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zpbcon (3)
  • >> zpbcon (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         zpbcon - estimate the reciprocal of the condition number (in
         the  1-norm)  of  a complex Hermitian positive definite band
         matrix using the Cholesky factorization A = U**H*U  or  A  =
         L*L**H computed by ZPBTRF
    
    SYNOPSIS
         SUBROUTINE ZPBCON( UPLO, N,  KD,  AB,  LDAB,  ANORM,  RCOND,
                   WORK, RWORK, INFO )
    
         CHARACTER UPLO
    
         INTEGER INFO, KD, LDAB, N
    
         DOUBLE PRECISION ANORM, RCOND
    
         DOUBLE PRECISION RWORK( * )
    
         COMPLEX*16 AB( LDAB, * ), WORK( * )
    
    
    
         #include <sunperf.h>
    
         void zpbcon(char uplo, int n, int  kd,  doublecomplex  *zab,
                   int   ldab,  double  anorm,  double  *drcond,  int
                   *info);
    
    PURPOSE
         ZPBCON estimates the reciprocal of the condition number  (in
         the  1-norm)  of  a complex Hermitian positive definite band
         matrix using the Cholesky factorization A = U**H*U  or  A  =
         L*L**H computed by ZPBTRF.
    
         An estimate is obtained for norm(inv(A)), and the reciprocal
         of  the condition number is computed as RCOND = 1 / (ANORM *
         norm(inv(A))).
    
    
    ARGUMENTS
         UPLO      (input) CHARACTER*1
                   = 'U':  Upper triangular factor stored in AB;
                   = 'L':  Lower triangular factor stored in AB.
    
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         KD        (input) INTEGER
                   The number of superdiagonals of the  matrix  A  if
                   UPLO = 'U', or the number of sub-diagonals if UPLO
                   = 'L'.  KD >= 0.
    
         AB        (input) COMPLEX*16 array, dimension (LDAB,N)
                   The triangular factor U or  L  from  the  Cholesky
                   factorization A = U**H*U or A = L*L**H of the band
                   matrix A, stored in the first  KD+1  rows  of  the
                   array.  The j-th column of U or L is stored in the
                   j-th column of the array AB as follows:   if  UPLO
                   ='U',   AB(kd+1+i-j,j)   =   U(i,j)  for  max(1,j-
                   kd)<=i<=j; if UPLO ='L', AB(1+i-j,j)     =  L(i,j)
                   for j<=i<=min(n,j+kd).
    
         LDAB      (input) INTEGER
                   The leading dimension of the array  AB.   LDAB  >=
                   KD+1.
    
         ANORM     (input) DOUBLE PRECISION
                   The 1-norm (or  infinity-norm)  of  the  Hermitian
                   band matrix A.
    
         RCOND     (output) DOUBLE PRECISION
                   The reciprocal of  the  condition  number  of  the
                   matrix  A, computed as RCOND = 1/(ANORM * AINVNM),
                   where AINVNM is  an  estimate  of  the  1-norm  of
                   inv(A) computed in this routine.
    
         WORK      (workspace) COMPLEX*16 array, dimension (2*N)
    
         RWORK     (workspace) DOUBLE PRECISION array, dimension (N)
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value
    
    
    
    


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