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 band matrix, with ( k + 1 )
diagonals.
Namespace: Extreme.Mathematics.LinearAlgebra.ImplementationAssembly: Extreme.Numerics.SinglePrecision.Net40 (in Extreme.Numerics.SinglePrecision.Net40.dll) Version: 6.0.16073.0 (6.0.16096.0)
public override void BandTriangularSolveInPlace(
MatrixTriangle storedTriangle,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
int k,
Array2D<Complex<float>> a,
ArraySlice<Complex<float>> x
)
Public Overrides Sub BandTriangularSolveInPlace (
storedTriangle As MatrixTriangle,
trans As TransposeOperation,
diag As MatrixDiagonal,
n As Integer,
k As Integer,
a As Array2D(Of Complex(Of Single)),
x As ArraySlice(Of Complex(Of Single))
)
public:
virtual void BandTriangularSolveInPlace(
MatrixTriangle storedTriangle,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
int k,
Array2D<Complex<float>> a,
ArraySlice<Complex<float>> x
) override
abstract BandTriangularSolveInPlace :
storedTriangle : MatrixTriangle *
trans : TransposeOperation *
diag : MatrixDiagonal *
n : int *
k : int *
a : Array2D<Complex<float32>> *
x : ArraySlice<Complex<float32>> -> unit
override BandTriangularSolveInPlace :
storedTriangle : MatrixTriangle *
trans : TransposeOperation *
diag : MatrixDiagonal *
n : int *
k : int *
a : Array2D<Complex<float32>> *
x : ArraySlice<Complex<float32>> -> unit
Parameters
- storedTriangle
- 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.
- k
- Type: SystemInt32
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
- Type: Extreme.CollectionsArray2DComplexSingle
A is COMPLEX*16 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
- Type: Extreme.CollectionsArraySliceComplexSingle
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.
Implements
ILinearAlgebraOperationsTBandTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2DT, ArraySliceT)
No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
This method is based on the BLAS routine ZTBSV.
Numerical Libraries
Supported in: 6.0
Reference