Performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C, where op( X ) is one of op( X ) = X or op( X ) = XT, alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.

## Definition

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

#### Parameters

operations  ILinearAlgebraOperations<T>

transa  TransposeOperation
```             On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n',  op( A ) = A.
TRANSA = 'T' or 't',  op( A ) = AT.
TRANSA = 'C' or 'c',  op( A ) = AT.
```
transb  TransposeOperation
```             On entry, TRANSB specifies the form of op( B ) to be used in
the matrix multiplication as follows:
TRANSB = 'N' or 'n',  op( B ) = B.
TRANSB = 'T' or 't',  op( B ) = BT.
TRANSB = 'C' or 'c',  op( B ) = BT.
```
m  Int32
```             On entry,  M  specifies  the number  of rows  of the  matrix
op( A )  and of the  matrix  C.  M  must  be at least  zero.
```
n  Int32
```             On entry,  N  specifies the number  of columns of the matrix
op( B ) and the number of columns of the matrix C. N must be
at least zero.
```
k  Int32
```             On entry,  K  specifies  the number of columns of the matrix
op( A ) and the number of rows of the matrix op( 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  TRANSA = 'N' or 'n',  and is  m  otherwise.
Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
part of the array  A  must contain the matrix  A,  otherwise
the leading  k by m  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  TRANSA = 'N' or 'n' then
LDA must be at least  max( 1, m ), otherwise  LDA must be at
least  max( 1, k ).
```
```            B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
part of the array  B  must contain the matrix  B,  otherwise
the leading  n by k  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  TRANSB = 'N' or 'n' then
LDB must be at least  max( 1, k ), otherwise  LDB must be at
least  max( 1, n ).
```
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  matrix
( alpha*op( A )*op( B ) + beta*C ).
```
```             On entry, LDC specifies the first dimension of C as declared
in  the  calling  (sub)  program.   LDC  must  be  at  least
max( 1, m ).
```

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,