LinearAlgebraOperationsExtensions.SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpanSlice<T>, Span2D<T>) Method

Performs the symmetric rank 1 operation A := alpha*x*x**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix.

Definition

Namespace: Extreme.Collections
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 9.0.0
C#
public static void SymmetricRankUpdate<T>(
	this ILinearAlgebraOperations<T> operations,
	MatrixTriangle uplo,
	int n,
	T alpha,
	ReadOnlySpanSlice<T> x,
	Span2D<T> a
)

Parameters

operations  ILinearAlgebraOperations<T>
 
uplo  MatrixTriangle
             On entry, UPLO specifies whether the upper or lower
             triangular part of the array A is to be referenced as
             follows:
                UPLO = 'U' or 'u'   Only the upper triangular part of A
                                    is to be referenced.
                UPLO = 'L' or 'l'   Only the lower triangular part of A
                                    is to be referenced.
            
n  Int32
             On entry, N specifies the order of the matrix A.
             N must be at least zero.
            
alpha  T
            ALPHA is DOUBLE PRECISION.
             On entry, ALPHA specifies the scalar alpha.
            
x  ReadOnlySpanSlice<T>
            X is DOUBLE PRECISION array of dimension at least
             ( 1 + ( n - 1 )*abs( INCX ) ).
             Before entry, the incremented array X must contain the n
             element vector x.
            
             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.
            
a  Span2D<T>
            A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
             Before entry with  UPLO = 'U' or 'u', the leading n by n
             upper triangular part of the array A must contain the upper
             triangular part of the symmetric matrix and the strictly
             lower triangular part of A is not referenced. On exit, the
             upper triangular part of the array A is overwritten by the
             upper triangular part of the updated matrix.
             Before entry with UPLO = 'L' or 'l', the leading n by n
             lower triangular part of the array A must contain the lower
             triangular part of the symmetric matrix and the strictly
             upper triangular part of A is not referenced. On exit, the
             lower triangular part of the array A is overwritten by the
             lower triangular part of the updated matrix.
            
             On entry, LDA specifies the first dimension of A as declared
             in the calling (sub) program. LDA must be at least
             max( 1, n ).
            

Type Parameters

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

Further Details:

            Level 2 LinearAlgebra routine.
            -- Written on 22-October-1986.
               Jack Dongarra, Argonne National Lab.
               Jeremy Du Croz, Nag Central Office.
               Sven Hammarling, Nag Central Office.
               Richard Hanson, Sandia National Labs.
            

Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011

See Also