LinearAlgebraOperationsExtensions.SymmetricMultiplyAndAddInPlace Method

Definition

Namespace: Numerics.NET.Collections
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.4

Overload List

SymmetricMultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpanSlice<T>, T, SpanSlice<T>)	Performs the matrix-vector operation y := alphaAx + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix.
SymmetricMultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpan2D<T>, T, Span2D<T>)	Performs one of the matrix-matrix operations C := alphaAB + betaC, or C := alphaBA + betaC, where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices.
SymmetricMultiplyAndAddInPlace<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, Int32, Int32, T, TStorage2D, TStorage2D, T, TStorage2D)	Sum of the product of a symmetric and a general matrix and a scaled matrix.
SymmetricMultiplyAndAddInPlace<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, TStorage2D, TStorage, T, TStorage)	Product of a symmetric matrix and a vector.

SymmetricMultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpanSlice<T>, T, SpanSlice<T>)

Performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix.

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

Visual Basic

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

C++/CLI

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

[<ExtensionAttribute>]
static member SymmetricMultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        uplo : MatrixTriangle * 
        n : 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 array A is to be referenced as
             follows:
                UPLO = 'U' or 'u'   Only the upper triangular part of A
                                    is to be referenced.
                UPLO = 'L' or 'l'   Only the lower triangular part of A
                                    is to be referenced.

n Int32

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

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 n by n
             upper triangular part of the array A must contain the upper
             triangular part of the symmetric matrix and the strictly
             lower triangular part of A is not referenced.
             Before entry with UPLO = 'L' or 'l', the leading n by n
             lower triangular part of the array A must contain the lower
             triangular part of the symmetric matrix and the strictly
             upper triangular part of A is not referenced.

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

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 n
             element 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 + ( n - 1 )*abs( INCY ) ).
             Before entry, the incremented array Y must contain the n
             element 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

In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).

Remarks

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

SymmetricMultiplyAndAddInPlace<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, TStorage2D, TStorage, T, TStorage)

Product of a symmetric matrix and a vector.

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

Visual Basic

<ExtensionAttribute>
Public Shared Sub SymmetricMultiplyAndAddInPlace(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,
	alpha As T,
	a As TStorage2D,
	x As TStorage,
	beta As T,
	y As TStorage
)

C++/CLI

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

[<ExtensionAttribute>]
static member SymmetricMultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        storedTriangle : MatrixTriangle * 
        n : 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.
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

Remarks

This method is similar to the BLAS routine DSYMV.

SymmetricMultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpan2D<T>, T, Span2D<T>)

Performs one of the matrix-matrix operations C := alpha*A*B + beta*C, or C := alpha*B*A + beta*C, where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices.

public static void SymmetricMultiplyAndAddInPlace<T>(
	this ILinearAlgebraOperations<T> operations,
	MatrixOperationSide side,
	MatrixTriangle uplo,
	int m,
	int n,
	T alpha,
	ReadOnlySpan2D<T> a,
	ReadOnlySpan2D<T> b,
	T beta,
	Span2D<T> c
)

Visual Basic

<ExtensionAttribute>
Public Shared Sub SymmetricMultiplyAndAddInPlace(Of T) ( 
	operations As ILinearAlgebraOperations(Of T),
	side As MatrixOperationSide,
	uplo As MatrixTriangle,
	m As Integer,
	n As Integer,
	alpha As T,
	a As ReadOnlySpan2D(Of T),
	b As ReadOnlySpan2D(Of T),
	beta As T,
	c As Span2D(Of T)
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T>
static void SymmetricMultiplyAndAddInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixOperationSide side, 
	MatrixTriangle uplo, 
	int m, 
	int n, 
	T alpha, 
	ReadOnlySpan2D<T> a, 
	ReadOnlySpan2D<T> b, 
	T beta, 
	Span2D<T> c
)

[<ExtensionAttribute>]
static member SymmetricMultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        side : MatrixOperationSide * 
        uplo : MatrixTriangle * 
        m : int * 
        n : int * 
        alpha : 'T * 
        a : ReadOnlySpan2D<'T> * 
        b : ReadOnlySpan2D<'T> * 
        beta : 'T * 
        c : Span2D<'T> -> unit

Parameters

operations ILinearAlgebraOperations<T>

The object that performs the operation.

side MatrixOperationSide

             On entry,  SIDE  specifies whether  the  symmetric matrix  A
             appears on the  left or right  in the  operation as follows:
                SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
                SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,

uplo MatrixTriangle

             On  entry,   UPLO  specifies  whether  the  upper  or  lower
             triangular  part  of  the  symmetric  matrix   A  is  to  be
             referenced as follows:
                UPLO = 'U' or 'u'   Only the upper triangular part of the
                                    symmetric matrix is to be referenced.
                UPLO = 'L' or 'l'   Only the lower triangular part of the
                                    symmetric matrix is to be referenced.

m Int32

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

n Int32

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

alpha T

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

a ReadOnlySpan2D<T>

            A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
             m  when  SIDE = 'L' or 'l'  and is  n otherwise.
             Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
             the array  A  must contain the  symmetric matrix,  such that
             when  UPLO = 'U' or 'u', the leading m by m upper triangular
             part of the array  A  must contain the upper triangular part
             of the  symmetric matrix and the  strictly  lower triangular
             part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
             the leading  m by m  lower triangular part  of the  array  A
             must  contain  the  lower triangular part  of the  symmetric
             matrix and the  strictly upper triangular part of  A  is not
             referenced.
             Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
             the array  A  must contain the  symmetric matrix,  such that
             when  UPLO = 'U' or 'u', the leading n by n upper triangular
             part of the array  A  must contain the upper triangular part
             of the  symmetric matrix and the  strictly  lower triangular
             part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
             the leading  n by n  lower triangular part  of the  array  A
             must  contain  the  lower triangular part  of the  symmetric
             matrix and the  strictly upper triangular part of  A  is not
             referenced.

