Solves one of the systems of equations
A*x = b, or AT*x = b, or AH*x = b,
where b and x are n element vectors and A is an n by n unit, or
non-unit, upper or lower triangular matrix, supplied in packed form.
Namespace: Extreme.Mathematics.Generic.LinearAlgebra.ImplementationAssembly: Extreme.Numerics.Net40 (in Extreme.Numerics.Net40.dll) Version: 6.0.16073.0 (6.0.17114.0)
public void PackedTriangularSolveInPlace(
MatrixTriangle uplo,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
Array1D<Complex<T>> ap,
ArraySlice<Complex<T>> x
)
Public Sub PackedTriangularSolveInPlace (
uplo As MatrixTriangle,
trans As TransposeOperation,
diag As MatrixDiagonal,
n As Integer,
ap As Array1D(Of Complex(Of T)),
x As ArraySlice(Of Complex(Of T))
)
public:
void PackedTriangularSolveInPlace(
MatrixTriangle uplo,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
Array1D<Complex<T>> ap,
ArraySlice<Complex<T>> x
)
member PackedTriangularSolveInPlace :
uplo : MatrixTriangle *
trans : TransposeOperation *
diag : MatrixDiagonal *
n : int *
ap : Array1D<Complex<'T>> *
x : ArraySlice<Complex<'T>> -> unit
Parameters
- uplo
- Type: Extreme.MathematicsMatrixTriangle
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
- Type: Extreme.MathematicsTransposeOperation
On entry, TRANS specifies the equations to be solved as
follows:
TRANS = 'N' or 'n' A*x = b.
TRANS = 'T' or 't' AT*x = b.
TRANS = 'C' or 'c' AH*x = b.
- diag
- Type: Extreme.MathematicsMatrixDiagonal
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
- Type: SystemInt32
On entry, N specifies the order of the matrix A.
N must be at least zero.
- ap
- Type: Extreme.CollectionsArray1DComplexT
AP is COMPLEX*16 array of DIMENSION at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = 'U' or 'u', the array AP must
contain the upper triangular matrix packed sequentially,
column by column, so that AP( 1 ) contains a( 1, 1 ),
AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
respectively, and so on.
Before entry with UPLO = 'L' or 'l', the array AP must
contain the lower triangular matrix packed sequentially,
column by column, so that AP( 1 ) contains a( 1, 1 ),
AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
respectively, and so on.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced, but are assumed to be unity.
- x
- Type: Extreme.CollectionsArraySliceComplexT
X is COMPLEX*16 array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element right-hand side vector b. On exit, X is overwritten
with the solution vector x.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
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
Numerical Libraries
Supported in: 5.x
Reference