GenericLinearAlgebraOperations<T>.PackedHermitianRankUpdate Method

Definition

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

Overload List

PackedHermitianRankUpdate(MatrixTriangle, Int32, T, ArraySlice<Complex<T>>, Array1D<Complex<T>>)

Performs the hermitian rank 1 operation A := alpha*x*x**H + A, where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix, supplied in packed form.

PackedHermitianRankUpdate(MatrixTriangle, Int32, Complex<T>, ArraySlice<Complex<T>>, ArraySlice<Complex<T>>, Array1D<Complex<T>>)

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

PackedHermitianRankUpdate(MatrixTriangle, Int32, T, ArraySlice<Complex<T>>, Array1D<Complex<T>>)

Performs the hermitian rank 1 operation A := alpha*x*x**H + A, where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix, supplied in packed form.

C# 
public void PackedHermitianRankUpdate(
	MatrixTriangle uplo,
	int n,
	T alpha,
	ArraySlice<Complex<T>> x,
	Array1D<Complex<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<Complex<T>>
            X is COMPLEX*16 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<Complex<T>>
            AP is COMPLEX*16 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 hermitian 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 hermitian 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.
             Note that the imaginary parts of the diagonal elements need
             not be set, they are assumed to be zero, and on exit they
             are set to zero.

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

PackedHermitianRankUpdate(MatrixTriangle, Int32, Complex<T>, ArraySlice<Complex<T>>, ArraySlice<Complex<T>>, Array1D<Complex<T>>)

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

C# 
public void PackedHermitianRankUpdate(
	MatrixTriangle uplo,
	int n,
	Complex<T> alpha,
	ArraySlice<Complex<T>> x,
	ArraySlice<Complex<T>> y,
	Array1D<Complex<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  Complex<T>
             On entry, ALPHA specifies the scalar alpha.
x  ArraySlice<Complex<T>>
            X is COMPLEX*16 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<Complex<T>>
            Y is COMPLEX*16 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<Complex<T>>
            AP is COMPLEX*16 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 hermitian 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 hermitian 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.
             Note that the imaginary parts of the diagonal elements need
             not be set, they are assumed to be zero, and on exit they
             are set to zero.

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