LinearAlgebraOperations<T>.BandMultiplyAndAddInPlace Method

Definition

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

Overload List

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

Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*AT*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.

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*AT*x + beta*y, or y := alpha*AH*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.

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

Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*AT*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.

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

Parameters

trans  TransposeOperation
             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*AT*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*AT*x + beta*y.
m  Int32
             On entry, M specifies the number of rows of the matrix A.
             M must be at least zero.
n  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  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.

Implements

ILinearAlgebraOperations<T>.BandMultiplyAndAddInPlace(TransposeOperation, Int32, Int32, Int32, Int32, T, Array2D<T>, ArraySlice<T>, 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

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*AT*x + beta*y, or y := alpha*AH*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.

C# 
public abstract 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
)

Parameters

trans  TransposeOperation
             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*AT*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*AH*x + beta*y.
m  Int32
             On entry, M specifies the number of rows of the matrix A.
             M must be at least zero.
n  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  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.

Implements

ILinearAlgebraOperations<T>.BandMultiplyAndAddInPlace(TransposeOperation, Int32, Int32, Int32, Int32, T, Array2D<T>, ArraySlice<T>, 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

See Also