the following is full  c# class, if you received part of the class then tell me where the code cut off and I will provide you the rest, before we move on with my requests

using System.Buffers; using System.Collections; using System.Numerics; using System.Text; using System.Text.Json; namespace HyperMath.Core { public class Tensor<T> : IDisposable, ICloneable, IEquatable<Tensor<T>>, IEnumerable<T> where T : unmanaged, INumber<T>, IExponentialFunctions<T>, ITrigonometricFunctions<T> { #region Fields and Properties private readonly T[] data; private readonly int[] shape; private readonly int[] strides; private readonly int totalSize; private bool disposed = false; 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(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(); strides = CalculateStrides(shape); totalSize = strides[0] * shape[0]; data = ArrayPool<T>.Shared.Rent(totalSize); Array.Clear(data, 0, totalSize); } 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; } } 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; 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]; } return flatIndex; } #endregion #region Cloning and Equality public object Clone() { EnsureNotDisposed(); T[] newData = ArrayPool<T>.Shared.Rent(totalSize); Array.Copy(data, 0, newData, 0, totalSize); int[] newShape = (int[])shape.Clone(); int[] newStrides = (int[])strides.Clone(); return new Tensor<T>(newData, newShape, newStrides); } public bool Equals(Tensor<T>? other) { EnsureNotDisposed(); if (other == null) return false; if (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<T> 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<T> operator +(Tensor<T> a, Tensor<T> b) { return a.Add(b); } public static Tensor<T> operator -(Tensor<T> a, Tensor<T> b) { return a.Subtract(b); } public static Tensor<T> operator *(Tensor<T> a, Tensor<T> b) { return a.Multiply(b); } public static Tensor<T> operator /(Tensor<T> a, Tensor<T> b) { return a.Divide(b); } public static Tensor<T> operator +(Tensor<T> a, T scalar) { return a.AddScalar(scalar); } public static Tensor<T> operator +(T scalar, Tensor<T> a) { return a.AddScalar(scalar); } public static Tensor<T> operator -(Tensor<T> a, T scalar) { return a.SubtractScalar(scalar); } public static Tensor<T> operator -(T scalar, Tensor<T> a) { return a.Negate().AddScalar(scalar); } public static Tensor<T> operator *(Tensor<T> a, T scalar) { return a.MultiplyScalar(scalar); } public static Tensor<T> operator *(T scalar, Tensor<T> a) { return a.MultiplyScalar(scalar); } public static Tensor<T> operator /(Tensor<T> a, T scalar) { return a.DivideScalar(scalar); } public static Tensor<T> operator /(T scalar, Tensor<T> a) { return a.Reciprocal().MultiplyScalar(scalar); } public Tensor<T> Add(Tensor<T> other) { return ElementWiseOperation(other, (x, y) => x + y); } public Tensor<T> Subtract(Tensor<T> other) { return ElementWiseOperation(other, (x, y) => x - y); } public Tensor<T> Multiply(Tensor<T> other) { return ElementWiseOperation(other, (x, y) => x * y); } public Tensor<T> Divide(Tensor<T> other) { return ElementWiseOperation(other, (x, y) => x / y); } public Tensor<T> AddScalar(T scalar) { return ScalarOperation((x) => x + scalar); } public Tensor<T> SubtractScalar(T scalar) { return ScalarOperation((x) => x - scalar); } public Tensor<T> MultiplyScalar(T scalar) { return ScalarOperation((x) => x * scalar); } public Tensor<T> DivideScalar(T scalar) { return ScalarOperation((x) => x / scalar); } public Tensor<T> Negate() { return ScalarOperation((x) => -x); } public Tensor<T> Reciprocal() { return ScalarOperation((x) => T.One / x); } public async Task<Tensor<T>> AddAsync(Tensor<T> other) { return await Task.Run(() => Add(other)); } public async Task<Tensor<T>> SubtractAsync(Tensor<T> other) { return await Task.Run(() => Subtract(other)); } public async Task<Tensor<T>> MultiplyAsync(Tensor<T> other) { return await Task.Run(() => Multiply(other)); } public async Task<Tensor<T>> DivideAsync(Tensor<T> 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<T> Sum(int axis) { return Reduce(axis, (a, b) => a + b, T.Zero); } public Tensor<T> Mean(int axis) { var sumTensor = Sum(axis); int reduceDim = shape[axis]; T divisor = T.CreateChecked(reduceDim); return sumTensor.DivideScalar(divisor); } public Tensor<T> Max(int axis) { return Reduce(axis, (a, b) => a > b ? a : b); } public Tensor<T> Min(int axis) { return