - batchShape.Length; for (int i = 0; i < batchShape.Length; i++) { int index = batchIndices[i]; int stride = strides[i + rankOffset]; offset += index * stride; } return offset; } public Tensor Transpose(int axis1, int axis2) { EnsureNotDisposed(); if (axis1 < 0 || axis1 >= shape.Length) throw new ArgumentOutOfRangeException(nameof(axis1), "Axis1 is out of bounds."); if (axis2 < 0 || axis2 >= shape.Length) throw new ArgumentOutOfRangeException(nameof(axis2), "Axis2 is out of bounds."); int[] newShape = (int[])shape.Clone(); int[] newStrides = (int[])strides.Clone(); (newShape[axis1], newShape[axis2]) = (newShape[axis2], newShape[axis1]); (newStrides[axis1], newStrides[axis2]) = (newStrides[axis2], newStrides[axis1]); T[] newData = ArrayPool.Shared.Rent(totalSize); int[] indices = new int[shape.Length]; for (int i = 0; i < totalSize; i++) { int remaining = i; for (int j = 0; j < shape.Length; j++) { indices[j] = remaining / strides[j]; remaining %= strides[j]; } (indices[axis1], indices[axis2]) = (indices[axis2], indices[axis1]); int newFlatIndex = 0; for (int j = 0; j < newShape.Length; j++) { newFlatIndex += indices[j] * newStrides[j]; } newData[newFlatIndex] = data[i]; } return new Tensor(newData, newShape, newStrides); } #endregion #region Caching Broadcasting private class BroadcastCacheEntry { public ImmutableArray ResultShape { get; } public ImmutableArray BroadcastStridesA { get; } public ImmutableArray BroadcastStridesB { get; } public BroadcastCacheEntry(ImmutableArray resultShape, ImmutableArray broadcastStridesA, ImmutableArray broadcastStridesB) { ResultShape = resultShape; BroadcastStridesA = broadcastStridesA; BroadcastStridesB = broadcastStridesB; } } private class BroadcastCacheKeyComparer : IEqualityComparer<(ImmutableArray, ImmutableArray)> { public bool Equals((ImmutableArray, ImmutableArray) x, (ImmutableArray, ImmutableArray) y) { if (x.Item1.Length != y.Item1.Length || x.Item2.Length != y.Item2.Length) return false; for (int i = 0; i < x.Item1.Length; i++) { if (x.Item1[i] != y.Item1[i]) return false; } for (int i = 0; i < x.Item2.Length; i++) { if (x.Item2[i] != y.Item2[i]) return false; } return true; } public int GetHashCode((ImmutableArray, ImmutableArray) obj) { int hash = 17; foreach (var dim in obj.Item1) { hash = hash * 31 + dim.GetHashCode(); } foreach (var dim in obj.Item2) { hash = hash * 31 + dim.GetHashCode(); } return hash; } } private class LruCache<K, V> where K : notnull { private readonly int capacity; private readonly LinkedList lruList; private readonly Dictionary<K, (V Value, LinkedListNode Node)> cache; private readonly IEqualityComparer comparer; public LruCache(int capacity, IEqualityComparer? comparer = null) { if (capacity <= 0) throw new ArgumentOutOfRangeException(nameof(capacity), "Capacity must be greater than zero."); this.capacity = capacity; lruList = new LinkedList(); this.comparer = comparer ?? EqualityComparer.Default; cache = new Dictionary<K, (V, LinkedListNode)>(this.comparer); } public bool TryGet(K key, out V? value) { if (cache.TryGetValue(key, out var entry)) { lruList.Remove(entry.Node); lruList.AddFirst(entry.Node); value = entry.Value; return true; } value = default(V); return false; } public void Add(K key, V value) { if (cache.ContainsKey(key)) { var existing = cache[key]; lruList.Remove(existing.Node); lruList.AddFirst(existing.Node); cache[key] = (value, existing.Node); } else { if (cache.Count >= capacity) { if (lruList.Last != null) { var lruKey = lruList.Last.Value; lruList.RemoveLast(); cache.Remove(lruKey); } else { throw new InvalidOperationException("LRU list is empty, cannot remove item."); } } var node = new LinkedListNode(key); lruList.AddFirst(node); cache[key] = (value, node); } } } private static readonly LruCache<(ImmutableArray, ImmutableArray), BroadcastCacheEntry> BroadcastCache = new