internal T DeterminantLaplace(int diagLength) { if (diagLength == 1) { return(ConstantsAndFunctions <T> .Forward(this.GetValueNoCheck(0, 0))); } var det = ConstantsAndFunctions <T> .CreateZero(); var sign = ConstantsAndFunctions <T> .CreateOne(); var temp = SquareMatrixFactory <T> .GetMatrix(diagLength); for (int i = 0; i < diagLength; i++) { GetCofactor(this, temp, 0, i, diagLength); det = ConstantsAndFunctions <T> .Add(det, ConstantsAndFunctions <T> .Multiply( sign, ConstantsAndFunctions <T> .Multiply( this.GetValueNoCheck(0, i), temp.DeterminantLaplace(diagLength - 1) )) ); sign = ConstantsAndFunctions <T> .Negate(sign); } return(det); }
private GenTensor <SafeDivisionWrapper <T> > InnerGaussianEliminationSafeDivision(int n) { InitIfNotInitted(); var elemMatrix = GenTensor <SafeDivisionWrapper <T> > .CreateMatrix(n, n, (x, y) => new SafeDivisionWrapper <T>(ConstantsAndFunctions <T> .Forward(this.GetValueNoCheck(x, y))) ); for (int k = 1; k < n; k++) { for (int j = k; j < n; j++) { var m = ConstantsAndFunctions <SafeDivisionWrapper <T> > .Divide( elemMatrix.GetValueNoCheck(j, k - 1), elemMatrix.GetValueNoCheck(k - 1, k - 1) ); for (int i = 0; i < n; i++) { var curr = elemMatrix.GetValueNoCheck(j, i); elemMatrix.SetValueNoCheck(ConstantsAndFunctions <SafeDivisionWrapper <T> > .Subtract( curr, ConstantsAndFunctions <SafeDivisionWrapper <T> > .Multiply( m, elemMatrix.GetValueNoCheck(k - 1, i) ) ), j, i); } } } return(elemMatrix); }
internal void Assign(GenTensor <T> genTensor) { foreach (var(index, value) in genTensor.Iterate()) { this.SetValueNoCheck(ConstantsAndFunctions <T> .Forward(value), index); } }
/// <summary> /// You might need it to make sure you don't copy /// your data but recreate a wrapper (if have one) /// /// O(V) /// </summary> public GenTensor <T> Forward() { var res = new GenTensor <T>(Shape); foreach (var index in res.IterateOverElements()) { res.SetValueNoCheck(ConstantsAndFunctions <T> .Forward(GetValueNoCheck(index)), index); } return(res); }
/// <summary> /// [i, j, k...]th element of the resulting tensor is /// operation(a[i, j, k...], b[i, j, k...]) /// </summary> public static GenTensor <T> Zip(GenTensor <T> a, GenTensor <T> b, Func <T, T, T> operation) { #if ALLOW_EXCEPTIONS if (a.Shape != b.Shape) { throw new InvalidShapeException("Arguments should be of the same shape"); } #endif var res = new GenTensor <T>(a.Shape); if (res.Shape.shape.Length == 1) { for (int x = 0; x < res.Shape.shape[0]; x++) { res.Data[x] = ConstantsAndFunctions <T> .Forward( operation(a.GetValueNoCheck(x), b.GetValueNoCheck(x))); } } else if (res.Shape.shape.Length == 2) { for (int x = 0; x < res.Shape.shape[0]; x++) { for (int y = 0; y < res.Shape.shape[1]; y++) { res.Data[x * res.Blocks[0] + y] = ConstantsAndFunctions <T> .Forward( operation(a.GetValueNoCheck(x, y), b.GetValueNoCheck(x, y))); } } } else if (res.Shape.shape.Length == 3) { for (int x = 0; x < res.Shape.shape[0]; x++) { for (int y = 0; y < res.Shape.shape[1]; y++) { for (int z = 0; z < res.Shape.shape[2]; z++) { res.Data[x * res.Blocks[0] + y * res.Blocks[1] + z] = ConstantsAndFunctions <T> .Forward( operation(a.GetValueNoCheck(x, y, z), b.GetValueNoCheck(x, y, z))); } } } } else { foreach (var index in res.IterateOverElements()) { res.SetValueNoCheck(ConstantsAndFunctions <T> .Forward( operation(a.GetValueNoCheck(index), b.GetValueNoCheck(index))), index); } } return(res); }
