Linear Algebra Operations &lt; T &gt; . Band Multiply And Add In Place Method

             On entry, TRANS specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                TRANS = 'T' or 't'   y := alpha*A^T*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*A^T*x + beta*y.

             On entry, M specifies the number of rows of the matrix A.
             M must be at least zero.

             On entry, N specifies the number of columns of the matrix A.
             N must be at least zero.

kl Int32

             On entry, KL specifies the number of sub-diagonals of the
             matrix A. KL must satisfy  0 .le. KL.

ku Int32

             On entry, KU specifies the number of super-diagonals of the
             matrix A. KU must satisfy  0 .le. KU.

alpha T

            ALPHA is DOUBLE PRECISION.
             On entry, ALPHA specifies the scalar alpha.

a Array2D<T>

            A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
             Before entry, the leading ( kl + ku + 1 ) by n part of the
             array A must contain the matrix of coefficients, supplied
             column by column, with the leading diagonal of the matrix in
             row ( ku + 1 ) of the array, the first super-diagonal
             starting at position 2 in row ku, the first sub-diagonal
             starting at position 1 in row ( ku + 2 ), and so on.
             Elements in the array A that do not correspond to elements
             in the band matrix (such as the top left ku by ku triangle)
             are not referenced.
             The following program segment will transfer a band matrix
             from conventional full matrix storage to band storage:
                   DO 20, J = 1, N
                      K = KU + 1 - J
                      DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
                         A( K + I, J ) = matrix( I, J )
                10    CONTINUE
                20 CONTINUE

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

x ArraySlice<T>

            X is DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
             Before entry, the incremented array X must contain the
             vector x.

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.

beta T

            BETA is DOUBLE PRECISION.
             On entry, BETA specifies the scalar beta. When BETA is
             supplied as zero then Y need not be set on input.

y ArraySlice<T>

            Y is DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
             Before entry, the incremented array Y must contain the
             vector y. On exit, Y is overwritten by the updated vector y.

             On entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.

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

BandMultiplyAndAddInPlace(TransposeOperation, Int32, Int32, Int32, Int32, Complex<T>, Array2D<Complex<T>>, ArraySlice<Complex<T>>, Complex<T>, ArraySlice<Complex<T>>)

Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A^T*x + beta*y, or y := alpha*A^H*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals.

public void BandMultiplyAndAddInPlace(
	TransposeOperation trans,
	int m,
	int n,
	int kl,
	int ku,
	Complex<T> alpha,
	Array2D<Complex<T>> a,
	ArraySlice<Complex<T>> x,
	Complex<T> beta,
	ArraySlice<Complex<T>> y
)

Visual Basic

Public Sub BandMultiplyAndAddInPlace ( 
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	kl As Integer,
	ku As Integer,
	alpha As Complex(Of T),
	a As Array2D(Of Complex(Of T)),
	x As ArraySlice(Of Complex(Of T)),
	beta As Complex(Of T),
	y As ArraySlice(Of Complex(Of T))
)

C++/CLI

public:
void BandMultiplyAndAddInPlace(
	TransposeOperation trans, 
	int m, 
	int n, 
	int kl, 
	int ku, 
	Complex<T> alpha, 
	Array2D<Complex<T>> a, 
	ArraySlice<Complex<T>> x, 
	Complex<T> beta, 
	ArraySlice<Complex<T>> y
)

member BandMultiplyAndAddInPlace : 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        kl : int * 
        ku : int * 
        alpha : Complex<'T> * 
        a : Array2D<Complex<'T>> * 
        x : ArraySlice<Complex<'T>> * 
        beta : Complex<'T> * 
        y : ArraySlice<Complex<'T>> -> unit

Parameters

             On entry, TRANS specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                TRANS = 'T' or 't'   y := alpha*A^T*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*A^H*x + beta*y.

             On entry, M specifies the number of rows of the matrix A.
             M must be at least zero.

