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using IStation.Numerics.LinearAlgebra.Factorization;
using Complex = System.Numerics.Complex;

namespace IStation.Numerics.Providers.LinearAlgebra
{
    /// <summary>
    /// How to transpose a matrix.
    /// </summary>
    public enum Transpose
    {
        /// <summary>
        /// Don't transpose a matrix.
        /// </summary>
        DontTranspose = 111,

        /// <summary>
        /// Transpose a matrix.
        /// </summary>
        Transpose = 112,

        /// <summary>
        /// Conjugate transpose a complex matrix.
        /// </summary>
        /// <remarks>If a conjugate transpose is used with a real matrix, then the matrix is just transposed.</remarks>
        ConjugateTranspose = 113
    }

    /// <summary>
    /// Types of matrix norms.
    /// </summary>
    public enum Norm : byte
    {
        /// <summary>
        /// The 1-norm.
        /// </summary>
        OneNorm = (byte) '1',

        /// <summary>
        /// The Frobenius norm.
        /// </summary>
        FrobeniusNorm = (byte) 'f',

        /// <summary>
        /// The infinity norm.
        /// </summary>
        InfinityNorm = (byte) 'i',

        /// <summary>
        /// The largest absolute value norm.
        /// </summary>
        LargestAbsoluteValue = (byte) 'm'
    }

    /// <summary>
    /// Interface to linear algebra algorithms that work off 1-D arrays.
    /// </summary>
    public interface ILinearAlgebraProvider :
        ILinearAlgebraProvider<double>,
        ILinearAlgebraProvider<float>,
        ILinearAlgebraProvider<Complex>,
        ILinearAlgebraProvider<Complex32>
    {
        /// <summary>
        /// Try to find out whether the provider is available, at least in principle.
        /// Verification may still fail if available, but it will certainly fail if unavailable.
        /// </summary>
        bool IsAvailable();

        /// <summary>
        /// Initialize and verify that the provided is indeed available. If not, fall back to alternatives like the managed provider
        /// </summary>
        void InitializeVerify();

        /// <summary>
        /// Frees memory buffers, caches and handles allocated in or to the provider.
        /// Does not unload the provider itself, it is still usable afterwards.
        /// </summary>
        void FreeResources();
    }

    /// <summary>
    /// Interface to linear algebra algorithms that work off 1-D arrays.
    /// </summary>
    /// <typeparam name="T">Supported data types are Double, Single, Complex, and Complex32.</typeparam>
    public interface ILinearAlgebraProvider<T>
        where T : struct
    {
        /*/// <summary>
        /// Queries the provider for the optimal, workspace block size
        /// for the given routine.
        /// </summary>
        /// <param name="methodName">Name of the method to query.</param>
        /// <returns>-1 if the provider cannot compute the workspace size; otherwise
        /// the suggested block size.</returns>
        int QueryWorkspaceBlockSize(string methodName);*/

        /// <summary>
        /// Adds a scaled vector to another: <c>result = y + alpha*x</c>.
        /// </summary>
        /// <param name="y">The vector to update.</param>
        /// <param name="alpha">The value to scale <paramref name="x"/> by.</param>
        /// <param name="x">The vector to add to <paramref name="y"/>.</param>
        /// <param name="result">The result of the addition.</param>
        /// <remarks>This is similar to the AXPY BLAS routine.</remarks>
        void AddVectorToScaledVector(T[] y, T alpha, T[] x, T[] result);

        /// <summary>
        /// Scales an array. Can be used to scale a vector and a matrix.
        /// </summary>
        /// <param name="alpha">The scalar.</param>
        /// <param name="x">The values to scale.</param>
        /// <param name="result">This result of the scaling.</param>
        /// <remarks>This is similar to the SCAL BLAS routine.</remarks>
        void ScaleArray(T alpha, T[] x, T[] result);

        /// <summary>
        /// Conjugates an array. Can be used to conjugate a vector and a matrix.
        /// </summary>
        /// <param name="x">The values to conjugate.</param>
        /// <param name="result">This result of the conjugation.</param>
        void ConjugateArray(T[] x, T[] result);

        /// <summary>
        /// Computes the dot product of x and y.
        /// </summary>
        /// <param name="x">The vector x.</param>
        /// <param name="y">The vector y.</param>
        /// <returns>The dot product of x and y.</returns>
        /// <remarks>This is equivalent to the DOT BLAS routine.</remarks>
        T DotProduct(T[] x, T[] y);

