LinearAlgebraOperationsExtensions.SymmetricRankUpdate Method

Definition

Namespace: Numerics.NET.Collections
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.2

Overload List

SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpanSlice<T>, Span2D<T>)	Performs the symmetric rank 1 operation A := alphaxx**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix.
SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpanSlice<T>, ReadOnlySpanSlice<T>, Span2D<T>)	Performs the symmetric rank 2 operation A := alphaxy*T + alphayx*T + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix.
SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, ReadOnlySpan2D<T>, T, Span2D<T>)	Performs one of the symmetric rank k operations C := alphaAA^T + betaC, or C := alphaA^TA + betaC, where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.
SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpan2D<T>, T, Span2D<T>)	Performs one of the symmetric rank 2k operations C := alphaAB^T + alphaBA^T + betaC, or C := alphaA^TB + alphaB^TA + betaC, where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.
SymmetricRankUpdate<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, TStorage2D, T, TStorage2D)	Performs a rank k update of a symmetric matrix.
SymmetricRankUpdate<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, TStorage2D, TStorage2D, T, TStorage2D)	Performs a rank k update of a symmetric matrix.
SymmetricRankUpdate<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, TStorage, TStorage2D)	Performs a rank one update of a symmetric matrix.
SymmetricRankUpdate<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, TStorage, TStorage, TStorage2D)	Performs a symmetric rank two update of a symmetric matrix.

SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpanSlice<T>, Span2D<T>)

Performs the symmetric rank 1 operation A := alpha*x*x**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix.

public static void SymmetricRankUpdate<T>(
	this ILinearAlgebraOperations<T> operations,
	MatrixTriangle uplo,
	int n,
	T alpha,
	ReadOnlySpanSlice<T> x,
	Span2D<T> a
)

Visual Basic

<ExtensionAttribute>
Public Shared Sub SymmetricRankUpdate(Of T) ( 
	operations As ILinearAlgebraOperations(Of T),
	uplo As MatrixTriangle,
	n As Integer,
	alpha As T,
	x As ReadOnlySpanSlice(Of T),
	a As Span2D(Of T)
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T>
static void SymmetricRankUpdate(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixTriangle uplo, 
	int n, 
	T alpha, 
	ReadOnlySpanSlice<T> x, 
	Span2D<T> a
)

[<ExtensionAttribute>]
static member SymmetricRankUpdate : 
        operations : ILinearAlgebraOperations<'T> * 
        uplo : MatrixTriangle * 
        n : int * 
        alpha : 'T * 
        x : ReadOnlySpanSlice<'T> * 
        a : Span2D<'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.

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.

a Span2D<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. On exit, the
             upper triangular part of the array A is overwritten by the
             upper triangular part of the updated matrix.
             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 exit, the
             lower triangular part of the array A is overwritten by the
             lower triangular part of the updated matrix.

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

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.
            -- 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

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

Performs a rank one update of a symmetric matrix.

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

Visual Basic

<ExtensionAttribute>
Public Shared Sub SymmetricRankUpdate(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,
	x As TStorage,
	a As TStorage2D
)

C++/CLI

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

[<ExtensionAttribute>]
static member SymmetricRankUpdate : 
        operations : ILinearAlgebraOperations<'T> * 
        storedTriangle : MatrixTriangle * 
        n : int * 
        alpha : 'T * 
        x : 'TStorage * 
        a : 'TStorage2D -> 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 outer product.
x TStorage: A reference to a one-dimensional array containing the elements of the vector x.
a TStorage2D: A span that contains the elements of the matrix.

Type Parameters

T
TStorage
TStorage2D

Usage Note

Remarks

This method is similar to the BLAS routine DSYR.

SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpanSlice<T>, ReadOnlySpanSlice<T>, Span2D<T>)

Performs the symmetric rank 2 operation A := alpha*x*y**T + alpha*y*x**T + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix.

public static void SymmetricRankUpdate<T>(
	this ILinearAlgebraOperations<T> operations,
	MatrixTriangle uplo,
	int n,
	T alpha,
	ReadOnlySpanSlice<T> x,
	ReadOnlySpanSlice<T> y,
	Span2D<T> a
)

Visual Basic

<ExtensionAttribute>
Public Shared Sub SymmetricRankUpdate(Of T) ( 
	operations As ILinearAlgebraOperations(Of T),
	uplo As MatrixTriangle,
	n As Integer,
	alpha As T,
	x As ReadOnlySpanSlice(Of T),
	y As ReadOnlySpanSlice(Of T),
	a As Span2D(Of T)
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T>
static void SymmetricRankUpdate(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixTriangle uplo, 
	int n, 
	T alpha, 
	ReadOnlySpanSlice<T> x, 
	ReadOnlySpanSlice<T> y, 
	Span2D<T> a
)

[<ExtensionAttribute>]
static member SymmetricRankUpdate : 
        operations : ILinearAlgebraOperations<'T> * 
        uplo : MatrixTriangle * 
        n : int * 
        alpha : 'T * 
        x : ReadOnlySpanSlice<'T> * 
        y : ReadOnlySpanSlice<'T> * 
        a : Span2D<'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.

