/// <summary>Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general rectangular matrix.
/// </summary>
/// <param name="matrixNormType">The type of the matrix norm.</param>
/// <param name="m">Th enumber of rows.</param>
/// <param name="n">The number of columns.</param>
/// <param name="a">The <paramref name="m"/>-by-<paramref name="n"/> dense matrix provided column-by-column.</param>
/// <param name="work">A workspace array which is referenced in the case of infinity norm only. In this case the length must be at least <paramref name="m"/>.</param>
/// <returns>The value of the specific matrix norm.</returns>
public double dlange(MatrixNormType matrixNormType, int m, int n, double[] a, double[] work)
{
var norm = LapackNativeWrapper.GetMatrixNormType(matrixNormType);
int lda = Math.Max(1, m);
return(_dlange(ref norm, ref m, ref n, a, ref lda, work));
}
/// <summary>Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of symmetric matrix supplied in packed form.
/// </summary>
/// <param name="matrixNormType">The type of the matrix norm.</param>
/// <param name="n">The order of the matrix.</param>
/// <param name="ap">The specified symmetric matrix in packed form, i.e. either upper or lower triangle as specified in <paramref name="triangularMatrixType"/> with at least <paramref name="n"/> * (<paramref name="n"/> + 1) / 2 elements.</param>
/// <param name="work">A workspace array which is referenced in the case of 1- or infinity-norm only. In this case the length must be at least <paramref name="n"/>.</param>
/// <param name="triangularMatrixType">A value indicating whether the upper or lower triangular part of the symmetric input matrix is stored.</param>
/// <returns>The value of the specific matrix norm.</returns>
public double zlansp(MatrixNormType matrixNormType, int n, Complex[] ap, Complex[] work, BLAS.TriangularMatrixType triangularMatrixType = BLAS.TriangularMatrixType.LowerTriangularMatrix)
{
var norm = LapackNativeWrapper.GetMatrixNormType(matrixNormType);
var uplo = LapackNativeWrapper.GetUplo(triangularMatrixType);
return(_zlansp(ref norm, ref uplo, ref n, ap, work));
}
/// <summary>Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.
/// </summary>
/// <param name="matrixNormType">The type of the matrix norm.</param>
/// <param name="n">The order of the quadratic general band matrix.</param>
/// <param name="kl">The number of sub-diagonals of the specific general band matrix.</param>
/// <param name="ku">The number of super-diagonals of the specific general band matrix.</param>
/// <param name="a">The general band matrix stored in general band matrix storage, i.e. column-by-column, where each column contains exactly <paramref name="kl" /> + <paramref name="ku" /> + 1 elements.</param>
/// <param name="work">A workspace array which is referenced in the case of infinity norm only. In this case the length must be at least <paramref name="n" />.</param>
/// <returns>The value of the specific matrix norm.</returns>
public double zlangb(MatrixNormType matrixNormType, int n, int kl, int ku, Complex[] a, Complex[] work)
{
var norm = LapackNativeWrapper.GetMatrixNormType(matrixNormType);
int ldab = kl + ku + 1;
return(_zlangb(ref norm, ref n, ref kl, ref ku, a, ref ldab, work));
}
/// <summary>Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of symmetric matrix supplied in packed form.
/// </summary>
/// <param name="matrixNormType">The type of the matrix norm.</param>
/// <param name="n">The order of the matrix.</param>
/// <param name="ap">The specified symmetric matrix in packed form, i.e. either upper or lower triangle as specified in <paramref name="triangularMatrixType"/> with at least <paramref name="n"/> * (<paramref name="n"/> + 1) / 2 elements.</param>
/// <param name="work">A workspace array which is referenced in the case of 1- or infinity-norm only. In this case the length must be at least <paramref name="n"/>.</param>
/// <param name="triangularMatrixType">A value indicating whether the upper or lower triangular part of the symmetric input matrix is stored.</param>
/// <returns>The value of the specific matrix norm.</returns>
public double dlansp(MatrixNormType matrixNormType, int n, double[] ap, double[] work, BLAS.TriangularMatrixType triangularMatrixType = BLAS.TriangularMatrixType.LowerTriangularMatrix)
{
var norm = LAPACK.GetMatrixNormType(matrixNormType);
var uplo = LAPACK.GetUplo(triangularMatrixType);
return(_dlansp(ref norm, ref uplo, ref n, ap, work));
}
/// <summary>Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general rectangular matrix.
