GenericLinearAlgebraOperations<T>.PackedSymmetricMultiplyAndAddInPlace Method

Performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form.

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics.Generic (in Extreme.Numerics.Generic.dll) Version: 8.1.4
C#
public void PackedSymmetricMultiplyAndAddInPlace(
	MatrixTriangle uplo,
	int n,
	T alpha,
	Array1D<T> ap,
	ArraySlice<T> x,
	T beta,
	ArraySlice<T> y
)

Parameters

uplo  MatrixTriangle
             On entry, UPLO specifies whether the upper or lower
             triangular part of the matrix A is supplied in the packed
             array AP as follows:
                UPLO = 'U' or 'u'   The upper triangular part of A is
                                    supplied in AP.
                UPLO = 'L' or 'l'   The lower triangular part of A is
                                    supplied in AP.
            
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.
            
ap  Array1D<T>
            AP is DOUBLE PRECISION array of DIMENSION at least
             ( ( n*( n + 1 ) )/2 ).
             Before entry with UPLO = 'U' or 'u', the array AP must
             contain the upper triangular part of the symmetric matrix
             packed sequentially, column by column, so that AP( 1 )
             contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
             and a( 2, 2 ) respectively, and so on.
             Before entry with UPLO = 'L' or 'l', the array AP must
             contain the lower triangular part of the symmetric matrix
             packed sequentially, column by column, so that AP( 1 )
             contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
             and a( 3, 1 ) respectively, and so on.
            
x  ArraySlice<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.
            
beta  T
            BETA is DOUBLE PRECISION.
             On entry, BETA specifies the scalar beta. When BETA is
             supplied as zero then Y need not be set on input.
            
y  ArraySlice<T>
            Y is DOUBLE PRECISION array of dimension at least
             ( 1 + ( n - 1 )*abs( INCY ) ).
             Before entry, the incremented array Y must contain the n
             element vector y. On exit, Y is overwritten by the updated
             vector y.
            
             On entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.
            

Remarks

Further Details:

            Level 2 LinearAlgebra routine.
            The vector and matrix arguments are not referenced when N = 0, or M = 0
            -- 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