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

Text File | 2002-10-03 | 5.8 KB | 199 lines

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

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     SUBROUTINE CTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX,
                        FERR, BERR, WORK, RWORK, INFO )

         CHARACTER      DIAG, TRANS, UPLO

         INTEGER        INFO, LDA, LDB, LDX, N, NRHS

         REAL           BERR( * ), FERR( * ), RWORK( * )

         COMPLEX        A( LDA, * ), B( LDB, * ), WORK( * ), X( LDX, * )

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     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.

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


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     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)

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



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

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

     A       (input) COMPLEX array, dimension (LDA,N)
             The triangular matrix A.  If UPLO = 'U', the leading N-by-N upper
             triangular part of the array A contains the upper triangular
             matrix, and the strictly lower triangular part of A is not
             referenced.  If UPLO = 'L', the leading N-by-N lower triangular
             part of the array A contains the lower triangular matrix, and the
             strictly upper triangular part of A is not referenced.  If DIAG =
             'U', the diagonal elements of A are also not referenced and are
             assumed to be 1.

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

     B       (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)
             The solution matrix X.

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

     FERR    (output) REAL 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) REAL 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).

     WORK    (workspace) COMPLEX array, dimension (2*N)

     RWORK   (workspace) REAL array, dimension (N)






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

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     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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