--- 
:name: zgbrfs
:md5sum: ff6b0a35d16530b0e7721261123bb43e
:category: :subroutine
:arguments: 
- trans: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- kl: 
    :type: integer
    :intent: input
- ku: 
    :type: integer
    :intent: input
- nrhs: 
    :type: integer
    :intent: input
- ab: 
    :type: doublecomplex
    :intent: input
    :dims: 
    - ldab
    - n
- ldab: 
    :type: integer
    :intent: input
- afb: 
    :type: doublecomplex
    :intent: input
    :dims: 
    - ldafb
    - n
- ldafb: 
    :type: integer
    :intent: input
- ipiv: 
    :type: integer
    :intent: input
    :dims: 
    - n
- b: 
    :type: doublecomplex
    :intent: input
    :dims: 
    - ldb
    - nrhs
- ldb: 
    :type: integer
    :intent: input
- x: 
    :type: doublecomplex
    :intent: input/output
    :dims: 
    - ldx
    - nrhs
- ldx: 
    :type: integer
    :intent: input
- ferr: 
    :type: doublereal
    :intent: output
    :dims: 
    - nrhs
- berr: 
    :type: doublereal
    :intent: output
    :dims: 
    - nrhs
- work: 
    :type: doublecomplex
    :intent: workspace
    :dims: 
    - 2*n
- rwork: 
    :type: doublereal
    :intent: workspace
    :dims: 
    - n
- info: 
    :type: integer
    :intent: output
:substitutions: {}

:fortran_help: "      SUBROUTINE ZGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  ZGBRFS improves the computed solution to a system of linear\n\
  *  equations when the coefficient matrix is banded, and provides\n\
  *  error bounds and backward error estimates for the solution.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  TRANS   (input) CHARACTER*1\n\
  *          Specifies the form of the system of equations:\n\
  *          = 'N':  A * X = B     (No transpose)\n\
  *          = 'T':  A**T * X = B  (Transpose)\n\
  *          = 'C':  A**H * X = B  (Conjugate transpose)\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The order of the matrix A.  N >= 0.\n\
  *\n\
  *  KL      (input) INTEGER\n\
  *          The number of subdiagonals within the band of A.  KL >= 0.\n\
  *\n\
  *  KU      (input) INTEGER\n\
  *          The number of superdiagonals within the band of A.  KU >= 0.\n\
  *\n\
  *  NRHS    (input) INTEGER\n\
  *          The number of right hand sides, i.e., the number of columns\n\
  *          of the matrices B and X.  NRHS >= 0.\n\
  *\n\
  *  AB      (input) COMPLEX*16 array, dimension (LDAB,N)\n\
  *          The original band matrix A, stored in rows 1 to KL+KU+1.\n\
  *          The j-th column of A is stored in the j-th column of the\n\
  *          array AB as follows:\n\
  *          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).\n\
  *\n\
  *  LDAB    (input) INTEGER\n\
  *          The leading dimension of the array AB.  LDAB >= KL+KU+1.\n\
  *\n\
  *  AFB     (input) COMPLEX*16 array, dimension (LDAFB,N)\n\
  *          Details of the LU factorization of the band matrix A, as\n\
  *          computed by ZGBTRF.  U is stored as an upper triangular band\n\
  *          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and\n\
  *          the multipliers used during the factorization are stored in\n\
  *          rows KL+KU+2 to 2*KL+KU+1.\n\
  *\n\
  *  LDAFB   (input) INTEGER\n\
  *          The leading dimension of the array AFB.  LDAFB >= 2*KL*KU+1.\n\
  *\n\
  *  IPIV    (input) INTEGER array, dimension (N)\n\
  *          The pivot indices from ZGBTRF; for 1<=i<=N, row i of the\n\
  *          matrix was interchanged with row IPIV(i).\n\
  *\n\
  *  B       (input) COMPLEX*16 array, dimension (LDB,NRHS)\n\
  *          The right hand side matrix B.\n\
  *\n\
  *  LDB     (input) INTEGER\n\
  *          The leading dimension of the array B.  LDB >= max(1,N).\n\
  *\n\
  *  X       (input/output) COMPLEX*16 array, dimension (LDX,NRHS)\n\
  *          On entry, the solution matrix X, as computed by ZGBTRS.\n\
  *          On exit, the improved solution matrix X.\n\
  *\n\
  *  LDX     (input) INTEGER\n\
  *          The leading dimension of the array X.  LDX >= max(1,N).\n\
  *\n\
  *  FERR    (output) DOUBLE PRECISION array, dimension (NRHS)\n\
  *          The estimated forward error bound for each solution vector\n\
  *          X(j) (the j-th column of the solution matrix X).\n\
  *          If XTRUE is the true solution corresponding to X(j), FERR(j)\n\
  *          is an estimated upper bound for the magnitude of the largest\n\
  *          element in (X(j) - XTRUE) divided by the magnitude of the\n\
  *          largest element in X(j).  The estimate is as reliable as\n\
  *          the estimate for RCOND, and is almost always a slight\n\
  *          overestimate of the true error.\n\
  *\n\
  *  BERR    (output) DOUBLE PRECISION array, dimension (NRHS)\n\
  *          The componentwise relative backward error of each solution\n\
  *          vector X(j) (i.e., the smallest relative change in\n\
  *          any element of A or B that makes X(j) an exact solution).\n\
  *\n\
  *  WORK    (workspace) COMPLEX*16 array, dimension (2*N)\n\
  *\n\
  *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)\n\
  *\n\
  *  INFO    (output) INTEGER\n\
  *          = 0:  successful exit\n\
  *          < 0:  if INFO = -i, the i-th argument had an illegal value\n\
  *\n\
  *  Internal Parameters\n\
  *  ===================\n\
  *\n\
  *  ITMAX is the maximum number of steps of iterative refinement.\n\
  *\n\n\
  *  =====================================================================\n\
  *\n"