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.

y ReadOnlySpanSlice<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 entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.

a Span2D<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. On exit, the
             upper triangular part of the array A is overwritten by the
             upper triangular part of the updated matrix.
             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 exit, the
             lower triangular part of the array A is overwritten by the
             lower triangular part of the updated matrix.

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

Type Parameters

T

Usage Note

Remarks

Further Details:

            Level 2 LinearAlgebra routine.
            -- 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

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

Performs a symmetric rank two update of a symmetric matrix.

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

Visual Basic

<ExtensionAttribute>
Public Shared Sub SymmetricRankUpdate(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,
	x As TStorage,
	y As TStorage,
	a As TStorage2D
)

C++/CLI

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

[<ExtensionAttribute>]
static member SymmetricRankUpdate : 
        operations : ILinearAlgebraOperations<'T> * 
        storedTriangle : MatrixTriangle * 
        n : int * 
        alpha : 'T * 
        x : 'TStorage * 
        y : 'TStorage * 
        a : 'TStorage2D -> 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 outer product.
x TStorage: A reference to a one-dimensional array containing the elements of the vector x.
y TStorage: A reference to a one-dimensional array containing the elements of the vector y.
a TStorage2D: A span that contains the elements of the matrix.

Type Parameters

T
TStorage
TStorage2D

Usage Note

Remarks

This method is similar to the BLAS routine DSYR2.

SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, ReadOnlySpan2D<T>, T, Span2D<T>)

Performs one of the symmetric rank k operations C := alpha*A*A^T + beta*C, or C := alpha*A^T*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

public static void SymmetricRankUpdate<T>(
	this ILinearAlgebraOperations<T> operations,
	MatrixTriangle uplo,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	ReadOnlySpan2D<T> a,
	T beta,
	Span2D<T> c
)

Visual Basic

<ExtensionAttribute>
Public Shared Sub SymmetricRankUpdate(Of T) ( 
	operations As ILinearAlgebraOperations(Of T),
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k As Integer,
	alpha As T,
	a As ReadOnlySpan2D(Of T),
	beta As T,
	c As Span2D(Of T)
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T>
static void SymmetricRankUpdate(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	int n, 
	int k, 
	T alpha, 
	ReadOnlySpan2D<T> a, 
	T beta, 
	Span2D<T> c
)

[<ExtensionAttribute>]
static member SymmetricRankUpdate : 
        operations : ILinearAlgebraOperations<'T> * 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : ReadOnlySpan2D<'T> * 
        beta : 'T * 
        c : Span2D<'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  C  is to be  referenced  as
             follows:
                UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                    is to be referenced.
                UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                    is to be referenced.

trans TransposeOperation

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

n Int32

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

k Int32

             On entry with  TRANS = 'N' or 'n',  K  specifies  the number
             of  columns   of  the   matrix   A,   and  on   entry   with
             TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
             of rows of the matrix  A.  K 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
             k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
             Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
             part of the array  A  must contain the matrix  A,  otherwise
             the leading  k by n  part of the array  A  must contain  the
             matrix A.

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

beta T

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

c Span2D<T>

            C is DOUBLE PRECISION array of DIMENSION ( LDC, n ).
             Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
             upper triangular part of the array C must contain the upper
             triangular part  of the  symmetric matrix  and the strictly
             lower triangular part of C is not referenced.  On exit, the
             upper triangular part of the array  C is overwritten by the
             upper triangular part of the updated matrix.
             Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
             lower triangular part of the array C must contain the lower
             triangular part  of the  symmetric matrix  and the strictly
             upper triangular part of C is not referenced.  On exit, the
             lower triangular part of the array  C is overwritten by the
             lower triangular part of the 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, n ).

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

SymmetricRankUpdate<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, TStorage2D, T, TStorage2D)

Performs a rank k update of a symmetric matrix.

public static void SymmetricRankUpdate<T, TStorage2D>(
	this ILinearAlgebraOperations<T> operations,
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	TStorage2D a,
	T beta,
	TStorage2D c
)
where TStorage2D : Object, IStorage2D<T>

Visual Basic

<ExtensionAttribute>
Public Shared Sub SymmetricRankUpdate(Of T, TStorage2D As {Object, IStorage2D(Of T)}) ( 
	operations As ILinearAlgebraOperations(Of T),
	storedTriangle As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k As Integer,
	alpha As T,
	a As TStorage2D,
	beta As T,
	c As TStorage2D
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T, typename TStorage2D>
where TStorage2D : Object, IStorage2D<T>
static void SymmetricRankUpdate(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixTriangle storedTriangle, 
	TransposeOperation trans, 
	int n, 
	int k, 
	T alpha, 
	TStorage2D a, 
	T beta, 
	TStorage2D c
)

[<ExtensionAttribute>]
static member SymmetricRankUpdate : 
        operations : ILinearAlgebraOperations<'T> * 
        storedTriangle : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : '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.
storedTriangle MatrixTriangle: Specifies whether the elements of the matrix a are stored in the upper or lower triangular part.
trans TransposeOperation: Specifies the operation to be performed on the matrix a.
n Int32: The number of rows and columns in the matrix c.
k Int32: The number of columns in the matrix a transformed as specified by trans.
alpha T: The scalar used to multiply the matrix-matrix product.
a TStorage2D: A span that contains the elements of the first 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

