Linear Algebra Operations &lt; T &gt; . Hermitian Rank Update Method

             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.

             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 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, ReadOnlySpanSlice<Complex<T>>, Span2D<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.

public void HermitianRankUpdate(
	MatrixTriangle uplo,
	int n,
	T alpha,
	ReadOnlySpanSlice<Complex<T>> x,
	Span2D<Complex<T>> a
)

Visual Basic

Public Sub HermitianRankUpdate ( 
	uplo As MatrixTriangle,
	n As Integer,
	alpha As T,
	x As ReadOnlySpanSlice(Of Complex(Of T)),
	a As Span2D(Of Complex(Of T))
)

C++/CLI

public:
void HermitianRankUpdate(
	MatrixTriangle uplo, 
	int n, 
	T alpha, 
	ReadOnlySpanSlice<Complex<T>> x, 
	Span2D<Complex<T>> a
)

member HermitianRankUpdate : 
        uplo : MatrixTriangle * 
        n : int * 
        alpha : 'T * 
        x : ReadOnlySpanSlice<Complex<'T>> * 
        a : Span2D<Complex<'T>> -> unit

Parameters

             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.

             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 ReadOnlySpanSlice<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 Span2D<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.

public void HermitianRankUpdate(
	MatrixTriangle storedTriangle,
	int n,
	T alpha,
	ArraySlice<T> x,
	ArraySlice<T> y,
	Array2D<T> a
)

Visual Basic

Public Sub HermitianRankUpdate ( 
	storedTriangle As MatrixTriangle,
	n As Integer,
	alpha As T,
	x As ArraySlice(Of T),
	y As ArraySlice(Of T),
	a As Array2D(Of T)
)

C++/CLI

public:
void HermitianRankUpdate(
	MatrixTriangle storedTriangle, 
	int n, 
	T alpha, 
	ArraySlice<T> x, 
	ArraySlice<T> y, 
	Array2D<T> a
)

member HermitianRankUpdate : 
        storedTriangle : MatrixTriangle * 
        n : int * 
        alpha : 'T * 
        x : ArraySlice<'T> * 
        y : ArraySlice<'T> * 
        a : Array2D<'T> -> unit

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>: A span 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.

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

Visual Basic

Public Sub HermitianRankUpdate ( 
	uplo As MatrixTriangle,
	n As Integer,
	alpha As Complex(Of T),
	x As ArraySlice(Of Complex(Of T)),
	y As ArraySlice(Of Complex(Of T)),
	a As Array2D(Of Complex(Of T))
)

C++/CLI

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

member HermitianRankUpdate : 
        uplo : MatrixTriangle * 
        n : int * 
        alpha : Complex<'T> * 
        x : ArraySlice<Complex<'T>> * 
        y : ArraySlice<Complex<'T>> * 
        a : Array2D<Complex<'T>> -> unit

Parameters

             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.

             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 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, Complex<T>, ReadOnlySpanSlice<Complex<T>>, ReadOnlySpanSlice<Complex<T>>, Span2D<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.

public void HermitianRankUpdate(
	MatrixTriangle uplo,
	int n,
	Complex<T> alpha,
	ReadOnlySpanSlice<Complex<T>> x,
	ReadOnlySpanSlice<Complex<T>> y,
	Span2D<Complex<T>> a
)

Visual Basic

Public Sub HermitianRankUpdate ( 
	uplo As MatrixTriangle,
	n As Integer,
	alpha As Complex(Of T),
	x As ReadOnlySpanSlice(Of Complex(Of T)),
	y As ReadOnlySpanSlice(Of Complex(Of T)),
	a As Span2D(Of Complex(Of T))
)

C++/CLI

public:
void HermitianRankUpdate(
	MatrixTriangle uplo, 
	int n, 
	Complex<T> alpha, 
	ReadOnlySpanSlice<Complex<T>> x, 
	ReadOnlySpanSlice<Complex<T>> y, 
	Span2D<Complex<T>> a
)

member HermitianRankUpdate : 
        uplo : MatrixTriangle * 
        n : int * 
        alpha : Complex<'T> * 
        x : ReadOnlySpanSlice<Complex<'T>> * 
        y : ReadOnlySpanSlice<Complex<'T>> * 
        a : Span2D<Complex<'T>> -> unit

Parameters

             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.

