/home/abui...hef_rook.f(3)

💖 NAME 💖

Okay so this is a Library Functions Manual page for /home/abui...hef_rook.f(3), and the NAME is literally this source-file path, bestie:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlahef_rook.f

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine ZLAHEF_ROOK (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)

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🌸 Function/Subroutine Documentation 🌸

subroutine ZLAHEF_ROOK (character uplo, integer n, integer nb, integer kb,
    complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * )
    ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)

🎀 Purpose

ZLAHEF_ROOK computes a partial factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman () 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.

ZLAHEF_ROOK is an auxiliary routine called by ZHETRF_ROOK. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L').

💅 Parameters

• 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
• N — is INTEGER. The order of the matrix A. N >= 0.
• 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.
• 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.
• A — is COMPLEX*16 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.
• LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• 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 (sic), 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 (sic), D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

• W — is COMPLEX*16 array, dimension (LDW,NB).
• LDW — is INTEGER. The leading dimension of the array W. LDW >= max(1,N).
• 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.

👑 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🦋 Contributors

• 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 182 of file zlahef_rook.f.

That’s the exact line, no cap: line 182 of file zlahef_rook.f.

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💀 Author

Generated automatically by Doxygen for LAPACK from the source code.

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