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 : 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; 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.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.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 (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(); 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 result = new Tensor(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 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 Helper Methods private Tensor ElementWiseOperation(Tensor 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 result = new Tensor(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 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); int reduceDim = shape[axis]; int newTotalSize = newShape.Aggregate(1, (a, b) => a * b); T[] resultData = ArrayPool.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(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); int newTotalSize = newShape.Aggregate(1, (a, b) => a * b); T[] resultData = ArrayPool.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(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)); } #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

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

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

let's break this down into steps and take it step by step, break down each point in it's response, for each step you are required to think thoroughly to find the best implementation that best fit for my class, generate new or updated code to reflect the full changes and don't give me example or parts and leave other parts, 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
give me the best answer