        /// <summary>
        /// Does a point wise add of two arrays <c>z = x + y</c>. This can be used
        /// to add vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the addition.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        void AddArrays(T[] x, T[] y, T[] result);

        /// <summary>
        /// Does a point wise subtraction of two arrays <c>z = x - y</c>. This can be used
        /// to subtract vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the subtraction.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        void SubtractArrays(T[] x, T[] y, T[] result);

        /// <summary>
        /// Does a point wise multiplication of two arrays <c>z = x * y</c>. This can be used
        /// to multiply elements of vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the point wise multiplication.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        void PointWiseMultiplyArrays(T[] x, T[] y, T[] result);

        /// <summary>
        /// Does a point wise division of two arrays <c>z = x / y</c>. This can be used
        /// to divide elements of vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the point wise division.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        void PointWiseDivideArrays(T[] x, T[] y, T[] result);

        /// <summary>
        /// Does a point wise power of two arrays <c>z = x ^ y</c>. This can be used
        /// to raise elements of vectors or matrices to the powers of another vector or matrix.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the point wise power.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        void PointWisePowerArrays(T[] x, T[] y, T[] result);

        /// <summary>
        /// Computes the requested <see cref="Norm"/> of the matrix.
        /// </summary>
        /// <param name="norm">The type of norm to compute.</param>
        /// <param name="rows">The number of rows.</param>
        /// <param name="columns">The number of columns.</param>
        /// <param name="matrix">The matrix to compute the norm from.</param>
        /// <returns>
        /// The requested <see cref="Norm"/> of the matrix.
        /// </returns>
        double MatrixNorm(Norm norm, int rows, int columns, T[] matrix);

        /// <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>
        void MatrixMultiply(T[] x, int rowsX, int columnsX, T[] y, int rowsY, int columnsY, T[] 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>
        void MatrixMultiplyWithUpdate(Transpose transposeA, Transpose transposeB, T alpha, T[] a, int rowsA, int columnsA, T[] b, int rowsB, int columnsB, T beta, T[] c);

        /// <summary>
        /// Computes the LUP factorization of A. P*A = L*U.
        /// </summary>
        /// <param name="data">An <paramref name="order"/> by <paramref name="order"/> matrix. The matrix is overwritten with the
        /// the LU factorization on exit. The lower triangular factor L is stored in under the diagonal of <paramref name="data"/> (the diagonal is always 1.0
        /// for the L factor). The upper triangular factor U is stored on and above the diagonal of <paramref name="data"/>.</param>
        /// <param name="order">The order of the square matrix <paramref name="data"/>.</param>
        /// <param name="ipiv">On exit, it contains the pivot indices. The size of the array must be <paramref name="order"/>.</param>
        /// <remarks>This is equivalent to the GETRF LAPACK routine.</remarks>
        void LUFactor(T[] data, int order, int[] ipiv);

        /// <summary>
        /// Computes the inverse of matrix using LU factorization.
        /// </summary>
        /// <param name="a">The N by N matrix to invert. Contains the inverse On exit.</param>
        /// <param name="order">The order of the square matrix <paramref name="a"/>.</param>
        /// <remarks>This is equivalent to the GETRF and GETRI LAPACK routines.</remarks>
        void LUInverse(T[] a, int order);

        /// <summary>
        /// Computes the inverse of a previously factored matrix.
        /// </summary>
        /// <param name="a">The LU factored N by N matrix.  Contains the inverse On exit.</param>
        /// <param name="order">The order of the square matrix <paramref name="a"/>.</param>
        /// <param name="ipiv">The pivot indices of <paramref name="a"/>.</param>
        /// <remarks>This is equivalent to the GETRI LAPACK routine.</remarks>
        void LUInverseFactored(T[] a, int order, int[] ipiv);

        /// <summary>
        /// Solves A*X=B for X using LU factorization.
        /// </summary>
        /// <param name="columnsOfB">The number of columns of B.</param>
        /// <param name="a">The square matrix A.</param>
        /// <param name="order">The order of the square matrix <paramref name="a"/>.</param>
        /// <param name="b">On entry the B matrix; on exit the X matrix.</param>
        /// <remarks>This is equivalent to the GETRF and GETRS LAPACK routines.</remarks>
        void LUSolve(int columnsOfB, T[] a, int order, T[] b);

