cpbcon(3S)

NAME
     CPBCON - 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 CPBTRF

SYNOPSIS
     SUBROUTINE CPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, RWORK, INFO
                        )

         CHARACTER      UPLO

         INTEGER        INFO, KD, LDAB, N

         REAL           ANORM, RCOND

         REAL           RWORK( * )

         COMPLEX        AB( LDAB, * ), WORK( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     CPBCON 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 CPBTRF. 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 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) REAL
             The 1-norm (or infinity-norm) of the Hermitian band matrix A.

     RCOND   (output) REAL
             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 array, dimension (2*N)

     RWORK   (workspace) REAL array, dimension (N)

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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