LinearAlgebraOperations<T>.BandSymmetricMultiplyAndAddInPlace Method

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

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

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

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

            ALPHA is DOUBLE PRECISION.
             On entry, ALPHA specifies the scalar alpha.
            

a  Array2D<T>

            A is DOUBLE PRECISION 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 symmetric 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 symmetric 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 symmetric 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 symmetric 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
            

             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<T>

            X is DOUBLE PRECISION 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  T

            BETA is DOUBLE PRECISION.
             On entry, BETA specifies the scalar beta.
            

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
             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

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

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

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

abstract BandSymmetricMultiplyAndAddInPlace : 
        uplo : MatrixTriangle * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : ReadOnlySpan<'T> * 
        lda : int * 
        x : ReadOnlySpan<'T> * 
        incx : int * 
        beta : 'T * 
        y : Span<'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  T

            ALPHA is DOUBLE PRECISION.
             On entry, ALPHA specifies the scalar alpha.
            

a  ReadOnlySpan<T>

            A is DOUBLE PRECISION 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 symmetric 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 symmetric 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 symmetric 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 symmetric 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
            

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<T>

            X is DOUBLE PRECISION 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  T

            BETA is DOUBLE PRECISION.
             On entry, BETA specifies the scalar beta.
            

y  Span<T>

            Y is DOUBLE PRECISION 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.
            

Implements

 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