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zgbrfs.f(3) LAPACK zgbrfs.f(3)

zgbrfs.f -


subroutine zgbrfs (TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
 
ZGBRFS

ZGBRFS
Purpose:
 ZGBRFS 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.
Parameters:
TRANS
          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
          N is INTEGER
          The order of the matrix A.  N >= 0.
KL
          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.
KU
          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 0.
NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.
AB
          AB is COMPLEX*16 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
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KL+KU+1.
AFB
          AFB is COMPLEX*16 array, dimension (LDAFB,N)
          Details of the LU factorization of the band matrix A, as
          computed by ZGBTRF.  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
          LDAFB is INTEGER
          The leading dimension of the array AFB.  LDAFB >= 2*KL*KU+1.
IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices from ZGBTRF; for 1<=i<=N, row i of the
          matrix was interchanged with row IPIV(i).
B
          B is COMPLEX*16 array, dimension (LDB,NRHS)
          The right hand side matrix B.
LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
X
          X is COMPLEX*16 array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by ZGBTRS.
          On exit, the improved solution matrix X.
LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
FERR
          FERR is 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
          BERR is 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).
WORK
          WORK is COMPLEX*16 array, dimension (2*N)
RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
INFO
          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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 205 of file zgbrfs.f.

Generated automatically by Doxygen for LAPACK from the source code.
Sat Nov 16 2013 Version 3.4.2

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