Linear Algebra Operations<T>.Conjugate Rank Update Method
Definition
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Overload List
Conjugate | Performs a rank one update of a matrix. |
Conjugate | Performs the rank 1 operation A := alpha*x*y**H + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. |
Conjugate | Performs the rank 1 operation A := alpha*x*y**H + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. |
Conjugate | Performs a rank one update of a matrix. |
Conjugate | Performs the rank 1 operation A := alpha*x*y**H + A, where alpha is a scalar, x, incx is an m element vector, y, incy is an n element vector and A is an m by n matrix. |
ConjugateRankUpdate(Int32, Int32, T, ArraySlice<T>, ArraySlice<T>, Array2D<T>)
public void ConjugateRankUpdate(
int m,
int n,
T alpha,
ArraySlice<T> x,
ArraySlice<T> y,
Array2D<T> a
)
Parameters
- m Int32
- The number of rows in the matrix a.
- n Int32
- The number of columns in the matrix a.
- alpha T
- The scalar used to multiply the 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.
ConjugateRankUpdate(Int32, Int32, Complex<T>, ArraySlice<Complex<T>>, ArraySlice<Complex<T>>, Array2D<Complex<T>>)
Performs the rank 1 operation A := alpha*x*y**H + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.
public void ConjugateRankUpdate(
int m,
int n,
Complex<T> alpha,
ArraySlice<Complex<T>> x,
ArraySlice<Complex<T>> y,
Array2D<Complex<T>> a
)
Parameters
- m Int32
On entry, M specifies the number of rows of the matrix A. M must be at least zero.
- n Int32
On entry, N specifies the number of columns of the matrix A. N must be at least zero.
- alpha Complex<T>
On entry, ALPHA specifies the scalar alpha.
- x ArraySlice<Complex<T>>
X is complex array of dimension at least ( 1 + ( m - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m 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, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by the updated matrix.
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ).
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
ConjugateRankUpdate(Int32, Int32, Complex<T>, ReadOnlySpanSlice<Complex<T>>, ReadOnlySpanSlice<Complex<T>>, Span2D<Complex<T>>)
Performs the rank 1 operation A := alpha*x*y**H + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.
public void ConjugateRankUpdate(
int m,
int n,
Complex<T> alpha,
ReadOnlySpanSlice<Complex<T>> x,
ReadOnlySpanSlice<Complex<T>> y,
Span2D<Complex<T>> a
)
Parameters
- m Int32
On entry, M specifies the number of rows of the matrix A. M must be at least zero.
- n Int32
On entry, N specifies the number of columns of the matrix A. N must be at least zero.
- alpha Complex<T>
On entry, ALPHA specifies the scalar alpha.
- x ReadOnlySpanSlice<Complex<T>>
X is complex array of dimension at least ( 1 + ( m - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m 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, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by the updated matrix.
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ).
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
ConjugateRankUpdate(Int32, Int32, T, ReadOnlySpan<T>, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32)
public void ConjugateRankUpdate(
int m,
int n,
T alpha,
ReadOnlySpan<T> x,
int incx,
ReadOnlySpan<T> y,
int incy,
Span<T> a,
int lda
)
Parameters
- m Int32
- The number of rows in the matrix a.
- n Int32
- The number of columns in the matrix a.
- alpha T
- The scalar used to multiply the 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.
ConjugateRankUpdate(Int32, Int32, Complex<T>, ReadOnlySpan<Complex<T>>, Int32, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32)
Performs the rank 1 operation A := alpha*x*y**H + A, where alpha is a scalar, x, incx is an m element vector, y, incy is an n element vector and A is an m by n matrix.
public abstract void ConjugateRankUpdate(
int m,
int n,
Complex<T> alpha,
ReadOnlySpan<Complex<T>> x,
int incx,
ReadOnlySpan<Complex<T>> y,
int incy,
Span<Complex<T>> a,
int lda
)
Parameters
- m Int32
On entry, M specifies the number of rows of the matrix A. M must be at least zero.
- n Int32
On entry, N specifies the number of columns of the matrix A. N must be at least zero.
- alpha Complex<T>
On entry, ALPHA specifies the scalar alpha.
- x ReadOnlySpan<Complex<T>>
X is complex array of dimension at least ( 1 + ( m - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m 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, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by the updated matrix.
- 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, m ).
Implements
ILinearAlgebraOperations<T>.ConjugateRankUpdate(Int32, Int32, T, ReadOnlySpan<T>, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32)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