IRIX Base Documentation 2002 November/SGI IRIX Base Documentation 2002 November.iso/usr/share/catman/p_man/cat3/SCSL/dtbrfs.z/dtbrfs

Text File | 2002-10-03 | 6.0 KB | 199 lines

DDDDTTTTBBBBRRRRFFFFSSSS((((3333SSSS))))                                                          DDDDTTTTBBBBRRRRFFFFSSSS((((3333SSSS))))



NNNNAAAAMMMMEEEE
     DTBRFS - provide error bounds and backward error estimates for the
     solution to a system of linear equations with a triangular band
     coefficient matrix

SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     SUBROUTINE DTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X,
                        LDX, FERR, BERR, WORK, IWORK, INFO )

         CHARACTER      DIAG, TRANS, UPLO

         INTEGER        INFO, KD, LDAB, LDB, LDX, N, NRHS

         INTEGER        IWORK( * )

         DOUBLE         PRECISION AB( LDAB, * ), B( LDB, * ), BERR( * ), FERR(
                        * ), WORK( * ), X( LDX, * )

IIIIMMMMPPPPLLLLEEEEMMMMEEEENNNNTTTTAAAATTTTIIIIOOOONNNN
     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.

PPPPUUUURRRRPPPPOOOOSSSSEEEE
     DTBRFS provides error bounds and backward error estimates for the
     solution to a system of linear equations with a triangular band
     coefficient matrix. The solution matrix X must be computed by DTBTRS or
     some other means before entering this routine.  DTBRFS does not do
     iterative refinement because doing so cannot improve the backward error.


AAAARRRRGGGGUUUUMMMMEEEENNNNTTTTSSSS
     UPLO    (input) CHARACTER*1
             = 'U':  A is upper triangular;
             = 'L':  A is lower triangular.

     TRANS   (input) CHARACTER*1
             Specifies the form of the system of equations:
             = 'N':  A * X = B  (No transpose)
             = 'T':  A**T * X = B  (Transpose)
             = 'C':  A**H * X = B  (Conjugate transpose = Transpose)






                                                                        PPPPaaaaggggeeee 1111






DDDDTTTTBBBBRRRRFFFFSSSS((((3333SSSS))))                                                          DDDDTTTTBBBBRRRRFFFFSSSS((((3333SSSS))))



     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.

     NRHS    (input) INTEGER
             The number of right hand sides, i.e., the number of columns of
             the matrices B and X.  NRHS >= 0.

     AB      (input) DOUBLE PRECISION 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.

     B       (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
             The right hand side matrix B.

     LDB     (input) INTEGER
             The leading dimension of the array B.  LDB >= max(1,N).

     X       (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
             The solution matrix X.

     LDX     (input) INTEGER
             The leading dimension of the array X.  LDX >= max(1,N).

     FERR    (output) DOUBLE PRECISION array, dimension (NRHS)
             The estimated forward error bound for each solution vector X(j)
             (the j-th column of the solution matrix X).  If XTRUE is the true
             solution corresponding to X(j), FERR(j) is an estimated upper
             bound for the magnitude of the largest element in (X(j) - XTRUE)
             divided by the magnitude of the largest element in X(j).  The
             estimate is as reliable as the estimate for RCOND, and is almost
             always a slight overestimate of the true error.

     BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
             The componentwise relative backward error of each solution vector
             X(j) (i.e., the smallest relative change in any element of A or B
             that makes X(j) an exact solution).




                                                                        PPPPaaaaggggeeee 2222






DDDDTTTTBBBBRRRRFFFFSSSS((((3333SSSS))))                                                          DDDDTTTTBBBBRRRRFFFFSSSS((((3333SSSS))))



     WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)

     IWORK   (workspace) INTEGER array, dimension (N)

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

SSSSEEEEEEEE AAAALLLLSSSSOOOO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.











































                                                                        PPPPaaaaggggeeee 3333