// TODO: how to avoid code duplication? /// <summary> /// Performs simple Gaussian elimination method on a tensor /// /// O(N^3) /// </summary> public T DeterminantGaussianSimple() { #if ALLOW_EXCEPTIONS if (!IsMatrix) { throw new InvalidShapeException("this should be matrix"); } if (Shape[0] != Shape[1]) { throw new InvalidShapeException("this should be square matrix"); } #endif if (Shape[0] == 1) { return(ConstantsAndFunctions <T> .Forward(this.GetValueNoCheck(0, 0))); } var n = Shape[0]; var elemMatrix = this.Forward(); for (int k = 1; k < n; k++) { for (int j = k; j < n; j++) { var m = ConstantsAndFunctions <T> .Divide( ConstantsAndFunctions <T> .Forward(elemMatrix.GetValueNoCheck(j, k - 1)), ConstantsAndFunctions <T> .Forward(elemMatrix.GetValueNoCheck(k - 1, k - 1)) ); for (int i = 0; i < n; i++) { var curr = ConstantsAndFunctions <T> .Forward(elemMatrix.GetValueNoCheck(j, i)); elemMatrix.SetValueNoCheck(ConstantsAndFunctions <T> .Subtract( curr, ConstantsAndFunctions <T> .Multiply( m, elemMatrix.GetValueNoCheck(k - 1, i) ) ), j, i); } } } var det = ConstantsAndFunctions <T> .CreateOne(); for (int i = 0; i < n; i++) { det = ConstantsAndFunctions <T> .Multiply(det, elemMatrix.GetValueNoCheck(i, i)); } return(det); }
public static GenTensor <T> Concat(GenTensor <T> a, GenTensor <T> b) { #if ALLOW_EXCEPTIONS if (a.Shape.SubShape(1, 0) != b.Shape.SubShape(1, 0)) { throw new InvalidShapeException("Excluding the first dimension, all others should match"); } #endif if (a.IsVector) { var resultingVector = GenTensor <T> .CreateVector(a.Shape.shape[0] + b.Shape.shape[0]); for (int i = 0; i < a.Shape.shape[0]; i++) { resultingVector.SetValueNoCheck(ConstantsAndFunctions <T> .Forward(a.GetValueNoCheck(i)), i); } for (int i = 0; i < b.Shape.shape[0]; i++) { resultingVector.SetValueNoCheck(ConstantsAndFunctions <T> .Forward(b.GetValueNoCheck(i)), i + a.Shape.shape[0]); } return(resultingVector); } else { var newShape = a.Shape.Copy(); newShape.shape[0] = a.Shape.shape[0] + b.Shape.shape[0]; var res = new GenTensor <T>(newShape); for (int i = 0; i < a.Shape.shape[0]; i++) { res.SetSubtensor(a.GetSubtensor(i), i); } for (int i = 0; i < b.Shape.shape[0]; i++) { res.SetSubtensor(b.GetSubtensor(i), i + a.Shape.shape[0]); } return(res); } }
/// <summary> /// Copies a tensor calling each cell with a .Copy() /// /// O(V) /// </summary> public GenTensor <T> Copy(bool copyElements) { var res = new GenTensor <T>(Shape); if (!copyElements) { foreach (var index in res.IterateOverElements()) { res.SetValueNoCheck(ConstantsAndFunctions <T> .Forward(GetValueNoCheck(index)), index); } } else { foreach (var index in res.IterateOverElements()) { res.SetValueNoCheck(ConstantsAndFunctions <T> .Copy(GetValueNoCheck(index)), index); } } return(res); }
/// <summary> /// Finds Determinant with possible overflow /// because it uses fractions for avoiding division /// /// O(N^3) /// </summary> internal T DeterminantGaussianSafeDivision(int diagLength) { InitIfNotInitted(); #if ALLOW_EXCEPTIONS if (!IsMatrix) { throw new InvalidShapeException("this should be matrix"); } if (Shape[0] != Shape[1]) { throw new InvalidShapeException("this should be square matrix"); } #endif if (Shape[0] == 1) { return(ConstantsAndFunctions <T> .Forward(this.GetValueNoCheck(0, 0))); } var n = diagLength; var elemMatrix = InnerGaussianEliminationSafeDivision(n); var det = ConstantsAndFunctions <SafeDivisionWrapper <T> > .CreateOne(); for (int i = 0; i < n; i++) { det = ConstantsAndFunctions <SafeDivisionWrapper <T> > .Multiply(det, elemMatrix.GetValueNoCheck(i, i)); } if (ConstantsAndFunctions <T> .IsZero(det.den)) { return(ConstantsAndFunctions <T> .CreateZero()); } return(det.Count()); }