LruCache<(ImmutableArray, ImmutableArray), BroadcastCacheEntry>(capacity: 1024, comparer: new BroadcastCacheKeyComparer()); private BroadcastCacheEntry GetOrAddBroadcastCache(int[] shapeA, int[] shapeB, int[] otherStrides) { var keyA = shapeA.ToImmutableArray(); var keyB = shapeB.ToImmutableArray(); var cacheKey = (keyA, keyB); if (BroadcastCache.TryGet(cacheKey, out var cachedEntry)) { return cachedEntry; } else { int[] resultShapeArray = BroadcastShapes(shapeA, shapeB); int[] broadcastStridesAArray = GetBroadcastStrides(shapeA, resultShapeArray, this.strides); int[] broadcastStridesBArray = GetBroadcastStrides(shapeB, resultShapeArray, otherStrides); var resultShape = resultShapeArray.ToImmutableArray(); var broadcastStridesA = broadcastStridesAArray.ToImmutableArray(); var broadcastStridesB = broadcastStridesBArray.ToImmutableArray(); var newEntry = new BroadcastCacheEntry(resultShape, broadcastStridesA, broadcastStridesB); BroadcastCache.Add(cacheKey, newEntry); return newEntry; } } #endregion #region Helper Methods private Tensor ElementWiseOperation(Tensor other, Func<T, T, T> operation) { EnsureNotDisposed(); other.EnsureNotDisposed(); var broadcastInfo = GetOrAddBroadcastCache(this.shape, other.shape, other.strides); int[] resultShape = broadcastInfo.ResultShape.ToArray(); int resultSize = resultShape.Aggregate(1, (a, b) => a * b); Tensor result = new Tensor(resultShape); if (resultSize >= ParallelizationThreshold) { Parallel.For(0, resultSize, i => { int[] indices = UnflattenIndex(i, resultShape); int indexA = GetFlatIndex(indices, broadcastInfo.BroadcastStridesA.ToArray(), isRowMajor); int indexB = GetFlatIndex(indices, broadcastInfo.BroadcastStridesB.ToArray(), isRowMajor); result.data[i] = operation(this.data[indexA], other.data[indexB]); }); } else { for (int i = 0; i < resultSize; i++) { int[] indices = UnflattenIndex(i, resultShape); int indexA = GetFlatIndex(indices, broadcastInfo.BroadcastStridesA.ToArray(), isRowMajor); int indexB = GetFlatIndex(indices, broadcastInfo.BroadcastStridesB.ToArray(), isRowMajor); result.data[i] = operation(this.data[indexA], other.data[indexB]); } } return result; } private Tensor ScalarOperation(Func<T, T> operation) { EnsureNotDisposed(); T[] resultData = ArrayPool.Shared.Rent(totalSize); if (totalSize >= ParallelizationThreshold) { Parallel.For(0, totalSize, i => { resultData[i] = operation(data[i]); }); } else { for (int i = 0; i < totalSize; i++) { resultData[i] = operation(data[i]); } } return new Tensor(resultData, (int[])shape.Clone(), (int[])strides.Clone()); } private Tensor Reduce(int axis, Func<T, T, T> reduction, T initial) { EnsureNotDisposed(); if (axis < 0 || axis >= shape.Length) throw new ArgumentOutOfRangeException(nameof(axis)); int[] newShape = shape.Where((s, i) => i != axis).ToArray(); int[] newStrides = CalculateStrides(newShape, isRowMajor); int reduceDim = shape[axis]; int newTotalSize = newShape.Aggregate(1, (a, b) => a * b); T[] resultData = ArrayPool.Shared.Rent(newTotalSize); if (newTotalSize == 0) throw new InvalidOperationException("Reduction resulted in an empty tensor."); Array.Fill(resultData, initial); if (totalSize >= ParallelizationThreshold) { object lockObj = new object(); Parallel.For(0, totalSize, () => new T[1] { initial }, (i, state, localValue) => { var indices = UnflattenIndex(i, shape); int resultIndex = CalculateResultIndex(indices, axis, newStrides); localValue[0] = reduction(localValue[0], data[i]); return localValue; }, (localValue) => { if (localValue[0].Equals(initial) && !initial.Equals(default(T))) return; lock (lockObj) { for (int j = 0; j < 1; j++) { resultData[j] = reduction(resultData[j], localValue[j]); } } }); } else { for (int i = 0; i < totalSize; i++) { var indices = UnflattenIndex(i, shape); int resultIndex = CalculateResultIndex(indices, axis, newStrides); resultData[resultIndex] = reduction(resultData[resultIndex], data[i]); } } return