GenericLinearAlgebraOperations<T>.BandTriangularMultiplyInPlace Method

Definition

Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET.Generic (in Numerics.NET.Generic.dll) Version: 9.0.1

Overload List

BandTriangularMultiplyInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2D<Complex<T>>, ArraySlice<Complex<T>>) 
BandTriangularMultiplyInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2D<Complex<T>>, ArraySlice<Complex<T>>)

Performs one of the matrix-vector operations x := A*x, or x := AT*x, or x := AH*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.

BandTriangularMultiplyInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan2D<Complex<T>>, SpanSlice<Complex<T>>)

Performs one of the matrix-vector operations x := A*x, or x := AT*x, or x := AH*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.

BandTriangularMultiplyInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32)

Performs one of the matrix-vector operations x := A*x, or x := AT*x, or x := AH*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.

BandTriangularMultiplyInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32)

Performs one of the matrix-vector operations x := A*x, or x := AT*x, or x := AH*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.

BandTriangularMultiplyInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32)

Performs one of the matrix-vector operations x := A*x, or x := AT*x, or x := AH*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.

C# 
public override void BandTriangularMultiplyInPlace(
	MatrixTriangle uplo,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	int k,
	ReadOnlySpan<T> a,
	int lda,
	Span<T> x,
	int incx
)

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 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 := AH*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  ReadOnlySpan<T>
            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<T>
            X is (input/output) complex 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.
incx  Int32
             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.

Implements

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

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,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

BandTriangularMultiplyInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32)

Performs one of the matrix-vector operations x := A*x, or x := AT*x, or x := AH*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.

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

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 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 := AH*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  ReadOnlySpan<Complex<T>>
            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<T>>
            X is (input/output) complex 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.
incx  Int32
             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.

Implements

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

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,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

See Also