LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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ctbrfs.f File Reference

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Function/Subroutine Documentation

subroutine ctbrfs ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  KD,
integer  NRHS,
complex, dimension( ldab, * )  AB,
integer  LDAB,
complex, dimension( ldb, * )  B,
integer  LDB,
complex, dimension( ldx, * )  X,
integer  LDX,
real, dimension( * )  FERR,
real, dimension( * )  BERR,
complex, dimension( * )  WORK,
real, dimension( * )  RWORK,
integer  INFO 


Download CTBRFS + dependencies [TGZ] [ZIP] [TXT]
 CTBRFS 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 CTBTRS or some other
 means before entering this routine.  CTBRFS does not do iterative
 refinement because doing so cannot improve the backward error.
          UPLO is CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular.
          TRANS is 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 is CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular.
          N is INTEGER
          The order of the matrix A.  N >= 0.
          KD is INTEGER
          The number of superdiagonals or subdiagonals of the
          triangular band matrix A.  KD >= 0.
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.
          AB is 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 is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side matrix B.
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
          X is COMPLEX array, dimension (LDX,NRHS)
          The solution matrix X.
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
          FERR is 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 is 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 is COMPLEX array, dimension (2*N)
          RWORK is REAL array, dimension (N)
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
November 2011

Definition at line 188 of file ctbrfs.f.

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