             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 ReadOnlySpanSlice<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 ReadOnlySpanSlice<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 Span2D<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, ReadOnlySpan<T>, Int32, Span<T>, Int32)

Performs a rank one update of a hermitian.

public void HermitianRankUpdate(
	MatrixTriangle storedTriangle,
	int n,
	T alpha,
	ReadOnlySpan<T> x,
	int incx,
	Span<T> a,
	int lda
)

Visual Basic

Public Sub HermitianRankUpdate ( 
	storedTriangle As MatrixTriangle,
	n As Integer,
	alpha As T,
	x As ReadOnlySpan(Of T),
	incx As Integer,
	a As Span(Of T),
	lda As Integer
)

C++/CLI

public:
void HermitianRankUpdate(
	MatrixTriangle storedTriangle, 
	int n, 
	T alpha, 
	ReadOnlySpan<T> x, 
	int incx, 
	Span<T> a, 
	int lda
)

member HermitianRankUpdate : 
        storedTriangle : MatrixTriangle * 
        n : int * 
        alpha : 'T * 
        x : ReadOnlySpan<'T> * 
        incx : int * 
        a : Span<'T> * 
        lda : int -> unit

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 ReadOnlySpan<T>: A reference to a one-dimensional array containing the elements of the vector x.
incx Int32: The distance between elements in x.
a Span<T>: A span that contains the elements of the matrix.
lda Int32: The leading dimension of the matrix a.

HermitianRankUpdate(MatrixTriangle, Int32, T, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32)

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

public abstract void HermitianRankUpdate(
	MatrixTriangle uplo,
	int n,
	T alpha,
	ReadOnlySpan<Complex<T>> x,
	int incx,
	Span<Complex<T>> a,
	int lda
)

Visual Basic

Public MustOverride Sub HermitianRankUpdate ( 
	uplo As MatrixTriangle,
	n As Integer,
	alpha As T,
	x As ReadOnlySpan(Of Complex(Of T)),
	incx As Integer,
	a As Span(Of Complex(Of T)),
	lda As Integer
)

C++/CLI

public:
virtual void HermitianRankUpdate(
	MatrixTriangle uplo, 
	int n, 
	T alpha, 
	ReadOnlySpan<Complex<T>> x, 
	int incx, 
	Span<Complex<T>> a, 
	int lda
) abstract

abstract HermitianRankUpdate : 
        uplo : MatrixTriangle * 
        n : int * 
        alpha : 'T * 
        x : ReadOnlySpan<Complex<'T>> * 
        incx : int * 
        a : Span<Complex<'T>> * 
        lda : int -> unit

Parameters

             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.

             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 ReadOnlySpan<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.

incx Int32

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.

a Span<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.

lda Int32

             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, TransposeOperation, Int32, Int32, T, Array2D<T>, T, Array2D<T>)

Performs a rank k update of a hermitian matrix.

public void HermitianRankUpdate(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	Array2D<T> a,
	T beta,
	Array2D<T> c
)

Visual Basic

Public Sub HermitianRankUpdate ( 
	storedTriangle As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k As Integer,
	alpha As T,
	a As Array2D(Of T),
	beta As T,
	c As Array2D(Of T)
)

C++/CLI

public:
void HermitianRankUpdate(
	MatrixTriangle storedTriangle, 
	TransposeOperation trans, 
	int n, 
	int k, 
	T alpha, 
	Array2D<T> a, 
	T beta, 
	Array2D<T> c
)

member HermitianRankUpdate : 
        storedTriangle : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : Array2D<'T> * 
        beta : 'T * 
        c : Array2D<'T> -> unit

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>: A span that contains the elements of the first matrix.
beta T: The scalar used to multiply c.
c Array2D<T>: A span 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*A^H + beta*C, or C := alpha*A^H*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.

public void HermitianRankUpdate(
	MatrixTriangle uplo,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	Array2D<Complex<T>> a,
	T beta,
	Array2D<Complex<T>> c
)

Visual Basic

Public Sub HermitianRankUpdate ( 
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k As Integer,
	alpha As T,
	a As Array2D(Of Complex(Of T)),
	beta As T,
	c As Array2D(Of Complex(Of T))
)

C++/CLI

public:
void HermitianRankUpdate(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	int n, 
	int k, 
	T alpha, 
	Array2D<Complex<T>> a, 
	T beta, 
	Array2D<Complex<T>> c
)

member HermitianRankUpdate : 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : Array2D<Complex<'T>> * 
        beta : 'T * 
        c : Array2D<Complex<'T>> -> unit

Parameters

             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.

