Generic
Definition
Assembly: Numerics.NET.Generic (in Numerics.NET.Generic.dll) Version: 9.0.3
Overload List
| Band | 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. |
| Band | 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. |
| Band | 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. |
| Band | 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. |
| Band | 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, incx 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, ReadOnlySpan<T>, Int32, ReadOnlySpan<T>, Int32, T, Span<T>, Int32)
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.
public override 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
)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 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
ILinearAlgebraOperations<T>.BandMultiplyAndAddInPlace(TransposeOperation, Int32, Int32, Int32, Int32, T, ReadOnlySpan<T>, Int32, ReadOnlySpan<T>, Int32, T, 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
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*AT*x + beta*y, or y := alpha*AH*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 override 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
)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 ReadOnlySpan<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- 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<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.- incx Int32
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 Span<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.- incy Int32
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, ReadOnlySpan<T>, Int32, ReadOnlySpan<T>, Int32, T, 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