             On entry, N specifies the number of columns of the matrix A.
             N must be at least zero.

kl Int32

             On entry, KL specifies the number of sub-diagonals of the
             matrix A. KL must satisfy  0 .le. KL.

ku Int32

             On entry, KU specifies the number of super-diagonals of the
             matrix A. KU must satisfy  0 .le. KU.

alpha Complex<T>

             On entry, ALPHA specifies the scalar alpha.

a Array2D<Complex<T>>

            A is complex array of DIMENSION ( LDA, n ).
             Before entry, the leading ( kl + ku + 1 ) by n part of the
             array A must contain the matrix of coefficients, supplied
             column by column, with the leading diagonal of the matrix in
             row ( ku + 1 ) of the array, the first super-diagonal
             starting at position 2 in row ku, the first sub-diagonal
             starting at position 1 in row ( ku + 2 ), and so on.
             Elements in the array A that do not correspond to elements
             in the band matrix (such as the top left ku by ku triangle)
             are not referenced.
             The following program segment will transfer a band matrix
             from conventional full matrix storage to band storage:
                   DO 20, J = 1, N
                      K = KU + 1 - J
                      DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
                         A( K + I, J ) = matrix( I, J )
                10    CONTINUE
                20 CONTINUE

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

x ArraySlice<Complex<T>>

            X is complex array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
             Before entry, the incremented array X must contain the
             vector x.

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.

beta Complex<T>

             On entry, BETA specifies the scalar beta. When BETA is
             supplied as zero then Y need not be set on input.

y ArraySlice<Complex<T>>

            Y is complex array of DIMENSION at least
             ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
             Before entry, the incremented array Y must contain the
             vector y. On exit, Y is overwritten by the updated vector y.

             On entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.

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

BandMultiplyAndAddInPlace(TransposeOperation, Int32, Int32, Int32, Int32, Complex<T>, ReadOnlySpan2D<Complex<T>>, ReadOnlySpanSlice<Complex<T>>, Complex<T>, SpanSlice<Complex<T>>)

public void BandMultiplyAndAddInPlace(
	TransposeOperation trans,
	int m,
	int n,
	int kl,
	int ku,
	Complex<T> alpha,
	ReadOnlySpan2D<Complex<T>> a,
	ReadOnlySpanSlice<Complex<T>> x,
	Complex<T> beta,
	SpanSlice<Complex<T>> y
)

Visual Basic

Public Sub BandMultiplyAndAddInPlace ( 
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	kl As Integer,
	ku As Integer,
	alpha As Complex(Of T),
	a As ReadOnlySpan2D(Of Complex(Of T)),
	x As ReadOnlySpanSlice(Of Complex(Of T)),
	beta As Complex(Of T),
	y As SpanSlice(Of Complex(Of T))
)

C++/CLI

public:
void BandMultiplyAndAddInPlace(
	TransposeOperation trans, 
	int m, 
	int n, 
	int kl, 
	int ku, 
	Complex<T> alpha, 
	ReadOnlySpan2D<Complex<T>> a, 
	ReadOnlySpanSlice<Complex<T>> x, 
	Complex<T> beta, 
	SpanSlice<Complex<T>> y
)

member BandMultiplyAndAddInPlace : 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        kl : int * 
        ku : int * 
        alpha : Complex<'T> * 
        a : ReadOnlySpan2D<Complex<'T>> * 
        x : ReadOnlySpanSlice<Complex<'T>> * 
        beta : Complex<'T> * 
        y : SpanSlice<Complex<'T>> -> unit

Parameters

             On entry, TRANS specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                TRANS = 'T' or 't'   y := alpha*A^T*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*A^H*x + beta*y.

             On entry, M specifies the number of rows of the matrix A.
             M must be at least zero.