Reduce(axis, (a, b) => a < b ? a : b); } #endregion #region Advanced Operations public Tensor<T> MatMul(Tensor<T> other) { EnsureNotDisposed(); other.EnsureNotDisposed(); if (this.Rank != 2 || other.Rank != 2) throw new ArgumentException("MatMul is only supported for 2D tensors."); if (this.shape[1] != other.shape[0]) throw new ArgumentException($"Inner tensor dimensions must match for MatMul. Found {this.shape[1]} and {other.shape[0]}."); int m = this.shape[0]; int n = this.shape[1]; int p = other.shape[1]; Tensor<T> result = new Tensor<T>(m, p); if (totalSize >= ParallelizationThreshold) { Parallel.For(0, m, i => { for (int j = 0; j < p; j++) { T sum = T.Zero; for (int k = 0; k < n; k++) { sum += this[i, k] * other[k, j]; } result[i, j] = sum; } }); } else { for (int i = 0; i < m; i++) { for (int j = 0; j < p; j++) { T sum = T.Zero; for (int k = 0; k < n; k++) { sum += this[i, k] * other[k, j]; } result[i, j] = sum; } } } return result; } public Tensor<T> 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<T>.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<T>(newData, newShape, newStrides); } #endregion #region Helper Methods private Tensor<T> ElementWiseOperation(Tensor<T> other, Func<T, T, T> operation) { EnsureNotDisposed(); other.EnsureNotDisposed(); int[] resultShape = BroadcastShapes(this.shape, other.shape); int resultSize = resultShape.Aggregate(1, (a, b) => a * b); Tensor<T> result = new Tensor<T>(resultShape); int[] broadcastStridesA = GetBroadcastStrides(this.shape, resultShape, this.strides); int[] broadcastStridesB = GetBroadcastStrides(other.shape, resultShape, other.strides); if (resultSize >= ParallelizationThreshold) { Parallel.For(0, resultSize, i => { int[] indices = UnflattenIndex(i, resultShape); int indexA = GetFlatIndex(indices, broadcastStridesA); int indexB = GetFlatIndex(indices, broadcastStridesB); 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, broadcastStridesA); int indexB = GetFlatIndex(indices, broadcastStridesB); result.data[i] = operation(this.data[indexA], other.data[indexB]); } } return result; } private Tensor<T> ScalarOperation(Func<T, T> operation) { EnsureNotDisposed(); T[] resultData = ArrayPool<T>.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<T>(resultData, (int[])shape.Clone(), (int[])strides.Clone()); } private Tensor<T> 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); int reduceDim = shape[axis]; int newTotalSize = newShape.Aggregate(1, (a, b) => a * b); T[] resultData = ArrayPool<T>.Shared.Rent(newTotalSize); for (int i = 0; i < newTotalSize; i++) { resultData[i] = initial; } int[][] indicesMap = new int[totalSize][]; if (totalSize >= ParallelizationThreshold) { Parallel.For(0, totalSize, i => { indicesMap[i] = UnflattenIndex(i, shape); }); } else { for (int i = 0; i < totalSize; i++) { indicesMap[i] = UnflattenIndex(i, shape); } } if (totalSize >= ParallelizationThreshold) { object lockObj = new object(); Parallel.For(0, totalSize, i => { var indices = indicesMap[i]; int resultIndex = 0; int stride = 1; for (int j = newShape.Length - 1, k = shape.Length - 1; j >= 0; j--, k--) { if (k == axis) k--; resultIndex += indices[k] * stride; stride *= newShape[j]; } T value = data[i]; lock (lockObj) { resultData[resultIndex] = reduction(resultData[resultIndex], value); } }); } else { for (int i = 0; i < totalSize; i++) { var indices = indicesMap[i]; int resultIndex = 0; int stride = 1; for (int j = newShape.Length - 1, k = shape.Length - 1; j >= 0; j--, k--) { if (k == axis) k--; resultIndex += indices[k] * stride; stride *= newShape[j]; } T value = data[i]; resultData[resultIndex] = reduction(resultData[resultIndex], value); } } return new Tensor<T>(resultData, newShape, newStrides); } private Tensor<T> 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); int newTotalSize = newShape.Aggregate(1, (a, b) => a * b); T[] resultData = ArrayPool<T>.Shared.Rent(newTotalSize); bool[] initialized = new bool[newTotalSize]; int[][] indicesMap = new int[totalSize][]; for (int i = 0; i < totalSize; i++) { indicesMap[i] = UnflattenIndex(i, shape); } for (int i = 0; i < totalSize; i++) { var indices = indicesMap[i]; int resultIndex = 0; int stride = 1; for (int j = newShape.Length - 1, k = shape.Length - 1; j >= 0; j--, k--) { if (k == axis) k--; resultIndex += indices[k] * stride; stride *= newShape[j]; } T value = data[i]; if (!initialized[resultIndex]) { resultData[resultIndex] = value; initialized[resultIndex] = true; } else { resultData[resultIndex] = reduction(resultData[resultIndex], value); } } return new Tensor<T>(resultData, newShape, newStrides); } private static int[] CalculateStrides(int[] shape) { int[] strides = new int[shape.Length]; int stride = 1; for (int i = shape.Length - 1; i >= 0; i--) { strides[i] = stride; stride *= shape[i]; } return strides; } 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[] broadcastStrides = new int[resultShape.Length]; int offset = resultShape.Length - originalShape.Length; for (int i = resultShape.Length - 1; i >= 0; i--) { if (i - offset >= 0) { 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."); } else { broadcastStrides[i] = 0; } } return broadcastStrides; } private int[] UnflattenIndex(int flatIndex, int[] shape) { int[] indices = new int[shape.Length]; for (int i = 0; i < shape.Length; i++) { indices[i] = flatIndex / strides[i]; flatIndex %= strides[i]; } return indices; } private static int GetFlatIndex(int[] indices, int[] strides) { int flatIndex = 0; for (int i = 0; i < indices.Length; i++) { flatIndex += indices[i] * strides[i]; } return flatIndex; } private void EnsureNotDisposed() { if (disposed) throw new ObjectDisposedException(nameof(Tensor<T>)); } #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($"Unsupported type {typeof(T)}"); } writer.WriteEndArray(); writer.WriteEndObject(); } public static Tensor<T> FromJson(Stream stream) { using var jsonDoc = JsonDocument.Parse(stream); var root = jsonDoc.RootElement; var shapeElement = root.GetProperty("shape"); int[] shape = shapeElement.EnumerateArray().Select(x => x.GetInt32()).ToArray(); var tensor = new Tensor<T>(shape); var dataElement = root.GetProperty("data"); int index = 0; var data = tensor.data; foreach (var item in dataElement.EnumerateArray()) { if (typeof(T) == typeof(float)) data[index++] = (T)(object)item.GetSingle(); else if (typeof(T) == typeof(double)) data[index++] = (T)(object)item.GetDouble(); else if (typeof(T) == typeof(int)) data[index++] = (T)(object)item.GetInt32(); else if (typeof(T) == typeof(long)) data[index++] = (T)(object)item.GetInt64(); else throw new InvalidOperationException($"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($"Unsupported type {typeof(T)}"); } } public static Tensor<T> FromBinary(Stream stream) { using var reader = new BinaryReader(stream, System.Text.Encoding.UTF8, leaveOpen: true); int dimensions = reader.ReadInt32(); int[] shape = new int[dimensions]; for (int i = 0; i < dimensions; i++) { shape[i] = reader.ReadInt32(); } var tensor = new Tensor<T>(shape); var data = tensor.data; for (int i = 0; i < tensor.totalSize; i++) { if (typeof(T) == typeof(float)) data[i] = (T)(object)reader.ReadSingle(); else if (typeof(T) == typeof(double)) data[i] = (T)(object)reader.ReadDouble(); else if (typeof(T) == typeof(int)) data[i] = (T)(object)reader.ReadInt32(); else if (typeof(T) == typeof(long)) data[i] = (T)(object)reader.ReadInt64(); else throw new InvalidOperationException($"Unsupported type {typeof(T)}"); } return tensor; } #endregion #region Dispose Pattern public void Dispose() { if (!disposed) { ArrayPool<T>.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 

1-Thread-Safety:
In the Reduce method, you're using a lock when working in parallel mode. This can become a bottleneck if many threads attempt to access the lock simultaneously. Consider more advanced techniques, like parallel reduction algorithms, to minimize locking contention.

2-Ensure that ArrayPool<T>.Shared.Return is called in all possible code paths, even if exceptions occur, to prevent memory leaks.

3-Consider caching the broadcasting strides and shape calculations if these operations are repeatedly applied to the same tensor shapes.

4-Lazy Evaluation for Mathematical Operations:
Introduce lazy evaluation for operations like addition, multiplication, and subtraction. This means delaying the computation until the result is actually needed, improving efficiency in cases where multiple operations are chained.

5-Matrix/Tensor Decompositions:
Implement support for matrix/tensor decompositions (LU, QR, SVD), which are essential for neural network computations.

take your time to think and plan, only generate new code or code changes with explanation so I can  avoid any copy paste errors and to avoid human confusion