        /// <summary>
        /// Solves A*X=B for X using a previously factored A matrix.
        /// </summary>
        /// <param name="columnsOfB">The number of columns of B.</param>
        /// <param name="a">The factored A matrix.</param>
        /// <param name="order">The order of the square matrix <paramref name="a"/>.</param>
        /// <param name="ipiv">The pivot indices of <paramref name="a"/>.</param>
        /// <param name="b">On entry the B matrix; on exit the X matrix.</param>
        /// <remarks>This is equivalent to the GETRS LAPACK routine.</remarks>
        void LUSolveFactored(int columnsOfB, T[] a, int order, int[] ipiv, T[] b);

        /// <summary>
        /// Computes the Cholesky factorization of A.
        /// </summary>
        /// <param name="a">On entry, a square, positive definite matrix. On exit, the matrix is overwritten with the
        /// the Cholesky factorization.</param>
        /// <param name="order">The number of rows or columns in the matrix.</param>
        /// <remarks>This is equivalent to the POTRF LAPACK routine.</remarks>
        void CholeskyFactor(T[] a, int order);

        /// <summary>
        /// Solves A*X=B for X using Cholesky factorization.
        /// </summary>
        /// <param name="a">The square, positive definite matrix A.</param>
        /// <param name="orderA">The number of rows and columns in A.</param>
        /// <param name="b">On entry the B matrix; on exit the X matrix.</param>
        /// <param name="columnsB">The number of columns in the B matrix.</param>
        /// <remarks>This is equivalent to the POTRF add POTRS LAPACK routines.</remarks>
        void CholeskySolve(T[] a, int orderA, T[] b, int columnsB);

        /// <summary>
        /// Solves A*X=B for X using a previously factored A matrix.
        /// </summary>
        /// <param name="a">The square, positive definite matrix A.</param>
        /// <param name="orderA">The number of rows and columns in A.</param>
        /// <param name="b">On entry the B matrix; on exit the X matrix.</param>
        /// <param name="columnsB">The number of columns in the B matrix.</param>
        /// <remarks>This is equivalent to the POTRS LAPACK routine.</remarks>
        void CholeskySolveFactored(T[] a, int orderA, T[] b, int columnsB);

        /// <summary>
        /// Computes the full QR factorization of A.
        /// </summary>
        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
        /// it is overwritten with the R matrix of the QR factorization.</param>
        /// <param name="rowsA">The number of rows in the A matrix.</param>
        /// <param name="columnsA">The number of columns in the A matrix.</param>
        /// <param name="q">On exit, A M by M matrix that holds the Q matrix of the
        /// QR factorization.</param>
        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
        /// to be used by the QR solve routine.</param>
        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
        void QRFactor(T[] a, int rowsA, int columnsA, T[] q, T[] tau);

        /// <summary>
        /// Computes the thin QR factorization of A where M &gt; N.
        /// </summary>
        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
        /// it is overwritten with the Q matrix of the QR factorization.</param>
        /// <param name="rowsA">The number of rows in the A matrix.</param>
        /// <param name="columnsA">The number of columns in the A matrix.</param>
        /// <param name="r">On exit, A N by N matrix that holds the R matrix of the
        /// QR factorization.</param>
        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
        /// to be used by the QR solve routine.</param>
        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
        void ThinQRFactor(T[] a, int rowsA, int columnsA, T[] r, T[] tau);

        /// <summary>
        /// Solves A*X=B for X using QR factorization of A.
        /// </summary>
        /// <param name="a">The A matrix.</param>
        /// <param name="rows">The number of rows in the A matrix.</param>
        /// <param name="columns">The number of columns in the A matrix.</param>
        /// <param name="b">The B matrix.</param>
        /// <param name="columnsB">The number of columns of B.</param>
        /// <param name="x">On exit, the solution matrix.</param>
        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
        /// <remarks>Rows must be greater or equal to columns.</remarks>
        void QRSolve(T[] a, int rows, int columns, T[] b, int columnsB, T[] x, QRMethod method = QRMethod.Full);

