LinearAlgebraOperations<T>.SymmetricMatrixNorm Method

public T SymmetricMatrixNorm(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	int n,
	Array2D<T> a
)

Public Function SymmetricMatrixNorm ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	n As Integer,
	a As Array2D(Of T)
) As T

public:
T SymmetricMatrixNorm(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	int n, 
	Array2D<T> a
)

member SymmetricMatrixNorm : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        n : int * 
        a : Array2D<'T> -> 'T 

Parameters

norm  MatrixNorm

            Specifies the value to be returned in DLANSY as described
            above.
            

storedTriangle  MatrixTriangle

            Specifies whether the upper or lower triangular part of the
            symmetric matrix A is to be referenced.
            = 'U':  Upper triangular part of A is referenced
            = 'L':  Lower triangular part of A is referenced
            

n  Int32

            The order of the matrix A.  N >= 0.  When N = 0, DLANSY is
            set to zero.
            

a  Array2D<T>

            Dimension (LDA,N)
            The symmetric matrix A.  If UPLO = 'U', the leading n by n
            upper triangular part of A contains the upper triangular part
            of the matrix A, and the strictly lower triangular part of A
            is not referenced.  If UPLO = 'L', the leading n by n lower
            triangular part of A contains the lower triangular part of
            the matrix A, and the strictly upper triangular part of A is
            not referenced.
            

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

Return Value

            DLANSY = ( 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 DLANSY.

public T SymmetricMatrixNorm(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	int n,
	Array2D<Complex<T>> a
)

Public Function SymmetricMatrixNorm ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	n As Integer,
	a As Array2D(Of Complex(Of T))
) As T

public:
T SymmetricMatrixNorm(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	int n, 
	Array2D<Complex<T>> a
)

member SymmetricMatrixNorm : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        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 elements are stored in the upper or lower triangle.

n  Int32

The number of rows and columns of the matrix.

a  Array2D<Complex<T>>

A complex array that contains the elements of the matrix.

Return Value

public T SymmetricMatrixNorm(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	int n,
	ReadOnlySpan2D<Complex<T>> a
)

Public Function SymmetricMatrixNorm ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	n As Integer,
	a As ReadOnlySpan2D(Of Complex(Of T))
) As T

public:
T SymmetricMatrixNorm(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	int n, 
	ReadOnlySpan2D<Complex<T>> a
)

member SymmetricMatrixNorm : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        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 elements are stored in the upper or lower triangle.

n  Int32

The number of rows and columns of the matrix.

a  ReadOnlySpan2D<Complex<T>>

A complex array that contains the elements of the matrix.

Return Value

public abstract T SymmetricMatrixNorm(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	int n,
	ReadOnlySpan<T> a,
	int lda
)

Public MustOverride Function SymmetricMatrixNorm ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	n As Integer,
	a As ReadOnlySpan(Of T),
	lda As Integer
) As T

public:
virtual T SymmetricMatrixNorm(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	int n, 
	ReadOnlySpan<T> a, 
	int lda
) abstract

abstract SymmetricMatrixNorm : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        n : int * 
        a : ReadOnlySpan<'T> * 
        lda : int -> 'T 

Parameters

norm  MatrixNorm

            Specifies the value to be returned in DLANSY as described
            above.
            

storedTriangle  MatrixTriangle

            Specifies whether the upper or lower triangular part of the
            symmetric matrix A is to be referenced.
            = 'U':  Upper triangular part of A is referenced
            = 'L':  Lower triangular part of A is referenced
            

n  Int32

            The order of the matrix A.  N >= 0.  When N = 0, DLANSY is
            set to zero.
            

a  ReadOnlySpan<T>

            Dimension (LDA,N)
            The symmetric matrix A.  If UPLO = 'U', the leading n by n
            upper triangular part of A contains the upper triangular part
            of the matrix A, and the strictly lower triangular part of A
            is not referenced.  If UPLO = 'L', the leading n by n lower
            triangular part of A contains the lower triangular part of
            the matrix A, and the strictly upper triangular part of A is
            not referenced.
            

lda  Int32

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

Return Value

Implements

            DLANSY = ( 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 DLANSY.

public abstract T SymmetricMatrixNorm(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	int n,
	ReadOnlySpan<Complex<T>> a,
	int lda
)

Public MustOverride Function SymmetricMatrixNorm ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	n As Integer,
	a As ReadOnlySpan(Of Complex(Of T)),
	lda As Integer
) As T

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

abstract SymmetricMatrixNorm : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        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 elements are stored in the upper or lower triangle.

n  Int32

The number of rows and 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