GenericLinearAlgebraOperations<T>.PackedSymmetricRankUpdate Method

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics.Generic (in Extreme.Numerics.Generic.dll) Version: 8.1.4

Overload List

PackedSymmetricRankUpdate(MatrixTriangle, Int32, T, ArraySlice<T>, Array1D<T>)

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, supplied in packed form.

PackedSymmetricRankUpdate(MatrixTriangle, Int32, T, ArraySlice<T>, ArraySlice<T>, Array1D<T>)

Performs the symmetric rank 2 operation A := alpha*x*y**T + alpha*y*x**T + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form.

PackedSymmetricRankUpdate(MatrixTriangle, Int32, T, ArraySlice<T>, Array1D<T>)

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, supplied in packed form.

C# 
public void PackedSymmetricRankUpdate(
	MatrixTriangle uplo,
	int n,
	T alpha,
	ArraySlice<T> x,
	Array1D<T> ap
)

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.
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.
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. On exit, the array
             AP is overwritten by the upper triangular part of the
             updated matrix.
             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. On exit, the array
             AP is overwritten by the lower triangular part of the
             updated matrix.

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

PackedSymmetricRankUpdate(MatrixTriangle, Int32, T, ArraySlice<T>, ArraySlice<T>, Array1D<T>)

Performs the symmetric rank 2 operation A := alpha*x*y**T + alpha*y*x**T + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form.

C# 
public void PackedSymmetricRankUpdate(
	MatrixTriangle uplo,
	int n,
	T alpha,
	ArraySlice<T> x,
	ArraySlice<T> y,
	Array1D<T> ap
)

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.
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.
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 entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.
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. On exit, the array
             AP is overwritten by the upper triangular part of the
             updated matrix.
             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. On exit, the array
             AP is overwritten by the lower triangular part of the
             updated matrix.

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