LinearAlgebraOperationsExtensions.MultiplyAndAddInPlace Method

Definition

Namespace: Numerics.NET.Collections
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.2

Overload List

MultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, Int32, T, ReadOnlySpanSlice<T>, SpanSlice<T>)	Constant times a vector plus a vector.
MultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, TransposeOperation, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpanSlice<T>, T, SpanSlice<T>)	Performs one of the matrix-vector operations y := alphaAx + betay, or y := alphaA^Tx + betay, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.
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 := alphaop( A )op( B ) + beta*C, where op( X ) is one of op( X ) = X or op( X ) = X^T, 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.
MultiplyAndAddInPlace<T, TStorage>(ILinearAlgebraOperations<T>, Int32, T, TStorage, TStorage)	Evaluates a vector plus the product of a scalar and a vector
MultiplyAndAddInPlace<T, TStorage2D>(ILinearAlgebraOperations<T>, TransposeOperation, TransposeOperation, Int32, Int32, Int32, T, TStorage2D, TStorage2D, T, TStorage2D)	Sum of the product of two general matrices and a scaled matrix.
MultiplyAndAddInPlace<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, TransposeOperation, Int32, Int32, T, TStorage2D, TStorage, T, TStorage)	Sum of the product of a general matrix and vector and a scaled vector.

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
)

Visual Basic

<ExtensionAttribute>
Public Shared Sub MultiplyAndAddInPlace(Of T) ( 
	operations As ILinearAlgebraOperations(Of T),
	n As Integer,
	a As T,
	x As ReadOnlySpanSlice(Of T),
	y As SpanSlice(Of T)
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T>
static void MultiplyAndAddInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	int n, 
	T a, 
	ReadOnlySpanSlice<T> x, 
	SpanSlice<T> y
)

[<ExtensionAttribute>]
static member MultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        n : int * 
        a : 'T * 
        x : ReadOnlySpanSlice<'T> * 
        y : SpanSlice<'T> -> unit

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)

Evaluates a vector plus the product of a scalar and a vector

public static void MultiplyAndAddInPlace<T, TStorage>(
	this ILinearAlgebraOperations<T> operations,
	int n,
	T alpha,
	TStorage x,
	TStorage y
)
where TStorage : Object, IStorageSlice<T>

Visual Basic

<ExtensionAttribute>
Public Shared Sub MultiplyAndAddInPlace(Of T, TStorage As {Object, IStorageSlice(Of T)}) ( 
	operations As ILinearAlgebraOperations(Of T),
	n As Integer,
	alpha As T,
	x As TStorage,
	y As TStorage
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T, typename TStorage>
where TStorage : Object, IStorageSlice<T>
static void MultiplyAndAddInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	int n, 
	T alpha, 
	TStorage x, 
	TStorage y
)

[<ExtensionAttribute>]
static member MultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        n : int * 
        alpha : 'T * 
        x : 'TStorage * 
        y : 'TStorage -> unit  when 'TStorage : Object and 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

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*A^T*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
)

Visual Basic

<ExtensionAttribute>
Public Shared Sub MultiplyAndAddInPlace(Of T) ( 
	operations As ILinearAlgebraOperations(Of T),
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	alpha As T,
	a As ReadOnlySpan2D(Of T),
	x As ReadOnlySpanSlice(Of T),
	beta As T,
	y As SpanSlice(Of T)
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T>
static void MultiplyAndAddInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	TransposeOperation trans, 
	int m, 
	int n, 
	T alpha, 
	ReadOnlySpan2D<T> a, 
	ReadOnlySpanSlice<T> x, 
	T beta, 
	SpanSlice<T> y
)

[<ExtensionAttribute>]
static member MultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        alpha : 'T * 
        a : ReadOnlySpan2D<'T> * 
        x : ReadOnlySpanSlice<'T> * 
        beta : 'T * 
        y : SpanSlice<'T> -> unit

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*A^T*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*A^T*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

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)

Sum of the product of a general matrix and vector and a scaled vector.

