/// <summary>
/// Performs the matrix-vector multiplication: oper(this) * <paramref name="vector"/>.
/// To multiply this * columnVector, set <paramref name="transposeThis"/> to false.
/// To multiply rowVector * this, set <paramref name="transposeThis"/> to true.
/// The resulting vector will be written in a new vector and returned.
/// </summary>
/// <param name="vector">
/// A vector with Length being equal to the <see cref="IIndexable2D.NumColumns"/> of oper(this).
/// </param>
/// <param name="transposeThis">If true, oper(this) = transpose(this). Otherwise oper(this) = this.</param>
/// <exception cref="NonMatchingDimensionsException">
/// Thrown if <paramref name="vector"/>.Length is different than the <see cref="IIndexable2D.NumColumns"/> of oper(this).
/// </exception>
public static double[] Multiply(this IMatrixView matrix, double[] vector, bool transposeThis = false)
{
var result = new double[transposeThis ? matrix.NumColumns : matrix.NumRows];
matrix.MultiplyIntoResult(Vector.CreateFromArray(vector), Vector.CreateFromArray(result), transposeThis);
return(result);
}
/// <summary>
/// Performs the matrix-vector multiplication: <paramref name="rhsVector"/> = oper(this) * <paramref name="lhsVector"/>.
/// To multiply this * columnVector, set <paramref name="transposeThis"/> to false.
/// To multiply rowVector * this, set <paramref name="transposeThis"/> to true.
/// The resulting vector will overwrite the entries of <paramref name="rhsVector"/>.
/// </summary>
/// <param name="lhsVector">
/// The vector that will be multiplied by this matrix. It sits on the left hand side of the equation y = oper(A) * x.
/// Constraints: <paramref name="lhsVector"/>.Length == oper(this).<see cref="IIndexable2D.NumColumns"/>.
/// </param>
/// <param name="rhsVector">
/// The vector that will be overwritten by the result of the multiplication. It sits on the right hand side of the
/// equation y = oper(A) * x. Constraints: <paramref name="rhsVector"/>.Length
/// == oper(this).<see cref="IIndexable2D.NumRows"/>.
/// </param>
/// <param name="transposeThis">If true, oper(this) = transpose(this). Otherwise oper(this) = this.</param>
/// <exception cref="NonMatchingDimensionsException">
/// Thrown if the <paramref name="lhsVector"/>.Length or <paramref name="rhsVector"/>.Length violate the described
/// constraints.
/// </exception>
/// <exception cref="PatternModifiedException">
/// Thrown if the storage format of <paramref name="rhsVector"/> does not support overwritting the entries that this
/// method will try to.
/// </exception>
public static void MultiplyIntoResult(this IMatrixView matrix, double[] lhsVector, double[] rhsVector,
bool transposeThis = false)
=> matrix.MultiplyIntoResult(Vector.CreateFromArray(lhsVector), Vector.CreateFromArray(rhsVector), transposeThis);