LinearAlgebraOperations<T>.HermitianRankUpdate Method

Definition

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

Overload List

HermitianRankUpdate(MatrixTriangle, Int32, T, ArraySlice<T>, Array2D<T>) Performs a rank one update of a hermitian.
HermitianRankUpdate(MatrixTriangle, Int32, T, ArraySlice<Complex<T>>, Array2D<Complex<T>>)

Performs the hermitian rank 1 operation A := alpha*x*x**H + A, where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix.

HermitianRankUpdate(MatrixTriangle, Int32, T, ArraySlice<T>, ArraySlice<T>, Array2D<T>) Performs a hermitian rank two update of a hermitian matrix.
HermitianRankUpdate(MatrixTriangle, Int32, Complex<T>, ArraySlice<Complex<T>>, ArraySlice<Complex<T>>, Array2D<Complex<T>>)

Performs the hermitian rank 2 operation A := alpha*x*y**H + conjg( alpha )*y*x**H + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix.

HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, T, Array2D<T>) Performs a rank k update of a hermitian matrix.
HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<Complex<T>>, T, Array2D<Complex<T>>)

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

HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, Array2D<T>, T, Array2D<T>) Performs a rank 2k update of a hermitian matrix.
HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, Complex<T>, Array2D<Complex<T>>, Array2D<Complex<T>>, T, Array2D<Complex<T>>)

Performs one of the hermitian rank 2k operations C := alpha*A*BH + conjg( alpha )*B*AH + beta*C, or C := alpha*AH*B + conjg( alpha )*BH*A + beta*C, where alpha and beta are scalars with beta real, C is an n by n hermitian matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

HermitianRankUpdate(MatrixTriangle, Int32, T, ArraySlice<T>, Array2D<T>)

Performs a rank one update of a hermitian.
C# 
public void HermitianRankUpdate(
	MatrixTriangle storedTriangle,
	int n,
	T alpha,
	ArraySlice<T> x,
	Array2D<T> 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  T
The scalar used to multiply the outer product.
x  ArraySlice<T>
A reference to a one-dimensional array containing the elements of the vector x.
a  Array2D<T>
Reference to the first element in a one-dimensional array that contains the elements of the matrix.

HermitianRankUpdate(MatrixTriangle, Int32, T, ArraySlice<Complex<T>>, Array2D<Complex<T>>)

Performs the hermitian rank 1 operation A := alpha*x*x**H + A, where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix.

C# 
public abstract void HermitianRankUpdate(
	MatrixTriangle uplo,
	int n,
	T alpha,
	ArraySlice<Complex<T>> x,
	Array2D<Complex<T>> a
)

Parameters

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.
x  ArraySlice<Complex<T>>
            X is complex 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.
a  Array2D<Complex<T>>
            A is complex 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 hermitian matrix and the strictly
             lower triangular part of A is not referenced. On exit, the
             upper triangular part of the array A 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 A must contain the lower
             triangular part of the hermitian matrix and the strictly
             upper triangular part of A is not referenced. On exit, the
             lower triangular part of the array A is overwritten by the
             lower triangular part of the updated matrix.
             Note that the imaginary parts of the diagonal elements need
             not be set, they are assumed to be zero, and on exit they
             are set to zero.
            
             On entry, LDA specifies the first dimension of A as declared
             in the calling (sub) program. LDA must be at least
             max( 1, n ).

Remarks

 Further Details:
            Level 2 LinearAlgebra routine.
            -- 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

HermitianRankUpdate(MatrixTriangle, Int32, T, ArraySlice<T>, ArraySlice<T>, Array2D<T>)

Performs a hermitian rank two update of a hermitian matrix.
C# 
public void HermitianRankUpdate(
	MatrixTriangle storedTriangle,
	int n,
	T alpha,
	ArraySlice<T> x,
	ArraySlice<T> y,
	Array2D<T> 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  T
The scalar used to multiply the outer product.
x  ArraySlice<T>
A reference to a one-dimensional array containing the elements of the vector x.
y  ArraySlice<T>
A reference to a one-dimensional array containing the elements of the vector y.
a  Array2D<T>
Reference to the first element in a one-dimensional array that contains the elements of the matrix.

HermitianRankUpdate(MatrixTriangle, Int32, Complex<T>, ArraySlice<Complex<T>>, ArraySlice<Complex<T>>, Array2D<Complex<T>>)

Performs the hermitian rank 2 operation A := alpha*x*y**H + conjg( alpha )*y*x**H + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix.

C# 
public abstract void HermitianRankUpdate(
	MatrixTriangle uplo,
	int n,
	Complex<T> alpha,
	ArraySlice<Complex<T>> x,
	ArraySlice<Complex<T>> y,
	Array2D<Complex<T>> a
)

Parameters

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  Complex<T>
             On entry, ALPHA specifies the scalar alpha.
x  ArraySlice<Complex<T>>
            X is complex 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.
y  ArraySlice<Complex<T>>
            Y is complex array of dimension at least
             ( 1 + ( n - 1 )*abs( INCY ) ).
             Before entry, the incremented array Y must contain the n
             element vector y.
            
