Generic Linear Algebra Operations<T>.Hermitian Rank Update Method
Definition
Assembly: Numerics.NET.Generic (in Numerics.NET.Generic.dll) Version: 9.0.1
Overload List
Hermitian | |
Hermitian | |
Hermitian | 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. |
Hermitian | 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. |
Hermitian | Performs a hermitian rank two update of a hermitian matrix. |
Hermitian | 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. |
Hermitian | 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. |
Hermitian | 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. |
Hermitian | 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. |
Hermitian | 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. |
Hermitian | 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. |
Hermitian | 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. |
Hermitian | Performs a rank 2k update of a hermitian matrix. |
Hermitian | 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. |
Hermitian | 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. |
Hermitian | Performs a hermitian rank two update of a hermitian matrix. |
Hermitian | 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. |
Hermitian | 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. |
Hermitian | 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. |
Hermitian | Performs a rank 2k update of a hermitian matrix. |
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 override void HermitianRankUpdate(
MatrixTriangle uplo,
int n,
T alpha,
ReadOnlySpan<Complex<T>> x,
int incx,
Span<Complex<T>> a,
int lda
)
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 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, 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 override 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
)
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 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
ILinearAlgebraOperations<T>.HermitianRankUpdate(MatrixTriangle, 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
HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, ReadOnlySpan<Complex<T>>, Int32, T, Span<Complex<T>>, Int32)
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.
public override 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
)
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 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, Complex<T>, ReadOnlySpan<Complex<T>>, Int32, ReadOnlySpan<Complex<T>>, Int32, T, Span<Complex<T>>, Int32)
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.
public override 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
)
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 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 ).
- b ReadOnlySpan<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.
- ldb Int32
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 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