/// </summary>
/// <param name="matrixNormType">The type of the matrix norm.</param>
/// <param name="m">Th enumber of rows.</param>
/// <param name="n">The number of columns.</param>
/// <param name="a">The <paramref name="m"/>-by-<paramref name="n"/> dense matrix provided column-by-column.</param>
/// <param name="work">A workspace array which is referenced in the case of infinity norm only. In this case the length must be at least <paramref name="m"/>.</param>
/// <returns>The value of the specific matrix norm.</returns>
public double zlange(MatrixNormType matrixNormType, int m, int n, Complex[] a, Complex[] work)
{
var norm = LAPACK.GetMatrixNormType(matrixNormType);
int lda = Math.Max(1, m);
return(_zlange(ref norm, ref m, ref n, a, ref lda, work));
}
/// <summary>Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.
/// </summary>
/// <param name="matrixNormType">The type of the matrix norm.</param>
/// <param name="n">The order of the quadratic general band matrix.</param>
/// <param name="kl">The number of sub-diagonals of the specific general band matrix.</param>
/// <param name="ku">The number of super-diagonals of the specific general band matrix.</param>
/// <param name="a">The general band matrix stored in general band matrix storage, i.e. column-by-column, where each column contains exactly <paramref name="kl" /> + <paramref name="ku" /> + 1 elements.</param>
/// <param name="work">A workspace array which is referenced in the case of infinity norm only. In this case the length must be at least <paramref name="n" />.</param>
/// <returns>The value of the specific matrix norm.</returns>
public double dlangb(MatrixNormType matrixNormType, int n, int kl, int ku, double[] a, double[] work)
{
var norm = LAPACK.GetMatrixNormType(matrixNormType);
int ldab = kl + ku + 1;
return(_dlangb(ref norm, ref n, ref kl, ref ku, a, ref ldab, work));
}
private static void CalcNorm(MCJRMatrix matrix, MatrixNormType normType)
{
var lib = new MLapackLib();
double norm = lib.norm(Convert.ToSByte(normType), matrix);
Console.WriteLine("norm = " + norm);
}
/// <summary>Gets a specific norm of the current matrix object.
/// </summary>
/// <param name="normType">The type of the (matrix) norm.</param>
/// <returns>The norm of the current instance with respect to the <paramref name="normType" />.</returns>
public double GetNorm(MatrixNormType normType)
{
switch (normType)
{
case MatrixNormType.OneNorm: // for a diagonal matrix some matrix norms are identical
case MatrixNormType.Infinity:
case MatrixNormType.LargestAbsoluteValue:
return(Data[BLAS.Level1.idamax(Dimension, Data)]);
case MatrixNormType.Frobenius:
return(BLAS.Level1.dnrm2(Dimension, Data));
default: throw new NotImplementedException();
}
}
/// <summary>Gets a specific norm of the current matrix object.
/// </summary>
/// <param name="normType">The type of the (matrix) norm.</param>
/// <returns>The norm of the current instance with respect to the <paramref name="normType"/>.</returns>
public double GetNorm(MatrixNormType normType = MatrixNormType.Frobenius)
{
/* in the case of a transposed matrix: all norms are identical except 1- and Infinity matrix norm which have to be replaced by each other: */
MatrixNormType adjNormType = normType;
if (m_TransposeState == BLAS.MatrixTransposeState.Transpose)
{
if (normType == MatrixNormType.Infinity)
{
adjNormType = MatrixNormType.OneNorm;
}
else if (normType == MatrixNormType.OneNorm)
{
adjNormType = MatrixNormType.Infinity;
}
}
double[] work = (adjNormType != MatrixNormType.Infinity) ? null : new double[m_RowCount];
return(LAPACK.AuxiliaryRoutines.Matrix.dlange(adjNormType, m_RowCount, m_ColumnCount, m_Data, work));
}
/// <summary>Gets a specific norm of the current matrix object.