             On entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.
a  Array2D<Complex<T>>
            A is complex 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 hermitian matrix and the strictly
             lower triangular part of A is not referenced. On exit, the
             upper triangular part of the array A 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 A must contain the lower
             triangular part of the hermitian matrix and the strictly
             upper triangular part of A is not referenced. On exit, the
             lower triangular part of the array A is overwritten by the
             lower triangular part of the updated matrix.
             Note that the imaginary parts of the diagonal elements need
             not be set, they are assumed to be zero, and on exit they
             are set to zero.
            
             On entry, LDA specifies the first dimension of A as declared
             in the calling (sub) program. LDA must be at least
             max( 1, n ).

Implements

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

Remarks

 Further Details:
            Level 2 LinearAlgebra routine.
            -- 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

HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, T, Array2D<T>)

Performs a rank k update of a hermitian matrix.
C# 
public void HermitianRankUpdate(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	Array2D<T> a,
	T beta,
	Array2D<T> 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  T
The scalar used to multiply the matrix-matrix product.
a  Array2D<T>
Reference to the first element in a one-dimensional array that contains the elements of the first matrix.
beta  T
The scalar used to multiply c.
c  Array2D<T>
Reference to the first element in a one-dimensional array that contains the elements of the third matrix.

HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<Complex<T>>, T, Array2D<Complex<T>>)

Performs one of the hermitian rank k operations C := alpha*A*AH + beta*C, or C := alpha*AH*A + beta*C, where alpha and beta are real scalars, C is an n by n hermitian 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 abstract void HermitianRankUpdate(
	MatrixTriangle uplo,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	Array2D<Complex<T>> a,
	T beta,
	Array2D<Complex<T>> c
)

Parameters

uplo  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*AH + beta*C.
                TRANS = 'C' or 'c'   C := alpha*AH*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 = 'C' or 'c',  K  specifies  the number of rows of the
             matrix A.  K must be at least zero.
alpha  T
            ALPHA is DOUBLE PRECISION .
             On entry, ALPHA specifies the scalar alpha.
a  Array2D<Complex<T>>
            A is complex 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  T
            BETA is DOUBLE PRECISION.
             On entry, BETA specifies the scalar beta.
c  Array2D<Complex<T>>
            C is complex 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  hermitian 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  hermitian 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.
             Note that the imaginary parts of the diagonal elements need
             not be set,  they are assumed to be zero,  and on exit they
             are set to zero.
            
             On entry, LDC specifies the first dimension of C as declared
             in  the  calling  (sub)  program.   LDC  must  be  at  least
             max( 1, n ).

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.
            -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
               Ed Anderson, Cray Research Inc.
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, Array2D<T>, T, Array2D<T>)

Performs a rank 2k update of a hermitian matrix.
C# 
public void HermitianRankUpdate(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	Array2D<T> a,
	Array2D<T> b,
	T beta,
	Array2D<T> 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  T
The scalar used to multiply the matrix-matrix product.
a  Array2D<T>
Reference to the first element in a one-dimensional array that contains the elements of the first matrix.
b  Array2D<T>
Reference to the first element in a one-dimensional array that contains the elements of the second matrix.
beta  T
The scalar used to multiply c.
c  Array2D<T>
Reference to the first element in a one-dimensional array that contains the elements of the third matrix.

HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, Complex<T>, Array2D<Complex<T>>, Array2D<Complex<T>>, T, Array2D<Complex<T>>)

Performs one of the hermitian rank 2k operations C := alpha*A*BH + conjg( alpha )*B*AH + beta*C, or C := alpha*AH*B + conjg( alpha )*BH*A + beta*C, where alpha and beta are scalars with beta real, C is an n by n hermitian 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 abstract void HermitianRankUpdate(
	MatrixTriangle uplo,
	TransposeOperation trans,
	int n,
	int k,
	Complex<T> alpha,
	Array2D<Complex<T>> a,
	Array2D<Complex<T>> b,
	T beta,
	Array2D<Complex<T>> c
)

Parameters

uplo  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*BH          +
                                           conjg( alpha )*B*AH +
                                           beta*C.
                TRANS = 'C' or 'c'    C := alpha*AH*B          +
                                           conjg( alpha )*BH*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 = 'C' or 'c',  K  specifies  the number of rows of the
             matrices  A and B.  K must be at least zero.
alpha  Complex<T>
            ALPHA is complex .
             On entry, ALPHA specifies the scalar alpha.
a  Array2D<Complex<T>>
            A is complex 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<T>>
            B is complex 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 ).
             Unchanged on exit.
beta  T
            BETA is DOUBLE PRECISION .
             On entry, BETA specifies the scalar beta.
c  Array2D<Complex<T>>
            C is complex 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  hermitian 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  hermitian 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.
             Note that the imaginary parts of the diagonal elements need
             not be set,  they are assumed to be zero,  and on exit they
             are set to zero.
            
             On entry, LDC specifies the first dimension of C as declared
             in  the  calling  (sub)  program.   LDC  must  be  at  least
             max( 1, n ).

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.
            -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
               Ed Anderson, Cray Research Inc.
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

See Also