new Tensor(resultData, newShape, newStrides); } private Tensor Reduce(int axis, Func<T, T, T> reduction) { EnsureNotDisposed(); if (axis < 0 || axis >= shape.Length) throw new ArgumentOutOfRangeException(nameof(axis)); int[] newShape = shape.Where((s, i) => i != axis).ToArray(); int[] newStrides = CalculateStrides(newShape, isRowMajor); int newTotalSize = newShape.Aggregate(1, (a, b) => a * b); T[] resultData = ArrayPool.Shared.Rent(newTotalSize); bool[] initialized = new bool[newTotalSize]; for (int i = 0; i < totalSize; i++) { var indices = UnflattenIndex(i, shape); int resultIndex = CalculateResultIndex(indices, axis, newStrides); T value = data[i]; if (!initialized[resultIndex]) { resultData[resultIndex] = value; initialized[resultIndex] = true; } else { resultData[resultIndex] = reduction(resultData[resultIndex], value); } } return new Tensor(resultData, newShape, newStrides); } private static int[] CalculateStrides(int[] shape, bool isRowMajor) { int[] strides = new int[shape.Length]; if (isRowMajor) { int stride = 1; for (int i = shape.Length - 1; i >= 0; i--) { strides[i] = stride; stride *= shape[i]; } } else { int stride = 1; for (int i = 0; i < shape.Length; i++) { strides[i] = stride; stride *= shape[i]; } } return strides; } private int CalculateFlatIndex(int[] indices) { if (indices == null) throw new ArgumentNullException(nameof(indices)); if (indices.Length != shape.Length) throw new ArgumentException("Number of indices must match number of tensor dimensions.", nameof(indices)); int flatIndex = 0; if (isRowMajor) { for (int i = 0; i < indices.Length; i++) { int index = indices[i]; int dim = shape[i]; if (index < 0 || index >= dim) throw new ArgumentOutOfRangeException(nameof(indices), $"Index {index} out of bounds for dimension {i} of size {dim}."); flatIndex += indices[i] * strides[i]; } } else { for (int i = indices.Length - 1; i >= 0; i--) { int index = indices[i]; int dim = shape[i]; if (index < 0 || index >= dim) throw new ArgumentOutOfRangeException(nameof(indices), $"Index {index} out of bounds for dimension {i} of size {dim}."); flatIndex += indices[i] * strides[i]; } } return flatIndex; } private int[] UnflattenIndex(int flatIndex, int[] shape) { int[] indices = new int[shape.Length]; if (isRowMajor) { for (int i = 0; i < shape.Length; i++) { indices[i] = flatIndex / strides[i]; flatIndex %= strides[i]; } } else { for (int i = shape.Length - 1; i >= 0; i--) { indices[i] = flatIndex / strides[i]; flatIndex %= strides[i]; } } return indices; } private static int GetFlatIndex(int[] indices, int[] strides, bool isRowMajor) { int flatIndex = 0; if (isRowMajor) { for (int i = 0; i < indices.Length; i++) { flatIndex += indices[i] * strides[i]; } } else { for (int i = indices.Length - 1; i >= 0; i--) { flatIndex += indices[i] * strides[i]; } } return flatIndex; } private static int[] BroadcastShapes(int[] shapeA, int[] shapeB) { int maxRank = Math.Max(shapeA.Length, shapeB.Length); int[] resultShape = new int[maxRank]; for (int i = 0; i < maxRank; i++) { int dimA = i < (maxRank - shapeA.Length) ? 1 : shapeA[i - (maxRank - shapeA.Length)]; int dimB = i < (maxRank - shapeB.Length) ? 1 : shapeB[i - (maxRank - shapeB.Length)]; if (dimA != dimB && dimA != 1 && dimB != 1) throw new InvalidOperationException("Shapes are not broadcastable."); resultShape[i] = Math.Max(dimA, dimB); } return resultShape; } private static int[] GetBroadcastStrides(int[] originalShape, int[] resultShape, int[] originalStrides) { int originalRank = originalShape.Length; int resultRank = resultShape.Length; int offset = resultRank - originalRank; int[] broadcastStrides = new int[resultRank]; for (int i = 0; i < resultRank; i++) { if (i < offset) { broadcastStrides[i] = 0; } else { if (originalShape[i - offset] == resultShape[i]) broadcastStrides[i] = originalStrides[i - offset]; else if (originalShape[i - offset] == 1) broadcastStrides[i] = 0; else throw new InvalidOperationException("Shapes are not broadcastable."); } } return broadcastStrides; } private int CalculateResultIndex(int[] indices, int axis, int[] newStrides) { int resultIndex = 0; for (int j = 0; j < indices.Length; j++) { if (j == axis) continue; resultIndex += indices[j] * newStrides[j < axis ? j : j - 1]; } return resultIndex; } private void EnsureNotDisposed() { if (disposed) throw new ObjectDisposedException(nameof(Tensor)); } #endregion #region Serialization public string Display() { EnsureNotDisposed(); StringBuilder display = new StringBuilder(); if (shape.Length == 1) { display.Append("["); for (int i = 0; i < shape[0]; i++) { display.Append(this[i]); if (i < shape[0] - 1) display.Append(", "); } display.AppendLine("]"); } else if (shape.Length == 2) { for (int i = 0; i < shape[0]; i++) { display.Append("["); for (int j = 0; j < shape[1]; j++) { display.Append(this[i, j]); if (j < shape[1] - 1) display.Append(", "); } display.AppendLine("]"); } } else { display.AppendLine("Tensor data display is only implemented for 1D and 2D tensors."); } return display.ToString(); } public void ToJson(Stream stream) { EnsureNotDisposed(); using var writer = new Utf8JsonWriter(stream, new JsonWriterOptions { Indented = false }); writer.WriteStartObject(); writer.WritePropertyName("shape"); writer.WriteStartArray(); foreach (var dim in shape) { writer.WriteNumberValue(dim); } writer.WriteEndArray(); writer.WritePropertyName("data"); writer.WriteStartArray(); for (int i = 0; i < totalSize; i++) { if (typeof(T) == typeof(float)) writer.WriteNumberValue(Convert.ToSingle(data[i])); else if (typeof(T) == typeof(double)) writer.WriteNumberValue(Convert.ToDouble(data[i])); else if (typeof(T) == typeof(int)) writer.WriteNumberValue(Convert.ToInt32(data[i])); else if (typeof(T) == typeof(long)) writer.WriteNumberValue(Convert.ToInt64(data[i])); else throw new InvalidOperationException($"Unsupported type {typeof(T)}"); } writer.WriteEndArray(); writer.WriteEndObject(); } public static Tensor FromJson(Stream stream) { using var jsonDoc = JsonDocument.Parse(stream); var root = jsonDoc.RootElement; var shapeElement = root.GetProperty("shape"); int[] shape = shapeElement.EnumerateArray().Select(x => x.GetInt32()).ToArray(); var tensor = new Tensor(shape); var dataElement = root.GetProperty("data"); int index = 0; var data = tensor.data; foreach (var item in dataElement.EnumerateArray()) { if (typeof(T) == typeof(float)) data[index++] = (T)(object)item.GetSingle(); else if (typeof(T) == typeof(double)) data[index++] = (T)(object)item.GetDouble(); else if (typeof(T) == typeof(int)) data[index++] = (T)(object)item.GetInt32(); else if (typeof(T) == typeof(long)) data[index++] = (T)(object)item.GetInt64(); else throw new InvalidOperationException($"Unsupported type {typeof(T)}"); } return tensor; } public void ToBinary(Stream stream) { EnsureNotDisposed(); using var writer = new BinaryWriter(stream, System.Text.Encoding.UTF8, leaveOpen: true); writer.Write(shape.Length); foreach (var dim in shape) { writer.Write(dim); } for (int i = 0; i < totalSize; i++) { if (typeof(T) == typeof(float)) writer.Write(Convert.ToSingle(data[i])); else if (typeof(T) == typeof(double)) writer.Write(Convert.ToDouble(data[i])); else if (typeof(T) == typeof(int)) writer.Write(Convert.ToInt32(data[i])); else if (typeof(T) == typeof(long)) writer.Write(Convert.ToInt64(data[i])); else throw new InvalidOperationException($"Unsupported type {typeof(T)}"); } } public static Tensor FromBinary(Stream stream) { using var reader = new BinaryReader(stream, System.Text.Encoding.UTF8, leaveOpen: true); int dimensions = reader.ReadInt32(); int[] shape = new int[dimensions]; for (int i = 0; i < dimensions; i++) { shape[i] = reader.ReadInt32(); } var tensor = new Tensor(shape); var data = tensor.data; for (int i = 0; i < tensor.totalSize; i++) { if (typeof(T) == typeof(float)) data[i] = (T)(object)reader.ReadSingle(); else if (typeof(T) == typeof(double)) data[i] = (T)(object)reader.ReadDouble(); else if (typeof(T) == typeof(int)) data[i] = (T)(object)reader.ReadInt32(); else if (typeof(T) == typeof(long)) data[i] = (T)(object)reader.ReadInt64(); else throw new InvalidOperationException($"Unsupported type {typeof(T)}"); } return tensor; } #endregion #region Dispose Pattern public void Dispose() { if (!disposed) { ArrayPool.Shared.Return(data, clearArray: true); disposed = true; } } #endregion } }
based on best practices and academic knowledge in software engineering and numerical computing implement the following improvements
only generate new code or code changes, don't generate unchanged code and make it focused on the task at hand and provide explanation so I can avoid any copy paste errors and to avoid human confusion.
Review the reduction methods (Reduce, Sum, Max, Min) to ensure thread safety and correctness when using parallel processing. Consider using appropriate synchronization mechanisms.
Provide methods for common tensor operations such as dot, slicing, stacking, and reshaping beyond what is currently implemented. This will enhance the usability of the class in neural network implementations.
Implement automatic differentiation capabilities or provide mechanisms to compute gradients efficiently.ASSISTANT
**1. Reviewing and fixing the reduction methods for thread safety and correctness:**
The reduction methods `Reduce`, `Sum`, `Max`, and `Min` need to be thread-safe and correct when using parallel processing. Here is the revised `Reduce` method with proper parallelization:
```csharp
private Tensor Reduce(int axis, Func<T, T, T> reduction, T initial)
{
EnsureNotDisposed();
if (axis < 0 || axis >= shape.Length)
throw new ArgumentOutOfRangeException(nameof(axis));
int[] newShape = shape.Where((s, i) => i != axis).ToArray();
int[] newStrides = CalculateStrides(newShape, isRowMajor);
int newTotalSize = newShape.Aggregate(1, (a, b) => a * b);
T[] resultData = ArrayPool<T>.Shared.Rent(newTotalSize);
// Initialize resultData with the initial value
for (int i = 0; i < newTotalSize; i++)
{
resultData[i] = initial;
}
if (newTotalSize >= ParallelizationThreshold)
{
Parallel.For(0, newTotalSize, resultIndex =>
{
T aggregatedValue = initial;
var resultIndices = UnflattenIndex(resultIndex, newShape);
for (int axisIndex = 0; axisIndex < shape[axis]; axisIndex++)
{
// Build indices for the original tensor
int[] dataIndices = new int[shape.Length];
int resultDim = 0;
for (int i = 0; i < shape.Length; i++)
{
if (i == axis)
{
dataIndices[i] = axisIndex;
}
else
{
dataIndices[i] = resultIndices[resultDim++];
}
}
int flatIndex = CalculateFlatIndex(dataIndices);
aggregatedValue = reduction(aggregatedValue, data[flatIndex]);
}
resultData[resultIndex] = aggregatedValue;
});
}
else
{
for (int resultIndex = 0; resultIndex < newTotalSize; resultIndex++)
{
T aggregatedValue = initial;
var resultIndices = UnflattenIndex(resultIndex, newShape);
for (int axisIndex = 0; axisIndex < shape[axis]; axisIndex++)
{
// Build indices for the original tensor
int[] dataIndices = new int[shape.Length];
int resultDim = 0;
for (int i = 0; i < shape.Length; i++)
{
if (i == axis)
{
dataIndices[i] = axisIndex;
}
else
{
dataIndices[i] = resultIndices[resultDim++];
}
}
int flatIndex = CalculateFlatIndex(dataIndices);
aggregatedValue = reduction(aggregatedValue, data[flatIndex]);
}
resultData[resultIndex] = aggregatedValue;
}
}
return new Tensor(resultData, newShape, newStrides);
}
```
**Explanation:**
- **Thread Safety and Correctness:** The revised `Reduce` method ensures that there's no shared state mutation across threads. Each thread operates on its own `aggregatedValue` and writes to a unique position in `resultData`, avoiding data races.
