# LinearAlgebraOperationsExtensions.BandTriangularMultiplyInPlace<T>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan2D<T>, SpanSlice<T>) Method

Performs one of the matrix-vector operations x := A*x, or x := AT*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals.

## Definition

Namespace: Extreme.Collections
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 9.0.0
C#
``````public static void BandTriangularMultiplyInPlace<T>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle uplo,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
int k,
SpanSlice<T> x
)
``````

#### Parameters

operations  ILinearAlgebraOperations<T>

uplo  MatrixTriangle
```             On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u'   A is an upper triangular matrix.
UPLO = 'L' or 'l'   A is a lower triangular matrix.
```
trans  TransposeOperation
```             On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n'   x := A*x.
TRANS = 'T' or 't'   x := AT*x.
TRANS = 'C' or 'c'   x := AT*x.
```
diag  MatrixDiagonal
```             On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u'   A is assumed to be unit triangular.
DIAG = 'N' or 'n'   A is not assumed to be unit
triangular.
```
n  Int32
```             On entry, N specifies the order of the matrix A.
N must be at least zero.
```
k  Int32
```             On entry with UPLO = 'U' or 'u', K specifies the number of
super-diagonals of the matrix A.
On entry with UPLO = 'L' or 'l', K specifies the number of
sub-diagonals of the matrix A.
K must satisfy  0 .le. K.
```
```            A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
by n part of the array A must contain the upper triangular
band part of the matrix of coefficients, supplied column by
column, with the leading diagonal of the matrix in row
( k + 1 ) of the array, the first super-diagonal starting at
position 2 in row k, and so on. The top left k by k triangle
of the array A is not referenced.
The following program segment will transfer an upper
triangular band matrix from conventional full matrix storage
to band storage:
DO 20, J = 1, N
M = K + 1 - J
DO 10, I = MAX( 1, J - K ), J
A( M + I, J ) = matrix( I, J )
10    CONTINUE
20 CONTINUE
Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
by n part of the array A must contain the lower triangular
band part of the matrix of coefficients, supplied column by
column, with the leading diagonal of the matrix in row 1 of
the array, the first sub-diagonal starting at position 1 in
row 2, and so on. The bottom right k by k triangle of the
array A is not referenced.
The following program segment will transfer a lower
triangular band matrix from conventional full matrix storage
to band storage:
DO 20, J = 1, N
M = 1 - J
DO 10, I = J, MIN( N, J + K )
A( M + I, J ) = matrix( I, J )
10    CONTINUE
20 CONTINUE
Note that when DIAG = 'U' or 'u' the elements of the array A
corresponding to the diagonal elements of the matrix are not
referenced, but are assumed to be unity.
```
```             On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
( k + 1 ).
```
x  SpanSlice<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 exit, X is overwritten with the
tranformed vector x.
```
```             On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
```

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,