--- 
:name: chprfs
:md5sum: 4d6e9e2939bf43ccc422bd54c7607c95
:category: :subroutine
:arguments: 
- uplo: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- nrhs: 
    :type: integer
    :intent: input
- ap: 
    :type: complex
    :intent: input
    :dims: 
    - n*(n+1)/2
- afp: 
    :type: complex
    :intent: input
    :dims: 
    - n*(n+1)/2
- ipiv: 
    :type: integer
    :intent: input
    :dims: 
    - n
- b: 
    :type: complex
    :intent: input
    :dims: 
    - ldb
    - nrhs
- ldb: 
    :type: integer
    :intent: input
- x: 
    :type: complex
    :intent: input/output
    :dims: 
    - ldx
    - nrhs
- ldx: 
    :type: integer
    :intent: input
- ferr: 
    :type: real
    :intent: output
    :dims: 
    - nrhs
- berr: 
    :type: real
    :intent: output
    :dims: 
    - nrhs
- work: 
    :type: complex
    :intent: workspace
    :dims: 
    - 2*n
- rwork: 
    :type: real
    :intent: workspace
    :dims: 
    - n
- info: 
    :type: integer
    :intent: output
:substitutions: {}

:fortran_help: "      SUBROUTINE CHPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  CHPRFS improves the computed solution to a system of linear\n\
  *  equations when the coefficient matrix is Hermitian indefinite\n\
  *  and packed, and provides error bounds and backward error estimates\n\
  *  for the solution.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  UPLO    (input) CHARACTER*1\n\
  *          = 'U':  Upper triangle of A is stored;\n\
  *          = 'L':  Lower triangle of A is stored.\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 matrices B and X.  NRHS >= 0.\n\
  *\n\
  *  AP      (input) COMPLEX array, dimension (N*(N+1)/2)\n\
  *          The upper or lower triangle of the Hermitian matrix A, packed\n\
  *          columnwise in a linear array.  The j-th column of A is stored\n\
  *          in the array AP as follows:\n\
  *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;\n\
  *          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.\n\
  *\n\
  *  AFP     (input) COMPLEX array, dimension (N*(N+1)/2)\n\
  *          The factored form of the matrix A.  AFP contains the block\n\
  *          diagonal matrix D and the multipliers used to obtain the\n\
  *          factor U or L from the factorization A = U*D*U**H or\n\
  *          A = L*D*L**H as computed by CHPTRF, stored as a packed\n\
  *          triangular matrix.\n\
  *\n\
  *  IPIV    (input) INTEGER array, dimension (N)\n\
  *          Details of the interchanges and the block structure of D\n\
  *          as determined by CHPTRF.\n\
  *\n\
  *  B       (input) COMPLEX 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 array, dimension (LDX,NRHS)\n\
  *          On entry, the solution matrix X, as computed by CHPTRS.\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) REAL 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) REAL 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 array, dimension (2*N)\n\
  *\n\
  *  RWORK   (workspace) REAL 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"
