LinearAlgebraOperationsExtensions.SymmetricMatrixNorm<T>(ILinearAlgebraOperations<T>, MatrixNorm, MatrixTriangle, Int32, ReadOnlySpan2D<T>) Method

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

Definition

Namespace: Extreme.Collections
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 9.0.0
C#
public static T SymmetricMatrixNorm<T>(
	this ILinearAlgebraOperations<T> operations,
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	int n,
	ReadOnlySpan2D<T> a
)

Parameters

operations  ILinearAlgebraOperations<T>
 
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  ReadOnlySpan2D<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).
            

Type Parameters

T

Return Value

T

Usage Note

In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).

Remarks

            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.

See Also