ManagedLinearAlgebraOperations.SymmetricRankUpdate Method

Definition

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

Overload List

SymmetricRankUpdate(MatrixTriangle, Int32, Double, ArraySlice<Double>, Array2D<Double>) Performs a rank one update of a symmetric matrix.
SymmetricRankUpdate(MatrixTriangle, Int32, Double, ArraySlice<Double>, ArraySlice<Double>, Array2D<Double>) Performs a symmetric rank two update of a symmetric matrix.
SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, Complex<Double>, Array2D<Complex<Double>>, Complex<Double>, Array2D<Complex<Double>>)

Performs one of the symmetric rank k operations C := alpha*A*AT + beta*C, or C := alpha*AT*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, Double, Array2D<Double>, Double, Array2D<Double>) Performs a rank k update of a symmetric matrix.
SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, Complex<Double>, Array2D<Complex<Double>>, Array2D<Complex<Double>>, Complex<Double>, Array2D<Complex<Double>>)

Performs one of the symmetric rank 2k operations C := alpha*A*BT + alpha*B*AT + beta*C, or C := alpha*AT*B + alpha*BT*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, Double, Array2D<Double>, Array2D<Double>, Double, Array2D<Double>) Performs a rank 2k update of a symmetric matrix.

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

Performs a rank one update of a symmetric matrix.
C# 
public override void SymmetricRankUpdate(
	MatrixTriangle storedTriangle,
	int n,
	double alpha,
	ArraySlice<double> x,
	Array2D<double> a
)

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 outer product.
x  ArraySlice<Double>
A reference to a one-dimensional array containing the elements of the vector x.
a  Array2D<Double>
Reference to the first element in a one-dimensional array that contains the elements of the matrix.

Implements

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

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

Performs a symmetric rank two update of a symmetric matrix.
C# 
public override void SymmetricRankUpdate(
	MatrixTriangle storedTriangle,
	int n,
	double alpha,
	ArraySlice<double> x,
	ArraySlice<double> y,
	Array2D<double> a
)

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 outer product.
x  ArraySlice<Double>
A reference to a one-dimensional array containing the elements of the vector x.
y  ArraySlice<Double>
A reference to a one-dimensional array containing the elements of the vector y.
a  Array2D<Double>
Reference to the first element in a one-dimensional array that contains the elements of the matrix.

Implements

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

SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, Complex<Double>, Array2D<Complex<Double>>, Complex<Double>, Array2D<Complex<Double>>)

Performs one of the symmetric rank k operations C := alpha*A*AT + beta*C, or C := alpha*AT*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

C# 
public override void SymmetricRankUpdate(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	int n,
	int k,
	Complex<double> alpha,
	Array2D<Complex<double>> a,
	Complex<double> beta,
	Array2D<Complex<double>> c
)

Parameters

storedTriangle  MatrixTriangle
             On  entry,   UPLO  specifies  whether  the  upper  or  lower
             triangular  part  of the  array  C  is to be  referenced  as
             follows:
                UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                    is to be referenced.
                UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                    is to be referenced.
trans  TransposeOperation
             On entry,  TRANS  specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   C := alpha*A*AT + beta*C.
                TRANS = 'T' or 't'   C := alpha*AT*A + beta*C.
n  Int32
             On entry,  N specifies the order of the matrix C.  N must be
             at least zero.
k  Int32
             On entry with  TRANS = 'N' or 'n',  K  specifies  the number
             of  columns   of  the   matrix   A,   and  on   entry   with
             TRANS = 'T' or 't',  K  specifies  the number of rows of the
             matrix A.  K 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
             k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
             Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
             part of the array  A  must contain the matrix  A,  otherwise
             the leading  k by n  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  TRANS = 'N' or 'n'
             then  LDA must be at least  max( 1, n ), otherwise  LDA must
             be at least  max( 1, k ).
beta  Complex<Double>
             On entry, BETA specifies the scalar beta.
c  Array2D<Complex<Double>>
            C is COMPLEX*16 array of DIMENSION ( LDC, n ).
             Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
             upper triangular part of the array C must contain the upper
             triangular part  of the  symmetric matrix  and the strictly
             lower triangular part of C is not referenced.  On exit, the
             upper triangular part of the array  C is overwritten by the
             upper triangular part of the updated matrix.
             Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
             lower triangular part of the array C must contain the lower
             triangular part  of the  symmetric matrix  and the strictly
             upper triangular part of C is not referenced.  On exit, the
             lower triangular part of the array  C is overwritten by the
             lower triangular part of the 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, n ).