             On entry,  TRANS  specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   C := alpha*A*A^H + beta*C.
                TRANS = 'C' or 'c'   C := alpha*A^H*A + beta*C.

             On entry,  N specifies the order of the matrix C.  N must be
             at least zero.

             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 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, ReadOnlySpan2D<Complex<T>>, T, Span2D<Complex<T>>)

public void HermitianRankUpdate(
	MatrixTriangle uplo,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	ReadOnlySpan2D<Complex<T>> a,
	T beta,
	Span2D<Complex<T>> c
)

Visual Basic

Public Sub HermitianRankUpdate ( 
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k As Integer,
	alpha As T,
	a As ReadOnlySpan2D(Of Complex(Of T)),
	beta As T,
	c As Span2D(Of Complex(Of T))
)

C++/CLI

public:
void HermitianRankUpdate(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	int n, 
	int k, 
	T alpha, 
	ReadOnlySpan2D<Complex<T>> a, 
	T beta, 
	Span2D<Complex<T>> c
)

member HermitianRankUpdate : 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : ReadOnlySpan2D<Complex<'T>> * 
        beta : 'T * 
        c : Span2D<Complex<'T>> -> unit

Parameters

             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.

             On entry,  TRANS  specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   C := alpha*A*A^H + beta*C.
                TRANS = 'C' or 'c'   C := alpha*A^H*A + beta*C.

             On entry,  N specifies the order of the matrix C.  N must be
             at least zero.

             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 ReadOnlySpan2D<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 Span2D<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.

public void HermitianRankUpdate(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	Array2D<T> a,
	Array2D<T> b,
	T beta,
	Array2D<T> c
)

Visual Basic

Public Sub HermitianRankUpdate ( 
	storedTriangle As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k As Integer,
	alpha As T,
	a As Array2D(Of T),
	b As Array2D(Of T),
	beta As T,
	c As Array2D(Of T)
)

C++/CLI

public:
void HermitianRankUpdate(
	MatrixTriangle storedTriangle, 
	TransposeOperation trans, 
	int n, 
	int k, 
	T alpha, 
	Array2D<T> a, 
	Array2D<T> b, 
	T beta, 
	Array2D<T> c
)

member HermitianRankUpdate : 
        storedTriangle : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : Array2D<'T> * 
        b : Array2D<'T> * 
        beta : 'T * 
        c : Array2D<'T> -> unit

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>: A span that contains the elements of the first matrix.
b Array2D<T>: A span that contains the elements of the second matrix.
beta T: The scalar used to multiply c.
c Array2D<T>: A span 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*B^H + conjg( alpha )*B*A^H + beta*C, or C := alpha*A^H*B + conjg( alpha )*B^H*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.

public 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
)

Visual Basic

Public Sub HermitianRankUpdate ( 
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k As Integer,
	alpha As Complex(Of T),
	a As Array2D(Of Complex(Of T)),
	b As Array2D(Of Complex(Of T)),
	beta As T,
	c As Array2D(Of Complex(Of T))
)

C++/CLI

public:
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
)

member HermitianRankUpdate : 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : int * 
        alpha : Complex<'T> * 
        a : Array2D<Complex<'T>> * 
        b : Array2D<Complex<'T>> * 
        beta : 'T * 
        c : Array2D<Complex<'T>> -> unit

Parameters

             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.

             On entry,  TRANS  specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'    C := alpha*A*B^H          +
                                           conjg( alpha )*B*A^H +
                                           beta*C.
                TRANS = 'C' or 'c'    C := alpha*A^H*B          +
                                           conjg( alpha )*B^H*A +
                                           beta*C.

