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cgbrfs.f - Man Page




subroutine cgbrfs (trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)

Function/Subroutine Documentation

subroutine cgbrfs (character trans, integer n, integer kl, integer ku, integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, 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)



 CGBRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is banded, and provides
 error bounds and backward error estimates for the solution.


          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)


          N is INTEGER
          The order of the matrix A.  N >= 0.


          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.


          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 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 original band matrix A, stored in rows 1 to KL+KU+1.
          The j-th column of A is stored in the j-th column of the
          array AB as follows:
          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).


          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KL+KU+1.


          AFB is COMPLEX array, dimension (LDAFB,N)
          Details of the LU factorization of the band matrix A, as
          computed by CGBTRF.  U is stored as an upper triangular band
          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
          the multipliers used during the factorization are stored in
          rows KL+KU+2 to 2*KL+KU+1.


          LDAFB is INTEGER
          The leading dimension of the array AFB.  LDAFB >= 2*KL*KU+1.


          IPIV is INTEGER array, dimension (N)
          The pivot indices from CGBTRF; for 1<=i<=N, row i of the
          matrix was interchanged with row IPIV(i).


          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)
          On entry, the solution matrix X, as computed by CGBTRS.
          On exit, the improved 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

Internal Parameters:

  ITMAX is the maximum number of steps of iterative refinement.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 203 of file cgbrfs.f.


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Referenced By

The man page cgbrfs(3) is an alias of cgbrfs.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK