Linear Algebra Operations Extensions.Multiply And Add In Place Method
Definition
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Overload List
MultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, Int32, T, ReadOnlySpanSlice<T>, SpanSlice<T>)
Constant times a vector plus a vector.
public static void MultiplyAndAddInPlace<T>(
this ILinearAlgebraOperations<T> operations,
int n,
T a,
ReadOnlySpanSlice<T> x,
SpanSlice<T> y
)
Parameters
- operations ILinearAlgebraOperations<T>
- n Int32
- a T
- x ReadOnlySpanSlice<T>
- y SpanSlice<T>
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
uses unrolled loops for increments equal to one.
Further Details:
jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*)
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
MultiplyAndAddInPlace<T, TStorage>(ILinearAlgebraOperations<T>, Int32, T, TStorage, TStorage)
public static void MultiplyAndAddInPlace<T, TStorage>(
this ILinearAlgebraOperations<T> operations,
int n,
T alpha,
TStorage x,
TStorage y
)
where TStorage : Object, IStorageSlice<T>
Parameters
- operations ILinearAlgebraOperations<T>
- The linear algebra operations instance used to perform the calculation.
- n Int32
- The number of elements in the vectors x and y.
- alpha T
- The scalar value used to multiply the elements of x.
- x TStorage
- A reference to a one-dimensional array containing the elements of the vector x.
- 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
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).MultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, TransposeOperation, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpanSlice<T>, T, SpanSlice<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 matrix.
public static void MultiplyAndAddInPlace<T>(
this ILinearAlgebraOperations<T> operations,
TransposeOperation trans,
int m,
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.
- 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.
- 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, the leading m by n part of the array A must contain the matrix of coefficients.
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ).
- x ReadOnlySpanSlice<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 SpanSlice<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 with BETA non-zero, 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.
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
MultiplyAndAddInPlace<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, TransposeOperation, Int32, Int32, T, TStorage2D, TStorage, T, TStorage)
public static void MultiplyAndAddInPlace<T, TStorage, TStorage2D>(
this ILinearAlgebraOperations<T> operations,
TransposeOperation transposeOperation,
int m,
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.
- transposeOperation TransposeOperation
- Specifies the operation to be performed on the matrix a.
- m Int32
- The number of rows in the matrix a.
- n Int32
- The number of 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 DGEMV.
MultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, TransposeOperation, TransposeOperation, Int32, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpan2D<T>, T, Span2D<T>)
Performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C, where op( X ) is one of op( X ) = X or op( X ) = XT, alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
public static void MultiplyAndAddInPlace<T>(
this ILinearAlgebraOperations<T> operations,
TransposeOperation transa,
TransposeOperation transb,
int m,
int n,
int k,
T alpha,
ReadOnlySpan2D<T> a,
ReadOnlySpan2D<T> b,
T beta,
Span2D<T> c
)
Parameters
- operations ILinearAlgebraOperations<T>
- The object that performs the operation.
- transa TransposeOperation
On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n', op( A ) = A. TRANSA = 'T' or 't', op( A ) = AT. TRANSA = 'C' or 'c', op( A ) = AT.
- transb TransposeOperation
On entry, TRANSB specifies the form of op( B ) to be used in the matrix multiplication as follows: TRANSB = 'N' or 'n', op( B ) = B. TRANSB = 'T' or 't', op( B ) = BT. TRANSB = 'C' or 'c', op( B ) = BT.
- m Int32
On entry, M specifies the number of rows of the matrix op( A ) and of the matrix C. M must be at least zero.
- n Int32
On entry, N specifies the number of columns of the matrix op( B ) and the number of columns of the matrix C. N must be at least zero.
- k Int32
On entry, K specifies the number of columns of the matrix op( A ) and the number of rows of the matrix op( B ). K 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 k when TRANSA = 'N' or 'n', and is m otherwise. Before entry with TRANSA = 'N' or 'n', the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m part of the array A must contain the matrix A.
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANSA = 'N' or 'n' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ).
- b ReadOnlySpan2D<T>
B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is n when TRANSB = 'N' or 'n', and is k otherwise. Before entry with TRANSB = 'N' or 'n', the leading k by n part of the array B must contain the matrix B, otherwise the leading n by k 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. When TRANSB = 'N' or 'n' then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ).
- 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 matrix ( alpha*op( A )*op( B ) + beta*C ).
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
MultiplyAndAddInPlace<T, TStorage2D>(ILinearAlgebraOperations<T>, TransposeOperation, TransposeOperation, Int32, Int32, Int32, T, TStorage2D, TStorage2D, T, TStorage2D)
public static void MultiplyAndAddInPlace<T, TStorage2D>(
this ILinearAlgebraOperations<T> operations,
TransposeOperation transA,
TransposeOperation transB,
int m,
int n,
int k,
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.
- transA TransposeOperation
- Specifies the operation to be performed on the matrix a.
- transB TransposeOperation
- Specifies the operation to be performed on the matrix b.
- m Int32
- The number of rows in the matrix a transformed as specified by transA, and the matrix c.
- n Int32
- The number of columns in the matrix b transformed as specified by transB, and the matrix c.
- k Int32
- The number of columns in the matrix a transformed as specified by transA, and the number of rows of the matrix b transformed as specified by transB.
- 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