- **Efficient Parallelization:** We parallelize over `newTotalSize`, which represents the size of the reduced tensor. Each thread computes reduction over the specified axis for a slice of the tensor.
- **Avoiding Locks:** Since each thread writes to a unique index in `resultData`, we don't need synchronization mechanisms like locks, enhancing performance.
**Updated `Sum`, `Mean`, `Max`, and `Min` methods using the revised `Reduce`:**
```csharp
public T Sum()
{
EnsureNotDisposed();
T sum = T.Zero;
if (totalSize >= ParallelizationThreshold)
{
object lockObj = new object();
Parallel.For(0, totalSize, () => T.Zero, (i, state, localSum) =>
{
localSum += data[i];
return localSum;
},
localSum =>
{
lock (lockObj)
{
sum += localSum;
}
});
}
else
{
for (int i = 0; i < totalSize; i++)
{
sum += data[i];
}
}
return sum;
}
public T Max()
{
EnsureNotDisposed();
if (totalSize == 0)
throw new InvalidOperationException("Cannot compute Max of an empty tensor.");
T max = data[0];
if (totalSize >= ParallelizationThreshold)
{
object lockObj = new object();
Parallel.For(0, totalSize, () => data[0], (i, state, localMax) =>
{
if (data[i] > localMax) localMax = data[i];
return localMax;
},
localMax =>
{
lock (lockObj)
{
if (localMax > max) max = localMax;
}
});
}
else
{
for (int i = 1; i < totalSize; i++)
{
if (data[i] > max) max = data[i];
}
}
return max;
}
public T Min()
{
EnsureNotDisposed();
if (totalSize == 0)
throw new InvalidOperationException("Cannot compute Min of an empty tensor.");
T min = data[0];
if (totalSize >= ParallelizationThreshold)
{
object lockObj = new object();
Parallel.For(0, totalSize, () => data[0], (i, state, localMin) =>
{
if (data[i] < localMin) localMin = data[i];
return localMin;
},
localMin =>
{
lock (lockObj)
{
if (localMin < min) min = localMin;
}
});
}
else
{
for (int i = 1; i < totalSize; i++)
{
if (data[i] < min) min = data[i];
}
}
return min;
}
public Tensor Sum(int axis)
{
return Reduce(axis, (a, b) => a + b, T.Zero);
}
public Tensor Mean(int axis)
{
var sumTensor = Sum(axis);
int reduceDim = shape[axis];
T divisor = T.CreateChecked(reduceDim);
return sumTensor.DivideScalar(divisor);
}
public Tensor Max(int axis)
{
EnsureNotDisposed();
return Reduce(axis, (a, b) => (a > b) ? a : b, data[0]);
}
public Tensor Min(int axis)
{
EnsureNotDisposed();
return Reduce(axis, (a, b) => (a < b) ? a : b, data[0]);
}
```
**Changes in `Max` and `Min`:**
- **Added `EnsureNotDisposed()` calls** to prevent operations on disposed objects.
- **Provided initial values for reduction:** For `Max`, initialized with the first element `data[0]` to ensure correctness.
---
**2. Implementing common tensor operations: `Dot`, `Slice`, `Stack`, and enhancing `Reshape`:**
**a. Adding a `Dot` product method:**
```csharp
public T Dot(Tensor other)
{
EnsureNotDisposed();
other.EnsureNotDisposed();
if (this.Rank != 1 || other.Rank != 1)
throw new InvalidOperationException("Dot product is only defined for vectors.");
if (this.shape[0] != other.shape[0])
throw new InvalidOperationException("Vectors must be of the same length.");
T result = T.Zero;
if (this.totalSize >= ParallelizationThreshold)
{
object lockObj = new object();
Parallel.For(0, this.totalSize, () => T.Zero, (i, state, localSum) =>
{
localSum += this.data[i] * other.data[i];
return localSum;
},
localSum =>
{
lock (lockObj)
{
result += localSum;
}
});
}
else
{
for (int i = 0; i < this.totalSize; i++)
{
result += this.data[i] * other.data[i];
}
}
return result;
}
```
**Explanation:**
- Provided a method `Dot` for computing the dot product of two vectors.
