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); }
/// <summary> /// Finds matrix multiplication result /// a and b are matrices /// a.Shape[1] should be equal to b.Shape[0] /// the resulting matrix is [a.Shape[0] x b.Shape[1]] shape /// /// O(N^3) /// </summary> public static GenTensor <T> MatrixMultiply(GenTensor <T> a, GenTensor <T> b) { #if ALLOW_EXCEPTIONS if (!a.IsMatrix || !b.IsMatrix) { throw new InvalidShapeException($"Both {nameof(a)} and {nameof(b)} should be matrices"); } if (a.Shape[1] != b.Shape[0]) { throw new InvalidShapeException($"{nameof(a)}'s height must be equal to {nameof(b)}'s width"); } #endif var width = a.Shape[0]; var height = b.Shape[1]; var row = a.Shape[1]; var res = CreateMatrix(width, height); for (int x = 0; x < width; x++) { for (int y = 0; y < height; y++) { var s = ConstantsAndFunctions <T> .CreateZero(); for (int i = 0; i < row; i++) { var v1 = a.GetValueNoCheck(x, i); var v2 = b.GetValueNoCheck(i, y); s = ConstantsAndFunctions <T> .Add(s, ConstantsAndFunctions <T> .Multiply(v1, v2)); } res.SetValueNoCheck(s, x, y); } } return(res); }
/// <summary> /// Creates an indentity matrix whose width and height are equal to diag /// 1 is achieved with TWrapper.SetOne() /// 0 is achieved with TWrapper.SetZero() /// </summary> public static GenTensor <T> CreateIdentityMatrix(int diag) { var res = new GenTensor <T>(diag, diag); for (int i = 0; i < res.Data.Length; i++) { res.Data[i] = ConstantsAndFunctions <T> .CreateZero(); } for (int i = 0; i < diag; i++) { res.SetValueNoCheck(ConstantsAndFunctions <T> .CreateOne, i, i); } return(res); }
/// <summary> /// Finds the scalar product of two vectors /// /// O(N) /// </summary> public static T VectorDotProduct(GenTensor <T> a, GenTensor <T> b) { #if ALLOW_EXCEPTIONS if (!a.IsVector || !b.IsVector) { throw new InvalidShapeException($"{nameof(a)} and {nameof(b)} should be vectors"); } if (a.Shape[0] != b.Shape[0]) { throw new InvalidShapeException($"{nameof(a)}'s length should be the same as {nameof(b)}'s"); } #endif var res = ConstantsAndFunctions <T> .CreateZero(); for (int i = 0; i < a.Shape[0]; i++) { res = ConstantsAndFunctions <T> .Add(res, ConstantsAndFunctions <T> .Multiply(a.GetValueNoCheck(i), b.GetValueNoCheck(i))); } 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()); }