GenericLinearAlgebraOperations<T>.BandHermitianMultiplyAndAddInPlace Method

public override void BandHermitianMultiplyAndAddInPlace(
	MatrixTriangle uplo,
	int n,
	int k,
	Complex<T> alpha,
	ReadOnlySpan<Complex<T>> a,
	int lda,
	ReadOnlySpan<Complex<T>> x,
	int incx,
	Complex<T> beta,
	Span<Complex<T>> y,
	int incy
)

Public Overrides Sub BandHermitianMultiplyAndAddInPlace ( 
	uplo As MatrixTriangle,
	n As Integer,
	k As Integer,
	alpha As Complex(Of T),
	a As ReadOnlySpan(Of Complex(Of T)),
	lda As Integer,
	x As ReadOnlySpan(Of Complex(Of T)),
	incx As Integer,
	beta As Complex(Of T),
	y As Span(Of Complex(Of T)),
	incy As Integer
)

public:
virtual void BandHermitianMultiplyAndAddInPlace(
	MatrixTriangle uplo, 
	int n, 
	int k, 
	Complex<T> alpha, 
	ReadOnlySpan<Complex<T>> a, 
	int lda, 
	ReadOnlySpan<Complex<T>> x, 
	int incx, 
	Complex<T> beta, 
	Span<Complex<T>> y, 
	int incy
) override

abstract BandHermitianMultiplyAndAddInPlace : 
        uplo : MatrixTriangle * 
        n : int * 
        k : int * 
        alpha : Complex<'T> * 
        a : ReadOnlySpan<Complex<'T>> * 
        lda : int * 
        x : ReadOnlySpan<Complex<'T>> * 
        incx : int * 
        beta : Complex<'T> * 
        y : Span<Complex<'T>> * 
        incy : int -> unit 
override BandHermitianMultiplyAndAddInPlace : 
        uplo : MatrixTriangle * 
        n : int * 
        k : int * 
        alpha : Complex<'T> * 
        a : ReadOnlySpan<Complex<'T>> * 
        lda : int * 
        x : ReadOnlySpan<Complex<'T>> * 
        incx : int * 
        beta : Complex<'T> * 
        y : Span<Complex<'T>> * 
        incy : int -> unit 

Parameters

uplo  MatrixTriangle

             On entry, UPLO specifies whether the upper or lower
             triangular part of the band matrix A is being supplied as
             follows:
                UPLO = 'U' or 'u'   The upper triangular part of A is
                                    being supplied.
                UPLO = 'L' or 'l'   The lower triangular part of A is
                                    being supplied.
            

n  Int32

             On entry, N specifies the order of the matrix A.
             N must be at least zero.
            

k  Int32

             On entry, K specifies the number of super-diagonals of the
             matrix A. K must satisfy  0 .le. K.
            

alpha  Complex<T>

             On entry, ALPHA specifies the scalar alpha.
            

a  ReadOnlySpan<Complex<T>>

            A is complex array of DIMENSION ( LDA, n ).
             Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
             by n part of the array A must contain the upper triangular
             band part of the hermitian matrix, supplied column by
             column, with the leading diagonal of the matrix in row
             ( k + 1 ) of the array, the first super-diagonal starting at
             position 2 in row k, and so on. The top left k by k triangle
             of the array A is not referenced.
             The following program segment will transfer the upper
             triangular part of a hermitian band matrix from conventional
             full matrix storage to band storage:
                   DO 20, J = 1, N
                      M = K + 1 - J
                      DO 10, I = MAX( 1, J - K ), J
                         A( M + I, J ) = matrix( I, J )
                10    CONTINUE
                20 CONTINUE
             Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
             by n part of the array A must contain the lower triangular
             band part of the hermitian matrix, supplied column by
             column, with the leading diagonal of the matrix in row 1 of
             the array, the first sub-diagonal starting at position 1 in
             row 2, and so on. The bottom right k by k triangle of the
             array A is not referenced.
             The following program segment will transfer the lower
             triangular part of a hermitian band matrix from conventional
             full matrix storage to band storage:
                   DO 20, J = 1, N
                      M = 1 - J
                      DO 10, I = J, MIN( N, J + K )
                         A( M + I, J ) = matrix( I, J )
                10    CONTINUE
                20 CONTINUE
             Note that the imaginary parts of the diagonal elements need
             not be set and are assumed to be zero.
            

lda  Int32

             On entry, LDA specifies the first dimension of A as declared
             in the calling (sub) program. LDA must be at least
             ( k + 1 ).
            

x  ReadOnlySpan<Complex<T>>

            X is complex array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCX ) ).
             Before entry, the incremented array X must contain the
             vector x.
            

incx  Int32

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.
            

beta  Complex<T>

             On entry, BETA specifies the scalar beta.
            

y  Span<Complex<T>>

            Y is complex array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCY ) ).
             Before entry, the incremented array Y must contain the
             vector y. On exit, Y is overwritten by the updated vector y.
            

incy  Int32

             On entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.
            

 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

Reference