- Ensured thread safety using a lock when accumulating the result in parallel.
- Checked that both tensors are vectors of the same length.
**b. Implementing `Slice` method:**
```csharp
public Tensor Slice(params (int start, int? end, int step)[] slices)
{
EnsureNotDisposed();
if (slices.Length != shape.Length)
throw new ArgumentException("Number of slices must match tensor rank.");
List<int> newShape = new List<int>();
List<int> offsets = new List<int>();
List<int> steps = new List<int>();
for (int i = 0; i < shape.Length; i++)
{
int dimSize = shape[i];
var (start, end, step) = slices[i];
if (step == 0)
throw new ArgumentException("Step cannot be zero.", nameof(slices));
int sliceStart = start < 0 ? dimSize + start : start;
int sliceEnd = end.HasValue ? (end.Value < 0 ? dimSize + end.Value : end.Value) : dimSize;
int sliceLength = (int)Math.Ceiling((double)(sliceEnd - sliceStart) / step);
if (sliceLength <= 0)
throw new ArgumentException($"Invalid slice parameters for dimension {i}.");
newShape.Add(sliceLength);
offsets.Add(sliceStart);
steps.Add(step);
}
T[] newData = new T[newShape.Aggregate(1, (a, b) => a * b)];
int[] newStrides = CalculateStrides(newShape.ToArray(), isRowMajor);
if (newData.Length >= ParallelizationThreshold)
{
Parallel.For(0, newData.Length, idx =>
{
int[] newIndices = UnflattenIndex(idx, newShape.ToArray());
int[] originalIndices = new int[shape.Length];
for (int i = 0; i < shape.Length; i++)
{
originalIndices[i] = offsets[i] + newIndices[i] * steps[i];
}
int originalFlatIndex = CalculateFlatIndex(originalIndices);
newData[idx] = data[originalFlatIndex];
});
}
else
{
for (int idx = 0; idx < newData.Length; idx++)
{
int[] newIndices = UnflattenIndex(idx, newShape.ToArray());
int[] originalIndices = new int[shape.Length];
for (int i = 0; i < shape.Length; i++)
{
originalIndices[i] = offsets[i] + newIndices[i] * steps[i];
}
int originalFlatIndex = CalculateFlatIndex(originalIndices);
newData[idx] = data[originalFlatIndex];
}
}
return new Tensor(newData, newShape.ToArray(), newStrides);
}
```
**Explanation:**
- The `Slice` method allows slicing the tensor similar to NumPy's slicing.
- Each slice is defined by a tuple `(start, end, step)`.
- Computes the new shape, offsets, and steps for each dimension.
- Copies the sliced data into a new tensor.
**c. Implementing `Stack` method:**
```csharp
public static Tensor Stack(Tensor[] tensors, int axis = 0)
{
if (tensors == null || tensors.Length == 0)
throw new ArgumentException("At least one tensor must be provided.", nameof(tensors));
int rank = tensors[0].Rank;
foreach (var tensor in tensors)
{
if (tensor.Rank != rank)
throw new ArgumentException("All tensors must have the same rank.", nameof(tensors));
if (!tensor.shape.SequenceEqual(tensors[0].shape))
throw new ArgumentException("All tensors must have the same shape.", nameof(tensors));
}
int[] newShape = tensors[0].shape.ToList();
newShape.Insert(axis, tensors.Length);
int[] newStrides = CalculateStrides(newShape, tensors[0].isRowMajor);
T[] newData = new T[newShape.Aggregate(1, (a, b) => a * b)];
if (newData.Length >= tensors[0].ParallelizationThreshold)
{
Parallel.For(0, tensors.Length, t =>
{
var tensor = tensors[t];
int offset = t * newStrides[axis];
Array.Copy(tensor.data, 0, newData, offset, tensor.totalSize);
});
}
else
{
int offset = 0;
foreach (var tensor in tensors)
{
Array.Copy(tensor.data, 0, newData, offset, tensor.totalSize);
offset += newStrides[axis];
}
}
return new Tensor(newData, newShape.ToArray(), newStrides);
}
```
**Explanation:**
- The `Stack` method stacks a list of tensors along a new axis.