Implements

ILinearAlgebraOperations<T>.SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, T, Array2D<T>)

SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, Double, Array2D<Double>, Double, Array2D<Double>)

Performs a rank k update of a symmetric matrix.
C# 
public override void SymmetricRankUpdate(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	int n,
	int k,
	double alpha,
	Array2D<double> a,
	double beta,
	Array2D<double> c
)

Parameters

storedTriangle  MatrixTriangle
Specifies whether the elements of the matrix a are stored in the upper or lower triangular part.
trans  TransposeOperation
Specifies the operation to be performed on the matrix a.
n  Int32
The number of rows and columns in the matrix c.
k  Int32
The number of columns in the matrix a transformed as specified by trans.
alpha  Double
The scalar used to multiply the matrix-matrix product.
a  Array2D<Double>
Reference to the first element in a one-dimensional array that contains the elements of the first 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>.SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, T, Array2D<T>)

SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, Complex<Double>, Array2D<Complex<Double>>, Array2D<Complex<Double>>, Complex<Double>, Array2D<Complex<Double>>)

Performs one of the symmetric rank 2k operations C := alpha*A*BT + alpha*B*AT + beta*C, or C := alpha*AT*B + alpha*BT*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

C# 
public override void SymmetricRankUpdate(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	int n,
	int k,
	Complex<double> alpha,
	Array2D<Complex<double>> a,
	Array2D<Complex<double>> b,
	Complex<double> beta,
	Array2D<Complex<double>> c
)

Parameters

storedTriangle  MatrixTriangle
             On  entry,   UPLO  specifies  whether  the  upper  or  lower
             triangular  part  of the  array  C  is to be  referenced  as
             follows:
                UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                    is to be referenced.
                UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                    is to be referenced.
trans  TransposeOperation
             On entry,  TRANS  specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'    C := alpha*A*BT + alpha*B*AT +
                                           beta*C.
                TRANS = 'T' or 't'    C := alpha*AT*B + alpha*BT*A +
                                           beta*C.
n  Int32
             On entry,  N specifies the order of the matrix C.  N must be
             at least zero.
k  Int32
             On entry with  TRANS = 'N' or 'n',  K  specifies  the number
             of  columns  of the  matrices  A and B,  and on  entry  with
             TRANS = 'T' or 't',  K  specifies  the number of rows of the
             matrices  A and B.  K 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
             k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
             Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
             part of the array  A  must contain the matrix  A,  otherwise
             the leading  k by n  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  TRANS = 'N' or 'n'
             then  LDA must be at least  max( 1, n ), otherwise  LDA must
             be at least  max( 1, k ).
b  Array2D<Complex<Double>>
            B is COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is
             k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
             Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
             part of the array  B  must contain the matrix  B,  otherwise
             the leading  k 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.   When  TRANS = 'N' or 'n'
             then  LDB must be at least  max( 1, n ), otherwise  LDB must
             be at least  max( 1, k ).
beta  Complex<Double>
             On entry, BETA specifies the scalar beta.
c  Array2D<Complex<Double>>
            C is COMPLEX*16 array of DIMENSION ( LDC, n ).
             Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
             upper triangular part of the array C must contain the upper
             triangular part  of the  symmetric matrix  and the strictly
             lower triangular part of C is not referenced.  On exit, the
             upper triangular part of the array  C is overwritten by the
             upper triangular part of the updated matrix.
             Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
             lower triangular part of the array C must contain the lower
             triangular part  of the  symmetric matrix  and the strictly
             upper triangular part of C is not referenced.  On exit, the
             lower triangular part of the array  C is overwritten by the
             lower triangular part of the 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, n ).

Implements

ILinearAlgebraOperations<T>.SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, Array2D<T>, T, Array2D<T>)

SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, Double, Array2D<Double>, Array2D<Double>, Double, Array2D<Double>)

Performs a rank 2k update of a symmetric matrix.
C# 
public override void SymmetricRankUpdate(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	int n,
	int k,
	double alpha,
	Array2D<double> a,
	Array2D<double> b,
	double beta,
	Array2D<double> c
)

Parameters

storedTriangle  MatrixTriangle
Specifies whether the elements of the matrix a are stored in the upper or lower triangular part.
trans  TransposeOperation
Specifies the operation to be performed on the matrix a.
n  Int32
The number of rows and columns in the matrix c.
k  Int32
The number of columns in the matrix a transformed as specified by trans.
alpha  Double
The scalar used to multiply the matrix-matrix 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>.SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, Array2D<T>, T, Array2D<T>)

See Also