             On entry,  N specifies the order of the matrix C.  N must be
             at least zero.

             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 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

HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, Complex<T>, ReadOnlySpan2D<Complex<T>>, ReadOnlySpan2D<Complex<T>>, T, Span2D<Complex<T>>)

public void HermitianRankUpdate(
	MatrixTriangle uplo,
	TransposeOperation trans,
	int n,
	int k,
	Complex<T> alpha,
	ReadOnlySpan2D<Complex<T>> a,
	ReadOnlySpan2D<Complex<T>> b,
	T beta,
	Span2D<Complex<T>> c
)

Visual Basic

Public Sub HermitianRankUpdate ( 
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k As Integer,
	alpha As Complex(Of T),
	a As ReadOnlySpan2D(Of Complex(Of T)),
	b As ReadOnlySpan2D(Of Complex(Of T)),
	beta As T,
	c As Span2D(Of Complex(Of T))
)

C++/CLI

public:
void HermitianRankUpdate(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	int n, 
	int k, 
	Complex<T> alpha, 
	ReadOnlySpan2D<Complex<T>> a, 
	ReadOnlySpan2D<Complex<T>> b, 
	T beta, 
	Span2D<Complex<T>> c
)

member HermitianRankUpdate : 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : int * 
        alpha : Complex<'T> * 
        a : ReadOnlySpan2D<Complex<'T>> * 
        b : ReadOnlySpan2D<Complex<'T>> * 
        beta : 'T * 
        c : Span2D<Complex<'T>> -> unit

Parameters

             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.

             On entry,  TRANS  specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'    C := alpha*A*B^H          +
                                           conjg( alpha )*B*A^H +
                                           beta*C.
                TRANS = 'C' or 'c'    C := alpha*A^H*B          +
                                           conjg( alpha )*B^H*A +
                                           beta*C.

             On entry,  N specifies the order of the matrix C.  N must be
             at least zero.

             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 ReadOnlySpan2D<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 ReadOnlySpan2D<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 Span2D<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, Int32, T, ReadOnlySpan<T>, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32)

Performs a hermitian rank two update of a hermitian matrix.

public void HermitianRankUpdate(
	MatrixTriangle storedTriangle,
	int n,
	T alpha,
	ReadOnlySpan<T> x,
	int incx,
	ReadOnlySpan<T> y,
	int incy,
	Span<T> a,
	int lda
)

Visual Basic

Public Sub HermitianRankUpdate ( 
	storedTriangle As MatrixTriangle,
	n As Integer,
	alpha As T,
	x As ReadOnlySpan(Of T),
	incx As Integer,
	y As ReadOnlySpan(Of T),
	incy As Integer,
	a As Span(Of T),
	lda As Integer
)

C++/CLI

public:
void HermitianRankUpdate(
	MatrixTriangle storedTriangle, 
	int n, 
	T alpha, 
	ReadOnlySpan<T> x, 
	int incx, 
	ReadOnlySpan<T> y, 
	int incy, 
	Span<T> a, 
	int lda
)

member HermitianRankUpdate : 
        storedTriangle : MatrixTriangle * 
        n : int * 
        alpha : 'T * 
        x : ReadOnlySpan<'T> * 
        incx : int * 
        y : ReadOnlySpan<'T> * 
        incy : int * 
        a : Span<'T> * 
        lda : int -> unit

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 ReadOnlySpan<T>: A reference to a one-dimensional array containing the elements of the vector x.
incx Int32: The distance between elements in x.
y ReadOnlySpan<T>: A reference to a one-dimensional array containing the elements of the vector y.
incy Int32: The distance between elements in y.
a Span<T>: A span that contains the elements of the matrix.
lda Int32: The leading dimension of the matrix a.

