ManagedLinearAlgebraOperations.SymmetricMultiplyAndAddInPlace Method

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23

Overload List

SymmetricMultiplyAndAddInPlace(MatrixTriangle, Int32, Double, Array2D<Double>, ArraySlice<Double>, Double, ArraySlice<Double>)

Product of a symmetric matrix and a vector.
C# 
public override void SymmetricMultiplyAndAddInPlace(
	MatrixTriangle storedTriangle,
	int n,
	double alpha,
	Array2D<double> a,
	ArraySlice<double> x,
	double beta,
	ArraySlice<double> y
)

Parameters

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  Double
The scalar used to multiply the matrix-vector product.
a  Array2D<Double>
Reference to the first element in a one-dimensional array that contains the elements of the matrix.
x  ArraySlice<Double>
A reference to a one-dimensional array containing the elements of the vector x.
beta  Double
The scalar used to multiply y.
y  ArraySlice<Double>
A reference to a one-dimensional array containing the elements of the vector y. The elements of y are overwritten with the result.

Implements

ILinearAlgebraOperations<T>.SymmetricMultiplyAndAddInPlace(MatrixTriangle, Int32, T, Array2D<T>, ArraySlice<T>, T, ArraySlice<T>)

SymmetricMultiplyAndAddInPlace(MatrixOperationSide, MatrixTriangle, Int32, Int32, Complex<Double>, Array2D<Complex<Double>>, Array2D<Complex<Double>>, Complex<Double>, Array2D<Complex<Double>>)

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.

C# 
public override void SymmetricMultiplyAndAddInPlace(
	MatrixOperationSide side,
	MatrixTriangle storedTriangle,
	int m,
	int n,
	Complex<double> alpha,
	Array2D<Complex<double>> a,
	Array2D<Complex<double>> b,
	Complex<double> beta,
	Array2D<Complex<double>> 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,
storedTriangle  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<Double>
             On entry, ALPHA specifies the scalar alpha.
a  Array2D<Complex<Double>>
            A is COMPLEX*16 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<Double>>
            B is COMPLEX*16 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<Double>
             On entry,  BETA  specifies the scalar  beta.  When  BETA  is
             supplied as zero then C need not be set on input.
c  Array2D<Complex<Double>>
            C is COMPLEX*16 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>)

SymmetricMultiplyAndAddInPlace(MatrixOperationSide, MatrixTriangle, Int32, Int32, Double, Array2D<Double>, Array2D<Double>, Double, Array2D<Double>)

Sum of the product of a symmetric and a general matrix and a scaled matrix.
C# 
public override void SymmetricMultiplyAndAddInPlace(
	MatrixOperationSide side,
	MatrixTriangle storedTriangle,
	int m,
	int n,
	double alpha,
	Array2D<double> a,
	Array2D<double> b,
	double beta,
	Array2D<double> c
)

Parameters

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 b.
n  Int32
The number of columns in the matrix b.
alpha  Double
The scalar used to multiply the matrix-vector product.
a  Array2D<Double>
Reference to the first element in a one-dimensional array that contains the elements of the first matrix.
b  Array2D<Double>
Reference to the first element in a one-dimensional array that contains the elements of the second matrix.
beta  Double
The scalar used to multiply c.
c  Array2D<Double>
Reference to the first element in a one-dimensional array that contains the elements of the third matrix.

Implements

ILinearAlgebraOperations<T>.SymmetricMultiplyAndAddInPlace(MatrixOperationSide, MatrixTriangle, Int32, Int32, T, Array2D<T>, Array2D<T>, T, Array2D<T>)

See Also