/// <summary>
/// Computes the solution to a real system of linear equations
/// A * X = B, where A is a band matrix.
/// </summary>
/// <param name="A">The band matrix.</param>
/// <param name="B">The vector containing the right-hand side of the linear system.</param>
/// <returns>A vector containing the solution to the linear system of equations.</returns>
public Vector Solve(BandMatrix A, Vector B)
{
Matrix myB = B;
Vector solution = this.Solve(A, myB).GetColumnVector(0);
return(this.Solve(A, B));
}
/// <summary>
/// Scalar-Matrix multiplication.
/// </summary>
/// <param name="s"> The left side scalar of the multiplication operator.</param>
/// <param name="A">The right side matrix of the multiplication operator.</param>
/// <returns>A matrix that represents the result of the multiplication.</returns>
public static BandMatrix operator *(double s, BandMatrix A)
{
BandMatrix C = new BandMatrix(A.RowCount, A.ColumnCount, A.LowerBandWidth, A.UpperBandWidth);
double[] AData = A.Data;
double[] CData = C.Data;
Matrix.MultiplicationSM(s, AData, CData);
return C;
}
/// <summary>
/// Scalar-Matrix multiplication.
/// </summary>
/// <param name="s"> The left side scalar of the multiplication operator.</param>
/// <param name="A">The right side matrix of the multiplication operator.</param>
/// <returns>A matrix that represents the result of the multiplication.</returns>
public static BandMatrix operator *(double s, BandMatrix A)
{
BandMatrix C = new BandMatrix(A.RowCount, A.ColumnCount, A.LowerBandWidth, A.UpperBandWidth);
double[] AData = A.Data;
double[] CData = C.Data;
Matrix.MultiplicationSM(s, AData, CData);
return(C);
}
/// <summary>
/// Computes the solution to a real system of linear equations
/// A * X = B, where A is a band matrix.
/// </summary>
/// <param name="A">The band matrix.</param>
/// <param name="B">The matrix containing the right-hand side of the linear system.</param>
/// <returns>A matrix containing the solution to the linear system of equations.</returns>
public Matrix Solve(BandMatrix A, Matrix B)
{
if (this._dgbsv == null)
{
this._dgbsv = new DGBSV();
}
this.CheckDimensions(A, B);
Matrix Solution = B.Clone();
Matrix ExtendedMatrix = A.GetBandPackedMatrix();
double[] BAData = ExtendedMatrix.Data;
double[] SolutionData = Solution.Data;
int[] IPIV = new int[A.RowCount];
int Info = 0;
this._dgbsv.Run(A.RowCount, A.LowerBandWidth, A.UpperBandWidth, B.ColumnCount, ref BAData, 0, ExtendedMatrix.RowCount, ref IPIV, 0, ref SolutionData, 0, Solution.RowCount, ref Info);
#region Error
/// = 0: successful exit
/// .LT. 0: if INFO = -i, the i-th argument had an illegal value
/// .GT. 0: if INFO = i, U(i,i) is exactly zero. The factorization
/// has been completed, but the factor U is exactly
/// singular, and the solution has not been computed.
///</param>
if (Info < 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new ArgumentException("the " + infoSTg + " -th argument had an illegal value");
}
else if (Info > 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new Exception("U(" + infoSTg + "," + infoSTg + ") is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.");
}
#endregion
return(Solution);
}
/// <summary>Generate a BandMatrix with random elements</summary>
/// <param name="rows">Number of rows.</param>
/// <param name="columns">Number of columns.</param>
/// <param name="lowerBandWidth">Number of bands below the main diagonal</param>
/// <param name="upperBandWidth">Number of bands above the main diagonal</param>
public static BandMatrix Random(int rows, int columns, int lowerBandWidth, int upperBandWidth)
{
System.Random random = new System.Random();
BandMatrix X = new BandMatrix(rows, columns, lowerBandWidth, upperBandWidth);
double[] XData = X.Data;
for (int j = 0; j < X.ColumnCount; j++)
{
for (int i = 0; i < X.RowCount; i++)
{
X[i, j] = random.NextDouble();
}
}
return(X);
}
/// <summary>
/// Matrix subtraction.
/// </summary>
/// <param name="A"> The left side matrix of the subtraction operator.</param>
/// <param name="B">The right side matrix of the subtraction operator.</param>
/// <returns>A matrix that represents the result of the matrix subtraction.</returns>
public static BandMatrix operator -(BandMatrix A, BandMatrix B)
{
if (B.RowCount != A.RowCount || B.ColumnCount != A.ColumnCount || B.LowerBandWidth != A.LowerBandWidth || B.UpperBandWidth != A.UpperBandWidth)
{
throw new System.ArgumentException("Matrix dimensions are not valid.");
}
BandMatrix C = new BandMatrix(A.RowCount, A.ColumnCount, A.LowerBandWidth, B.UpperBandWidth);
double[] AData = A.Data;
double[] BData = B.Data;
double[] CData = C.Data;
for (int i = 0; i < AData.Length; i++)
{
CData[i] = AData[i] - BData[i];
}
return(C);
}
/// <summary>
/// Matrix addition.
