LinearAlgebraOperations<T>.TriangularMatrixNorm Method

public T TriangularMatrixNorm(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	MatrixDiagonal diag,
	int m,
	int n,
	Array2D<T> a
)

Public Function TriangularMatrixNorm ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	diag As MatrixDiagonal,
	m As Integer,
	n As Integer,
	a As Array2D(Of T)
) As T

public:
T TriangularMatrixNorm(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal diag, 
	int m, 
	int n, 
	Array2D<T> a
)

member TriangularMatrixNorm : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        diag : MatrixDiagonal * 
        m : int * 
        n : int * 
        a : Array2D<'T> -> 'T 

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<T>

            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

            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.

public T TriangularMatrixNorm(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	MatrixDiagonal diag,
	int m,
	int n,
	Array2D<Complex<T>> a
)

Public Function TriangularMatrixNorm ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	diag As MatrixDiagonal,
	m As Integer,
	n As Integer,
	a As Array2D(Of Complex(Of T))
) As T

public:
T TriangularMatrixNorm(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal diag, 
	int m, 
	int n, 
	Array2D<Complex<T>> a
)

member TriangularMatrixNorm : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        diag : MatrixDiagonal * 
        m : int * 
        n : int * 
        a : Array2D<Complex<'T>> -> 'T 

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<T>>

A complex array that contains the elements of the matrix.

Return Value

public T TriangularMatrixNorm(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	MatrixDiagonal diag,
	int m,
	int n,
	ReadOnlySpan2D<Complex<T>> a
)

Public Function TriangularMatrixNorm ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	diag As MatrixDiagonal,
	m As Integer,
	n As Integer,
	a As ReadOnlySpan2D(Of Complex(Of T))
) As T

public:
T TriangularMatrixNorm(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal diag, 
	int m, 
	int n, 
	ReadOnlySpan2D<Complex<T>> a
)

member TriangularMatrixNorm : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        diag : MatrixDiagonal * 
        m : int * 
        n : int * 
        a : ReadOnlySpan2D<Complex<'T>> -> 'T 

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  ReadOnlySpan2D<Complex<T>>

A complex array that contains the elements of the matrix.

Return Value

public abstract T TriangularMatrixNorm(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	MatrixDiagonal diag,
	int m,
	int n,
	ReadOnlySpan<T> a,
	int lda
)

Public MustOverride Function TriangularMatrixNorm ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	diag As MatrixDiagonal,
	m As Integer,
	n As Integer,
	a As ReadOnlySpan(Of T),
	lda As Integer
) As T

public:
virtual T TriangularMatrixNorm(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal diag, 
	int m, 
	int n, 
	ReadOnlySpan<T> a, 
	int lda
) abstract

abstract TriangularMatrixNorm : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        diag : MatrixDiagonal * 
        m : int * 
        n : int * 
        a : ReadOnlySpan<'T> * 
        lda : int -> 'T 

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  ReadOnlySpan<T>

            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.
            

lda  Int32

            The leading dimension of the array A.  LDA >= max(M,1).
            

Return Value

Implements

            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.

public abstract T TriangularMatrixNorm(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	MatrixDiagonal diag,
	int m,
	int n,
	ReadOnlySpan<Complex<T>> a,
	int lda
)

Public MustOverride Function TriangularMatrixNorm ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	diag As MatrixDiagonal,
	m As Integer,
	n As Integer,
	a As ReadOnlySpan(Of Complex(Of T)),
	lda As Integer
) As T

public:
virtual T TriangularMatrixNorm(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal diag, 
	int m, 
	int n, 
	ReadOnlySpan<Complex<T>> a, 
	int lda
) abstract

abstract TriangularMatrixNorm : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        diag : MatrixDiagonal * 
        m : int * 
        n : int * 
        a : ReadOnlySpan<Complex<'T>> * 
        lda : int -> 'T 

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  ReadOnlySpan<Complex<T>>

A complex array that contains the elements of the matrix.

lda  Int32

The leading dimension of the matrix a.

Return Value

Reference