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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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| subroutine clahef_rook | ( | character | UPLO, |
| integer | N, | ||
| integer | NB, | ||
| integer | KB, | ||
| complex, dimension( lda, * ) | A, | ||
| integer | LDA, | ||
| integer, dimension( * ) | IPIV, | ||
| complex, dimension( ldw, * ) | W, | ||
| integer | LDW, | ||
| integer | INFO | ||
| ) |
Download CLAHEF_ROOK + dependencies [TGZ] [ZIP] [TXT]
CLAHEF_ROOK computes a partial factorization of a complex Hermitian
matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting
method. The partial factorization has the form:
A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or:
( 0 U22 ) ( 0 D ) ( U12**H U22**H )
A = ( L11 0 ) ( D 0 ) ( L11**H L21**H ) if UPLO = 'L'
( L21 I ) ( 0 A22 ) ( 0 I )
where the order of D is at most NB. The actual order is returned in
the argument KB, and is either NB or NB-1, or N if N <= NB.
Note that U**H denotes the conjugate transpose of U.
CLAHEF_ROOK is an auxiliary routine called by CHETRF_ROOK. It uses
blocked code (calling Level 3 BLAS) to update the submatrix
A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). | [in] | UPLO | UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular |
| [in] | N | N is INTEGER
The order of the matrix A. N >= 0. |
| [in] | NB | NB is INTEGER
The maximum number of columns of the matrix A that should be
factored. NB should be at least 2 to allow for 2-by-2 pivot
blocks. |
| [out] | KB | KB is INTEGER
The number of columns of A that were actually factored.
KB is either NB-1 or NB, or N if N <= NB. |
| [in,out] | A | A is COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading n-by-n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, A contains details of the partial factorization. |
| [in] | LDA | LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N). |
| [out] | IPIV | IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D.
If UPLO = 'U':
Only the last KB elements of IPIV are set.
If IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1-by-1 diagonal block.
If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k-1 and -IPIV(k-1) were inerchaged,
D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
If UPLO = 'L':
Only the first KB elements of IPIV are set.
If IPIV(k) > 0, then rows and columns k and IPIV(k)
were interchanged and D(k,k) is a 1-by-1 diagonal block.
If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k+1 and -IPIV(k+1) were inerchaged,
D(k:k+1,k:k+1) is a 2-by-2 diagonal block. |
| [out] | W | W is COMPLEX array, dimension (LDW,NB) |
| [in] | LDW | LDW is INTEGER
The leading dimension of the array W. LDW >= max(1,N). |
| [out] | INFO | INFO is INTEGER
= 0: successful exit
> 0: if INFO = k, D(k,k) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular. |
November 2013, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester Definition at line 186 of file clahef_rook.f.
1.8.10