             On entry, N specifies the number of columns of the matrix A.
             N must be at least zero.

kl Int32

             On entry, KL specifies the number of sub-diagonals of the
             matrix A. KL must satisfy  0 .le. KL.

ku Int32

             On entry, KU specifies the number of super-diagonals of the
             matrix A. KU must satisfy  0 .le. KU.

alpha Complex<T>

             On entry, ALPHA specifies the scalar alpha.

a ReadOnlySpan2D<Complex<T>>

            A is complex array of DIMENSION ( LDA, n ).
             Before entry, the leading ( kl + ku + 1 ) by n part of the
             array A must contain the matrix of coefficients, supplied
             column by column, with the leading diagonal of the matrix in
             row ( ku + 1 ) of the array, the first super-diagonal
             starting at position 2 in row ku, the first sub-diagonal
             starting at position 1 in row ( ku + 2 ), and so on.
             Elements in the array A that do not correspond to elements
             in the band matrix (such as the top left ku by ku triangle)
             are not referenced.
             The following program segment will transfer a band matrix
             from conventional full matrix storage to band storage:
                   DO 20, J = 1, N
                      K = KU + 1 - J
                      DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
                         A( K + I, J ) = matrix( I, J )
                10    CONTINUE
                20 CONTINUE

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

x ReadOnlySpanSlice<Complex<T>>

            X is complex array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
             Before entry, the incremented array X must contain the
             vector x.

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.

beta Complex<T>

             On entry, BETA specifies the scalar beta. When BETA is
             supplied as zero then Y need not be set on input.

y SpanSlice<Complex<T>>

            Y is complex array of DIMENSION at least
             ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
             Before entry, the incremented array Y must contain the
             vector y. On exit, Y is overwritten by the updated vector y.

             On entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.

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

BandMultiplyAndAddInPlace(TransposeOperation, Int32, Int32, Int32, Int32, T, ReadOnlySpan<T>, Int32, ReadOnlySpan<T>, Int32, T, Span<T>, Int32)

public abstract void BandMultiplyAndAddInPlace(
	TransposeOperation trans,
	int m,
	int n,
	int kl,
	int ku,
	T alpha,
	ReadOnlySpan<T> a,
	int lda,
	ReadOnlySpan<T> x,
	int incx,
	T beta,
	Span<T> y,
	int incy
)

Visual Basic

Public MustOverride Sub BandMultiplyAndAddInPlace ( 
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	kl As Integer,
	ku As Integer,
	alpha As T,
	a As ReadOnlySpan(Of T),
	lda As Integer,
	x As ReadOnlySpan(Of T),
	incx As Integer,
	beta As T,
	y As Span(Of T),
	incy As Integer
)

C++/CLI

public:
virtual void BandMultiplyAndAddInPlace(
	TransposeOperation trans, 
	int m, 
	int n, 
	int kl, 
	int ku, 
	T alpha, 
	ReadOnlySpan<T> a, 
	int lda, 
	ReadOnlySpan<T> x, 
	int incx, 
	T beta, 
	Span<T> y, 
	int incy
) abstract

abstract BandMultiplyAndAddInPlace : 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        kl : int * 
        ku : int * 
        alpha : 'T * 
        a : ReadOnlySpan<'T> * 
        lda : int * 
        x : ReadOnlySpan<'T> * 
        incx : int * 
        beta : 'T * 
        y : Span<'T> * 
        incy : int -> unit

Parameters

             On entry, TRANS specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                TRANS = 'T' or 't'   y := alpha*A^T*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*A^T*x + beta*y.

             On entry, M specifies the number of rows of the matrix A.
             M must be at least zero.