HermitianRankUpdate(MatrixTriangle, Int32, Complex<T>, ReadOnlySpan<Complex<T>>, Int32, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32)

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

public abstract void HermitianRankUpdate(
	MatrixTriangle uplo,
	int n,
	Complex<T> alpha,
	ReadOnlySpan<Complex<T>> x,
	int incx,
	ReadOnlySpan<Complex<T>> y,
	int incy,
	Span<Complex<T>> a,
	int lda
)

Visual Basic

Public MustOverride Sub HermitianRankUpdate ( 
	uplo As MatrixTriangle,
	n As Integer,
	alpha As Complex(Of T),
	x As ReadOnlySpan(Of Complex(Of T)),
	incx As Integer,
	y As ReadOnlySpan(Of Complex(Of T)),
	incy As Integer,
	a As Span(Of Complex(Of T)),
	lda As Integer
)

C++/CLI

public:
virtual void HermitianRankUpdate(
	MatrixTriangle uplo, 
	int n, 
	Complex<T> alpha, 
	ReadOnlySpan<Complex<T>> x, 
	int incx, 
	ReadOnlySpan<Complex<T>> y, 
	int incy, 
	Span<Complex<T>> a, 
	int lda
) abstract

abstract HermitianRankUpdate : 
        uplo : MatrixTriangle * 
        n : int * 
        alpha : Complex<'T> * 
        x : ReadOnlySpan<Complex<'T>> * 
        incx : int * 
        y : ReadOnlySpan<Complex<'T>> * 
        incy : int * 
        a : Span<Complex<'T>> * 
        lda : int -> unit

Parameters

             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.

ILinearAlgebraOperations<T>.HermitianRankUpdate(MatrixTriangle, Int32, T, ReadOnlySpan<T>, Int32, ReadOnlySpan<T>, Int32, Span<T>, 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 ReadOnlySpan<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.

incx Int32

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.

y ReadOnlySpan<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.

incy Int32

             On entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.

a Span<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.

lda Int32

             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

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, ReadOnlySpan<T>, Int32, T, Span<T>, Int32)

Performs a rank k update of a hermitian matrix.

public void HermitianRankUpdate(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	ReadOnlySpan<T> a,
	int lda,
	T beta,
	Span<T> c,
	int ldc
)

Visual Basic

Public Sub HermitianRankUpdate ( 
	storedTriangle As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k As Integer,
	alpha As T,
	a As ReadOnlySpan(Of T),
	lda As Integer,
	beta As T,
	c As Span(Of T),
	ldc As Integer
)

C++/CLI

public:
void HermitianRankUpdate(
	MatrixTriangle storedTriangle, 
	TransposeOperation trans, 
	int n, 
	int k, 
	T alpha, 
	ReadOnlySpan<T> a, 
	int lda, 
	T beta, 
	Span<T> c, 
	int ldc
)

member HermitianRankUpdate : 
        storedTriangle : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : ReadOnlySpan<'T> * 
        lda : int * 
        beta : 'T * 
        c : Span<'T> * 
        ldc : int -> unit

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 ReadOnlySpan<T>: A span that contains the elements of the first matrix.
lda Int32: The leading dimension of the matrix a.
beta T: The scalar used to multiply c.
c Span<T>: A span that contains the elements of the third matrix.
ldc Int32: The leading dimension of the matrix c.

HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, ReadOnlySpan<Complex<T>>, Int32, T, Span<Complex<T>>, Int32)

public abstract void HermitianRankUpdate(
	MatrixTriangle uplo,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	ReadOnlySpan<Complex<T>> a,
	int lda,
	T beta,
	Span<Complex<T>> c,
	int ldc
)

Visual Basic

Public MustOverride Sub HermitianRankUpdate ( 
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k As Integer,
	alpha As T,
	a As ReadOnlySpan(Of Complex(Of T)),
	lda As Integer,
	beta As T,
	c As Span(Of Complex(Of T)),
	ldc As Integer
)

C++/CLI

public:
virtual void HermitianRankUpdate(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	int n, 
	int k, 
	T alpha, 
	ReadOnlySpan<Complex<T>> a, 
	int lda, 
	T beta, 
	Span<Complex<T>> c, 
	int ldc
) abstract

abstract HermitianRankUpdate : 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : ReadOnlySpan<Complex<'T>> * 
        lda : int * 
        beta : 'T * 
        c : Span<Complex<'T>> * 
        ldc : int -> unit

Parameters

             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.

             On entry,  TRANS  specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   C := alpha*A*A^H + beta*C.
                TRANS = 'C' or 'c'   C := alpha*A^H*A + beta*C.

