--- 
:name: zhpsvx
:md5sum: 1b089b8de3c3c23cb14a6227f6eccf46
:category: :subroutine
:arguments: 
- fact: 
    :type: char
    :intent: input
- uplo: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- nrhs: 
    :type: integer
    :intent: input
- ap: 
    :type: doublecomplex
    :intent: input
    :dims: 
    - n*(n+1)/2
- afp: 
    :type: doublecomplex
    :intent: input/output
    :dims: 
    - n*(n+1)/2
- ipiv: 
    :type: integer
    :intent: input/output
    :dims: 
    - n
- b: 
    :type: doublecomplex
    :intent: input
    :dims: 
    - ldb
    - nrhs
- ldb: 
    :type: integer
    :intent: input
- x: 
    :type: doublecomplex
    :intent: output
    :dims: 
    - ldx
    - nrhs
- ldx: 
    :type: integer
    :intent: input
- rcond: 
    :type: doublereal
    :intent: output
- 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: 
  ldx: MAX(1,n)
:fortran_help: "      SUBROUTINE ZHPSVX( FACT, UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  ZHPSVX uses the diagonal pivoting factorization A = U*D*U**H or\n\
  *  A = L*D*L**H to compute the solution to a complex system of linear\n\
  *  equations A * X = B, where A is an N-by-N Hermitian matrix stored\n\
  *  in packed format and X and B are N-by-NRHS matrices.\n\
  *\n\
  *  Error bounds on the solution and a condition estimate are also\n\
  *  provided.\n\
  *\n\
  *  Description\n\
  *  ===========\n\
  *\n\
  *  The following steps are performed:\n\
  *\n\
  *  1. If FACT = 'N', the diagonal pivoting method is used to factor A as\n\
  *        A = U * D * U**H,  if UPLO = 'U', or\n\
  *        A = L * D * L**H,  if UPLO = 'L',\n\
  *     where U (or L) is a product of permutation and unit upper (lower)\n\
  *     triangular matrices and D is Hermitian and block diagonal with\n\
  *     1-by-1 and 2-by-2 diagonal blocks.\n\
  *\n\
  *  2. If some D(i,i)=0, so that D is exactly singular, then the routine\n\
  *     returns with INFO = i. Otherwise, the factored form of A is used\n\
  *     to estimate the condition number of the matrix A.  If the\n\
  *     reciprocal of the condition number is less than machine precision,\n\
  *     INFO = N+1 is returned as a warning, but the routine still goes on\n\
  *     to solve for X and compute error bounds as described below.\n\
  *\n\
  *  3. The system of equations is solved for X using the factored form\n\
  *     of A.\n\
  *\n\
  *  4. Iterative refinement is applied to improve the computed solution\n\
  *     matrix and calculate error bounds and backward error estimates\n\
  *     for it.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  FACT    (input) CHARACTER*1\n\
  *          Specifies whether or not the factored form of A has been\n\
  *          supplied on entry.\n\
  *          = 'F':  On entry, AFP and IPIV contain the factored form of\n\
  *                  A.  AFP and IPIV will not be modified.\n\
  *          = 'N':  The matrix A will be copied to AFP and factored.\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 number of linear equations, i.e., the order of the\n\
  *          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*16 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\
  *          See below for further details.\n\
  *\n\
  *  AFP     (input or output) COMPLEX*16 array, dimension (N*(N+1)/2)\n\
  *          If FACT = 'F', then AFP is an input argument and on entry\n\
  *          contains the block diagonal matrix D and the multipliers used\n\
  *          to obtain the factor U or L from the factorization\n\
  *          A = U*D*U**H or A = L*D*L**H as computed by ZHPTRF, stored as\n\
  *          a packed triangular matrix in the same storage format as A.\n\
  *\n\
  *          If FACT = 'N', then AFP is an output argument and on exit\n\
  *          contains the block diagonal matrix D and the multipliers used\n\
  *          to obtain the factor U or L from the factorization\n\
  *          A = U*D*U**H or A = L*D*L**H as computed by ZHPTRF, stored as\n\
  *          a packed triangular matrix in the same storage format as A.\n\
  *\n\
  *  IPIV    (input or output) INTEGER array, dimension (N)\n\
  *          If FACT = 'F', then IPIV is an input argument and on entry\n\
  *          contains details of the interchanges and the block structure\n\
  *          of D, as determined by ZHPTRF.\n\
  *          If IPIV(k) > 0, then rows and columns k and IPIV(k) were\n\
  *          interchanged and D(k,k) is a 1-by-1 diagonal block.\n\
  *          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and\n\
  *          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)\n\
  *          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =\n\
  *          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were\n\
  *          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.\n\
  *\n\
  *          If FACT = 'N', then IPIV is an output argument and on exit\n\
  *          contains details of the interchanges and the block structure\n\
  *          of D, as determined by ZHPTRF.\n\
  *\n\
  *  B       (input) COMPLEX*16 array, dimension (LDB,NRHS)\n\
  *          The N-by-NRHS 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       (output) COMPLEX*16 array, dimension (LDX,NRHS)\n\
  *          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.\n\
  *\n\
  *  LDX     (input) INTEGER\n\
  *          The leading dimension of the array X.  LDX >= max(1,N).\n\
  *\n\
  *  RCOND   (output) DOUBLE PRECISION\n\
  *          The estimate of the reciprocal condition number of the matrix\n\
  *          A.  If RCOND is less than the machine precision (in\n\
  *          particular, if RCOND = 0), the matrix is singular to working\n\
  *          precision.  This condition is indicated by a return code of\n\
  *          INFO > 0.\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\
  *          > 0:  if INFO = i, and i is\n\
  *                <= N:  D(i,i) is exactly zero.  The factorization\n\
  *                       has been completed but the factor D is exactly\n\
  *                       singular, so the solution and error bounds could\n\
  *                       not be computed. RCOND = 0 is returned.\n\
  *                = N+1: D is nonsingular, but RCOND is less than machine\n\
  *                       precision, meaning that the matrix is singular\n\
  *                       to working precision.  Nevertheless, the\n\
  *                       solution and error bounds are computed because\n\
  *                       there are a number of situations where the\n\
  *                       computed solution can be more accurate than the\n\
  *                       value of RCOND would suggest.\n\
  *\n\n\
  *  Further Details\n\
  *  ===============\n\
  *\n\
  *  The packed storage scheme is illustrated by the following example\n\
  *  when N = 4, UPLO = 'U':\n\
  *\n\
  *  Two-dimensional storage of the Hermitian matrix A:\n\
  *\n\
  *     a11 a12 a13 a14\n\
  *         a22 a23 a24\n\
  *             a33 a34     (aij = conjg(aji))\n\
  *                 a44\n\
  *\n\
  *  Packed storage of the upper triangle of A:\n\
  *\n\
  *  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]\n\
  *\n\
  *  =====================================================================\n\
  *\n"