ILinearAlgebraOperations<T>.BandMultiplyAndAddInPlace(TransposeOperation, Int32, Int32, Int32, Int32, T, ReadOnlySpan<T>, Int32, ReadOnlySpan<T>, Int32, T, Span<T>, Int32)

             On entry, N specifies the number of columns of the matrix A.
             N must be at least zero.

kl Int32

             On entry, KL specifies the number of sub-diagonals of the
             matrix A. KL must satisfy  0 .le. KL.

ku Int32

             On entry, KU specifies the number of super-diagonals of the
             matrix A. KU must satisfy  0 .le. KU.

alpha T

            ALPHA is DOUBLE PRECISION.
             On entry, ALPHA specifies the scalar alpha.

a ReadOnlySpan<T>

            A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
             Before entry, the leading ( kl + ku + 1 ) by n part of the
             array A must contain the matrix of coefficients, supplied
             column by column, with the leading diagonal of the matrix in
             row ( ku + 1 ) of the array, the first super-diagonal
             starting at position 2 in row ku, the first sub-diagonal
             starting at position 1 in row ( ku + 2 ), and so on.
             Elements in the array A that do not correspond to elements
             in the band matrix (such as the top left ku by ku triangle)
             are not referenced.
             The following program segment will transfer a band matrix
             from conventional full matrix storage to band storage:
                   DO 20, J = 1, N
                      K = KU + 1 - J
                      DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
                         A( K + I, J ) = matrix( I, J )
                10    CONTINUE
                20 CONTINUE

lda Int32

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

x ReadOnlySpan<T>

            X is DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
             Before entry, the incremented array X must contain the
             vector x.

incx Int32

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.

beta T

            BETA is DOUBLE PRECISION.
             On entry, BETA specifies the scalar beta. When BETA is
             supplied as zero then Y need not be set on input.

y Span<T>

            Y is DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
             Before entry, the incremented array Y must contain the
             vector y. On exit, Y is overwritten by the updated vector y.

incy Int32

             On entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.

Implements

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

BandMultiplyAndAddInPlace(TransposeOperation, Int32, Int32, Int32, Int32, Complex<T>, ReadOnlySpan<Complex<T>>, Int32, ReadOnlySpan<Complex<T>>, Int32, Complex<T>, Span<Complex<T>>, Int32)

Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A^T*x + beta*y, or y := alpha*A^H*x + beta*y, where alpha and beta are scalars, x, incx and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals.

public abstract void BandMultiplyAndAddInPlace(
	TransposeOperation trans,
	int m,
	int n,
	int kl,
	int ku,
	Complex<T> alpha,
	ReadOnlySpan<Complex<T>> a,
	int lda,
	ReadOnlySpan<Complex<T>> x,
	int incx,
	Complex<T> beta,
	Span<Complex<T>> y,
	int incy
)

Visual Basic

Public MustOverride Sub BandMultiplyAndAddInPlace ( 
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	kl As Integer,
	ku As Integer,
	alpha As Complex(Of T),
	a As ReadOnlySpan(Of Complex(Of T)),
	lda As Integer,
	x As ReadOnlySpan(Of Complex(Of T)),
	incx As Integer,
	beta As Complex(Of T),
	y As Span(Of Complex(Of T)),
	incy As Integer
)

C++/CLI

public:
virtual void BandMultiplyAndAddInPlace(
	TransposeOperation trans, 
	int m, 
	int n, 
	int kl, 
	int ku, 
	Complex<T> alpha, 
	ReadOnlySpan<Complex<T>> a, 
	int lda, 
	ReadOnlySpan<Complex<T>> x, 
	int incx, 
	Complex<T> beta, 
	Span<Complex<T>> y, 
	int incy
) abstract

abstract BandMultiplyAndAddInPlace : 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        kl : int * 
        ku : int * 
        alpha : Complex<'T> * 
        a : ReadOnlySpan<Complex<'T>> * 
        lda : int * 
        x : ReadOnlySpan<Complex<'T>> * 
        incx : int * 
        beta : Complex<'T> * 
        y : Span<Complex<'T>> * 
        incy : int -> unit

Parameters

             On entry, TRANS specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                TRANS = 'T' or 't'   y := alpha*A^T*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*A^H*x + beta*y.

             On entry, M specifies the number of rows of the matrix A.
             M must be at least zero.