ManagedLinearAlgebraOperationsOfSingle.BandTriangularSolveInPlace Method

Definition

Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET.SinglePrecision (in Numerics.NET.SinglePrecision.dll) Version: 9.0.0

Overload List

BandTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2D<Complex<T>>, ArraySlice<Complex<T>>) 
BandTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2D<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 band matrix, with ( k + 1 ) diagonals.

BandTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan2D<Complex<T>>, SpanSlice<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 band matrix, with ( k + 1 ) diagonals.

BandTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<Complex<Single>>, Int32, Span<Complex<Single>>, Int32)

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.

BandTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<Single>, Int32, Span<Single>, Int32)

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.

BandTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<Complex<Single>>, Int32, Span<Complex<Single>>, Int32)

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.

C# 
public override void BandTriangularSolveInPlace(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	int k,
	ReadOnlySpan<Complex<float>> a,
	int lda,
	Span<Complex<float>> x,
	int incx
)

Parameters

storedTriangle  MatrixTriangle
Specifies whether the matrix is an upper or 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.
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  ReadOnlySpan<Complex<Single>>
            A is complex 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.
lda  Int32
             On entry, LDA specifies the first dimension of A as declared
             in the calling (sub) program. LDA must be at least
             ( k + 1 ).
x  Span<Complex<Single>>
            X is complex 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.
incx  Int32
             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.

Implements

ILinearAlgebraOperations<T>.BandTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32)

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

BandTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<Single>, Int32, Span<Single>, Int32)

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.

C# 
public override void BandTriangularSolveInPlace(
	MatrixTriangle storedTriangle,
	TransposeOperation transA,
	MatrixDiagonal diag,
	int n,
	int k,
	ReadOnlySpan<float> a,
	int lda,
	Span<float> x,
	int incx
)

Parameters

storedTriangle  MatrixTriangle
Specifies whether the matrix is an upper or lower triangular matrix.
transA  TransposeOperation
 
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  ReadOnlySpan<Single>
            A is complex 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.
lda  Int32
             On entry, LDA specifies the first dimension of A as declared
             in the calling (sub) program. LDA must be at least
             ( k + 1 ).
x  Span<Single>
            X is complex 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.
incx  Int32
             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.

Implements

ILinearAlgebraOperations<T>.BandTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32)

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

See Also