/// <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>
public virtual void SvdSolve(Complex[] a, int rowsA, int columnsA, Complex[] b, int columnsB, Complex[] x)
{
if (a == null)
{
throw new ArgumentNullException("a");
}
if (b == null)
{
throw new ArgumentNullException("b");
}
if (x == null)
{
throw new ArgumentNullException("x");
}
if (b.Length != rowsA*columnsB)
{
throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
}
if (x.Length != columnsA*columnsB)
{
throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
}
var work = new Complex[rowsA];
var s = new Complex[Math.Min(rowsA, columnsA)];
var u = new Complex[rowsA*rowsA];
var vt = new Complex[columnsA*columnsA];
var clone = new Complex[a.Length];
a.Copy(clone);
SingularValueDecomposition(true, clone, rowsA, columnsA, s, u, vt, work);
SvdSolveFactored(rowsA, columnsA, s, u, vt, b, columnsB, x);
}
/// <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>
public virtual void AddVectorToScaledVector(Complex[] y, Complex alpha, Complex[] x, Complex[] result)
{
if (y == null)
{
throw new ArgumentNullException("y");
}
if (x == null)
{
throw new ArgumentNullException("x");
}
if (y.Length != x.Length)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLength);
}
if (y.Length != x.Length)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLength);
}
if (alpha.IsZero())
{
y.Copy(result);
}
else if (alpha.IsOne())
{
if (Control.ParallelizeOperation(x.Length))
{
CommonParallel.For(0, y.Length, 4096, (a, b) =>
{
for (int i = a; i < b; i++)
{
result[i] = y[i] + x[i];
}
});
}
else
{
for (var index = 0; index < x.Length; index++)
{
result[index] = y[index] + x[index];
}
}
}
else
{
if (Control.ParallelizeOperation(x.Length))
{
CommonParallel.For(0, y.Length, 4096, (a, b) =>
{
for (int i = a; i < b; i++)
{
result[i] = y[i] + (alpha*x[i]);
}
});
}
else
{
for (var index = 0; index < x.Length; index++)
{
result[index] = y[index] + (alpha*x[index]);
}
}
}
}
/// <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="work">The work array. The array must have a length of at least N,
/// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
/// work size value.</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>
public virtual void QRSolve(Complex[] a, int rows, int columns, Complex[] b, int columnsB, Complex[] x, Complex[] work, QRMethod method = QRMethod.Full)
{
if (a == null)
{
throw new ArgumentNullException("a");
}
if (b == null)
{
throw new ArgumentNullException("b");
}
if (x == null)
{
throw new ArgumentNullException("x");
}
if (work == null)
{
throw new ArgumentNullException("work");
}
if (a.Length != rows*columns)
{
throw new ArgumentException(Resources.ArgumentArraysSameLength, "a");
}
if (b.Length != rows*columnsB)
{
throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
}
if (rows < columns)
{
throw new ArgumentException(Resources.RowsLessThanColumns);
}
if (x.Length != columns*columnsB)
{
throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
}
if (work.Length < rows*columns)
{
work[0] = rows*columns;
throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
}
var clone = new Complex[a.Length];
a.Copy(clone);
if (method == QRMethod.Full)
{
var q = new Complex[rows*rows];
QRFactor(clone, rows, columns, q, work);
QRSolveFactored(q, clone, rows, columns, null, b, columnsB, x, method);
}
else
{
var r = new Complex[columns*columns];
ThinQRFactor(clone, rows, columns, r, work);
QRSolveFactored(clone, r, rows, columns, null, b, columnsB, x, method);
}
work[0] = rows*columns;
}
/// <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>
public virtual void CholeskySolve(Complex[] a, int orderA, Complex[] b, int columnsB)
{
if (a == null)
{
throw new ArgumentNullException("a");
}
if (b == null)
{
throw new ArgumentNullException("b");
}
if (b.Length != orderA*columnsB)
{
throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
}
if (ReferenceEquals(a, b))
{
throw new ArgumentException(Resources.ArgumentReferenceDifferent);
}
var clone = new Complex[a.Length];
a.Copy(clone);
CholeskyFactor(clone, orderA);
CholeskySolveFactored(clone, orderA, b, columnsB);
}
/// <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>
public virtual void ScaleArray(Complex alpha, Complex[] x, Complex[] result)
{
if (x == null)
{
throw new ArgumentNullException("x");
}
if (alpha.IsZero())
{
Array.Clear(result, 0, result.Length);
}
else if (alpha.IsOne())
{
x.Copy(result);
}
else
{
if (Control.ParallelizeOperation(x.Length))
{
CommonParallel.For(0, x.Length, 4096, (a, b) =>
{
for (int i = a; i < b; i++)
{
result[i] = alpha*x[i];
}
});
}
else
{
for (var index = 0; index < x.Length; index++)
{
result[index] = alpha*x[index];
}
}
}
}
/// <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>
public virtual void LUSolve(int columnsOfB, Complex[] a, int order, Complex[] b)
{
if (a == null)
{
throw new ArgumentNullException("a");
}
if (b == null)
{
throw new ArgumentNullException("b");
}
if (a.Length != order*order)
{
throw new ArgumentException(Resources.ArgumentArraysSameLength, "a");
}
if (b.Length != order*columnsOfB)
{
throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
}
if (ReferenceEquals(a, b))
{
throw new ArgumentException(Resources.ArgumentReferenceDifferent);
}
var ipiv = new int[order];
var clone = new Complex[a.Length];
a.Copy(clone);
LUFactor(clone, order, ipiv);
LUSolveFactored(columnsOfB, clone, order, ipiv, b);
}
/// <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>
public virtual void LUInverseFactored(Complex[] a, int order, int[] ipiv)
{
if (a == null)
{
throw new ArgumentNullException("a");
}
if (ipiv == null)
{
throw new ArgumentNullException("ipiv");
}
if (a.Length != order*order)
{
throw new ArgumentException(Resources.ArgumentArraysSameLength, "a");
}
if (ipiv.Length != order)
{
throw new ArgumentException(Resources.ArgumentArraysSameLength, "ipiv");
}
var inverse = new Complex[a.Length];
for (var i = 0; i < order; i++)
{
inverse[i + (order*i)] = Complex.One;
}
LUSolveFactored(order, a, order, ipiv, inverse);
inverse.Copy(a);
}