GenericLinearAlgebraOperations<T>.BandHermitianMultiplyAndAddInPlace Method

public void BandHermitianMultiplyAndAddInPlace(
	MatrixTriangle uplo,
	int n,
	int k,
	Complex<T> alpha,
	Array2D<Complex<T>> a,
	ArraySlice<Complex<T>> x,
	Complex<T> beta,
	ArraySlice<Complex<T>> y
)

Public Sub BandHermitianMultiplyAndAddInPlace ( 
	uplo As MatrixTriangle,
	n As Integer,
	k As Integer,
	alpha As Complex(Of T),
	a As Array2D(Of Complex(Of T)),
	x As ArraySlice(Of Complex(Of T)),
	beta As Complex(Of T),
	y As ArraySlice(Of Complex(Of T))
)

public:
void BandHermitianMultiplyAndAddInPlace(
	MatrixTriangle uplo, 
	int n, 
	int k, 
	Complex<T> alpha, 
	Array2D<Complex<T>> a, 
	ArraySlice<Complex<T>> x, 
	Complex<T> beta, 
	ArraySlice<Complex<T>> y
)

member BandHermitianMultiplyAndAddInPlace : 
        uplo : MatrixTriangle * 
        n : int * 
        k : int * 
        alpha : Complex<'T> * 
        a : Array2D<Complex<'T>> * 
        x : ArraySlice<Complex<'T>> * 
        beta : Complex<'T> * 
        y : ArraySlice<Complex<'T>> -> 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  Array2D<Complex<T>>

            A is COMPLEX*16 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.
            

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

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
             vector x.
            

             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  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
             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.
            

 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