- Checks that all tensors have the same shape.
- Inserts the new axis into the shape and strides.
- Copies data from each tensor into the new tensor at the correct offset.
- Uses parallelization to speed up stacking when dealing with large data.
**d. Enhancing the `Reshape` method:**
The `Reshape` method is already implemented; however, to enhance usability, we can add support for accepting `-1` for unknown dimensions and ensure that reshaping is compatible with the tensor's size.
The existing `Reshape` method already supports `-1` for one dimension. Ensure that this behavior is correct.
**No change needed here since the `Reshape` method already supports this functionality.**
---
**3. Implementing Automatic Differentiation Capabilities:**
Introducing automatic differentiation would involve significant changes to the tensor class. We need to:
- Keep track of operations performed on tensors.
- Build a computation graph.
- Implement a backward pass to compute gradients.
Here's a simplified implementation introducing a `GradTensor` subclass that supports automatic differentiation:
**Modify the `Tensor` class to include gradient tracking:**
```csharp
public partial class Tensor
{
// Existing code...
// For gradient tracking
internal Func<Tensor, Tensor>? GradFunc { get; private set; }
public Tensor? Grad { get; private set; }
public bool RequiresGrad { get; set; } = false;
// Constructors need to set RequiresGrad accordingly.
public Tensor(bool isRowMajor, bool requiresGrad, params int[] dimensions)
: this(isRowMajor, dimensions)
{
RequiresGrad = requiresGrad;
}
public Tensor(bool requiresGrad, params int[] dimensions)
: this(true, requiresGrad, dimensions)
{
}
// Method to zero gradients
public void ZeroGrad()
{
if (RequiresGrad)
{
Grad = null;
}
}
// Backpropagate the gradients
public void Backward(Tensor? gradOutput = null)
{
if (!RequiresGrad)
throw new InvalidOperationException("Cannot call Backward on a tensor that does not require gradients.");
if (gradOutput == null)
{
// If gradOutput is not provided, assume gradient of 1 (scalar output)
gradOutput = new Tensor(T.One);
}
if (Grad == null)
{
Grad = gradOutput;
}
else
{
Grad = Grad.Add(gradOutput);
}
if (GradFunc != null)
{
var inputGrad = GradFunc(gradOutput);
// Assuming single input for simplicity
// In a full implementation, we would need to backpropagate to all inputs
}
}
// Defining operation methods that track gradients
public Tensor Add(Tensor other)
{
var result = ElementWiseOperation(other, (x, y) => x + y);
if (this.RequiresGrad || other.RequiresGrad)
{
result.RequiresGrad = true;
result.GradFunc = (gradOutput) =>
{
if (this.RequiresGrad)
{
this.Backward(gradOutput);
}
if (other.RequiresGrad)
{
other.Backward(gradOutput);
}
return gradOutput;
};
}
return result;
}
// Similar modifications to other operation methods...
}
```
**Explanation:**
- **Gradient Tracking:** Added properties `RequiresGrad`, `GradFunc`, and `Grad` to track gradients and operations.
- **Backward Method:** Implements backpropagation by accumulating gradients and calling gradient functions.
- **Operation Methods:** Modified the `Add` method (as an example) to set up gradient functions when necessary.
**Note:** This is a simplified example to illustrate the concept. In practice, implementing automatic differentiation would require a more robust computation graph, handling multiple inputs and outputs, and carefully managing memory and performance.
---
**Summary:**
- **Reduction Methods:** Corrected the `Reduce` method to ensure thread safety and correctness during parallel execution.
- **Common Tensor Operations:** Added methods for `Dot`, `Slice`, and `Stack`, enhancing the tensor class's usability, especially in neural network implementations.
- **Automatic Differentiation:** Introduced basic gradient tracking and backpropagation mechanics to enable gradient computations.
Please integrate these code changes into your existing `Tensor` class. Remember to validate and test each method thoroughly to ensure correctness.