Linear
Definition
Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
Overload List
| Symmetric | Performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix. |
| Symmetric | Performs one of the matrix-matrix operations C := alpha*A*B + beta*C, or C := alpha*B*A + beta*C, where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices. |
| Symmetric | Performs one of the matrix-matrix operations C := alpha*A*B + beta*C, or C := alpha*B*A + beta*C, where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices. |
SymmetricMultiplyAndAddInPlace(MatrixTriangle, Int32, T, Array2D<T>, ArraySlice<T>, T, ArraySlice<T>)
Performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix.
public abstract void SymmetricMultiplyAndAddInPlace(
MatrixTriangle uplo,
int n,
T alpha,
Array2D<T> a,
ArraySlice<T> x,
T beta,
ArraySlice<T> y
)Parameters
- uplo MatrixTriangle
On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced.- n Int32
On entry, N specifies the order of the matrix A. N must be at least zero.- 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 with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced.On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).- 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 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 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element 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>.SymmetricMultiplyAndAddInPlace(MatrixTriangle, 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
SymmetricMultiplyAndAddInPlace(MatrixOperationSide, MatrixTriangle, Int32, Int32, T, Array2D<T>, Array2D<T>, T, Array2D<T>)
Performs one of the matrix-matrix operations C := alpha*A*B + beta*C, or C := alpha*B*A + beta*C, where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices.
public abstract void SymmetricMultiplyAndAddInPlace(
MatrixOperationSide side,
MatrixTriangle uplo,
int m,
int n,
T alpha,
Array2D<T> a,
Array2D<T> b,
T beta,
Array2D<T> c
)Parameters
- side MatrixOperationSide
On entry, SIDE specifies whether the symmetric matrix A appears on the left or right in the operation as follows: SIDE = 'L' or 'l' C := alpha*A*B + beta*C, SIDE = 'R' or 'r' C := alpha*B*A + beta*C,- uplo MatrixTriangle
On entry, UPLO specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of the symmetric matrix is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of the symmetric matrix is to be referenced.- m Int32
On entry, M specifies the number of rows of the matrix C. M must be at least zero.- n Int32
On entry, N specifies the number of columns of the matrix C. N must be at least zero.- alpha T
ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.- a Array2D<T>
A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is m when SIDE = 'L' or 'l' and is n otherwise. Before entry with SIDE = 'L' or 'l', the m by m part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading m by m upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = 'L' or 'l', the leading m by m lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. Before entry with SIDE = 'R' or 'r', the n by n part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced.On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, n ).- b Array2D<T>
B is DOUBLE PRECISION array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the matrix B.On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).- beta T
BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.- c Array2D<T>
C is DOUBLE PRECISION array of DIMENSION ( LDC, n ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n updated matrix.On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ).
Implements
ILinearAlgebraOperations<T>.SymmetricMultiplyAndAddInPlace(MatrixOperationSide, MatrixTriangle, Int32, Int32, T, Array2D<T>, Array2D<T>, T, Array2D<T>)Remarks
Further Details:
Level 3 LinearAlgebra routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
SymmetricMultiplyAndAddInPlace(MatrixOperationSide, MatrixTriangle, Int32, Int32, Complex<T>, Array2D<Complex<T>>, Array2D<Complex<T>>, Complex<T>, Array2D<Complex<T>>)
Performs one of the matrix-matrix operations C := alpha*A*B + beta*C, or C := alpha*B*A + beta*C, where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices.
public abstract void SymmetricMultiplyAndAddInPlace(
MatrixOperationSide side,
MatrixTriangle uplo,
int m,
int n,
Complex<T> alpha,
Array2D<Complex<T>> a,
Array2D<Complex<T>> b,
Complex<T> beta,
Array2D<Complex<T>> c
)Parameters
- side MatrixOperationSide
On entry, SIDE specifies whether the symmetric matrix A appears on the left or right in the operation as follows: SIDE = 'L' or 'l' C := alpha*A*B + beta*C, SIDE = 'R' or 'r' C := alpha*B*A + beta*C,- uplo MatrixTriangle
On entry, UPLO specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of the symmetric matrix is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of the symmetric matrix is to be referenced.- m Int32
On entry, M specifies the number of rows of the matrix C. M must be at least zero.- n Int32
On entry, N specifies the number of columns of the matrix C. N must be at least zero.- alpha Complex<T>
On entry, ALPHA specifies the scalar alpha.- a Array2D<Complex<T>>
A is complex array of DIMENSION ( LDA, ka ), where ka is m when SIDE = 'L' or 'l' and is n otherwise. Before entry with SIDE = 'L' or 'l', the m by m part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading m by m upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = 'L' or 'l', the leading m by m lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. Before entry with SIDE = 'R' or 'r', the n by n part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced.On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, n ).- b Array2D<Complex<T>>
B is complex array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the matrix B.On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).- beta Complex<T>
On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.- c Array2D<Complex<T>>
C is complex array of DIMENSION ( LDC, n ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n updated matrix.On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ).
Implements
ILinearAlgebraOperations<T>.SymmetricMultiplyAndAddInPlace(MatrixOperationSide, MatrixTriangle, Int32, Int32, T, Array2D<T>, Array2D<T>, T, Array2D<T>)Remarks
Further Details:
Level 3 LinearAlgebra routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011