ctbcon(3S)

NAME
     CTBCON - estimate the reciprocal of the condition number of a triangular
     band matrix A, in either the 1-norm or the infinity-norm

SYNOPSIS
     SUBROUTINE CTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, RWORK,
                        INFO )

         CHARACTER      DIAG, NORM, UPLO

         INTEGER        INFO, KD, LDAB, N

         REAL           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
     CTBCON estimates the reciprocal of the condition number of a triangular
     band matrix A, in either the 1-norm or the infinity-norm. The norm of A
     is computed and an estimate is obtained for norm(inv(A)), then the
     reciprocal of the condition number is computed as
        RCOND = 1 / ( norm(A) * norm(inv(A)) ).


ARGUMENTS
     NORM    (input) CHARACTER*1
             Specifies whether the 1-norm condition number or the infinity-
             norm condition number is required:
             = '1' or 'O':  1-norm;
             = 'I':         Infinity-norm.

     UPLO    (input) CHARACTER*1
             = 'U':  A is upper triangular;
             = 'L':  A is lower triangular.
     DIAG    (input) CHARACTER*1
             = 'N':  A is non-unit triangular;
             = 'U':  A is unit triangular.

     N       (input) INTEGER
             The order of the matrix A.  N >= 0.

     KD      (input) INTEGER
             The number of superdiagonals or subdiagonals of the triangular
             band matrix A.  KD >= 0.

     AB      (input) COMPLEX array, dimension (LDAB,N)
             The upper or lower triangular band matrix A, stored in the first
             kd+1 rows of the array. The j-th column of A is stored in the j-
             th column of the array AB as follows:  if UPLO = 'U', AB(kd+1+i-
             j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j)
             = A(i,j) for j<=i<=min(n,j+kd).  If DIAG = 'U', the diagonal
             elements of A are not referenced and are assumed to be 1.

     LDAB    (input) INTEGER
             The leading dimension of the array AB.  LDAB >= KD+1.

     RCOND   (output) REAL
             The reciprocal of the condition number of the matrix A, computed
             as RCOND = 1/(norm(A) * norm(inv(A))).

     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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