/// </summary>
/// <param name="A">The left side matrix of the addition operator.</param>
/// <param name="B">The right side matrix of the addition operator.</param>
/// <returns>A matrix that represents the result of the matrix addition.</returns>
public static BandMatrix operator +(BandMatrix A, BandMatrix B)
{
if (B.RowCount != A.RowCount || B.ColumnCount != A.ColumnCount || B.LowerBandWidth != A.LowerBandWidth || B.UpperBandWidth != A.UpperBandWidth)
{
throw new System.ArgumentException("Matrix dimensions are not valid.");
}
BandMatrix C = new BandMatrix(A.RowCount, A.ColumnCount, A.LowerBandWidth, B.UpperBandWidth);
double[] AData = A.Data;
double[] BData = B.Data;
double[] CData = C.Data;
for (int i = 0; i < AData.Length; i++)
{
CData[i] = AData[i] + BData[i];
}
return C;
}
/// <summary>
/// Creates a copy of the matrix.
/// </summary>
/// <returns>The copy of the Matrix.</returns>
public BandMatrix Clone()
{
BandMatrix NewBandMatix = new BandMatrix(this._RowCount, this._ColumnCount, this.MeLowerBandWidth, this.MeUpperBandWidth, this._Data);
return NewBandMatix;
}
/// <summary>Generate a BandMatrix with random elements</summary>
/// <param name="rows">Number of rows.</param>
/// <param name="columns">Number of columns.</param>
/// <param name="lowerBandWidth">Number of bands below the main diagonal</param>
/// <param name="upperBandWidth">Number of bands above the main diagonal</param>
public static BandMatrix Random(int rows, int columns, int lowerBandWidth, int upperBandWidth)
{
System.Random random = new System.Random();
BandMatrix X = new BandMatrix(rows, columns, lowerBandWidth, upperBandWidth);
double[] XData = X.Data;
for (int j = 0; j < X.ColumnCount; j++)
{
for (int i = 0; i < X.RowCount; i++)
{
X[i, j] = random.NextDouble();
}
}
return X;
}
/// <summary>
/// Computes the solution to a real system of linear equations
/// A * X = B, where A is a band matrix.
/// </summary>
/// <param name="A">The band matrix.</param>
/// <param name="B">The matrix containing the right-hand side of the linear system.</param>
/// <returns>A matrix containing the solution to the linear system of equations.</returns>
public Matrix Solve(BandMatrix A, Matrix B)
{
if (this._dgbsv == null) this._dgbsv = new DGBSV();
this.CheckDimensions(A, B);
Matrix Solution = B.Clone();
Matrix ExtendedMatrix = A.GetBandPackedMatrix();
double[] BAData = ExtendedMatrix.Data;
double[] SolutionData = Solution.Data;
int[] IPIV = new int[A.RowCount];
int Info = 0;
this._dgbsv.Run(A.RowCount, A.LowerBandWidth, A.UpperBandWidth, B.ColumnCount, ref BAData, 0, ExtendedMatrix.RowCount, ref IPIV, 0, ref SolutionData, 0, Solution.RowCount, ref Info);
#region Error
/// = 0: successful exit
/// .LT. 0: if INFO = -i, the i-th argument had an illegal value
/// .GT. 0: if INFO = i, U(i,i) is exactly zero. The factorization
/// has been completed, but the factor U is exactly
/// singular, and the solution has not been computed.
///</param>
if (Info < 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new ArgumentException("the " + infoSTg + " -th argument had an illegal value");
}
else if (Info > 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new Exception("U(" + infoSTg + "," + infoSTg + ") is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.");
}
#endregion
return Solution;
}
/// <summary>
/// Computes the solution to a real system of linear equations
/// A * X = B, where A is a band matrix.
/// </summary>
/// <param name="A">The band matrix.</param>
/// <param name="B">The vector containing the right-hand side of the linear system.</param>
/// <returns>A vector containing the solution to the linear system of equations.</returns>
public Vector Solve(BandMatrix A, Vector B)
{
Matrix myB = B;
Vector solution = this.Solve(A, myB).GetColumnVector(0);
return this.Solve(A, B);
}
/// <summary>
/// Creates a copy of the matrix.
/// </summary>
/// <returns>The copy of the Matrix.</returns>
public BandMatrix Clone()
{
BandMatrix NewBandMatix = new BandMatrix(this._RowCount, this._ColumnCount, this.MeLowerBandWidth, this.MeUpperBandWidth, this._Data);
return(NewBandMatix);
}