/// <summary> /// Возвращает спектр сигнала, вычесленное по быстрому алгоритму фурье /// </summary> /// <param name="input">Массив значений сигнала</param> /// <returns>Массив со значениями спектра сигнала</returns> public static Complex[] FastTransform(Complex[] input) { double log = Math.Log(input.Length, 2); Complex[] x; if (log - Math.Round(log) != 0) { x = new Complex[(int) Math.Pow(2,(int)log + 1)]; input.CopyTo(x, 0); } else { x = (Complex[]) input.Clone(); } Complex[] X; int N = x.Length; if (N == 2) { X = new Complex[2]; X[0] = x[0] + x[1]; X[1] = x[0] - x[1]; } else { Complex[] x_even = new Complex[N / 2]; Complex[] x_odd = new Complex[N / 2]; for (int i = 0; i < N / 2; i++) { x_even[i] = x[2 * i]; x_odd[i] = x[2 * i + 1]; } Complex[] X_even = UnsafeFastTransform(x_even); Complex[] X_odd = UnsafeFastTransform(x_odd); X = new Complex[N]; for (int i = 0; i < N / 2; i++) { X[i] = X_even[i] + Module(i, N) * X_odd[i]; X[i + N / 2] = X_even[i] - Module(i, N) * X_odd[i]; } } return X; }
/// <summary> /// Initializes a new instance of the <see cref="UserDefinedVector"/> class for an array. /// </summary> /// <param name="data">The array to create this vector from.</param> public UserDefinedVector(Complex[] data) : base(data.Length) { _data = (Complex[])data.Clone(); }
/// <summary> /// Multiplies two matrices and updates another with the result. <c>c = alpha*op(a)*op(b) + beta*c</c> /// </summary> /// <param name="transposeA">How to transpose the <paramref name="a"/> matrix.</param> /// <param name="transposeB">How to transpose the <paramref name="b"/> matrix.</param> /// <param name="alpha">The value to scale <paramref name="a"/> matrix.</param> /// <param name="a">The a matrix.</param> /// <param name="rowsA">The number of rows in the <paramref name="a"/> matrix.</param> /// <param name="columnsA">The number of columns in the <paramref name="a"/> matrix.</param> /// <param name="b">The b matrix</param> /// <param name="rowsB">The number of rows in the <paramref name="b"/> matrix.</param> /// <param name="columnsB">The number of columns in the <paramref name="b"/> matrix.</param> /// <param name="beta">The value to scale the <paramref name="c"/> matrix.</param> /// <param name="c">The c matrix.</param> public virtual void MatrixMultiplyWithUpdate(Transpose transposeA, Transpose transposeB, Complex alpha, Complex[] a, int rowsA, int columnsA, Complex[] b, int rowsB, int columnsB, Complex beta, Complex[] c) { int m; // The number of rows of matrix op(A) and of the matrix C. int n; // The number of columns of matrix op(B) and of the matrix C. int k; // The number of columns of matrix op(A) and the rows of the matrix op(B). // First check some basic requirement on the parameters of the matrix multiplication. if (a == null) { throw new ArgumentNullException("a"); } if (b == null) { throw new ArgumentNullException("b"); } if ((int) transposeA > 111 && (int) transposeB > 111) { if (rowsA != columnsB) { throw new ArgumentOutOfRangeException(); } if (columnsA*rowsB != c.Length) { throw new ArgumentOutOfRangeException(); } m = columnsA; n = rowsB; k = rowsA; } else if ((int) transposeA > 111) { if (rowsA != rowsB) { throw new ArgumentOutOfRangeException(); } if (columnsA*columnsB != c.Length) { throw new ArgumentOutOfRangeException(); } m = columnsA; n = columnsB; k = rowsA; } else if ((int) transposeB > 111) { if (columnsA != columnsB) { throw new ArgumentOutOfRangeException(); } if (rowsA*rowsB != c.Length) { throw new ArgumentOutOfRangeException(); } m = rowsA; n = rowsB; k = columnsA; } else { if (columnsA != rowsB) { throw new ArgumentOutOfRangeException(); } if (rowsA*columnsB != c.Length) { throw new ArgumentOutOfRangeException(); } m = rowsA; n = columnsB; k = columnsA; } if (alpha.IsZero() && beta.IsZero()) { Array.Clear(c, 0, c.Length); return; } // Check whether we will be overwriting any of our inputs and make copies if necessary. // TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory // as result, we can do it on a row wise basis. We should investigate this. Complex[] adata; if (ReferenceEquals(a, c)) { adata = (Complex[]) a.Clone(); } else { adata = a; } Complex[] bdata; if (ReferenceEquals(b, c)) { bdata = (Complex[]) b.Clone(); } else { bdata = b; } if (beta.IsZero()) { Array.Clear(c, 0, c.Length); } else if (!beta.IsOne()) { Control.LinearAlgebraProvider.ScaleArray(beta, c, c); } if (alpha.IsZero()) { return; } CacheObliviousMatrixMultiply(transposeA, transposeB, alpha, adata, 0, 0, bdata, 0, 0, c, 0, 0, m, n, k, m, n, k, true); }
/// <summary> /// Multiples two matrices. <c>result = x * y</c> /// </summary> /// <param name="x">The x matrix.</param> /// <param name="rowsX">The number of rows in the x matrix.</param> /// <param name="columnsX">The number of columns in the x matrix.</param> /// <param name="y">The y matrix.</param> /// <param name="rowsY">The number of rows in the y matrix.</param> /// <param name="columnsY">The number of columns in the y matrix.</param> /// <param name="result">Where to store the result of the multiplication.</param> /// <remarks>This is a simplified version of the BLAS GEMM routine with alpha /// set to 1.0 and beta set to 0.0, and x and y are not transposed.</remarks> public virtual void MatrixMultiply(Complex[] x, int rowsX, int columnsX, Complex[] y, int rowsY, int columnsY, Complex[] result) { // First check some basic requirement on the parameters of the matrix multiplication. if (x == null) { throw new ArgumentNullException("x"); } if (y == null) { throw new ArgumentNullException("y"); } if (result == null) { throw new ArgumentNullException("result"); } if (rowsX*columnsX != x.Length) { throw new ArgumentException("x.Length != xRows * xColumns"); } if (rowsY*columnsY != y.Length) { throw new ArgumentException("y.Length != yRows * yColumns"); } if (columnsX != rowsY) { throw new ArgumentException("xColumns != yRows"); } if (rowsX*columnsY != result.Length) { throw new ArgumentException("xRows * yColumns != result.Length"); } // Check whether we will be overwriting any of our inputs and make copies if necessary. // TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory // as result, we can do it on a row wise basis. We should investigate this. Complex[] xdata; if (ReferenceEquals(x, result)) { xdata = (Complex[]) x.Clone(); } else { xdata = x; } Complex[] ydata; if (ReferenceEquals(y, result)) { ydata = (Complex[]) y.Clone(); } else { ydata = y; } MatrixMultiplyWithUpdate(Transpose.DontTranspose, Transpose.DontTranspose, Complex.One, xdata, rowsX, columnsX, ydata, rowsY, columnsY, Complex.Zero, result); }
/// <summary> /// Multiplies two matrices and updates another with the result. <c>c = alpha*op(a)*op(b) + beta*c</c> /// </summary> /// <param name="transposeA">How to transpose the <paramref name="a"/> matrix.</param> /// <param name="transposeB">How to transpose the <paramref name="b"/> matrix.</param> /// <param name="alpha">The value to scale <paramref name="a"/> matrix.</param> /// <param name="a">The a matrix.</param> /// <param name="rowsA">The number of rows in the <paramref name="a"/> matrix.</param> /// <param name="columnsA">The number of columns in the <paramref name="a"/> matrix.</param> /// <param name="b">The b matrix</param> /// <param name="rowsB">The number of rows in the <paramref name="b"/> matrix.</param> /// <param name="columnsB">The number of columns in the <paramref name="b"/> matrix.</param> /// <param name="beta">The value to scale the <paramref name="c"/> matrix.</param> /// <param name="c">The c matrix.