Linear Algebra Operations Extensions.Symmetric Multiply And Add In Place Method
Definition
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Overload List
SymmetricMultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpanSlice<T>, T, SpanSlice<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 static void SymmetricMultiplyAndAddInPlace<T>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle uplo,
int n,
T alpha,
ReadOnlySpan2D<T> a,
ReadOnlySpanSlice<T> x,
T beta,
SpanSlice<T> y
)
Parameters
- operations ILinearAlgebraOperations<T>
- The object that performs the operation.
- 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 ReadOnlySpan2D<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 ReadOnlySpanSlice<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 SpanSlice<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.
Type Parameters
- T
Usage Note
In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).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<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, TStorage2D, TStorage, T, TStorage)
public static void SymmetricMultiplyAndAddInPlace<T, TStorage, TStorage2D>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle storedTriangle,
int n,
T alpha,
TStorage2D a,
TStorage x,
T beta,
TStorage y
)
where TStorage : Object, IStorageSlice<T>
where TStorage2D : Object, IStorage2D<T>
Parameters
- operations ILinearAlgebraOperations<T>
- The linear algebra operations instance used to perform the calculation.
- storedTriangle MatrixTriangle
- Specifies whether the matrix is an upper or lower triangular matrix.
- n Int32
- The number of rows and columns in the matrix a.
- alpha T
- The scalar used to multiply the matrix-vector product.
- a TStorage2D
- A span that contains the elements of the matrix.
- x TStorage
- A reference to a one-dimensional array containing the elements of the vector x.
- beta T
- The scalar used to multiply y.
- y TStorage
- A reference to a one-dimensional array containing the elements of the vector y. The elements of y are overwritten with the result.
Type Parameters
- T
- TStorage
- TStorage2D
Usage Note
In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).Remarks
This method is similar to the BLAS routine DSYMV.
SymmetricMultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpan2D<T>, T, Span2D<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 static void SymmetricMultiplyAndAddInPlace<T>(
this ILinearAlgebraOperations<T> operations,
MatrixOperationSide side,
MatrixTriangle uplo,
int m,
int n,
T alpha,
ReadOnlySpan2D<T> a,
ReadOnlySpan2D<T> b,
T beta,
Span2D<T> c
)
Parameters
- operations ILinearAlgebraOperations<T>
- The object that performs the operation.
- 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 ReadOnlySpan2D<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 ReadOnlySpan2D<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 Span2D<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 ).
Type Parameters
- T
Usage Note
In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).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<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, Int32, Int32, T, TStorage2D, TStorage2D, T, TStorage2D)
public static void SymmetricMultiplyAndAddInPlace<T, TStorage2D>(
this ILinearAlgebraOperations<T> operations,
MatrixOperationSide side,
MatrixTriangle storedTriangle,
int m,
int n,
T alpha,
TStorage2D a,
TStorage2D b,
T beta,
TStorage2D c
)
where TStorage2D : Object, IStorage2D<T>
Parameters
- operations ILinearAlgebraOperations<T>
- The linear algebra operations instance used to perform the calculation.
- side MatrixOperationSide
- Specifies on which side the symmetric matrix a is to be multiplied.
- storedTriangle MatrixTriangle
- Specifies whether the elements of the matrix a are stored in the upper or lower triangular part.
- m Int32
- The number of rows in the matrix a and the matrix c.
- n Int32
- The number of columns in the matrix b and the matrix c.
- alpha T
- The scalar used to multiply the matrix-vector product.
- a TStorage2D
- A span that contains the elements of the first matrix.
- b TStorage2D
- A span that contains the elements of the second matrix.
- beta T
- The scalar used to multiply c.
- c TStorage2D
- A span that contains the elements of the third matrix.
Type Parameters
- T
- TStorage2D