Generic
Definition
Assembly: Extreme.Numerics.Generic (in Extreme.Numerics.Generic.dll) Version: 8.1.4
Overload List
| Packed | Solves one of the systems of equations A*x = b, or AT*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. |
| Packed | 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. |
PackedTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Array1D<T>, ArraySlice<T>)
Solves one of the systems of equations A*x = b, or AT*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.
public void PackedTriangularSolveInPlace(
MatrixTriangle uplo,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
Array1D<T> ap,
ArraySlice<T> x
)Parameters
- 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 equations to be solved as follows: TRANS = 'N' or 'n' A*x = b. TRANS = 'T' or 't' AT*x = b. TRANS = 'C' or 'c' AT*x = b.- 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.- ap Array1D<T>
AP is DOUBLE PRECISION 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 ArraySlice<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 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.
Remarks
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
PackedTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Array1D<Complex<T>>, ArraySlice<Complex<T>>)
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.
public void PackedTriangularSolveInPlace(
MatrixTriangle uplo,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
Array1D<Complex<T>> ap,
ArraySlice<Complex<T>> x
)Parameters
- 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 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 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.- ap Array1D<Complex<T>>
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 ArraySlice<Complex<T>>
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.
Remarks
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