</param> public void MatrixMultiplyWithUpdate(Transpose transposeA, Transpose transposeB, Complex alpha, Complex[] a, int rowsA, int columnsA, Complex[] b, int rowsB, int columnsB, Complex beta, Complex[] c) { // Choose nonsensical values for the number of rows in c; fill them in depending // on the operations on a and b. int rowsC; // First check some basic requirement on the parameters of the matrix multiplication. if (a == null) { throw new ArgumentNullException("a"); } if (b == null) { throw new ArgumentNullException("b"); } if ((int)transposeA > 111 && (int)transposeB > 111) { if (rowsA != columnsB) { throw new ArgumentOutOfRangeException(); } if (columnsA * rowsB != c.Length) { throw new ArgumentOutOfRangeException(); } rowsC = columnsA; } else if ((int)transposeA > 111) { if (rowsA != rowsB) { throw new ArgumentOutOfRangeException(); } if (columnsA * columnsB != c.Length) { throw new ArgumentOutOfRangeException(); } rowsC = columnsA; } else if ((int)transposeB > 111) { if (columnsA != columnsB) { throw new ArgumentOutOfRangeException(); } if (rowsA * rowsB != c.Length) { throw new ArgumentOutOfRangeException(); } rowsC = rowsA; } else { if (columnsA != rowsB) { throw new ArgumentOutOfRangeException(); } if (rowsA * columnsB != c.Length) { throw new ArgumentOutOfRangeException(); } rowsC = rowsA; } if (alpha == 0.0 && beta == 0.0) { Array.Clear(c, 0, c.Length); return; } // Check whether we will be overwriting any of our inputs and make copies if necessary. // TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory // as result, we can do it on a row wise basis. We should investigate this. Complex[] adata; if (ReferenceEquals(a, c)) { adata = (Complex[])a.Clone(); } else { adata = a; } Complex[] bdata; if (ReferenceEquals(b, c)) { bdata = (Complex[])b.Clone(); } else { bdata = b; } if (alpha == 1.0) { if (beta == 0.0) { if ((int)transposeA > 111 && (int)transposeB > 111) { CommonParallel.For( 0, columnsA, j => { var jIndex = j * rowsC; for (var i = 0; i != rowsB; i++) { var iIndex = i * rowsA; Complex s = 0; for (var l = 0; l != columnsB; l++) { s += adata[iIndex + l] * bdata[(l * rowsB) + j]; } c[jIndex + i] = s; } }); } else if ((int)transposeA > 111) { CommonParallel.For( 0, columnsB, j => { var jcIndex = j * rowsC; var jbIndex = j * rowsB; for (var i = 0; i != columnsA; i++) { var iIndex = i * rowsA; Complex s = 0; for (var l = 0; l != rowsA; l++) { s += adata[iIndex + l] * bdata[jbIndex + l]; } c[jcIndex + i] = s; } }); } else if ((int)transposeB > 111) { CommonParallel.For( 0, rowsB, j => { var jIndex = j * rowsC; for (var i = 0; i != rowsA; i++) { Complex s = 0; for (var l = 0; l != columnsA; l++) { s += adata[(l * rowsA) + i] * bdata[(l * rowsB) + j]; } c[jIndex + i] = s; } }); } else { CommonParallel.For( 0, columnsB, j => { var jcIndex = j * rowsC; var jbIndex = j * rowsB; for (var i = 0; i != rowsA; i++) { Complex s = 0; for (var l = 0; l != columnsA; l++) { s += adata[(l * rowsA) + i] * bdata[jbIndex + l]; } c[jcIndex + i] = s; } }); } } else { if ((int)transposeA > 111 && (int)transposeB > 111) { CommonParallel.For( 0, columnsA, j => { var jIndex = j * rowsC; for (var i = 0; i != rowsB; i++) { var iIndex = i * rowsA; Complex s = 0; for (var l = 0; l != columnsB; l++) { s += adata[iIndex + l] * bdata[(l * rowsB) + j]; } c[jIndex + i] = (c[jIndex + i] * beta) + s; } }); } else if ((int)transposeA > 111) { CommonParallel.For( 0, columnsB, j => { var jcIndex = j * rowsC; var jbIndex = j * rowsB; for (var i = 0; i != columnsA; i++) { var iIndex = i * rowsA; Complex s = 0; for (var l = 0; l != rowsA; l++) { s += adata[iIndex + l] * bdata[jbIndex + l]; } c[jcIndex + i] = s + (c[jcIndex + i] * beta); } }); } else if ((int)transposeB > 111) { CommonParallel.For( 0, rowsB, j => { var jIndex = j * rowsC; for (var i = 0; i != rowsA; i++) { Complex s = 0; for (var l = 0; l != columnsA; l++) { s += adata[(l * rowsA) + i] * bdata[(l * rowsB) + j]; } c[jIndex + i] = s + (c[jIndex + i] * beta); } }); } else { CommonParallel.For( 0, columnsB, j => { var jcIndex = j * rowsC; var jbIndex = j * rowsB; for (var i = 0; i != rowsA; i++) { Complex s = 0; for (var l = 0; l != columnsA; l++) { s += adata[(l * rowsA) + i] * bdata[jbIndex + l]; } c[jcIndex + i] = s + (c[jcIndex + i] * beta); } }); } } } else { if ((int)transposeA > 111 && (int)transposeB > 111) { CommonParallel.For( 0, columnsA, j => { var jIndex = j * rowsC; for (var i = 0; i != rowsB; i++) { var iIndex = i * rowsA; Complex s = 0; for (var l = 0; l != columnsB; l++) { s += adata[iIndex + l] * bdata[(l * rowsB) + j]; } c[jIndex + i] = (c[jIndex + i] * beta) + (alpha * s); } }); } else if ((int)transposeA > 111) { CommonParallel.For( 0, columnsB, j => { var jcIndex = j * rowsC; var jbIndex = j * rowsB; for (var i = 0; i != columnsA; i++) { var iIndex = i * rowsA; Complex s = 0; for (var l = 0; l != rowsA; l++) { s += adata[iIndex + l] * bdata[jbIndex + l]; } c[jcIndex + i] = (alpha * s) + (c[jcIndex + i] * beta); } }); } else if ((int)transposeB > 111) { CommonParallel.For( 0, rowsB, j => { var jIndex = j * rowsC; for (var i = 0; i != rowsA; i++) { Complex s = 0; for (var l = 0; l != columnsA; l++) { s += adata[(l * rowsA) + i] * bdata[(l * rowsB) + j]; } c[jIndex + i] = (alpha * s) + (c[jIndex + i] * beta); } }); } else { CommonParallel.For( 0, columnsB, j => { var jcIndex = j * rowsC; var jbIndex = j * rowsB; for (var i = 0; i != rowsA; i++) { Complex s = 0; for (var l = 0; l != columnsA; l++) { s += adata[(l * rowsA) + i] * bdata[jbIndex + l]; } c[jcIndex + i] = (alpha * s) + (c[jcIndex + i] * beta); } }); } } }
/// <summary> /// Multiples two matrices. <c>result = x * y</c> /// </summary> /// <param name="x">The x matrix.</param> /// <param name="rowsX">The number of rows in the x matrix.</param> /// <param name="columnsX">The number of columns in the x matrix.</param> /// <param name="y">The y matrix.</param> /// <param name="rowsY">The number of rows in the y matrix.</param> /// <param name="columnsY">The number of columns in the y matrix.</param> /// <param name="result">Where to store the result of the multiplication.</param> /// <remarks>This is a simplified version of the BLAS GEMM routine with alpha /// set to 1.0 and beta set to 0.0, and x and y are not transposed.</remarks> public void MatrixMultiply(Complex[] x, int rowsX, int columnsX, Complex[] y, int rowsY, int columnsY, Complex[] result) { // First check some basic requirement on the parameters of the matrix multiplication. if (x == null) { throw new ArgumentNullException("x"); } if (y == null) { throw new ArgumentNullException("y"); } if (result == null) { throw new ArgumentNullException("result"); } if (rowsX * columnsX != x.Length) { throw new ArgumentException("x.Length != xRows * xColumns"); } if (rowsY * columnsY != y.Length) { throw new ArgumentException("y.Length != yRows * yColumns"); } if (columnsX != rowsY) { throw new ArgumentException("xColumns != yRows"); } if (rowsX * columnsY != result.Length) { throw new ArgumentException("xRows * yColumns != result.Length"); } // Check whether we will be overwriting any of our inputs and make copies if necessary. // TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory // as result, we can do it on a row wise basis. We should investigate this. Complex[] xdata; if (ReferenceEquals(x, result)) { xdata = (Complex[])x.Clone(); } else { xdata = x; } Complex[] ydata; if (ReferenceEquals(y, result)) { ydata = (Complex[])y.Clone(); } else { ydata = y; } // Start the actual matrix multiplication. // TODO - For small matrices we should get rid of the parallelism because of startup costs. // Perhaps the following implementations would be a good one // http://blog.feradz.com/2009/01/cache-efficient-matrix-multiplication/ MatrixMultiplyWithUpdate(Transpose.DontTranspose, Transpose.DontTranspose, Complex.One, xdata, rowsX, columnsX, ydata, rowsY, columnsY, Complex.Zero, result); }
/// <summary> /// Initializes a new instance of the <see cref="UserDefinedMatrix"/> class from a 2D array. /// </summary> /// <param name="data">The 2D array to create this matrix from.</param> public UserDefinedMatrix(Complex[,] data) : base(data.GetLength(0), data.GetLength(1)) { _data = (Complex[,])data.Clone(); }