--- 
:name: zptrfs
:md5sum: b039702b9cb6d623dbf01d6a72aa8bd3
:category: :subroutine
:arguments: 
- uplo: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- nrhs: 
    :type: integer
    :intent: input
- d: 
    :type: doublereal
    :intent: input
    :dims: 
    - n
- e: 
    :type: doublecomplex
    :intent: input
    :dims: 
    - n-1
- df: 
    :type: doublereal
    :intent: input
    :dims: 
    - n
- ef: 
    :type: doublecomplex
    :intent: input
    :dims: 
    - n-1
- 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: 
    - n
- rwork: 
    :type: doublereal
    :intent: workspace
    :dims: 
    - n
- info: 
    :type: integer
    :intent: output
:substitutions: {}

:fortran_help: "      SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  ZPTRFS improves the computed solution to a system of linear\n\
  *  equations when the coefficient matrix is Hermitian positive definite\n\
  *  and tridiagonal, and provides error bounds and backward error\n\
  *  estimates for the solution.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  UPLO    (input) CHARACTER*1\n\
  *          Specifies whether the superdiagonal or the subdiagonal of the\n\
  *          tridiagonal matrix A is stored and the form of the\n\
  *          factorization:\n\
  *          = 'U':  E is the superdiagonal of A, and A = U**H*D*U;\n\
  *          = 'L':  E is the subdiagonal of A, and A = L*D*L**H.\n\
  *          (The two forms are equivalent if A is real.)\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The order of the matrix A.  N >= 0.\n\
  *\n\
  *  NRHS    (input) INTEGER\n\
  *          The number of right hand sides, i.e., the number of columns\n\
  *          of the matrix B.  NRHS >= 0.\n\
  *\n\
  *  D       (input) DOUBLE PRECISION array, dimension (N)\n\
  *          The n real diagonal elements of the tridiagonal matrix A.\n\
  *\n\
  *  E       (input) COMPLEX*16 array, dimension (N-1)\n\
  *          The (n-1) off-diagonal elements of the tridiagonal matrix A\n\
  *          (see UPLO).\n\
  *\n\
  *  DF      (input) DOUBLE PRECISION array, dimension (N)\n\
  *          The n diagonal elements of the diagonal matrix D from\n\
  *          the factorization computed by ZPTTRF.\n\
  *\n\
  *  EF      (input) COMPLEX*16 array, dimension (N-1)\n\
  *          The (n-1) off-diagonal elements of the unit bidiagonal\n\
  *          factor U or L from the factorization computed by ZPTTRF\n\
  *          (see UPLO).\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 ZPTTRS.\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 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).\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 (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"
