LinearAlgebraOperationsExtensions.BandSymmetricMultiplyAndAddInPlace Method

public static void BandSymmetricMultiplyAndAddInPlace<T>(
	this ILinearAlgebraOperations<T> operations,
	MatrixTriangle uplo,
	int n,
	int k,
	T alpha,
	ReadOnlySpan2D<T> a,
	ReadOnlySpanSlice<T> x,
	T beta,
	SpanSlice<T> y
)

<ExtensionAttribute>
Public Shared Sub BandSymmetricMultiplyAndAddInPlace(Of T) ( 
	operations As ILinearAlgebraOperations(Of T),
	uplo As MatrixTriangle,
	n As Integer,
	k As Integer,
	alpha As T,
	a As ReadOnlySpan2D(Of T),
	x As ReadOnlySpanSlice(Of T),
	beta As T,
	y As SpanSlice(Of T)
)

public:
[ExtensionAttribute]
generic<typename T>
static void BandSymmetricMultiplyAndAddInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixTriangle uplo, 
	int n, 
	int k, 
	T alpha, 
	ReadOnlySpan2D<T> a, 
	ReadOnlySpanSlice<T> x, 
	T beta, 
	SpanSlice<T> y
)

[<ExtensionAttribute>]
static member BandSymmetricMultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        uplo : MatrixTriangle * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : ReadOnlySpan2D<'T> * 
        x : ReadOnlySpanSlice<'T> * 
        beta : 'T * 
        y : SpanSlice<'T> -> unit 

Parameters

operations  ILinearAlgebraOperations<T>

The object that performs the operation.

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  ReadOnlySpan2D<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  ReadOnlySpanSlice<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  SpanSlice<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.
            

Type Parameters

T

Usage Note

 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 static void BandSymmetricMultiplyAndAddInPlace<T, TStorage, TStorage2D>(
	this ILinearAlgebraOperations<T> operations,
	MatrixTriangle storedTriangle,
	int n,
	int k,
	T alpha,
	TStorage2D a,
	TStorage x,
	T beta,
	TStorage y
)
where TStorage : Object, IStorageSlice<T>
where TStorage2D : Object, IStorage2D<T>

<ExtensionAttribute>
Public Shared Sub BandSymmetricMultiplyAndAddInPlace(Of T, TStorage As {Object, IStorageSlice(Of T)}, TStorage2D As {Object, IStorage2D(Of T)}) ( 
	operations As ILinearAlgebraOperations(Of T),
	storedTriangle As MatrixTriangle,
	n As Integer,
	k As Integer,
	alpha As T,
	a As TStorage2D,
	x As TStorage,
	beta As T,
	y As TStorage
)

public:
[ExtensionAttribute]
generic<typename T, typename TStorage, typename TStorage2D>
where TStorage : Object, IStorageSlice<T>
where TStorage2D : Object, IStorage2D<T>
static void BandSymmetricMultiplyAndAddInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixTriangle storedTriangle, 
	int n, 
	int k, 
	T alpha, 
	TStorage2D a, 
	TStorage x, 
	T beta, 
	TStorage y
)

[<ExtensionAttribute>]
static member BandSymmetricMultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        storedTriangle : MatrixTriangle * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : 'TStorage2D * 
        x : 'TStorage * 
        beta : 'T * 
        y : 'TStorage -> unit  when 'TStorage : Object and IStorageSlice<'T> when 'TStorage2D : Object and IStorage2D<'T>

Parameters

operations  ILinearAlgebraOperations<T>

The linear algebra operations instance used to perform the calculation.

storedTriangle  MatrixTriangle

Specifies whether the matrix is an upper or lower triangular matrix.

n  Int32

The number of rows and columns in the matrix a.

k  Int32

The bandwidth of the matrix a.

alpha  T

The scalar used to multiply the matrix-vector product.

a  TStorage2D

A span that contains the elements of the matrix.

x  TStorage

A reference to a one-dimensional array containing the elements of the vector x.

beta  T

The scalar used to multiply y.

y  TStorage

A reference to a one-dimensional array containing the elements of the vector y. The elements of y are overwritten with the result.

Type Parameters

T

TStorage

TStorage2D

Usage Note

This method is similar to the BLAS routine DSBMV.

Reference