Usage Note

SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpan2D<T>, T, Span2D<T>)

Performs one of the symmetric rank 2k operations C := alpha*A*B^T + alpha*B*A^T + beta*C, or C := alpha*A^T*B + alpha*B^T*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

public static void SymmetricRankUpdate<T>(
	this ILinearAlgebraOperations<T> operations,
	MatrixTriangle uplo,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	ReadOnlySpan2D<T> a,
	ReadOnlySpan2D<T> b,
	T beta,
	Span2D<T> c
)

Visual Basic

<ExtensionAttribute>
Public Shared Sub SymmetricRankUpdate(Of T) ( 
	operations As ILinearAlgebraOperations(Of T),
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k 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 SymmetricRankUpdate(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	int n, 
	int k, 
	T alpha, 
	ReadOnlySpan2D<T> a, 
	ReadOnlySpan2D<T> b, 
	T beta, 
	Span2D<T> c
)

[<ExtensionAttribute>]
static member SymmetricRankUpdate : 
        operations : ILinearAlgebraOperations<'T> * 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : 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.

uplo MatrixTriangle

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

trans TransposeOperation

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

n Int32

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

k Int32

             On entry with  TRANS = 'N' or 'n',  K  specifies  the number
             of  columns  of the  matrices  A and B,  and on  entry  with
             TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
             of rows of the matrices  A and B.  K 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
             k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
             Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
             part of the array  A  must contain the matrix  A,  otherwise
             the leading  k by n  part of the array  A  must contain  the
             matrix A.

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

b ReadOnlySpan2D<T>

            B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
             k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
             Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
             part of the array  B  must contain the matrix  B,  otherwise
             the leading  k 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.   When  TRANS = 'N' or 'n'
             then  LDB must be at least  max( 1, n ), otherwise  LDB must
             be at least  max( 1, k ).

beta T

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

c Span2D<T>

            C is DOUBLE PRECISION array of DIMENSION ( LDC, n ).
             Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
             upper triangular part of the array C must contain the upper
             triangular part  of the  symmetric matrix  and the strictly
             lower triangular part of C is not referenced.  On exit, the
             upper triangular part of the array  C is overwritten by the
             upper triangular part of the updated matrix.
             Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
             lower triangular part of the array C must contain the lower
             triangular part  of the  symmetric matrix  and the strictly
             upper triangular part of C is not referenced.  On exit, the
             lower triangular part of the array  C is overwritten by the
             lower triangular part of the 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, n ).

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

SymmetricRankUpdate<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, TStorage2D, TStorage2D, T, TStorage2D)

Performs a rank k update of a symmetric matrix.

public static void SymmetricRankUpdate<T, TStorage2D>(
	this ILinearAlgebraOperations<T> operations,
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	TStorage2D a,
	TStorage2D b,
	T beta,
	TStorage2D c
)
where TStorage2D : Object, IStorage2D<T>

Visual Basic

<ExtensionAttribute>
Public Shared Sub SymmetricRankUpdate(Of T, TStorage2D As {Object, IStorage2D(Of T)}) ( 
	operations As ILinearAlgebraOperations(Of T),
	storedTriangle As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k 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 SymmetricRankUpdate(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixTriangle storedTriangle, 
	TransposeOperation trans, 
	int n, 
	int k, 
	T alpha, 
	TStorage2D a, 
	TStorage2D b, 
	T beta, 
	TStorage2D c
)

[<ExtensionAttribute>]
static member SymmetricRankUpdate : 
        operations : ILinearAlgebraOperations<'T> * 
        storedTriangle : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : 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.
storedTriangle MatrixTriangle: Specifies whether the elements of the matrix a are stored in the upper or lower triangular part.
trans TransposeOperation: Specifies the operation to be performed on the matrix a.
n Int32: The number of rows and columns in the matrix c.
k Int32: The number of columns in the matrix a transformed as specified by trans.
alpha T: The scalar used to multiply the matrix-matrix 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.SymmetricRankUpdate Method

Definition

Overload List

SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpanSlice<T>, Span2D<T>)

Parameters

Type Parameters

Usage Note

Remarks

Further Details:

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

Parameters

Type Parameters

Usage Note

Remarks

SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpanSlice<T>, ReadOnlySpanSlice<T>, Span2D<T>)

Parameters

Type Parameters

Usage Note

Remarks

Further Details:

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

Parameters

Type Parameters

Usage Note

Remarks

SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, ReadOnlySpan2D<T>, T, Span2D<T>)

Parameters

Type Parameters

Usage Note

Remarks

Further Details:

SymmetricRankUpdate<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, TStorage2D, T, TStorage2D)

Parameters

Type Parameters

Usage Note

SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpan2D<T>, T, Span2D<T>)

Parameters

Type Parameters

Usage Note

Remarks

Further Details:

SymmetricRankUpdate<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, TStorage2D, TStorage2D, T, TStorage2D)

Parameters

Type Parameters

Usage Note

See Also

Reference