LinearAlgebraOperationsExtensions.BandMultiplyAndAddInPlace Method

public static void BandMultiplyAndAddInPlace<T>(
	this ILinearAlgebraOperations<T> operations,
	TransposeOperation trans,
	int m,
	int n,
	int kl,
	int ku,
	T alpha,
	ReadOnlySpan2D<T> a,
	ReadOnlySpanSlice<T> x,
	T beta,
	SpanSlice<T> y
)

<ExtensionAttribute>
Public Shared Sub BandMultiplyAndAddInPlace(Of T) ( 
	operations As ILinearAlgebraOperations(Of T),
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	kl As Integer,
	ku 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 BandMultiplyAndAddInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	TransposeOperation trans, 
	int m, 
	int n, 
	int kl, 
	int ku, 
	T alpha, 
	ReadOnlySpan2D<T> a, 
	ReadOnlySpanSlice<T> x, 
	T beta, 
	SpanSlice<T> y
)

[<ExtensionAttribute>]
static member BandMultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        kl : int * 
        ku : 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.

trans  TransposeOperation

             On entry, TRANS specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                TRANS = 'T' or 't'   y := alpha*AT*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*AT*x + beta*y.
            

m  Int32

             On entry, M specifies the number of rows of the matrix A.
             M must be at least zero.
            

n  Int32

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

kl  Int32

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

ku  Int32

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

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, the leading ( kl + ku + 1 ) by n part of the
             array A must contain the matrix of coefficients, supplied
             column by column, with the leading diagonal of the matrix in
             row ( ku + 1 ) of the array, the first super-diagonal
             starting at position 2 in row ku, the first sub-diagonal
             starting at position 1 in row ( ku + 2 ), and so on.
             Elements in the array A that do not correspond to elements
             in the band matrix (such as the top left ku by ku triangle)
             are not referenced.
             The following program segment will transfer a band matrix
             from conventional full matrix storage to band storage:
                   DO 20, J = 1, N
                      K = KU + 1 - J
                      DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
                         A( K + 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
             ( kl + ku + 1 ).
            

x  ReadOnlySpanSlice<T>

            X is DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
             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. When BETA is
             supplied as zero then Y need not be set on input.
            

y  SpanSlice<T>

            Y is DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
             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 BandMultiplyAndAddInPlace<T, TStorage, TStorage2D>(
	this ILinearAlgebraOperations<T> operations,
	TransposeOperation transposeOperation,
	int m,
	int n,
	int kl,
	int ku,
	T alpha,
	TStorage2D a,
	TStorage x,
	T beta,
	TStorage y
)
where TStorage : Object, IStorageSlice<T>
where TStorage2D : Object, IStorage2D<T>

<ExtensionAttribute>
Public Shared Sub BandMultiplyAndAddInPlace(Of T, TStorage As {Object, IStorageSlice(Of T)}, TStorage2D As {Object, IStorage2D(Of T)}) ( 
	operations As ILinearAlgebraOperations(Of T),
	transposeOperation As TransposeOperation,
	m As Integer,
	n As Integer,
	kl As Integer,
	ku 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 BandMultiplyAndAddInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	TransposeOperation transposeOperation, 
	int m, 
	int n, 
	int kl, 
	int ku, 
	T alpha, 
	TStorage2D a, 
	TStorage x, 
	T beta, 
	TStorage y
)

[<ExtensionAttribute>]
static member BandMultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        transposeOperation : TransposeOperation * 
        m : int * 
        n : int * 
        kl : int * 
        ku : 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.

transposeOperation  TransposeOperation

Specifies the operation to be performed on the matrix a.

m  Int32

The number of rows in the matrix a.

n  Int32

The number of columns in the matrix a.

kl  Int32

The lower bandwidth of the matrix a.

ku  Int32

The upper 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 DGBMV.

Reference