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clahef (3)
  • >> clahef (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         clahef - compute a partial factorization of a complex Hermi-
         tian  matrix  A  using  the  Bunch-Kaufman diagonal pivoting
         method
    
    SYNOPSIS
         SUBROUTINE CLAHEF( UPLO, N, NB, KB, A, LDA,  IPIV,  W,  LDW,
                   INFO )
    
         CHARACTER UPLO
    
         INTEGER INFO, KB, LDA, LDW, N, NB
    
         INTEGER IPIV( * )
    
         COMPLEX A( LDA, * ), W( LDW, * )
    
    
    
         #include <sunperf.h>
    
         void clahef(char uplo, int n, int nb, int *kb, complex  *ca,
                   int  lda,  int  *ipivot,  complex *w, int ldw, int
                   *info);
    
    PURPOSE
         CLAHEF computes a partial factorization of a complex  Hermi-
         tian  matrix  A  using  the  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' U22' )
    
         A  =  ( L11  0 ) (  D   0  ) ( L11' L21' )  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' denotes the conjugate transpose of
         U.
    
         CLAHEF is an auxiliary routine called  by  CHETRF.  It  uses
         blocked  code (calling Level 3 BLAS) to update the submatrix
         A11 (if UPLO = 'U') or A22 (if UPLO = 'L').
    
    
    ARGUMENTS
         UPLO      (input) CHARACTER*1
                   Specifies whether the upper  or  lower  triangular
                   part of the Hermitian matrix A is stored:
                   = 'U':  Upper triangular
                   = 'L':  Lower triangular
    
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         NB        (input) 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        (output) INTEGER
                   The number of columns of A that were actually fac-
                   tored.  KB is either NB-1 or NB, or N if N <= NB.
    
         A         (input/output) COMPLEX array, dimension (LDA,N)
                   On entry, the Hermitian matrix A.  If UPLO =  'U',
                   the leading n-by-n upper triangular part of A con-
                   tains 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 tri-
                   angular part of the matrix  A,  and  the  strictly
                   upper  triangular part of A is not referenced.  On
                   exit, A contains details of the partial factoriza-
                   tion.
    
         LDA       (input) INTEGER
                   The leading dimension of  the  array  A.   LDA  >=
                   max(1,N).
    
         IPIV      (output) INTEGER array, dimension (N)
                   Details of the interchanges and the  block  struc-
                   ture  of  D.  If UPLO = 'U', only the last KB ele-
                   ments of IPIV are set; if UPLO  =  'L',  only  the
                   first KB elements 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  UPLO  =  'U'  and  IPIV(k)  =
                   IPIV(k-1)  <  0,  then  rows  and  columns k-1 and
                   -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a
                   2-by-2  diagonal block.  If UPLO = 'L' and IPIV(k)
                   = IPIV(k+1) < 0, then rows  and  columns  k+1  and
                   -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a
                   2-by-2 diagonal block.
    
         W         (workspace) COMPLEX array, dimension (LDW,NB)
    
         LDW       (input) INTEGER
                   The leading dimension of  the  array  W.   LDW  >=
                   max(1,N).
    
         INFO      (output) 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.
    
    
    
    


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