ManagedLinearAlgebraOperationsOfSingle.TriangularMatrixNorm Method

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics.SinglePrecision (in Extreme.Numerics.SinglePrecision.dll) Version: 8.1.4

Overload List

TriangularMatrixNorm(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, Int32, Array2D<Complex<Single>>) Computes the norm of a triangular matrix.
TriangularMatrixNorm(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, Int32, Array2D<Single>)

Returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A.

TriangularMatrixNorm(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, Int32, Array2D<Complex<Single>>)

Computes the norm of a triangular matrix.
C#
public override float TriangularMatrixNorm(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	MatrixDiagonal diag,
	int m,
	int n,
	Array2D<Complex<float>> a
)

Parameters

norm  MatrixNorm
A MatrixNorm that specifies the type of norm to compute.
storedTriangle  MatrixTriangle
A MatrixTriangle value that specifies whether the matrix is upper or lower triangular.
diag  MatrixDiagonal
A MatrixDiagonal value that indicates whether the diagonal elements are all equal to one.
m  Int32
The number of rows of the matrix.
n  Int32
The number of columns of the matrix.
a  Array2D<Complex<Single>>
A complex number array that contains the elements of the matrix.

Return Value

Single
The norm of the matrix.

Remarks

This method corresponds to the LAPACK routine ?LANTR.

TriangularMatrixNorm(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, Int32, Array2D<Single>)

Returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A.

C#
public override float TriangularMatrixNorm(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	MatrixDiagonal diag,
	int m,
	int n,
	Array2D<float> a
)

Parameters

norm  MatrixNorm
            Specifies the value to be returned in DLANTR as described
            above.
            
storedTriangle  MatrixTriangle
            Specifies whether the matrix A is upper or lower trapezoidal.
            = 'U':  Upper trapezoidal
            = 'L':  Lower trapezoidal
            Note that A is triangular instead of trapezoidal if M = N.
            
diag  MatrixDiagonal
            Specifies whether or not the matrix A has unit diagonal.
            = 'N':  Non-unit diagonal
            = 'U':  Unit diagonal
            
m  Int32
            The number of rows of the matrix A.  M >= 0, and if
            UPLO = 'U', M <= N.  When M = 0, DLANTR is set to zero.
            
n  Int32
            The number of columns of the matrix A.  N >= 0, and if
            UPLO = 'L', N <= M.  When N = 0, DLANTR is set to zero.
            
a  Array2D<Single>
            Dimension (LDA,N)
            The trapezoidal matrix A (A is triangular if M = N).
            If UPLO = 'U', the leading m by n upper trapezoidal part of
            the array A contains the upper trapezoidal matrix, and the
            strictly lower triangular part of A is not referenced.
            If UPLO = 'L', the leading m by n lower trapezoidal part of
            the array A contains the lower trapezoidal matrix, and the
            strictly upper triangular part of A is not referenced.  Note
            that when DIAG = 'U', the diagonal elements of A are not
            referenced and are assumed to be one.
            
            The leading dimension of the array A.  LDA >= max(M,1).
            

Return Value

Single

Implements

ILinearAlgebraOperations<T>.TriangularMatrixNorm(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, Int32, Array2D<T>)

Remarks

            DLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
                     (
                     ( norm1(A),         NORM = '1', 'O' or 'o'
                     (
                     ( normI(A),         NORM = 'I' or 'i'
                     (
                     ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
            ere  norm1  denotes the  one norm of a matrix (maximum column sum),
            ormI  denotes the  infinity norm  of a matrix  (maximum row sum) and
            normF  denotes the  Frobenius norm of a matrix (square root of sum of
            squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
            

This method corresponds to the LAPACK routine DLANTR.

See Also