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>

Visual Basic

<ExtensionAttribute>
Public Shared Sub MultiplyAndAddInPlace(Of T, TStorage As {Object, IStorageSlice(Of T)}, TStorage2D As {Object, IStorage2D(Of T)}) ( 
	operations As ILinearAlgebraOperations(Of T),
	transposeOperation As TransposeOperation,
	m As Integer,
	n As Integer,
	alpha As T,
	a As TStorage2D,
	x As TStorage,
	beta As T,
	y As TStorage
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T, typename TStorage, typename TStorage2D>
where TStorage : Object, IStorageSlice<T>
where TStorage2D : Object, IStorage2D<T>
static void MultiplyAndAddInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	TransposeOperation transposeOperation, 
	int m, 
	int n, 
	T alpha, 
	TStorage2D a, 
	TStorage x, 
	T beta, 
	TStorage y
)

[<ExtensionAttribute>]
static member MultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        transposeOperation : TransposeOperation * 
        m : int * 
        n : int * 
        alpha : 'T * 
        a : 'TStorage2D * 
        x : 'TStorage * 
        beta : 'T * 
        y : 'TStorage -> unit  when 'TStorage : Object and IStorageSlice<'T> when 'TStorage2D : Object and 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

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 ) = X^T, 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
)

Visual Basic

<ExtensionAttribute>
Public Shared Sub MultiplyAndAddInPlace(Of T) ( 
	operations As ILinearAlgebraOperations(Of T),
	transa As TransposeOperation,
	transb As TransposeOperation,
	m As Integer,
	n As Integer,
	k As Integer,
	alpha As T,
	a As ReadOnlySpan2D(Of T),
	b As ReadOnlySpan2D(Of T),
	beta As T,
	c As Span2D(Of T)
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T>
static void MultiplyAndAddInPlace(
	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
)

[<ExtensionAttribute>]
static member MultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        transa : TransposeOperation * 
        transb : TransposeOperation * 
        m : int * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : ReadOnlySpan2D<'T> * 
        b : ReadOnlySpan2D<'T> * 
        beta : 'T * 
        c : Span2D<'T> -> unit

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 ) = A^T.
                TRANSA = 'C' or 'c',  op( A ) = A^T.

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 ) = B^T.
                TRANSB = 'C' or 'c',  op( B ) = B^T.

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

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)

Sum of the product of two general matrices and a scaled matrix.

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>

Visual Basic

<ExtensionAttribute>
Public Shared Sub MultiplyAndAddInPlace(Of T, TStorage2D As {Object, IStorage2D(Of T)}) ( 
	operations As ILinearAlgebraOperations(Of T),
	transA As TransposeOperation,
	transB As TransposeOperation,
	m As Integer,
	n As Integer,
	k As Integer,
	alpha As T,
	a As TStorage2D,
	b As TStorage2D,
	beta As T,
	c As TStorage2D
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T, typename TStorage2D>
where TStorage2D : Object, IStorage2D<T>
static void MultiplyAndAddInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	TransposeOperation transA, 
	TransposeOperation transB, 
	int m, 
	int n, 
	int k, 
	T alpha, 
	TStorage2D a, 
	TStorage2D b, 
	T beta, 
	TStorage2D c
)

[<ExtensionAttribute>]
static member MultiplyAndAddInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        transA : TransposeOperation * 
        transB : TransposeOperation * 
        m : int * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : 'TStorage2D * 
        b : 'TStorage2D * 
        beta : 'T * 
        c : 'TStorage2D -> unit  when 'TStorage2D : Object and 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

LinearAlgebraOperationsExtensions.MultiplyAndAddInPlace Method

Definition

Overload List

MultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, Int32, T, ReadOnlySpanSlice<T>, SpanSlice<T>)

Parameters

Type Parameters

Usage Note

Remarks

Further Details:

MultiplyAndAddInPlace<T, TStorage>(ILinearAlgebraOperations<T>, Int32, T, TStorage, TStorage)

Parameters

Type Parameters

Usage Note

MultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, TransposeOperation, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpanSlice<T>, T, SpanSlice<T>)

Parameters

Type Parameters

Usage Note

Remarks

Further Details:

MultiplyAndAddInPlace<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, TransposeOperation, Int32, Int32, T, TStorage2D, TStorage, T, TStorage)

Parameters

Type Parameters

Usage Note

Remarks

MultiplyAndAddInPlace<T>(ILinearAlgebraOperations<T>, TransposeOperation, TransposeOperation, Int32, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpan2D<T>, T, Span2D<T>)

Parameters

Type Parameters

Usage Note

Remarks

Further Details:

MultiplyAndAddInPlace<T, TStorage2D>(ILinearAlgebraOperations<T>, TransposeOperation, TransposeOperation, Int32, Int32, Int32, T, TStorage2D, TStorage2D, T, TStorage2D)

Parameters

Type Parameters

Usage Note

See Also

Reference