# LinearAlgebraOperationsExtensions.SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpan2D<T>, T, Span2D<T>) Method

Performs one of the symmetric rank 2k operations C := alpha*A*BT + alpha*B*AT + beta*C, or C := alpha*AT*B + alpha*BT*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.

## Definition

Namespace: Extreme.Collections
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 9.0.0
C#
``````public static void SymmetricRankUpdate<T>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle uplo,
TransposeOperation trans,
int n,
int k,
T alpha,
T beta,
Span2D<T> c
)
``````

#### Parameters

operations  ILinearAlgebraOperations<T>

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*BT + alpha*B*AT +
beta*C.
TRANS = 'T' or 't'   C := alpha*AT*B + alpha*BT*A +
beta*C.
TRANS = 'C' or 'c'   C := alpha*AT*B + alpha*BT*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 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 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 ).
```

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 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,