/// </summary>
/// <param name="normType">The type of the (matrix) norm.</param>
/// <returns>The norm of the current instance with respect to the <paramref name="normType"/>.</returns>
public double GetNorm(MatrixNormType normType)
{
if (IsQuadratic == true) // apply LAPACK function if available
{
/* in the case of a transposed matrix: all norms are identical except 1- and Infinity matrix norm which have to be replaced by each other: */
MatrixNormType adjNormType = normType;
if (m_TransposeState == BLAS.MatrixTransposeState.Transpose)
{
if (normType == MatrixNormType.Infinity)
{
adjNormType = MatrixNormType.OneNorm;
}
else if (normType == MatrixNormType.OneNorm)
{
adjNormType = MatrixNormType.Infinity;
}
}
double[] work = (adjNormType != MatrixNormType.Infinity) ? null : new double[m_RowCount];
return(LAPACK.AuxiliaryRoutines.Matrix.dlangb(adjNormType, m_RowCount, m_SubDiagonalCount, m_SuperDiagonalCount, m_Data, work));
}
var norm = 0.0;
int k = m_SubDiagonalCount + m_SuperDiagonalCount + 1;
switch (normType)
{
case MatrixNormType.Frobenius:
NormLoop(x => { norm += x * x; });
return(Math.Sqrt(norm));
case MatrixNormType.LargestAbsoluteValue:
norm = Double.MinValue;
NormLoop(x => { norm = ((Math.Abs(x) > norm) ? Math.Abs(x) : norm); });
return(norm);
case MatrixNormType.Infinity: // max. row sum
norm = Double.MinValue;
if (m_TransposeState == BLAS.MatrixTransposeState.NoTranspose)
{
for (int i = 0; i < m_RowCount; i++)
{
double temp = 0.0;
for (int j = Math.Max(0, i - SubDiagonalCount); j <= Math.Min(m_ColumnCount - 1, i + SuperDiagonalCount); j++)
{
temp += Math.Abs(m_Data[i - j + m_SuperDiagonalCount + j * k]);
}
norm = (temp > norm) ? temp : norm;
}
}
else
{
for (int i = 0; i < m_ColumnCount; i++)
{
double temp = 0.0;
for (int j = Math.Max(0, i - SubDiagonalCount); j <= Math.Min(m_RowCount - 1, i + SuperDiagonalCount); j++)
{
temp += Math.Abs(m_Data[j - i + m_SuperDiagonalCount + i * k]);
}
norm = (temp > norm) ? temp : norm;
}
}
return(norm);
case MatrixNormType.OneNorm: // max. column sum
if (m_TransposeState == BLAS.MatrixTransposeState.NoTranspose)
{
for (int j = 0; j < m_ColumnCount; j++)
{
int iMin = j - m_SuperDiagonalCount;
int iMax = j + m_SubDiagonalCount;
var temp = 0.0;
for (int i = Math.Max(0, iMin); i < Math.Min(m_RowCount, iMax); i++)
{
temp += Math.Abs(m_Data[i - j + m_SuperDiagonalCount + j * k]);
}
norm = (temp > norm) ? temp : norm;
}
}
else
{
for (int j = 0; j < m_RowCount; j++)
{
int iMin = j - m_SubDiagonalCount;
int iMax = j + m_SuperDiagonalCount;
var temp = 0.0;
for (int i = Math.Max(0, iMin); i < Math.Min(m_ColumnCount, iMax); i++)
{
temp += Math.Abs(m_Data[j - i + m_SuperDiagonalCount + i * k]);
}
norm = (temp > norm) ? temp : norm;
}
}
return(norm);
default: throw new NotImplementedException();
}
}
public double zlansp(MatrixNormType matrixNormType, int n, Complex[] ap, Complex[] work, BLAS.TriangularMatrixType triangularMatrixType = BLAS.TriangularMatrixType.LowerTriangularMatrix)
{
throw new NotImplementedException();
}
public double zlange(MatrixNormType matrixNormType, int m, int n, Complex[] a, Complex[] work)
{
throw new NotImplementedException();
}
public double dlangb(MatrixNormType matrixNormType, int n, int kl, int ku, double[] a, double[] work)
{
throw new NotImplementedException();
}
/// <summary>Gets a specific norm of the current matrix object.
/// </summary>
/// <param name="normType">The type of the (matrix) norm.</param>
/// <returns>The norm of the current instance with respect to the <paramref name="normType" />.</returns>
public double GetNorm(MatrixNormType normType)
{
double[] work = (normType == MatrixNormType.Infinity) || (normType == MatrixNormType.OneNorm) ? new double[Dimension] : null;
return(LAPACK.AuxiliaryRoutines.Matrix.dlansp(normType, Dimension, Data, work));
}
private static void CalcNorm(MCJRMatrix matrix, MatrixNormType normType)
{
var lib = new MLapackLib();
double norm = lib.norm(Convert.ToSByte(normType), matrix);
Console.WriteLine("norm = " + norm);
}