             On entry,  N specifies the order of the matrix C.  N must be
             at least zero.

             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 ReadOnlySpan<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.

lda Int32

             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 Span<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.

ldc Int32

             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, ReadOnlySpan<T>, Int32, ReadOnlySpan<T>, Int32, T, Span<T>, Int32)

Performs a rank 2k update of a hermitian matrix.

public void HermitianRankUpdate(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	int n,
	int k,
	T alpha,
	ReadOnlySpan<T> a,
	int lda,
	ReadOnlySpan<T> b,
	int ldb,
	T beta,
	Span<T> c,
	int ldc
)

Visual Basic

Public Sub HermitianRankUpdate ( 
	storedTriangle As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k As Integer,
	alpha As T,
	a As ReadOnlySpan(Of T),
	lda As Integer,
	b As ReadOnlySpan(Of T),
	ldb As Integer,
	beta As T,
	c As Span(Of T),
	ldc As Integer
)

C++/CLI

public:
void HermitianRankUpdate(
	MatrixTriangle storedTriangle, 
	TransposeOperation trans, 
	int n, 
	int k, 
	T alpha, 
	ReadOnlySpan<T> a, 
	int lda, 
	ReadOnlySpan<T> b, 
	int ldb, 
	T beta, 
	Span<T> c, 
	int ldc
)

member HermitianRankUpdate : 
        storedTriangle : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : ReadOnlySpan<'T> * 
        lda : int * 
        b : ReadOnlySpan<'T> * 
        ldb : int * 
        beta : 'T * 
        c : Span<'T> * 
        ldc : int -> unit

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 ReadOnlySpan<T>: A span that contains the elements of the first matrix.
lda Int32: The leading dimension of the matrix a.
b ReadOnlySpan<T>: A span that contains the elements of the second matrix.
ldb Int32: The leading dimension of the matrix b.
beta T: The scalar used to multiply c.
c Span<T>: A span that contains the elements of the third matrix.
ldc Int32: The leading dimension of the matrix c.

HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, Complex<T>, ReadOnlySpan<Complex<T>>, Int32, ReadOnlySpan<Complex<T>>, Int32, T, Span<Complex<T>>, Int32)

public abstract void HermitianRankUpdate(
	MatrixTriangle uplo,
	TransposeOperation trans,
	int n,
	int k,
	Complex<T> alpha,
	ReadOnlySpan<Complex<T>> a,
	int lda,
	ReadOnlySpan<Complex<T>> b,
	int ldb,
	T beta,
	Span<Complex<T>> c,
	int ldc
)

Visual Basic

Public MustOverride Sub HermitianRankUpdate ( 
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	n As Integer,
	k As Integer,
	alpha As Complex(Of T),
	a As ReadOnlySpan(Of Complex(Of T)),
	lda As Integer,
	b As ReadOnlySpan(Of Complex(Of T)),
	ldb As Integer,
	beta As T,
	c As Span(Of Complex(Of T)),
	ldc As Integer
)

C++/CLI

public:
virtual void HermitianRankUpdate(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	int n, 
	int k, 
	Complex<T> alpha, 
	ReadOnlySpan<Complex<T>> a, 
	int lda, 
	ReadOnlySpan<Complex<T>> b, 
	int ldb, 
	T beta, 
	Span<Complex<T>> c, 
	int ldc
) abstract

abstract HermitianRankUpdate : 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        n : int * 
        k : int * 
        alpha : Complex<'T> * 
        a : ReadOnlySpan<Complex<'T>> * 
        lda : int * 
        b : ReadOnlySpan<Complex<'T>> * 
        ldb : int * 
        beta : 'T * 
        c : Span<Complex<'T>> * 
        ldc : int -> unit

Parameters

             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.

             On entry,  TRANS  specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'    C := alpha*A*B^H          +
                                           conjg( alpha )*B*A^H +
                                           beta*C.
                TRANS = 'C' or 'c'    C := alpha*A^H*B          +
                                           conjg( alpha )*B^H*A +
                                           beta*C.

             On entry,  N specifies the order of the matrix C.  N must be
             at least zero.