             On entry, LDA specifies the first dimension of A as declared
             in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
             LDA must be at least  max( 1, m ), otherwise  LDA must be at
             least  max( 1, n ).

b ReadOnlySpan2D<T>

            B is DOUBLE PRECISION array of DIMENSION ( LDB, n ).
             Before entry, the leading  m by n part of the array  B  must
             contain the matrix B.

             On entry, LDB specifies the first dimension of B as declared
             in  the  calling  (sub)  program.   LDB  must  be  at  least
             max( 1, m ).

beta T

            BETA is DOUBLE PRECISION.
             On entry,  BETA  specifies the scalar  beta.  When  BETA  is
             supplied as zero then C need not be set on input.

c Span2D<T>

            C is DOUBLE PRECISION array of DIMENSION ( LDC, n ).
             Before entry, the leading  m by n  part of the array  C must
             contain the matrix  C,  except when  beta  is zero, in which
             case C need not be set on entry.
             On exit, the array  C  is overwritten by the  m by n updated
             matrix.

             On entry, LDC specifies the first dimension of C as declared
             in  the  calling  (sub)  program.   LDC  must  be  at  least
             max( 1, m ).

Type Parameters

T

Usage Note

Remarks

Further Details:

            Level 3 LinearAlgebra routine.
            -- Written on 8-February-1989.
               Jack Dongarra, Argonne National Laboratory.
               Iain Duff, AERE Harwell.
               Jeremy Du Croz, Numerical Algorithms Group Ltd.
               Sven Hammarling, Numerical Algorithms Group Ltd.

Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011

SymmetricMultiplyAndAddInPlace<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, Int32, Int32, T, TStorage2D, TStorage2D, T, TStorage2D)

Sum of the product of a symmetric and a general matrix and a scaled matrix.

public static void SymmetricMultiplyAndAddInPlace<T, TStorage2D>(
	this ILinearAlgebraOperations<T> operations,
	MatrixOperationSide side,
	MatrixTriangle storedTriangle,
	int m,
	int n,
	T alpha,
	TStorage2D a,
	TStorage2D b,
	T beta,
	TStorage2D c
)
where TStorage2D : Object, IStorage2D<T>

Visual Basic

<ExtensionAttribute>
Public Shared Sub SymmetricMultiplyAndAddInPlace(Of T, TStorage2D As {Object, IStorage2D(Of T)}) ( 
	operations As ILinearAlgebraOperations(Of T),
	side As MatrixOperationSide,
	storedTriangle As MatrixTriangle,
	m As Integer,
	n As Integer,
	alpha As T,
	a As TStorage2D,
	b As TStorage2D,
	beta As T,
	c As TStorage2D
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T, typename TStorage2D>
where TStorage2D : Object, IStorage2D<T>
static void SymmetricMultiplyAndAddInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixOperationSide side, 
	MatrixTriangle storedTriangle, 
	int m, 
	int n, 
	T alpha, 
	TStorage2D a, 
	TStorage2D b, 
	T beta, 
	TStorage2D c
)

[<ExtensionAttribute>]
static member SymmetricMultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        side : MatrixOperationSide * 
        storedTriangle : MatrixTriangle * 
        m : int * 
        n : int * 
        alpha : 'T * 
        a : 'TStorage2D * 
        b : 'TStorage2D * 
        beta : 'T * 
        c : 'TStorage2D -> unit  when 'TStorage2D : Object and IStorage2D<'T>

Parameters

operations ILinearAlgebraOperations<T>: The linear algebra operations instance used to perform the calculation.
side MatrixOperationSide: Specifies on which side the symmetric matrix a is to be multiplied.
storedTriangle MatrixTriangle: Specifies whether the elements of the matrix a are stored in the upper or lower triangular part.
m Int32: The number of rows in the matrix a and the matrix c.
n Int32: The number of columns in the matrix b and the matrix c.
alpha T: The scalar used to multiply the matrix-vector product.
a TStorage2D: A span that contains the elements of the first matrix.
b TStorage2D: A span that contains the elements of the second matrix.
beta T: The scalar used to multiply c.
c TStorage2D: A span that contains the elements of the third matrix.

Type Parameters

T
TStorage2D

LinearAlgebraOperationsExtensions.SymmetricMultiplyAndAddInPlace Method

Definition

Overload List

SymmetricMultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpanSlice<T>, T, SpanSlice<T>)

Parameters

Type Parameters

Usage Note

Remarks

Further Details:

SymmetricMultiplyAndAddInPlace<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, TStorage2D, TStorage, T, TStorage)

Parameters

Type Parameters

Usage Note

Remarks

SymmetricMultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpan2D<T>, T, Span2D<T>)

Parameters

Type Parameters

Usage Note

Remarks

Further Details:

SymmetricMultiplyAndAddInPlace<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, Int32, Int32, T, TStorage2D, TStorage2D, T, TStorage2D)

Parameters

Type Parameters

Usage Note

See Also

Reference