LinearAlgebraOperations<T>.BandTriangularMultiplyInPlace Method

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23

Overload List

BandTriangularMultiplyInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2D<T>, ArraySlice<T>)	Performs one of the matrix-vector operations x := Ax, or x := A^Tx, 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, Array2D<Complex<T>>, ArraySlice<Complex<T>>)	Performs one of the matrix-vector operations x := Ax, or x := A^Tx, or x := A^H*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, Array2D<T>, ArraySlice<T>)

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

public abstract void BandTriangularMultiplyInPlace(
	MatrixTriangle uplo,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	int k,
	Array2D<T> a,
	ArraySlice<T> x
)

Visual Basic

Public MustOverride Sub BandTriangularMultiplyInPlace ( 
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	diag As MatrixDiagonal,
	n As Integer,
	k As Integer,
	a As Array2D(Of T),
	x As ArraySlice(Of T)
)

C++/CLI

public:
virtual void BandTriangularMultiplyInPlace(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	int k, 
	Array2D<T> a, 
	ArraySlice<T> x
) abstract

abstract BandTriangularMultiplyInPlace : 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        k : int * 
        a : Array2D<'T> * 
        x : ArraySlice<'T> -> unit

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 := A^T*x.
                TRANS = 'C' or 'c'   x := A^T*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 Array2D<T>

            A is DOUBLE PRECISION 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 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 vector x. On exit, X is overwritten with the
             tranformed vector x.

             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, Array2D<T>, ArraySlice<T>)

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, Array2D<Complex<T>>, ArraySlice<Complex<T>>)

Performs one of the matrix-vector operations x := A*x, or x := A^T*x, or x := A^H*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.

public abstract void BandTriangularMultiplyInPlace(
	MatrixTriangle uplo,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	int k,
	Array2D<Complex<T>> a,
	ArraySlice<Complex<T>> x
)

Visual Basic

Public MustOverride Sub BandTriangularMultiplyInPlace ( 
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	diag As MatrixDiagonal,
	n As Integer,
	k As Integer,
	a As Array2D(Of Complex(Of T)),
	x As ArraySlice(Of Complex(Of T))
)

C++/CLI

public:
virtual void BandTriangularMultiplyInPlace(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	int k, 
	Array2D<Complex<T>> a, 
	ArraySlice<Complex<T>> x
) abstract

abstract BandTriangularMultiplyInPlace : 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        k : int * 
        a : Array2D<Complex<'T>> * 
        x : ArraySlice<Complex<'T>> -> unit

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 := A^T*x.
                TRANS = 'C' or 'c'   x := A^H*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 Array2D<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.

             On entry, LDA specifies the first dimension of A as declared
             in the calling (sub) program. LDA must be at least
             ( k + 1 ).

x ArraySlice<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.

             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, Array2D<T>, ArraySlice<T>)

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

LinearAlgebraOperations<T>.BandTriangularMultiplyInPlace Method

Definition

Overload List

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

Parameters

Implements

Remarks

Further Details:

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

Parameters

Implements

Remarks

Further Details:

See Also

Reference