        /// <summary>
        /// Solves A*X=B for X using a previously QR factored matrix.
        /// </summary>
        /// <param name="q">The Q matrix obtained by QR factor. This is only used for the managed provider and can be
        /// <c>null</c> for the native provider. The native provider uses the Q portion stored in the R matrix.</param>
        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(T[],int,int,T[],T[])"/>. </param>
        /// <param name="rowsA">The number of rows in the A matrix.</param>
        /// <param name="columnsA">The number of columns in the A matrix.</param>
        /// <param name="tau">Contains additional information on Q. Only used for the native solver
        /// and can be <c>null</c> for the managed provider.</param>
        /// <param name="b">On entry the B matrix; on exit the X matrix.</param>
        /// <param name="columnsB">The number of columns of B.</param>
        /// <param name="x">On exit, the solution matrix.</param>
        /// <remarks>Rows must be greater or equal to columns.</remarks>
        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
        void QRSolveFactored(T[] q, T[] r, int rowsA, int columnsA, T[] tau, T[] b, int columnsB, T[] x, QRMethod method = QRMethod.Full);

        /// <summary>
        /// Computes the singular value decomposition of A.
        /// </summary>
        /// <param name="computeVectors">Compute the singular U and VT vectors or not.</param>
        /// <param name="a">On entry, the M by N matrix to decompose. On exit, A may be overwritten.</param>
        /// <param name="rowsA">The number of rows in the A matrix.</param>
        /// <param name="columnsA">The number of columns in the A matrix.</param>
        /// <param name="s">The singular values of A in ascending value. </param>
        /// <param name="u">If <paramref name="computeVectors"/> is <c>true</c>, on exit U contains the left
        /// singular vectors.</param>
        /// <param name="vt">If <paramref name="computeVectors"/> is <c>true</c>, on exit VT contains the transposed
        /// right singular vectors.</param>
        /// <remarks>This is equivalent to the GESVD LAPACK routine.</remarks>
        void SingularValueDecomposition(bool computeVectors, T[] a, int rowsA, int columnsA, T[] s, T[] u, T[] vt);

        /// <summary>
        /// Solves A*X=B for X using the singular value decomposition of A.
        /// </summary>
        /// <param name="a">On entry, the M by N matrix to decompose.</param>
        /// <param name="rowsA">The number of rows in the A matrix.</param>
        /// <param name="columnsA">The number of columns in the A matrix.</param>
        /// <param name="b">The B matrix.</param>
        /// <param name="columnsB">The number of columns of B.</param>
        /// <param name="x">On exit, the solution matrix.</param>
        void SvdSolve(T[] a, int rowsA, int columnsA, T[] b, int columnsB, T[] x);

        /// <summary>
        /// Solves A*X=B for X using a previously SVD decomposed matrix.
        /// </summary>
        /// <param name="rowsA">The number of rows in the A matrix.</param>
        /// <param name="columnsA">The number of columns in the A matrix.</param>
        /// <param name="s">The s values returned by <see cref="SingularValueDecomposition(bool,T[],int,int,T[],T[],T[])"/>.</param>
        /// <param name="u">The left singular vectors returned by  <see cref="SingularValueDecomposition(bool,T[],int,int, T[],T[],T[])"/>.</param>
        /// <param name="vt">The right singular  vectors returned by  <see cref="SingularValueDecomposition(bool,T[],int,int,T[],T[],T[])"/>.</param>
        /// <param name="b">The B matrix</param>
        /// <param name="columnsB">The number of columns of B.</param>
        /// <param name="x">On exit, the solution matrix.</param>
        void SvdSolveFactored(int rowsA, int columnsA, T[] s, T[] u, T[] vt, T[] b, int columnsB, T[] x);

        /// <summary>
        /// Computes the eigenvalues and eigenvectors of a matrix.
        /// </summary>
        /// <param name="isSymmetric">Whether the matrix is symmetric or not.</param>
        /// <param name="order">The order of the matrix.</param>
        /// <param name="matrix">The matrix to decompose. The length of the array must be order * order.</param>
        /// <param name="matrixEv">On output, the matrix contains the eigen vectors. The length of the array must be order * order.</param>
        /// <param name="vectorEv">On output, the eigen values (λ) of matrix in ascending value. The length of the array must <paramref name="order"/>.</param>
        /// <param name="matrixD">On output, the block diagonal eigenvalue matrix. The length of the array must be order * order.</param>
        void EigenDecomp(bool isSymmetric, int order, T[] matrix, T[] matrixEv, Complex[] vectorEv, T[] matrixD);
    }
}